Subgroups — C₁₀₉×#34655 #42152649

Order 27904.

3910 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₀₉	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₁₀₉×#2463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2456	C₂	1	2	yes	maximal, complemented
5	C₁₀₉×#2455	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₉×#2449	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#2443	C₂	1	2	yes	maximal, complemented
8	C₁₀₉×#2437	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₉×#2424	C₂	1	2	yes	maximal, complemented
10	C₁₀₉×#2418	C₂	1	2	yes	maximal, complemented
11	C₁₀₉×#2410	C₂	1	2	yes	maximal, complemented
12	C₁₀₉×#2403	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₀₉×#2397	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₀₉×#2392	C₂	1	2	yes	maximal, complemented
15	C₁₀₉×#2388	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#121×C₁₀₉	C₂	1	2	yes	maximal, complemented
17	C₄×#120×C₁₀₉	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₀₉×#2290	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₁₀₉	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₁₀₉	C₂²	1	2	yes	complemented
24	#525×C₁₀₉	—	2	16	no	—
25	C₂×#123×C₁₀₉	C₂²	1	2	yes	complemented
26	C₂×#123×C₁₀₉	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
29	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₀₉	C₂²	1	2	yes	complemented
32	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
33	C₂×#120×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
35	C₂×#120×C₁₀₉	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₁₀₉	—	2	16	no	—
37	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₁₀₉	C₂²	1	2	yes	complemented
51	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
52	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
54	C₂²×C₄²×C₁₀₉	C₂²	1	2	yes	complemented
55	#399×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	#399×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#399×C₁₀₉	C₂²	1	2	yes	complemented
58	#398×C₁₀₉	C₂²	1	2	yes	complemented
59	#397×C₁₀₉	C₂²	1	2	yes	complemented
60	#396×C₁₀₉	C₂²	1	2	yes	complemented
61	#396×C₁₀₉	C₂²	1	2	yes	complemented
62	#395×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
63	#394×C₁₀₉	C₂²	1	2	yes	complemented
64	#394×C₁₀₉	C₂²	1	2	yes	complemented
65	#394×C₁₀₉	C₂²	1	2	yes	complemented
66	#394×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
67	#394×C₁₀₉	C₂²	1	2	yes	complemented
68	#393×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
69	#392×C₁₀₉	C₂²	1	1	yes	characteristic
70	#392×C₁₀₉	C₂²	1	2	yes	—
71	#392×C₁₀₉	C₂²	1	1	yes	characteristic
72	#392×C₁₀₉	C₂²	1	2	yes	complemented
73	#392×C₁₀₉	C₂²	1	2	yes	complemented
74	#392×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
75	#390×C₁₀₉	C₂²	1	2	yes	complemented
76	#389×C₁₀₉	C₂²	1	2	yes	complemented
77	#388×C₁₀₉	C₂²	1	2	yes	complemented
78	#388×C₁₀₉	C₂²	1	2	yes	complemented
79	#388×C₁₀₉	C₂²	1	2	yes	complemented
80	#388×C₁₀₉	C₂²	1	2	yes	complemented
81	#387×C₁₀₉	C₂²	1	2	yes	complemented
82	#387×C₁₀₉	C₂²	1	2	yes	complemented
83	#386×C₁₀₉	C₂²	1	2	yes	—
84	#386×C₁₀₉	C₂²	1	2	yes	—
85	#386×C₁₀₉	C₂²	1	2	yes	—
86	#386×C₁₀₉	C₂²	1	2	yes	—
87	#386×C₁₀₉	C₂²	1	2	yes	complemented
88	#386×C₁₀₉	C₂²	1	2	yes	complemented
89	#386×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
90	#386×C₁₀₉	C₂²	1	2	yes	complemented
91	#386×C₁₀₉	C₂²	1	2	yes	complemented
92	#385×C₁₀₉	C₂²	1	2	yes	complemented
93	#385×C₁₀₉	C₂²	1	2	yes	complemented
94	#385×C₁₀₉	C₂²	1	2	yes	complemented
95	#385×C₁₀₉	C₂²	1	2	yes	complemented
96	#385×C₁₀₉	C₂²	1	2	yes	complemented
97	#385×C₁₀₉	C₂²	1	2	yes	complemented
98	#385×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
99	#380×C₁₀₉	C₂²	1	2	yes	complemented
100	#379×C₁₀₉	C₂²	1	1	yes	characteristic
101	#379×C₁₀₉	C₂²	1	2	yes	complemented
102	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
108	#376×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
109	C₂⁵×C₁₀₉	C₂³	1	2	yes	—
110	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂×#41×C₁₀₉	—	2	8	no	—
112	C₂×#41×C₁₀₉	—	4	2	no	—
113	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₀₉	—	2	8	no	—
115	C₂²×D₄×C₁₀₉	—	2	8	no	—
116	C₂²×D₄×C₁₀₉	—	2	8	no	—
117	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
120	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
121	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
