Subgroups — C₇×#62856 #13240072

Order 1792.

7086 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	8	yes	maximal, complemented
2	C₇×#3511	C₂	1	8	yes	maximal, complemented
3	C₇×#3505	C₂	1	8	yes	maximal, complemented
4	C₇×#3495	C₂	1	8	yes	maximal, complemented
5	C₇×#3494	C₂	1	8	yes	maximal, complemented
6	C₇×#3493	C₂	1	4	yes	maximal, complemented
7	C₇×#3492	C₂	1	4	yes	maximal, complemented
8	C₇×#3461	C₂	1	4	yes	maximal, complemented
9	C₇×#3460	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3449	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#537	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3428	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₇×#41	C₂²	1	2	yes	—
17	C₇×#556	C₂²	1	16	yes	complemented
18	C₇×#555	C₂²	1	16	yes	complemented
19	C₇×#554	C₂²	1	16	yes	complemented
20	C₇×#553	C₂²	1	16	yes	complemented
21	C₇×#553	C₂²	1	16	yes	complemented
22	C₇×#553	C₂²	1	32	yes	complemented
23	C₇×#553	C₂²	1	16	yes	complemented
24	C₇×#552	C₂²	1	16	yes	complemented
25	C₇×#552	C₂²	1	16	yes	complemented
26	C₇×#552	C₂²	1	16	yes	complemented
27	C₇×#551	C₂²	1	32	yes	complemented
28	C₇×#548	C₂²	1	16	yes	complemented
29	C₇×#547	C₂²	1	16	yes	complemented
30	C₇×#546	C₂²	1	16	yes	complemented
31	C₇×#544	C₂²	1	4	yes	complemented
32	C₇×#544	C₂²	1	4	yes	complemented
33	C₇×#544	C₂²	1	8	yes	complemented
34	C₇×#542	C₂²	1	16	yes	complemented
35	C₇×#542	C₂²	1	16	yes	complemented
36	C₇×#541	C₂²	1	16	yes	complemented
37	C₇×#540	C₂²	1	16	yes	complemented
38	C₇×#539	C₂²	1	16	yes	complemented
39	C₇×#538	C₂²	1	16	yes	complemented
40	C₇×#537	C₂²	1	4	yes	—
41	C₇×#537	C₂²	1	4	yes	—
42	C₇×#537	C₂²	1	8	yes	complemented
43	C₇×#537	C₂²	1	4	yes	complemented
44	C₇×#537	C₂²	1	4	yes	complemented
45	C₇×#536	C₂²	1	4	yes	—
46	C₇×#536	C₂²	1	4	yes	complemented
47	C₇×#535	C₂²	1	4	yes	—
48	C₇×#535	C₂²	1	4	yes	complemented
49	C₇×#534	C₂²	1	8	yes	—
50	C₇×#533	C₂²	1	16	yes	complemented
51	C₇×#532	C₂²	1	8	yes	complemented
52	C₇×#532	C₂²	1	16	yes	complemented
53	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
54	C₇×#529	C₂²	1	16	yes	complemented
55	C₇×#529	C₂²	1	16	yes	complemented
56	C₇×#529	C₂²	1	16	yes	complemented
57	C₂×C₇×#125	C₂²	1	4	yes	complemented
58	C₇×#525	C₂²	1	8	yes	—
59	C₇×#525	C₂²	1	8	yes	complemented
60	C₇×#525	C₂²	1	16	yes	complemented
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₇×#121	C₂²	1	4	yes	—
64	C₂×C₇×#121	C₂²	1	4	yes	complemented
65	C₇×#520	C₂²	1	8	yes	—
66	C₇×#520	C₂²	1	8	yes	complemented
67	C₇×#520	C₂²	1	4	yes	complemented
68	C₇×#520	C₂²	1	4	yes	complemented
69	C₇×#520	C₂²	1	4	yes	complemented
70	C₇×#520	C₂²	1	4	yes	complemented
71	C₇×#519	C₂²	1	4	yes	complemented
72	C₇×#518	C₂²	1	8	yes	—
73	C₇×#518	C₂²	1	4	yes	complemented
74	C₄×C₇×#41	C₂²	1	8	yes	complemented
75	C₄×C₇×#41	C₂²	1	8	yes	complemented
76	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
77	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
78	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
79	C₂×C₇×#117	C₂²	1	1	yes	characteristic
80	C₂×C₇×#117	C₂²	1	2	yes	—
81	C₂×C₇×#117	C₂²	1	2	yes	complemented
82	C₂×C₇×#117	C₂²	1	8	yes	complemented
83	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
84	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
85	#62856	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂×C₇×#41	—	2	8	no	—
87	C₂×C₇×#41	—	2	16	no	—
88	C₂×C₇×#41	C₂³	1	4	yes	—
89	C₂×C₇×#41	C₂³	1	4	yes	—
90	C₂×C₇×#41	C₂³	1	4	yes	—
91	C₂×C₇×#41	C₂³	1	4	yes	—
