Subgroups — C₁₀₉×#35055 #42153049

Order 27904.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉×#2853	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₉×#2849	C₂	1	1	yes	maximal, characteristic
4	C₁₀₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#2665	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₉×#2663	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₉×#2653	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₉×#2652	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₉×#2564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₉×#2561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₉×#2549	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₀₉×#2534	C₂	1	1	yes	maximal, characteristic
13	C₁₀₉×#2530	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₀₉×#2527	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₀₉×#2521	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₀₉×#2515	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₀₉×#2493	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₀₉×#2488	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₀₉×#2480	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₀₉×#2477	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₀₉×#2472	C₂	1	1	yes	maximal, characteristic
22	C₁₀₉×#2470	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₀₉×#2465	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₀₉×#2458	C₂	1	1	yes	maximal, characteristic, complemented
25	C₁₀₉×#2337	C₂	1	1	yes	maximal, characteristic, complemented
26	C₁₀₉×#2335	C₂	1	1	yes	maximal, characteristic, complemented
27	C₁₀₉×#2334	C₂	1	1	yes	maximal, characteristic, complemented
28	C₁₀₉×#2332	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
30	C₁₀₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
33	C₂×#126×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂×#123×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂×#123×C₁₀₉	C₂²	1	1	yes	characteristic
37	C₂×#123×C₁₀₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
43	C₂×#120×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
51	#401×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
52	#400×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	#400×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
54	#400×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	#400×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	#400×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#400×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	#399×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	#398×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	#398×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	#397×C₁₀₉	C₂²	1	1	yes	characteristic
62	#397×C₁₀₉	C₂²	1	1	yes	characteristic
63	#397×C₁₀₉	C₂²	1	1	yes	characteristic
64	#397×C₁₀₉	C₂²	1	1	yes	characteristic
65	#397×C₁₀₉	C₂²	1	1	yes	characteristic
66	#397×C₁₀₉	C₂²	1	1	yes	characteristic
67	#397×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
68	#396×C₁₀₉	C₂²	1	1	yes	characteristic
69	#396×C₁₀₉	C₂²	1	1	yes	characteristic
70	#396×C₁₀₉	C₂²	1	1	yes	characteristic
71	#395×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
72	#395×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
73	#395×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
74	#394×C₁₀₉	C₂²	1	1	yes	characteristic
75	#394×C₁₀₉	C₂²	1	1	yes	characteristic
76	#394×C₁₀₉	C₂²	1	1	yes	characteristic
77	#394×C₁₀₉	C₂²	1	1	yes	characteristic
78	#393×C₁₀₉	C₂²	1	1	yes	characteristic
79	#393×C₁₀₉	C₂²	1	1	yes	characteristic
80	#393×C₁₀₉	C₂²	1	1	yes	characteristic
81	#393×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
82	#393×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
83	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
84	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
85	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
86	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
87	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
88	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
89	#390×C₁₀₉	C₂²	1	1	yes	characteristic
90	#389×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
91	#389×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
92	#389×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
93	#389×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
94	#389×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
95	#388×C₁₀₉	C₂²	1	1	yes	characteristic
96	#388×C₁₀₉	C₂²	1	1	yes	characteristic
97	#388×C₁₀₉	C₂²	1	1	yes	characteristic
98	#388×C₁₀₉	C₂²	1	1	yes	characteristic
99	#388×C₁₀₉	C₂²	1	1	yes	characteristic
100	#388×C₁₀₉	C₂²	1	1	yes	characteristic
101	#388×C₁₀₉	C₂²	1	1	yes	characteristic
102	#388×C₁₀₉	C₂²	1	1	yes	characteristic
103	#388×C₁₀₉	C₂²	1	1	yes	characteristic
104	#388×C₁₀₉	C₂²	1	1	yes	characteristic
105	#388×C₁₀₉	C₂²	1	1	yes	characteristic
106	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
107	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
108	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
109	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
110	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
111	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
112	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
113	#388×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
114	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
116	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
117	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
118	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
120	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
122	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
124	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
125	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
126	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
127	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
128	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
129	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
130	#387×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
131	#386×C₁₀₉	C₂²	1	1	yes	characteristic
132	#386×C₁₀₉	C₂²	1	1	yes	characteristic
133	#386×C₁₀₉	C₂²	1	1	yes	characteristic
134	#386×C₁₀₉	C₂²	1	1	yes	characteristic
135	#386×C₁₀₉	C₂²	1	1	yes	characteristic
136	#386×C₁₀₉	C₂²	1	1	yes	characteristic
137	#386×C₁₀₉	C₂²	1	1	yes	characteristic
138	#386×C₁₀₉	C₂²	1	1	yes	characteristic
139	#385×C₁₀₉	C₂²	1	1	yes	characteristic
140	#385×C₁₀₉	C₂²	1	1	yes	characteristic
141	#385×C₁₀₉	C₂²	1	1	yes	characteristic