123	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₀₉	—	2	8	no	—
129	C₂³×C₄×C₁₀₉	—	2	8	no	—
130	C₂³×C₄×C₁₀₉	—	2	8	no	—
131	C₂³×C₄×C₁₀₉	—	4	2	no	—
132	C₂³×C₄×C₁₀₉	—	4	4	no	—
133	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
145	#123×C₁₀₉	—	2	8	no	—
146	#123×C₁₀₉	—	2	8	no	—
147	C₂²⋊Q₈×C₁₀₉	—	2	8	no	—
148	C₂²⋊Q₈×C₁₀₉	—	2	8	no	—
149	#121×C₁₀₉	—	2	8	no	—
150	#121×C₁₀₉	—	2	8	no	—
151	#121×C₁₀₉	—	2	8	no	—
152	#120×C₁₀₉	—	2	4	no	—
153	#120×C₁₀₉	—	2	8	no	—
154	#120×C₁₀₉	—	2	8	no	—
155	#120×C₁₀₉	—	2	8	no	—
156	C₄×D₄×C₁₀₉	—	2	8	no	—
157	C₄×D₄×C₁₀₉	—	2	8	no	—
158	C₄×D₄×C₁₀₉	—	2	8	no	—
159	C₄×D₄×C₁₀₉	—	2	8	no	—
160	C₄×D₄×C₁₀₉	—	2	8	no	—
161	C₄×D₄×C₁₀₉	—	2	8	no	—
162	C₄×D₄×C₁₀₉	—	2	8	no	—
163	C₄×D₄×C₁₀₉	—	2	8	no	—
164	C₄×D₄×C₁₀₉	—	2	8	no	—
165	C₄×D₄×C₁₀₉	—	2	8	no	—
166	C₄×D₄×C₁₀₉	—	4	2	no	—
167	C₄×D₄×C₁₀₉	—	4	2	no	—
168	C₄×D₄×C₁₀₉	D₄	1	16	yes	complemented
169	#117×C₁₀₉	—	2	8	no	—
170	C₂×C₄⋊C₄×C₁₀₉	—	2	8	no	—
171	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
185	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
186	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₀₉	—	2	8	no	—
215	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
216	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
219	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
221	#95×C₁₀₉	C₂³	1	1	yes	characteristic
222	#95×C₁₀₉	C₂³	1	2	yes	—
223	#95×C₁₀₉	C₂³	1	1	yes	characteristic
224	#95×C₁₀₉	C₂³	1	1	yes	characteristic
225	#95×C₁₀₉	C₂³	1	2	yes	—
226	#95×C₁₀₉	C₂³	1	2	yes	—
227	#95×C₁₀₉	C₂³	1	2	yes	—
228	#95×C₁₀₉	C₂³	1	2	yes	—
229	#95×C₁₀₉	C₂³	1	2	yes	—
230	#95×C₁₀₉	C₂³	1	2	yes	—
231	#95×C₁₀₉	C₂³	1	2	yes	—
232	#95×C₁₀₉	C₂³	1	1	yes	characteristic
233	#95×C₁₀₉	C₂³	1	2	yes	—
234	#95×C₁₀₉	C₂³	1	2	yes	—
235	C₂⁴×C₁₀₉	—	2	4	no	—
236	C₂⁴×C₁₀₉	—	2	4	no	—
237	C₂⁴×C₁₀₉	—	2	4	no	—
238	C₂⁴×C₁₀₉	—	2	4	no	—
239	C₂⁴×C₁₀₉	—	2	4	no	—
240	C₂⁴×C₁₀₉	—	2	4	no	—
241	C₂⁴×C₁₀₉	—	2	4	no	—
242	C₂⁴×C₁₀₉	—	4	1	no	—
243	C₂⁴×C₁₀₉	—	4	2	no	—
244	C₂⁴×C₁₀₉	—	4	1	no	—
245	C₂⁴×C₁₀₉	—	4	2	no	—
246	C₂⁴×C₁₀₉	#41	1	4	yes	complemented
247	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
249	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
250	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
252	#41×C₁₀₉	—	4	16	no	—
253	C₂×Q₈×C₁₀₉	—	2	4	no	—
254	C₂×Q₈×C₁₀₉	—	4	1	no	—
255	C₂×D₄×C₁₀₉	—	2	64	no	—
256	C₂×D₄×C₁₀₉	—	2	4	no	—
257	C₂×D₄×C₁₀₉	—	2	4	no	—
258	C₂×D₄×C₁₀₉	—	2	4	no	—
259	C₂×D₄×C₁₀₉	—	2	4	no	—
260	C₂×D₄×C₁₀₉	—	2	4	no	—
261	C₂×D₄×C₁₀₉	—	2	4	no	—
262	C₂×D₄×C₁₀₉	—	2	4	no	—
263	C₂×D₄×C₁₀₉	—	2	4	no	—
264	C₂×D₄×C₁₀₉	—	2	4	no	—
265	C₂×D₄×C₁₀₉	—	2	4	no	—
266	C₂×D₄×C₁₀₉	—	2	4	no	—
267	C₂×D₄×C₁₀₉	—	2	4	no	—
268	C₂×D₄×C₁₀₉	—	2	4	no	—
269	C₂×D₄×C₁₀₉	—	2	4	no	—
270	C₂×D₄×C₁₀₉	—	2	2	no	—
271	C₂×D₄×C₁₀₉	—	2	4	no	—
272	C₂×D₄×C₁₀₉	—	2	4	no	—
273	C₂×D₄×C₁₀₉	—	2	4	no	—
274	C₂×D₄×C₁₀₉	—	2	4	no	—
275	C₂×D₄×C₁₀₉	—	2	4	no	—
276	C₂×D₄×C₁₀₉	—	2	4	no	—
277	C₂×D₄×C₁₀₉	—	2	4	no	—
278	C₂×D₄×C₁₀₉	—	4	1	no	—
279	C₂×D₄×C₁₀₉	—	4	1	no	—
280	C₂×D₄×C₁₀₉	—	4	2	no	—
281	C₂×D₄×C₁₀₉	—	4	1	no	—
282	C₂×D₄×C₁₀₉	—	4	2	no	—
283	C₂×D₄×C₁₀₉	—	4	2	no	—
284	C₂×D₄×C₁₀₉	—	4	1	no	—
285	C₂×D₄×C₁₀₉	C₂×D₄	1	8	yes	—
286	C₂×D₄×C₁₀₉	#41	1	8	yes	complemented
287	C₂²×C₄×C₁₀₉	—	2	4	no	—
288	C₂²×C₄×C₁₀₉	—	2	4	no	—
289	C₂²×C₄×C₁₀₉	—	2	4	no	—
290	C₂²×C₄×C₁₀₉	—	2	4	no	—
291	C₂²×C₄×C₁₀₉	—	2	4	no	—
292	C₂²×C₄×C₁₀₉	—	2	4	no	—
293	C₂²×C₄×C₁₀₉	—	2	4	no	—
294	C₂²×C₄×C₁₀₉	—	2	4	no	—
295	C₂²×C₄×C₁₀₉	—	2	4	no	—
296	C₂²×C₄×C₁₀₉	—	2	4	no	—
297	C₂²×C₄×C₁₀₉	—	2	4	no	—
298	C₂²×C₄×C₁₀₉	—	2	4	no	—
299	C₂²×C₄×C₁₀₉	—	2	4	no	—
300	C₂²×C₄×C₁₀₉	—	2	4	no	—
301	C₂²×C₄×C₁₀₉	—	2	4	no	—
302	C₂²×C₄×C₁₀₉	—	2	4	no	—
303	C₂²×C₄×C₁₀₉	—	2	4	no	—
304	C₂²×C₄×C₁₀₉	—	2	4	no	—
305	C₂²×C₄×C₁₀₉	—	2	4	no	—
306	C₂²×C₄×C₁₀₉	—	2	4	no	—
307	C₂²×C₄×C₁₀₉	—	2	4	no	—
308	C₂²×C₄×C₁₀₉	—	2	4	no	—
309	C₂²×C₄×C₁₀₉	—	2	2	no	—
310	C₂²×C₄×C₁₀₉	—	2	4	no	—
311	C₂²×C₄×C₁₀₉	—	2	2	no	—
312	C₂²×C₄×C₁₀₉	—	4	1	no	—
313	C₂²×C₄×C₁₀₉	—	4	2	no	—
314	C₂²×C₄×C₁₀₉	—	4	2	no	—
315	C₂²×C₄×C₁₀₉	—	4	2	no	—
316	C₂²×C₄×C₁₀₉	—	4	2	no	—
317	C₂²×C₄×C₁₀₉	—	4	2	no	—
318	C₂²×C₄×C₁₀₉	—	4	16	no	—
319	C₂²×C₄×C₁₀₉	—	4	32	no	—
320	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	—
321	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	complemented
322	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
336	C₄⋊C₄×C₁₀₉	—	2	4	no	—
337	C₄⋊C₄×C₁₀₉	—	2	4	no	—
338	C₄⋊C₄×C₁₀₉	—	2	4	no	—
339	C₄⋊C₄×C₁₀₉	—	2	4	no	—
340	C₄⋊C₄×C₁₀₉	—	2	4	no	—
