Subgroups — C₇×#62800 #13240016

Order 1792.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3522	C₂	1	2	yes	maximal, complemented
2	C₇×#3519	C₂	1	6	yes	maximal, complemented
3	C₇×#3517	C₂	1	2	yes	maximal, complemented
4	C₇×#3514	C₂	1	6	yes	maximal, complemented
5	C₇×#3511	C₂	1	3	yes	maximal, complemented
6	C₇×#3508	C₂	1	3	yes	maximal, complemented
7	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3494	C₂	1	6	yes	maximal, complemented
10	C₇×#3488	C₂	1	2	yes	maximal, complemented
11	C₇×#3483	C₂	1	2	yes	maximal, complemented
12	C₇×#3481	C₂	1	6	yes	maximal, complemented
13	C₇×#3480	C₂	1	2	yes	maximal, complemented
14	C₇×D₄×#41	C₂	1	6	yes	maximal, complemented
15	C₇×#3460	C₂	1	6	yes	maximal, complemented
16	C₇×#3444	C₂	1	3	yes	maximal, complemented
17	C₂×C₇×#532	C₂	1	3	yes	maximal, complemented
18	C₄×C₇×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
22	C₂²×C₇×#41	C₂²	1	6	yes	complemented
23	C₇×#559	C₂²	1	6	yes	complemented
24	C₇×#559	C₂²	1	6	yes	complemented
25	C₇×Q₈²	C₂²	1	2	yes	complemented
26	C₇×#557	C₂²	1	2	yes	complemented
27	C₇×#556	C₂²	1	6	yes	complemented
28	C₇×#555	C₂²	1	12	yes	complemented
29	C₇×#555	C₂²	1	6	yes	complemented
30	C₇×#554	C₂²	1	6	yes	complemented
31	C₇×#554	C₂²	1	6	yes	complemented
32	C₇×#553	C₂²	1	12	yes	complemented
33	C₇×#553	C₂²	1	12	yes	complemented
34	C₇×#553	C₂²	1	12	yes	complemented
35	C₇×#551	C₂²	1	24	yes	complemented
36	C₇×#550	C₂²	1	6	yes	complemented
37	C₇×#550	C₂²	1	2	yes	complemented
38	C₇×#550	C₂²	1	4	yes	complemented
39	C₇×#550	C₂²	1	2	yes	complemented
40	C₇×#550	C₂²	1	6	yes	complemented
41	C₇×D₄×Q₈	C₂²	1	6	yes	complemented
42	C₇×#548	C₂²	1	12	yes	complemented
43	C₇×#548	C₂²	1	4	yes	complemented
44	C₇×#547	C₂²	1	12	yes	complemented
45	C₇×#547	C₂²	1	6	yes	complemented
46	C₇×#546	C₂²	1	24	yes	complemented
47	C₇×#546	C₂²	1	12	yes	complemented
48	C₇×#546	C₂²	1	12	yes	complemented
49	C₇×#546	C₂²	1	12	yes	complemented
50	C₇×D₄²	C₂²	1	12	yes	complemented
51	C₇×D₄²	C₂²	1	6	yes	complemented
52	C₇×D₄²	C₂²	1	6	yes	complemented
53	C₇×#544	C₂²	1	6	yes	complemented
54	C₇×#542	C₂²	1	12	yes	complemented
55	C₇×#542	C₂²	1	12	yes	complemented
56	C₇×#540	C₂²	1	12	yes	complemented
57	C₇×#540	C₂²	1	12	yes	complemented
58	C₇×#538	C₂²	1	24	yes	complemented
59	C₇×#537	C₂²	1	6	yes	complemented
60	C₇×#535	C₂²	1	6	yes	complemented
61	C₇×#535	C₂²	1	6	yes	complemented
62	C₇×#533	C₂²	1	1	yes	characteristic, complemented
63	C₇×#533	C₂²	1	3	yes	complemented
64	C₇×#533	C₂²	1	3	yes	complemented
65	C₇×#532	C₂²	1	3	yes	complemented
66	C₇×#532	C₂²	1	6	yes	complemented
67	C₇×#532	C₂²	1	6	yes	complemented
68	C₇×#532	C₂²	1	6	yes	complemented
69	C₇×#532	C₂²	1	6	yes	complemented
70	C₇×#532	C₂²	1	6	yes	complemented
71	C₇×#532	C₂²	1	6	yes	complemented
72	C₇×#532	C₂²	1	6	yes	complemented
73	C₇×#532	C₂²	1	3	yes	complemented
74	C₇×#532	C₂²	1	3	yes	complemented
75	C₇×#532	C₂²	1	12	yes	complemented
76	C₂×C₇×C₄⋊Q₈	C₂²	1	3	yes	complemented
77	C₂×C₇×#127	C₂²	1	3	yes	complemented
78	C₇×#529	C₂²	1	6	yes	complemented
79	C₇×#529	C₂²	1	6	yes	complemented
80	C₇×#529	C₂²	1	6	yes	complemented
81	C₇×#529	C₂²	1	6	yes	complemented
82	C₇×#529	C₂²	1	6	yes	complemented
83	C₇×#529	C₂²	1	6	yes	complemented
84	C₇×#529	C₂²	1	12	yes	complemented
85	C₂×C₇×#124	C₂²	1	6	yes	complemented
86	C₇×#525	C₂²	1	6	yes	complemented
87	C₇×#525	C₂²	1	6	yes	complemented
88	C₇×#525	C₂²	1	6	yes	complemented
89	C₇×#525	C₂²	1	24	yes	complemented
90	C₂×C₇×#121	C₂²	1	6	yes	complemented
91	C₂×C₇×#121	C₂²	1	6	yes	complemented
92	C₇×#520	C₂²	1	2	yes	—
93	C₇×#520	C₂²	1	6	yes	complemented
94	C₇×#520	C₂²	1	4	yes	complemented
95	C₇×#518	C₂²	1	6	yes	complemented
96	C₇×#518	C₂²	1	12	yes	complemented
97	C₄×C₇×#41	C₂²	1	1	yes	characteristic
98	C₄×C₇×#41	C₂²	1	1	yes	characteristic
99	C₄×C₇×#41	C₂²	1	3	yes	complemented
100	C₄×C₇×#41	C₂²	1	3	yes	complemented
101	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×#41	C₂²	1	3	yes	complemented
103	C₄×C₇×#41	C₂²	1	3	yes	complemented
104	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₇×#41	C₂²	1	6	yes	complemented
106	C₄×C₇×#41	C₂²	1	4	yes	complemented
107	C₄×C₇×#41	C₂²	1	6	yes	complemented
108	C₄×C₇×#41	C₂²	1	6	yes	complemented
109	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×C₇×D₄	C₂²	1	3	yes	complemented
112	C₂×C₄×C₇×D₄	C₂²	1	3	yes	complemented
113	C₂×C₄×C₇×D₄	C₂²	1	6	yes	complemented
114	C₂×C₄×C₇×D₄	C₂²	1	12	yes	complemented
115	C₂×C₄×C₇×D₄	C₂²	1	6	yes	complemented
116	C₂×C₇×#117	C₂²	1	3	yes	complemented
117	C₂²×C₄²×C₇	C₂²	1	3	yes	complemented
118	#62800	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₇×H(5,𝔽₂)	—	2	16	no	—
120	C₂×C₇×#41	—	2	8	no	—
121	C₂×C₇×#41	—	4	24	no	—
122	C₂×C₇×#41	C₂³	1	3	yes	—
123	C₂×C₇×#41	C₂³	1	3	yes	—
124	C₂×C₇×#41	C₂³	1	1	yes	characteristic
125	C₂×C₇×#41	C₂³	1	6	yes	—
126	C₂×C₇×#41	C₂³	1	6	yes	—
127	C₂×C₇×#41	C₂³	1	4	yes	—
128	C₂×C₇×#41	C₂³	1	12	yes	—
129	C₂×C₇×#41	C₂³	1	12	yes	—
130	C₂×C₇×#41	C₂³	1	12	yes	—
131	C₂×C₇×#41	C₂³	1	6	yes	—
132	C₂×C₇×#41	C₂³	1	1	yes	characteristic
133	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×C₇×Q₈	C₂³	1	6	yes	—
135	C₂²×C₇×D₄	C₂³	1	3	yes	—
136	C₂²×C₇×D₄	C₂³	1	6	yes	—
137	C₂²×C₇×D₄	C₂³	1	12	yes	—
138	C₂²×C₇×D₄	C₂³	1	12	yes	—
139	C₂²×C₇×D₄	C₂³	1	6	yes	—
140	C₂²×C₇×D₄	C₂³	1	6	yes	—
141	C₂³×C₄×C₇	C₂³	1	3	yes	—
142	C₂³×C₄×C₇	C₂³	1	3	yes	—
143	C₂³×C₄×C₇	C₂³	1	12	yes	—
