Subgroups — C₇×#62820 #13240036

Order 1792.

7382 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3535	C₂	1	8	yes	maximal, complemented
2	C₇×#3534	C₂	1	8	yes	maximal, complemented
3	C₇×#3533	C₂	1	8	yes	maximal, complemented
4	C₇×#3513	C₂	1	16	yes	maximal, complemented
5	C₇×#3492	C₂	1	4	yes	maximal, complemented
6	C₇×#3491	C₂	1	4	yes	maximal, complemented
7	C₇×#3490	C₂	1	2	yes	maximal, complemented
8	C₇×#3490	C₂	1	4	yes	maximal, complemented
9	C₇×#3485	C₂	1	4	yes	maximal, complemented
10	C₇×#3484	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂²×C₇×#41	C₂²	1	2	yes	complemented
15	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
17	C₇×#563	C₂²	1	8	yes	complemented
18	C₇×#562	C₂²	1	16	yes	complemented
19	C₇×#560	C₂²	1	8	yes	complemented
20	C₇×#559	C₂²	1	8	yes	complemented
21	C₇×#554	C₂²	1	16	yes	complemented
22	C₇×#553	C₂²	1	16	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×#551	C₂²	1	16	yes	complemented
27	C₇×#551	C₂²	1	16	yes	complemented
28	C₇×#551	C₂²	1	16	yes	complemented
29	C₇×#551	C₂²	1	16	yes	complemented
30	C₇×#551	C₂²	1	8	yes	complemented
31	C₇×#547	C₂²	1	16	yes	complemented
32	C₇×#547	C₂²	1	16	yes	complemented
33	C₇×#546	C₂²	1	16	yes	complemented
34	C₇×#546	C₂²	1	16	yes	complemented
35	C₇×#546	C₂²	1	16	yes	complemented
36	C₇×#546	C₂²	1	16	yes	complemented
37	C₇×#546	C₂²	1	16	yes	complemented
38	C₇×D₄²	C₂²	1	16	yes	complemented
39	C₇×#544	C₂²	1	4	yes	complemented
40	C₇×#543	C₂²	1	2	yes	complemented
41	C₇×#543	C₂²	1	4	yes	complemented
42	C₇×#542	C₂²	1	16	yes	complemented
43	C₇×#540	C₂²	1	16	yes	complemented
44	C₇×#539	C₂²	1	8	yes	complemented
45	C₇×#539	C₂²	1	8	yes	complemented
46	C₇×#539	C₂²	1	16	yes	complemented
47	C₇×#539	C₂²	1	16	yes	complemented
48	C₇×#538	C₂²	1	8	yes	complemented
49	C₇×#538	C₂²	1	8	yes	complemented
50	C₇×#538	C₂²	1	8	yes	complemented
51	C₇×#538	C₂²	1	16	yes	complemented
52	C₇×#537	C₂²	1	4	yes	complemented
53	C₇×#536	C₂²	1	8	yes	complemented
54	C₇×#535	C₂²	1	4	yes	complemented
55	C₇×#534	C₂²	1	4	yes	—
56	C₇×#534	C₂²	1	4	yes	complemented
57	C₇×#534	C₂²	1	2	yes	complemented
58	C₇×#534	C₂²	1	4	yes	complemented
59	C₇×#534	C₂²	1	8	yes	complemented
60	C₇×#529	C₂²	1	16	yes	complemented
61	C₇×#525	C₂²	1	8	yes	complemented
62	C₇×#525	C₂²	1	4	yes	complemented
63	C₇×#525	C₂²	1	8	yes	complemented
64	C₇×#525	C₂²	1	8	yes	complemented
65	C₇×#525	C₂²	1	8	yes	complemented
66	C₇×#525	C₂²	1	8	yes	complemented
67	C₇×#525	C₂²	1	8	yes	complemented
68	C₂×C₇×#123	C₂²	1	4	yes	complemented
69	C₂×C₇×#123	C₂²	1	8	yes	complemented
70	C₂×C₇×#123	C₂²	1	4	yes	complemented
71	C₂×C₇×#123	C₂²	1	8	yes	complemented
72	C₂×C₇×#123	C₂²	1	4	yes	complemented
73	C₂×C₇×#123	C₂²	1	8	yes	complemented
74	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
75	C₂×C₇×#121	C₂²	1	4	yes	complemented
76	C₂×C₇×#120	C₂²	1	4	yes	complemented
77	C₂×C₇×#120	C₂²	1	4	yes	complemented
78	C₇×#520	C₂²	1	8	yes	complemented
79	C₇×#518	C₂²	1	2	yes	complemented
80	C₇×#518	C₂²	1	4	yes	complemented
81	C₇×#518	C₂²	1	8	yes	complemented
82	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
83	C₂×C₇×#117	C₂²	1	2	yes	complemented
84	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
87	#62820	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁵×C₇	C₂³	1	1	yes	characteristic
89	C₂⁵×C₇	C₂³	1	1	yes	characteristic
90	C₇×H(5,𝔽₂)	—	4	8	no	—
91	C₂×C₇×#41	—	4	8	no	—
92	C₂×C₇×#41	C₂³	1	8	yes	—
93	C₂×C₇×#41	C₂³	1	4	yes	—
94	C₂×C₇×#41	C₂³	1	8	yes	—
95	C₂×C₇×#41	C₂³	1	8	yes	—
96	C₂×C₇×#41	C₂³	1	8	yes	complemented
97	C₂²×C₇×Q₈	C₂³	1	2	yes	complemented
98	C₂²×C₇×D₄	—	4	4	no	—
99	C₂²×C₇×D₄	C₂³	1	2	yes	—
100	C₂²×C₇×D₄	C₂³	1	4	yes	—
101	C₂²×C₇×D₄	C₂³	1	2	yes	—
102	C₂²×C₇×D₄	C₂³	1	8	yes	—
103	C₂²×C₇×D₄	C₂³	1	4	yes	—
104	C₂²×C₇×D₄	C₂³	1	8	yes	—
105	C₂²×C₇×D₄	C₂³	1	8	yes	—
106	C₂²×C₇×D₄	C₂³	1	8	yes	—
107	C₂²×C₇×D₄	C₂³	1	2	yes	complemented
108	C₂³×C₄×C₇	—	4	4	no	—
109	C₂³×C₄×C₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₇	C₂³	1	4	yes	—
114	C₂³×C₄×C₇	C₂³	1	4	yes	—
115	C₂³×C₄×C₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₇	C₂³	1	4	yes	complemented
117	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
118	C₇×#127	C₂³	1	8	yes	—
119	C₇×#126	C₂³	1	16	yes	complemented
120	C₇×#126	C₂³	1	16	yes	complemented
121	C₇×#126	C₂³	1	16	yes	complemented
122	C₇×#126	C₂³	1	16	yes	complemented
