Subgroups — C₁₀₉×#35039 #42153033

Order 27904.

1708 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉×#2863	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#2652	C₂	1	2	yes	maximal, complemented
6	C₁₀₉×#2638	C₂	1	2	yes	maximal
7	C₁₀₉×#2588	C₂	1	2	yes	maximal, complemented
8	C₁₀₉×#2577	C₂	1	2	yes	maximal, complemented
9	C₁₀₉×#2523	C₂	1	2	yes	maximal, complemented
10	C₁₀₉×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₉×#2499	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₀₉×#2495	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₀₉×#2485	C₂	1	1	yes	maximal, characteristic
14	C₁₀₉×#2460	C₂	1	2	yes	maximal
15	C₁₀₉×#2451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₀₉×#2439	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₀₉×#2421	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₀₉×#2415	C₂	1	1	yes	maximal, characteristic
19	C₁₀₉×#2336	C₂	1	2	yes	maximal, complemented
20	C₁₀₉×#2332	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₀₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₁₀₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
37	#400×C₁₀₉	C₂²	1	2	yes	—
38	#400×C₁₀₉	C₂²	1	2	yes	—
39	#400×C₁₀₉	C₂²	1	2	yes	—
40	#398×C₁₀₉	C₂²	1	2	yes	—
41	#398×C₁₀₉	C₂²	1	2	yes	—
42	#397×C₁₀₉	C₂²	1	2	yes	—
43	#397×C₁₀₉	C₂²	1	2	yes	—
44	#397×C₁₀₉	C₂²	1	2	yes	—
45	#397×C₁₀₉	C₂²	1	2	yes	—
46	#397×C₁₀₉	C₂²	1	2	yes	—
47	#397×C₁₀₉	C₂²	1	2	yes	—
48	#396×C₁₀₉	C₂²	1	2	yes	—
49	#395×C₁₀₉	C₂²	1	2	yes	—
50	#394×C₁₀₉	C₂²	1	2	yes	—
51	#394×C₁₀₉	C₂²	1	2	yes	—
52	#393×C₁₀₉	C₂²	1	2	yes	—
53	#391×C₁₀₉	C₂²	1	2	yes	—
54	#391×C₁₀₉	C₂²	1	1	yes	characteristic
55	#391×C₁₀₉	C₂²	1	2	yes	—
56	#391×C₁₀₉	C₂²	1	1	yes	characteristic
57	#391×C₁₀₉	C₂²	1	1	yes	characteristic
58	#391×C₁₀₉	C₂²	1	2	yes	—
59	#391×C₁₀₉	C₂²	1	1	yes	characteristic
60	#389×C₁₀₉	C₂²	1	1	yes	characteristic
61	#389×C₁₀₉	C₂²	1	1	yes	characteristic
62	#389×C₁₀₉	C₂²	1	1	yes	characteristic
63	#389×C₁₀₉	C₂²	1	1	yes	characteristic
64	#389×C₁₀₉	C₂²	1	1	yes	characteristic
65	#389×C₁₀₉	C₂²	1	1	yes	characteristic
66	#389×C₁₀₉	C₂²	1	1	yes	characteristic
67	#389×C₁₀₉	C₂²	1	1	yes	characteristic
68	#389×C₁₀₉	C₂²	1	1	yes	characteristic
69	#389×C₁₀₉	C₂²	1	1	yes	characteristic
70	#389×C₁₀₉	C₂²	1	2	yes	—
71	#389×C₁₀₉	C₂²	1	2	yes	—
72	#388×C₁₀₉	C₂²	1	2	yes	—
73	#388×C₁₀₉	C₂²	1	2	yes	—
74	#388×C₁₀₉	C₂²	1	2	yes	—
75	#388×C₁₀₉	C₂²	1	2	yes	—
76	#387×C₁₀₉	C₂²	1	2	yes	—
77	#387×C₁₀₉	C₂²	1	2	yes	—
78	#387×C₁₀₉	C₂²	1	2	yes	—
79	#387×C₁₀₉	C₂²	1	2	yes	—
80	#387×C₁₀₉	C₂²	1	2	yes	—
81	#387×C₁₀₉	C₂²	1	2	yes	—
82	#387×C₁₀₉	C₂²	1	2	yes	—
83	#387×C₁₀₉	C₂²	1	2	yes	—
84	#387×C₁₀₉	C₂²	1	2	yes	—
85	#387×C₁₀₉	C₂²	1	2	yes	—
86	#387×C₁₀₉	C₂²	1	2	yes	—
87	#387×C₁₀₉	C₂²	1	2	yes	—