144	C₂³×C₄×C₇	C₂³	1	3	yes	—
145	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
146	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
147	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
148	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
149	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₇×C₄⋊Q₈	C₂³	1	12	yes	—
152	C₇×#127	C₂³	1	3	yes	—
153	C₇×#127	C₂³	1	6	yes	—
154	C₇×#127	C₂³	1	6	yes	—
155	C₇×#127	C₂³	1	6	yes	—
156	C₇×#127	C₂³	1	12	yes	—
157	C₇×#126	C₂³	1	12	yes	—
158	C₇×#126	C₂³	1	12	yes	—
159	C₇×#126	C₂³	1	24	yes	—
160	C₇×#125	C₂³	1	2	yes	—
161	C₇×#125	C₂³	1	6	yes	—
162	C₇×#125	C₂³	1	6	yes	—
163	C₇×#125	C₂³	1	12	yes	—
164	C₇×#124	C₂³	1	6	yes	—
165	C₇×#124	C₂³	1	12	yes	—
166	C₇×#124	C₂³	1	12	yes	—
167	C₇×#124	C₂³	1	12	yes	—
168	C₇×#124	C₂³	1	6	yes	—
169	C₇×#124	C₂³	1	6	yes	—
170	C₇×#124	C₂³	1	12	yes	—
171	C₇×#124	C₂³	1	24	yes	—
172	C₇×#123	C₂³	1	12	yes	—
173	C₇×#123	C₂³	1	12	yes	—
174	C₇×#123	C₂³	1	12	yes	—
175	C₇×#123	C₂³	1	24	yes	—
176	C₇×#123	C₂³	1	24	yes	—
177	C₇×#123	C₂³	1	24	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
183	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
184	C₇×C₂²⋊Q₈	C₂³	1	24	yes	—
185	C₇×C₂²⋊Q₈	C₂³	1	24	yes	—
186	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
187	C₇×#121	C₂³	1	6	yes	—
188	C₇×#121	C₂³	1	6	yes	—
189	C₇×#121	C₂³	1	12	yes	—
190	C₇×#121	C₂³	1	12	yes	—
191	C₇×#121	C₂³	1	12	yes	—
192	C₇×#121	C₂³	1	12	yes	—
193	C₇×#121	C₂³	1	12	yes	—
194	C₇×#121	C₂³	1	12	yes	—
195	C₇×#121	C₂³	1	6	yes	—
196	C₇×#121	C₂³	1	6	yes	—
197	C₇×#121	C₂³	1	6	yes	—
198	C₇×#121	C₂³	1	6	yes	—
199	C₇×#121	C₂³	1	24	yes	—
200	C₇×#121	C₂³	1	24	yes	—
201	C₇×#121	C₂³	1	12	yes	—
202	C₇×#121	C₂³	1	12	yes	—
203	C₇×#121	C₂³	1	12	yes	—
204	C₇×#121	C₂³	1	24	yes	—
205	C₇×#120	C₂³	1	12	yes	—
206	C₇×#120	C₂³	1	24	yes	—
207	C₇×#120	C₂³	1	24	yes	—
208	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
209	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
210	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
211	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
212	C₄×C₇×Q₈	C₂³	1	3	yes	—
213	C₄×C₇×Q₈	C₂³	1	3	yes	—
214	C₄×C₇×Q₈	C₂³	1	3	yes	—
215	C₄×C₇×Q₈	C₂³	1	3	yes	—
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	2	yes	—
218	C₄×C₇×Q₈	C₂³	1	4	yes	—
219	C₄×C₇×Q₈	C₂³	1	6	yes	—
220	C₄×C₇×Q₈	C₂³	1	6	yes	—
221	C₄×C₇×Q₈	C₂³	1	6	yes	—
222	C₄×C₇×Q₈	C₂³	1	6	yes	—
223	C₄×C₇×D₄	C₂³	1	3	yes	—
224	C₄×C₇×D₄	C₂³	1	12	yes	—
225	C₄×C₇×D₄	C₂³	1	6	yes	—
226	C₄×C₇×D₄	C₂³	1	12	yes	—
227	C₄×C₇×D₄	C₂³	1	6	yes	—
228	C₄×C₇×D₄	C₂³	1	3	yes	—
229	C₄×C₇×D₄	C₂³	1	3	yes	—
230	C₄×C₇×D₄	C₂³	1	3	yes	—
231	C₄×C₇×D₄	C₂³	1	6	yes	—
232	C₄×C₇×D₄	C₂³	1	3	yes	—
233	C₄×C₇×D₄	C₂³	1	6	yes	—
234	C₄×C₇×D₄	C₂³	1	3	yes	—
235	C₄×C₇×D₄	C₂³	1	6	yes	—
236	C₄×C₇×D₄	C₂³	1	6	yes	—
237	C₄×C₇×D₄	C₂³	1	3	yes	—
238	C₄×C₇×D₄	C₂³	1	3	yes	—
239	C₄×C₇×D₄	C₂³	1	12	yes	—
240	C₄×C₇×D₄	C₂³	1	12	yes	—
241	C₄×C₇×D₄	C₂³	1	12	yes	—
242	C₄×C₇×D₄	C₂³	1	24	yes	—
243	C₄×C₇×D₄	C₂³	1	12	yes	—
244	C₄×C₇×D₄	C₂³	1	12	yes	—
245	C₄×C₇×D₄	C₂³	1	12	yes	—
246	C₄×C₇×D₄	C₂³	1	12	yes	—
247	C₄×C₇×D₄	C₂³	1	12	yes	—
248	C₄×C₇×D₄	C₂³	1	6	yes	—
249	C₄×C₇×D₄	C₂³	1	12	yes	—
250	C₄×C₇×D₄	C₂³	1	12	yes	—
251	C₄×C₇×D₄	C₂³	1	12	yes	—
252	C₄×C₇×D₄	C₂³	1	12	yes	—
253	C₄×C₇×D₄	C₂³	1	12	yes	—
254	C₄×C₇×D₄	C₂³	1	6	yes	—
255	C₄×C₇×D₄	C₂³	1	6	yes	—
256	C₄×C₇×D₄	C₂³	1	6	yes	—
257	C₇×#117	C₂³	1	3	yes	—
258	C₇×#117	C₂³	1	3	yes	—
259	C₇×#117	C₂³	1	6	yes	—
260	C₇×#117	C₂³	1	6	yes	—
261	C₇×#117	C₂³	1	3	yes	—
262	C₇×#117	C₂³	1	3	yes	—
263	C₇×#117	C₂³	1	2	yes	—
264	C₇×#117	C₂³	1	6	yes	—
265	C₇×#117	C₂³	1	12	yes	—
266	C₇×#117	C₂³	1	12	yes	—
267	C₇×#117	C₂³	1	12	yes	—
268	C₇×#117	C₂³	1	6	yes	—
269	C₇×#117	C₂³	1	12	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
272	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
273	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
275	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
276	C₂×C₇×C₂²⋊C₄	C₂³	1	12	yes	—
277	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
278	C₂×C₇×C₂²⋊C₄	C₂³	1	12	yes	—
279	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₇	C₂³	1	3	yes	—
281	C₂×C₄²×C₇	C₂³	1	3	yes	—
282	C₂×C₄²×C₇	C₂³	1	3	yes	—
283	C₂×C₄²×C₇	C₂³	1	3	yes	—
284	C₂×C₄²×C₇	C₂³	1	3	yes	—
285	C₂×C₄²×C₇	C₂³	1	3	yes	—
286	C₂×C₄²×C₇	C₂³	1	3	yes	—
287	C₂×C₄²×C₇	C₂³	1	3	yes	—
288	C₂×C₄²×C₇	C₂³	1	3	yes	—
289	C₂×C₄²×C₇	C₂³	1	3	yes	—
290	C₂×C₄²×C₇	C₂³	1	3	yes	—
291	C₂×C₄²×C₇	C₂³	1	12	yes	—
292	#3522	C₂×C₇	1	2	yes	complemented
293	#3519	C₂×C₇	1	6	yes	complemented
294	#3517	C₂×C₇	1	2	yes	complemented
295	#3514	C₂×C₇	1	6	yes	complemented
296	#3511	C₂×C₇	1	3	yes	complemented
297	#3508	C₂×C₇	1	3	yes	complemented
298	#3503	C₂×C₇	1	1	yes	characteristic, complemented
299	#3498	C₂×C₇	1	1	yes	characteristic, complemented
300	#3494	C₂×C₇	1	6	yes	complemented
301	#3488	C₂×C₇	1	2	yes	complemented
302	#3483	C₂×C₇	1	2	yes	complemented
303	#3481	C₂×C₇	1	6	yes	complemented
304	#3480	C₂×C₇	1	2	yes	complemented
305	D₄×#41	C₂×C₇	1	6	yes	complemented
306	#3460	C₂×C₇	1	6	yes	complemented
307	#3444	C₂×C₇	1	3	yes	complemented
308	C₂×#532	C₂×C₇	1	3	yes	complemented
309	C₄×H(5,𝔽₂)	C₂×C₇	1	2	yes	complemented
310	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
311	C₂⁴×C₇	C₂⁴	1	3	yes	—
312	C₂⁴×C₇	C₂⁴	1	12	yes	—
313	C₇×#41	—	2	4	no	—
314	C₇×#41	—	2	16	no	—
315	C₇×#41	—	2	12	no	—
