Subgroups — C₇×#62818 #13240034

Order 1792.

8042 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3542	C₂	1	8	yes	maximal, complemented
2	C₇×#3537	C₂	1	4	yes	maximal, complemented
3	C₇×#3536	C₂	1	4	yes	maximal, complemented
4	C₇×#3534	C₂	1	8	yes	maximal, complemented
5	C₇×#3519	C₂	1	8	yes	maximal, complemented
6	C₇×#3505	C₂	1	4	yes	maximal, complemented
7	C₇×#3496	C₂	1	4	yes	maximal, complemented
8	C₇×#3494	C₂	1	4	yes	maximal, complemented
9	C₇×#3492	C₂	1	2	yes	maximal, complemented
10	C₇×#3490	C₂	1	4	yes	maximal, complemented
11	C₇×#3488	C₂	1	4	yes	maximal, complemented
12	C₇×#3484	C₂	1	2	yes	maximal, complemented
13	C₇×#3484	C₂	1	4	yes	maximal, complemented
14	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂×C₇×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂²×C₇×#41	C₂²	1	2	yes	complemented
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
21	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
22	C₇×#562	C₂²	1	16	yes	complemented
23	C₇×#560	C₂²	1	16	yes	complemented
24	C₇×#555	C₂²	1	8	yes	complemented
25	C₇×#554	C₂²	1	8	yes	complemented
26	C₇×#553	C₂²	1	8	yes	complemented
27	C₇×#553	C₂²	1	8	yes	complemented
28	C₇×#553	C₂²	1	8	yes	complemented
29	C₇×#553	C₂²	1	16	yes	complemented
30	C₇×#552	C₂²	1	8	yes	complemented
31	C₇×#551	C₂²	1	16	yes	complemented
32	C₇×#551	C₂²	1	16	yes	complemented
33	C₇×#550	C₂²	1	8	yes	complemented
34	C₇×#548	C₂²	1	8	yes	complemented
35	C₇×#547	C₂²	1	8	yes	complemented
36	C₇×#547	C₂²	1	8	yes	complemented
37	C₇×#546	C₂²	1	16	yes	complemented
38	C₇×#546	C₂²	1	8	yes	complemented
39	C₇×#546	C₂²	1	16	yes	complemented
40	C₇×#546	C₂²	1	8	yes	complemented
41	C₇×#546	C₂²	1	16	yes	complemented
42	C₇×#546	C₂²	1	16	yes	complemented
43	C₇×#546	C₂²	1	8	yes	complemented
44	C₇×#546	C₂²	1	16	yes	complemented
45	C₇×D₄²	C₂²	1	16	yes	complemented
46	C₇×D₄²	C₂²	1	8	yes	complemented
47	C₇×D₄²	C₂²	1	8	yes	complemented
48	C₇×D₄²	C₂²	1	16	yes	complemented
49	C₇×D₄²	C₂²	1	8	yes	complemented
50	C₇×#544	C₂²	1	2	yes	complemented
51	C₇×#543	C₂²	1	4	yes	complemented
52	C₇×#542	C₂²	1	8	yes	complemented
53	C₇×#540	C₂²	1	8	yes	complemented
54	C₇×#540	C₂²	1	16	yes	complemented
55	C₇×#539	C₂²	1	8	yes	complemented
56	C₇×#539	C₂²	1	8	yes	complemented
57	C₇×#538	C₂²	1	8	yes	complemented
58	C₇×#538	C₂²	1	8	yes	complemented
59	C₇×#538	C₂²	1	8	yes	complemented
60	C₇×#538	C₂²	1	16	yes	complemented
61	C₇×#537	C₂²	1	2	yes	complemented
62	C₇×#537	C₂²	1	8	yes	complemented
63	C₇×#537	C₂²	1	8	yes	complemented
64	C₇×#535	C₂²	1	4	yes	complemented
65	C₇×#535	C₂²	1	8	yes	complemented
66	C₇×#535	C₂²	1	8	yes	complemented
67	C₇×#534	C₂²	1	8	yes	complemented
68	C₇×#534	C₂²	1	8	yes	complemented
69	C₇×#534	C₂²	1	8	yes	complemented
70	C₇×#534	C₂²	1	4	yes	complemented
71	C₇×#534	C₂²	1	8	yes	complemented
72	C₇×#532	C₂²	1	8	yes	complemented
73	C₇×#529	C₂²	1	8	yes	complemented
74	C₇×#525	C₂²	1	4	yes	complemented
75	C₇×#525	C₂²	1	4	yes	complemented
76	C₇×#525	C₂²	1	8	yes	complemented
77	C₇×#525	C₂²	1	4	yes	complemented
78	C₇×#525	C₂²	1	4	yes	complemented
79	C₇×#525	C₂²	1	4	yes	complemented
80	C₇×#525	C₂²	1	4	yes	complemented
81	C₇×#525	C₂²	1	4	yes	complemented
82	C₇×#525	C₂²	1	4	yes	complemented
83	C₇×#525	C₂²	1	8	yes	complemented
84	C₂×C₇×#123	C₂²	1	4	yes	complemented
85	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
86	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
87	C₂×C₇×#121	C₂²	1	4	yes	complemented
88	C₂×C₇×#121	C₂²	1	4	yes	complemented
89	C₂×C₇×#121	C₂²	1	4	yes	complemented
90	C₂×C₇×#121	C₂²	1	4	yes	complemented
91	C₂×C₇×#121	C₂²	1	4	yes	complemented
92	C₂×C₇×#121	C₂²	1	4	yes	complemented
93	C₂×C₇×#121	C₂²	1	2	yes	complemented
94	C₂×C₇×#121	C₂²	1	2	yes	complemented
95	C₂×C₇×#121	C₂²	1	8	yes	complemented
96	C₂×C₇×#120	C₂²	1	4	yes	complemented
97	C₂×C₇×#120	C₂²	1	8	yes	complemented
98	C₇×#520	C₂²	1	4	yes	complemented
99	C₇×#518	C₂²	1	2	yes	complemented
100	C₇×#518	C₂²	1	4	yes	complemented
101	C₇×#518	C₂²	1	8	yes	complemented
102	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
103	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
104	C₂×C₇×#117	C₂²	1	2	yes	complemented
105	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	#62818	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂⁵×C₇	C₂³	1	2	yes	—
110	C₇×H(5,𝔽₂)	—	4	16	no	—
111	C₇×H(5,𝔽₂)	—	4	8	no	—
112	C₂×C₇×#41	—	4	8	no	—
113	C₂×C₇×#41	C₂³	1	4	yes	—
114	C₂×C₇×#41	C₂³	1	4	yes	—
115	C₂×C₇×#41	C₂³	1	8	yes	—
116	C₂×C₇×#41	C₂³	1	4	yes	complemented
117	C₂×C₇×#41	C₂³	1	4	yes	complemented
118	C₂×C₇×#41	C₂³	1	8	yes	complemented
119	C₂×C₇×#41	C₂³	1	16	yes	complemented
120	C₂²×C₇×Q₈	C₂³	1	2	yes	complemented
121	C₂²×C₇×D₄	—	4	4	no	—
122	C₂²×C₇×D₄	—	4	8	no	—
123	C₂²×C₇×D₄	C₂³	1	4	yes	—
124	C₂²×C₇×D₄	C₂³	1	2	yes	—
125	C₂²×C₇×D₄	C₂³	1	4	yes	—
126	C₂²×C₇×D₄	C₂³	1	2	yes	—
127	C₂²×C₇×D₄	C₂³	1	4	yes	—
128	C₂²×C₇×D₄	C₂³	1	4	yes	—
129	C₂²×C₇×D₄	C₂³	1	4	yes	—
130	C₂²×C₇×D₄	C₂³	1	8	yes	—
131	C₂²×C₇×D₄	C₂³	1	8	yes	—
132	C₂²×C₇×D₄	C₂³	1	4	yes	—
133	C₂²×C₇×D₄	C₂³	1	8	yes	—
134	C₂²×C₇×D₄	C₂³	1	8	yes	—
135	C₂²×C₇×D₄	C₂³	1	4	yes	—
136	C₂²×C₇×D₄	C₂³	1	8	yes	—
137	C₂²×C₇×D₄	C₂³	1	2	yes	complemented
138	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
139	C₂²×C₇×D₄	C₂³	1	8	yes	complemented
140	C₂³×C₄×C₇	—	4	4	no	—
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₇	C₂³	1	4	yes	complemented
151	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
152	C₇×#127	C₂³	1	8	yes	complemented
153	C₇×#127	C₂³	1	16	yes	complemented
154	C₇×#126	C₂³	1	16	yes	complemented
155	C₇×#126	C₂³	1	16	yes	complemented
156	C₇×#126	C₂³	1	16	yes	complemented
157	C₇×#125	C₂³	1	8	yes	complemented
158	C₇×#125	C₂³	1	16	yes	complemented
159	C₇×#124	C₂³	1	8	yes	complemented
160	C₇×#124	C₂³	1	16	yes	complemented
161	C₇×#124	C₂³	1	16	yes	complemented
162	C₇×#124	C₂³	1	16	yes	complemented
163	C₇×#123	C₂³	1	8	yes	—
164	C₇×#123	C₂³	1	8	yes	—
165	C₇×#123	C₂³	1	16	yes	—
166	C₇×#123	C₂³	1	8	yes	complemented
167	C₇×#123	C₂³	1	8	yes	complemented
168	C₇×#123	C₂³	1	16	yes	complemented