123	C₇×#126	C₂³	1	16	yes	complemented
124	C₇×#125	C₂³	1	16	yes	complemented
125	C₇×#125	C₂³	1	16	yes	complemented
126	C₇×#125	C₂³	1	16	yes	complemented
127	C₇×#124	C₂³	1	8	yes	—
128	C₇×#124	C₂³	1	16	yes	complemented
129	C₇×#124	C₂³	1	16	yes	complemented
130	C₇×#124	C₂³	1	16	yes	complemented
131	C₇×#123	C₂³	1	8	yes	—
132	C₇×#123	C₂³	1	8	yes	—
133	C₇×#123	C₂³	1	16	yes	—
134	C₇×#123	C₂³	1	16	yes	—
135	C₇×#123	C₂³	1	8	yes	—
136	C₇×#123	C₂³	1	8	yes	—
137	C₇×#123	C₂³	1	16	yes	—
138	C₇×#123	C₂³	1	8	yes	—
139	C₇×#123	C₂³	1	8	yes	—
140	C₇×#123	C₂³	1	16	yes	—
141	C₇×#123	C₂³	1	8	yes	—
142	C₇×#123	C₂³	1	8	yes	complemented
143	C₇×#123	C₂³	1	8	yes	complemented
144	C₇×#123	C₂³	1	8	yes	complemented
145	C₇×#123	C₂³	1	16	yes	complemented
146	C₇×#123	C₂³	1	16	yes	complemented
147	C₇×#123	C₂³	1	16	yes	complemented
148	C₇×#123	C₂³	1	16	yes	complemented
149	C₇×#123	C₂³	1	16	yes	complemented
150	C₇×#123	C₂³	1	16	yes	complemented
151	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
157	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
158	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
159	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
160	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
161	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
162	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
163	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
164	C₇×#121	C₂³	1	8	yes	—
165	C₇×#121	C₂³	1	8	yes	—
166	C₇×#121	C₂³	1	8	yes	—
167	C₇×#121	C₂³	1	8	yes	—
168	C₇×#121	C₂³	1	8	yes	—
169	C₇×#121	C₂³	1	16	yes	—
170	C₇×#121	C₂³	1	16	yes	—
171	C₇×#121	C₂³	1	16	yes	—
172	C₇×#121	C₂³	1	8	yes	complemented
173	C₇×#121	C₂³	1	8	yes	complemented
174	C₇×#121	C₂³	1	16	yes	complemented
175	C₇×#121	C₂³	1	16	yes	complemented
176	C₇×#121	C₂³	1	16	yes	complemented
177	C₇×#121	C₂³	1	16	yes	complemented
178	C₇×#120	C₂³	1	8	yes	—
179	C₇×#120	C₂³	1	8	yes	—
180	C₇×#120	C₂³	1	16	yes	—
181	C₇×#120	C₂³	1	8	yes	—
182	C₇×#120	C₂³	1	16	yes	—
183	C₇×#120	C₂³	1	8	yes	—
184	C₇×#120	C₂³	1	8	yes	—
185	C₇×#120	C₂³	1	8	yes	complemented
186	C₇×#120	C₂³	1	16	yes	complemented
187	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
188	C₄×C₇×D₄	C₂³	1	16	yes	—
189	C₄×C₇×D₄	C₂³	1	16	yes	—
190	C₄×C₇×D₄	C₂³	1	16	yes	—
191	C₄×C₇×D₄	C₂³	1	16	yes	—
192	C₄×C₇×D₄	C₂³	1	16	yes	—
193	C₄×C₇×D₄	C₂³	1	16	yes	—
194	C₄×C₇×D₄	C₂³	1	16	yes	complemented
195	C₄×C₇×D₄	C₂³	1	16	yes	complemented
196	C₄×C₇×D₄	C₂³	1	16	yes	complemented
197	C₄×C₇×D₄	C₂³	1	16	yes	complemented
198	C₄×C₇×D₄	C₂³	1	16	yes	complemented
199	C₄×C₇×D₄	C₂³	1	16	yes	complemented
200	C₇×#117	C₂³	1	8	yes	—
201	C₇×#117	C₂³	1	4	yes	—
202	C₇×#117	C₂³	1	8	yes	—
203	C₇×#117	C₂³	1	8	yes	complemented
204	C₇×#117	C₂³	1	8	yes	complemented
205	C₇×#117	C₂³	1	16	yes	complemented
206	C₇×#117	C₂³	1	16	yes	complemented
207	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
210	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
211	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
212	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
213	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	complemented
226	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	complemented
227	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
228	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
229	#3535	C₂×C₇	1	8	yes	complemented
230	#3534	C₂×C₇	1	8	yes	complemented
231	#3533	C₂×C₇	1	8	yes	complemented
232	#3513	C₂×C₇	1	16	yes	complemented
233	#3492	C₂×C₇	1	4	yes	complemented
234	#3491	C₂×C₇	1	4	yes	complemented
235	#3490	C₂×C₇	1	2	yes	complemented
236	#3490	C₂×C₇	1	4	yes	complemented
237	#3485	C₂×C₇	1	4	yes	complemented
238	#3484	C₂×C₇	1	2	yes	complemented
239	C₂×#525	C₂×C₇	1	2	yes	complemented
240	C₂²×#123	C₂×C₇	1	1	yes	characteristic, complemented
241	C₂⁴×C₇	—	2	4	no	—
242	C₂⁴×C₇	—	4	4	no	—
243	C₂⁴×C₇	—	4	2	no	—
244	C₂⁴×C₇	—	4	4	no	—
245	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
246	C₂⁴×C₇	C₂⁴	1	4	yes	—
247	C₂⁴×C₇	C₂⁴	1	2	yes	—
248	C₂⁴×C₇	C₂⁴	1	4	yes	—
249	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₇	C₂⁴	1	4	yes	—
251	C₂⁴×C₇	C₂⁴	1	4	yes	—
252	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
253	C₇×#41	—	4	16	no	—
254	C₇×#41	—	4	16	no	—
255	C₇×#41	—	4	16	no	—
256	C₇×#41	—	4	8	no	—
257	C₇×#41	—	4	16	no	—
258	C₂×C₇×Q₈	—	4	4	no	—
259	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