316	C₇×#41	—	2	12	no	—
317	C₇×#41	—	2	24	no	—
318	C₇×#41	—	2	24	no	—
319	C₇×#41	—	4	24	no	—
320	C₇×#41	—	4	24	no	—
321	C₇×#41	—	4	24	no	—
322	C₇×#41	—	4	12	no	—
323	C₇×#41	#41	1	8	yes	complemented
324	C₂×C₇×Q₈	—	2	4	no	—
325	C₂×C₇×Q₈	—	4	12	no	—
326	C₂×C₇×Q₈	C₂⁴	1	3	yes	—
327	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
328	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
329	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
330	C₂×C₇×Q₈	C₂⁴	1	12	yes	—
331	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×C₇×D₄	—	2	12	no	—
333	C₂×C₇×D₄	—	2	48	no	—
334	C₂×C₇×D₄	—	2	24	no	—
335	C₂×C₇×D₄	—	4	12	no	—
336	C₂×C₇×D₄	—	4	12	no	—
337	C₂×C₇×D₄	—	4	24	no	—
338	C₂×C₇×D₄	C₂⁴	1	6	yes	—
339	C₂×C₇×D₄	C₂⁴	1	12	yes	—
340	C₂×C₇×D₄	C₂⁴	1	6	yes	—
341	C₂×C₇×D₄	C₂⁴	1	12	yes	—
342	C₂×C₇×D₄	C₂⁴	1	6	yes	—
343	C₂×C₇×D₄	C₂⁴	1	3	yes	—
344	C₂×C₇×D₄	C₂⁴	1	12	yes	—
345	C₂×C₇×D₄	C₂⁴	1	6	yes	—
346	C₂×C₇×D₄	C₂⁴	1	12	yes	—
347	C₂×C₇×D₄	C₂⁴	1	12	yes	—
348	C₂×C₇×D₄	C₂⁴	1	12	yes	—
349	C₂×C₇×D₄	C₂⁴	1	24	yes	—
350	C₂×C₇×D₄	C₂⁴	1	3	yes	—
351	C₂²×C₄×C₇	—	2	12	no	—
352	C₂²×C₄×C₇	—	2	12	no	—
353	C₂²×C₄×C₇	—	4	6	no	—
354	C₂²×C₄×C₇	—	4	24	no	—
355	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
358	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
359	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
360	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
363	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
364	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
365	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
366	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
367	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
369	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
370	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
371	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
372	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
373	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
374	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
375	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
376	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
377	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
378	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
379	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
380	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
381	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
382	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
383	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
384	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
385	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
386	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
387	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
388	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
389	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
390	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
391	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
392	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
393	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
394	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
395	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
396	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
397	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
398	C₇×C₂²⋊C₄	C₂⁴	1	6	yes	—
399	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
400	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
401	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
402	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
403	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
404	C₇×C₂²⋊C₄	C₂⁴	1	6	yes	—
405	C₇×C₂²⋊C₄	C₂⁴	1	6	yes	—
406	C₇×C₂²⋊C₄	C₂⁴	1	6	yes	—
407	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
408	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
409	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
410	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
411	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
412	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
413	C₄²×C₇	C₂⁴	1	1	yes	characteristic
414	C₄²×C₇	C₂⁴	1	1	yes	characteristic
415	C₄²×C₇	C₂⁴	1	3	yes	—
416	C₄²×C₇	C₂⁴	1	3	yes	—
417	C₄²×C₇	C₂⁴	1	3	yes	—
418	C₄²×C₇	C₂⁴	1	3	yes	—
419	C₄²×C₇	C₂⁴	1	3	yes	—
420	C₄²×C₇	C₂⁴	1	3	yes	—
421	C₄²×C₇	C₂⁴	1	3	yes	—
422	C₄²×C₇	C₂⁴	1	3	yes	—
423	C₄²×C₇	C₂⁴	1	3	yes	—
424	C₄²×C₇	C₂⁴	1	3	yes	—
425	C₄²×C₇	C₂⁴	1	12	yes	—
426	C₄²×C₇	C₂⁴	1	12	yes	—
427	C₄²×C₇	C₂⁴	1	1	yes	characteristic
428	C₄²×C₇	C₂⁴	1	3	yes	—
429	C₄²×C₇	C₂⁴	1	1	yes	characteristic
430	C₄²×C₇	C₂⁴	1	3	yes	—
431	C₄²×C₇	C₂⁴	1	4	yes	—
432	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
433	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
434	C₂²×#41	C₂²×C₇	1	6	yes	complemented
435	#559	C₂²×C₇	1	6	yes	complemented
436	#559	C₂²×C₇	1	6	yes	complemented
437	Q₈²	C₂²×C₇	1	2	yes	complemented
438	#557	C₂²×C₇	1	2	yes	complemented
439	#556	C₂²×C₇	1	6	yes	complemented
440	#555	C₂²×C₇	1	12	yes	complemented
441	#555	C₂²×C₇	1	6	yes	complemented
442	#554	C₂²×C₇	1	6	yes	complemented
443	#554	C₂²×C₇	1	6	yes	complemented
444	#553	C₂²×C₇	1	12	yes	complemented
445	#553	C₂²×C₇	1	12	yes	complemented
446	#553	C₂²×C₇	1	12	yes	complemented
