Subgroups — C₇×#61207 #13238423

Order 1792.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3500	C₂	1	1	yes	maximal, characteristic
3	C₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₇×#3323	C₂	1	2	yes	maximal, complemented
5	C₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₇×#3314	C₂	1	2	yes	maximal, complemented
7	C₇×#3313	C₂	1	2	yes	maximal, complemented
8	C₇×#3311	C₂	1	2	yes	maximal, complemented
9	C₇×#3300	C₂	1	2	yes	maximal, complemented
10	C₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic
27	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
31	C₇×#559	—	2	1	no	—
32	C₇×#557	—	2	1	no	—
33	C₇×#556	—	2	1	no	—
34	C₇×#556	—	2	1	no	—
35	C₇×#556	C₂²	1	2	yes	complemented
36	C₇×#554	C₂²	1	2	yes	complemented
37	C₇×#552	C₂²	1	2	yes	complemented
38	C₇×#552	C₂²	1	2	yes	complemented
39	C₇×#548	C₂²	1	2	yes	—
40	C₇×#548	C₂²	1	2	yes	—
41	C₇×#546	—	2	2	no	—
42	C₇×#546	—	2	2	no	—
43	C₇×#546	C₂²	1	2	yes	—
44	C₇×#546	C₂²	1	2	yes	—
45	C₇×#539	—	2	2	no	—
46	C₇×#536	—	2	1	no	—
47	C₇×#536	C₂²	1	1	yes	characteristic
48	C₇×#536	C₂²	1	1	yes	characteristic
49	C₇×#536	C₂²	1	1	yes	characteristic, complemented
50	C₇×#535	—	2	1	no	—
51	C₇×#535	C₂²	1	1	yes	characteristic
52	C₇×#533	C₂²	1	1	yes	characteristic, complemented
53	C₇×#532	—	2	1	no	—
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#529	—	2	2	no	—
56	C₂×C₇×#124	—	2	1	no	—
57	C₂×C₇×#124	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₇×#41	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₇×#489	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#488	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#484	C₂²	1	2	yes	complemented
69	C₇×#483	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#482	C₂²	1	2	yes	complemented
72	C₇×#481	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	1	yes	characteristic, complemented
75	C₇×#479	C₂²	1	1	yes	characteristic, complemented
76	C₇×#478	C₂²	1	1	yes	characteristic, complemented
77	C₇×#478	C₂²	1	1	yes	characteristic, complemented
78	C₇×#477	C₂²	1	1	yes	characteristic, complemented
79	C₇×#476	C₂²	1	1	yes	characteristic, complemented
80	C₇×#475	C₂²	1	1	yes	characteristic, complemented
81	C₇×#474	C₂²	1	1	yes	characteristic, complemented
82	C₇×#470	C₂²	1	2	yes	complemented
83	C₇×#470	C₂²	1	2	yes	complemented
84	C₇×#468	C₂²	1	2	yes	complemented
85	C₇×#468	C₂²	1	2	yes	complemented
86	C₇×#467	C₂²	1	2	yes	complemented
87	C₇×#467	C₂²	1	2	yes	complemented
88	C₇×#465	C₂²	1	2	yes	complemented
89	C₇×#465	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#464	C₂²	1	2	yes	complemented
92	C₇×#464	C₂²	1	2	yes	complemented
93	C₇×#464	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	—
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#452	C₂²	1	2	yes	complemented
97	C₇×#452	C₂²	1	2	yes	complemented
98	C₇×#451	C₂²	1	2	yes	complemented
99	C₇×#451	C₂²	1	2	yes	complemented
100	C₇×#450	C₂²	1	2	yes	—
101	C₇×#450	C₂²	1	2	yes	—
102	C₇×#441	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	complemented
107	C₇×#435	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₇×#427	C₂²	1	1	yes	characteristic, complemented
112	C₇×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
114	C₇×#419	C₂²	1	1	yes	characteristic, complemented
115	C₇×#419	C₂²	1	1	yes	characteristic, complemented
116	C₇×#419	C₂²	1	2	yes	complemented
117	C₇×#419	C₂²	1	1	yes	characteristic, complemented
118	C₇×#418	C₂²	1	1	yes	characteristic
119	C₇×#418	C₂²	1	2	yes	—
120	C₇×#418	C₂²	1	1	yes	characteristic
121	C₇×#417	C₂²	1	1	yes	characteristic
122	C₇×#417	C₂²	1	2	yes	—
123	C₇×#417	C₂²	1	2	yes	complemented
124	C₇×#416	C₂²	1	1	yes	characteristic
125	C₇×#416	C₂²	1	1	yes	characteristic
126	C₇×#416	C₂²	1	2	yes	—
127	C₇×#416	C₂²	1	2	yes	complemented
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#103	C₂²	1	2	yes	complemented
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic
131	C₂×C₇×#102	C₂²	1	2	yes	—
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	#61207	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₇×H(5,𝔽₂)	—	2	4	no	—
139	C₇×H(5,𝔽₂)	—	4	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	2	no	—
143	C₂×C₇×#41	C₂³	1	2	yes	—
144	C₂×C₇×#41	C₂³	1	2	yes	—
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂²×C₇×Q₈	—	2	1	no	—