169	C₇×#123	C₂³	1	16	yes	complemented
170	C₇×#123	C₂³	1	16	yes	complemented
171	C₇×#123	C₂³	1	16	yes	complemented
172	C₇×#123	C₂³	1	16	yes	complemented
173	C₇×#123	C₂³	1	16	yes	complemented
174	C₇×#123	C₂³	1	16	yes	complemented
175	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
176	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
182	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
183	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
184	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
185	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
186	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
187	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
188	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
189	C₇×#121	C₂³	1	8	yes	—
190	C₇×#121	C₂³	1	8	yes	—
191	C₇×#121	C₂³	1	8	yes	—
192	C₇×#121	C₂³	1	8	yes	—
193	C₇×#121	C₂³	1	8	yes	—
194	C₇×#121	C₂³	1	8	yes	—
195	C₇×#121	C₂³	1	8	yes	—
196	C₇×#121	C₂³	1	8	yes	—
197	C₇×#121	C₂³	1	4	yes	—
198	C₇×#121	C₂³	1	4	yes	—
199	C₇×#121	C₂³	1	4	yes	—
200	C₇×#121	C₂³	1	4	yes	—
201	C₇×#121	C₂³	1	8	yes	—
202	C₇×#121	C₂³	1	8	yes	—
203	C₇×#121	C₂³	1	4	yes	complemented
204	C₇×#121	C₂³	1	4	yes	complemented
205	C₇×#121	C₂³	1	4	yes	complemented
206	C₇×#121	C₂³	1	4	yes	complemented
207	C₇×#121	C₂³	1	16	yes	complemented
208	C₇×#121	C₂³	1	8	yes	complemented
209	C₇×#121	C₂³	1	8	yes	complemented
210	C₇×#121	C₂³	1	16	yes	complemented
211	C₇×#121	C₂³	1	8	yes	complemented
212	C₇×#121	C₂³	1	16	yes	complemented
213	C₇×#121	C₂³	1	16	yes	complemented
214	C₇×#121	C₂³	1	16	yes	complemented
215	C₇×#121	C₂³	1	16	yes	complemented
216	C₇×#121	C₂³	1	16	yes	complemented
217	C₇×#121	C₂³	1	16	yes	complemented
218	C₇×#121	C₂³	1	16	yes	complemented
219	C₇×#121	C₂³	1	16	yes	complemented
220	C₇×#120	C₂³	1	8	yes	—
221	C₇×#120	C₂³	1	8	yes	—
222	C₇×#120	C₂³	1	8	yes	—
223	C₇×#120	C₂³	1	8	yes	—
224	C₇×#120	C₂³	1	16	yes	—
225	C₇×#120	C₂³	1	16	yes	—
226	C₇×#120	C₂³	1	16	yes	—
227	C₇×#120	C₂³	1	16	yes	complemented
228	C₇×#120	C₂³	1	16	yes	complemented
229	C₇×#120	C₂³	1	16	yes	complemented
230	C₇×#120	C₂³	1	16	yes	complemented
231	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
232	C₄×C₇×D₄	C₂³	1	8	yes	—
233	C₄×C₇×D₄	C₂³	1	8	yes	—
234	C₄×C₇×D₄	C₂³	1	8	yes	—
235	C₄×C₇×D₄	C₂³	1	8	yes	—
236	C₄×C₇×D₄	C₂³	1	16	yes	—
237	C₄×C₇×D₄	C₂³	1	16	yes	—
238	C₄×C₇×D₄	C₂³	1	8	yes	complemented
239	C₄×C₇×D₄	C₂³	1	8	yes	complemented
240	C₄×C₇×D₄	C₂³	1	8	yes	complemented
241	C₄×C₇×D₄	C₂³	1	8	yes	complemented
242	C₄×C₇×D₄	C₂³	1	16	yes	complemented
243	C₄×C₇×D₄	C₂³	1	16	yes	complemented
244	C₄×C₇×D₄	C₂³	1	16	yes	complemented
245	C₄×C₇×D₄	C₂³	1	8	yes	complemented
246	C₄×C₇×D₄	C₂³	1	16	yes	complemented
247	C₄×C₇×D₄	C₂³	1	8	yes	complemented
248	C₄×C₇×D₄	C₂³	1	8	yes	complemented
249	C₇×#117	C₂³	1	4	yes	—
250	C₇×#117	C₂³	1	4	yes	—
251	C₇×#117	C₂³	1	8	yes	—
252	C₇×#117	C₂³	1	4	yes	complemented
253	C₇×#117	C₂³	1	4	yes	complemented
254	C₇×#117	C₂³	1	16	yes	complemented
255	C₇×#117	C₂³	1	8	yes	complemented
256	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
259	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
260	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
261	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
262	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
263	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
264	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
265	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
266	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
267	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
268	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
269	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
270	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
271	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
272	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
273	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
274	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
275	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	complemented
276	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	complemented
277	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
278	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
279	#3542	C₂×C₇	1	8	yes	complemented
280	#3537	C₂×C₇	1	4	yes	complemented
281	#3536	C₂×C₇	1	4	yes	complemented
282	#3534	C₂×C₇	1	8	yes	complemented
283	#3519	C₂×C₇	1	8	yes	complemented
284	#3505	C₂×C₇	1	4	yes	complemented
285	#3496	C₂×C₇	1	4	yes	complemented
286	#3494	C₂×C₇	1	4	yes	complemented
287	#3492	C₂×C₇	1	2	yes	complemented
288	#3490	C₂×C₇	1	4	yes	complemented
289	#3488	C₂×C₇	1	4	yes	complemented
290	#3484	C₂×C₇	1	2	yes	complemented
291	#3484	C₂×C₇	1	4	yes	complemented
292	C₂×#525	C₂×C₇	1	2	yes	complemented
293	C₂²×#121	C₂×C₇	1	1	yes	characteristic, complemented
294	C₂⁴×C₇	—	2	4	no	—
295	C₂⁴×C₇	—	4	2	no	—
296	C₂⁴×C₇	—	4	2	no	—
297	C₂⁴×C₇	—	4	4	no	—
298	C₂⁴×C₇	—	4	4	no	—
299	C₂⁴×C₇	—	4	4	no	—
300	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
301	C₂⁴×C₇	C₂⁴	1	2	yes	—
302	C₂⁴×C₇	C₂⁴	1	2	yes	—
303	C₂⁴×C₇	C₂⁴	1	4	yes	—
304	C₂⁴×C₇	C₂⁴	1	4	yes	—
305	C₂⁴×C₇	C₂⁴	1	4	yes	—
306	C₂⁴×C₇	C₂⁴	1	4	yes	—
307	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
308	C₂⁴×C₇	C₂⁴	1	8	yes	—
309	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
310	C₇×#41	—	2	16	no	—
311	C₇×#41	—	4	8	no	—
312	C₇×#41	—	4	8	no	—
313	C₇×#41	—	4	16	no	—
314	C₇×#41	—	4	32	no	—
315	C₇×#41	—	4	8	no	—
316	C₇×#41	—	4	16	no	—
317	C₂×C₇×Q₈	—	4	4	no	—
318	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
319	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
320	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
321	C₂×C₇×D₄	—	2	16	no	—
322	C₂×C₇×D₄	—	2	16	no	—
323	C₂×C₇×D₄	—	2	8	no	—
324	C₂×C₇×D₄	—	4	8	no	—
325	C₂×C₇×D₄	—	4	8	no	—
326	C₂×C₇×D₄	—	4	4	no	—
327	C₂×C₇×D₄	—	4	16	no	—
328	C₂×C₇×D₄	—	4	4	no	—
329	C₂×C₇×D₄	—	4	8	no	—
330	C₂×C₇×D₄	—	4	16	no	—
331	C₂×C₇×D₄	—	4	16	no	—
332	C₂×C₇×D₄	—	4	8	no	—