92	C₂×C₇×#41	C₂³	1	4	yes	—
93	C₂×C₇×#41	C₂³	1	4	yes	—
94	C₂×C₇×#41	C₂³	1	16	yes	—
95	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₇×Q₈	C₂³	1	2	yes	—
97	C₂²×C₇×Q₈	C₂³	1	4	yes	—
98	C₂²×C₇×D₄	C₂³	1	2	yes	—
99	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
100	C₂²×C₇×D₄	C₂³	1	4	yes	—
101	C₂²×C₇×D₄	C₂³	1	2	yes	—
102	C₂²×C₇×D₄	C₂³	1	4	yes	—
103	C₂³×C₄×C₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₇	C₂³	1	4	yes	—
105	C₂³×C₄×C₇	C₂³	1	2	yes	—
106	C₂³×C₄×C₇	C₂³	1	4	yes	—
107	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
109	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
110	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
111	C₇×#127	C₂³	1	8	yes	—
112	C₇×#126	C₂³	1	32	yes	—
113	C₇×#126	C₂³	1	32	yes	—
114	C₇×#126	C₂³	1	32	yes	—
115	C₇×#125	C₂³	1	16	yes	—
116	C₇×#125	C₂³	1	16	yes	—
117	C₇×#125	C₂³	1	16	yes	—
118	C₇×#125	C₂³	1	32	yes	—
119	C₇×#124	C₂³	1	8	yes	—
120	C₇×#124	C₂³	1	8	yes	—
121	C₇×#124	C₂³	1	16	yes	—
122	C₇×#124	C₂³	1	32	yes	—
123	C₇×#123	C₂³	1	16	yes	—
124	C₇×#123	C₂³	1	16	yes	—
125	C₇×#123	C₂³	1	32	yes	—
126	C₇×#123	C₂³	1	32	yes	—
127	C₇×#123	C₂³	1	32	yes	—
128	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
130	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
131	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
132	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
135	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
136	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
137	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
138	C₇×#121	C₂³	1	16	yes	—
139	C₇×#121	C₂³	1	16	yes	—
140	C₇×#121	C₂³	1	16	yes	—
141	C₇×#121	C₂³	1	16	yes	—
142	C₇×#121	C₂³	1	8	yes	—
143	C₇×#121	C₂³	1	8	yes	—
144	C₇×#121	C₂³	1	8	yes	—
145	C₇×#121	C₂³	1	8	yes	—
146	C₇×#121	C₂³	1	16	yes	—
147	C₇×#121	C₂³	1	16	yes	—
148	C₇×#121	C₂³	1	16	yes	—
149	C₇×#121	C₂³	1	32	yes	—
150	C₇×#120	C₂³	1	16	yes	—
151	C₇×#120	C₂³	1	16	yes	—
152	C₄×C₇×Q₈	C₂³	1	16	yes	—
153	C₄×C₇×Q₈	C₂³	1	8	yes	—
154	C₄×C₇×Q₈	C₂³	1	8	yes	—
155	C₄×C₇×Q₈	C₂³	1	8	yes	—
156	C₄×C₇×Q₈	C₂³	1	8	yes	—
157	C₄×C₇×Q₈	C₂³	1	16	yes	—
158	C₄×C₇×D₄	C₂³	1	16	yes	—
159	C₄×C₇×D₄	C₂³	1	16	yes	—
160	C₄×C₇×D₄	C₂³	1	16	yes	—
161	C₄×C₇×D₄	C₂³	1	16	yes	—
162	C₄×C₇×D₄	C₂³	1	16	yes	—
163	C₄×C₇×D₄	C₂³	1	16	yes	—
164	C₄×C₇×D₄	C₂³	1	16	yes	—
165	C₄×C₇×D₄	C₂³	1	8	yes	—
166	C₄×C₇×D₄	C₂³	1	8	yes	—
167	C₄×C₇×D₄	C₂³	1	8	yes	—
168	C₄×C₇×D₄	C₂³	1	8	yes	—
169	C₄×C₇×D₄	C₂³	1	16	yes	—
170	C₄×C₇×D₄	C₂³	1	16	yes	—
171	C₄×C₇×D₄	C₂³	1	32	yes	—
172	C₄×C₇×D₄	C₂³	1	16	yes	—
173	C₇×#117	C₂³	1	4	yes	—
174	C₇×#117	C₂³	1	4	yes	—
175	C₇×#117	C₂³	1	4	yes	—
176	C₇×#117	C₂³	1	4	yes	—
177	C₇×#117	C₂³	1	4	yes	—
178	C₇×#117	C₂³	1	4	yes	—
179	C₇×#117	C₂³	1	16	yes	—
180	C₇×#117	C₂³	1	16	yes	—
181	C₇×#117	C₂³	1	16	yes	—
182	C₇×#117	C₂³	1	8	yes	—
183	C₇×#117	C₂³	1	8	yes	—
184	C₇×#117	C₂³	1	16	yes	—
185	C₇×#117	C₂³	1	32	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	C₂³	1	4	yes	—
208	C₂×C₄²×C₇	C₂³	1	4	yes	—
209	C₂×C₄²×C₇	C₂³	1	16	yes	—
210	#3512	C₂×C₇	1	8	yes	complemented
211	#3511	C₂×C₇	1	8	yes	complemented
212	#3505	C₂×C₇	1	8	yes	complemented
213	#3495	C₂×C₇	1	8	yes	complemented
214	#3494	C₂×C₇	1	8	yes	complemented
215	#3493	C₂×C₇	1	4	yes	complemented
216	#3492	C₂×C₇	1	4	yes	complemented
217	#3461	C₂×C₇	1	4	yes	complemented
218	#3460	C₂×C₇	1	4	yes	complemented
219	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
220	#3449	C₂×C₇	1	2	yes	complemented
221	C₂×#537	C₂×C₇	1	1	yes	characteristic, complemented