447	#551	C₂²×C₇	1	24	yes	complemented
448	#550	C₂²×C₇	1	6	yes	complemented
449	#550	C₂²×C₇	1	2	yes	complemented
450	#550	C₂²×C₇	1	4	yes	complemented
451	#550	C₂²×C₇	1	2	yes	complemented
452	#550	C₂²×C₇	1	6	yes	complemented
453	D₄×Q₈	C₂²×C₇	1	6	yes	complemented
454	#548	C₂²×C₇	1	12	yes	complemented
455	#548	C₂²×C₇	1	4	yes	complemented
456	#547	C₂²×C₇	1	12	yes	complemented
457	#547	C₂²×C₇	1	6	yes	complemented
458	#546	C₂²×C₇	1	24	yes	complemented
459	#546	C₂²×C₇	1	12	yes	complemented
460	#546	C₂²×C₇	1	12	yes	complemented
461	#546	C₂²×C₇	1	12	yes	complemented
462	D₄²	C₂²×C₇	1	12	yes	complemented
463	D₄²	C₂²×C₇	1	6	yes	complemented
464	D₄²	C₂²×C₇	1	6	yes	complemented
465	#544	C₂²×C₇	1	6	yes	complemented
466	#542	C₂²×C₇	1	12	yes	complemented
467	#542	C₂²×C₇	1	12	yes	complemented
468	#540	C₂²×C₇	1	12	yes	complemented
469	#540	C₂²×C₇	1	12	yes	complemented
470	#538	C₂²×C₇	1	24	yes	complemented
471	#537	C₂²×C₇	1	6	yes	complemented
472	#535	C₂²×C₇	1	6	yes	complemented
473	#535	C₂²×C₇	1	6	yes	complemented
474	#533	C₂²×C₇	1	1	yes	characteristic, complemented
475	#533	C₂²×C₇	1	3	yes	complemented
476	#533	C₂²×C₇	1	3	yes	complemented
477	#532	C₂²×C₇	1	3	yes	complemented
478	#532	C₂²×C₇	1	6	yes	complemented
479	#532	C₂²×C₇	1	6	yes	complemented
480	#532	C₂²×C₇	1	6	yes	complemented
481	#532	C₂²×C₇	1	6	yes	complemented
482	#532	C₂²×C₇	1	6	yes	complemented
483	#532	C₂²×C₇	1	6	yes	complemented
484	#532	C₂²×C₇	1	6	yes	complemented
485	#532	C₂²×C₇	1	3	yes	complemented
486	#532	C₂²×C₇	1	3	yes	complemented
487	#532	C₂²×C₇	1	12	yes	complemented
488	C₂×C₄⋊Q₈	C₂²×C₇	1	3	yes	complemented
489	C₂×#127	C₂²×C₇	1	3	yes	complemented
490	#529	C₂²×C₇	1	6	yes	complemented
491	#529	C₂²×C₇	1	6	yes	complemented
492	#529	C₂²×C₇	1	6	yes	complemented
493	#529	C₂²×C₇	1	6	yes	complemented
494	#529	C₂²×C₇	1	6	yes	complemented
495	#529	C₂²×C₇	1	6	yes	complemented
496	#529	C₂²×C₇	1	12	yes	complemented
497	C₂×#124	C₂²×C₇	1	6	yes	complemented
498	#525	C₂²×C₇	1	6	yes	complemented
499	#525	C₂²×C₇	1	6	yes	complemented
500	#525	C₂²×C₇	1	6	yes	complemented
501	#525	C₂²×C₇	1	24	yes	complemented
502	C₂×#121	C₂²×C₇	1	6	yes	complemented
503	C₂×#121	C₂²×C₇	1	6	yes	complemented
504	#520	C₂²×C₇	1	2	yes	—
505	#520	C₂²×C₇	1	6	yes	complemented
506	#520	C₂²×C₇	1	4	yes	complemented
507	#518	C₂²×C₇	1	6	yes	complemented
508	#518	C₂²×C₇	1	12	yes	complemented
509	C₄×#41	C₂²×C₇	1	1	yes	characteristic
510	C₄×#41	C₂²×C₇	1	1	yes	characteristic
511	C₄×#41	C₂²×C₇	1	3	yes	complemented
512	C₄×#41	C₂²×C₇	1	3	yes	complemented
513	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
514	C₄×#41	C₂²×C₇	1	3	yes	complemented
515	C₄×#41	C₂²×C₇	1	3	yes	complemented
516	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
517	C₄×#41	C₂²×C₇	1	6	yes	complemented
518	C₄×#41	C₂²×C₇	1	4	yes	complemented
519	C₄×#41	C₂²×C₇	1	6	yes	complemented
520	C₄×#41	C₂²×C₇	1	6	yes	complemented
521	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
522	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
523	C₂×C₄×D₄	C₂²×C₇	1	3	yes	complemented
524	C₂×C₄×D₄	C₂²×C₇	1	3	yes	complemented
525	C₂×C₄×D₄	C₂²×C₇	1	6	yes	complemented
526	C₂×C₄×D₄	C₂²×C₇	1	12	yes	complemented
527	C₂×C₄×D₄	C₂²×C₇	1	6	yes	complemented
528	C₂×#117	C₂²×C₇	1	3	yes	complemented
529	C₂²×C₄²	C₂²×C₇	1	3	yes	complemented
530	C₂³×C₇	—	2	6	no	—
531	C₂³×C₇	—	2	6	no	—
532	C₂³×C₇	—	2	24	no	—
533	C₂³×C₇	—	4	3	no	—
534	C₂³×C₇	—	4	12	no	—
535	C₂³×C₇	—	4	12	no	—
536	C₂³×C₇	C₂⁵	1	12	yes	—
537	C₂³×C₇	C₂⁵	1	3	yes	—
538	C₂³×C₇	C₂⁵	1	3	yes	—
539	C₂³×C₇	C₂⁵	1	1	yes	characteristic
540	C₇×Q₈	—	2	6	no	—
541	C₇×Q₈	—	2	4	no	—
542	C₇×Q₈	—	2	12	no	—
543	C₇×Q₈	—	2	4	no	—
544	C₇×Q₈	—	4	12	no	—
545	C₇×Q₈	C₂×#41	1	4	yes	complemented
546	C₇×D₄	—	2	24	no	—
547	C₇×D₄	—	2	12	no	—
548	C₇×D₄	—	2	24	no	—
549	C₇×D₄	—	2	24	no	—
550	C₇×D₄	—	2	12	no	—
551	C₇×D₄	—	2	6	no	—
552	C₇×D₄	—	2	12	no	—
553	C₇×D₄	—	2	12	no	—
554	C₇×D₄	—	4	12	no	—
555	C₇×D₄	—	4	12	no	—
556	C₇×D₄	—	4	24	no	—
557	C₇×D₄	—	4	12	no	—
558	C₇×D₄	C₂×#41	1	12	yes	complemented
559	C₂×C₄×C₇	—	2	6	no	—
560	C₂×C₄×C₇	—	2	6	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	6	no	—
563	C₂×C₄×C₇	—	2	6	no	—
564	C₂×C₄×C₇	—	2	6	no	—
565	C₂×C₄×C₇	—	2	24	no	—
566	C₂×C₄×C₇	—	2	6	no	—
567	C₂×C₄×C₇	—	2	6	no	—
568	C₂×C₄×C₇	—	2	6	no	—
569	C₂×C₄×C₇	—	2	6	no	—
570	C₂×C₄×C₇	—	2	24	no	—
571	C₂×C₄×C₇	—	2	2	no	—
572	C₂×C₄×C₇	—	2	6	no	—
573	C₂×C₄×C₇	—	2	6	no	—
574	C₂×C₄×C₇	—	4	3	no	—
575	C₂×C₄×C₇	—	4	3	no	—
576	C₂×C₄×C₇	—	4	3	no	—
577	C₂×C₄×C₇	—	4	12	no	—
578	C₂×C₄×C₇	—	4	24	no	—
579	C₂×C₄×C₇	—	4	12	no	—
580	C₂×C₄×C₇	C₂×#41	1	12	yes	complemented
581	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	complemented
582	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
583	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
584	C₂×C₄×C₇	C₂⁵	1	3	yes	—
585	C₂×C₄×C₇	C₂⁵	1	3	yes	—
586	C₂×C₄×C₇	C₂⁵	1	4	yes	—
587	C₂×C₄×C₇	C₂⁵	1	4	yes	—
588	C₂×C₄×C₇	C₂⁵	1	3	yes	—
589	C₂×C₄×C₇	C₂⁵	1	3	yes	—
590	C₂×C₄×C₇	C₂⁵	1	3	yes	—
591	C₂×C₄×C₇	C₂⁵	1	12	yes	—
592	C₂×C₄×C₇	C₂⁵	1	3	yes	—
593	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
594	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
595	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
596	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
597	H(5,𝔽₂)	—	2	16	no	—
598	C₂×#41	—	2	8	no	—
599	C₂×#41	—	4	24	no	—
600	C₂×#41	C₂³×C₇	1	3	yes	—