333	C₂×C₇×D₄	—	4	16	no	—
334	C₂×C₇×D₄	—	4	8	no	—
335	C₂×C₇×D₄	—	4	16	no	—
336	C₂×C₇×D₄	—	4	16	no	—
337	C₂×C₇×D₄	—	4	32	no	—
338	C₂×C₇×D₄	C₂⁴	1	8	yes	—
339	C₂×C₇×D₄	C₂⁴	1	8	yes	—
340	C₂×C₇×D₄	C₂⁴	1	8	yes	—
341	C₂×C₇×D₄	C₂⁴	1	8	yes	—
342	C₂×C₇×D₄	C₂⁴	1	16	yes	—
343	C₂×C₇×D₄	C₂⁴	1	8	yes	—
344	C₂×C₇×D₄	C₂⁴	1	4	yes	—
345	C₂×C₇×D₄	C₂⁴	1	16	yes	—
346	C₂×C₇×D₄	C₂⁴	1	8	yes	—
347	C₂×C₇×D₄	C₂⁴	1	8	yes	—
348	C₂×C₇×D₄	C₂⁴	1	16	yes	—
349	C₂×C₇×D₄	C₂⁴	1	16	yes	—
350	C₂×C₇×D₄	C₂⁴	1	4	yes	—
351	C₂×C₇×D₄	C₂⁴	1	8	yes	—
352	C₂×C₇×D₄	C₂⁴	1	8	yes	—
353	C₂×C₇×D₄	C₂⁴	1	16	yes	—
354	C₂²×C₄×C₇	—	2	4	no	—
355	C₂²×C₄×C₇	—	2	8	no	—
356	C₂²×C₄×C₇	—	4	4	no	—
357	C₂²×C₄×C₇	—	4	4	no	—
358	C₂²×C₄×C₇	—	4	4	no	—
359	C₂²×C₄×C₇	—	4	4	no	—
360	C₂²×C₄×C₇	—	4	8	no	—
361	C₂²×C₄×C₇	—	4	4	no	—
362	C₂²×C₄×C₇	—	4	2	no	—
363	C₂²×C₄×C₇	—	4	4	no	—
364	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
373	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
376	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
384	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
388	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
389	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
392	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
393	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
394	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
395	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
396	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
397	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
398	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
399	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
400	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
401	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
402	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
403	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
404	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
405	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
406	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
407	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
408	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
409	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
410	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
411	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
412	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
413	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
415	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
416	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
417	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
418	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
419	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
420	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
421	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
422	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
423	C₄²×C₇	C₂⁴	1	8	yes	—
424	C₄²×C₇	C₂⁴	1	8	yes	—
425	C₄²×C₇	C₂⁴	1	16	yes	—
426	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	complemented
427	C₂×H(5,𝔽₂)	C₂²×C₇	1	4	yes	complemented
428	C₂²×#41	C₂²×C₇	1	2	yes	complemented
429	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
430	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
431	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
432	#562	C₂²×C₇	1	16	yes	complemented
433	#560	C₂²×C₇	1	16	yes	complemented
434	#555	C₂²×C₇	1	8	yes	complemented
435	#554	C₂²×C₇	1	8	yes	complemented
436	#553	C₂²×C₇	1	8	yes	complemented
437	#553	C₂²×C₇	1	8	yes	complemented
438	#553	C₂²×C₇	1	8	yes	complemented
439	#553	C₂²×C₇	1	16	yes	complemented
440	#552	C₂²×C₇	1	8	yes	complemented
441	#551	C₂²×C₇	1	16	yes	complemented
442	#551	C₂²×C₇	1	16	yes	complemented
443	#550	C₂²×C₇	1	8	yes	complemented
444	#548	C₂²×C₇	1	8	yes	complemented
445	#547	C₂²×C₇	1	8	yes	complemented
446	#547	C₂²×C₇	1	8	yes	complemented
447	#546	C₂²×C₇	1	16	yes	complemented
448	#546	C₂²×C₇	1	8	yes	complemented
449	#546	C₂²×C₇	1	16	yes	complemented
450	#546	C₂²×C₇	1	8	yes	complemented
451	#546	C₂²×C₇	1	16	yes	complemented
452	#546	C₂²×C₇	1	16	yes	complemented
453	#546	C₂²×C₇	1	8	yes	complemented
454	#546	C₂²×C₇	1	16	yes	complemented
455	D₄²	C₂²×C₇	1	16	yes	complemented
456	D₄²	C₂²×C₇	1	8	yes	complemented
457	D₄²	C₂²×C₇	1	8	yes	complemented
458	D₄²	C₂²×C₇	1	16	yes	complemented
459	D₄²	C₂²×C₇	1	8	yes	complemented
460	#544	C₂²×C₇	1	2	yes	complemented
461	#543	C₂²×C₇	1	4	yes	complemented
462	#542	C₂²×C₇	1	8	yes	complemented
463	#540	C₂²×C₇	1	8	yes	complemented
464	#540	C₂²×C₇	1	16	yes	complemented
465	#539	C₂²×C₇	1	8	yes	complemented
466	#539	C₂²×C₇	1	8	yes	complemented
467	#538	C₂²×C₇	1	8	yes	complemented
468	#538	C₂²×C₇	1	8	yes	complemented
469	#538	C₂²×C₇	1	8	yes	complemented
470	#538	C₂²×C₇	1	16	yes	complemented
471	#537	C₂²×C₇	1	2	yes	complemented
472	#537	C₂²×C₇	1	8	yes	complemented
473	#537	C₂²×C₇	1	8	yes	complemented
474	#535	C₂²×C₇	1	4	yes	complemented
475	#535	C₂²×C₇	1	8	yes	complemented
476	#535	C₂²×C₇	1	8	yes	complemented
477	#534	C₂²×C₇	1	8	yes	complemented
478	#534	C₂²×C₇	1	8	yes	complemented
479	#534	C₂²×C₇	1	8	yes	complemented
480	#534	C₂²×C₇	1	4	yes	complemented
481	#534	C₂²×C₇	1	8	yes	complemented
482	#532	C₂²×C₇	1	8	yes	complemented
483	#529	C₂²×C₇	1	8	yes	complemented
484	#525	C₂²×C₇	1	4	yes	complemented
485	#525	C₂²×C₇	1	4	yes	complemented
486	#525	C₂²×C₇	1	8	yes	complemented
487	#525	C₂²×C₇	1	4	yes	complemented
488	#525	C₂²×C₇	1	4	yes	complemented
489	#525	C₂²×C₇	1	4	yes	complemented
490	#525	C₂²×C₇	1	4	yes	complemented
491	#525	C₂²×C₇	1	4	yes	complemented
492	#525	C₂²×C₇	1	4	yes	complemented
493	#525	C₂²×C₇	1	8	yes	complemented
494	C₂×#123	C₂²×C₇	1	4	yes	complemented
495	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
496	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
497	C₂×#121	C₂²×C₇	1	4	yes	complemented
498	C₂×#121	C₂²×C₇	1	4	yes	complemented
499	C₂×#121	C₂²×C₇	1	4	yes	complemented
500	C₂×#121	C₂²×C₇	1	4	yes	complemented