222	#3428	C₂×C₇	1	2	yes	complemented
223	C₂×#520	C₂×C₇	1	1	yes	characteristic, complemented
224	C₂⁴×C₇	C₂⁴	1	4	yes	—
225	C₂⁴×C₇	C₂⁴	1	2	yes	—
226	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
227	C₇×#41	—	2	16	no	—
228	C₇×#41	—	2	16	no	—
229	C₇×#41	—	2	16	no	—
230	C₇×#41	—	2	16	no	—
231	C₇×#41	—	2	16	no	—
232	C₇×#41	—	2	16	no	—
233	C₇×#41	—	8	16	no	—
234	C₂×C₇×Q₈	—	2	8	no	—
235	C₂×C₇×Q₈	—	2	4	no	—
236	C₂×C₇×Q₈	—	8	4	no	—
237	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
238	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
239	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
240	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
241	C₂×C₇×D₄	—	2	8	no	—
242	C₂×C₇×D₄	—	2	16	no	—
243	C₂×C₇×D₄	—	2	8	no	—
244	C₂×C₇×D₄	—	2	4	no	—
245	C₂×C₇×D₄	—	8	4	no	—
246	C₂×C₇×D₄	C₂⁴	1	4	yes	—
247	C₂×C₇×D₄	C₂⁴	1	8	yes	—
248	C₂×C₇×D₄	C₂⁴	1	4	yes	—
249	C₂×C₇×D₄	C₂⁴	1	8	yes	—
250	C₂×C₇×D₄	C₂⁴	1	4	yes	—
251	C₂×C₇×D₄	C₂⁴	1	4	yes	—
252	C₂×C₇×D₄	C₂⁴	1	4	yes	—
253	C₂×C₇×D₄	C₂⁴	1	16	yes	—
254	C₂×C₇×D₄	C₂⁴	1	16	yes	—
255	C₂×C₇×D₄	C₂⁴	1	16	yes	—
256	C₂²×C₄×C₇	—	2	16	no	—
257	C₂²×C₄×C₇	—	2	8	no	—
258	C₂²×C₄×C₇	—	8	2	no	—
259	C₂²×C₄×C₇	—	8	4	no	—
260	C₂²×C₄×C₇	#41	1	8	yes	complemented
261	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
272	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
273	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
283	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
286	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
287	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
296	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
297	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
298	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
299	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
300	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
301	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
302	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
303	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
304	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
305	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
306	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
307	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
308	C₄²×C₇	C₂⁴	1	8	yes	—
309	C₄²×C₇	C₂⁴	1	8	yes	—
310	C₄²×C₇	C₂⁴	1	16	yes	—
311	C₄²×C₇	C₂⁴	1	16	yes	—
312	C₄²×C₇	C₂⁴	1	16	yes	—
313	C₄²×C₇	C₂⁴	1	8	yes	—
314	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
315	C₂²×#41	C₂²×C₇	1	2	yes	—
316	#556	C₂²×C₇	1	16	yes	complemented
317	#555	C₂²×C₇	1	16	yes	complemented
318	#554	C₂²×C₇	1	16	yes	complemented
319	#553	C₂²×C₇	1	16	yes	complemented
320	#553	C₂²×C₇	1	16	yes	complemented
321	#553	C₂²×C₇	1	32	yes	complemented
322	#553	C₂²×C₇	1	16	yes	complemented
323	#552	C₂²×C₇	1	16	yes	complemented
324	#552	C₂²×C₇	1	16	yes	complemented
325	#552	C₂²×C₇	1	16	yes	complemented
326	#551	C₂²×C₇	1	32	yes	complemented
327	#548	C₂²×C₇	1	16	yes	complemented
328	#547	C₂²×C₇	1	16	yes	complemented
329	#546	C₂²×C₇	1	16	yes	complemented
330	#544	C₂²×C₇	1	4	yes	complemented
331	#544	C₂²×C₇	1	4	yes	complemented
332	#544	C₂²×C₇	1	8	yes	complemented
333	#542	C₂²×C₇	1	16	yes	complemented
334	#542	C₂²×C₇	1	16	yes	complemented
335	#541	C₂²×C₇	1	16	yes	complemented
336	#540	C₂²×C₇	1	16	yes	complemented
337	#539	C₂²×C₇	1	16	yes	complemented
338	#538	C₂²×C₇	1	16	yes	complemented
339	#537	C₂²×C₇	1	4	yes	—