149	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	C₂³	1	2	yes	—
152	C₂²×C₇×D₄	—	2	1	no	—
153	C₂²×C₇×D₄	—	2	2	no	—
154	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₇×D₄	C₂³	1	2	yes	—
156	C₇×#137	—	2	4	no	—
157	C₂×C₇×Q₁₆	—	4	2	no	—
158	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
159	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₇×SD₁₆	—	4	2	no	—
162	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
165	C₇×#131	—	4	2	no	—
166	C₇×#131	—	4	2	no	—
167	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₇×M₁₆	C₂³	1	2	yes	—
170	C₂×C₇×M₁₆	C₂³	1	2	yes	—
171	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
172	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
173	C₂²×C₇×C₈	C₂³	1	2	yes	—
174	C₂²×C₇×C₈	C₂³	1	2	yes	—
175	C₇×C₄⋊Q₈	—	2	1	no	—
176	C₇×C₄⋊Q₈	—	2	1	no	—
177	C₇×C₄⋊Q₈	—	2	1	no	—
178	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
179	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₇×#127	—	2	1	no	—
182	C₇×#127	D₄	1	1	yes	characteristic
183	C₇×#126	—	2	2	no	—
184	C₇×#126	—	2	2	no	—
185	C₇×#126	—	2	2	no	—
186	C₇×#126	—	2	2	no	—
187	C₇×#125	—	2	2	no	—
188	C₇×#125	—	2	2	no	—
189	C₇×#125	—	2	2	no	—
190	C₇×#125	C₂³	1	1	yes	characteristic
191	C₇×#125	C₂³	1	1	yes	characteristic
192	C₇×#124	—	2	1	no	—
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	1	no	—
196	C₇×#124	—	2	1	no	—
197	C₇×#124	—	2	2	no	—
198	C₇×#124	—	2	2	no	—
199	C₇×#124	—	2	1	no	—
200	C₇×#124	—	2	1	no	—
201	C₇×#124	D₄	1	1	yes	characteristic
202	C₇×#124	D₄	1	1	yes	characteristic
203	C₇×#124	C₂³	1	2	yes	—
204	C₇×#124	C₂³	1	2	yes	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	—	2	2	no	—
207	C₇×#123	—	2	2	no	—
208	C₇×#123	—	2	2	no	—
209	C₇×#123	—	2	2	no	—
210	C₇×#123	—	2	2	no	—
211	C₇×#123	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	1	no	—
213	C₇×C₂²⋊Q₈	—	2	1	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	—	2	2	no	—
218	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	D₄	1	2	yes	—
229	C₇×#121	D₄	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₄×C₇×Q₈	—	2	1	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	—	2	2	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	1	no	—
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	2	yes	—
246	C₄×C₇×D₄	—	2	2	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₇×#117	—	2	2	no	—
260	C₇×#117	—	2	2	no	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	C₂³	1	2	yes	—
263	C₇×#117	C₂³	1	2	yes	—
264	C₇×#117	C₂³	1	1	yes	characteristic
265	C₇×#117	C₂³	1	1	yes	characteristic
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²×C₇	—	2	1	no	—
276	C₂×C₄²×C₇	—	2	1	no	—
277	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
278	C₇×#107	C₂³	1	1	yes	characteristic
279	C₇×#107	C₂³	1	1	yes	characteristic
280	C₇×#107	C₂³	1	1	yes	characteristic
281	C₇×#107	C₂³	1	1	yes	characteristic
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#106	C₂³	1	1	yes	characteristic
284	C₇×#106	C₂³	1	1	yes	characteristic
285	C₇×#106	C₂³	1	1	yes	characteristic
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#103	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×#102	C₂³	1	1	yes	characteristic
309	C₇×#102	C₂³	1	1	yes	characteristic
310	C₇×#102	C₂³	1	1	yes	characteristic
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	2	yes	—
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×#102	C₂³	1	2	yes	—
315	C₇×#102	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3507	C₂×C₇	1	1	yes	characteristic, complemented
323	#3500	C₂×C₇	1	1	yes	characteristic
324	#3327	C₂×C₇	1	2	yes	complemented
325	#3323	C₂×C₇	1	2	yes	complemented
326	#3316	C₂×C₇	1	2	yes	complemented
327	#3314	C₂×C₇	1	2	yes	complemented
328	#3313	C₂×C₇	1	2	yes	complemented
329	#3311	C₂×C₇	1	2	yes	complemented
330	#3300	C₂×C₇	1	2	yes	complemented
331	#3296	C₂×C₇	1	2	yes	complemented
332	#3140	C₂×C₇	1	1	yes	characteristic, complemented
333	#3097	C₂×C₇	1	1	yes	characteristic, complemented
334	#3096	C₂×C₇	1	1	yes	characteristic, complemented
335	#3076	C₂×C₇	1	1	yes	characteristic, complemented
336	#3059	C₂×C₇	1	1	yes	characteristic, complemented
337	#3057	C₂×C₇	1	1	yes	characteristic, complemented
338	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
339	#3011	C₂×C₇	1	1	yes	characteristic, complemented