88	#387×C₁₀₉	C₂²	1	2	yes	—
89	#387×C₁₀₉	C₂²	1	2	yes	—
90	#387×C₁₀₉	C₂²	1	2	yes	—
91	#387×C₁₀₉	C₂²	1	2	yes	—
92	#387×C₁₀₉	C₂²	1	2	yes	—
93	#385×C₁₀₉	C₂²	1	2	yes	—
94	#385×C₁₀₉	C₂²	1	2	yes	—
95	#385×C₁₀₉	C₂²	1	2	yes	—
96	#385×C₁₀₉	C₂²	1	2	yes	—
97	#384×C₁₀₉	C₂²	1	1	yes	characteristic
98	#383×C₁₀₉	C₂²	1	2	yes	—
99	#383×C₁₀₉	C₂²	1	2	yes	—
100	#382×C₁₀₉	C₂²	1	1	yes	characteristic
101	#382×C₁₀₉	C₂²	1	1	yes	characteristic
102	#381×C₁₀₉	C₂²	1	2	yes	—
103	#380×C₁₀₉	C₂²	1	1	yes	characteristic
104	#380×C₁₀₉	C₂²	1	2	yes	—
105	#380×C₁₀₉	C₂²	1	1	yes	characteristic
106	#380×C₁₀₉	C₂²	1	1	yes	characteristic
107	#380×C₁₀₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₀₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₀₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₁₀₉	—	4	2	no	—
133	#125×C₁₀₉	—	2	8	no	—
134	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
135	C₂²⋊Q₈×C₁₀₉	—	2	8	no	—
136	C₂²⋊Q₈×C₁₀₉	—	4	2	no	—
137	C₄×Q₈×C₁₀₉	—	4	2	no	—
138	C₄×D₄×C₁₀₉	—	2	4	no	—
139	C₄×D₄×C₁₀₉	—	2	4	no	—
140	C₄×D₄×C₁₀₉	—	2	4	no	—
141	#117×C₁₀₉	—	2	4	no	—
142	#117×C₁₀₉	—	4	2	no	—
143	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₀₉	—	4	2	no	—
184	C₂×C₄²×C₁₀₉	—	4	2	no	—
185	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
202	#95×C₁₀₉	C₂³	1	1	yes	characteristic
203	#95×C₁₀₉	C₂³	1	1	yes	characteristic
204	#95×C₁₀₉	C₂³	1	1	yes	characteristic
205	#95×C₁₀₉	C₂³	1	1	yes	characteristic
206	#95×C₁₀₉	C₂³	1	1	yes	characteristic
207	#95×C₁₀₉	C₂³	1	1	yes	characteristic
208	#95×C₁₀₉	C₂³	1	2	yes	—
209	#95×C₁₀₉	C₂³	1	2	yes	—
210	#95×C₁₀₉	C₂³	1	2	yes	—
211	#95×C₁₀₉	C₂³	1	2	yes	—
212	#95×C₁₀₉	C₂³	1	2	yes	—
213	#95×C₁₀₉	C₂³	1	2	yes	—
214	#95×C₁₀₉	C₂³	1	2	yes	—
215	#95×C₁₀₉	C₂³	1	2	yes	—
216	#95×C₁₀₉	C₂³	1	2	yes	—
217	#95×C₁₀₉	C₂³	1	2	yes	—
218	#95×C₁₀₉	C₂³	1	2	yes	—
219	#95×C₁₀₉	C₂³	1	2	yes	—
220	#95×C₁₀₉	C₂³	1	2	yes	—
221	#95×C₁₀₉	C₂³	1	2	yes	—
222	#95×C₁₀₉	C₂³	1	2	yes	—
223	#95×C₁₀₉	C₂³	1	2	yes	—
224	#95×C₁₀₉	C₂³	1	2	yes	—
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	2	yes	—
233	#95×C₁₀₉	C₂³	1	2	yes	—
234	#95×C₁₀₉	C₂³	1	2	yes	—
235	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₁₀₉	—	2	2	no	—
238	C₂×Q₈×C₁₀₉	—	2	4	no	—
239	C₂×Q₈×C₁₀₉	—	2	2	no	—
240	C₂×Q₈×C₁₀₉	—	2	2	no	—
241	C₂×Q₈×C₁₀₉	—	4	2	no	—
242	C₂×Q₈×C₁₀₉	—	4	2	no	—
243	C₂×D₄×C₁₀₉	—	2	2	no	—
244	C₂×D₄×C₁₀₉	—	2	2	no	—
245	C₂×D₄×C₁₀₉	—	2	2	no	—
246	C₂²×C₄×C₁₀₉	—	2	2	no	—
247	C₂²×C₄×C₁₀₉	—	2	2	no	—
248	C₂²×C₄×C₁₀₉	—	2	2	no	—
249	C₂²×C₄×C₁₀₉	—	2	2	no	—
250	C₂²×C₄×C₁₀₉	—	2	2	no	—
251	C₂²×C₄×C₁₀₉	—	2	2	no	—
252	C₂²×C₄×C₁₀₉	—	2	2	no	—
253	C₂²×C₄×C₁₀₉	—	2	2	no	—
254	C₂²×C₄×C₁₀₉	—	2	2	no	—
255	C₂²×C₄×C₁₀₉	—	2	2	no	—
256	C₂²×C₄×C₁₀₉	—	4	1	no	—
257	C₂²×C₄×C₁₀₉	—	4	1	no	—