340	#537	C₂²×C₇	1	4	yes	—
341	#537	C₂²×C₇	1	8	yes	complemented
342	#537	C₂²×C₇	1	4	yes	complemented
343	#537	C₂²×C₇	1	4	yes	complemented
344	#536	C₂²×C₇	1	4	yes	—
345	#536	C₂²×C₇	1	4	yes	complemented
346	#535	C₂²×C₇	1	4	yes	—
347	#535	C₂²×C₇	1	4	yes	complemented
348	#534	C₂²×C₇	1	8	yes	—
349	#533	C₂²×C₇	1	16	yes	complemented
350	#532	C₂²×C₇	1	8	yes	complemented
351	#532	C₂²×C₇	1	16	yes	complemented
352	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
353	#529	C₂²×C₇	1	16	yes	complemented
354	#529	C₂²×C₇	1	16	yes	complemented
355	#529	C₂²×C₇	1	16	yes	complemented
356	C₂×#125	C₂²×C₇	1	4	yes	complemented
357	#525	C₂²×C₇	1	8	yes	—
358	#525	C₂²×C₇	1	8	yes	complemented
359	#525	C₂²×C₇	1	16	yes	complemented
360	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
361	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
362	C₂×#121	C₂²×C₇	1	4	yes	—
363	C₂×#121	C₂²×C₇	1	4	yes	complemented
364	#520	C₂²×C₇	1	8	yes	—
365	#520	C₂²×C₇	1	8	yes	complemented
366	#520	C₂²×C₇	1	4	yes	complemented
367	#520	C₂²×C₇	1	4	yes	complemented
368	#520	C₂²×C₇	1	4	yes	complemented
369	#520	C₂²×C₇	1	4	yes	complemented
370	#519	C₂²×C₇	1	4	yes	complemented
371	#518	C₂²×C₇	1	8	yes	—
372	#518	C₂²×C₇	1	4	yes	complemented
373	C₄×#41	C₂²×C₇	1	8	yes	complemented
374	C₄×#41	C₂²×C₇	1	8	yes	complemented
375	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
376	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
377	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
378	C₂×#117	C₂²×C₇	1	1	yes	characteristic
379	C₂×#117	C₂²×C₇	1	2	yes	—
380	C₂×#117	C₂²×C₇	1	2	yes	complemented
381	C₂×#117	C₂²×C₇	1	8	yes	complemented
382	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
384	C₂³×C₇	—	2	4	no	—
385	C₂³×C₇	—	2	8	no	—
386	C₂³×C₇	—	4	1	no	—
387	C₂³×C₇	—	4	2	no	—
388	C₂³×C₇	—	4	1	no	—
389	C₂³×C₇	—	4	2	no	—
390	C₂³×C₇	—	4	4	no	—
391	C₂³×C₇	—	4	4	no	—
392	C₂³×C₇	C₂×#41	1	4	yes	—
393	C₂³×C₇	C₂⁵	1	4	yes	—
394	C₂³×C₇	C₂⁵	1	8	yes	—
395	C₂³×C₇	C₂⁵	1	1	yes	characteristic
396	C₂³×C₇	C₂⁵	1	1	yes	characteristic
397	C₂³×C₇	C₂⁵	1	1	yes	characteristic
398	C₇×Q₈	—	2	8	no	—
399	C₇×Q₈	—	2	8	no	—
400	C₇×Q₈	—	2	8	no	—
401	C₇×Q₈	—	4	16	no	—
402	C₇×D₄	—	2	8	no	—
403	C₇×D₄	—	2	16	no	—
404	C₇×D₄	—	2	8	no	—
405	C₇×D₄	—	2	16	no	—
406	C₇×D₄	—	2	8	no	—
407	C₇×D₄	—	2	8	no	—
408	C₇×D₄	—	2	8	no	—
409	C₇×D₄	—	4	16	no	—
410	C₇×D₄	—	4	16	no	—
411	C₇×D₄	—	4	16	no	—
412	C₂×C₄×C₇	—	2	8	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	16	no	—
415	C₂×C₄×C₇	—	2	16	no	—
416	C₂×C₄×C₇	—	2	16	no	—
417	C₂×C₄×C₇	—	4	2	no	—
418	C₂×C₄×C₇	—	4	4	no	—
419	C₂×C₄×C₇	—	4	4	no	—
420	C₂×C₄×C₇	—	4	4	no	—
421	C₂×C₄×C₇	—	4	16	no	—
422	C₂×C₄×C₇	—	4	2	no	—
423	C₂×C₄×C₇	—	4	16	no	—
424	C₂×C₄×C₇	—	4	4	no	—
425	C₂×C₄×C₇	—	4	4	no	—
426	C₂×C₄×C₇	—	4	16	no	—
427	C₂×C₄×C₇	C₂×#41	1	8	yes	—
428	C₂×C₄×C₇	C₂×#41	1	4	yes	—
429	C₂×C₄×C₇	C₂×#41	1	4	yes	—
430	C₂×C₄×C₇	C₂×#41	1	8	yes	—
431	C₂×C₄×C₇	C₂⁵	1	4	yes	—
432	C₂×C₄×C₇	C₂⁵	1	4	yes	—
433	C₂×C₄×C₇	C₂⁵	1	8	yes	—
434	C₂×C₄×C₇	C₂⁵	1	8	yes	—
435	C₂×C₄×C₇	C₂⁵	1	4	yes	—
436	C₂×C₄×C₇	C₂⁵	1	8	yes	—
437	C₂×C₄×C₇	C₂⁵	1	8	yes	—
438	C₂×C₄×C₇	C₂⁵	1	2	yes	—
439	C₂×C₄×C₇	C₂⁵	1	2	yes	—
440	C₂×#41	—	2	8	no	—
441	C₂×#41	—	2	16	no	—
442	C₂×#41	C₂³×C₇	1	4	yes	—
443	C₂×#41	C₂³×C₇	1	4	yes	—
444	C₂×#41	C₂³×C₇	1	4	yes	—
445	C₂×#41	C₂³×C₇	1	4	yes	—
446	C₂×#41	C₂³×C₇	1	4	yes	—
447	C₂×#41	C₂³×C₇	1	4	yes	—
448	C₂×#41	C₂³×C₇	1	16	yes	—
449	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
450	C₂²×Q₈	C₂³×C₇	1	2	yes	—