142	#385×C₁₀₉	C₂²	1	1	yes	characteristic
143	#385×C₁₀₉	C₂²	1	1	yes	characteristic
144	#385×C₁₀₉	C₂²	1	1	yes	characteristic
145	#385×C₁₀₉	C₂²	1	1	yes	characteristic
146	#385×C₁₀₉	C₂²	1	1	yes	characteristic
147	#385×C₁₀₉	C₂²	1	1	yes	characteristic
148	#385×C₁₀₉	C₂²	1	1	yes	characteristic
149	#385×C₁₀₉	C₂²	1	1	yes	characteristic
150	#385×C₁₀₉	C₂²	1	1	yes	characteristic
151	#385×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
152	#385×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
153	#383×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
154	#382×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
155	#381×C₁₀₉	C₂²	1	1	yes	characteristic
156	#381×C₁₀₉	C₂²	1	1	yes	characteristic
157	#381×C₁₀₉	C₂²	1	1	yes	characteristic
158	#381×C₁₀₉	C₂²	1	1	yes	characteristic
159	#381×C₁₀₉	C₂²	1	1	yes	characteristic
160	#380×C₁₀₉	C₂²	1	1	yes	characteristic
161	#380×C₁₀₉	C₂²	1	1	yes	characteristic
162	#380×C₁₀₉	C₂²	1	1	yes	characteristic
163	#380×C₁₀₉	C₂²	1	1	yes	characteristic
164	#380×C₁₀₉	C₂²	1	1	yes	characteristic
165	#379×C₁₀₉	C₂²	1	1	yes	characteristic
166	#379×C₁₀₉	C₂²	1	1	yes	characteristic
167	#379×C₁₀₉	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
169	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
184	#376×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
185	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic
186	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic
187	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₁₀₉	—	2	4	no	—
195	C₂³×C₄×C₁₀₉	—	4	2	no	—
196	C₂³×C₄×C₁₀₉	—	4	2	no	—
197	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
208	#126×C₁₀₉	—	2	4	no	—
209	#124×C₁₀₉	—	2	4	no	—
210	#123×C₁₀₉	—	2	4	no	—
211	#123×C₁₀₉	—	4	2	no	—
212	#123×C₁₀₉	—	4	2	no	—
213	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
214	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
215	C₂²⋊Q₈×C₁₀₉	—	4	2	no	—
216	C₂²⋊Q₈×C₁₀₉	—	4	2	no	—
217	C₂²⋊Q₈×C₁₀₉	—	4	2	no	—
218	#120×C₁₀₉	—	4	2	no	—
219	C₄×Q₈×C₁₀₉	—	4	2	no	—
220	C₄×D₄×C₁₀₉	—	2	4	no	—
221	#117×C₁₀₉	—	4	2	no	—
222	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
253	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
254	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₁₀₉	—	4	2	no	—
295	C₂×C₄²×C₁₀₉	—	4	2	no	—
296	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
311	#95×C₁₀₉	C₂³	1	1	yes	characteristic
312	#95×C₁₀₉	C₂³	1	1	yes	characteristic
313	#95×C₁₀₉	C₂³	1	1	yes	characteristic
314	#95×C₁₀₉	C₂³	1	1	yes	characteristic
315	#95×C₁₀₉	C₂³	1	1	yes	characteristic
316	#95×C₁₀₉	C₂³	1	1	yes	characteristic
317	#95×C₁₀₉	C₂³	1	1	yes	characteristic
318	#95×C₁₀₉	C₂³	1	1	yes	characteristic
319	#95×C₁₀₉	C₂³	1	1	yes	characteristic
320	#95×C₁₀₉	C₂³	1	1	yes	characteristic
321	#95×C₁₀₉	C₂³	1	1	yes	characteristic
322	#95×C₁₀₉	C₂³	1	1	yes	characteristic
323	#95×C₁₀₉	C₂³	1	1	yes	characteristic
324	#95×C₁₀₉	C₂³	1	1	yes	characteristic
325	#95×C₁₀₉	C₂³	1	1	yes	characteristic
326	#95×C₁₀₉	C₂³	1	1	yes	characteristic
327	#95×C₁₀₉	C₂³	1	1	yes	characteristic
328	#95×C₁₀₉	C₂³	1	1	yes	characteristic
329	#95×C₁₀₉	C₂³	1	1	yes	characteristic
330	#95×C₁₀₉	C₂³	1	1	yes	characteristic
331	#95×C₁₀₉	C₂³	1	1	yes	characteristic
332	#95×C₁₀₉	C₂³	1	1	yes	characteristic
333	#95×C₁₀₉	C₂³	1	1	yes	characteristic
334	#95×C₁₀₉	C₂³	1	1	yes	characteristic
335	#95×C₁₀₉	C₂³	1	1	yes	characteristic
336	#95×C₁₀₉	C₂³	1	1	yes	characteristic
337	#95×C₁₀₉	C₂³	1	1	yes	characteristic
338	#95×C₁₀₉	C₂³	1	1	yes	characteristic
339	#95×C₁₀₉	C₂³	1	1	yes	characteristic
340	#95×C₁₀₉	C₂³	1	1	yes	characteristic
341	#95×C₁₀₉	C₂³	1	1	yes	characteristic
342	#95×C₁₀₉	C₂³	1	1	yes	characteristic
343	#95×C₁₀₉	C₂³	1	1	yes	characteristic
344	#95×C₁₀₉	C₂³	1	1	yes	characteristic
345	#95×C₁₀₉	C₂³	1	1	yes	characteristic
346	#95×C₁₀₉	C₂³	1	1	yes	characteristic
347	#95×C₁₀₉	C₂³	1	1	yes	characteristic
348	#95×C₁₀₉	C₂³	1	1	yes	characteristic
349	#95×C₁₀₉	C₂³	1	1	yes	characteristic
350	#95×C₁₀₉	C₂³	1	1	yes	characteristic
351	#95×C₁₀₉	C₂³	1	1	yes	characteristic
352	#95×C₁₀₉	C₂³	1	1	yes	characteristic
353	#95×C₁₀₉	C₂³	1	1	yes	characteristic
354	#95×C₁₀₉	C₂³	1	1	yes	characteristic
355	#95×C₁₀₉	C₂³	1	1	yes	characteristic
356	#95×C₁₀₉	C₂³	1	1	yes	characteristic
357	#95×C₁₀₉	C₂³	1	1	yes	characteristic
358	#95×C₁₀₉	C₂³	1	1	yes	characteristic
359	#95×C₁₀₉	C₂³	1	1	yes	characteristic
360	#95×C₁₀₉	C₂³	1	1	yes	characteristic
361	#95×C₁₀₉	C₂³	1	1	yes	characteristic
362	#95×C₁₀₉	C₂³	1	1	yes	characteristic
363	C₂⁴×C₁₀₉	—	2	2	no	—
364	C₂⁴×C₁₀₉	—	2	2	no	—
365	C₂⁴×C₁₀₉	—	2	2	no	—
366	C₂⁴×C₁₀₉	—	2	2	no	—
367	C₂⁴×C₁₀₉	—	2	2	no	—
368	C₂⁴×C₁₀₉	—	4	1	no	—
369	C₂⁴×C₁₀₉	—	4	1	no	—
370	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
374	C₂×Q₈×C₁₀₉	—	2	2	no	—
375	C₂×Q₈×C₁₀₉	—	2	2	no	—
376	C₂×Q₈×C₁₀₉	—	2	2	no	—
377	C₂×Q₈×C₁₀₉	—	4	1	no	—
378	C₂×Q₈×C₁₀₉	—	4	1	no	—
379	C₂×Q₈×C₁₀₉	—	4	1	no	—
380	C₂×Q₈×C₁₀₉	—	4	1	no	—
381	C₂×Q₈×C₁₀₉	—	4	1	no	—
382	C₂×Q₈×C₁₀₉	—	4	1	no	—
383	C₂×D₄×C₁₀₉	—	2	2	no	—
384	C₂×D₄×C₁₀₉	—	2	2	no	—
385	C₂×D₄×C₁₀₉	—	2	2	no	—
386	C₂×D₄×C₁₀₉	—	2	2	no	—
387	C₂×D₄×C₁₀₉	—	2	2	no	—
388	C₂×D₄×C₁₀₉	—	4	1	no	—
389	C₂×D₄×C₁₀₉	—	4	1	no	—
390	C₂×D₄×C₁₀₉	—	4	1	no	—
391	C₂×D₄×C₁₀₉	—	4	1	no	—
392	C₂²×C₄×C₁₀₉	—	2	2	no	—
393	C₂²×C₄×C₁₀₉	—	2	2	no	—
394	C₂²×C₄×C₁₀₉	—	2	2	no	—
395	C₂²×C₄×C₁₀₉	—	2	2	no	—
396	C₂²×C₄×C₁₀₉	—	2	2	no	—
397	C₂²×C₄×C₁₀₉	—	2	2	no	—
398	C₂²×C₄×C₁₀₉	—	2	2	no	—
399	C₂²×C₄×C₁₀₉	—	2	2	no	—
400	C₂²×C₄×C₁₀₉	—	2	2	no	—
401	C₂²×C₄×C₁₀₉	—	2	2	no	—
402	C₂²×C₄×C₁₀₉	—	2	2	no	—
403	C₂²×C₄×C₁₀₉	—	2	2	no	—
404	C₂²×C₄×C₁₀₉	—	2	2	no	—
405	C₂²×C₄×C₁₀₉	—	2	2	no	—
406	C₂²×C₄×C₁₀₉	—	2	2	no	—
407	C₂²×C₄×C₁₀₉	—	2	2	no	—
408	C₂²×C₄×C₁₀₉	—	2	2	no	—
409	C₂²×C₄×C₁₀₉	—	2	2	no	—
410	C₂²×C₄×C₁₀₉	—	4	1	no	—
411	C₂²×C₄×C₁₀₉	—	4	1	no	—
412	C₂²×C₄×C₁₀₉	—	4	1	no	—
413	C₂²×C₄×C₁₀₉	—	4	1	no	—
414	C₂²×C₄×C₁₀₉	—	4	1	no	—
415	C₂²×C₄×C₁₀₉	—	4	1	no	—
416	C₂²×C₄×C₁₀₉	—	4	1	no	—
417	C₂²×C₄×C₁₀₉	—	4	1	no	—
418	C₂²×C₄×C₁₀₉	—	4	1	no	—
419	C₂²×C₄×C₁₀₉	—	4	1	no	—
420	C₂²×C₄×C₁₀₉	—	4	1	no	—
421	C₂²×C₄×C₁₀₉	—	4	1	no	—
422	C₂²×C₄×C₁₀₉	—	4	1	no	—
423	C₂²×C₄×C₁₀₉	—	4	16	no	—
424	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
425	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
426	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₁₀₉	—	2	2	no	—
454	C₄⋊C₄×C₁₀₉	—	2	2	no	—
455	C₄⋊C₄×C₁₀₉	—	2	2	no	—
456	C₄⋊C₄×C₁₀₉	—	2	2	no	—
457	C₄⋊C₄×C₁₀₉	—	2	2	no	—
458	C₄⋊C₄×C₁₀₉	—	2	2	no	—
459	C₄⋊C₄×C₁₀₉	—	2	2	no	—
460	C₄⋊C₄×C₁₀₉	—	2	2	no	—
461	C₄⋊C₄×C₁₀₉	—	2	2	no	—
462	C₄⋊C₄×C₁₀₉	—	2	2	no	—
463	C₄⋊C₄×C₁₀₉	—	2	2	no	—
464	C₄⋊C₄×C₁₀₉	—	2	2	no	—
465	C₄⋊C₄×C₁₀₉	—	2	2	no	—
466	C₄⋊C₄×C₁₀₉	—	2	2	no	—
467	C₄⋊C₄×C₁₀₉	—	2	2	no	—
468	C₄⋊C₄×C₁₀₉	—	4	1	no	—