501	C₂×#121	C₂²×C₇	1	4	yes	complemented
502	C₂×#121	C₂²×C₇	1	4	yes	complemented
503	C₂×#121	C₂²×C₇	1	2	yes	complemented
504	C₂×#121	C₂²×C₇	1	2	yes	complemented
505	C₂×#121	C₂²×C₇	1	8	yes	complemented
506	C₂×#120	C₂²×C₇	1	4	yes	complemented
507	C₂×#120	C₂²×C₇	1	8	yes	complemented
508	#520	C₂²×C₇	1	4	yes	complemented
509	#518	C₂²×C₇	1	2	yes	complemented
510	#518	C₂²×C₇	1	4	yes	complemented
511	#518	C₂²×C₇	1	8	yes	complemented
512	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
513	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
514	C₂×#117	C₂²×C₇	1	2	yes	complemented
515	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
517	C₂³×C₇	—	2	2	no	—
518	C₂³×C₇	—	2	2	no	—
519	C₂³×C₇	—	2	2	no	—
520	C₂³×C₇	—	2	4	no	—
521	C₂³×C₇	—	2	4	no	—
522	C₂³×C₇	—	2	4	no	—
523	C₂³×C₇	—	2	2	no	—
524	C₂³×C₇	—	2	4	no	—
525	C₂³×C₇	—	2	8	no	—
526	C₂³×C₇	—	2	8	no	—
527	C₂³×C₇	—	2	8	no	—
528	C₂³×C₇	—	2	8	no	—
529	C₂³×C₇	—	4	1	no	—
530	C₂³×C₇	—	4	2	no	—
531	C₂³×C₇	—	4	1	no	—
532	C₂³×C₇	—	4	1	no	—
533	C₂³×C₇	—	4	2	no	—
534	C₂³×C₇	—	4	1	no	—
535	C₂³×C₇	—	4	4	no	—
536	C₂³×C₇	—	4	4	no	—
537	C₂³×C₇	—	4	4	no	—
538	C₂³×C₇	—	4	4	no	—
539	C₂³×C₇	—	4	4	no	—
540	C₂³×C₇	—	4	4	no	—
541	C₂³×C₇	—	4	4	no	—
542	C₂³×C₇	—	4	4	no	—
543	C₂³×C₇	—	4	8	no	—
544	C₂³×C₇	—	4	8	no	—
545	C₂³×C₇	—	4	8	no	—
546	C₂³×C₇	—	4	16	no	—
547	C₂³×C₇	—	8	16	no	—
548	C₂³×C₇	H(5,𝔽₂)	1	4	yes	complemented
549	C₂³×C₇	C₂⁵	1	8	yes	—
550	C₂³×C₇	C₂⁵	1	2	yes	—
551	C₂³×C₇	C₂⁵	1	8	yes	—
552	C₂³×C₇	C₂⁵	1	1	yes	characteristic
553	C₂³×C₇	C₂⁵	1	1	yes	characteristic
554	C₂³×C₇	C₂⁵	1	2	yes	—
555	C₂³×C₇	C₂⁵	1	1	yes	characteristic
556	C₇×Q₈	—	2	8	no	—
557	C₇×Q₈	—	4	4	no	—
558	C₇×Q₈	—	4	8	no	—
559	C₇×D₄	—	2	32	no	—
560	C₇×D₄	—	2	16	no	—
561	C₇×D₄	—	2	16	no	—
562	C₇×D₄	—	2	16	no	—
563	C₇×D₄	—	2	16	no	—
564	C₇×D₄	—	2	16	no	—
565	C₇×D₄	—	2	8	no	—
566	C₇×D₄	—	4	8	no	—
567	C₇×D₄	—	4	16	no	—
568	C₇×D₄	—	4	8	no	—
569	C₇×D₄	—	4	16	no	—
570	C₇×D₄	—	4	16	no	—
571	C₇×D₄	—	4	16	no	—
572	C₇×D₄	—	4	8	no	—
573	C₇×D₄	—	4	4	no	—
574	C₇×D₄	—	4	8	no	—
575	C₂×C₄×C₇	—	2	2	no	—
576	C₂×C₄×C₇	—	2	4	no	—
577	C₂×C₄×C₇	—	2	8	no	—
578	C₂×C₄×C₇	—	2	8	no	—
579	C₂×C₄×C₇	—	2	4	no	—
580	C₂×C₄×C₇	—	2	4	no	—
581	C₂×C₄×C₇	—	2	4	no	—
582	C₂×C₄×C₇	—	2	4	no	—
583	C₂×C₄×C₇	—	2	4	no	—
584	C₂×C₄×C₇	—	2	4	no	—
585	C₂×C₄×C₇	—	2	16	no	—
586	C₂×C₄×C₇	—	4	1	no	—
587	C₂×C₄×C₇	—	4	2	no	—
588	C₂×C₄×C₇	—	4	2	no	—
589	C₂×C₄×C₇	—	4	2	no	—
590	C₂×C₄×C₇	—	4	2	no	—
591	C₂×C₄×C₇	—	4	2	no	—
592	C₂×C₄×C₇	—	4	1	no	—
593	C₂×C₄×C₇	—	4	4	no	—
594	C₂×C₄×C₇	—	4	4	no	—
595	C₂×C₄×C₇	—	4	4	no	—
596	C₂×C₄×C₇	—	4	8	no	—
597	C₂×C₄×C₇	—	4	4	no	—
598	C₂×C₄×C₇	—	4	8	no	—
599	C₂×C₄×C₇	—	4	16	no	—
600	C₂×C₄×C₇	—	4	8	no	—
601	C₂×C₄×C₇	—	4	8	no	—
602	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	complemented
603	C₂×C₄×C₇	C₂⁵	1	8	yes	—
604	C₂×C₄×C₇	C₂⁵	1	2	yes	—
605	C₂×C₄×C₇	C₂⁵	1	8	yes	—
606	C₂×C₄×C₇	C₂⁵	1	8	yes	—
607	C₂×C₄×C₇	C₂⁵	1	8	yes	—
608	C₂×C₄×C₇	C₂⁵	1	2	yes	—
609	C₂×C₄×C₇	C₂⁵	1	2	yes	—
610	C₂×C₄×C₇	C₂⁵	1	2	yes	—
611	C₂⁵	C₂³×C₇	1	1	yes	characteristic
612	C₂⁵	C₂³×C₇	1	2	yes	—
613	H(5,𝔽₂)	—	4	16	no	—
614	H(5,𝔽₂)	—	4	8	no	—
615	C₂×#41	—	4	8	no	—
616	C₂×#41	C₂³×C₇	1	4	yes	—
617	C₂×#41	C₂³×C₇	1	4	yes	—
618	C₂×#41	C₂³×C₇	1	8	yes	—
619	C₂×#41	C₂³×C₇	1	4	yes	complemented
620	C₂×#41	C₂³×C₇	1	4	yes	complemented
621	C₂×#41	C₂³×C₇	1	8	yes	complemented
622	C₂×#41	C₂³×C₇	1	16	yes	complemented
623	C₂²×Q₈	C₂³×C₇	1	2	yes	complemented
624	C₂²×D₄	—	4	4	no	—
625	C₂²×D₄	—	4	8	no	—
626	C₂²×D₄	C₂³×C₇	1	4	yes	—
627	C₂²×D₄	C₂³×C₇	1	4	yes	—
628	C₂²×D₄	C₂³×C₇	1	2	yes	—
629	C₂²×D₄	C₂³×C₇	1	4	yes	—
630	C₂²×D₄	C₂³×C₇	1	8	yes	—
631	C₂²×D₄	C₂³×C₇	1	4	yes	—
632	C₂²×D₄	C₂³×C₇	1	8	yes	—
633	C₂²×D₄	C₂³×C₇	1	8	yes	—
634	C₂²×D₄	C₂³×C₇	1	2	yes	—
635	C₂²×D₄	C₂³×C₇	1	4	yes	—
636	C₂²×D₄	C₂³×C₇	1	4	yes	—
637	C₂²×D₄	C₂³×C₇	1	4	yes	—
638	C₂²×D₄	C₂³×C₇	1	8	yes	—
639	C₂²×D₄	C₂³×C₇	1	8	yes	—
640	C₂²×D₄	C₂³×C₇	1	2	yes	complemented
641	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
642	C₂²×D₄	C₂³×C₇	1	8	yes	complemented
643	C₂³×C₄	—	4	4	no	—
644	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₇	1	2	yes	—
646	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₇	1	2	yes	—
648	C₂³×C₄	C₂³×C₇	1	2	yes	—
649	C₂³×C₄	C₂³×C₇	1	2	yes	—
650	C₂³×C₄	C₂³×C₇	1	2	yes	—
651	C₂³×C₄	C₂³×C₇	1	2	yes	—
652	C₂³×C₄	C₂³×C₇	1	2	yes	—
653	C₂³×C₄	C₂³×C₇	1	4	yes	complemented
654	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
655	#127	C₂³×C₇	1	8	yes	complemented
656	#127	C₂³×C₇	1	16	yes	complemented
657	#126	C₂³×C₇	1	16	yes	complemented
658	#126	C₂³×C₇	1	16	yes	complemented
659	#126	C₂³×C₇	1	16	yes	complemented
660	#125	C₂³×C₇	1	8	yes	complemented
661	#125	C₂³×C₇	1	16	yes	complemented
662	#124	C₂³×C₇	1	8	yes	complemented
663	#124	C₂³×C₇	1	16	yes	complemented
664	#124	C₂³×C₇	1	16	yes	complemented
665	#124	C₂³×C₇	1	16	yes	complemented
666	#123	C₂³×C₇	1	8	yes	—
667	#123	C₂³×C₇	1	8	yes	—
668	#123	C₂³×C₇	1	16	yes	—
669	#123	C₂³×C₇	1	8	yes	complemented
670	#123	C₂³×C₇	1	8	yes	complemented
671	#123	C₂³×C₇	1	16	yes	complemented
672	#123	C₂³×C₇	1	16	yes	complemented
673	#123	C₂³×C₇	1	16	yes	complemented
674	#123	C₂³×C₇	1	16	yes	complemented
675	#123	C₂³×C₇	1	16	yes	complemented
676	#123	C₂³×C₇	1	16	yes	complemented
677	#123	C₂³×C₇	1	16	yes	complemented
678	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
679	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
680	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
681	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
682	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
683	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
684	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
685	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
686	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
687	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
688	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
689	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
690	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