601	C₂×#41	C₂³×C₇	1	3	yes	—
602	C₂×#41	C₂³×C₇	1	1	yes	characteristic
603	C₂×#41	C₂³×C₇	1	6	yes	—
604	C₂×#41	C₂³×C₇	1	4	yes	—
605	C₂×#41	C₂³×C₇	1	6	yes	—
606	C₂×#41	C₂³×C₇	1	6	yes	—
607	C₂×#41	C₂³×C₇	1	12	yes	—
608	C₂×#41	C₂³×C₇	1	12	yes	—
609	C₂×#41	C₂³×C₇	1	12	yes	—
610	C₂×#41	C₂³×C₇	1	1	yes	characteristic
611	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
612	C₂²×Q₈	C₂³×C₇	1	6	yes	—
613	C₂²×D₄	C₂³×C₇	1	3	yes	—
614	C₂²×D₄	C₂³×C₇	1	6	yes	—
615	C₂²×D₄	C₂³×C₇	1	12	yes	—
616	C₂²×D₄	C₂³×C₇	1	6	yes	—
617	C₂²×D₄	C₂³×C₇	1	12	yes	—
618	C₂²×D₄	C₂³×C₇	1	6	yes	—
619	C₂³×C₄	C₂³×C₇	1	3	yes	—
620	C₂³×C₄	C₂³×C₇	1	3	yes	—
621	C₂³×C₄	C₂³×C₇	1	12	yes	—
622	C₂³×C₄	C₂³×C₇	1	3	yes	—
623	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
624	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
625	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
626	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
627	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
628	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
629	C₄⋊Q₈	C₂³×C₇	1	12	yes	—
630	#127	C₂³×C₇	1	3	yes	—
631	#127	C₂³×C₇	1	6	yes	—
632	#127	C₂³×C₇	1	6	yes	—
633	#127	C₂³×C₇	1	6	yes	—
634	#127	C₂³×C₇	1	12	yes	—
635	#126	C₂³×C₇	1	12	yes	—
636	#126	C₂³×C₇	1	12	yes	—
637	#126	C₂³×C₇	1	24	yes	—
638	#125	C₂³×C₇	1	2	yes	—
639	#125	C₂³×C₇	1	6	yes	—
640	#125	C₂³×C₇	1	6	yes	—
641	#125	C₂³×C₇	1	12	yes	—
642	#124	C₂³×C₇	1	6	yes	—
643	#124	C₂³×C₇	1	12	yes	—
644	#124	C₂³×C₇	1	12	yes	—
645	#124	C₂³×C₇	1	12	yes	—
646	#124	C₂³×C₇	1	6	yes	—
647	#124	C₂³×C₇	1	6	yes	—
648	#124	C₂³×C₇	1	12	yes	—
649	#124	C₂³×C₇	1	24	yes	—
650	#123	C₂³×C₇	1	12	yes	—
651	#123	C₂³×C₇	1	12	yes	—
652	#123	C₂³×C₇	1	12	yes	—
653	#123	C₂³×C₇	1	24	yes	—
654	#123	C₂³×C₇	1	24	yes	—
655	#123	C₂³×C₇	1	24	yes	—
656	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
657	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
658	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
659	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
660	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
661	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
662	C₂²⋊Q₈	C₂³×C₇	1	24	yes	—
663	C₂²⋊Q₈	C₂³×C₇	1	24	yes	—
664	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
665	#121	C₂³×C₇	1	6	yes	—
666	#121	C₂³×C₇	1	6	yes	—
667	#121	C₂³×C₇	1	12	yes	—
668	#121	C₂³×C₇	1	12	yes	—
669	#121	C₂³×C₇	1	12	yes	—
670	#121	C₂³×C₇	1	12	yes	—
671	#121	C₂³×C₇	1	12	yes	—
672	#121	C₂³×C₇	1	12	yes	—
673	#121	C₂³×C₇	1	6	yes	—
674	#121	C₂³×C₇	1	6	yes	—
675	#121	C₂³×C₇	1	6	yes	—
676	#121	C₂³×C₇	1	6	yes	—
677	#121	C₂³×C₇	1	24	yes	—
678	#121	C₂³×C₇	1	24	yes	—
679	#121	C₂³×C₇	1	12	yes	—
680	#121	C₂³×C₇	1	12	yes	—
681	#121	C₂³×C₇	1	12	yes	—
682	#121	C₂³×C₇	1	24	yes	—
683	#120	C₂³×C₇	1	12	yes	—
684	#120	C₂³×C₇	1	24	yes	—
685	#120	C₂³×C₇	1	24	yes	—
686	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
687	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
688	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
689	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
690	C₄×Q₈	C₂³×C₇	1	3	yes	—
691	C₄×Q₈	C₂³×C₇	1	3	yes	—
692	C₄×Q₈	C₂³×C₇	1	3	yes	—
693	C₄×Q₈	C₂³×C₇	1	3	yes	—
694	C₄×Q₈	C₂³×C₇	1	2	yes	—
695	C₄×Q₈	C₂³×C₇	1	2	yes	—
696	C₄×Q₈	C₂³×C₇	1	4	yes	—
697	C₄×Q₈	C₂³×C₇	1	6	yes	—
698	C₄×Q₈	C₂³×C₇	1	6	yes	—
699	C₄×Q₈	C₂³×C₇	1	6	yes	—
700	C₄×Q₈	C₂³×C₇	1	6	yes	—
701	C₄×D₄	C₂³×C₇	1	3	yes	—
702	C₄×D₄	C₂³×C₇	1	12	yes	—
703	C₄×D₄	C₂³×C₇	1	6	yes	—
704	C₄×D₄	C₂³×C₇	1	12	yes	—
705	C₄×D₄	C₂³×C₇	1	6	yes	—
706	C₄×D₄	C₂³×C₇	1	3	yes	—
707	C₄×D₄	C₂³×C₇	1	3	yes	—
708	C₄×D₄	C₂³×C₇	1	3	yes	—
709	C₄×D₄	C₂³×C₇	1	6	yes	—
710	C₄×D₄	C₂³×C₇	1	3	yes	—
711	C₄×D₄	C₂³×C₇	1	6	yes	—
712	C₄×D₄	C₂³×C₇	1	3	yes	—
713	C₄×D₄	C₂³×C₇	1	6	yes	—
714	C₄×D₄	C₂³×C₇	1	6	yes	—
715	C₄×D₄	C₂³×C₇	1	3	yes	—
716	C₄×D₄	C₂³×C₇	1	3	yes	—
717	C₄×D₄	C₂³×C₇	1	12	yes	—
718	C₄×D₄	C₂³×C₇	1	12	yes	—
719	C₄×D₄	C₂³×C₇	1	12	yes	—
720	C₄×D₄	C₂³×C₇	1	24	yes	—
721	C₄×D₄	C₂³×C₇	1	12	yes	—
722	C₄×D₄	C₂³×C₇	1	12	yes	—
723	C₄×D₄	C₂³×C₇	1	12	yes	—
724	C₄×D₄	C₂³×C₇	1	12	yes	—
725	C₄×D₄	C₂³×C₇	1	12	yes	—
726	C₄×D₄	C₂³×C₇	1	6	yes	—
727	C₄×D₄	C₂³×C₇	1	12	yes	—
728	C₄×D₄	C₂³×C₇	1	12	yes	—
729	C₄×D₄	C₂³×C₇	1	12	yes	—
730	C₄×D₄	C₂³×C₇	1	12	yes	—
731	C₄×D₄	C₂³×C₇	1	12	yes	—
732	C₄×D₄	C₂³×C₇	1	6	yes	—
733	C₄×D₄	C₂³×C₇	1	6	yes	—
734	C₄×D₄	C₂³×C₇	1	6	yes	—
735	#117	C₂³×C₇	1	3	yes	—
736	#117	C₂³×C₇	1	3	yes	—
737	#117	C₂³×C₇	1	6	yes	—
738	#117	C₂³×C₇	1	6	yes	—
739	#117	C₂³×C₇	1	3	yes	—
740	#117	C₂³×C₇	1	3	yes	—
741	#117	C₂³×C₇	1	2	yes	—
742	#117	C₂³×C₇	1	6	yes	—
743	#117	C₂³×C₇	1	12	yes	—
744	#117	C₂³×C₇	1	12	yes	—
745	#117	C₂³×C₇	1	12	yes	—
746	#117	C₂³×C₇	1	6	yes	—
747	#117	C₂³×C₇	1	12	yes	—
748	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
749	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
750	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
751	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
752	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₇	1	12	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₇	1	12	yes	—
757	C₂×C₄²	C₂³×C₇	1	3	yes	—
758	C₂×C₄²	C₂³×C₇	1	3	yes	—
759	C₂×C₄²	C₂³×C₇	1	3	yes	—
760	C₂×C₄²	C₂³×C₇	1	3	yes	—
761	C₂×C₄²	C₂³×C₇	1	3	yes	—
762	C₂×C₄²	C₂³×C₇	1	12	yes	—
763	C₂×C₄²	C₂³×C₇	1	3	yes	—
764	C₂×C₄²	C₂³×C₇	1	3	yes	—
765	C₂×C₄²	C₂³×C₇	1	3	yes	—
766	C₂×C₄²	C₂³×C₇	1	3	yes	—
767	C₂×C₄²	C₂³×C₇	1	3	yes	—