469	C₄⋊C₄×C₁₀₉	—	4	1	no	—
470	C₄⋊C₄×C₁₀₉	—	4	1	no	—
471	C₄⋊C₄×C₁₀₉	—	4	1	no	—
472	C₄⋊C₄×C₁₀₉	—	4	1	no	—
473	C₄⋊C₄×C₁₀₉	—	4	1	no	—
474	C₄⋊C₄×C₁₀₉	—	4	1	no	—
475	C₄⋊C₄×C₁₀₉	—	4	1	no	—
476	C₄⋊C₄×C₁₀₉	—	4	1	no	—
477	C₄⋊C₄×C₁₀₉	—	4	1	no	—
478	C₄⋊C₄×C₁₀₉	—	4	1	no	—
479	C₄⋊C₄×C₁₀₉	—	4	1	no	—
480	C₄⋊C₄×C₁₀₉	—	4	1	no	—
481	C₄⋊C₄×C₁₀₉	—	4	1	no	—
482	C₄⋊C₄×C₁₀₉	—	4	1	no	—
483	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
484	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
485	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
486	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
487	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
488	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
489	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
490	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
491	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
492	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
493	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
494	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
495	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
496	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
497	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
498	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
499	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
500	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
501	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
502	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
503	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
504	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
505	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
506	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
507	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
508	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
509	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
510	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
511	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
512	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
513	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
514	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
515	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
516	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
517	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
518	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
519	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
520	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
521	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
522	C₂²⋊C₄×C₁₀₉	#41	1	4	yes	—
523	C₄²×C₁₀₉	—	2	2	no	—
524	C₄²×C₁₀₉	—	2	2	no	—
525	C₄²×C₁₀₉	—	2	2	no	—
526	C₄²×C₁₀₉	—	2	2	no	—
527	C₄²×C₁₀₉	—	2	2	no	—
528	C₄²×C₁₀₉	—	4	1	no	—
529	C₄²×C₁₀₉	—	4	1	no	—
530	C₄²×C₁₀₉	—	4	1	no	—
531	C₄²×C₁₀₉	—	4	1	no	—
532	C₄²×C₁₀₉	—	4	1	no	—
533	C₄²×C₁₀₉	—	4	1	no	—
534	C₄²×C₁₀₉	—	4	1	no	—
535	C₄²×C₁₀₉	—	4	1	no	—
536	C₄²×C₁₀₉	—	4	1	no	—
537	C₄²×C₁₀₉	—	4	1	no	—
538	C₂³×C₁₀₉	—	2	1	no	—
539	C₂³×C₁₀₉	—	2	1	no	—
540	C₂³×C₁₀₉	—	2	1	no	—
541	C₂³×C₁₀₉	—	2	1	no	—
542	C₂³×C₁₀₉	—	2	8	no	—
543	C₂³×C₁₀₉	—	2	1	no	—
544	C₂³×C₁₀₉	—	2	1	no	—
545	C₂³×C₁₀₉	—	2	1	no	—
546	C₂³×C₁₀₉	—	2	1	no	—
547	C₂³×C₁₀₉	—	2	1	no	—
548	C₂³×C₁₀₉	—	2	1	no	—
549	C₂³×C₁₀₉	—	2	1	no	—
550	C₂³×C₁₀₉	—	2	1	no	—
551	C₂³×C₁₀₉	—	2	1	no	—
552	C₂³×C₁₀₉	—	2	1	no	—
553	C₂³×C₁₀₉	—	2	1	no	—
554	C₂³×C₁₀₉	—	2	1	no	—
555	C₂³×C₁₀₉	—	2	1	no	—
556	C₂³×C₁₀₉	—	2	1	no	—
557	C₂³×C₁₀₉	—	2	1	no	—
558	C₂³×C₁₀₉	—	2	1	no	—
559	C₂³×C₁₀₉	—	2	1	no	—
560	C₂³×C₁₀₉	—	2	1	no	—
561	C₂³×C₁₀₉	—	2	1	no	—
562	C₂³×C₁₀₉	—	4	4	no	—
563	C₂³×C₁₀₉	—	4	4	no	—
564	C₂³×C₁₀₉	—	4	4	no	—
565	C₂³×C₁₀₉	—	4	4	no	—
566	C₂³×C₁₀₉	—	4	4	no	—
567	C₂³×C₁₀₉	—	4	4	no	—
568	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
569	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
570	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
571	C₂³×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
572	C₂³×C₁₀₉	2₋¹⁺⁴	1	2	yes	—
573	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
574	Q₈×C₁₀₉	—	4	4	no	—
575	Q₈×C₁₀₉	—	8	2	no	—
576	Q₈×C₁₀₉	—	8	2	no	—
577	D₄×C₁₀₉	—	4	4	no	—
578	D₄×C₁₀₉	—	8	2	no	—
579	D₄×C₁₀₉	—	8	2	no	—
580	C₂×C₄×C₁₀₉	—	2	8	no	—
581	C₂×C₄×C₁₀₉	—	2	1	no	—
582	C₂×C₄×C₁₀₉	—	2	1	no	—
583	C₂×C₄×C₁₀₉	—	2	1	no	—
584	C₂×C₄×C₁₀₉	—	2	1	no	—
585	C₂×C₄×C₁₀₉	—	2	1	no	—
586	C₂×C₄×C₁₀₉	—	2	1	no	—
587	C₂×C₄×C₁₀₉	—	2	1	no	—
588	C₂×C₄×C₁₀₉	—	2	1	no	—
589	C₂×C₄×C₁₀₉	—	2	1	no	—
590	C₂×C₄×C₁₀₉	—	2	1	no	—
591	C₂×C₄×C₁₀₉	—	2	1	no	—
592	C₂×C₄×C₁₀₉	—	2	1	no	—
593	C₂×C₄×C₁₀₉	—	2	1	no	—
594	C₂×C₄×C₁₀₉	—	2	1	no	—
595	C₂×C₄×C₁₀₉	—	2	1	no	—
596	C₂×C₄×C₁₀₉	—	2	1	no	—
597	C₂×C₄×C₁₀₉	—	2	1	no	—
598	C₂×C₄×C₁₀₉	—	2	1	no	—
599	C₂×C₄×C₁₀₉	—	2	1	no	—
600	C₂×C₄×C₁₀₉	—	2	1	no	—
601	C₂×C₄×C₁₀₉	—	2	1	no	—
602	C₂×C₄×C₁₀₉	—	2	1	no	—
603	C₂×C₄×C₁₀₉	—	2	1	no	—
604	C₂×C₄×C₁₀₉	—	2	1	no	—
605	C₂×C₄×C₁₀₉	—	2	1	no	—
606	C₂×C₄×C₁₀₉	—	2	1	no	—
607	C₂×C₄×C₁₀₉	—	2	1	no	—
608	C₂×C₄×C₁₀₉	—	2	1	no	—
609	C₂×C₄×C₁₀₉	—	2	1	no	—
610	C₂×C₄×C₁₀₉	—	2	1	no	—
611	C₂×C₄×C₁₀₉	—	2	1	no	—
612	C₂×C₄×C₁₀₉	—	2	1	no	—
613	C₂×C₄×C₁₀₉	—	2	1	no	—
614	C₂×C₄×C₁₀₉	—	2	1	no	—
615	C₂×C₄×C₁₀₉	—	2	1	no	—
616	C₂×C₄×C₁₀₉	—	2	1	no	—
617	C₂×C₄×C₁₀₉	—	2	1	no	—
618	C₂×C₄×C₁₀₉	—	2	1	no	—
619	C₂×C₄×C₁₀₉	—	2	1	no	—
620	C₂×C₄×C₁₀₉	—	2	1	no	—
621	C₂×C₄×C₁₀₉	—	2	1	no	—
622	C₂×C₄×C₁₀₉	—	2	1	no	—
623	C₂×C₄×C₁₀₉	—	2	1	no	—
624	C₂×C₄×C₁₀₉	—	2	1	no	—
625	C₂×C₄×C₁₀₉	—	2	1	no	—
626	C₂×C₄×C₁₀₉	—	2	1	no	—
627	C₂×C₄×C₁₀₉	—	2	1	no	—
628	C₂×C₄×C₁₀₉	—	2	1	no	—
629	C₂×C₄×C₁₀₉	—	2	1	no	—
630	C₂×C₄×C₁₀₉	—	2	1	no	—
631	C₂×C₄×C₁₀₉	—	2	1	no	—
632	C₂×C₄×C₁₀₉	—	2	1	no	—
633	C₂×C₄×C₁₀₉	—	2	1	no	—
634	C₂×C₄×C₁₀₉	—	2	1	no	—
635	C₂×C₄×C₁₀₉	—	2	1	no	—
636	C₂×C₄×C₁₀₉	—	2	1	no	—
637	C₂×C₄×C₁₀₉	—	2	1	no	—
638	C₂×C₄×C₁₀₉	—	2	1	no	—
639	C₂×C₄×C₁₀₉	—	2	1	no	—
640	C₂×C₄×C₁₀₉	—	2	1	no	—
641	C₂×C₄×C₁₀₉	—	2	1	no	—
642	C₂×C₄×C₁₀₉	—	2	1	no	—
643	C₂×C₄×C₁₀₉	—	2	1	no	—
644	C₂×C₄×C₁₀₉	—	2	1	no	—
645	C₂×C₄×C₁₀₉	—	2	1	no	—
646	C₂×C₄×C₁₀₉	—	2	1	no	—
647	C₂×C₄×C₁₀₉	—	2	1	no	—
648	C₂×C₄×C₁₀₉	—	2	1	no	—
649	C₂×C₄×C₁₀₉	—	2	1	no	—
650	C₂×C₄×C₁₀₉	—	2	1	no	—
651	C₂×C₄×C₁₀₉	—	2	1	no	—
652	C₂×C₄×C₁₀₉	—	2	1	no	—
653	C₂×C₄×C₁₀₉	—	2	1	no	—
654	C₂×C₄×C₁₀₉	—	2	1	no	—
655	C₂×C₄×C₁₀₉	—	4	4	no	—
656	C₂×C₄×C₁₀₉	—	4	4	no	—
657	C₂×C₄×C₁₀₉	—	4	4	no	—
658	C₂×C₄×C₁₀₉	—	4	4	no	—
659	C₂×C₄×C₁₀₉	—	4	4	no	—
660	C₂×C₄×C₁₀₉	—	4	4	no	—
661	C₂×C₄×C₁₀₉	—	4	4	no	—
662	C₂×C₄×C₁₀₉	—	4	4	no	—
663	C₂×C₄×C₁₀₉	—	4	4	no	—
664	C₂×C₄×C₁₀₉	—	4	4	no	—
665	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
666	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