691	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
692	#121	C₂³×C₇	1	8	yes	—
693	#121	C₂³×C₇	1	8	yes	—
694	#121	C₂³×C₇	1	8	yes	—
695	#121	C₂³×C₇	1	8	yes	—
696	#121	C₂³×C₇	1	8	yes	—
697	#121	C₂³×C₇	1	8	yes	—
698	#121	C₂³×C₇	1	8	yes	—
699	#121	C₂³×C₇	1	8	yes	—
700	#121	C₂³×C₇	1	4	yes	—
701	#121	C₂³×C₇	1	4	yes	—
702	#121	C₂³×C₇	1	4	yes	—
703	#121	C₂³×C₇	1	4	yes	—
704	#121	C₂³×C₇	1	8	yes	—
705	#121	C₂³×C₇	1	8	yes	—
706	#121	C₂³×C₇	1	4	yes	complemented
707	#121	C₂³×C₇	1	4	yes	complemented
708	#121	C₂³×C₇	1	4	yes	complemented
709	#121	C₂³×C₇	1	4	yes	complemented
710	#121	C₂³×C₇	1	16	yes	complemented
711	#121	C₂³×C₇	1	8	yes	complemented
712	#121	C₂³×C₇	1	8	yes	complemented
713	#121	C₂³×C₇	1	16	yes	complemented
714	#121	C₂³×C₇	1	8	yes	complemented
715	#121	C₂³×C₇	1	16	yes	complemented
716	#121	C₂³×C₇	1	16	yes	complemented
717	#121	C₂³×C₇	1	16	yes	complemented
718	#121	C₂³×C₇	1	16	yes	complemented
719	#121	C₂³×C₇	1	16	yes	complemented
720	#121	C₂³×C₇	1	16	yes	complemented
721	#121	C₂³×C₇	1	16	yes	complemented
722	#121	C₂³×C₇	1	16	yes	complemented
723	#120	C₂³×C₇	1	8	yes	—
724	#120	C₂³×C₇	1	8	yes	—
725	#120	C₂³×C₇	1	8	yes	—
726	#120	C₂³×C₇	1	8	yes	—
727	#120	C₂³×C₇	1	16	yes	—
728	#120	C₂³×C₇	1	16	yes	—
729	#120	C₂³×C₇	1	16	yes	—
730	#120	C₂³×C₇	1	16	yes	complemented
731	#120	C₂³×C₇	1	16	yes	complemented
732	#120	C₂³×C₇	1	16	yes	complemented
733	#120	C₂³×C₇	1	16	yes	complemented
734	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
735	C₄×D₄	C₂³×C₇	1	8	yes	—
736	C₄×D₄	C₂³×C₇	1	8	yes	—
737	C₄×D₄	C₂³×C₇	1	8	yes	—
738	C₄×D₄	C₂³×C₇	1	8	yes	—
739	C₄×D₄	C₂³×C₇	1	16	yes	—
740	C₄×D₄	C₂³×C₇	1	16	yes	—
741	C₄×D₄	C₂³×C₇	1	8	yes	complemented
742	C₄×D₄	C₂³×C₇	1	8	yes	complemented
743	C₄×D₄	C₂³×C₇	1	8	yes	complemented
744	C₄×D₄	C₂³×C₇	1	8	yes	complemented
745	C₄×D₄	C₂³×C₇	1	16	yes	complemented
746	C₄×D₄	C₂³×C₇	1	16	yes	complemented
747	C₄×D₄	C₂³×C₇	1	16	yes	complemented
748	C₄×D₄	C₂³×C₇	1	8	yes	complemented
749	C₄×D₄	C₂³×C₇	1	16	yes	complemented
750	C₄×D₄	C₂³×C₇	1	8	yes	complemented
751	C₄×D₄	C₂³×C₇	1	8	yes	complemented
752	#117	C₂³×C₇	1	4	yes	—
753	#117	C₂³×C₇	1	4	yes	—
754	#117	C₂³×C₇	1	8	yes	—
755	#117	C₂³×C₇	1	4	yes	complemented
756	#117	C₂³×C₇	1	4	yes	complemented
757	#117	C₂³×C₇	1	16	yes	complemented
758	#117	C₂³×C₇	1	8	yes	complemented
759	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
762	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
763	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
764	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
765	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
766	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
767	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
768	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	complemented
779	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	complemented
780	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
781	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
782	C₂²×C₇	—	2	8	no	—
783	C₂²×C₇	—	2	2	no	—
784	C₂²×C₇	—	2	1	no	—
785	C₂²×C₇	—	2	1	no	—
786	C₂²×C₇	—	2	1	no	—
787	C₂²×C₇	—	2	1	no	—
788	C₂²×C₇	—	2	2	no	—
789	C₂²×C₇	—	2	1	no	—
790	C₂²×C₇	—	2	1	no	—
791	C₂²×C₇	—	2	2	no	—
792	C₂²×C₇	—	2	8	no	—
793	C₂²×C₇	—	2	8	no	—
794	C₂²×C₇	—	2	8	no	—
795	C₂²×C₇	—	2	8	no	—
796	C₂²×C₇	—	2	2	no	—
797	C₂²×C₇	—	2	8	no	—
798	C₂²×C₇	—	2	8	no	—
799	C₂²×C₇	—	2	2	no	—
800	C₂²×C₇	—	4	4	no	—
801	C₂²×C₇	—	4	8	no	—
802	C₂²×C₇	—	4	8	no	—
803	C₂²×C₇	—	4	4	no	—
804	C₂²×C₇	—	8	8	no	—
805	C₂²×C₇	—	8	8	no	—
806	C₂²×C₇	—	8	8	no	—
807	C₂²×C₇	—	8	8	no	—
808	C₂²×C₇	—	16	8	no	—
809	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
810	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
811	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
812	C₂²×C₇	#585	1	2	yes	—
813	C₂²×C₇	C₂⁶	1	1	yes	characteristic
814	C₄×C₇	—	2	2	no	—
815	C₄×C₇	—	2	2	no	—
816	C₄×C₇	—	2	2	no	—
817	C₄×C₇	—	2	8	no	—
818	C₄×C₇	—	2	8	no	—
819	C₄×C₇	—	2	8	no	—
820	C₄×C₇	—	2	8	no	—
821	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
822	C₂⁴	—	2	4	no	—
823	C₂⁴	—	4	2	no	—
824	C₂⁴	—	4	2	no	—
825	C₂⁴	—	4	4	no	—
826	C₂⁴	—	4	4	no	—
827	C₂⁴	—	4	4	no	—
828	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
829	C₂⁴	C₂⁴×C₇	1	2	yes	—
830	C₂⁴	C₂⁴×C₇	1	2	yes	—
831	C₂⁴	C₂⁴×C₇	1	4	yes	—
832	C₂⁴	C₂⁴×C₇	1	4	yes	—
833	C₂⁴	C₂⁴×C₇	1	4	yes	—
834	C₂⁴	C₂⁴×C₇	1	4	yes	—
835	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
836	C₂⁴	C₂⁴×C₇	1	8	yes	—
837	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
838	#41	—	2	16	no	—
839	#41	—	4	8	no	—
840	#41	—	4	8	no	—
841	#41	—	4	16	no	—
842	#41	—	4	32	no	—
843	#41	—	4	8	no	—
844	#41	—	4	16	no	—
845	C₂×Q₈	—	4	4	no	—
846	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
847	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
848	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
849	C₂×D₄	—	2	16	no	—
850	C₂×D₄	—	2	16	no	—
851	C₂×D₄	—	2	8	no	—
852	C₂×D₄	—	4	8	no	—
853	C₂×D₄	—	4	8	no	—
854	C₂×D₄	—	4	4	no	—
855	C₂×D₄	—	4	16	no	—
856	C₂×D₄	—	4	4	no	—
857	C₂×D₄	—	4	8	no	—
858	C₂×D₄	—	4	16	no	—
859	C₂×D₄	—	4	16	no	—
860	C₂×D₄	—	4	8	no	—
861	C₂×D₄	—	4	8	no	—
862	C₂×D₄	—	4	16	no	—
863	C₂×D₄	—	4	16	no	—
864	C₂×D₄	—	4	16	no	—
865	C₂×D₄	—	4	32	no	—
866	C₂×D₄	C₂⁴×C₇	1	8	yes	—
867	C₂×D₄	C₂⁴×C₇	1	8	yes	—
868	C₂×D₄	C₂⁴×C₇	1	8	yes	—
869	C₂×D₄	C₂⁴×C₇	1	8	yes	—
870	C₂×D₄	C₂⁴×C₇	1	16	yes	—
871	C₂×D₄	C₂⁴×C₇	1	8	yes	—
872	C₂×D₄	C₂⁴×C₇	1	4	yes	—
873	C₂×D₄	C₂⁴×C₇	1	16	yes	—
874	C₂×D₄	C₂⁴×C₇	1	8	yes	—
875	C₂×D₄	C₂⁴×C₇	1	8	yes	—
876	C₂×D₄	C₂⁴×C₇	1	16	yes	—
877	C₂×D₄	C₂⁴×C₇	1	16	yes	—
878	C₂×D₄	C₂⁴×C₇	1	4	yes	—
879	C₂×D₄	C₂⁴×C₇	1	8	yes	—
880	C₂×D₄	C₂⁴×C₇	1	8	yes	—
881	C₂×D₄	C₂⁴×C₇	1	16	yes	—
882	C₂²×C₄	—	2	4	no	—
883	C₂²×C₄	—	2	8	no	—
884	C₂²×C₄	—	4	4	no	—
885	C₂²×C₄	—	4	4	no	—
886	C₂²×C₄	—	4	4	no	—
887	C₂²×C₄	—	4	4	no	—
888	C₂²×C₄	—	4	8	no	—
889	C₂²×C₄	—	4	4	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	—	4	4	no	—
892	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
894	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