341	C₄⋊C₄×C₁₀₉	—	2	4	no	—
342	C₄⋊C₄×C₁₀₉	—	2	4	no	—
343	C₄⋊C₄×C₁₀₉	—	2	4	no	—
344	C₄⋊C₄×C₁₀₉	—	2	4	no	—
345	C₄⋊C₄×C₁₀₉	—	4	2	no	—
346	C₄⋊C₄×C₁₀₉	—	4	1	no	—
347	C₄⋊C₄×C₁₀₉	—	4	1	no	—
348	C₄⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	complemented
349	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
350	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
351	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
352	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
353	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
355	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
356	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
360	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
362	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
363	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
367	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
368	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
369	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
370	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
371	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
372	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
373	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
374	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
375	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
376	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	complemented
377	C₄²×C₁₀₉	—	2	4	no	—
378	C₄²×C₁₀₉	—	2	4	no	—
379	C₄²×C₁₀₉	—	2	4	no	—
380	C₄²×C₁₀₉	—	2	4	no	—
381	C₄²×C₁₀₉	—	2	2	no	—
382	C₄²×C₁₀₉	C₂×D₄	1	8	yes	complemented
383	C₂³×C₁₀₉	—	2	2	no	—
384	C₂³×C₁₀₉	—	2	2	no	—
385	C₂³×C₁₀₉	—	2	2	no	—
386	C₂³×C₁₀₉	—	2	2	no	—
387	C₂³×C₁₀₉	—	2	16	no	—
388	C₂³×C₁₀₉	—	2	16	no	—
389	C₂³×C₁₀₉	—	2	2	no	—
390	C₂³×C₁₀₉	—	2	2	no	—
391	C₂³×C₁₀₉	—	2	2	no	—
392	C₂³×C₁₀₉	—	2	2	no	—
393	C₂³×C₁₀₉	—	2	2	no	—
394	C₂³×C₁₀₉	—	2	2	no	—
395	C₂³×C₁₀₉	—	2	2	no	—
396	C₂³×C₁₀₉	—	2	2	no	—
397	C₂³×C₁₀₉	—	2	2	no	—
398	C₂³×C₁₀₉	—	2	2	no	—
399	C₂³×C₁₀₉	—	2	1	no	—
400	C₂³×C₁₀₉	—	2	2	no	—
401	C₂³×C₁₀₉	—	2	2	no	—
402	C₂³×C₁₀₉	—	2	1	no	—
403	C₂³×C₁₀₉	—	2	2	no	—
404	C₂³×C₁₀₉	—	2	2	no	—
405	C₂³×C₁₀₉	—	2	2	no	—
406	C₂³×C₁₀₉	—	2	2	no	—
407	C₂³×C₁₀₉	—	2	1	no	—
408	C₂³×C₁₀₉	—	2	1	no	—
409	C₂³×C₁₀₉	—	2	1	no	—
410	C₂³×C₁₀₉	—	4	4	no	—
411	C₂³×C₁₀₉	—	4	4	no	—
412	C₂³×C₁₀₉	—	4	8	no	—
413	C₂³×C₁₀₉	—	4	8	no	—
414	C₂³×C₁₀₉	—	4	8	no	—
415	C₂³×C₁₀₉	—	4	8	no	—
416	C₂³×C₁₀₉	—	4	4	no	—
417	C₂³×C₁₀₉	—	4	8	no	—
418	C₂³×C₁₀₉	—	4	8	no	—
419	C₂³×C₁₀₉	—	4	8	no	—
420	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
421	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
422	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
423	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
424	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
425	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
426	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
427	Q₈×C₁₀₉	—	4	4	no	—
428	D₄×C₁₀₉	—	2	16	no	—
429	D₄×C₁₀₉	—	2	16	no	—
430	D₄×C₁₀₉	—	2	16	no	—
431	D₄×C₁₀₉	—	2	16	no	—
432	D₄×C₁₀₉	—	4	8	no	—
433	D₄×C₁₀₉	—	4	8	no	—
434	D₄×C₁₀₉	—	4	8	no	—
435	D₄×C₁₀₉	—	4	4	no	—
436	D₄×C₁₀₉	—	4	4	no	—
437	D₄×C₁₀₉	—	4	4	no	—
438	D₄×C₁₀₉	—	4	8	no	—
439	C₂×C₄×C₁₀₉	—	2	16	no	—
440	C₂×C₄×C₁₀₉	—	2	2	no	—
441	C₂×C₄×C₁₀₉	—	2	2	no	—
442	C₂×C₄×C₁₀₉	—	2	2	no	—
443	C₂×C₄×C₁₀₉	—	2	2	no	—
444	C₂×C₄×C₁₀₉	—	2	2	no	—
445	C₂×C₄×C₁₀₉	—	2	2	no	—
446	C₂×C₄×C₁₀₉	—	2	2	no	—
447	C₂×C₄×C₁₀₉	—	2	2	no	—
448	C₂×C₄×C₁₀₉	—	2	2	no	—
449	C₂×C₄×C₁₀₉	—	2	2	no	—
450	C₂×C₄×C₁₀₉	—	2	16	no	—
451	C₂×C₄×C₁₀₉	—	2	16	no	—
452	C₂×C₄×C₁₀₉	—	2	2	no	—
453	C₂×C₄×C₁₀₉	—	2	2	no	—
454	C₂×C₄×C₁₀₉	—	2	2	no	—
455	C₂×C₄×C₁₀₉	—	2	2	no	—
456	C₂×C₄×C₁₀₉	—	2	2	no	—
457	C₂×C₄×C₁₀₉	—	2	2	no	—
458	C₂×C₄×C₁₀₉	—	2	2	no	—
459	C₂×C₄×C₁₀₉	—	2	2	no	—
460	C₂×C₄×C₁₀₉	—	2	2	no	—
461	C₂×C₄×C₁₀₉	—	2	1	no	—
462	C₂×C₄×C₁₀₉	—	2	2	no	—
463	C₂×C₄×C₁₀₉	—	2	2	no	—
464	C₂×C₄×C₁₀₉	—	2	2	no	—
465	C₂×C₄×C₁₀₉	—	2	1	no	—
466	C₂×C₄×C₁₀₉	—	2	1	no	—
467	C₂×C₄×C₁₀₉	—	2	2	no	—
468	C₂×C₄×C₁₀₉	—	2	1	no	—
469	C₂×C₄×C₁₀₉	—	2	1	no	—
470	C₂×C₄×C₁₀₉	—	2	1	no	—
471	C₂×C₄×C₁₀₉	—	2	2	no	—
472	C₂×C₄×C₁₀₉	—	2	2	no	—
473	C₂×C₄×C₁₀₉	—	4	4	no	—
474	C₂×C₄×C₁₀₉	—	4	8	no	—
475	C₂×C₄×C₁₀₉	—	4	8	no	—
476	C₂×C₄×C₁₀₉	—	4	8	no	—
477	C₂×C₄×C₁₀₉	—	4	8	no	—
478	C₂×C₄×C₁₀₉	—	4	8	no	—
479	C₂×C₄×C₁₀₉	—	4	8	no	—
480	C₂×C₄×C₁₀₉	—	4	4	no	—
481	C₂×C₄×C₁₀₉	—	4	4	no	—
482	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