260	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
261	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
262	C₂×C₇×D₄	—	2	8	no	—
263	C₂×C₇×D₄	—	2	16	no	—
264	C₂×C₇×D₄	—	4	4	no	—
265	C₂×C₇×D₄	—	4	4	no	—
266	C₂×C₇×D₄	—	4	16	no	—
267	C₂×C₇×D₄	—	4	16	no	—
268	C₂×C₇×D₄	—	4	16	no	—
269	C₂×C₇×D₄	—	4	16	no	—
270	C₂×C₇×D₄	—	4	8	no	—
271	C₂×C₇×D₄	C₂⁴	1	16	yes	—
272	C₂×C₇×D₄	C₂⁴	1	8	yes	—
273	C₂×C₇×D₄	C₂⁴	1	8	yes	—
274	C₂×C₇×D₄	C₂⁴	1	8	yes	—
275	C₂×C₇×D₄	C₂⁴	1	16	yes	—
276	C₂×C₇×D₄	C₂⁴	1	16	yes	—
277	C₂×C₇×D₄	C₂⁴	1	8	yes	—
278	C₂×C₇×D₄	C₂⁴	1	8	yes	—
279	C₂×C₇×D₄	C₂⁴	1	8	yes	—
280	C₂×C₇×D₄	C₂⁴	1	8	yes	—
281	C₂×C₇×D₄	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₇	—	2	8	no	—
283	C₂²×C₄×C₇	—	4	8	no	—
284	C₂²×C₄×C₇	—	4	8	no	—
285	C₂²×C₄×C₇	—	4	4	no	—
286	C₂²×C₄×C₇	—	4	4	no	—
287	C₂²×C₄×C₇	—	4	4	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	—	4	8	no	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
324	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
337	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
338	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
339	C₄²×C₇	C₂⁴	1	16	yes	—
340	C₄²×C₇	C₂⁴	1	8	yes	—
341	C₄²×C₇	C₂⁴	1	16	yes	—
342	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	complemented
343	C₂²×#41	C₂²×C₇	1	2	yes	complemented
344	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
345	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
346	#563	C₂²×C₇	1	8	yes	complemented
347	#562	C₂²×C₇	1	16	yes	complemented
348	#560	C₂²×C₇	1	8	yes	complemented
349	#559	C₂²×C₇	1	8	yes	complemented
350	#554	C₂²×C₇	1	16	yes	complemented
351	#553	C₂²×C₇	1	16	yes	complemented
352	#553	C₂²×C₇	1	16	yes	complemented
353	#552	C₂²×C₇	1	16	yes	complemented
354	#552	C₂²×C₇	1	16	yes	complemented
355	#551	C₂²×C₇	1	16	yes	complemented
356	#551	C₂²×C₇	1	16	yes	complemented
357	#551	C₂²×C₇	1	16	yes	complemented
358	#551	C₂²×C₇	1	16	yes	complemented
359	#551	C₂²×C₇	1	8	yes	complemented
360	#547	C₂²×C₇	1	16	yes	complemented
361	#547	C₂²×C₇	1	16	yes	complemented
362	#546	C₂²×C₇	1	16	yes	complemented
363	#546	C₂²×C₇	1	16	yes	complemented
364	#546	C₂²×C₇	1	16	yes	complemented
365	#546	C₂²×C₇	1	16	yes	complemented
366	#546	C₂²×C₇	1	16	yes	complemented
367	D₄²	C₂²×C₇	1	16	yes	complemented
368	#544	C₂²×C₇	1	4	yes	complemented
369	#543	C₂²×C₇	1	2	yes	complemented
370	#543	C₂²×C₇	1	4	yes	complemented
371	#542	C₂²×C₇	1	16	yes	complemented
372	#540	C₂²×C₇	1	16	yes	complemented
373	#539	C₂²×C₇	1	8	yes	complemented
374	#539	C₂²×C₇	1	8	yes	complemented
375	#539	C₂²×C₇	1	16	yes	complemented
376	#539	C₂²×C₇	1	16	yes	complemented
377	#538	C₂²×C₇	1	8	yes	complemented
378	#538	C₂²×C₇	1	8	yes	complemented
379	#538	C₂²×C₇	1	8	yes	complemented
380	#538	C₂²×C₇	1	16	yes	complemented
381	#537	C₂²×C₇	1	4	yes	complemented
382	#536	C₂²×C₇	1	8	yes	complemented
383	#535	C₂²×C₇	1	4	yes	complemented
384	#534	C₂²×C₇	1	4	yes	—
385	#534	C₂²×C₇	1	4	yes	complemented
386	#534	C₂²×C₇	1	2	yes	complemented
387	#534	C₂²×C₇	1	4	yes	complemented
388	#534	C₂²×C₇	1	8	yes	complemented
389	#529	C₂²×C₇	1	16	yes	complemented
390	#525	C₂²×C₇	1	8	yes	complemented
391	#525	C₂²×C₇	1	4	yes	complemented
392	#525	C₂²×C₇	1	8	yes	complemented
393	#525	C₂²×C₇	1	8	yes	complemented
394	#525	C₂²×C₇	1	8	yes	complemented
395	#525	C₂²×C₇	1	8	yes	complemented
396	#525	C₂²×C₇	1	8	yes	complemented
397	C₂×#123	C₂²×C₇	1	4	yes	complemented
398	C₂×#123	C₂²×C₇	1	8	yes	complemented
399	C₂×#123	C₂²×C₇	1	4	yes	complemented
400	C₂×#123	C₂²×C₇	1	8	yes	complemented
401	C₂×#123	C₂²×C₇	1	4	yes	complemented
402	C₂×#123	C₂²×C₇	1	8	yes	complemented
403	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
404	C₂×#121	C₂²×C₇	1	4	yes	complemented
405	C₂×#120	C₂²×C₇	1	4	yes	complemented
406	C₂×#120	C₂²×C₇	1	4	yes	complemented
407	#520	C₂²×C₇	1	8	yes	complemented
408	#518	C₂²×C₇	1	2	yes	complemented
409	#518	C₂²×C₇	1	4	yes	complemented
410	#518	C₂²×C₇	1	8	yes	complemented
411	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
412	C₂×#117	C₂²×C₇	1	2	yes	complemented
413	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
414	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
415	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	4	no	—
418	C₂³×C₇	—	2	8	no	—
419	C₂³×C₇	—	2	2	no	—
420	C₂³×C₇	—	2	8	no	—
421	C₂³×C₇	—	2	8	no	—