258	C₂²×C₄×C₁₀₉	—	4	1	no	—
259	C₂²×C₄×C₁₀₉	—	4	1	no	—
260	C₂²×C₄×C₁₀₉	—	4	1	no	—
261	C₂²×C₄×C₁₀₉	—	4	1	no	—
262	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
263	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
264	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₁₀₉	—	2	2	no	—
286	C₄⋊C₄×C₁₀₉	—	2	2	no	—
287	C₄⋊C₄×C₁₀₉	—	2	2	no	—
288	C₄⋊C₄×C₁₀₉	—	2	2	no	—
289	C₄⋊C₄×C₁₀₉	—	2	4	no	—
290	C₄⋊C₄×C₁₀₉	—	2	2	no	—
291	C₄⋊C₄×C₁₀₉	—	2	4	no	—
292	C₄⋊C₄×C₁₀₉	—	2	4	no	—
293	C₄⋊C₄×C₁₀₉	—	2	4	no	—
294	C₄⋊C₄×C₁₀₉	—	2	4	no	—
295	C₄⋊C₄×C₁₀₉	—	2	4	no	—
296	C₄⋊C₄×C₁₀₉	—	2	4	no	—
297	C₄⋊C₄×C₁₀₉	—	2	4	no	—
298	C₄⋊C₄×C₁₀₉	—	2	4	no	—
299	C₄⋊C₄×C₁₀₉	—	2	2	no	—
300	C₄⋊C₄×C₁₀₉	—	2	2	no	—
301	C₄⋊C₄×C₁₀₉	—	2	2	no	—
302	C₄⋊C₄×C₁₀₉	—	2	4	no	—
303	C₄⋊C₄×C₁₀₉	—	2	2	no	—
304	C₄⋊C₄×C₁₀₉	—	4	2	no	—
305	C₄⋊C₄×C₁₀₉	—	4	2	no	—
306	C₄⋊C₄×C₁₀₉	—	4	2	no	—
307	C₄⋊C₄×C₁₀₉	—	4	2	no	—
308	C₄⋊C₄×C₁₀₉	—	4	2	no	—
309	C₄⋊C₄×C₁₀₉	—	4	2	no	—
310	C₄⋊C₄×C₁₀₉	#41	1	4	yes	—
311	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
313	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
314	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
316	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
317	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
318	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
319	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
320	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
321	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
322	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
323	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
324	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
325	C₄²×C₁₀₉	—	2	4	no	—
326	C₄²×C₁₀₉	—	2	2	no	—
327	C₄²×C₁₀₉	—	2	2	no	—
328	C₄²×C₁₀₉	—	2	2	no	—
329	C₄²×C₁₀₉	—	2	4	no	—
330	C₄²×C₁₀₉	—	2	2	no	—
331	C₄²×C₁₀₉	—	2	2	no	—
332	C₄²×C₁₀₉	—	2	2	no	—
333	C₄²×C₁₀₉	—	2	2	no	—
334	C₄²×C₁₀₉	—	2	2	no	—
335	C₄²×C₁₀₉	—	4	1	no	—
336	C₄²×C₁₀₉	—	4	1	no	—
337	C₄²×C₁₀₉	—	4	1	no	—
338	C₄²×C₁₀₉	—	4	1	no	—
339	C₄²×C₁₀₉	—	4	1	no	—
340	C₄²×C₁₀₉	—	4	2	no	—
341	C₄²×C₁₀₉	—	4	2	no	—
342	C₂³×C₁₀₉	—	2	1	no	—
343	C₂³×C₁₀₉	—	2	1	no	—
344	C₂³×C₁₀₉	—	2	1	no	—
345	C₂³×C₁₀₉	—	2	1	no	—
346	C₂³×C₁₀₉	—	2	1	no	—
347	C₂³×C₁₀₉	—	2	1	no	—
348	C₂³×C₁₀₉	—	2	1	no	—
349	C₂³×C₁₀₉	—	2	1	no	—
350	C₂³×C₁₀₉	—	2	1	no	—
351	C₂³×C₁₀₉	—	2	1	no	—
352	C₂³×C₁₀₉	—	2	1	no	—
353	C₂³×C₁₀₉	—	2	1	no	—
354	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
355	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
356	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
357	Q₈×C₁₀₉	—	4	4	no	—
358	Q₈×C₁₀₉	—	8	4	no	—
359	D₄×C₁₀₉	—	2	8	no	—
360	C₂×C₄×C₁₀₉	—	2	1	no	—
361	C₂×C₄×C₁₀₉	—	2	1	no	—
362	C₂×C₄×C₁₀₉	—	2	1	no	—