768	C₂×C₄²	C₂³×C₇	1	3	yes	—
769	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
770	C₂²×C₇	—	2	1	no	—
771	C₂²×C₇	—	2	3	no	—
772	C₂²×C₇	—	2	1	no	—
773	C₂²×C₇	—	2	3	no	—
774	C₂²×C₇	—	2	3	no	—
775	C₂²×C₇	—	2	12	no	—
776	C₂²×C₇	—	2	3	no	—
777	C₂²×C₇	—	2	12	no	—
778	C₂²×C₇	—	2	3	no	—
779	C₂²×C₇	—	2	12	no	—
780	C₂²×C₇	—	4	12	no	—
781	C₂²×C₇	—	8	24	no	—
782	C₂²×C₇	C₂²×#41	1	6	yes	—
783	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
784	C₂²×C₇	C₂⁶	1	1	yes	characteristic
785	C₄×C₇	—	2	1	no	—
786	C₄×C₇	—	2	4	no	—
787	C₄×C₇	—	2	3	no	—
788	C₄×C₇	—	2	3	no	—
789	C₄×C₇	—	2	3	no	—
790	C₄×C₇	—	2	12	no	—
791	C₄×C₇	—	2	1	no	—
792	C₄×C₇	—	2	3	no	—
793	C₄×C₇	—	2	3	no	—
794	C₄×C₇	—	2	4	no	—
795	C₄×C₇	C₂²×#41	1	6	yes	—
796	C₄×C₇	C₂²×#41	1	2	yes	—
797	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
798	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
799	C₄×C₇	#585	1	2	yes	—
800	C₂⁴	C₂⁴×C₇	1	3	yes	—
801	C₂⁴	C₂⁴×C₇	1	12	yes	—
802	#41	—	2	4	no	—
803	#41	—	2	16	no	—
804	#41	—	2	12	no	—
805	#41	—	2	12	no	—
806	#41	—	2	24	no	—
807	#41	—	2	24	no	—
808	#41	—	4	24	no	—
809	#41	—	4	24	no	—
810	#41	—	4	24	no	—
811	#41	—	4	12	no	—
812	#41	C₇×#41	1	8	yes	complemented
813	C₂×Q₈	—	2	4	no	—
814	C₂×Q₈	—	4	12	no	—
815	C₂×Q₈	C₂⁴×C₇	1	3	yes	—
816	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
817	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
818	C₂×Q₈	C₂⁴×C₇	1	6	yes	—
819	C₂×Q₈	C₂⁴×C₇	1	12	yes	—
820	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
821	C₂×D₄	—	2	12	no	—
822	C₂×D₄	—	2	48	no	—
823	C₂×D₄	—	2	24	no	—
824	C₂×D₄	—	4	12	no	—
825	C₂×D₄	—	4	12	no	—
826	C₂×D₄	—	4	24	no	—
827	C₂×D₄	C₂⁴×C₇	1	6	yes	—
828	C₂×D₄	C₂⁴×C₇	1	12	yes	—
829	C₂×D₄	C₂⁴×C₇	1	6	yes	—
830	C₂×D₄	C₂⁴×C₇	1	12	yes	—
831	C₂×D₄	C₂⁴×C₇	1	6	yes	—
832	C₂×D₄	C₂⁴×C₇	1	3	yes	—
833	C₂×D₄	C₂⁴×C₇	1	12	yes	—
834	C₂×D₄	C₂⁴×C₇	1	6	yes	—
835	C₂×D₄	C₂⁴×C₇	1	12	yes	—
836	C₂×D₄	C₂⁴×C₇	1	12	yes	—
837	C₂×D₄	C₂⁴×C₇	1	12	yes	—
838	C₂×D₄	C₂⁴×C₇	1	24	yes	—
839	C₂×D₄	C₂⁴×C₇	1	3	yes	—
840	C₂²×C₄	—	2	12	no	—
841	C₂²×C₄	—	2	12	no	—
842	C₂²×C₄	—	4	6	no	—
843	C₂²×C₄	—	4	24	no	—
844	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
847	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
848	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
849	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
850	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
851	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
852	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
853	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
854	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
855	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
856	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
857	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
858	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
859	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
860	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
861	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
862	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
863	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
864	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
865	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
866	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
867	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
868	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
869	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
870	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
871	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
872	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
873	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
874	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
875	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
876	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
877	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
878	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
881	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
882	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
885	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
886	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
887	C₂²⋊C₄	C₂⁴×C₇	1	6	yes	—
888	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
889	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
890	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
891	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
892	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
893	C₂²⋊C₄	C₂⁴×C₇	1	6	yes	—
894	C₂²⋊C₄	C₂⁴×C₇	1	6	yes	—
895	C₂²⋊C₄	C₂⁴×C₇	1	6	yes	—
896	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
897	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
898	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
899	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
900	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
901	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
902	C₄²	C₂⁴×C₇	1	1	yes	characteristic
903	C₄²	C₂⁴×C₇	1	3	yes	—
904	C₄²	C₂⁴×C₇	1	1	yes	characteristic
905	C₄²	C₂⁴×C₇	1	1	yes	characteristic
906	C₄²	C₂⁴×C₇	1	1	yes	characteristic
907	C₄²	C₂⁴×C₇	1	3	yes	—
908	C₄²	C₂⁴×C₇	1	3	yes	—
909	C₄²	C₂⁴×C₇	1	3	yes	—
910	C₄²	C₂⁴×C₇	1	3	yes	—