483	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
484	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
485	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
486	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
487	C₂×C₄×C₁₀₉	C₂×#41	1	4	yes	—
488	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
489	C₂²×C₁₀₉	—	2	4	no	—
490	C₂²×C₁₀₉	—	2	4	no	—
491	C₂²×C₁₀₉	—	2	4	no	—
492	C₂²×C₁₀₉	—	2	4	no	—
493	C₂²×C₁₀₉	—	2	4	no	—
494	C₂²×C₁₀₉	—	2	4	no	—
495	C₂²×C₁₀₉	—	2	4	no	—
496	C₂²×C₁₀₉	—	2	4	no	—
497	C₂²×C₁₀₉	—	2	4	no	—
498	C₂²×C₁₀₉	—	2	2	no	—
499	C₂²×C₁₀₉	—	2	4	no	—
500	C₂²×C₁₀₉	—	2	4	no	—
501	C₂²×C₁₀₉	—	2	4	no	—
502	C₂²×C₁₀₉	—	2	4	no	—
503	C₂²×C₁₀₉	—	4	16	no	—
504	C₂²×C₁₀₉	—	4	32	no	—
505	C₂²×C₁₀₉	—	4	2	no	—
506	C₂²×C₁₀₉	—	4	2	no	—
507	C₂²×C₁₀₉	—	4	2	no	—
508	C₂²×C₁₀₉	—	4	2	no	—
509	C₂²×C₁₀₉	—	4	1	no	—
510	C₂²×C₁₀₉	—	4	2	no	—
511	C₂²×C₁₀₉	—	4	2	no	—
512	C₂²×C₁₀₉	—	4	2	no	—
513	C₂²×C₁₀₉	—	4	2	no	—
514	C₂²×C₁₀₉	—	4	2	no	—
515	C₂²×C₁₀₉	—	4	1	no	—
516	C₂²×C₁₀₉	—	4	2	no	—
517	C₂²×C₁₀₉	—	4	1	no	—
518	C₂²×C₁₀₉	—	4	1	no	—
519	C₂²×C₁₀₉	—	4	2	no	—
520	C₂²×C₁₀₉	—	4	1	no	—
521	C₂²×C₁₀₉	#525	1	8	yes	complemented
522	C₂²×C₁₀₉	C₂³×D₄	1	2	yes	—
523	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
524	C₂²×C₁₀₉	C₂²×#41	1	2	yes	—
525	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₁₀₉	#585	1	1	yes	characteristic
527	C₄×C₁₀₉	—	2	4	no	—
528	C₄×C₁₀₉	—	2	4	no	—
529	C₄×C₁₀₉	—	2	4	no	—
530	C₄×C₁₀₉	—	2	4	no	—
531	C₄×C₁₀₉	—	2	4	no	—
532	C₄×C₁₀₉	—	4	2	no	—
533	C₄×C₁₀₉	—	4	1	no	—
534	C₄×C₁₀₉	—	4	1	no	—
535	C₄×C₁₀₉	—	4	2	no	—
536	C₄×C₁₀₉	—	4	1	no	—
537	C₄×C₁₀₉	—	4	2	no	—
538	C₄×C₁₀₉	—	4	2	no	—
539	C₄×C₁₀₉	—	4	1	no	—
540	C₄×C₁₀₉	D₄²	1	4	yes	—
541	#34655	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
542	C₂×C₁₀₉	—	2	8	no	—
543	C₂×C₁₀₉	—	4	4	no	—
544	C₂×C₁₀₉	—	4	2	no	—
545	C₂×C₁₀₉	—	4	4	no	—
546	C₂×C₁₀₉	—	8	1	no	—
547	C₂×C₁₀₉	C₂×#525	1	2	yes	—
548	C₂×C₁₀₉	#3459	1	1	yes	characteristic
549	C₂×C₁₀₉	C₂×D₄²	1	1	yes	characteristic
550	C₂×C₁₀₉	D₄×#41	1	2	yes	—
551	C₂×C₁₀₉	#3481	1	1	yes	characteristic
552	C₂×#525	C₂×C₁₀₉	1	2	yes	complemented
553	C₂²×C₄×D₄	C₂×C₁₀₉	1	2	yes	complemented
554	#2463	C₂×C₁₀₉	1	1	yes	characteristic, complemented
555	#2456	C₂×C₁₀₉	1	2	yes	complemented
556	#2455	C₂×C₁₀₉	1	1	yes	characteristic, complemented
557	#2449	C₂×C₁₀₉	1	2	yes	complemented
558	#2443	C₂×C₁₀₉	1	2	yes	complemented
559	#2437	C₂×C₁₀₉	1	1	yes	characteristic, complemented
560	#2424	C₂×C₁₀₉	1	2	yes	complemented
561	#2418	C₂×C₁₀₉	1	2	yes	complemented
562	#2410	C₂×C₁₀₉	1	2	yes	complemented
563	#2403	C₂×C₁₀₉	1	1	yes	characteristic, complemented
564	#2397	C₂×C₁₀₉	1	1	yes	characteristic, complemented
565	#2392	C₂×C₁₀₉	1	2	yes	complemented
566	#2388	C₂×C₁₀₉	1	1	yes	characteristic, complemented
567	C₄×#121	C₂×C₁₀₉	1	2	yes	complemented
568	C₄×#120	C₂×C₁₀₉	1	2	yes	complemented
569	C₄×#120	C₂×C₁₀₉	1	1	yes	characteristic, complemented
570	#2290	C₂×C₁₀₉	1	2	yes	complemented
571	C₁₀₉	#34655	1	1	yes	characteristic, direct product factor, Sylow
572	C₂²×#41	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
573	C₂³×D₄	C₂²×C₁₀₉	1	2	yes	—
574	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
575	C₂⁴×C₄	C₂²×C₁₀₉	1	2	yes	complemented
576	#525	—	2	16	no	—
577	C₂×#123	C₂²×C₁₀₉	1	2	yes	complemented
578	C₂×#123	C₂²×C₁₀₉	1	2	yes	complemented
579	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
580	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
581	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
582	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
583	C₂×#121	C₂²×C₁₀₉	1	2	yes	complemented
584	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
585	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
586	C₂×#120	C₂²×C₁₀₉	1	1	yes	characteristic
587	C₂×#120	C₂²×C₁₀₉	1	2	yes	complemented
588	C₂×C₄×D₄	—	2	16	no	—
589	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
590	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
591	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
592	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
593	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
594	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
595	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
596	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
597	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