340	#3009	C₂×C₇	1	1	yes	characteristic, complemented
341	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
342	#2935	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	#2897	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	2	no	—
346	C₂⁴×C₇	—	2	1	no	—
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	4	no	—
353	C₇×#41	—	2	4	no	—
354	C₇×#41	—	4	2	no	—
355	C₇×#41	—	4	2	no	—
356	C₇×#41	—	4	4	no	—
357	C₇×#41	—	4	4	no	—
358	C₇×#41	—	4	8	no	—
359	C₇×#41	#41	1	4	yes	—
360	C₂×C₇×Q₈	—	2	1	no	—
361	C₂×C₇×Q₈	—	2	1	no	—
362	C₂×C₇×Q₈	—	2	2	no	—
363	C₂×C₇×Q₈	—	2	1	no	—
364	C₂×C₇×Q₈	—	2	1	no	—
365	C₂×C₇×Q₈	—	2	4	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	2	2	no	—
370	C₂×C₇×Q₈	—	4	2	no	—
371	C₂×C₇×Q₈	—	4	4	no	—
372	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
373	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
374	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
375	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
376	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×D₄	—	2	1	no	—
378	C₂×C₇×D₄	—	2	4	no	—
379	C₂×C₇×D₄	—	2	2	no	—
380	C₂×C₇×D₄	—	2	2	no	—
381	C₂×C₇×D₄	—	2	2	no	—
382	C₂×C₇×D₄	—	2	2	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	4	2	no	—
388	C₂×C₇×D₄	—	4	4	no	—
389	C₂×C₇×D₄	—	4	8	no	—
390	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
391	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
392	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
393	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	C₂⁴	1	2	yes	—
397	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₇	—	2	1	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	2	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	2	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
414	C₇×Q₁₆	—	2	4	no	—
415	C₇×Q₁₆	—	4	2	no	—
416	C₇×Q₁₆	—	4	2	no	—
417	C₇×SD₁₆	—	2	4	no	—
418	C₇×SD₁₆	—	4	2	no	—
419	C₇×SD₁₆	—	4	2	no	—
420	C₇×M₁₆	—	2	2	no	—
421	C₇×M₁₆	—	2	2	no	—
422	C₇×M₁₆	—	4	2	no	—
423	C₇×M₁₆	—	4	2	no	—
424	C₂×C₇×C₈	—	2	2	no	—
425	C₂×C₇×C₈	—	2	2	no	—
426	C₂×C₇×C₈	—	4	2	no	—
427	C₂×C₇×C₈	—	4	2	no	—
428	C₂×C₇×C₈	C₂⁴	1	2	yes	—
429	C₂×C₇×C₈	C₂⁴	1	2	yes	—
430	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	2	no	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	1	no	—
440	C₇×C₄⋊C₄	—	2	1	no	—
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	—	2	1	no	—
443	C₇×C₄⋊C₄	—	2	2	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	1	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	1	no	—
449	C₇×C₄⋊C₄	—	2	1	no	—
450	C₇×C₄⋊C₄	—	2	1	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
454	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
455	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
456	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
457	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
458	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
459	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
460	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
462	C₇×C₂²⋊C₄	—	2	2	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	2	no	—
466	C₇×C₂²⋊C₄	—	2	1	no	—
467	C₇×C₂²⋊C₄	—	2	1	no	—
468	C₇×C₂²⋊C₄	—	2	1	no	—
469	C₇×C₂²⋊C₄	—	2	2	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	2	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	—	2	2	no	—
476	C₇×C₂²⋊C₄	—	2	2	no	—
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
479	C₇×C₂²⋊C₄	—	2	1	no	—
480	C₇×C₂²⋊C₄	—	2	1	no	—
481	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
482	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
483	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
484	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
485	C₄²×C₇	—	2	2	no	—
486	C₄²×C₇	—	2	1	no	—
487	C₄²×C₇	—	2	1	no	—
488	C₄²×C₇	—	2	1	no	—
489	C₄²×C₇	—	2	2	no	—
490	C₄²×C₇	—	2	2	no	—
491	C₄²×C₇	—	2	2	no	—
492	C₄²×C₇	—	2	1	no	—
493	C₄²×C₇	—	2	1	no	—
494	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₇	C₂⁴	1	1	yes	characteristic
498	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
499	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
500	C₂×#137	C₂²×C₇	1	1	yes	characteristic
501	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
502	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