422	C₂³×C₇	—	2	4	no	—
423	C₂³×C₇	—	2	8	no	—
424	C₂³×C₇	—	4	2	no	—
425	C₂³×C₇	—	4	4	no	—
426	C₂³×C₇	—	4	2	no	—
427	C₂³×C₇	—	4	4	no	—
428	C₂³×C₇	—	4	8	no	—
429	C₂³×C₇	—	4	4	no	—
430	C₂³×C₇	—	4	4	no	—
431	C₂³×C₇	—	4	4	no	—
432	C₂³×C₇	—	4	8	no	—
433	C₂³×C₇	—	4	16	no	—
434	C₂³×C₇	—	8	8	no	—
435	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
436	C₂³×C₇	C₂⁵	1	4	yes	—
437	C₂³×C₇	C₂⁵	1	2	yes	—
438	C₂³×C₇	C₂⁵	1	8	yes	—
439	C₂³×C₇	C₂⁵	1	2	yes	—
440	C₂³×C₇	C₂⁵	1	1	yes	characteristic
441	C₂³×C₇	C₂⁵	1	2	yes	—
442	C₇×Q₈	—	4	8	no	—
443	C₇×Q₈	—	4	8	no	—
444	C₇×Q₈	—	4	4	no	—
445	C₇×D₄	—	2	16	no	—
446	C₇×D₄	—	2	16	no	—
447	C₇×D₄	—	2	16	no	—
448	C₇×D₄	—	2	32	no	—
449	C₇×D₄	—	4	8	no	—
450	C₇×D₄	—	4	4	no	—
451	C₇×D₄	—	4	8	no	—
452	C₇×D₄	—	4	16	no	—
453	C₇×D₄	—	4	16	no	—
454	C₇×D₄	—	4	8	no	—
455	C₇×D₄	—	4	8	no	—
456	C₂×C₄×C₇	—	2	4	no	—
457	C₂×C₄×C₇	—	2	4	no	—
458	C₂×C₄×C₇	—	2	8	no	—
459	C₂×C₄×C₇	—	2	8	no	—
460	C₂×C₄×C₇	—	2	4	no	—
461	C₂×C₄×C₇	—	2	8	no	—
462	C₂×C₄×C₇	—	2	8	no	—
463	C₂×C₄×C₇	—	4	2	no	—
464	C₂×C₄×C₇	—	4	2	no	—
465	C₂×C₄×C₇	—	4	4	no	—
466	C₂×C₄×C₇	—	4	4	no	—
467	C₂×C₄×C₇	—	4	2	no	—
468	C₂×C₄×C₇	—	4	2	no	—
469	C₂×C₄×C₇	—	4	4	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	—	4	4	no	—
472	C₂×C₄×C₇	—	4	16	no	—
473	C₂×C₄×C₇	—	4	8	no	—
474	C₂×C₄×C₇	—	4	8	no	—
475	C₂×C₄×C₇	—	4	8	no	—
476	C₂×C₄×C₇	—	4	4	no	—
477	C₂×C₄×C₇	—	4	16	no	—
478	C₂×C₄×C₇	C₂⁵	1	16	yes	—
479	C₂×C₄×C₇	C₂⁵	1	4	yes	—
480	C₂×C₄×C₇	C₂⁵	1	8	yes	—
481	C₂×C₄×C₇	C₂⁵	1	8	yes	—
482	C₂×C₄×C₇	C₂⁵	1	4	yes	—
483	C₂×C₄×C₇	C₂⁵	1	4	yes	—
484	C₂⁵	C₂³×C₇	1	1	yes	characteristic
485	C₂⁵	C₂³×C₇	1	1	yes	characteristic
486	H(5,𝔽₂)	—	4	8	no	—
487	C₂×#41	—	4	8	no	—
488	C₂×#41	C₂³×C₇	1	8	yes	—
489	C₂×#41	C₂³×C₇	1	8	yes	—
490	C₂×#41	C₂³×C₇	1	4	yes	—
491	C₂×#41	C₂³×C₇	1	8	yes	—
492	C₂×#41	C₂³×C₇	1	8	yes	complemented
493	C₂²×Q₈	C₂³×C₇	1	2	yes	complemented
494	C₂²×D₄	—	4	4	no	—
495	C₂²×D₄	C₂³×C₇	1	4	yes	—
496	C₂²×D₄	C₂³×C₇	1	2	yes	—
497	C₂²×D₄	C₂³×C₇	1	8	yes	—
498	C₂²×D₄	C₂³×C₇	1	8	yes	—
499	C₂²×D₄	C₂³×C₇	1	4	yes	—
500	C₂²×D₄	C₂³×C₇	1	2	yes	—
501	C₂²×D₄	C₂³×C₇	1	8	yes	—
502	C₂²×D₄	C₂³×C₇	1	8	yes	—
503	C₂²×D₄	C₂³×C₇	1	2	yes	complemented
504	C₂³×C₄	—	4	4	no	—
505	C₂³×C₄	C₂³×C₇	1	2	yes	—
506	C₂³×C₄	C₂³×C₇	1	2	yes	—
507	C₂³×C₄	C₂³×C₇	1	2	yes	—
508	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₇	1	4	yes	—
510	C₂³×C₄	C₂³×C₇	1	4	yes	—
511	C₂³×C₄	C₂³×C₇	1	2	yes	—
512	C₂³×C₄	C₂³×C₇	1	4	yes	complemented
513	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
514	#127	C₂³×C₇	1	8	yes	—
515	#126	C₂³×C₇	1	16	yes	complemented
516	#126	C₂³×C₇	1	16	yes	complemented
517	#126	C₂³×C₇	1	16	yes	complemented
518	#126	C₂³×C₇	1	16	yes	complemented
519	#126	C₂³×C₇	1	16	yes	complemented
520	#125	C₂³×C₇	1	16	yes	complemented
521	#125	C₂³×C₇	1	16	yes	complemented
522	#125	C₂³×C₇	1	16	yes	complemented
523	#124	C₂³×C₇	1	8	yes	—
524	#124	C₂³×C₇	1	16	yes	complemented
525	#124	C₂³×C₇	1	16	yes	complemented
526	#124	C₂³×C₇	1	16	yes	complemented
527	#123	C₂³×C₇	1	8	yes	—
528	#123	C₂³×C₇	1	8	yes	—
529	#123	C₂³×C₇	1	16	yes	—
530	#123	C₂³×C₇	1	16	yes	—
531	#123	C₂³×C₇	1	8	yes	—
532	#123	C₂³×C₇	1	8	yes	—
533	#123	C₂³×C₇	1	16	yes	—
534	#123	C₂³×C₇	1	8	yes	—
535	#123	C₂³×C₇	1	8	yes	—
536	#123	C₂³×C₇	1	16	yes	—
537	#123	C₂³×C₇	1	8	yes	—
538	#123	C₂³×C₇	1	8	yes	complemented
539	#123	C₂³×C₇	1	8	yes	complemented
540	#123	C₂³×C₇	1	8	yes	complemented
541	#123	C₂³×C₇	1	16	yes	complemented
542	#123	C₂³×C₇	1	16	yes	complemented
543	#123	C₂³×C₇	1	16	yes	complemented
544	#123	C₂³×C₇	1	16	yes	complemented
545	#123	C₂³×C₇	1	16	yes	complemented
546	#123	C₂³×C₇	1	16	yes	complemented
547	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
548	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
549	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
550	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
551	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
552	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
553	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
554	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
555	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
556	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
557	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
558	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