363	C₂×C₄×C₁₀₉	—	2	1	no	—
364	C₂×C₄×C₁₀₉	—	2	1	no	—
365	C₂×C₄×C₁₀₉	—	2	1	no	—
366	C₂×C₄×C₁₀₉	—	2	1	no	—
367	C₂×C₄×C₁₀₉	—	2	1	no	—
368	C₂×C₄×C₁₀₉	—	2	1	no	—
369	C₂×C₄×C₁₀₉	—	2	1	no	—
370	C₂×C₄×C₁₀₉	—	2	1	no	—
371	C₂×C₄×C₁₀₉	—	2	1	no	—
372	C₂×C₄×C₁₀₉	—	2	1	no	—
373	C₂×C₄×C₁₀₉	—	2	1	no	—
374	C₂×C₄×C₁₀₉	—	2	8	no	—
375	C₂×C₄×C₁₀₉	—	2	1	no	—
376	C₂×C₄×C₁₀₉	—	2	1	no	—
377	C₂×C₄×C₁₀₉	—	2	1	no	—
378	C₂×C₄×C₁₀₉	—	2	2	no	—
379	C₂×C₄×C₁₀₉	—	2	2	no	—
380	C₂×C₄×C₁₀₉	—	2	2	no	—
381	C₂×C₄×C₁₀₉	—	2	2	no	—
382	C₂×C₄×C₁₀₉	—	2	2	no	—
383	C₂×C₄×C₁₀₉	—	2	2	no	—
384	C₂×C₄×C₁₀₉	—	2	2	no	—
385	C₂×C₄×C₁₀₉	—	2	1	no	—
386	C₂×C₄×C₁₀₉	—	2	1	no	—
387	C₂×C₄×C₁₀₉	—	2	2	no	—
388	C₂×C₄×C₁₀₉	—	2	2	no	—
389	C₂×C₄×C₁₀₉	—	2	2	no	—
390	C₂×C₄×C₁₀₉	—	2	2	no	—
391	C₂×C₄×C₁₀₉	—	2	2	no	—
392	C₂×C₄×C₁₀₉	—	2	1	no	—
393	C₂×C₄×C₁₀₉	—	2	1	no	—
394	C₂×C₄×C₁₀₉	—	2	2	no	—
395	C₂×C₄×C₁₀₉	—	2	2	no	—
396	C₂×C₄×C₁₀₉	—	2	2	no	—
397	C₂×C₄×C₁₀₉	—	2	2	no	—
398	C₂×C₄×C₁₀₉	—	2	1	no	—
399	C₂×C₄×C₁₀₉	—	2	1	no	—
400	C₂×C₄×C₁₀₉	—	2	1	no	—
401	C₂×C₄×C₁₀₉	—	2	1	no	—
402	C₂×C₄×C₁₀₉	—	2	2	no	—
403	C₂×C₄×C₁₀₉	—	2	2	no	—
404	C₂×C₄×C₁₀₉	—	2	2	no	—
405	C₂×C₄×C₁₀₉	—	2	1	no	—
406	C₂×C₄×C₁₀₉	—	2	2	no	—
407	C₂×C₄×C₁₀₉	—	2	1	no	—
408	C₂×C₄×C₁₀₉	—	2	1	no	—
409	C₂×C₄×C₁₀₉	—	2	2	no	—
410	C₂×C₄×C₁₀₉	—	2	2	no	—
411	C₂×C₄×C₁₀₉	—	2	2	no	—
412	C₂×C₄×C₁₀₉	—	2	1	no	—
413	C₂×C₄×C₁₀₉	—	2	2	no	—
414	C₂×C₄×C₁₀₉	—	4	4	no	—
415	C₂×C₄×C₁₀₉	—	4	4	no	—
416	C₂×C₄×C₁₀₉	—	4	4	no	—
417	C₂×C₄×C₁₀₉	—	4	4	no	—
418	C₂×C₄×C₁₀₉	—	4	4	no	—
419	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
420	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
421	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
425	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
426	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
427	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	2	yes	—
428	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	2	yes	—
429	C₂²×C₁₀₉	—	2	2	no	—
430	C₂²×C₁₀₉	—	2	2	no	—
431	C₂²×C₁₀₉	—	2	2	no	—
432	C₂²×C₁₀₉	—	2	2	no	—
433	C₂²×C₁₀₉	—	2	2	no	—
434	C₂²×C₁₀₉	—	2	2	no	—
435	C₂²×C₁₀₉	—	4	1	no	—
436	C₂²×C₁₀₉	—	4	1	no	—
437	C₂²×C₁₀₉	—	4	1	no	—
438	C₂²×C₁₀₉	—	4	1	no	—
439	C₂²×C₁₀₉	—	4	1	no	—
440	C₂²×C₁₀₉	—	4	1	no	—
441	C₂²×C₁₀₉	—	4	1	no	—
442	C₂²×C₁₀₉	—	4	1	no	—
443	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²×C₁₀₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
448	C₂²×C₁₀₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂²×C₁₀₉	#585	1	1	yes	characteristic
450	C₄×C₁₀₉	—	2	2	no	—
451	C₄×C₁₀₉	—	2	2	no	—
452	C₄×C₁₀₉	—	2	2	no	—
453	C₄×C₁₀₉	—	2	2	no	—
454	C₄×C₁₀₉	—	2	2	no	—
455	C₄×C₁₀₉	—	2	2	no	—
456	C₄×C₁₀₉	—	2	2	no	—
457	C₄×C₁₀₉	—	4	2	no	—
458	C₄×C₁₀₉	—	4	2	no	—
459	C₄×C₁₀₉	—	4	1	no	—