503	C₂×#131	C₂²×C₇	1	1	yes	characteristic
504	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
505	#559	—	2	1	no	—
506	#557	—	2	1	no	—
507	#556	—	2	1	no	—
508	#556	—	2	1	no	—
509	#556	C₂²×C₇	1	2	yes	complemented
510	#554	C₂²×C₇	1	2	yes	complemented
511	#552	C₂²×C₇	1	2	yes	complemented
512	#552	C₂²×C₇	1	2	yes	complemented
513	#548	C₂²×C₇	1	2	yes	—
514	#548	C₂²×C₇	1	2	yes	—
515	#546	—	2	2	no	—
516	#546	—	2	2	no	—
517	#546	C₂²×C₇	1	2	yes	—
518	#546	C₂²×C₇	1	2	yes	—
519	#539	—	2	2	no	—
520	#536	—	2	1	no	—
521	#536	C₂²×C₇	1	1	yes	characteristic
522	#536	C₂²×C₇	1	1	yes	characteristic
523	#536	C₂²×C₇	1	1	yes	characteristic, complemented
524	#535	—	2	1	no	—
525	#535	C₂²×C₇	1	1	yes	characteristic
526	#533	C₂²×C₇	1	1	yes	characteristic, complemented
527	#532	—	2	1	no	—
528	#532	C₂²×C₇	1	1	yes	characteristic
529	#529	—	2	2	no	—
530	C₂×#124	—	2	1	no	—
531	C₂×#124	C₂²×C₇	1	1	yes	characteristic
532	#520	C₂²×C₇	1	1	yes	characteristic
533	#520	C₂²×C₇	1	1	yes	characteristic, complemented
534	C₄×#41	C₂²×C₇	1	1	yes	characteristic
535	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
536	#489	C₂²×C₇	1	2	yes	complemented
537	#489	C₂²×C₇	1	2	yes	complemented
538	#488	C₂²×C₇	1	2	yes	complemented
539	#488	C₂²×C₇	1	2	yes	complemented
540	#485	C₂²×C₇	1	2	yes	complemented
541	#485	C₂²×C₇	1	2	yes	complemented
542	#484	C₂²×C₇	1	2	yes	complemented
543	#483	C₂²×C₇	1	2	yes	complemented
544	#482	C₂²×C₇	1	2	yes	complemented
545	#482	C₂²×C₇	1	2	yes	complemented
546	#481	C₂²×C₇	1	2	yes	complemented
547	#480	C₂²×C₇	1	2	yes	complemented
548	#479	C₂²×C₇	1	1	yes	characteristic, complemented
549	#479	C₂²×C₇	1	1	yes	characteristic, complemented
550	#478	C₂²×C₇	1	1	yes	characteristic, complemented
551	#478	C₂²×C₇	1	1	yes	characteristic, complemented
552	#477	C₂²×C₇	1	1	yes	characteristic, complemented
553	#476	C₂²×C₇	1	1	yes	characteristic, complemented
554	#475	C₂²×C₇	1	1	yes	characteristic, complemented
555	#474	C₂²×C₇	1	1	yes	characteristic, complemented
556	#470	C₂²×C₇	1	2	yes	complemented
557	#470	C₂²×C₇	1	2	yes	complemented
558	#468	C₂²×C₇	1	2	yes	complemented
559	#468	C₂²×C₇	1	2	yes	complemented
560	#467	C₂²×C₇	1	2	yes	complemented
561	#467	C₂²×C₇	1	2	yes	complemented
562	#465	C₂²×C₇	1	2	yes	complemented
563	#465	C₂²×C₇	1	2	yes	complemented
564	#464	C₂²×C₇	1	2	yes	complemented
565	#464	C₂²×C₇	1	2	yes	complemented
566	#464	C₂²×C₇	1	2	yes	complemented
567	#464	C₂²×C₇	1	2	yes	complemented
568	#452	C₂²×C₇	1	2	yes	—
569	#452	C₂²×C₇	1	2	yes	—
570	#452	C₂²×C₇	1	2	yes	complemented
571	#452	C₂²×C₇	1	2	yes	complemented
572	#451	C₂²×C₇	1	2	yes	complemented
573	#451	C₂²×C₇	1	2	yes	complemented
574	#450	C₂²×C₇	1	2	yes	—
575	#450	C₂²×C₇	1	2	yes	—
576	#441	C₂²×C₇	1	2	yes	complemented
577	#440	C₂²×C₇	1	2	yes	complemented
578	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
579	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
580	#436	C₂²×C₇	1	2	yes	complemented
581	#435	C₂²×C₇	1	2	yes	complemented
582	#435	C₂²×C₇	1	2	yes	complemented
583	C₈×D₄	C₂²×C₇	1	2	yes	complemented
584	#428	C₂²×C₇	1	1	yes	characteristic, complemented
585	#427	C₂²×C₇	1	1	yes	characteristic, complemented
586	#427	C₂²×C₇	1	1	yes	characteristic, complemented
587	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
588	#419	C₂²×C₇	1	1	yes	characteristic, complemented
589	#419	C₂²×C₇	1	1	yes	characteristic, complemented
590	#419	C₂²×C₇	1	2	yes	complemented
591	#419	C₂²×C₇	1	1	yes	characteristic, complemented
592	#418	C₂²×C₇	1	1	yes	characteristic
593	#418	C₂²×C₇	1	1	yes	characteristic
594	#418	C₂²×C₇	1	2	yes	—
595	#417	C₂²×C₇	1	1	yes	characteristic
596	#417	C₂²×C₇	1	2	yes	—
597	#417	C₂²×C₇	1	2	yes	complemented
598	#416	C₂²×C₇	1	1	yes	characteristic
599	#416	C₂²×C₇	1	1	yes	characteristic
600	#416	C₂²×C₇	1	2	yes	—
601	#416	C₂²×C₇	1	2	yes	complemented
602	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
603	C₂×#103	C₂²×C₇	1	2	yes	complemented
604	C₂×#102	C₂²×C₇	1	1	yes	characteristic
605	C₂×#102	C₂²×C₇	1	2	yes	—
606	#408	C₂²×C₇	1	1	yes	characteristic
607	#408	C₂²×C₇	1	1	yes	characteristic, complemented
608	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
609	C₂³×C₇	—	2	1	no	—
610	C₂³×C₇	—	2	2	no	—
611	C₂³×C₇	—	4	4	no	—
612	C₂³×C₇	—	4	2	no	—