559	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
560	#121	C₂³×C₇	1	8	yes	—
561	#121	C₂³×C₇	1	8	yes	—
562	#121	C₂³×C₇	1	8	yes	—
563	#121	C₂³×C₇	1	8	yes	—
564	#121	C₂³×C₇	1	8	yes	—
565	#121	C₂³×C₇	1	16	yes	—
566	#121	C₂³×C₇	1	16	yes	—
567	#121	C₂³×C₇	1	16	yes	—
568	#121	C₂³×C₇	1	8	yes	complemented
569	#121	C₂³×C₇	1	8	yes	complemented
570	#121	C₂³×C₇	1	16	yes	complemented
571	#121	C₂³×C₇	1	16	yes	complemented
572	#121	C₂³×C₇	1	16	yes	complemented
573	#121	C₂³×C₇	1	16	yes	complemented
574	#120	C₂³×C₇	1	8	yes	—
575	#120	C₂³×C₇	1	8	yes	—
576	#120	C₂³×C₇	1	16	yes	—
577	#120	C₂³×C₇	1	8	yes	—
578	#120	C₂³×C₇	1	16	yes	—
579	#120	C₂³×C₇	1	8	yes	—
580	#120	C₂³×C₇	1	8	yes	—
581	#120	C₂³×C₇	1	8	yes	complemented
582	#120	C₂³×C₇	1	16	yes	complemented
583	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
584	C₄×D₄	C₂³×C₇	1	16	yes	—
585	C₄×D₄	C₂³×C₇	1	16	yes	—
586	C₄×D₄	C₂³×C₇	1	16	yes	—
587	C₄×D₄	C₂³×C₇	1	16	yes	—
588	C₄×D₄	C₂³×C₇	1	16	yes	—
589	C₄×D₄	C₂³×C₇	1	16	yes	—
590	C₄×D₄	C₂³×C₇	1	16	yes	complemented
591	C₄×D₄	C₂³×C₇	1	16	yes	complemented
592	C₄×D₄	C₂³×C₇	1	16	yes	complemented
593	C₄×D₄	C₂³×C₇	1	16	yes	complemented
594	C₄×D₄	C₂³×C₇	1	16	yes	complemented
595	C₄×D₄	C₂³×C₇	1	16	yes	complemented
596	#117	C₂³×C₇	1	8	yes	—
597	#117	C₂³×C₇	1	4	yes	—
598	#117	C₂³×C₇	1	8	yes	—
599	#117	C₂³×C₇	1	8	yes	complemented
600	#117	C₂³×C₇	1	8	yes	complemented
601	#117	C₂³×C₇	1	16	yes	complemented
602	#117	C₂³×C₇	1	16	yes	complemented
603	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
608	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
609	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	complemented
622	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	complemented
623	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
624	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
625	C₂²×C₇	—	2	8	no	—
626	C₂²×C₇	—	2	2	no	—
627	C₂²×C₇	—	2	2	no	—
628	C₂²×C₇	—	2	2	no	—
629	C₂²×C₇	—	2	4	no	—
630	C₂²×C₇	—	2	2	no	—
631	C₂²×C₇	—	2	8	no	—
632	C₂²×C₇	—	2	4	no	—
633	C₂²×C₇	—	2	16	no	—
634	C₂²×C₇	—	2	8	no	—
635	C₂²×C₇	—	2	4	no	—
636	C₂²×C₇	—	4	4	no	—
637	C₂²×C₇	—	4	16	no	—
638	C₂²×C₇	—	4	4	no	—
639	C₂²×C₇	—	8	8	no	—
640	C₂²×C₇	—	8	4	no	—
641	C₂²×C₇	—	8	8	no	—
642	C₂²×C₇	—	16	4	no	—
643	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
644	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
645	C₂²×C₇	#585	1	4	yes	—
646	C₂²×C₇	C₂⁶	1	1	yes	characteristic
647	C₄×C₇	—	2	4	no	—
648	C₄×C₇	—	2	4	no	—
649	C₄×C₇	—	2	4	no	—
650	C₄×C₇	—	2	8	no	—
651	C₄×C₇	—	2	8	no	—
652	C₄×C₇	—	2	16	no	—
653	C₂⁴	—	2	4	no	—
654	C₂⁴	—	4	4	no	—
655	C₂⁴	—	4	2	no	—
656	C₂⁴	—	4	4	no	—
657	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
658	C₂⁴	C₂⁴×C₇	1	4	yes	—
659	C₂⁴	C₂⁴×C₇	1	2	yes	—
660	C₂⁴	C₂⁴×C₇	1	4	yes	—
661	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₇	1	4	yes	—
663	C₂⁴	C₂⁴×C₇	1	4	yes	—
664	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
665	#41	—	4	16	no	—
666	#41	—	4	16	no	—
667	#41	—	4	8	no	—
668	#41	—	4	16	no	—
669	#41	—	4	16	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
672	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
673	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
674	C₂×D₄	—	2	8	no	—
675	C₂×D₄	—	2	16	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	4	no	—
678	C₂×D₄	—	4	16	no	—
679	C₂×D₄	—	4	16	no	—
680	C₂×D₄	—	4	16	no	—
681	C₂×D₄	—	4	16	no	—
682	C₂×D₄	—	4	8	no	—
683	C₂×D₄	C₂⁴×C₇	1	16	yes	—
684	C₂×D₄	C₂⁴×C₇	1	8	yes	—
685	C₂×D₄	C₂⁴×C₇	1	8	yes	—
686	C₂×D₄	C₂⁴×C₇	1	8	yes	—
687	C₂×D₄	C₂⁴×C₇	1	16	yes	—
688	C₂×D₄	C₂⁴×C₇	1	16	yes	—
689	C₂×D₄	C₂⁴×C₇	1	8	yes	—
690	C₂×D₄	C₂⁴×C₇	1	8	yes	—
691	C₂×D₄	C₂⁴×C₇	1	8	yes	—
692	C₂×D₄	C₂⁴×C₇	1	8	yes	—
693	C₂×D₄	C₂⁴×C₇	1	4	yes	—
694	C₂²×C₄	—	2	8	no	—
695	C₂²×C₄	—	4	8	no	—
696	C₂²×C₄	—	4	8	no	—
697	C₂²×C₄	—	4	4	no	—
698	C₂²×C₄	—	4	4	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	4	no	—
701	C₂²×C₄	—	4	8	no	—
702	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
716	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
717	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
718	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
719	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
721	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
723	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