451	C₂²×Q₈	C₂³×C₇	1	4	yes	—
452	C₂²×D₄	C₂³×C₇	1	2	yes	—
453	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₇	1	4	yes	—
455	C₂²×D₄	C₂³×C₇	1	2	yes	—
456	C₂²×D₄	C₂³×C₇	1	4	yes	—
457	C₂³×C₄	C₂³×C₇	1	2	yes	—
458	C₂³×C₄	C₂³×C₇	1	4	yes	—
459	C₂³×C₄	C₂³×C₇	1	2	yes	—
460	C₂³×C₄	C₂³×C₇	1	4	yes	—
461	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
463	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
464	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
465	#127	C₂³×C₇	1	8	yes	—
466	#126	C₂³×C₇	1	32	yes	—
467	#126	C₂³×C₇	1	32	yes	—
468	#126	C₂³×C₇	1	32	yes	—
469	#125	C₂³×C₇	1	16	yes	—
470	#125	C₂³×C₇	1	16	yes	—
471	#125	C₂³×C₇	1	16	yes	—
472	#125	C₂³×C₇	1	32	yes	—
473	#124	C₂³×C₇	1	8	yes	—
474	#124	C₂³×C₇	1	8	yes	—
475	#124	C₂³×C₇	1	16	yes	—
476	#124	C₂³×C₇	1	32	yes	—
477	#123	C₂³×C₇	1	16	yes	—
478	#123	C₂³×C₇	1	16	yes	—
479	#123	C₂³×C₇	1	32	yes	—
480	#123	C₂³×C₇	1	32	yes	—
481	#123	C₂³×C₇	1	32	yes	—
482	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
483	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
484	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
485	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
486	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
487	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
488	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
489	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
490	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
491	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
492	#121	C₂³×C₇	1	16	yes	—
493	#121	C₂³×C₇	1	16	yes	—
494	#121	C₂³×C₇	1	16	yes	—
495	#121	C₂³×C₇	1	16	yes	—
496	#121	C₂³×C₇	1	8	yes	—
497	#121	C₂³×C₇	1	8	yes	—
498	#121	C₂³×C₇	1	8	yes	—
499	#121	C₂³×C₇	1	8	yes	—
500	#121	C₂³×C₇	1	16	yes	—
501	#121	C₂³×C₇	1	16	yes	—
502	#121	C₂³×C₇	1	16	yes	—
503	#121	C₂³×C₇	1	32	yes	—
504	#120	C₂³×C₇	1	16	yes	—
505	#120	C₂³×C₇	1	16	yes	—
506	C₄×Q₈	C₂³×C₇	1	16	yes	—
507	C₄×Q₈	C₂³×C₇	1	8	yes	—
508	C₄×Q₈	C₂³×C₇	1	8	yes	—
509	C₄×Q₈	C₂³×C₇	1	8	yes	—
510	C₄×Q₈	C₂³×C₇	1	8	yes	—
511	C₄×Q₈	C₂³×C₇	1	16	yes	—
512	C₄×D₄	C₂³×C₇	1	16	yes	—
513	C₄×D₄	C₂³×C₇	1	16	yes	—
514	C₄×D₄	C₂³×C₇	1	16	yes	—
515	C₄×D₄	C₂³×C₇	1	16	yes	—
516	C₄×D₄	C₂³×C₇	1	16	yes	—
517	C₄×D₄	C₂³×C₇	1	16	yes	—
518	C₄×D₄	C₂³×C₇	1	16	yes	—
519	C₄×D₄	C₂³×C₇	1	8	yes	—
520	C₄×D₄	C₂³×C₇	1	8	yes	—
521	C₄×D₄	C₂³×C₇	1	8	yes	—
522	C₄×D₄	C₂³×C₇	1	8	yes	—
523	C₄×D₄	C₂³×C₇	1	16	yes	—
524	C₄×D₄	C₂³×C₇	1	16	yes	—
525	C₄×D₄	C₂³×C₇	1	32	yes	—
526	C₄×D₄	C₂³×C₇	1	16	yes	—
527	#117	C₂³×C₇	1	4	yes	—
528	#117	C₂³×C₇	1	4	yes	—
529	#117	C₂³×C₇	1	4	yes	—
530	#117	C₂³×C₇	1	4	yes	—
531	#117	C₂³×C₇	1	4	yes	—
532	#117	C₂³×C₇	1	4	yes	—
533	#117	C₂³×C₇	1	16	yes	—
534	#117	C₂³×C₇	1	16	yes	—
535	#117	C₂³×C₇	1	16	yes	—
536	#117	C₂³×C₇	1	8	yes	—
537	#117	C₂³×C₇	1	8	yes	—
538	#117	C₂³×C₇	1	16	yes	—
539	#117	C₂³×C₇	1	32	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
560	C₂×C₄²	C₂³×C₇	1	2	yes	—
561	C₂×C₄²	C₂³×C₇	1	4	yes	—
562	C₂×C₄²	C₂³×C₇	1	4	yes	—
563	C₂×C₄²	C₂³×C₇	1	16	yes	—
564	C₂²×C₇	—	2	1	no	—
565	C₂²×C₇	—	2	1	no	—
566	C₂²×C₇	—	2	1	no	—
567	C₂²×C₇	—	2	1	no	—
568	C₂²×C₇	—	2	1	no	—
569	C₂²×C₇	—	2	1	no	—
570	C₂²×C₇	—	2	4	no	—
571	C₂²×C₇	—	2	8	no	—
572	C₂²×C₇	—	2	4	no	—
573	C₂²×C₇	—	2	8	no	—
574	C₂²×C₇	—	2	8	no	—
575	C₂²×C₇	—	2	4	no	—
576	C₂²×C₇	—	4	4	no	—
577	C₂²×C₇	—	4	8	no	—
578	C₂²×C₇	—	8	8	no	—
579	C₂²×C₇	C₂²×#41	1	2	yes	—
580	C₂²×C₇	C₂²×#41	1	2	yes	—
581	C₂²×C₇	C₂²×#41	1	2	yes	—
582	C₂²×C₇	C₂⁶	1	1	yes	characteristic