667	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
668	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
669	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
670	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
671	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
672	C₂²×C₁₀₉	—	2	2	no	—
673	C₂²×C₁₀₉	—	2	2	no	—
674	C₂²×C₁₀₉	—	2	2	no	—
675	C₂²×C₁₀₉	—	2	2	no	—
676	C₂²×C₁₀₉	—	2	2	no	—
677	C₂²×C₁₀₉	—	2	2	no	—
678	C₂²×C₁₀₉	—	2	2	no	—
679	C₂²×C₁₀₉	—	2	2	no	—
680	C₂²×C₁₀₉	—	2	2	no	—
681	C₂²×C₁₀₉	—	2	2	no	—
682	C₂²×C₁₀₉	—	2	2	no	—
683	C₂²×C₁₀₉	—	2	2	no	—
684	C₂²×C₁₀₉	—	4	16	no	—
685	C₂²×C₁₀₉	—	4	1	no	—
686	C₂²×C₁₀₉	—	4	1	no	—
687	C₂²×C₁₀₉	—	4	1	no	—
688	C₂²×C₁₀₉	—	4	1	no	—
689	C₂²×C₁₀₉	—	4	1	no	—
690	C₂²×C₁₀₉	—	4	1	no	—
691	C₂²×C₁₀₉	—	4	1	no	—
692	C₂²×C₁₀₉	—	4	1	no	—
693	C₂²×C₁₀₉	—	4	1	no	—
694	C₂²×C₁₀₉	—	4	1	no	—
695	C₂²×C₁₀₉	—	4	1	no	—
696	C₂²×C₁₀₉	—	4	1	no	—
697	C₂²×C₁₀₉	—	4	1	no	—
698	C₂²×C₁₀₉	—	4	1	no	—
699	C₂²×C₁₀₉	—	4	1	no	—
700	C₂²×C₁₀₉	#542	1	4	yes	—
701	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
702	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
703	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
704	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²×C₁₀₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²×C₁₀₉	#585	1	1	yes	characteristic
708	C₄×C₁₀₉	—	2	2	no	—
709	C₄×C₁₀₉	—	2	2	no	—
710	C₄×C₁₀₉	—	2	2	no	—
711	C₄×C₁₀₉	—	2	2	no	—
712	C₄×C₁₀₉	—	2	2	no	—
713	C₄×C₁₀₉	—	2	2	no	—
714	C₄×C₁₀₉	—	2	2	no	—
715	C₄×C₁₀₉	—	4	1	no	—
716	C₄×C₁₀₉	—	4	1	no	—
717	C₄×C₁₀₉	—	4	1	no	—
718	C₄×C₁₀₉	—	4	1	no	—
719	C₄×C₁₀₉	—	4	1	no	—
720	C₄×C₁₀₉	—	4	1	no	—
721	C₄×C₁₀₉	—	4	1	no	—
722	C₄×C₁₀₉	—	4	1	no	—
723	C₄×C₁₀₉	—	4	1	no	—
724	C₄×C₁₀₉	—	4	1	no	—
725	C₄×C₁₀₉	—	4	1	no	—
726	C₄×C₁₀₉	—	4	1	no	—
727	C₄×C₁₀₉	—	4	1	no	—
728	C₄×C₁₀₉	—	4	1	no	—
729	C₄×C₁₀₉	—	4	1	no	—
730	C₄×C₁₀₉	—	4	1	no	—
731	C₄×C₁₀₉	—	4	1	no	—
732	C₄×C₁₀₉	—	4	1	no	—
733	C₄×C₁₀₉	—	4	1	no	—
734	C₄×C₁₀₉	—	4	1	no	—
735	#35055	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
736	C₂×C₁₀₉	—	2	4	no	—
737	C₂×C₁₀₉	—	4	2	no	—
738	C₂×C₁₀₉	—	4	2	no	—
739	C₂×C₁₀₉	—	8	1	no	—
740	C₂×C₁₀₉	#3444	1	1	yes	characteristic
741	C₂×C₁₀₉	C₂×#542	1	1	yes	characteristic
742	C₂×C₁₀₉	#3459	1	1	yes	characteristic
743	C₂×C₁₀₉	#3490	1	1	yes	characteristic
744	C₂×C₁₀₉	#3495	1	1	yes	characteristic
745	C₂×C₁₀₉	#3513	1	1	yes	characteristic
746	C₂×C₁₀₉	#3520	1	1	yes	characteristic
747	#2855	C₂×C₁₀₉	1	1	yes	characteristic, complemented
748	#2853	C₂×C₁₀₉	1	1	yes	characteristic, complemented
749	#2849	C₂×C₁₀₉	1	1	yes	characteristic
750	#2848	C₂×C₁₀₉	1	1	yes	characteristic, complemented
751	#2665	C₂×C₁₀₉	1	1	yes	characteristic, complemented
752	#2663	C₂×C₁₀₉	1	1	yes	characteristic, complemented
753	#2653	C₂×C₁₀₉	1	1	yes	characteristic, complemented
754	#2652	C₂×C₁₀₉	1	1	yes	characteristic, complemented
755	#2564	C₂×C₁₀₉	1	1	yes	characteristic, complemented
756	#2561	C₂×C₁₀₉	1	1	yes	characteristic, complemented
757	#2549	C₂×C₁₀₉	1	1	yes	characteristic, complemented
758	#2534	C₂×C₁₀₉	1	1	yes	characteristic
759	#2530	C₂×C₁₀₉	1	1	yes	characteristic, complemented
760	#2527	C₂×C₁₀₉	1	1	yes	characteristic, complemented
761	#2521	C₂×C₁₀₉	1	1	yes	characteristic, complemented
762	#2515	C₂×C₁₀₉	1	1	yes	characteristic, complemented
763	#2493	C₂×C₁₀₉	1	1	yes	characteristic, complemented
764	#2488	C₂×C₁₀₉	1	1	yes	characteristic, complemented
765	#2480	C₂×C₁₀₉	1	1	yes	characteristic, complemented
766	#2477	C₂×C₁₀₉	1	1	yes	characteristic, complemented
767	#2472	C₂×C₁₀₉	1	1	yes	characteristic
768	#2470	C₂×C₁₀₉	1	1	yes	characteristic, complemented
769	#2465	C₂×C₁₀₉	1	1	yes	characteristic, complemented
770	#2458	C₂×C₁₀₉	1	1	yes	characteristic, complemented
771	#2337	C₂×C₁₀₉	1	1	yes	characteristic, complemented
772	#2335	C₂×C₁₀₉	1	1	yes	characteristic, complemented
773	#2334	C₂×C₁₀₉	1	1	yes	characteristic, complemented
774	#2332	C₂×C₁₀₉	1	1	yes	characteristic, complemented
775	C₄×C₂²⋊Q₈	C₂×C₁₀₉	1	1	yes	characteristic, complemented
776	#2290	C₂×C₁₀₉	1	1	yes	characteristic, complemented
777	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
778	C₁₀₉	#35055	1	1	yes	characteristic, direct product factor, Sylow
779	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
780	C₂×#126	C₂²×C₁₀₉	1	1	yes	characteristic
781	C₂×#124	C₂²×C₁₀₉	1	1	yes	characteristic
782	C₂×#123	C₂²×C₁₀₉	1	1	yes	characteristic
783	C₂×#123	C₂²×C₁₀₉	1	1	yes	characteristic
784	C₂×#123	C₂²×C₁₀₉	1	1	yes	characteristic
785	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
786	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
787	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
788	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
789	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
790	C₂×#120	C₂²×C₁₀₉	1	1	yes	characteristic
791	C₂×C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
792	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
793	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
794	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
795	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
796	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
797	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
798	#401	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
799	#400	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
800	#400	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
801	#400	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
802	#400	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
803	#400	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
804	#400	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
805	#399	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
806	#398	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
807	#398	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
808	#397	C₂²×C₁₀₉	1	1	yes	characteristic
809	#397	C₂²×C₁₀₉	1	1	yes	characteristic
810	#397	C₂²×C₁₀₉	1	1	yes	characteristic
811	#397	C₂²×C₁₀₉	1	1	yes	characteristic
812	#397	C₂²×C₁₀₉	1	1	yes	characteristic
813	#397	C₂²×C₁₀₉	1	1	yes	characteristic
814	#397	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
815	#396	C₂²×C₁₀₉	1	1	yes	characteristic
816	#396	C₂²×C₁₀₉	1	1	yes	characteristic
817	#396	C₂²×C₁₀₉	1	1	yes	characteristic
818	#395	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
819	#395	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
820	#395	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
821	#394	C₂²×C₁₀₉	1	1	yes	characteristic
822	#394	C₂²×C₁₀₉	1	1	yes	characteristic
823	#394	C₂²×C₁₀₉	1	1	yes	characteristic