598	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
599	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
600	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
601	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
602	C₂×#117	C₂²×C₁₀₉	1	2	yes	complemented
603	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
604	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
605	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
606	C₂²×C₄²	C₂²×C₁₀₉	1	2	yes	complemented
607	#399	C₂²×C₁₀₉	1	2	yes	complemented
608	#399	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
609	#399	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
610	#398	C₂²×C₁₀₉	1	2	yes	complemented
611	#397	C₂²×C₁₀₉	1	2	yes	complemented
612	#396	C₂²×C₁₀₉	1	2	yes	complemented
613	#396	C₂²×C₁₀₉	1	2	yes	complemented
614	#395	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
615	#394	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
616	#394	C₂²×C₁₀₉	1	2	yes	complemented
617	#394	C₂²×C₁₀₉	1	2	yes	complemented
618	#394	C₂²×C₁₀₉	1	2	yes	complemented
619	#394	C₂²×C₁₀₉	1	2	yes	complemented
620	#393	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
621	#392	C₂²×C₁₀₉	1	1	yes	characteristic
622	#392	C₂²×C₁₀₉	1	2	yes	—
623	#392	C₂²×C₁₀₉	1	1	yes	characteristic
624	#392	C₂²×C₁₀₉	1	2	yes	complemented
625	#392	C₂²×C₁₀₉	1	2	yes	complemented
626	#392	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
627	#390	C₂²×C₁₀₉	1	2	yes	complemented
628	#389	C₂²×C₁₀₉	1	2	yes	complemented
629	#388	C₂²×C₁₀₉	1	2	yes	complemented
630	#388	C₂²×C₁₀₉	1	2	yes	complemented
631	#388	C₂²×C₁₀₉	1	2	yes	complemented
632	#388	C₂²×C₁₀₉	1	2	yes	complemented
633	#387	C₂²×C₁₀₉	1	2	yes	complemented
634	#387	C₂²×C₁₀₉	1	2	yes	complemented
635	#386	C₂²×C₁₀₉	1	2	yes	—
636	#386	C₂²×C₁₀₉	1	2	yes	—
637	#386	C₂²×C₁₀₉	1	2	yes	—
638	#386	C₂²×C₁₀₉	1	2	yes	—
639	#386	C₂²×C₁₀₉	1	2	yes	complemented
640	#386	C₂²×C₁₀₉	1	2	yes	complemented
641	#386	C₂²×C₁₀₉	1	2	yes	complemented
642	#386	C₂²×C₁₀₉	1	2	yes	complemented
643	#386	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
644	#385	C₂²×C₁₀₉	1	2	yes	complemented
645	#385	C₂²×C₁₀₉	1	2	yes	complemented
646	#385	C₂²×C₁₀₉	1	2	yes	complemented
647	#385	C₂²×C₁₀₉	1	2	yes	complemented
648	#385	C₂²×C₁₀₉	1	2	yes	complemented
649	#385	C₂²×C₁₀₉	1	2	yes	complemented
650	#385	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
651	#380	C₂²×C₁₀₉	1	2	yes	complemented
652	#379	C₂²×C₁₀₉	1	1	yes	characteristic
653	#379	C₂²×C₁₀₉	1	2	yes	complemented
654	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
655	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
656	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
657	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
658	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
659	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
660	#376	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
661	C₂⁵	C₂³×C₁₀₉	1	2	yes	—
662	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
663	C₂×#41	—	2	8	no	—
664	C₂×#41	—	4	2	no	—
665	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
666	C₂²×D₄	—	2	8	no	—
667	C₂²×D₄	—	2	8	no	—
668	C₂²×D₄	—	2	8	no	—
669	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
670	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
671	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
672	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
673	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
674	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
675	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
677	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
678	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
679	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
680	C₂³×C₄	—	2	8	no	—
681	C₂³×C₄	—	2	8	no	—
682	C₂³×C₄	—	2	8	no	—
683	C₂³×C₄	—	4	2	no	—
684	C₂³×C₄	—	4	4	no	—
685	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
686	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
687	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
690	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
691	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
692	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
693	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
694	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