911	C₄²	C₂⁴×C₇	1	4	yes	—
912	C₄²	C₂⁴×C₇	1	3	yes	—
913	C₄²	C₂⁴×C₇	1	3	yes	—
914	C₄²	C₂⁴×C₇	1	3	yes	—
915	C₄²	C₂⁴×C₇	1	3	yes	—
916	C₄²	C₂⁴×C₇	1	3	yes	—
917	C₄²	C₂⁴×C₇	1	3	yes	—
918	C₄²	C₂⁴×C₇	1	3	yes	—
919	C₄²	C₂⁴×C₇	1	12	yes	—
920	C₄²	C₂⁴×C₇	1	12	yes	—
921	C₂×C₇	—	2	2	no	—
922	C₂×C₇	—	2	6	no	—
923	C₂×C₇	—	4	3	no	—
924	C₂×C₇	—	4	12	no	—
925	C₂×C₇	C₂³×#41	1	1	yes	characteristic
926	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
927	C₂×C₇	C₂×#585	1	1	yes	characteristic
928	C₂³	—	2	6	no	—
929	C₂³	—	2	6	no	—
930	C₂³	—	2	24	no	—
931	C₂³	—	4	3	no	—
932	C₂³	—	4	12	no	—
933	C₂³	—	4	12	no	—
934	C₂³	C₂⁵×C₇	1	12	yes	—
935	C₂³	C₂⁵×C₇	1	3	yes	—
936	C₂³	C₂⁵×C₇	1	3	yes	—
937	C₂³	C₂⁵×C₇	1	1	yes	characteristic
938	Q₈	—	2	6	no	—
939	Q₈	—	2	4	no	—
940	Q₈	—	2	12	no	—
941	Q₈	—	2	4	no	—
942	Q₈	—	4	12	no	—
943	Q₈	C₂×C₇×#41	1	4	yes	complemented
944	D₄	—	2	24	no	—
945	D₄	—	2	12	no	—
946	D₄	—	2	24	no	—
947	D₄	—	2	24	no	—
948	D₄	—	2	12	no	—
949	D₄	—	2	6	no	—
950	D₄	—	2	12	no	—
951	D₄	—	2	12	no	—
952	D₄	—	4	12	no	—
953	D₄	—	4	12	no	—
954	D₄	—	4	24	no	—
955	D₄	—	4	12	no	—
956	D₄	C₂×C₇×#41	1	12	yes	complemented
957	C₂×C₄	—	2	6	no	—
958	C₂×C₄	—	2	6	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	6	no	—
961	C₂×C₄	—	2	6	no	—
962	C₂×C₄	—	2	6	no	—
963	C₂×C₄	—	2	24	no	—
964	C₂×C₄	—	2	6	no	—
965	C₂×C₄	—	2	6	no	—
966	C₂×C₄	—	2	6	no	—
967	C₂×C₄	—	2	6	no	—
968	C₂×C₄	—	2	24	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	6	no	—
971	C₂×C₄	—	2	6	no	—
972	C₂×C₄	—	4	3	no	—
973	C₂×C₄	—	4	3	no	—
974	C₂×C₄	—	4	3	no	—
975	C₂×C₄	—	4	12	no	—
976	C₂×C₄	—	4	24	no	—
977	C₂×C₄	—	4	12	no	—
978	C₂×C₄	C₂×C₇×#41	1	12	yes	complemented
979	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	complemented
980	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
981	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
982	C₂×C₄	C₂⁵×C₇	1	3	yes	—
983	C₂×C₄	C₂⁵×C₇	1	3	yes	—
984	C₂×C₄	C₂⁵×C₇	1	4	yes	—
985	C₂×C₄	C₂⁵×C₇	1	4	yes	—
986	C₂×C₄	C₂⁵×C₇	1	3	yes	—
987	C₂×C₄	C₂⁵×C₇	1	3	yes	—
988	C₂×C₄	C₂⁵×C₇	1	3	yes	—
989	C₂×C₄	C₂⁵×C₇	1	12	yes	—
990	C₂×C₄	C₂⁵×C₇	1	3	yes	—
991	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
992	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
993	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
994	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
995	C₇	#62800	1	1	yes	characteristic, direct product factor, Sylow
996	C₂²	—	2	1	no	—
997	C₂²	—	2	3	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	3	no	—
1000	C₂²	—	2	3	no	—
1001	C₂²	—	2	12	no	—
1002	C₂²	—	2	3	no	—
1003	C₂²	—	2	12	no	—
1004	C₂²	—	2	3	no	—
1005	C₂²	—	2	12	no	—
1006	C₂²	—	4	12	no	—
1007	C₂²	—	8	24	no	—
1008	C₂²	C₂²×C₇×#41	1	6	yes	—
1009	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1010	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	4	no	—
1013	C₄	—	2	3	no	—
1014	C₄	—	2	3	no	—
1015	C₄	—	2	3	no	—
1016	C₄	—	2	12	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	3	no	—
1019	C₄	—	2	3	no	—
1020	C₄	—	2	4	no	—
1021	C₄	C₂²×C₇×#41	1	6	yes	—
1022	C₄	C₂²×C₇×#41	1	2	yes	—
1023	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1024	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1025	C₄	C₇×#585	1	2	yes	—
1026	C₂	—	2	2	no	—
1027	C₂	—	2	6	no	—
1028	C₂	—	4	3	no	—
1029	C₂	—	4	12	no	—
1030	C₂	C₂³×C₇×#41	1	1	yes	characteristic
1031	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂	C₂×C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂²×C₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3522	C₂	semidirect
2. C₇×#3519	C₂	semidirect
3. C₇×#3517	C₂	semidirect
4. C₇×#3514	C₂	semidirect
5. C₇×#3511	C₂	semidirect
6. C₇×#3508	C₂	semidirect
7. C₇×#3503	C₂	semidirect
8. C₇×#3498	C₂	semidirect
9. C₇×#3494	C₂	semidirect
10. C₇×#3488	C₂	semidirect
11. C₇×#3483	C₂	semidirect
12. C₇×#3481	C₂	semidirect
13. C₇×#3480	C₂	semidirect
14. C₇×D₄×#41	C₂	semidirect
15. C₇×#3460	C₂	semidirect
16. C₇×#3444	C₂	semidirect
17. C₂×C₇×#532	C₂	semidirect
18. C₄×C₇×H(5,𝔽₂)	C₂	semidirect
19. C₂×C₄×C₇×#41	C₂	semidirect
22. C₂²×C₇×#41	C₂²	semidirect
23. C₇×#559	C₂²	semidirect
24. C₇×#559	C₂²	semidirect
25. C₇×Q₈²	C₂²	semidirect
26. C₇×#557	C₂²	semidirect
27. C₇×#556	C₂²	semidirect
28. C₇×#555	C₂²	semidirect
29. C₇×#555	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#553	C₂²	semidirect
34. C₇×#553	C₂²	semidirect
35. C₇×#551	C₂²	semidirect
36. C₇×#550	C₂²	semidirect
37. C₇×#550	C₂²	semidirect
38. C₇×#550	C₂²	semidirect
39. C₇×#550	C₂²	semidirect
40. C₇×#550	C₂²	semidirect
41. C₇×D₄×Q₈	C₂²	semidirect
42. C₇×#548	C₂²	semidirect
43. C₇×#548	C₂²	semidirect
44. C₇×#547	C₂²	semidirect
45. C₇×#547	C₂²	semidirect
46. C₇×#546	C₂²	semidirect
47. C₇×#546	C₂²	semidirect
48. C₇×#546	C₂²	semidirect
49. C₇×#546	C₂²	semidirect
50. C₇×D₄²	C₂²	semidirect
51. C₇×D₄²	C₂²	semidirect
52. C₇×D₄²	C₂²	semidirect
53. C₇×#544	C₂²	semidirect
54. C₇×#542	C₂²	semidirect
55. C₇×#542	C₂²	semidirect
56. C₇×#540	C₂²	semidirect
57. C₇×#540	C₂²	semidirect
58. C₇×#538	C₂²	semidirect
59. C₇×#537	C₂²	semidirect
60. C₇×#535	C₂²	semidirect
61. C₇×#535	C₂²	semidirect
62. C₇×#533	C₂²	semidirect
63. C₇×#533	C₂²	semidirect
64. C₇×#533	C₂²	semidirect
65. C₇×#532	C₂²	semidirect
66. C₇×#532	C₂²	semidirect
67. C₇×#532	C₂²	semidirect
68. C₇×#532	C₂²	semidirect
69. C₇×#532	C₂²	semidirect
70. C₇×#532	C₂²	semidirect
71. C₇×#532	C₂²	semidirect