583	C₄×C₇	—	2	8	no	—
584	C₄×C₇	—	2	4	no	—
585	C₄×C₇	—	2	4	no	—
586	C₄×C₇	—	2	8	no	—
587	C₄×C₇	—	2	8	no	—
588	C₄×C₇	—	2	4	no	—
589	C₄×C₇	—	2	8	no	—
590	C₄×C₇	C₂²×#41	1	4	yes	—
591	C₄×C₇	C₂²×#41	1	4	yes	—
592	C₂⁴	C₂⁴×C₇	1	4	yes	—
593	C₂⁴	C₂⁴×C₇	1	2	yes	—
594	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
595	#41	—	2	16	no	—
596	#41	—	2	16	no	—
597	#41	—	2	16	no	—
598	#41	—	2	16	no	—
599	#41	—	2	16	no	—
600	#41	—	2	16	no	—
601	#41	—	8	16	no	—
602	C₂×Q₈	—	2	8	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	8	4	no	—
605	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
606	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
607	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
608	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
609	C₂×D₄	—	2	8	no	—
610	C₂×D₄	—	2	16	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	8	4	no	—
614	C₂×D₄	C₂⁴×C₇	1	4	yes	—
615	C₂×D₄	C₂⁴×C₇	1	8	yes	—
616	C₂×D₄	C₂⁴×C₇	1	4	yes	—
617	C₂×D₄	C₂⁴×C₇	1	8	yes	—
618	C₂×D₄	C₂⁴×C₇	1	4	yes	—
619	C₂×D₄	C₂⁴×C₇	1	4	yes	—
620	C₂×D₄	C₂⁴×C₇	1	4	yes	—
621	C₂×D₄	C₂⁴×C₇	1	16	yes	—
622	C₂×D₄	C₂⁴×C₇	1	16	yes	—
623	C₂×D₄	C₂⁴×C₇	1	16	yes	—
624	C₂²×C₄	—	2	16	no	—
625	C₂²×C₄	—	2	8	no	—
626	C₂²×C₄	—	8	2	no	—
627	C₂²×C₄	—	8	4	no	—
628	C₂²×C₄	C₇×#41	1	8	yes	complemented
629	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
631	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
632	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
633	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
634	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
636	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
638	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
639	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
640	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
641	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
642	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
644	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
649	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
650	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
651	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
652	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
653	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
654	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
655	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
656	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
657	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
658	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
659	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
660	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
661	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
662	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
663	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
664	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
665	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
666	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
667	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
668	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
669	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
670	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
671	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
672	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
673	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