613	C₂³×C₇	—	8	1	no	—
614	C₂³×C₇	—	8	1	no	—
615	C₂³×C₇	—	8	2	no	—
616	C₂³×C₇	—	8	2	no	—
617	C₂³×C₇	C₂²×D₄	1	2	yes	—
618	C₂³×C₇	C₂²×D₄	1	2	yes	—
619	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₇×Q₈	—	2	2	no	—
621	C₇×Q₈	—	2	2	no	—
622	C₇×Q₈	—	2	1	no	—
623	C₇×Q₈	—	2	2	no	—
624	C₇×Q₈	—	2	2	no	—
625	C₇×Q₈	—	2	2	no	—
626	C₇×Q₈	—	2	2	no	—
627	C₇×Q₈	—	4	4	no	—
628	C₇×Q₈	—	4	2	no	—
629	C₇×Q₈	—	4	2	no	—
630	C₇×Q₈	—	4	2	no	—
631	C₇×Q₈	—	8	1	no	—
632	C₇×Q₈	C₂×#41	1	2	yes	—
633	C₇×D₄	—	2	4	no	—
634	C₇×D₄	—	2	4	no	—
635	C₇×D₄	—	2	4	no	—
636	C₇×D₄	—	2	2	no	—
637	C₇×D₄	—	2	2	no	—
638	C₇×D₄	—	2	2	no	—
639	C₇×D₄	—	2	1	no	—
640	C₇×D₄	—	2	2	no	—
641	C₇×D₄	—	4	2	no	—
642	C₇×D₄	—	4	2	no	—
643	C₇×D₄	—	4	4	no	—
644	C₇×D₄	—	4	4	no	—
645	C₇×D₄	—	4	4	no	—
646	C₇×D₄	—	4	2	no	—
647	C₇×D₄	—	8	2	no	—
648	C₇×D₄	—	8	2	no	—
649	C₇×D₄	C₂×#41	1	2	yes	—
650	C₂×C₄×C₇	—	2	1	no	—
651	C₂×C₄×C₇	—	2	4	no	—
652	C₂×C₄×C₇	—	2	2	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	2	no	—
655	C₂×C₄×C₇	—	2	2	no	—
656	C₂×C₄×C₇	—	2	2	no	—
657	C₂×C₄×C₇	—	2	1	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	1	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	1	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	2	no	—
665	C₂×C₄×C₇	—	4	1	no	—
666	C₂×C₄×C₇	—	4	1	no	—
667	C₂×C₄×C₇	—	4	4	no	—
668	C₂×C₄×C₇	—	4	4	no	—
669	C₂×C₄×C₇	—	4	4	no	—
670	C₂×C₄×C₇	—	4	2	no	—
671	C₂×C₄×C₇	—	4	2	no	—
672	C₂×C₄×C₇	—	8	1	no	—
673	C₂×C₄×C₇	—	8	1	no	—
674	C₂×C₄×C₇	—	8	1	no	—
675	C₂×C₄×C₇	—	8	2	no	—
676	C₂×C₄×C₇	—	8	2	no	—
677	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
678	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
679	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
680	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
681	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
682	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
683	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
684	C₂×C₄×C₇	C₂×#41	1	2	yes	—
685	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
686	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
687	C₇×C₈	—	2	2	no	—
688	C₇×C₈	—	2	1	no	—
689	C₇×C₈	—	2	1	no	—
690	C₇×C₈	—	2	1	no	—
691	C₇×C₈	—	2	1	no	—
692	C₇×C₈	—	2	2	no	—
693	2₋¹⁺⁴	—	2	4	no	—
694	2₋¹⁺⁴	—	4	2	no	—
695	H(5,𝔽₂)	—	2	4	no	—
696	H(5,𝔽₂)	—	4	2	no	—
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	2	no	—
700	C₂×#41	C₂³×C₇	1	2	yes	—
701	C₂×#41	C₂³×C₇	1	2	yes	—
702	C₂×#41	C₂³×C₇	1	1	yes	characteristic
703	C₂×#41	C₂³×C₇	1	1	yes	characteristic
704	C₂×#41	C₂³×C₇	1	1	yes	characteristic
705	C₂²×Q₈	—	2	1	no	—
706	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
708	C₂²×Q₈	C₂³×C₇	1	2	yes	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	—	2	2	no	—
711	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
712	C₂²×D₄	C₂³×C₇	1	2	yes	—
713	#137	—	2	4	no	—
714	C₂×Q₁₆	—	4	2	no	—
715	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
716	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
718	C₂×SD₁₆	—	4	2	no	—
719	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
722	#131	—	4	2	no	—
723	#131	—	4	2	no	—
724	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₇	1	2	yes	—
727	C₂×M₁₆	C₂³×C₇	1	2	yes	—
728	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₇	1	2	yes	—
731	C₂²×C₈	C₂³×C₇	1	2	yes	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
738	#127	—	2	1	no	—
739	#127	C₇×D₄	1	1	yes	characteristic
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	C₂³×C₇	1	1	yes	characteristic
748	#125	C₂³×C₇	1	1	yes	characteristic
749	#124	—	2	1	no	—
750	#124	—	2	1	no	—
751	#124	—	2	2	no	—
752	#124	—	2	1	no	—
753	#124	—	2	1	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	C₇×D₄	1	1	yes	characteristic
759	#124	C₇×D₄	1	1	yes	characteristic
760	#124	C₂³×C₇	1	2	yes	—
761	#124	C₂³×C₇	1	2	yes	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	C₇×D₄	1	2	yes	—
786	#121	C₇×D₄	1	2	yes	—
787	#121	C₂³×C₇	1	2	yes	—
788	#121	C₂³×C₇	1	2	yes	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	#120	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	C₂³×C₇	1	2	yes	—
800	C₄×Q₈	C₂³×C₇	1	2	yes	—
801	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₇	1	2	yes	—
815	C₄×D₄	C₂³×C₇	1	2	yes	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	1	no	—