72. C₇×#532	C₂²	semidirect
73. C₇×#532	C₂²	semidirect
74. C₇×#532	C₂²	semidirect
75. C₇×#532	C₂²	semidirect
76. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
77. C₂×C₇×#127	C₂²	semidirect
78. C₇×#529	C₂²	semidirect
79. C₇×#529	C₂²	semidirect
80. C₇×#529	C₂²	semidirect
81. C₇×#529	C₂²	semidirect
82. C₇×#529	C₂²	semidirect
83. C₇×#529	C₂²	semidirect
84. C₇×#529	C₂²	semidirect
85. C₂×C₇×#124	C₂²	semidirect
86. C₇×#525	C₂²	semidirect
87. C₇×#525	C₂²	semidirect
88. C₇×#525	C₂²	semidirect
89. C₇×#525	C₂²	semidirect
90. C₂×C₇×#121	C₂²	semidirect
91. C₂×C₇×#121	C₂²	semidirect
93. C₇×#520	C₂²	semidirect
94. C₇×#520	C₂²	semidirect
95. C₇×#518	C₂²	semidirect
96. C₇×#518	C₂²	semidirect
99. C₄×C₇×#41	C₂²	semidirect
100. C₄×C₇×#41	C₂²	semidirect
101. C₄×C₇×#41	C₂²	semidirect
102. C₄×C₇×#41	C₂²	semidirect
103. C₄×C₇×#41	C₂²	semidirect
104. C₄×C₇×#41	C₂²	semidirect
105. C₄×C₇×#41	C₂²	semidirect
106. C₄×C₇×#41	C₂²	semidirect
107. C₄×C₇×#41	C₂²	semidirect
108. C₄×C₇×#41	C₂²	semidirect
109. C₂×C₄×C₇×Q₈	C₂²	semidirect
110. C₂×C₄×C₇×Q₈	C₂²	semidirect
111. C₂×C₄×C₇×D₄	C₂²	semidirect
112. C₂×C₄×C₇×D₄	C₂²	semidirect
113. C₂×C₄×C₇×D₄	C₂²	semidirect
114. C₂×C₄×C₇×D₄	C₂²	semidirect
115. C₂×C₄×C₇×D₄	C₂²	semidirect
116. C₂×C₇×#117	C₂²	semidirect
117. C₂²×C₄²×C₇	C₂²	semidirect
118. #62800	C₇	direct (N × H)
292. #3522	C₂×C₇	semidirect
293. #3519	C₂×C₇	semidirect
294. #3517	C₂×C₇	semidirect
295. #3514	C₂×C₇	semidirect
296. #3511	C₂×C₇	semidirect
297. #3508	C₂×C₇	semidirect
298. #3503	C₂×C₇	semidirect
299. #3498	C₂×C₇	semidirect
300. #3494	C₂×C₇	semidirect
301. #3488	C₂×C₇	semidirect
302. #3483	C₂×C₇	semidirect
303. #3481	C₂×C₇	semidirect
304. #3480	C₂×C₇	semidirect
305. D₄×#41	C₂×C₇	semidirect
306. #3460	C₂×C₇	semidirect
307. #3444	C₂×C₇	semidirect
308. C₂×#532	C₂×C₇	semidirect
309. C₄×H(5,𝔽₂)	C₂×C₇	semidirect
310. C₂×C₄×#41	C₂×C₇	semidirect
323. C₇×#41	#41	semidirect
434. C₂²×#41	C₂²×C₇	semidirect
435. #559	C₂²×C₇	semidirect
436. #559	C₂²×C₇	semidirect
437. Q₈²	C₂²×C₇	semidirect
438. #557	C₂²×C₇	semidirect
439. #556	C₂²×C₇	semidirect
440. #555	C₂²×C₇	semidirect
441. #555	C₂²×C₇	semidirect
442. #554	C₂²×C₇	semidirect
443. #554	C₂²×C₇	semidirect
444. #553	C₂²×C₇	semidirect
445. #553	C₂²×C₇	semidirect
446. #553	C₂²×C₇	semidirect
447. #551	C₂²×C₇	semidirect
448. #550	C₂²×C₇	semidirect
449. #550	C₂²×C₇	semidirect
450. #550	C₂²×C₇	semidirect
451. #550	C₂²×C₇	semidirect
452. #550	C₂²×C₇	semidirect
453. D₄×Q₈	C₂²×C₇	semidirect
454. #548	C₂²×C₇	semidirect
455. #548	C₂²×C₇	semidirect
456. #547	C₂²×C₇	semidirect
457. #547	C₂²×C₇	semidirect
458. #546	C₂²×C₇	semidirect
459. #546	C₂²×C₇	semidirect
460. #546	C₂²×C₇	semidirect
461. #546	C₂²×C₇	semidirect
462. D₄²	C₂²×C₇	semidirect
463. D₄²	C₂²×C₇	semidirect
464. D₄²	C₂²×C₇	semidirect
465. #544	C₂²×C₇	semidirect
466. #542	C₂²×C₇	semidirect
467. #542	C₂²×C₇	semidirect
468. #540	C₂²×C₇	semidirect
469. #540	C₂²×C₇	semidirect
470. #538	C₂²×C₇	semidirect
471. #537	C₂²×C₇	semidirect
472. #535	C₂²×C₇	semidirect
473. #535	C₂²×C₇	semidirect
474. #533	C₂²×C₇	semidirect
475. #533	C₂²×C₇	semidirect
476. #533	C₂²×C₇	semidirect
477. #532	C₂²×C₇	semidirect
478. #532	C₂²×C₇	semidirect
479. #532	C₂²×C₇	semidirect
480. #532	C₂²×C₇	semidirect
481. #532	C₂²×C₇	semidirect
482. #532	C₂²×C₇	semidirect
483. #532	C₂²×C₇	semidirect
484. #532	C₂²×C₇	semidirect
485. #532	C₂²×C₇	semidirect
486. #532	C₂²×C₇	semidirect
487. #532	C₂²×C₇	semidirect
488. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
489. C₂×#127	C₂²×C₇	semidirect
490. #529	C₂²×C₇	semidirect
491. #529	C₂²×C₇	semidirect
492. #529	C₂²×C₇	semidirect
493. #529	C₂²×C₇	semidirect
494. #529	C₂²×C₇	semidirect
495. #529	C₂²×C₇	semidirect
496. #529	C₂²×C₇	semidirect
497. C₂×#124	C₂²×C₇	semidirect
498. #525	C₂²×C₇	semidirect
499. #525	C₂²×C₇	semidirect
500. #525	C₂²×C₇	semidirect
501. #525	C₂²×C₇	semidirect
502. C₂×#121	C₂²×C₇	semidirect
503. C₂×#121	C₂²×C₇	semidirect
505. #520	C₂²×C₇	semidirect
506. #520	C₂²×C₇	semidirect
507. #518	C₂²×C₇	semidirect
508. #518	C₂²×C₇	semidirect
511. C₄×#41	C₂²×C₇	semidirect
512. C₄×#41	C₂²×C₇	semidirect
513. C₄×#41	C₂²×C₇	semidirect
514. C₄×#41	C₂²×C₇	semidirect
515. C₄×#41	C₂²×C₇	semidirect
516. C₄×#41	C₂²×C₇	semidirect
517. C₄×#41	C₂²×C₇	semidirect
518. C₄×#41	C₂²×C₇	semidirect
519. C₄×#41	C₂²×C₇	semidirect
520. C₄×#41	C₂²×C₇	semidirect
521. C₂×C₄×Q₈	C₂²×C₇	semidirect
522. C₂×C₄×Q₈	C₂²×C₇	semidirect
523. C₂×C₄×D₄	C₂²×C₇	semidirect
524. C₂×C₄×D₄	C₂²×C₇	semidirect
525. C₂×C₄×D₄	C₂²×C₇	semidirect
526. C₂×C₄×D₄	C₂²×C₇	semidirect
527. C₂×C₄×D₄	C₂²×C₇	semidirect
528. C₂×#117	C₂²×C₇	semidirect
529. C₂²×C₄²	C₂²×C₇	semidirect
545. C₇×Q₈	C₂×#41	semidirect
558. C₇×D₄	C₂×#41	semidirect
580. C₂×C₄×C₇	C₂×#41	semidirect
581. C₂×C₄×C₇	H(5,𝔽₂)	semidirect
812. #41	C₇×#41	semidirect
943. Q₈	C₂×C₇×#41	semidirect
956. D₄	C₂×C₇×#41	semidirect
978. C₂×C₄	C₂×C₇×#41	semidirect
979. C₂×C₄	C₇×H(5,𝔽₂)	semidirect
995. C₇	#62800	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×#3522	2
C₇×#3519	2
C₇×#3517	2
C₇×#3514	2
C₇×#3511	2
C₇×#3508	2
C₇×#3503	2
C₇×#3498	2
C₇×#3494	2
C₇×#3488	2
C₇×#3483	2
C₇×#3481	2
C₇×#3480	2
C₇×D₄×#41	2
C₇×#3460	2
C₇×#3444	2
C₂×C₇×#532	2
C₄×C₇×H(5,𝔽₂)	2
C₂×C₄×C₇×#41	2
#62800	7

Subgroups — C7×#62800 #13240016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62800 #13240016