725	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
726	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
727	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
728	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
729	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
730	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
731	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
732	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
734	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
735	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
736	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
737	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
738	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
739	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
740	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
741	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
742	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
743	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
744	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
745	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
746	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
747	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
749	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
750	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
751	C₄²	C₂⁴×C₇	1	16	yes	—
752	C₄²	C₂⁴×C₇	1	8	yes	—
753	C₄²	C₂⁴×C₇	1	16	yes	—
754	C₂×C₇	—	2	2	no	—
755	C₂×C₇	—	2	4	no	—
756	C₂×C₇	—	2	4	no	—
757	C₂×C₇	—	4	2	no	—
758	C₂×C₇	—	4	4	no	—
759	C₂×C₇	—	4	8	no	—
760	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂×C₇	C₂×#585	1	2	yes	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	4	no	—
764	C₂³	—	2	8	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	8	no	—
767	C₂³	—	2	8	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	4	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	4	no	—
778	C₂³	—	4	8	no	—
779	C₂³	—	4	16	no	—
780	C₂³	—	8	8	no	—
781	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
782	C₂³	C₂⁵×C₇	1	4	yes	—
783	C₂³	C₂⁵×C₇	1	2	yes	—
784	C₂³	C₂⁵×C₇	1	8	yes	—
785	C₂³	C₂⁵×C₇	1	2	yes	—
786	C₂³	C₂⁵×C₇	1	1	yes	characteristic
787	C₂³	C₂⁵×C₇	1	2	yes	—
788	Q₈	—	4	8	no	—
789	Q₈	—	4	8	no	—
790	Q₈	—	4	4	no	—
791	D₄	—	2	16	no	—
792	D₄	—	2	16	no	—
793	D₄	—	2	16	no	—
794	D₄	—	2	32	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	8	no	—
798	D₄	—	4	16	no	—
799	D₄	—	4	16	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	8	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	8	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	8	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	16	no	—
819	C₂×C₄	—	4	8	no	—
820	C₂×C₄	—	4	8	no	—
821	C₂×C₄	—	4	8	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	16	no	—
824	C₂×C₄	C₂⁵×C₇	1	16	yes	—
825	C₂×C₄	C₂⁵×C₇	1	4	yes	—
826	C₂×C₄	C₂⁵×C₇	1	8	yes	—
827	C₂×C₄	C₂⁵×C₇	1	8	yes	—
828	C₂×C₄	C₂⁵×C₇	1	4	yes	—
829	C₂×C₄	C₂⁵×C₇	1	4	yes	—
830	C₇	#62820	1	1	yes	characteristic, direct product factor, Sylow
831	C₂²	—	2	8	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	8	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	16	no	—
840	C₂²	—	2	8	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	16	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	8	4	no	—
846	C₂²	—	8	8	no	—
847	C₂²	—	8	8	no	—
848	C₂²	—	16	4	no	—
849	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
850	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
851	C₂²	C₇×#585	1	4	yes	—
852	C₂²	C₂⁶×C₇	1	1	yes	characteristic
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	8	no	—
858	C₄	—	2	16	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	4	no	—
861	C₂	—	2	4	no	—
862	C₂	—	4	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	4	8	no	—
865	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
866	C₂	C₂×C₇×#585	1	2	yes	—

	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×#3535	C₂	semidirect
2. C₇×#3534	C₂	semidirect
3. C₇×#3533	C₂	semidirect
4. C₇×#3513	C₂	semidirect
5. C₇×#3492	C₂	semidirect
6. C₇×#3491	C₂	semidirect
7. C₇×#3490	C₂	semidirect
8. C₇×#3490	C₂	semidirect
9. C₇×#3485	C₂	semidirect
10. C₇×#3484	C₂	semidirect
11. C₂×C₇×#525	C₂	semidirect
12. C₂²×C₇×#123	C₂	semidirect
13. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
14. C₂²×C₇×#41	C₂²	semidirect