824	#394	C₂²×C₁₀₉	1	1	yes	characteristic
825	#393	C₂²×C₁₀₉	1	1	yes	characteristic
826	#393	C₂²×C₁₀₉	1	1	yes	characteristic
827	#393	C₂²×C₁₀₉	1	1	yes	characteristic
828	#393	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
829	#393	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
830	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
831	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
832	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
833	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
834	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
835	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
836	#390	C₂²×C₁₀₉	1	1	yes	characteristic
837	#389	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
838	#389	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
839	#389	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
840	#389	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
841	#389	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
842	#388	C₂²×C₁₀₉	1	1	yes	characteristic
843	#388	C₂²×C₁₀₉	1	1	yes	characteristic
844	#388	C₂²×C₁₀₉	1	1	yes	characteristic
845	#388	C₂²×C₁₀₉	1	1	yes	characteristic
846	#388	C₂²×C₁₀₉	1	1	yes	characteristic
847	#388	C₂²×C₁₀₉	1	1	yes	characteristic
848	#388	C₂²×C₁₀₉	1	1	yes	characteristic
849	#388	C₂²×C₁₀₉	1	1	yes	characteristic
850	#388	C₂²×C₁₀₉	1	1	yes	characteristic
851	#388	C₂²×C₁₀₉	1	1	yes	characteristic
852	#388	C₂²×C₁₀₉	1	1	yes	characteristic
853	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
854	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
855	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
856	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
857	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
858	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
859	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
860	#388	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
861	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
862	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
863	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
864	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
865	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
866	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
867	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
868	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
869	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
870	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
871	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
872	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
873	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
874	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
875	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
876	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
877	#387	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
878	#386	C₂²×C₁₀₉	1	1	yes	characteristic
879	#386	C₂²×C₁₀₉	1	1	yes	characteristic
880	#386	C₂²×C₁₀₉	1	1	yes	characteristic
881	#386	C₂²×C₁₀₉	1	1	yes	characteristic
882	#386	C₂²×C₁₀₉	1	1	yes	characteristic
883	#386	C₂²×C₁₀₉	1	1	yes	characteristic
884	#386	C₂²×C₁₀₉	1	1	yes	characteristic
885	#386	C₂²×C₁₀₉	1	1	yes	characteristic
886	#385	C₂²×C₁₀₉	1	1	yes	characteristic
887	#385	C₂²×C₁₀₉	1	1	yes	characteristic
888	#385	C₂²×C₁₀₉	1	1	yes	characteristic
889	#385	C₂²×C₁₀₉	1	1	yes	characteristic
890	#385	C₂²×C₁₀₉	1	1	yes	characteristic
891	#385	C₂²×C₁₀₉	1	1	yes	characteristic
892	#385	C₂²×C₁₀₉	1	1	yes	characteristic
893	#385	C₂²×C₁₀₉	1	1	yes	characteristic
894	#385	C₂²×C₁₀₉	1	1	yes	characteristic
895	#385	C₂²×C₁₀₉	1	1	yes	characteristic
896	#385	C₂²×C₁₀₉	1	1	yes	characteristic
897	#385	C₂²×C₁₀₉	1	1	yes	characteristic
898	#385	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
899	#385	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
900	#383	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
901	#382	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
902	#381	C₂²×C₁₀₉	1	1	yes	characteristic
903	#381	C₂²×C₁₀₉	1	1	yes	characteristic
904	#381	C₂²×C₁₀₉	1	1	yes	characteristic
905	#381	C₂²×C₁₀₉	1	1	yes	characteristic
906	#381	C₂²×C₁₀₉	1	1	yes	characteristic
907	#380	C₂²×C₁₀₉	1	1	yes	characteristic
908	#380	C₂²×C₁₀₉	1	1	yes	characteristic
909	#380	C₂²×C₁₀₉	1	1	yes	characteristic
910	#380	C₂²×C₁₀₉	1	1	yes	characteristic
911	#380	C₂²×C₁₀₉	1	1	yes	characteristic
912	#379	C₂²×C₁₀₉	1	1	yes	characteristic
913	#379	C₂²×C₁₀₉	1	1	yes	characteristic
914	#379	C₂²×C₁₀₉	1	1	yes	characteristic
915	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
916	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
917	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
918	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
919	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
920	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
921	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
922	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
923	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
924	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
925	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
926	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
927	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
928	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
929	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
930	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
931	#376	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
932	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic
933	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic
934	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
935	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
936	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
937	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
938	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
939	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
940	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
941	C₂³×C₄	—	2	4	no	—
942	C₂³×C₄	—	4	2	no	—
943	C₂³×C₄	—	4	2	no	—
944	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
945	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
946	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
947	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
948	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
949	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
950	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