460	C₄×C₁₀₉	—	4	2	no	—
461	C₄×C₁₀₉	—	4	1	no	—
462	C₄×C₁₀₉	—	4	2	no	—
463	C₄×C₁₀₉	—	4	1	no	—
464	C₄×C₁₀₉	—	4	2	no	—
465	C₄×C₁₀₉	—	4	2	no	—
466	C₄×C₁₀₉	—	4	1	no	—
467	C₄×C₁₀₉	—	4	1	no	—
468	C₄×C₁₀₉	—	4	2	no	—
469	C₄×C₁₀₉	—	4	2	no	—
470	C₄×C₁₀₉	#539	1	4	yes	—
471	#35039	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂×C₁₀₉	—	4	2	no	—
473	C₂×C₁₀₉	—	4	2	no	—
474	C₂×C₁₀₉	#3444	1	1	yes	characteristic
475	C₂×C₁₀₉	C₂×#539	1	1	yes	characteristic
476	C₂×C₁₀₉	#3461	1	1	yes	characteristic
477	C₂×C₁₀₉	#3505	1	1	yes	characteristic
478	C₂×C₁₀₉	#3509	1	1	yes	characteristic
479	C₂×C₁₀₉	#3518	1	1	yes	characteristic
480	C₂×C₁₀₉	#3520	1	1	yes	characteristic
481	#2864	C₂×C₁₀₉	1	1	yes	characteristic, complemented
482	#2863	C₂×C₁₀₉	1	1	yes	characteristic, complemented
483	#2857	C₂×C₁₀₉	1	1	yes	characteristic, complemented
484	#2855	C₂×C₁₀₉	1	1	yes	characteristic, complemented
485	#2652	C₂×C₁₀₉	1	2	yes	complemented
486	#2638	C₂×C₁₀₉	1	2	yes	—
487	#2588	C₂×C₁₀₉	1	2	yes	complemented
488	#2577	C₂×C₁₀₉	1	2	yes	complemented
489	#2523	C₂×C₁₀₉	1	2	yes	complemented
490	#2506	C₂×C₁₀₉	1	1	yes	characteristic, complemented
491	#2499	C₂×C₁₀₉	1	1	yes	characteristic, complemented
492	#2495	C₂×C₁₀₉	1	1	yes	characteristic, complemented
493	#2485	C₂×C₁₀₉	1	1	yes	characteristic
494	#2460	C₂×C₁₀₉	1	2	yes	—
495	#2451	C₂×C₁₀₉	1	1	yes	characteristic, complemented
496	#2439	C₂×C₁₀₉	1	1	yes	characteristic, complemented
497	#2421	C₂×C₁₀₉	1	1	yes	characteristic, complemented
498	#2415	C₂×C₁₀₉	1	1	yes	characteristic
499	#2336	C₂×C₁₀₉	1	2	yes	complemented
500	#2332	C₂×C₁₀₉	1	2	yes	complemented
501	C₄×C₂²⋊Q₈	C₂×C₁₀₉	1	1	yes	characteristic, complemented
502	#2296	C₂×C₁₀₉	1	1	yes	characteristic, complemented
503	C₄²×D₄	C₂×C₁₀₉	1	1	yes	characteristic
504	C₁₀₉	#35039	1	1	yes	characteristic, direct product factor, Sylow
505	C₂×C₄⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
506	C₂×#125	C₂²×C₁₀₉	1	2	yes	—
507	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	—
508	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
509	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
510	C₂×C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
511	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
512	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
513	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
514	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
515	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
516	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
517	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
518	#400	C₂²×C₁₀₉	1	2	yes	—
519	#400	C₂²×C₁₀₉	1	2	yes	—
520	#400	C₂²×C₁₀₉	1	2	yes	—
521	#398	C₂²×C₁₀₉	1	2	yes	—