696	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
697	#123	—	2	8	no	—
698	#123	—	2	8	no	—
699	C₂²⋊Q₈	—	2	8	no	—
700	C₂²⋊Q₈	—	2	8	no	—
701	#121	—	2	8	no	—
702	#121	—	2	8	no	—
703	#121	—	2	8	no	—
704	#120	—	2	4	no	—
705	#120	—	2	8	no	—
706	#120	—	2	8	no	—
707	#120	—	2	8	no	—
708	C₄×D₄	—	2	8	no	—
709	C₄×D₄	—	2	8	no	—
710	C₄×D₄	—	2	8	no	—
711	C₄×D₄	—	2	8	no	—
712	C₄×D₄	—	2	8	no	—
713	C₄×D₄	—	2	8	no	—
714	C₄×D₄	—	2	8	no	—
715	C₄×D₄	—	2	8	no	—
716	C₄×D₄	—	2	8	no	—
717	C₄×D₄	—	2	8	no	—
718	C₄×D₄	—	4	2	no	—
719	C₄×D₄	—	4	2	no	—
720	C₄×D₄	D₄×C₁₀₉	1	16	yes	complemented
721	#117	—	2	8	no	—
722	C₂×C₄⋊C₄	—	2	8	no	—
723	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
736	C₂×C₂²⋊C₄	—	2	8	no	—
737	C₂×C₂²⋊C₄	—	2	8	no	—
738	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
766	C₂×C₄²	—	2	8	no	—
767	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
768	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
769	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
770	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
771	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
773	#95	C₂³×C₁₀₉	1	1	yes	characteristic
774	#95	C₂³×C₁₀₉	1	2	yes	—
775	#95	C₂³×C₁₀₉	1	1	yes	characteristic
776	#95	C₂³×C₁₀₉	1	1	yes	characteristic
777	#95	C₂³×C₁₀₉	1	2	yes	—
778	#95	C₂³×C₁₀₉	1	2	yes	—
779	#95	C₂³×C₁₀₉	1	2	yes	—
780	#95	C₂³×C₁₀₉	1	2	yes	—
781	#95	C₂³×C₁₀₉	1	2	yes	—
782	#95	C₂³×C₁₀₉	1	2	yes	—
783	#95	C₂³×C₁₀₉	1	2	yes	—
784	#95	C₂³×C₁₀₉	1	1	yes	characteristic
785	#95	C₂³×C₁₀₉	1	2	yes	—
786	#95	C₂³×C₁₀₉	1	2	yes	—
787	C₂⁴	—	2	4	no	—
788	C₂⁴	—	2	4	no	—
789	C₂⁴	—	2	4	no	—
790	C₂⁴	—	2	4	no	—
791	C₂⁴	—	2	4	no	—
792	C₂⁴	—	2	4	no	—
793	C₂⁴	—	2	4	no	—
794	C₂⁴	—	4	1	no	—
795	C₂⁴	—	4	2	no	—
796	C₂⁴	—	4	1	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	#41×C₁₀₉	1	4	yes	complemented
799	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
801	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
802	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
803	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
804	#41	—	4	16	no	—
805	C₂×Q₈	—	2	4	no	—
806	C₂×Q₈	—	4	1	no	—
807	C₂×D₄	—	2	64	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	—	4	1	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	1	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	C₂×D₄×C₁₀₉	1	8	yes	—
838	C₂×D₄	#41×C₁₀₉	1	8	yes	complemented
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	4	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	4	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	4	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	4	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	16	no	—
871	C₂²×C₄	—	4	32	no	—
872	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	—
873	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	complemented
874	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	—	4	1	no	—
900	C₄⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	complemented
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	4	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	1	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	1	no	—
926	C₂²⋊C₄	—	4	1	no	—
927	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
928	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	complemented
929	C₄²	—	2	4	no	—
930	C₄²	—	2	4	no	—
931	C₄²	—	2	4	no	—
932	C₄²	—	2	4	no	—
933	C₄²	—	2	2	no	—
934	C₄²	C₂×D₄×C₁₀₉	1	8	yes	complemented
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	16	no	—
940	C₂³	—	2	16	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	4	4	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	8	no	—
965	C₂³	—	4	8	no	—
966	C₂³	—	4	8	no	—
967	C₂³	—	4	8	no	—
968	C₂³	—	4	4	no	—
969	C₂³	—	4	8	no	—
970	C₂³	—	4	8	no	—
971	C₂³	—	4	8	no	—
972	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
973	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
974	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
975	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
976	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
977	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
978	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
979	Q₈	—	4	4	no	—
980	D₄	—	2	16	no	—
981	D₄	—	2	16	no	—
982	D₄	—	2	16	no	—
983	D₄	—	2	16	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	8	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	8	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	4	8	no	—