951	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
952	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
953	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
954	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
955	#126	—	2	4	no	—
956	#124	—	2	4	no	—
957	#123	—	2	4	no	—
958	#123	—	4	2	no	—
959	#123	—	4	2	no	—
960	C₂²⋊Q₈	—	2	4	no	—
961	C₂²⋊Q₈	—	2	4	no	—
962	C₂²⋊Q₈	—	4	2	no	—
963	C₂²⋊Q₈	—	4	2	no	—
964	C₂²⋊Q₈	—	4	2	no	—
965	#120	—	4	2	no	—
966	C₄×Q₈	—	4	2	no	—
967	C₄×D₄	—	2	4	no	—
968	#117	—	4	2	no	—
969	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
982	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
983	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	—	2	4	no	—
1000	C₂×C₂²⋊C₄	—	2	4	no	—
1001	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1016	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1018	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
1041	C₂×C₄²	—	4	2	no	—
1042	C₂×C₄²	—	4	2	no	—
1043	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1044	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1045	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1046	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1047	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1048	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1049	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1050	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1051	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1052	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1053	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1054	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1055	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1056	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1057	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
1058	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1059	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1060	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1061	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1062	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1063	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1064	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1065	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1066	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1067	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1068	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1069	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1070	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1071	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1072	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1073	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1074	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1075	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1076	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1077	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1078	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1079	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1080	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1081	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1082	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1083	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1084	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1085	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1086	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1087	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1088	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1089	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1090	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1091	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1092	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1093	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1094	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1095	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1096	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1097	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1098	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1099	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1100	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1101	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1102	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1103	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1104	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1105	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1106	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1107	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1108	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1109	#95	C₂³×C₁₀₉	1	1	yes	characteristic
1110	C₂⁴	—	2	2	no	—
1111	C₂⁴	—	2	2	no	—
1112	C₂⁴	—	2	2	no	—
1113	C₂⁴	—	2	2	no	—
1114	C₂⁴	—	2	2	no	—
1115	C₂⁴	—	4	1	no	—
1116	C₂⁴	—	4	1	no	—
1117	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
1118	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
1119	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
1120	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
1121	C₂×Q₈	—	2	2	no	—
1122	C₂×Q₈	—	2	2	no	—
1123	C₂×Q₈	—	2	2	no	—
1124	C₂×Q₈	—	4	1	no	—
1125	C₂×Q₈	—	4	1	no	—
1126	C₂×Q₈	—	4	1	no	—
1127	C₂×Q₈	—	4	1	no	—
1128	C₂×Q₈	—	4	1	no	—
1129	C₂×Q₈	—	4	1	no	—
1130	C₂×D₄	—	2	2	no	—
1131	C₂×D₄	—	2	2	no	—
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	4	1	no	—
1136	C₂×D₄	—	4	1	no	—
1137	C₂×D₄	—	4	1	no	—
1138	C₂×D₄	—	4	1	no	—
1139	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	2	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	2	2	no	—
1144	C₂²×C₄	—	2	2	no	—
1145	C₂²×C₄	—	2	2	no	—
1146	C₂²×C₄	—	2	2	no	—
1147	C₂²×C₄	—	2	2	no	—
1148	C₂²×C₄	—	2	2	no	—
1149	C₂²×C₄	—	2	2	no	—
1150	C₂²×C₄	—	2	2	no	—
1151	C₂²×C₄	—	2	2	no	—
1152	C₂²×C₄	—	2	2	no	—
1153	C₂²×C₄	—	2	2	no	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	4	1	no	—
1158	C₂²×C₄	—	4	1	no	—
1159	C₂²×C₄	—	4	1	no	—
1160	C₂²×C₄	—	4	1	no	—
1161	C₂²×C₄	—	4	1	no	—
1162	C₂²×C₄	—	4	1	no	—
1163	C₂²×C₄	—	4	1	no	—
1164	C₂²×C₄	—	4	1	no	—
1165	C₂²×C₄	—	4	1	no	—
1166	C₂²×C₄	—	4	1	no	—
1167	C₂²×C₄	—	4	1	no	—
1168	C₂²×C₄	—	4	1	no	—
1169	C₂²×C₄	—	4	1	no	—
1170	C₂²×C₄	—	4	16	no	—
1171	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
1172	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