674	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
675	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
676	C₄²	C₂⁴×C₇	1	8	yes	—
677	C₄²	C₂⁴×C₇	1	8	yes	—
678	C₄²	C₂⁴×C₇	1	16	yes	—
679	C₄²	C₂⁴×C₇	1	16	yes	—
680	C₄²	C₂⁴×C₇	1	16	yes	—
681	C₄²	C₂⁴×C₇	1	8	yes	—
682	C₂×C₇	—	2	2	no	—
683	C₂×C₇	—	2	2	no	—
684	C₂×C₇	—	2	2	no	—
685	C₂×C₇	—	4	4	no	—
686	C₂×C₇	—	4	8	no	—
687	C₂×C₇	C₂³×#41	1	1	yes	characteristic
688	C₂×C₇	H(7,𝔽₂)	1	1	yes	characteristic
689	C₂×C₇	2₋¹⁺⁶	1	1	yes	characteristic
690	C₂³	—	2	4	no	—
691	C₂³	—	2	8	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	C₂×C₇×#41	1	4	yes	—
699	C₂³	C₂⁵×C₇	1	4	yes	—
700	C₂³	C₂⁵×C₇	1	8	yes	—
701	C₂³	C₂⁵×C₇	1	1	yes	characteristic
702	C₂³	C₂⁵×C₇	1	1	yes	characteristic
703	C₂³	C₂⁵×C₇	1	1	yes	characteristic
704	Q₈	—	2	8	no	—
705	Q₈	—	2	8	no	—
706	Q₈	—	2	8	no	—
707	Q₈	—	4	16	no	—
708	D₄	—	2	8	no	—
709	D₄	—	2	16	no	—
710	D₄	—	2	8	no	—
711	D₄	—	2	16	no	—
712	D₄	—	2	8	no	—
713	D₄	—	2	8	no	—
714	D₄	—	2	8	no	—
715	D₄	—	4	16	no	—
716	D₄	—	4	16	no	—
717	D₄	—	4	16	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	16	no	—
721	C₂×C₄	—	2	16	no	—
722	C₂×C₄	—	2	16	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	16	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	16	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	16	no	—
733	C₂×C₄	C₂×C₇×#41	1	8	yes	—
734	C₂×C₄	C₂×C₇×#41	1	4	yes	—
735	C₂×C₄	C₂×C₇×#41	1	4	yes	—
736	C₂×C₄	C₂×C₇×#41	1	8	yes	—
737	C₂×C₄	C₂⁵×C₇	1	4	yes	—
738	C₂×C₄	C₂⁵×C₇	1	4	yes	—
739	C₂×C₄	C₂⁵×C₇	1	8	yes	—
740	C₂×C₄	C₂⁵×C₇	1	8	yes	—
741	C₂×C₄	C₂⁵×C₇	1	4	yes	—
742	C₂×C₄	C₂⁵×C₇	1	8	yes	—
743	C₂×C₄	C₂⁵×C₇	1	8	yes	—
744	C₂×C₄	C₂⁵×C₇	1	2	yes	—
745	C₂×C₄	C₂⁵×C₇	1	2	yes	—
746	C₇	#62856	1	1	yes	characteristic, direct product factor, Sylow
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	8	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	8	no	—
757	C₂²	—	2	8	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	8	no	—
761	C₂²	—	8	8	no	—
762	C₂²	C₂²×C₇×#41	1	2	yes	—
763	C₂²	C₂²×C₇×#41	1	2	yes	—
764	C₂²	C₂²×C₇×#41	1	2	yes	—
765	C₂²	C₂⁶×C₇	1	1	yes	characteristic
766	C₄	—	2	8	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	8	no	—
770	C₄	—	2	8	no	—
771	C₄	—	2	4	no	—
772	C₄	—	2	8	no	—
773	C₄	C₂²×C₇×#41	1	4	yes	—
774	C₄	C₂²×C₇×#41	1	4	yes	—
775	C₂	—	2	2	no	—
776	C₂	—	2	2	no	—
777	C₂	—	2	2	no	—
778	C₂	—	4	4	no	—
779	C₂	—	4	8	no	—
780	C₂	C₂³×C₇×#41	1	1	yes	characteristic
781	C₂	C₇×H(7,𝔽₂)	1	1	yes	characteristic
782	C₂	C₇×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3511	C₂	semidirect
3. C₇×#3505	C₂	semidirect
4. C₇×#3495	C₂	semidirect
5. C₇×#3494	C₂	semidirect
6. C₇×#3493	C₂	semidirect
7. C₇×#3492	C₂	semidirect
8. C₇×#3461	C₂	semidirect
9. C₇×#3460	C₂	semidirect
10. C₂×C₇×#544	C₂	semidirect
11. C₇×#3449	C₂	semidirect
12. C₂×C₇×#537	C₂	semidirect
13. C₇×#3428	C₂	semidirect
14. C₂×C₇×#520	C₂	semidirect
17. C₇×#556	C₂²	semidirect
18. C₇×#555	C₂²	semidirect
19. C₇×#554	C₂²	semidirect
20. C₇×#553	C₂²	semidirect
21. C₇×#553	C₂²	semidirect
22. C₇×#553	C₂²	semidirect
23. C₇×#553	C₂²	semidirect
24. C₇×#552	C₂²	semidirect
25. C₇×#552	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×#548	C₂²	semidirect
29. C₇×#547	C₂²	semidirect
30. C₇×#546	C₂²	semidirect
31. C₇×#544	C₂²	semidirect
32. C₇×#544	C₂²	semidirect
33. C₇×#544	C₂²	semidirect
34. C₇×#542	C₂²	semidirect
35. C₇×#542	C₂²	semidirect
36. C₇×#541	C₂²	semidirect
37. C₇×#540	C₂²	semidirect
38. C₇×#539	C₂²	semidirect