522	#398	C₂²×C₁₀₉	1	2	yes	—
523	#397	C₂²×C₁₀₉	1	2	yes	—
524	#397	C₂²×C₁₀₉	1	2	yes	—
525	#397	C₂²×C₁₀₉	1	2	yes	—
526	#397	C₂²×C₁₀₉	1	2	yes	—
527	#397	C₂²×C₁₀₉	1	2	yes	—
528	#397	C₂²×C₁₀₉	1	2	yes	—
529	#396	C₂²×C₁₀₉	1	2	yes	—
530	#395	C₂²×C₁₀₉	1	2	yes	—
531	#394	C₂²×C₁₀₉	1	2	yes	—
532	#394	C₂²×C₁₀₉	1	2	yes	—
533	#393	C₂²×C₁₀₉	1	2	yes	—
534	#391	C₂²×C₁₀₉	1	2	yes	—
535	#391	C₂²×C₁₀₉	1	2	yes	—
536	#391	C₂²×C₁₀₉	1	2	yes	—
537	#391	C₂²×C₁₀₉	1	1	yes	characteristic
538	#391	C₂²×C₁₀₉	1	1	yes	characteristic
539	#391	C₂²×C₁₀₉	1	1	yes	characteristic
540	#391	C₂²×C₁₀₉	1	1	yes	characteristic
541	#389	C₂²×C₁₀₉	1	2	yes	—
542	#389	C₂²×C₁₀₉	1	2	yes	—
543	#389	C₂²×C₁₀₉	1	1	yes	characteristic
544	#389	C₂²×C₁₀₉	1	1	yes	characteristic
545	#389	C₂²×C₁₀₉	1	1	yes	characteristic
546	#389	C₂²×C₁₀₉	1	1	yes	characteristic
547	#389	C₂²×C₁₀₉	1	1	yes	characteristic
548	#389	C₂²×C₁₀₉	1	1	yes	characteristic
549	#389	C₂²×C₁₀₉	1	1	yes	characteristic
550	#389	C₂²×C₁₀₉	1	1	yes	characteristic
551	#389	C₂²×C₁₀₉	1	1	yes	characteristic
552	#389	C₂²×C₁₀₉	1	1	yes	characteristic
553	#388	C₂²×C₁₀₉	1	2	yes	—
554	#388	C₂²×C₁₀₉	1	2	yes	—
555	#388	C₂²×C₁₀₉	1	2	yes	—
556	#388	C₂²×C₁₀₉	1	2	yes	—
557	#387	C₂²×C₁₀₉	1	2	yes	—
558	#387	C₂²×C₁₀₉	1	2	yes	—
559	#387	C₂²×C₁₀₉	1	2	yes	—
560	#387	C₂²×C₁₀₉	1	2	yes	—
561	#387	C₂²×C₁₀₉	1	2	yes	—
562	#387	C₂²×C₁₀₉	1	2	yes	—
563	#387	C₂²×C₁₀₉	1	2	yes	—
564	#387	C₂²×C₁₀₉	1	2	yes	—
565	#387	C₂²×C₁₀₉	1	2	yes	—
566	#387	C₂²×C₁₀₉	1	2	yes	—
567	#387	C₂²×C₁₀₉	1	2	yes	—
568	#387	C₂²×C₁₀₉	1	2	yes	—
569	#387	C₂²×C₁₀₉	1	2	yes	—
570	#387	C₂²×C₁₀₉	1	2	yes	—
571	#387	C₂²×C₁₀₉	1	2	yes	—
572	#387	C₂²×C₁₀₉	1	2	yes	—
573	#387	C₂²×C₁₀₉	1	2	yes	—
574	#385	C₂²×C₁₀₉	1	2	yes	—
575	#385	C₂²×C₁₀₉	1	2	yes	—
576	#385	C₂²×C₁₀₉	1	2	yes	—
577	#385	C₂²×C₁₀₉	1	2	yes	—
578	#384	C₂²×C₁₀₉	1	1	yes	characteristic
579	#383	C₂²×C₁₀₉	1	2	yes	—
580	#383	C₂²×C₁₀₉	1	2	yes	—
581	#382	C₂²×C₁₀₉	1	1	yes	characteristic
582	#382	C₂²×C₁₀₉	1	1	yes	characteristic
583	#381	C₂²×C₁₀₉	1	2	yes	—
584	#380	C₂²×C₁₀₉	1	2	yes	—
585	#380	C₂²×C₁₀₉	1	1	yes	characteristic
586	#380	C₂²×C₁₀₉	1	1	yes	characteristic
587	#380	C₂²×C₁₀₉	1	1	yes	characteristic
588	#380	C₂²×C₁₀₉	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	—
591	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	—
592	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
596	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
597	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
598	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
603	C₄³	C₂²×C₁₀₉	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
605	C₂²×Q₈	C₂³×C₁₀₉	1	2	yes	—
606	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
613	C₄⋊Q₈	—	4	2	no	—