819	#117	C₂³×C₇	1	1	yes	characteristic
820	#117	C₂³×C₇	1	1	yes	characteristic
821	#117	C₂³×C₇	1	2	yes	—
822	#117	C₂³×C₇	1	1	yes	characteristic
823	#117	C₂³×C₇	1	2	yes	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
827	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
828	C₂×C₂²⋊C₄	—	2	1	no	—
829	C₂×C₂²⋊C₄	—	2	1	no	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
835	#107	C₂³×C₇	1	1	yes	characteristic
836	#107	C₂³×C₇	1	1	yes	characteristic
837	#107	C₂³×C₇	1	1	yes	characteristic
838	#107	C₂³×C₇	1	1	yes	characteristic
839	#107	C₂³×C₇	1	2	yes	—
840	#106	C₂³×C₇	1	1	yes	characteristic
841	#106	C₂³×C₇	1	1	yes	characteristic
842	#106	C₂³×C₇	1	1	yes	characteristic
843	#106	C₂³×C₇	1	1	yes	characteristic
844	#106	C₂³×C₇	1	2	yes	—
845	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
849	#103	C₂³×C₇	1	1	yes	characteristic
850	#103	C₂³×C₇	1	2	yes	—
851	#103	C₂³×C₇	1	2	yes	—
852	#103	C₂³×C₇	1	2	yes	—
853	#103	C₂³×C₇	1	2	yes	—
854	#103	C₂³×C₇	1	1	yes	characteristic
855	#103	C₂³×C₇	1	1	yes	characteristic
856	#103	C₂³×C₇	1	1	yes	characteristic
857	#103	C₂³×C₇	1	2	yes	—
858	#103	C₂³×C₇	1	2	yes	—
859	#103	C₂³×C₇	1	2	yes	—
860	#103	C₂³×C₇	1	2	yes	—
861	#103	C₂³×C₇	1	2	yes	—
862	#102	C₂³×C₇	1	1	yes	characteristic
863	#102	C₂³×C₇	1	2	yes	—
864	#102	C₂³×C₇	1	2	yes	—
865	#102	C₂³×C₇	1	2	yes	—
866	#102	C₂³×C₇	1	2	yes	—
867	#102	C₂³×C₇	1	1	yes	characteristic
868	#102	C₂³×C₇	1	1	yes	characteristic
869	#102	C₂³×C₇	1	1	yes	characteristic
870	#102	C₂³×C₇	1	2	yes	—
871	#102	C₂³×C₇	1	2	yes	—
872	#102	C₂³×C₇	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
877	#97	C₂³×C₇	1	2	yes	—
878	C₄×C₈	C₂³×C₇	1	2	yes	—
879	C₂²×C₇	—	2	1	no	—
880	C₂²×C₇	—	2	1	no	—
881	C₂²×C₇	—	2	2	no	—
882	C₂²×C₇	—	2	2	no	—
883	C₂²×C₇	—	2	2	no	—
884	C₂²×C₇	—	2	2	no	—
885	C₂²×C₇	—	2	2	no	—
886	C₂²×C₇	—	2	2	no	—
887	C₂²×C₇	—	2	2	no	—
888	C₂²×C₇	—	4	1	no	—
889	C₂²×C₇	—	4	1	no	—
890	C₂²×C₇	—	4	2	no	—
891	C₂²×C₇	—	4	2	no	—
892	C₂²×C₇	—	4	2	no	—
893	C₂²×C₇	—	16	2	no	—
894	C₂²×C₇	—	16	4	no	—
895	C₂²×C₇	#546	1	2	yes	—
896	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
897	C₄×C₇	—	2	1	no	—
898	C₄×C₇	—	2	1	no	—
899	C₄×C₇	—	2	1	no	—
900	C₄×C₇	—	2	1	no	—
901	C₄×C₇	—	2	2	no	—
902	C₄×C₇	—	2	2	no	—
903	C₄×C₇	—	2	2	no	—
904	C₄×C₇	—	4	2	no	—
905	C₄×C₇	—	4	1	no	—
906	C₄×C₇	—	4	1	no	—
907	C₄×C₇	—	4	1	no	—
908	C₄×C₇	—	4	1	no	—
909	C₄×C₇	—	4	1	no	—
910	C₄×C₇	—	4	1	no	—
911	C₄×C₇	—	4	2	no	—
912	C₄×C₇	—	4	2	no	—
913	C₄×C₇	#546	1	2	yes	—
914	C₄×C₇	C₂²×#41	1	1	yes	characteristic
915	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	1	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	2	2	no	—
922	#41	—	2	2	no	—
923	#41	—	2	4	no	—
924	#41	—	2	4	no	—
925	#41	—	4	2	no	—
926	#41	—	4	2	no	—
927	#41	—	4	4	no	—
928	#41	—	4	4	no	—
929	#41	—	4	8	no	—
930	#41	C₇×#41	1	4	yes	—
931	C₂×Q₈	—	2	1	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	1	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	2	4	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	2	no	—
939	C₂×Q₈	—	2	2	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	4	2	no	—
942	C₂×Q₈	—	4	4	no	—
943	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
944	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
946	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
947	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	4	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	4	4	no	—
960	C₂×D₄	—	4	8	no	—
961	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
962	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
963	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
964	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
965	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
966	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
967	C₂×D₄	C₂⁴×C₇	1	2	yes	—
968	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
981	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
982	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
983	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
984	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
985	Q₁₆	—	2	4	no	—
986	Q₁₆	—	4	2	no	—
987	Q₁₆	—	4	2	no	—
988	SD₁₆	—	2	4	no	—
989	SD₁₆	—	4	2	no	—
990	SD₁₆	—	4	2	no	—
991	M₁₆	—	2	2	no	—
992	M₁₆	—	2	2	no	—