991	C₂×C₄	—	2	16	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	16	no	—
1003	C₂×C₄	—	2	16	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	8	no	—
1027	C₂×C₄	—	4	8	no	—
1028	C₂×C₄	—	4	8	no	—
1029	C₂×C₄	—	4	8	no	—
1030	C₂×C₄	—	4	8	no	—
1031	C₂×C₄	—	4	8	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
1035	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
1036	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
1037	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
1038	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
1039	C₂×C₄	C₂×#41×C₁₀₉	1	4	yes	—
1040	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
1041	C₂²	—	2	4	no	—
1042	C₂²	—	2	4	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	2	4	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	2	4	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	4	no	—
1055	C₂²	—	4	16	no	—
1056	C₂²	—	4	32	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	#525×C₁₀₉	1	8	yes	complemented
1074	C₂²	C₂³×D₄×C₁₀₉	1	2	yes	—
1075	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
1076	C₂²	C₂²×#41×C₁₀₉	1	2	yes	—
1077	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
1078	C₂²	#585×C₁₀₉	1	1	yes	characteristic
1079	C₄	—	2	4	no	—
1080	C₄	—	2	4	no	—
1081	C₄	—	2	4	no	—
1082	C₄	—	2	4	no	—
1083	C₄	—	2	4	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	D₄²×C₁₀₉	1	4	yes	—
1093	C₂	—	2	8	no	—
1094	C₂	—	4	2	no	—
1095	C₂	—	4	4	no	—
1096	C₂	—	4	4	no	—
1097	C₂	—	8	1	no	—
1098	C₂	C₂×#525×C₁₀₉	1	2	yes	—
1099	C₂	C₁₀₉×#3459	1	1	yes	characteristic
1100	C₂	C₂×D₄²×C₁₀₉	1	1	yes	characteristic
1101	C₂	D₄×#41×C₁₀₉	1	2	yes	—
1102	C₂	C₁₀₉×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
socle	C₂³×C₁₀₉	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#525×C₁₀₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₀₉	C₂	semidirect
3. C₁₀₉×#2463	C₂	semidirect
4. C₁₀₉×#2456	C₂	semidirect
5. C₁₀₉×#2455	C₂	semidirect
6. C₁₀₉×#2449	C₂	semidirect
7. C₁₀₉×#2443	C₂	semidirect
8. C₁₀₉×#2437	C₂	semidirect
9. C₁₀₉×#2424	C₂	semidirect
10. C₁₀₉×#2418	C₂	semidirect
11. C₁₀₉×#2410	C₂	semidirect
12. C₁₀₉×#2403	C₂	semidirect
13. C₁₀₉×#2397	C₂	semidirect
14. C₁₀₉×#2392	C₂	semidirect
15. C₁₀₉×#2388	C₂	semidirect
16. C₄×#121×C₁₀₉	C₂	semidirect
17. C₄×#120×C₁₀₉	C₂	semidirect
18. C₄×#120×C₁₀₉	C₂	semidirect
19. C₁₀₉×#2290	C₂	semidirect
20. C₂²×#41×C₁₀₉	C₂²	semidirect
23. C₂⁴×C₄×C₁₀₉	C₂²	semidirect
25. C₂×#123×C₁₀₉	C₂²	semidirect
26. C₂×#123×C₁₀₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
31. C₂×#121×C₁₀₉	C₂²	semidirect
35. C₂×#120×C₁₀₉	C₂²	semidirect
41. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
42. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
43. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
44. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
46. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
47. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
48. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
49. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
50. C₂×#117×C₁₀₉	C₂²	semidirect
51. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
53. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
54. C₂²×C₄²×C₁₀₉	C₂²	semidirect
55. #399×C₁₀₉	C₂²	semidirect
56. #399×C₁₀₉	C₂²	semidirect
57. #399×C₁₀₉	C₂²	semidirect
58. #398×C₁₀₉	C₂²	semidirect
59. #397×C₁₀₉	C₂²	semidirect
60. #396×C₁₀₉	C₂²	semidirect
61. #396×C₁₀₉	C₂²	semidirect
62. #395×C₁₀₉	C₂²	semidirect
63. #394×C₁₀₉	C₂²	semidirect
64. #394×C₁₀₉	C₂²	semidirect
65. #394×C₁₀₉	C₂²	semidirect
66. #394×C₁₀₉	C₂²	semidirect
67. #394×C₁₀₉	C₂²	semidirect
68. #393×C₁₀₉	C₂²	semidirect
72. #392×C₁₀₉	C₂²	semidirect
73. #392×C₁₀₉	C₂²	semidirect
74. #392×C₁₀₉	C₂²	semidirect
75. #390×C₁₀₉	C₂²	semidirect
76. #389×C₁₀₉	C₂²	semidirect
77. #388×C₁₀₉	C₂²	semidirect
78. #388×C₁₀₉	C₂²	semidirect
79. #388×C₁₀₉	C₂²	semidirect
80. #388×C₁₀₉	C₂²	semidirect
81. #387×C₁₀₉	C₂²	semidirect
82. #387×C₁₀₉	C₂²	semidirect
87. #386×C₁₀₉	C₂²	semidirect
88. #386×C₁₀₉	C₂²	semidirect
89. #386×C₁₀₉	C₂²	semidirect
90. #386×C₁₀₉	C₂²	semidirect
91. #386×C₁₀₉	C₂²	semidirect
92. #385×C₁₀₉	C₂²	semidirect
93. #385×C₁₀₉	C₂²	semidirect
94. #385×C₁₀₉	C₂²	semidirect
95. #385×C₁₀₉	C₂²	semidirect
96. #385×C₁₀₉	C₂²	semidirect
97. #385×C₁₀₉	C₂²	semidirect
98. #385×C₁₀₉	C₂²	semidirect