614	#125	—	2	8	no	—
615	C₂²⋊Q₈	—	2	4	no	—
616	C₂²⋊Q₈	—	2	8	no	—
617	C₂²⋊Q₈	—	4	2	no	—
618	C₄×Q₈	—	4	2	no	—
619	C₄×D₄	—	2	4	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	4	no	—
622	#117	—	2	4	no	—
623	#117	—	4	2	no	—
624	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
664	C₂×C₄²	—	4	2	no	—
665	C₂×C₄²	—	4	2	no	—
666	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
667	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
677	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
678	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
683	#95	C₂³×C₁₀₉	1	1	yes	characteristic
684	#95	C₂³×C₁₀₉	1	1	yes	characteristic
685	#95	C₂³×C₁₀₉	1	1	yes	characteristic
686	#95	C₂³×C₁₀₉	1	1	yes	characteristic
687	#95	C₂³×C₁₀₉	1	1	yes	characteristic
688	#95	C₂³×C₁₀₉	1	1	yes	characteristic
689	#95	C₂³×C₁₀₉	1	2	yes	—
690	#95	C₂³×C₁₀₉	1	2	yes	—
691	#95	C₂³×C₁₀₉	1	2	yes	—
692	#95	C₂³×C₁₀₉	1	2	yes	—
693	#95	C₂³×C₁₀₉	1	2	yes	—
694	#95	C₂³×C₁₀₉	1	2	yes	—
695	#95	C₂³×C₁₀₉	1	2	yes	—
696	#95	C₂³×C₁₀₉	1	2	yes	—
697	#95	C₂³×C₁₀₉	1	2	yes	—
698	#95	C₂³×C₁₀₉	1	2	yes	—
699	#95	C₂³×C₁₀₉	1	2	yes	—
700	#95	C₂³×C₁₀₉	1	2	yes	—
701	#95	C₂³×C₁₀₉	1	2	yes	—
702	#95	C₂³×C₁₀₉	1	2	yes	—
703	#95	C₂³×C₁₀₉	1	2	yes	—
704	#95	C₂³×C₁₀₉	1	2	yes	—
705	#95	C₂³×C₁₀₉	1	2	yes	—
706	#95	C₂³×C₁₀₉	1	2	yes	—
707	#95	C₂³×C₁₀₉	1	2	yes	—
708	#95	C₂³×C₁₀₉	1	2	yes	—
709	#95	C₂³×C₁₀₉	1	2	yes	—
710	#95	C₂³×C₁₀₉	1	2	yes	—
711	#95	C₂³×C₁₀₉	1	2	yes	—
712	#95	C₂³×C₁₀₉	1	2	yes	—
713	#95	C₂³×C₁₀₉	1	2	yes	—
714	#95	C₂³×C₁₀₉	1	2	yes	—
715	#95	C₂³×C₁₀₉	1	2	yes	—
716	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	4	2	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
744	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
745	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	#41×C₁₀₉	1	4	yes	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₄²	—	2	4	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	4	1	no	—
817	C₄²	—	4	1	no	—
818	C₄²	—	4	1	no	—
819	C₄²	—	4	1	no	—
820	C₄²	—	4	1	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
836	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
837	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
838	Q₈	—	4	4	no	—
839	Q₈	—	8	4	no	—
840	D₄	—	2	8	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	4	4	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
901	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
902	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
903	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
904	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
905	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
906	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