993	M₁₆	—	4	2	no	—
994	M₁₆	—	4	2	no	—
995	C₂×C₈	—	2	2	no	—
996	C₂×C₈	—	2	2	no	—
997	C₂×C₈	—	4	2	no	—
998	C₂×C₈	—	4	2	no	—
999	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1000	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1004	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1025	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1026	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1029	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1053	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1054	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1055	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1066	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1067	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1069	C₂×C₇	—	2	2	no	—
1070	C₂×C₇	—	4	2	no	—
1071	C₂×C₇	—	4	2	no	—
1072	C₂×C₇	—	4	2	no	—
1073	C₂×C₇	—	8	2	no	—
1074	C₂×C₇	C₂×#546	1	1	yes	characteristic
1075	C₂×C₇	#3584	1	1	yes	characteristic
1076	C₂×C₇	#3586	1	1	yes	characteristic
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	4	4	no	—
1080	C₂³	—	4	2	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	C₂²×C₇×D₄	1	2	yes	—
1086	C₂³	C₂²×C₇×D₄	1	2	yes	—
1087	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	2	2	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	4	2	no	—
1098	Q₈	—	4	2	no	—
1099	Q₈	—	8	1	no	—
1100	Q₈	C₂×C₇×#41	1	2	yes	—
1101	D₄	—	2	4	no	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	4	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	2	2	no	—
1108	D₄	—	2	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	4	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	8	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	C₂×C₇×#41	1	2	yes	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	4	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	4	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1146	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1147	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1148	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1149	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1150	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1151	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1152	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1153	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1154	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1155	C₈	—	2	2	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	2	2	no	—
1161	C₇	#61207	1	1	yes	characteristic, direct product factor, Sylow
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	16	2	no	—
1177	C₂²	—	16	4	no	—
1178	C₂²	C₇×#546	1	2	yes	—
1179	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1180	C₄	—	2	1	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	2	no	—
1196	C₄	C₇×#546	1	2	yes	—
1197	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1198	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	8	2	no	—
1204	C₂	C₂×C₇×#546	1	1	yes	characteristic
1205	C₂	C₇×#3584	1	1	yes	characteristic
1206	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3507	C₂	semidirect
3. C₇×#3327	C₂	semidirect
4. C₇×#3323	C₂	semidirect
5. C₇×#3316	C₂	semidirect
6. C₇×#3314	C₂	semidirect
7. C₇×#3313	C₂	semidirect
8. C₇×#3311	C₂	semidirect
9. C₇×#3300	C₂	semidirect
10. C₇×#3296	C₂	semidirect
11. C₇×#3140	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3096	C₂	semidirect
14. C₇×#3076	C₂	semidirect
15. C₇×#3059	C₂	semidirect
16. C₇×#3057	C₂	semidirect
17. C₂×C₇×#464	C₂	semidirect
18. C₇×#3011	C₂	semidirect
19. C₇×#3009	C₂	semidirect
20. C₄×C₇×#137	C₂	semidirect
21. C₇×#2935	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2897	C₂	semidirect
27. C₂²×C₇×Q₁₆	C₂²	semidirect
30. C₂×C₇×#131	C₂²	semidirect
35. C₇×#556	C₂²	semidirect
36. C₇×#554	C₂²	semidirect
37. C₇×#552	C₂²	semidirect
38. C₇×#552	C₂²	semidirect
49. C₇×#536	C₂²	semidirect
52. C₇×#533	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
61. C₂×C₄×C₇×Q₈	C₂²	semidirect
62. C₇×#489	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#488	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#483	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#481	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#479	C₂²	semidirect