896	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
900	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
901	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
904	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
908	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
909	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
910	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
911	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
912	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
913	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
914	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
916	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
917	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
920	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
921	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
922	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
923	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
924	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
925	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
926	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
927	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
928	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
929	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
930	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
931	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
933	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
934	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
935	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
936	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
937	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
938	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
939	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
940	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
943	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
944	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
945	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
947	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
950	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
951	C₄²	C₂⁴×C₇	1	8	yes	—
952	C₄²	C₂⁴×C₇	1	8	yes	—
953	C₄²	C₂⁴×C₇	1	16	yes	—
954	C₂×C₇	—	2	2	no	—
955	C₂×C₇	—	2	2	no	—
956	C₂×C₇	—	2	2	no	—
957	C₂×C₇	—	2	4	no	—
958	C₂×C₇	—	4	2	no	—
959	C₂×C₇	—	4	8	no	—
960	C₂×C₇	—	4	8	no	—
961	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
963	C₂×C₇	C₂×#585	1	1	yes	characteristic
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	4	no	—
968	C₂³	—	2	4	no	—
969	C₂³	—	2	4	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	4	no	—
972	C₂³	—	2	8	no	—
973	C₂³	—	2	8	no	—
974	C₂³	—	2	8	no	—
975	C₂³	—	2	8	no	—
976	C₂³	—	4	1	no	—
977	C₂³	—	4	2	no	—
978	C₂³	—	4	1	no	—
979	C₂³	—	4	1	no	—
980	C₂³	—	4	2	no	—
981	C₂³	—	4	1	no	—
982	C₂³	—	4	4	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	4	4	no	—
985	C₂³	—	4	4	no	—
986	C₂³	—	4	4	no	—
987	C₂³	—	4	4	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	4	8	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	16	no	—
994	C₂³	—	8	16	no	—
995	C₂³	C₇×H(5,𝔽₂)	1	4	yes	complemented
996	C₂³	C₂⁵×C₇	1	8	yes	—
997	C₂³	C₂⁵×C₇	1	2	yes	—
998	C₂³	C₂⁵×C₇	1	8	yes	—
999	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1000	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1001	C₂³	C₂⁵×C₇	1	2	yes	—
1002	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1003	Q₈	—	2	8	no	—
1004	Q₈	—	4	4	no	—
1005	Q₈	—	4	8	no	—
1006	D₄	—	2	32	no	—
1007	D₄	—	2	16	no	—
1008	D₄	—	2	16	no	—
1009	D₄	—	2	16	no	—
1010	D₄	—	2	16	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	8	no	—
1013	D₄	—	4	8	no	—
1014	D₄	—	4	16	no	—
1015	D₄	—	4	8	no	—
1016	D₄	—	4	16	no	—
1017	D₄	—	4	16	no	—
1018	D₄	—	4	16	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	4	no	—
1021	D₄	—	4	8	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	4	no	—
1024	C₂×C₄	—	2	8	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	4	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	4	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	4	no	—
1031	C₂×C₄	—	2	4	no	—
1032	C₂×C₄	—	2	16	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	1	no	—
1040	C₂×C₄	—	4	4	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	8	no	—
1046	C₂×C₄	—	4	16	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	complemented
1050	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1051	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1052	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1053	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1054	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1055	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1056	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1057	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1058	C₇	#62818	1	1	yes	characteristic, direct product factor, Sylow
1059	C₂²	—	2	8	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	8	no	—
1070	C₂²	—	2	8	no	—
1071	C₂²	—	2	8	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	8	no	—
1075	C₂²	—	2	8	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	4	no	—
1078	C₂²	—	4	8	no	—
1079	C₂²	—	4	8	no	—
1080	C₂²	—	4	4	no	—
1081	C₂²	—	8	8	no	—
1082	C₂²	—	8	8	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	8	8	no	—
1085	C₂²	—	16	8	no	—
1086	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1087	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1088	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
1089	C₂²	C₇×#585	1	2	yes	—
1090	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	8	no	—
1096	C₄	—	2	8	no	—
1097	C₄	—	2	8	no	—
1098	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
1099	C₂	—	2	2	no	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	2	no	—
1102	C₂	—	2	4	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	8	no	—
1105	C₂	—	4	8	no	—