1173	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1174	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1175	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1176	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1178	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1179	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1180	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1181	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1182	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1183	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1184	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1185	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1186	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1187	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1188	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1189	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1190	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1191	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1192	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1193	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1194	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1195	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1196	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1197	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1198	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	2	no	—
1203	C₄⋊C₄	—	2	2	no	—
1204	C₄⋊C₄	—	2	2	no	—
1205	C₄⋊C₄	—	2	2	no	—
1206	C₄⋊C₄	—	2	2	no	—
1207	C₄⋊C₄	—	2	2	no	—
1208	C₄⋊C₄	—	2	2	no	—
1209	C₄⋊C₄	—	2	2	no	—
1210	C₄⋊C₄	—	2	2	no	—
1211	C₄⋊C₄	—	2	2	no	—
1212	C₄⋊C₄	—	2	2	no	—
1213	C₄⋊C₄	—	2	2	no	—
1214	C₄⋊C₄	—	2	2	no	—
1215	C₄⋊C₄	—	4	1	no	—
1216	C₄⋊C₄	—	4	1	no	—
1217	C₄⋊C₄	—	4	1	no	—
1218	C₄⋊C₄	—	4	1	no	—
1219	C₄⋊C₄	—	4	1	no	—
1220	C₄⋊C₄	—	4	1	no	—
1221	C₄⋊C₄	—	4	1	no	—
1222	C₄⋊C₄	—	4	1	no	—
1223	C₄⋊C₄	—	4	1	no	—
1224	C₄⋊C₄	—	4	1	no	—
1225	C₄⋊C₄	—	4	1	no	—
1226	C₄⋊C₄	—	4	1	no	—
1227	C₄⋊C₄	—	4	1	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	2	no	—
1232	C₂²⋊C₄	—	2	2	no	—
1233	C₂²⋊C₄	—	2	2	no	—
1234	C₂²⋊C₄	—	2	2	no	—
1235	C₂²⋊C₄	—	2	2	no	—
1236	C₂²⋊C₄	—	2	2	no	—
1237	C₂²⋊C₄	—	2	2	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	—	2	2	no	—
1246	C₂²⋊C₄	—	2	2	no	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	2	2	no	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	2	2	no	—
1251	C₂²⋊C₄	—	2	2	no	—
1252	C₂²⋊C₄	—	2	2	no	—
1253	C₂²⋊C₄	—	2	2	no	—
1254	C₂²⋊C₄	—	2	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	4	1	no	—
1257	C₂²⋊C₄	—	4	1	no	—
1258	C₂²⋊C₄	—	4	1	no	—
1259	C₂²⋊C₄	—	4	1	no	—
1260	C₂²⋊C₄	—	4	1	no	—
1261	C₂²⋊C₄	—	4	1	no	—
1262	C₂²⋊C₄	—	4	1	no	—
1263	C₂²⋊C₄	—	4	1	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	4	1	no	—
1266	C₂²⋊C₄	—	4	1	no	—
1267	C₂²⋊C₄	—	4	1	no	—
1268	C₂²⋊C₄	—	4	1	no	—
1269	C₂²⋊C₄	#41×C₁₀₉	1	4	yes	—
1270	C₄²	—	2	2	no	—
1271	C₄²	—	2	2	no	—
1272	C₄²	—	2	2	no	—
1273	C₄²	—	2	2	no	—
1274	C₄²	—	2	2	no	—
1275	C₄²	—	4	1	no	—
1276	C₄²	—	4	1	no	—
1277	C₄²	—	4	1	no	—
1278	C₄²	—	4	1	no	—
1279	C₄²	—	4	1	no	—
1280	C₄²	—	4	1	no	—
1281	C₄²	—	4	1	no	—
1282	C₄²	—	4	1	no	—
1283	C₄²	—	4	1	no	—
1284	C₄²	—	4	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	8	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	2	1	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	2	1	no	—
1305	C₂³	—	2	1	no	—
1306	C₂³	—	2	1	no	—
1307	C₂³	—	2	1	no	—
1308	C₂³	—	2	1	no	—
1309	C₂³	—	4	4	no	—
1310	C₂³	—	4	4	no	—
1311	C₂³	—	4	4	no	—
1312	C₂³	—	4	4	no	—
1313	C₂³	—	4	4	no	—
1314	C₂³	—	4	4	no	—
1315	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
1316	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
1317	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
1318	C₂³	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
1319	C₂³	2₋¹⁺⁴×C₁₀₉	1	2	yes	—
1320	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
1321	Q₈	—	4	4	no	—
1322	Q₈	—	8	2	no	—
1323	Q₈	—	8	2	no	—
1324	D₄	—	4	4	no	—
1325	D₄	—	8	2	no	—
1326	D₄	—	8	2	no	—
1327	C₂×C₄	—	2	8	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	4	4	no	—
1403	C₂×C₄	—	4	4	no	—
1404	C₂×C₄	—	4	4	no	—
1405	C₂×C₄	—	4	4	no	—
1406	C₂×C₄	—	4	4	no	—
1407	C₂×C₄	—	4	4	no	—
1408	C₂×C₄	—	4	4	no	—
1409	C₂×C₄	—	4	4	no	—
1410	C₂×C₄	—	4	4	no	—
1411	C₂×C₄	—	4	4	no	—
1412	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
1413	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
1414	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
1415	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
1416	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
1417	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
1418	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
1419	C₂²	—	2	2	no	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	2	2	no	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	2	2	no	—
1425	C₂²	—	2	2	no	—
1426	C₂²	—	2	2	no	—
1427	C₂²	—	2	2	no	—
1428	C₂²	—	2	2	no	—
1429	C₂²	—	2	2	no	—
1430	C₂²	—	2	2	no	—
1431	C₂²	—	4	16	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	1	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	1	no	—
1437	C₂²	—	4	1	no	—
1438	C₂²	—	4	1	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	4	1	no	—
1441	C₂²	—	4	1	no	—
1442	C₂²	—	4	1	no	—
1443	C₂²	—	4	1	no	—
1444	C₂²	—	4	1	no	—
1445	C₂²	—	4	1	no	—
1446	C₂²	—	4	1	no	—
1447	C₂²	#542×C₁₀₉	1	4	yes	—
1448	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
1449	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
1450	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
1451	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
1452	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
1453	C₂²	C₂×2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
1454	C₂²	#585×C₁₀₉	1	1	yes	characteristic
1455	C₄	—	2	2	no	—
1456	C₄	—	2	2	no	—
1457	C₄	—	2	2	no	—
1458	C₄	—	2	2	no	—
1459	C₄	—	2	2	no	—
1460	C₄	—	2	2	no	—
1461	C₄	—	2	2	no	—
1462	C₄	—	4	1	no	—
1463	C₄	—	4	1	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	4	1	no	—
1468	C₄	—	4	1	no	—
1469	C₄	—	4	1	no	—
1470	C₄	—	4	1	no	—
1471	C₄	—	4	1	no	—
1472	C₄	—	4	1	no	—
1473	C₄	—	4	1	no	—
1474	C₄	—	4	1	no	—
1475	C₄	—	4	1	no	—
1476	C₄	—	4	1	no	—
1477	C₄	—	4	1	no	—
1478	C₄	—	4	1	no	—
1479	C₄	—	4	1	no	—
1480	C₄	—	4	1	no	—
1481	C₄	—	4	1	no	—
1482	C₂	—	2	4	no	—
1483	C₂	—	4	2	no	—
1484	C₂	—	4	2	no	—
1485	C₂	—	8	1	no	—
1486	C₂	C₁₀₉×#3444	1	1	yes	characteristic
1487	C₂	C₂×#542×C₁₀₉	1	1	yes	characteristic
1488	C₂	C₁₀₉×#3459	1	1	yes	characteristic
1489	C₂	C₁₀₉×#3490	1	1	yes	characteristic
1490	C₂	C₁₀₉×#3495	1	1	yes	characteristic
1491	C₂	C₁₀₉×#3513	1	1	yes	characteristic
1492	C₂	C₁₀₉×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