907	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
908	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	2	yes	—
909	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	2	yes	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
925	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
926	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
927	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
928	C₂²	C₂×2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
929	C₂²	C₂×2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
930	C₂²	#585×C₁₀₉	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	#539×C₁₀₉	1	4	yes	—
952	C₂	—	4	2	no	—
953	C₂	—	4	2	no	—
954	C₂	C₁₀₉×#3444	1	1	yes	characteristic
955	C₂	C₂×#539×C₁₀₉	1	1	yes	characteristic
956	C₂	C₁₀₉×#3461	1	1	yes	characteristic
957	C₂	C₁₀₉×#3505	1	1	yes	characteristic
958	C₂	C₁₀₉×#3509	1	1	yes	characteristic
959	C₂	C₁₀₉×#3518	1	1	yes	characteristic
960	C₂	C₁₀₉×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
prime radical	C₂²×D₄×C₁₀₉	C₂³
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×#2864	C₂	semidirect
2. C₁₀₉×#2863	C₂	semidirect
3. C₁₀₉×#2857	C₂	semidirect
4. C₁₀₉×#2855	C₂	semidirect
5. C₁₀₉×#2652	C₂	semidirect
7. C₁₀₉×#2588	C₂	semidirect
8. C₁₀₉×#2577	C₂	semidirect
9. C₁₀₉×#2523	C₂	semidirect
10. C₁₀₉×#2506	C₂	semidirect
11. C₁₀₉×#2499	C₂	semidirect
12. C₁₀₉×#2495	C₂	semidirect
15. C₁₀₉×#2451	C₂	semidirect
16. C₁₀₉×#2439	C₂	semidirect
17. C₁₀₉×#2421	C₂	semidirect
19. C₁₀₉×#2336	C₂	semidirect
20. C₁₀₉×#2332	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₁₀₉	C₂	semidirect
22. C₁₀₉×#2296	C₂	semidirect
471. #35039	C₁₀₉	direct (N × H)
481. #2864	C₂×C₁₀₉	semidirect
482. #2863	C₂×C₁₀₉	semidirect
483. #2857	C₂×C₁₀₉	semidirect
484. #2855	C₂×C₁₀₉	semidirect
485. #2652	C₂×C₁₀₉	semidirect
487. #2588	C₂×C₁₀₉	semidirect
488. #2577	C₂×C₁₀₉	semidirect
489. #2523	C₂×C₁₀₉	semidirect
490. #2506	C₂×C₁₀₉	semidirect
491. #2499	C₂×C₁₀₉	semidirect
492. #2495	C₂×C₁₀₉	semidirect
495. #2451	C₂×C₁₀₉	semidirect
496. #2439	C₂×C₁₀₉	semidirect
497. #2421	C₂×C₁₀₉	semidirect
499. #2336	C₂×C₁₀₉	semidirect
500. #2332	C₂×C₁₀₉	semidirect
501. C₄×C₂²⋊Q₈	C₂×C₁₀₉	semidirect
502. #2296	C₂×C₁₀₉	semidirect
504. C₁₀₉	#35039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₉×#2864	2
C₁₀₉×#2863	2
C₁₀₉×#2857	2
C₁₀₉×#2855	2
C₁₀₉×#2652	2
C₁₀₉×#2638	2
C₁₀₉×#2588	2
C₁₀₉×#2577	2
C₁₀₉×#2523	2
C₁₀₉×#2506	2
C₁₀₉×#2499	2
C₁₀₉×#2495	2
C₁₀₉×#2485	2
C₁₀₉×#2460	2
C₁₀₉×#2451	2
C₁₀₉×#2439	2
C₁₀₉×#2421	2
C₁₀₉×#2415	2
C₁₀₉×#2336	2
C₁₀₉×#2332	2
C₄×C₂²⋊Q₈×C₁₀₉	2
C₁₀₉×#2296	2
C₄²×D₄×C₁₀₉	2
#35039	109

Subgroups — C109×#35039 #42153033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#35039 #42153033