1106	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1107	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂	C₂×C₇×#585	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×#3542	C₂	semidirect
2. C₇×#3537	C₂	semidirect
3. C₇×#3536	C₂	semidirect
4. C₇×#3534	C₂	semidirect
5. C₇×#3519	C₂	semidirect
6. C₇×#3505	C₂	semidirect
7. C₇×#3496	C₂	semidirect
8. C₇×#3494	C₂	semidirect
9. C₇×#3492	C₂	semidirect
10. C₇×#3490	C₂	semidirect
11. C₇×#3488	C₂	semidirect
12. C₇×#3484	C₂	semidirect
13. C₇×#3484	C₂	semidirect
14. C₂×C₇×#525	C₂	semidirect
15. C₂²×C₇×#121	C₂	semidirect
16. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₇×#41	C₂²	semidirect
19. C₂³×C₇×D₄	C₂²	semidirect
20. C₂³×C₇×D₄	C₂²	semidirect
21. C₂⁴×C₄×C₇	C₂²	semidirect
22. C₇×#562	C₂²	semidirect
23. C₇×#560	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#553	C₂²	semidirect
27. C₇×#553	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#553	C₂²	semidirect
30. C₇×#552	C₂²	semidirect
31. C₇×#551	C₂²	semidirect
32. C₇×#551	C₂²	semidirect
33. C₇×#550	C₂²	semidirect
34. C₇×#548	C₂²	semidirect
35. C₇×#547	C₂²	semidirect
36. C₇×#547	C₂²	semidirect
37. C₇×#546	C₂²	semidirect
38. C₇×#546	C₂²	semidirect
39. C₇×#546	C₂²	semidirect
40. C₇×#546	C₂²	semidirect
41. C₇×#546	C₂²	semidirect
42. C₇×#546	C₂²	semidirect
43. C₇×#546	C₂²	semidirect
44. C₇×#546	C₂²	semidirect
45. C₇×D₄²	C₂²	semidirect
46. C₇×D₄²	C₂²	semidirect
47. C₇×D₄²	C₂²	semidirect
48. C₇×D₄²	C₂²	semidirect
49. C₇×D₄²	C₂²	semidirect
50. C₇×#544	C₂²	semidirect
51. C₇×#543	C₂²	semidirect
52. C₇×#542	C₂²	semidirect
53. C₇×#540	C₂²	semidirect
54. C₇×#540	C₂²	semidirect
55. C₇×#539	C₂²	semidirect
56. C₇×#539	C₂²	semidirect
57. C₇×#538	C₂²	semidirect
58. C₇×#538	C₂²	semidirect
59. C₇×#538	C₂²	semidirect
60. C₇×#538	C₂²	semidirect
61. C₇×#537	C₂²	semidirect
62. C₇×#537	C₂²	semidirect
63. C₇×#537	C₂²	semidirect
64. C₇×#535	C₂²	semidirect
65. C₇×#535	C₂²	semidirect
66. C₇×#535	C₂²	semidirect
67. C₇×#534	C₂²	semidirect
68. C₇×#534	C₂²	semidirect
69. C₇×#534	C₂²	semidirect
70. C₇×#534	C₂²	semidirect
71. C₇×#534	C₂²	semidirect
72. C₇×#532	C₂²	semidirect
73. C₇×#529	C₂²	semidirect
74. C₇×#525	C₂²	semidirect
75. C₇×#525	C₂²	semidirect
76. C₇×#525	C₂²	semidirect
77. C₇×#525	C₂²	semidirect
78. C₇×#525	C₂²	semidirect
79. C₇×#525	C₂²	semidirect
80. C₇×#525	C₂²	semidirect
81. C₇×#525	C₂²	semidirect
82. C₇×#525	C₂²	semidirect
83. C₇×#525	C₂²	semidirect
84. C₂×C₇×#123	C₂²	semidirect
85. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₇×#121	C₂²	semidirect
88. C₂×C₇×#121	C₂²	semidirect
89. C₂×C₇×#121	C₂²	semidirect
90. C₂×C₇×#121	C₂²	semidirect
91. C₂×C₇×#121	C₂²	semidirect
92. C₂×C₇×#121	C₂²	semidirect
93. C₂×C₇×#121	C₂²	semidirect
94. C₂×C₇×#121	C₂²	semidirect
95. C₂×C₇×#121	C₂²	semidirect
96. C₂×C₇×#120	C₂²	semidirect
97. C₂×C₇×#120	C₂²	semidirect
98. C₇×#520	C₂²	semidirect
99. C₇×#518	C₂²	semidirect
100. C₇×#518	C₂²	semidirect
101. C₇×#518	C₂²	semidirect
102. C₂×C₄×C₇×D₄	C₂²	semidirect
103. C₂×C₄×C₇×D₄	C₂²	semidirect
104. C₂×C₇×#117	C₂²	semidirect
105. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
106. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
107. #62818	C₇	direct (N × H)
116. C₂×C₇×#41	C₂³	semidirect
117. C₂×C₇×#41	C₂³	semidirect
118. C₂×C₇×#41	C₂³	semidirect
119. C₂×C₇×#41	C₂³	semidirect
120. C₂²×C₇×Q₈	C₂³	semidirect
137. C₂²×C₇×D₄	C₂³	semidirect
138. C₂²×C₇×D₄	C₂³	semidirect
139. C₂²×C₇×D₄	C₂³	semidirect
150. C₂³×C₄×C₇	C₂³	semidirect
151. C₇×C₄⋊Q₈	C₂³	semidirect
152. C₇×#127	C₂³	semidirect
153. C₇×#127	C₂³	semidirect
154. C₇×#126	C₂³	semidirect
155. C₇×#126	C₂³	semidirect
156. C₇×#126	C₂³	semidirect
157. C₇×#125	C₂³	semidirect
158. C₇×#125	C₂³	semidirect
159. C₇×#124	C₂³	semidirect
160. C₇×#124	C₂³	semidirect
161. C₇×#124	C₂³	semidirect
162. C₇×#124	C₂³	semidirect
166. C₇×#123	C₂³	semidirect
167. C₇×#123	C₂³	semidirect
168. C₇×#123	C₂³	semidirect
169. C₇×#123	C₂³	semidirect
170. C₇×#123	C₂³	semidirect
171. C₇×#123	C₂³	semidirect
172. C₇×#123	C₂³	semidirect
173. C₇×#123	C₂³	semidirect
174. C₇×#123	C₂³	semidirect
181. C₇×C₂²⋊Q₈	C₂³	semidirect
182. C₇×C₂²⋊Q₈	C₂³	semidirect
183. C₇×C₂²⋊Q₈	C₂³	semidirect
184. C₇×C₂²⋊Q₈	C₂³	semidirect
185. C₇×C₂²⋊Q₈	C₂³	semidirect
186. C₇×C₂²⋊Q₈	C₂³	semidirect
187. C₇×C₂²⋊Q₈	C₂³	semidirect
188. C₇×C₂²⋊Q₈	C₂³	semidirect
203. C₇×#121	C₂³	semidirect
204. C₇×#121	C₂³	semidirect
205. C₇×#121	C₂³	semidirect
206. C₇×#121	C₂³	semidirect
207. C₇×#121	C₂³	semidirect
208. C₇×#121	C₂³	semidirect
209. C₇×#121	C₂³	semidirect
210. C₇×#121	C₂³	semidirect
211. C₇×#121	C₂³	semidirect
212. C₇×#121	C₂³	semidirect
213. C₇×#121	C₂³	semidirect
214. C₇×#121	C₂³	semidirect
215. C₇×#121	C₂³	semidirect
216. C₇×#121	C₂³	semidirect
217. C₇×#121	C₂³	semidirect
218. C₇×#121	C₂³	semidirect
219. C₇×#121	C₂³	semidirect
227. C₇×#120	C₂³	semidirect
228. C₇×#120	C₂³	semidirect
229. C₇×#120	C₂³	semidirect
230. C₇×#120	C₂³	semidirect
231. C₄×C₇×Q₈	C₂³	semidirect
238. C₄×C₇×D₄	C₂³	semidirect
239. C₄×C₇×D₄	C₂³	semidirect
240. C₄×C₇×D₄	C₂³	semidirect
241. C₄×C₇×D₄	C₂³	semidirect
242. C₄×C₇×D₄	C₂³	semidirect
243. C₄×C₇×D₄	C₂³	semidirect
244. C₄×C₇×D₄	C₂³	semidirect
245. C₄×C₇×D₄	C₂³	semidirect
246. C₄×C₇×D₄	C₂³	semidirect
247. C₄×C₇×D₄	C₂³	semidirect
248. C₄×C₇×D₄	C₂³	semidirect
252. C₇×#117	C₂³	semidirect
253. C₇×#117	C₂³	semidirect
254. C₇×#117	C₂³	semidirect
255. C₇×#117	C₂³	semidirect
260. C₂×C₇×C₄⋊C₄	C₂³	semidirect
261. C₂×C₇×C₄⋊C₄	C₂³	semidirect
262. C₂×C₇×C₄⋊C₄	C₂³	semidirect
263. C₂×C₇×C₄⋊C₄	C₂³	semidirect
264. C₂×C₇×C₄⋊C₄	C₂³	semidirect
275. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
276. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
277. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
278. C₂×C₄²×C₇	C₂³	semidirect
279. #3542	C₂×C₇	semidirect
280. #3537	C₂×C₇	semidirect
281. #3536	C₂×C₇	semidirect
282. #3534	C₂×C₇	semidirect
283. #3519	C₂×C₇	semidirect
284. #3505	C₂×C₇	semidirect
285. #3496	C₂×C₇	semidirect
286. #3494	C₂×C₇	semidirect
287. #3492	C₂×C₇	semidirect
288. #3490	C₂×C₇	semidirect