prime radical	C₂×#120×C₁₀₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₀₉×#2855	C₂	semidirect
2. C₁₀₉×#2853	C₂	semidirect
4. C₁₀₉×#2848	C₂	semidirect
5. C₁₀₉×#2665	C₂	semidirect
6. C₁₀₉×#2663	C₂	semidirect
7. C₁₀₉×#2653	C₂	semidirect
8. C₁₀₉×#2652	C₂	semidirect
9. C₁₀₉×#2564	C₂	semidirect
10. C₁₀₉×#2561	C₂	semidirect
11. C₁₀₉×#2549	C₂	semidirect
13. C₁₀₉×#2530	C₂	semidirect
14. C₁₀₉×#2527	C₂	semidirect
15. C₁₀₉×#2521	C₂	semidirect
16. C₁₀₉×#2515	C₂	semidirect
17. C₁₀₉×#2493	C₂	semidirect
18. C₁₀₉×#2488	C₂	semidirect
19. C₁₀₉×#2480	C₂	semidirect
20. C₁₀₉×#2477	C₂	semidirect
22. C₁₀₉×#2470	C₂	semidirect
23. C₁₀₉×#2465	C₂	semidirect
24. C₁₀₉×#2458	C₂	semidirect
25. C₁₀₉×#2337	C₂	semidirect
26. C₁₀₉×#2335	C₂	semidirect
27. C₁₀₉×#2334	C₂	semidirect
28. C₁₀₉×#2332	C₂	semidirect
29. C₄×C₂²⋊Q₈×C₁₀₉	C₂	semidirect
30. C₁₀₉×#2290	C₂	semidirect
31. C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	semidirect
44. C₂×C₄×Q₈×C₁₀₉	C₂²	semidirect
46. C₂×#117×C₁₀₉	C₂²	semidirect
51. #401×C₁₀₉	C₂²	semidirect
52. #400×C₁₀₉	C₂²	semidirect
53. #400×C₁₀₉	C₂²	semidirect
54. #400×C₁₀₉	C₂²	semidirect
55. #400×C₁₀₉	C₂²	semidirect
56. #400×C₁₀₉	C₂²	semidirect
57. #400×C₁₀₉	C₂²	semidirect
58. #399×C₁₀₉	C₂²	semidirect
59. #398×C₁₀₉	C₂²	semidirect
60. #398×C₁₀₉	C₂²	semidirect
67. #397×C₁₀₉	C₂²	semidirect
71. #395×C₁₀₉	C₂²	semidirect
72. #395×C₁₀₉	C₂²	semidirect
73. #395×C₁₀₉	C₂²	semidirect
81. #393×C₁₀₉	C₂²	semidirect
82. #393×C₁₀₉	C₂²	semidirect
83. #391×C₁₀₉	C₂²	semidirect
84. #391×C₁₀₉	C₂²	semidirect
85. #391×C₁₀₉	C₂²	semidirect
86. #391×C₁₀₉	C₂²	semidirect
87. #391×C₁₀₉	C₂²	semidirect
88. #391×C₁₀₉	C₂²	semidirect
90. #389×C₁₀₉	C₂²	semidirect
91. #389×C₁₀₉	C₂²	semidirect
92. #389×C₁₀₉	C₂²	semidirect
93. #389×C₁₀₉	C₂²	semidirect
94. #389×C₁₀₉	C₂²	semidirect
106. #388×C₁₀₉	C₂²	semidirect
107. #388×C₁₀₉	C₂²	semidirect
108. #388×C₁₀₉	C₂²	semidirect
109. #388×C₁₀₉	C₂²	semidirect
110. #388×C₁₀₉	C₂²	semidirect
111. #388×C₁₀₉	C₂²	semidirect
112. #388×C₁₀₉	C₂²	semidirect
113. #388×C₁₀₉	C₂²	semidirect
114. #387×C₁₀₉	C₂²	semidirect
115. #387×C₁₀₉	C₂²	semidirect
116. #387×C₁₀₉	C₂²	semidirect
117. #387×C₁₀₉	C₂²	semidirect
118. #387×C₁₀₉	C₂²	semidirect
119. #387×C₁₀₉	C₂²	semidirect
120. #387×C₁₀₉	C₂²	semidirect
121. #387×C₁₀₉	C₂²	semidirect
122. #387×C₁₀₉	C₂²	semidirect
123. #387×C₁₀₉	C₂²	semidirect
124. #387×C₁₀₉	C₂²	semidirect
125. #387×C₁₀₉	C₂²	semidirect
126. #387×C₁₀₉	C₂²	semidirect
127. #387×C₁₀₉	C₂²	semidirect
128. #387×C₁₀₉	C₂²	semidirect
129. #387×C₁₀₉	C₂²	semidirect
130. #387×C₁₀₉	C₂²	semidirect
151. #385×C₁₀₉	C₂²	semidirect
152. #385×C₁₀₉	C₂²	semidirect
153. #383×C₁₀₉	C₂²	semidirect
154. #382×C₁₀₉	C₂²	semidirect
168. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
169. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
170. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
171. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
183. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
184. #376×C₁₀₉	C₂²	semidirect
735. #35055	C₁₀₉	direct (N × H)
747. #2855	C₂×C₁₀₉	semidirect
748. #2853	C₂×C₁₀₉	semidirect
750. #2848	C₂×C₁₀₉	semidirect
751. #2665	C₂×C₁₀₉	semidirect
752. #2663	C₂×C₁₀₉	semidirect
753. #2653	C₂×C₁₀₉	semidirect
754. #2652	C₂×C₁₀₉	semidirect
755. #2564	C₂×C₁₀₉	semidirect
756. #2561	C₂×C₁₀₉	semidirect
757. #2549	C₂×C₁₀₉	semidirect
759. #2530	C₂×C₁₀₉	semidirect
760. #2527	C₂×C₁₀₉	semidirect
761. #2521	C₂×C₁₀₉	semidirect
762. #2515	C₂×C₁₀₉	semidirect
763. #2493	C₂×C₁₀₉	semidirect
764. #2488	C₂×C₁₀₉	semidirect
765. #2480	C₂×C₁₀₉	semidirect
766. #2477	C₂×C₁₀₉	semidirect
768. #2470	C₂×C₁₀₉	semidirect
769. #2465	C₂×C₁₀₉	semidirect
770. #2458	C₂×C₁₀₉	semidirect
771. #2337	C₂×C₁₀₉	semidirect
772. #2335	C₂×C₁₀₉	semidirect
773. #2334	C₂×C₁₀₉	semidirect
774. #2332	C₂×C₁₀₉	semidirect
775. C₄×C₂²⋊Q₈	C₂×C₁₀₉	semidirect
776. #2290	C₂×C₁₀₉	semidirect
777. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	semidirect
778. C₁₀₉	#35055	direct (N × H)
791. C₂×C₄×Q₈	C₂²×C₁₀₉	semidirect
793. C₂×#117	C₂²×C₁₀₉	semidirect
798. #401	C₂²×C₁₀₉	semidirect
799. #400	C₂²×C₁₀₉	semidirect
800. #400	C₂²×C₁₀₉	semidirect
801. #400	C₂²×C₁₀₉	semidirect
802. #400	C₂²×C₁₀₉	semidirect
803. #400	C₂²×C₁₀₉	semidirect
804. #400	C₂²×C₁₀₉	semidirect
805. #399	C₂²×C₁₀₉	semidirect
806. #398	C₂²×C₁₀₉	semidirect
807. #398	C₂²×C₁₀₉	semidirect
814. #397	C₂²×C₁₀₉	semidirect
818. #395	C₂²×C₁₀₉	semidirect
819. #395	C₂²×C₁₀₉	semidirect
820. #395	C₂²×C₁₀₉	semidirect
828. #393	C₂²×C₁₀₉	semidirect
829. #393	C₂²×C₁₀₉	semidirect
830. #391	C₂²×C₁₀₉	semidirect
831. #391	C₂²×C₁₀₉	semidirect
832. #391	C₂²×C₁₀₉	semidirect
833. #391	C₂²×C₁₀₉	semidirect
834. #391	C₂²×C₁₀₉	semidirect
835. #391	C₂²×C₁₀₉	semidirect
837. #389	C₂²×C₁₀₉	semidirect
838. #389	C₂²×C₁₀₉	semidirect
839. #389	C₂²×C₁₀₉	semidirect
840. #389	C₂²×C₁₀₉	semidirect
841. #389	C₂²×C₁₀₉	semidirect
853. #388	C₂²×C₁₀₉	semidirect
854. #388	C₂²×C₁₀₉	semidirect
855. #388	C₂²×C₁₀₉	semidirect
856. #388	C₂²×C₁₀₉	semidirect
857. #388	C₂²×C₁₀₉	semidirect
858. #388	C₂²×C₁₀₉	semidirect
859. #388	C₂²×C₁₀₉	semidirect
860. #388	C₂²×C₁₀₉	semidirect
861. #387	C₂²×C₁₀₉	semidirect
862. #387	C₂²×C₁₀₉	semidirect
863. #387	C₂²×C₁₀₉	semidirect
864. #387	C₂²×C₁₀₉	semidirect
865. #387	C₂²×C₁₀₉	semidirect
866. #387	C₂²×C₁₀₉	semidirect
867. #387	C₂²×C₁₀₉	semidirect
868. #387	C₂²×C₁₀₉	semidirect
869. #387	C₂²×C₁₀₉	semidirect
870. #387	C₂²×C₁₀₉	semidirect
871. #387	C₂²×C₁₀₉	semidirect
872. #387	C₂²×C₁₀₉	semidirect
873. #387	C₂²×C₁₀₉	semidirect
874. #387	C₂²×C₁₀₉	semidirect
875. #387	C₂²×C₁₀₉	semidirect
876. #387	C₂²×C₁₀₉	semidirect
877. #387	C₂²×C₁₀₉	semidirect
898. #385	C₂²×C₁₀₉	semidirect
899. #385	C₂²×C₁₀₉	semidirect
900. #383	C₂²×C₁₀₉	semidirect
901. #382	C₂²×C₁₀₉	semidirect
915. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
916. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
917. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
918. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
930. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
931. #376	C₂²×C₁₀₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₀₉×#2855	2
C₁₀₉×#2853	2
C₁₀₉×#2849	2
C₁₀₉×#2848	2
C₁₀₉×#2665	2
C₁₀₉×#2663	2
C₁₀₉×#2653	2
C₁₀₉×#2652	2
C₁₀₉×#2564	2
C₁₀₉×#2561	2
C₁₀₉×#2549	2
C₁₀₉×#2534	2
C₁₀₉×#2530	2
C₁₀₉×#2527	2
C₁₀₉×#2521	2
C₁₀₉×#2515	2
C₁₀₉×#2493	2
C₁₀₉×#2488	2
C₁₀₉×#2480	2
C₁₀₉×#2477	2
C₁₀₉×#2472	2
C₁₀₉×#2470	2
C₁₀₉×#2465	2
C₁₀₉×#2458	2
C₁₀₉×#2337	2
C₁₀₉×#2335	2
C₁₀₉×#2334	2
C₁₀₉×#2332	2
C₄×C₂²⋊Q₈×C₁₀₉	2
C₁₀₉×#2290	2
C₂×C₄×C₂²⋊C₄×C₁₀₉	2
#35055	109

Subgroups — C109×#35055 #42153049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#35055 #42153049