16. C₂⁴×C₄×C₇	C₂²	semidirect
17. C₇×#563	C₂²	semidirect
18. C₇×#562	C₂²	semidirect
19. C₇×#560	C₂²	semidirect
20. C₇×#559	C₂²	semidirect
21. C₇×#554	C₂²	semidirect
22. C₇×#553	C₂²	semidirect
23. C₇×#553	C₂²	semidirect
24. C₇×#552	C₂²	semidirect
25. C₇×#552	C₂²	semidirect
26. C₇×#551	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×#551	C₂²	semidirect
29. C₇×#551	C₂²	semidirect
30. C₇×#551	C₂²	semidirect
31. C₇×#547	C₂²	semidirect
32. C₇×#547	C₂²	semidirect
33. C₇×#546	C₂²	semidirect
34. C₇×#546	C₂²	semidirect
35. C₇×#546	C₂²	semidirect
36. C₇×#546	C₂²	semidirect
37. C₇×#546	C₂²	semidirect
38. C₇×D₄²	C₂²	semidirect
39. C₇×#544	C₂²	semidirect
40. C₇×#543	C₂²	semidirect
41. C₇×#543	C₂²	semidirect
42. C₇×#542	C₂²	semidirect
43. C₇×#540	C₂²	semidirect
44. C₇×#539	C₂²	semidirect
45. C₇×#539	C₂²	semidirect
46. C₇×#539	C₂²	semidirect
47. C₇×#539	C₂²	semidirect
48. C₇×#538	C₂²	semidirect
49. C₇×#538	C₂²	semidirect
50. C₇×#538	C₂²	semidirect
51. C₇×#538	C₂²	semidirect
52. C₇×#537	C₂²	semidirect
53. C₇×#536	C₂²	semidirect
54. C₇×#535	C₂²	semidirect
56. C₇×#534	C₂²	semidirect
57. C₇×#534	C₂²	semidirect
58. C₇×#534	C₂²	semidirect
59. C₇×#534	C₂²	semidirect
60. C₇×#529	C₂²	semidirect
61. C₇×#525	C₂²	semidirect
62. C₇×#525	C₂²	semidirect
63. C₇×#525	C₂²	semidirect
64. C₇×#525	C₂²	semidirect
65. C₇×#525	C₂²	semidirect
66. C₇×#525	C₂²	semidirect
67. C₇×#525	C₂²	semidirect
68. C₂×C₇×#123	C₂²	semidirect
69. C₂×C₇×#123	C₂²	semidirect
70. C₂×C₇×#123	C₂²	semidirect
71. C₂×C₇×#123	C₂²	semidirect
72. C₂×C₇×#123	C₂²	semidirect
73. C₂×C₇×#123	C₂²	semidirect
74. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
75. C₂×C₇×#121	C₂²	semidirect
76. C₂×C₇×#120	C₂²	semidirect
77. C₂×C₇×#120	C₂²	semidirect
78. C₇×#520	C₂²	semidirect
79. C₇×#518	C₂²	semidirect
80. C₇×#518	C₂²	semidirect
81. C₇×#518	C₂²	semidirect
82. C₂×C₄×C₇×D₄	C₂²	semidirect
83. C₂×C₇×#117	C₂²	semidirect
84. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
85. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
86. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
87. #62820	C₇	direct (N × H)
96. C₂×C₇×#41	C₂³	semidirect
97. C₂²×C₇×Q₈	C₂³	semidirect
107. C₂²×C₇×D₄	C₂³	semidirect
116. C₂³×C₄×C₇	C₂³	semidirect
117. C₇×C₄⋊Q₈	C₂³	semidirect
119. C₇×#126	C₂³	semidirect
120. C₇×#126	C₂³	semidirect
121. C₇×#126	C₂³	semidirect
122. C₇×#126	C₂³	semidirect
123. C₇×#126	C₂³	semidirect
124. C₇×#125	C₂³	semidirect
125. C₇×#125	C₂³	semidirect
126. C₇×#125	C₂³	semidirect
128. C₇×#124	C₂³	semidirect
129. C₇×#124	C₂³	semidirect
130. C₇×#124	C₂³	semidirect
142. C₇×#123	C₂³	semidirect
143. C₇×#123	C₂³	semidirect
144. C₇×#123	C₂³	semidirect
145. C₇×#123	C₂³	semidirect
146. C₇×#123	C₂³	semidirect
147. C₇×#123	C₂³	semidirect
148. C₇×#123	C₂³	semidirect
149. C₇×#123	C₂³	semidirect
150. C₇×#123	C₂³	semidirect
156. C₇×C₂²⋊Q₈	C₂³	semidirect
157. C₇×C₂²⋊Q₈	C₂³	semidirect
158. C₇×C₂²⋊Q₈	C₂³	semidirect
159. C₇×C₂²⋊Q₈	C₂³	semidirect
160. C₇×C₂²⋊Q₈	C₂³	semidirect
161. C₇×C₂²⋊Q₈	C₂³	semidirect
162. C₇×C₂²⋊Q₈	C₂³	semidirect
163. C₇×C₂²⋊Q₈	C₂³	semidirect
172. C₇×#121	C₂³	semidirect
173. C₇×#121	C₂³	semidirect
174. C₇×#121	C₂³	semidirect
175. C₇×#121	C₂³	semidirect
176. C₇×#121	C₂³	semidirect
177. C₇×#121	C₂³	semidirect
185. C₇×#120	C₂³	semidirect
186. C₇×#120	C₂³	semidirect
187. C₄×C₇×Q₈	C₂³	semidirect
194. C₄×C₇×D₄	C₂³	semidirect
195. C₄×C₇×D₄	C₂³	semidirect
196. C₄×C₇×D₄	C₂³	semidirect
197. C₄×C₇×D₄	C₂³	semidirect
198. C₄×C₇×D₄	C₂³	semidirect
199. C₄×C₇×D₄	C₂³	semidirect
203. C₇×#117	C₂³	semidirect
204. C₇×#117	C₂³	semidirect
205. C₇×#117	C₂³	semidirect
206. C₇×#117	C₂³	semidirect
211. C₂×C₇×C₄⋊C₄	C₂³	semidirect
212. C₂×C₇×C₄⋊C₄	C₂³	semidirect
213. C₂×C₇×C₄⋊C₄	C₂³	semidirect
225. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
226. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
227. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
228. C₂×C₄²×C₇	C₂³	semidirect
229. #3535	C₂×C₇	semidirect
230. #3534	C₂×C₇	semidirect
231. #3533	C₂×C₇	semidirect
232. #3513	C₂×C₇	semidirect
233. #3492	C₂×C₇	semidirect
234. #3491	C₂×C₇	semidirect
235. #3490	C₂×C₇	semidirect
236. #3490	C₂×C₇	semidirect
237. #3485	C₂×C₇	semidirect
238. #3484	C₂×C₇	semidirect
239. C₂×#525	C₂×C₇	semidirect
240. C₂²×#123	C₂×C₇	semidirect
342. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