39. C₇×#538	C₂²	semidirect
42. C₇×#537	C₂²	semidirect
43. C₇×#537	C₂²	semidirect
44. C₇×#537	C₂²	semidirect
46. C₇×#536	C₂²	semidirect
48. C₇×#535	C₂²	semidirect
50. C₇×#533	C₂²	semidirect
51. C₇×#532	C₂²	semidirect
52. C₇×#532	C₂²	semidirect
53. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
54. C₇×#529	C₂²	semidirect
55. C₇×#529	C₂²	semidirect
56. C₇×#529	C₂²	semidirect
57. C₂×C₇×#125	C₂²	semidirect
59. C₇×#525	C₂²	semidirect
60. C₇×#525	C₂²	semidirect
62. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₇×#121	C₂²	semidirect
66. C₇×#520	C₂²	semidirect
67. C₇×#520	C₂²	semidirect
68. C₇×#520	C₂²	semidirect
69. C₇×#520	C₂²	semidirect
70. C₇×#520	C₂²	semidirect
71. C₇×#519	C₂²	semidirect
73. C₇×#518	C₂²	semidirect
74. C₄×C₇×#41	C₂²	semidirect
75. C₄×C₇×#41	C₂²	semidirect
76. C₂×C₄×C₇×Q₈	C₂²	semidirect
78. C₂×C₄×C₇×D₄	C₂²	semidirect
81. C₂×C₇×#117	C₂²	semidirect
82. C₂×C₇×#117	C₂²	semidirect
84. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
85. #62856	C₇	direct (N × H)
210. #3512	C₂×C₇	semidirect
211. #3511	C₂×C₇	semidirect
212. #3505	C₂×C₇	semidirect
213. #3495	C₂×C₇	semidirect
214. #3494	C₂×C₇	semidirect
215. #3493	C₂×C₇	semidirect
216. #3492	C₂×C₇	semidirect
217. #3461	C₂×C₇	semidirect
218. #3460	C₂×C₇	semidirect
219. C₂×#544	C₂×C₇	semidirect
220. #3449	C₂×C₇	semidirect
221. C₂×#537	C₂×C₇	semidirect
222. #3428	C₂×C₇	semidirect
223. C₂×#520	C₂×C₇	semidirect
260. C₂²×C₄×C₇	#41	semidirect
316. #556	C₂²×C₇	semidirect
317. #555	C₂²×C₇	semidirect
318. #554	C₂²×C₇	semidirect
319. #553	C₂²×C₇	semidirect
320. #553	C₂²×C₇	semidirect
321. #553	C₂²×C₇	semidirect
322. #553	C₂²×C₇	semidirect
323. #552	C₂²×C₇	semidirect
324. #552	C₂²×C₇	semidirect
325. #552	C₂²×C₇	semidirect
326. #551	C₂²×C₇	semidirect
327. #548	C₂²×C₇	semidirect
328. #547	C₂²×C₇	semidirect
329. #546	C₂²×C₇	semidirect
330. #544	C₂²×C₇	semidirect
331. #544	C₂²×C₇	semidirect
332. #544	C₂²×C₇	semidirect
333. #542	C₂²×C₇	semidirect
334. #542	C₂²×C₇	semidirect
335. #541	C₂²×C₇	semidirect
336. #540	C₂²×C₇	semidirect
337. #539	C₂²×C₇	semidirect
338. #538	C₂²×C₇	semidirect
341. #537	C₂²×C₇	semidirect
342. #537	C₂²×C₇	semidirect
343. #537	C₂²×C₇	semidirect
345. #536	C₂²×C₇	semidirect
347. #535	C₂²×C₇	semidirect
349. #533	C₂²×C₇	semidirect
350. #532	C₂²×C₇	semidirect
351. #532	C₂²×C₇	semidirect
352. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
353. #529	C₂²×C₇	semidirect
354. #529	C₂²×C₇	semidirect
355. #529	C₂²×C₇	semidirect
356. C₂×#125	C₂²×C₇	semidirect
358. #525	C₂²×C₇	semidirect
359. #525	C₂²×C₇	semidirect
361. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
363. C₂×#121	C₂²×C₇	semidirect
365. #520	C₂²×C₇	semidirect
366. #520	C₂²×C₇	semidirect
367. #520	C₂²×C₇	semidirect
368. #520	C₂²×C₇	semidirect
369. #520	C₂²×C₇	semidirect
370. #519	C₂²×C₇	semidirect
372. #518	C₂²×C₇	semidirect
373. C₄×#41	C₂²×C₇	semidirect
374. C₄×#41	C₂²×C₇	semidirect
375. C₂×C₄×Q₈	C₂²×C₇	semidirect
377. C₂×C₄×D₄	C₂²×C₇	semidirect
380. C₂×#117	C₂²×C₇	semidirect
381. C₂×#117	C₂²×C₇	semidirect
383. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
628. C₂²×C₄	C₇×#41	semidirect
746. C₇	#62856	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3512	2
C₇×#3511	2
C₇×#3505	2
C₇×#3495	2
C₇×#3494	2
C₇×#3493	2
C₇×#3492	2
C₇×#3461	2
C₇×#3460	2
C₂×C₇×#544	2
C₇×#3449	2
C₂×C₇×#537	2
C₇×#3428	2
C₂×C₇×#520	2
#62856	7

Subgroups — C7×#62856 #13240072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62856 #13240072