99. #380×C₁₀₉	C₂²	semidirect
101. #379×C₁₀₉	C₂²	semidirect
102. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
107. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
108. #376×C₁₀₉	C₂²	semidirect
168. C₄×D₄×C₁₀₉	D₄	semidirect
246. C₂⁴×C₁₀₉	#41	semidirect
286. C₂×D₄×C₁₀₉	#41	semidirect
321. C₂²×C₄×C₁₀₉	C₂×D₄	semidirect
348. C₄⋊C₄×C₁₀₉	C₂×D₄	semidirect
376. C₂²⋊C₄×C₁₀₉	C₂×D₄	semidirect
382. C₄²×C₁₀₉	C₂×D₄	semidirect
521. C₂²×C₁₀₉	#525	semidirect
541. #34655	C₁₀₉	direct (N × H)
552. C₂×#525	C₂×C₁₀₉	semidirect
553. C₂²×C₄×D₄	C₂×C₁₀₉	semidirect
554. #2463	C₂×C₁₀₉	semidirect
555. #2456	C₂×C₁₀₉	semidirect
556. #2455	C₂×C₁₀₉	semidirect
557. #2449	C₂×C₁₀₉	semidirect
558. #2443	C₂×C₁₀₉	semidirect
559. #2437	C₂×C₁₀₉	semidirect
560. #2424	C₂×C₁₀₉	semidirect
561. #2418	C₂×C₁₀₉	semidirect
562. #2410	C₂×C₁₀₉	semidirect
563. #2403	C₂×C₁₀₉	semidirect
564. #2397	C₂×C₁₀₉	semidirect
565. #2392	C₂×C₁₀₉	semidirect
566. #2388	C₂×C₁₀₉	semidirect
567. C₄×#121	C₂×C₁₀₉	semidirect
568. C₄×#120	C₂×C₁₀₉	semidirect
569. C₄×#120	C₂×C₁₀₉	semidirect
570. #2290	C₂×C₁₀₉	semidirect
571. C₁₀₉	#34655	direct (N × H)
572. C₂²×#41	C₂²×C₁₀₉	semidirect
575. C₂⁴×C₄	C₂²×C₁₀₉	semidirect
577. C₂×#123	C₂²×C₁₀₉	semidirect
578. C₂×#123	C₂²×C₁₀₉	semidirect
579. C₂×C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
580. C₂×C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
583. C₂×#121	C₂²×C₁₀₉	semidirect
587. C₂×#120	C₂²×C₁₀₉	semidirect
593. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
594. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
595. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
596. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
597. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
598. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
599. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
600. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
601. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
602. C₂×#117	C₂²×C₁₀₉	semidirect
603. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
605. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
606. C₂²×C₄²	C₂²×C₁₀₉	semidirect
607. #399	C₂²×C₁₀₉	semidirect
608. #399	C₂²×C₁₀₉	semidirect
609. #399	C₂²×C₁₀₉	semidirect
610. #398	C₂²×C₁₀₉	semidirect
611. #397	C₂²×C₁₀₉	semidirect
612. #396	C₂²×C₁₀₉	semidirect
613. #396	C₂²×C₁₀₉	semidirect
614. #395	C₂²×C₁₀₉	semidirect
615. #394	C₂²×C₁₀₉	semidirect
616. #394	C₂²×C₁₀₉	semidirect
617. #394	C₂²×C₁₀₉	semidirect
618. #394	C₂²×C₁₀₉	semidirect
619. #394	C₂²×C₁₀₉	semidirect
620. #393	C₂²×C₁₀₉	semidirect
624. #392	C₂²×C₁₀₉	semidirect
625. #392	C₂²×C₁₀₉	semidirect
626. #392	C₂²×C₁₀₉	semidirect
627. #390	C₂²×C₁₀₉	semidirect
628. #389	C₂²×C₁₀₉	semidirect
629. #388	C₂²×C₁₀₉	semidirect
630. #388	C₂²×C₁₀₉	semidirect
631. #388	C₂²×C₁₀₉	semidirect
632. #388	C₂²×C₁₀₉	semidirect
633. #387	C₂²×C₁₀₉	semidirect
634. #387	C₂²×C₁₀₉	semidirect
639. #386	C₂²×C₁₀₉	semidirect
640. #386	C₂²×C₁₀₉	semidirect
641. #386	C₂²×C₁₀₉	semidirect
642. #386	C₂²×C₁₀₉	semidirect
643. #386	C₂²×C₁₀₉	semidirect
644. #385	C₂²×C₁₀₉	semidirect
645. #385	C₂²×C₁₀₉	semidirect
646. #385	C₂²×C₁₀₉	semidirect
647. #385	C₂²×C₁₀₉	semidirect
648. #385	C₂²×C₁₀₉	semidirect
649. #385	C₂²×C₁₀₉	semidirect
650. #385	C₂²×C₁₀₉	semidirect
651. #380	C₂²×C₁₀₉	semidirect
653. #379	C₂²×C₁₀₉	semidirect
654. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
655. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
656. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
657. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
658. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
659. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
660. #376	C₂²×C₁₀₉	semidirect
720. C₄×D₄	D₄×C₁₀₉	semidirect
798. C₂⁴	#41×C₁₀₉	semidirect
838. C₂×D₄	#41×C₁₀₉	semidirect
873. C₂²×C₄	C₂×D₄×C₁₀₉	semidirect
900. C₄⋊C₄	C₂×D₄×C₁₀₉	semidirect
928. C₂²⋊C₄	C₂×D₄×C₁₀₉	semidirect
934. C₄²	C₂×D₄×C₁₀₉	semidirect
1073. C₂²	#525×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₀₉	2
C₂²×C₄×D₄×C₁₀₉	2
C₁₀₉×#2463	2
C₁₀₉×#2456	2
C₁₀₉×#2455	2
C₁₀₉×#2449	2
C₁₀₉×#2443	2
C₁₀₉×#2437	2
C₁₀₉×#2424	2
C₁₀₉×#2418	2
C₁₀₉×#2410	2
C₁₀₉×#2403	2
C₁₀₉×#2397	2
C₁₀₉×#2392	2
C₁₀₉×#2388	2
C₄×#121×C₁₀₉	2
C₄×#120×C₁₀₉	2
C₁₀₉×#2290	2
#34655	109

Subgroups — C109×#34655 #42152649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#34655 #42152649