289. #3488	C₂×C₇	semidirect
290. #3484	C₂×C₇	semidirect
291. #3484	C₂×C₇	semidirect
292. C₂×#525	C₂×C₇	semidirect
293. C₂²×#121	C₂×C₇	semidirect
426. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
427. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
428. C₂²×#41	C₂²×C₇	semidirect
429. C₂³×D₄	C₂²×C₇	semidirect
430. C₂³×D₄	C₂²×C₇	semidirect
431. C₂⁴×C₄	C₂²×C₇	semidirect
432. #562	C₂²×C₇	semidirect
433. #560	C₂²×C₇	semidirect
434. #555	C₂²×C₇	semidirect
435. #554	C₂²×C₇	semidirect
436. #553	C₂²×C₇	semidirect
437. #553	C₂²×C₇	semidirect
438. #553	C₂²×C₇	semidirect
439. #553	C₂²×C₇	semidirect
440. #552	C₂²×C₇	semidirect
441. #551	C₂²×C₇	semidirect
442. #551	C₂²×C₇	semidirect
443. #550	C₂²×C₇	semidirect
444. #548	C₂²×C₇	semidirect
445. #547	C₂²×C₇	semidirect
446. #547	C₂²×C₇	semidirect
447. #546	C₂²×C₇	semidirect
448. #546	C₂²×C₇	semidirect
449. #546	C₂²×C₇	semidirect
450. #546	C₂²×C₇	semidirect
451. #546	C₂²×C₇	semidirect
452. #546	C₂²×C₇	semidirect
453. #546	C₂²×C₇	semidirect
454. #546	C₂²×C₇	semidirect
455. D₄²	C₂²×C₇	semidirect
456. D₄²	C₂²×C₇	semidirect
457. D₄²	C₂²×C₇	semidirect
458. D₄²	C₂²×C₇	semidirect
459. D₄²	C₂²×C₇	semidirect
460. #544	C₂²×C₇	semidirect
461. #543	C₂²×C₇	semidirect
462. #542	C₂²×C₇	semidirect
463. #540	C₂²×C₇	semidirect
464. #540	C₂²×C₇	semidirect
465. #539	C₂²×C₇	semidirect
466. #539	C₂²×C₇	semidirect
467. #538	C₂²×C₇	semidirect
468. #538	C₂²×C₇	semidirect
469. #538	C₂²×C₇	semidirect
470. #538	C₂²×C₇	semidirect
471. #537	C₂²×C₇	semidirect
472. #537	C₂²×C₇	semidirect
473. #537	C₂²×C₇	semidirect
474. #535	C₂²×C₇	semidirect
475. #535	C₂²×C₇	semidirect
476. #535	C₂²×C₇	semidirect
477. #534	C₂²×C₇	semidirect
478. #534	C₂²×C₇	semidirect
479. #534	C₂²×C₇	semidirect
480. #534	C₂²×C₇	semidirect
481. #534	C₂²×C₇	semidirect
482. #532	C₂²×C₇	semidirect
483. #529	C₂²×C₇	semidirect
484. #525	C₂²×C₇	semidirect
485. #525	C₂²×C₇	semidirect
486. #525	C₂²×C₇	semidirect
487. #525	C₂²×C₇	semidirect
488. #525	C₂²×C₇	semidirect
489. #525	C₂²×C₇	semidirect
490. #525	C₂²×C₇	semidirect
491. #525	C₂²×C₇	semidirect
492. #525	C₂²×C₇	semidirect
493. #525	C₂²×C₇	semidirect
494. C₂×#123	C₂²×C₇	semidirect
495. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
496. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
497. C₂×#121	C₂²×C₇	semidirect
498. C₂×#121	C₂²×C₇	semidirect
499. C₂×#121	C₂²×C₇	semidirect
500. C₂×#121	C₂²×C₇	semidirect
501. C₂×#121	C₂²×C₇	semidirect
502. C₂×#121	C₂²×C₇	semidirect
503. C₂×#121	C₂²×C₇	semidirect
504. C₂×#121	C₂²×C₇	semidirect
505. C₂×#121	C₂²×C₇	semidirect
506. C₂×#120	C₂²×C₇	semidirect
507. C₂×#120	C₂²×C₇	semidirect
508. #520	C₂²×C₇	semidirect
509. #518	C₂²×C₇	semidirect
510. #518	C₂²×C₇	semidirect
511. #518	C₂²×C₇	semidirect
512. C₂×C₄×D₄	C₂²×C₇	semidirect
513. C₂×C₄×D₄	C₂²×C₇	semidirect
514. C₂×#117	C₂²×C₇	semidirect
515. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
516. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
548. C₂³×C₇	H(5,𝔽₂)	semidirect
602. C₂×C₄×C₇	H(5,𝔽₂)	semidirect
619. C₂×#41	C₂³×C₇	semidirect
620. C₂×#41	C₂³×C₇	semidirect
621. C₂×#41	C₂³×C₇	semidirect
622. C₂×#41	C₂³×C₇	semidirect
623. C₂²×Q₈	C₂³×C₇	semidirect
640. C₂²×D₄	C₂³×C₇	semidirect
641. C₂²×D₄	C₂³×C₇	semidirect
642. C₂²×D₄	C₂³×C₇	semidirect
653. C₂³×C₄	C₂³×C₇	semidirect
654. C₄⋊Q₈	C₂³×C₇	semidirect
655. #127	C₂³×C₇	semidirect
656. #127	C₂³×C₇	semidirect
657. #126	C₂³×C₇	semidirect
658. #126	C₂³×C₇	semidirect
659. #126	C₂³×C₇	semidirect
660. #125	C₂³×C₇	semidirect
661. #125	C₂³×C₇	semidirect
662. #124	C₂³×C₇	semidirect
663. #124	C₂³×C₇	semidirect
664. #124	C₂³×C₇	semidirect
665. #124	C₂³×C₇	semidirect
669. #123	C₂³×C₇	semidirect
670. #123	C₂³×C₇	semidirect
671. #123	C₂³×C₇	semidirect
672. #123	C₂³×C₇	semidirect
673. #123	C₂³×C₇	semidirect
674. #123	C₂³×C₇	semidirect
675. #123	C₂³×C₇	semidirect
676. #123	C₂³×C₇	semidirect
677. #123	C₂³×C₇	semidirect
684. C₂²⋊Q₈	C₂³×C₇	semidirect
685. C₂²⋊Q₈	C₂³×C₇	semidirect
686. C₂²⋊Q₈	C₂³×C₇	semidirect
687. C₂²⋊Q₈	C₂³×C₇	semidirect
688. C₂²⋊Q₈	C₂³×C₇	semidirect
689. C₂²⋊Q₈	C₂³×C₇	semidirect
690. C₂²⋊Q₈	C₂³×C₇	semidirect
691. C₂²⋊Q₈	C₂³×C₇	semidirect
706. #121	C₂³×C₇	semidirect
707. #121	C₂³×C₇	semidirect
708. #121	C₂³×C₇	semidirect
709. #121	C₂³×C₇	semidirect
710. #121	C₂³×C₇	semidirect
711. #121	C₂³×C₇	semidirect
712. #121	C₂³×C₇	semidirect
713. #121	C₂³×C₇	semidirect
714. #121	C₂³×C₇	semidirect
715. #121	C₂³×C₇	semidirect
716. #121	C₂³×C₇	semidirect
717. #121	C₂³×C₇	semidirect
718. #121	C₂³×C₇	semidirect
719. #121	C₂³×C₇	semidirect
720. #121	C₂³×C₇	semidirect
721. #121	C₂³×C₇	semidirect
722. #121	C₂³×C₇	semidirect
730. #120	C₂³×C₇	semidirect
731. #120	C₂³×C₇	semidirect
732. #120	C₂³×C₇	semidirect
733. #120	C₂³×C₇	semidirect
734. C₄×Q₈	C₂³×C₇	semidirect
741. C₄×D₄	C₂³×C₇	semidirect
742. C₄×D₄	C₂³×C₇	semidirect
743. C₄×D₄	C₂³×C₇	semidirect
744. C₄×D₄	C₂³×C₇	semidirect
745. C₄×D₄	C₂³×C₇	semidirect
746. C₄×D₄	C₂³×C₇	semidirect
747. C₄×D₄	C₂³×C₇	semidirect
748. C₄×D₄	C₂³×C₇	semidirect
749. C₄×D₄	C₂³×C₇	semidirect
750. C₄×D₄	C₂³×C₇	semidirect
751. C₄×D₄	C₂³×C₇	semidirect
755. #117	C₂³×C₇	semidirect
756. #117	C₂³×C₇	semidirect
757. #117	C₂³×C₇	semidirect
758. #117	C₂³×C₇	semidirect
763. C₂×C₄⋊C₄	C₂³×C₇	semidirect
764. C₂×C₄⋊C₄	C₂³×C₇	semidirect
765. C₂×C₄⋊C₄	C₂³×C₇	semidirect
766. C₂×C₄⋊C₄	C₂³×C₇	semidirect
767. C₂×C₄⋊C₄	C₂³×C₇	semidirect
778. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
779. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
780. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
781. C₂×C₄²	C₂³×C₇	semidirect
995. C₂³	C₇×H(5,𝔽₂)	semidirect
1049. C₂×C₄	C₇×H(5,𝔽₂)	semidirect
1058. C₇	#62818	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×#3542	2
C₇×#3537	2
C₇×#3536	2
C₇×#3534	2
C₇×#3519	2
C₇×#3505	2
C₇×#3496	2
C₇×#3494	2
C₇×#3492	2
C₇×#3490	2
C₇×#3488	2
C₇×#3484	2
C₂×C₇×#525	2
C₂²×C₇×#121	2
#62818	7

Subgroups — C7×#62818 #13240034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62818 #13240034