76. C₇×#478	C₂²	semidirect
77. C₇×#478	C₂²	semidirect
78. C₇×#477	C₂²	semidirect
79. C₇×#476	C₂²	semidirect
80. C₇×#475	C₂²	semidirect
81. C₇×#474	C₂²	semidirect
82. C₇×#470	C₂²	semidirect
83. C₇×#470	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#467	C₂²	semidirect
87. C₇×#467	C₂²	semidirect
88. C₇×#465	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#464	C₂²	semidirect
92. C₇×#464	C₂²	semidirect
93. C₇×#464	C₂²	semidirect
96. C₇×#452	C₂²	semidirect
97. C₇×#452	C₂²	semidirect
98. C₇×#451	C₂²	semidirect
99. C₇×#451	C₂²	semidirect
102. C₇×#441	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×SD₁₆	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
107. C₇×#435	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₇×#427	C₂²	semidirect
112. C₇×#427	C₂²	semidirect
113. C₂×C₇×C₄⋊C₈	C₂²	semidirect
114. C₇×#419	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
116. C₇×#419	C₂²	semidirect
117. C₇×#419	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
127. C₇×#416	C₂²	semidirect
128. C₂×C₇×#103	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
133. C₇×#408	C₂²	semidirect
134. C₄×C₇×M₁₆	C₂²	semidirect
135. #61207	C₇	direct (N × H)
322. #3507	C₂×C₇	semidirect
324. #3327	C₂×C₇	semidirect
325. #3323	C₂×C₇	semidirect
326. #3316	C₂×C₇	semidirect
327. #3314	C₂×C₇	semidirect
328. #3313	C₂×C₇	semidirect
329. #3311	C₂×C₇	semidirect
330. #3300	C₂×C₇	semidirect
331. #3296	C₂×C₇	semidirect
332. #3140	C₂×C₇	semidirect
333. #3097	C₂×C₇	semidirect
334. #3096	C₂×C₇	semidirect
335. #3076	C₂×C₇	semidirect
336. #3059	C₂×C₇	semidirect
337. #3057	C₂×C₇	semidirect
338. C₂×#464	C₂×C₇	semidirect
339. #3011	C₂×C₇	semidirect
340. #3009	C₂×C₇	semidirect
341. C₄×#137	C₂×C₇	semidirect
342. #2935	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2897	C₂×C₇	semidirect
501. C₂²×Q₁₆	C₂²×C₇	semidirect
504. C₂×#131	C₂²×C₇	semidirect
509. #556	C₂²×C₇	semidirect
510. #554	C₂²×C₇	semidirect
511. #552	C₂²×C₇	semidirect
512. #552	C₂²×C₇	semidirect
523. #536	C₂²×C₇	semidirect
526. #533	C₂²×C₇	semidirect
533. #520	C₂²×C₇	semidirect
535. C₂×C₄×Q₈	C₂²×C₇	semidirect
536. #489	C₂²×C₇	semidirect
537. #489	C₂²×C₇	semidirect
538. #488	C₂²×C₇	semidirect
539. #488	C₂²×C₇	semidirect
540. #485	C₂²×C₇	semidirect
541. #485	C₂²×C₇	semidirect
542. #484	C₂²×C₇	semidirect
543. #483	C₂²×C₇	semidirect
544. #482	C₂²×C₇	semidirect
545. #482	C₂²×C₇	semidirect
546. #481	C₂²×C₇	semidirect
547. #480	C₂²×C₇	semidirect
548. #479	C₂²×C₇	semidirect
549. #479	C₂²×C₇	semidirect
550. #478	C₂²×C₇	semidirect
551. #478	C₂²×C₇	semidirect
552. #477	C₂²×C₇	semidirect
553. #476	C₂²×C₇	semidirect
554. #475	C₂²×C₇	semidirect
555. #474	C₂²×C₇	semidirect
556. #470	C₂²×C₇	semidirect
557. #470	C₂²×C₇	semidirect
558. #468	C₂²×C₇	semidirect
559. #468	C₂²×C₇	semidirect
560. #467	C₂²×C₇	semidirect
561. #467	C₂²×C₇	semidirect
562. #465	C₂²×C₇	semidirect
563. #465	C₂²×C₇	semidirect
564. #464	C₂²×C₇	semidirect
565. #464	C₂²×C₇	semidirect
566. #464	C₂²×C₇	semidirect
567. #464	C₂²×C₇	semidirect
570. #452	C₂²×C₇	semidirect
571. #452	C₂²×C₇	semidirect
572. #451	C₂²×C₇	semidirect
573. #451	C₂²×C₇	semidirect
576. #441	C₂²×C₇	semidirect
577. #440	C₂²×C₇	semidirect
578. C₄×Q₁₆	C₂²×C₇	semidirect
579. C₄×SD₁₆	C₂²×C₇	semidirect
580. #436	C₂²×C₇	semidirect
581. #435	C₂²×C₇	semidirect
582. #435	C₂²×C₇	semidirect
583. C₈×D₄	C₂²×C₇	semidirect
584. #428	C₂²×C₇	semidirect
585. #427	C₂²×C₇	semidirect
586. #427	C₂²×C₇	semidirect
587. C₂×C₄⋊C₈	C₂²×C₇	semidirect
588. #419	C₂²×C₇	semidirect
589. #419	C₂²×C₇	semidirect
590. #419	C₂²×C₇	semidirect
591. #419	C₂²×C₇	semidirect
597. #417	C₂²×C₇	semidirect
601. #416	C₂²×C₇	semidirect
602. C₂×#103	C₂²×C₇	semidirect
603. C₂×#103	C₂²×C₇	semidirect
607. #408	C₂²×C₇	semidirect
608. C₄×M₁₆	C₂²×C₇	semidirect
1161. C₇	#61207	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×#3507	2
C₇×#3500	2
C₇×#3327	2
C₇×#3323	2
C₇×#3316	2
C₇×#3314	2
C₇×#3313	2
C₇×#3311	2
C₇×#3300	2
C₇×#3296	2
C₇×#3140	2
C₇×#3097	2
C₇×#3096	2
C₇×#3076	2
C₇×#3059	2
C₇×#3057	2
C₂×C₇×#464	2
C₇×#3011	2
C₇×#3009	2
C₄×C₇×#137	2
C₇×#2935	2
C₇×#2898	2
C₇×#2897	2
#61207	7

Subgroups — C7×#61207 #13238423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61207 #13238423