343. C₂²×#41	C₂²×C₇	semidirect
345. C₂⁴×C₄	C₂²×C₇	semidirect
346. #563	C₂²×C₇	semidirect
347. #562	C₂²×C₇	semidirect
348. #560	C₂²×C₇	semidirect
349. #559	C₂²×C₇	semidirect
350. #554	C₂²×C₇	semidirect
351. #553	C₂²×C₇	semidirect
352. #553	C₂²×C₇	semidirect
353. #552	C₂²×C₇	semidirect
354. #552	C₂²×C₇	semidirect
355. #551	C₂²×C₇	semidirect
356. #551	C₂²×C₇	semidirect
357. #551	C₂²×C₇	semidirect
358. #551	C₂²×C₇	semidirect
359. #551	C₂²×C₇	semidirect
360. #547	C₂²×C₇	semidirect
361. #547	C₂²×C₇	semidirect
362. #546	C₂²×C₇	semidirect
363. #546	C₂²×C₇	semidirect
364. #546	C₂²×C₇	semidirect
365. #546	C₂²×C₇	semidirect
366. #546	C₂²×C₇	semidirect
367. D₄²	C₂²×C₇	semidirect
368. #544	C₂²×C₇	semidirect
369. #543	C₂²×C₇	semidirect
370. #543	C₂²×C₇	semidirect
371. #542	C₂²×C₇	semidirect
372. #540	C₂²×C₇	semidirect
373. #539	C₂²×C₇	semidirect
374. #539	C₂²×C₇	semidirect
375. #539	C₂²×C₇	semidirect
376. #539	C₂²×C₇	semidirect
377. #538	C₂²×C₇	semidirect
378. #538	C₂²×C₇	semidirect
379. #538	C₂²×C₇	semidirect
380. #538	C₂²×C₇	semidirect
381. #537	C₂²×C₇	semidirect
382. #536	C₂²×C₇	semidirect
383. #535	C₂²×C₇	semidirect
385. #534	C₂²×C₇	semidirect
386. #534	C₂²×C₇	semidirect
387. #534	C₂²×C₇	semidirect
388. #534	C₂²×C₇	semidirect
389. #529	C₂²×C₇	semidirect
390. #525	C₂²×C₇	semidirect
391. #525	C₂²×C₇	semidirect
392. #525	C₂²×C₇	semidirect
393. #525	C₂²×C₇	semidirect
394. #525	C₂²×C₇	semidirect
395. #525	C₂²×C₇	semidirect
396. #525	C₂²×C₇	semidirect
397. C₂×#123	C₂²×C₇	semidirect
398. C₂×#123	C₂²×C₇	semidirect
399. C₂×#123	C₂²×C₇	semidirect
400. C₂×#123	C₂²×C₇	semidirect
401. C₂×#123	C₂²×C₇	semidirect
402. C₂×#123	C₂²×C₇	semidirect
403. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
404. C₂×#121	C₂²×C₇	semidirect
405. C₂×#120	C₂²×C₇	semidirect
406. C₂×#120	C₂²×C₇	semidirect
407. #520	C₂²×C₇	semidirect
408. #518	C₂²×C₇	semidirect
409. #518	C₂²×C₇	semidirect
410. #518	C₂²×C₇	semidirect
411. C₂×C₄×D₄	C₂²×C₇	semidirect
412. C₂×#117	C₂²×C₇	semidirect
413. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
414. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
415. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
492. C₂×#41	C₂³×C₇	semidirect
493. C₂²×Q₈	C₂³×C₇	semidirect
503. C₂²×D₄	C₂³×C₇	semidirect
512. C₂³×C₄	C₂³×C₇	semidirect
513. C₄⋊Q₈	C₂³×C₇	semidirect
515. #126	C₂³×C₇	semidirect
516. #126	C₂³×C₇	semidirect
517. #126	C₂³×C₇	semidirect
518. #126	C₂³×C₇	semidirect
519. #126	C₂³×C₇	semidirect
520. #125	C₂³×C₇	semidirect
521. #125	C₂³×C₇	semidirect
522. #125	C₂³×C₇	semidirect
524. #124	C₂³×C₇	semidirect
525. #124	C₂³×C₇	semidirect
526. #124	C₂³×C₇	semidirect
538. #123	C₂³×C₇	semidirect
539. #123	C₂³×C₇	semidirect
540. #123	C₂³×C₇	semidirect
541. #123	C₂³×C₇	semidirect
542. #123	C₂³×C₇	semidirect
543. #123	C₂³×C₇	semidirect
544. #123	C₂³×C₇	semidirect
545. #123	C₂³×C₇	semidirect
546. #123	C₂³×C₇	semidirect
552. C₂²⋊Q₈	C₂³×C₇	semidirect
553. C₂²⋊Q₈	C₂³×C₇	semidirect
554. C₂²⋊Q₈	C₂³×C₇	semidirect
555. C₂²⋊Q₈	C₂³×C₇	semidirect
556. C₂²⋊Q₈	C₂³×C₇	semidirect
557. C₂²⋊Q₈	C₂³×C₇	semidirect
558. C₂²⋊Q₈	C₂³×C₇	semidirect
559. C₂²⋊Q₈	C₂³×C₇	semidirect
568. #121	C₂³×C₇	semidirect
569. #121	C₂³×C₇	semidirect
570. #121	C₂³×C₇	semidirect
571. #121	C₂³×C₇	semidirect
572. #121	C₂³×C₇	semidirect
573. #121	C₂³×C₇	semidirect
581. #120	C₂³×C₇	semidirect
582. #120	C₂³×C₇	semidirect
583. C₄×Q₈	C₂³×C₇	semidirect
590. C₄×D₄	C₂³×C₇	semidirect
591. C₄×D₄	C₂³×C₇	semidirect
592. C₄×D₄	C₂³×C₇	semidirect
593. C₄×D₄	C₂³×C₇	semidirect
594. C₄×D₄	C₂³×C₇	semidirect
595. C₄×D₄	C₂³×C₇	semidirect
599. #117	C₂³×C₇	semidirect
600. #117	C₂³×C₇	semidirect
601. #117	C₂³×C₇	semidirect
602. #117	C₂³×C₇	semidirect
607. C₂×C₄⋊C₄	C₂³×C₇	semidirect
608. C₂×C₄⋊C₄	C₂³×C₇	semidirect
609. C₂×C₄⋊C₄	C₂³×C₇	semidirect
621. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
622. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
623. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
624. C₂×C₄²	C₂³×C₇	semidirect
830. C₇	#62820	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×#3535	2
C₇×#3534	2
C₇×#3533	2
C₇×#3513	2
C₇×#3492	2
C₇×#3491	2
C₇×#3490	2
C₇×#3485	2
C₇×#3484	2
C₂×C₇×#525	2
C₂²×C₇×#123	2
#62820	7

Subgroups — C7×#62820 #13240036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62820 #13240036