Subgroups — C₇×#60313 #13237529

Order 1792.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3459	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₇×#2994	C₂	1	2	yes	maximal, complemented
4	C₇×#2993	C₂	1	2	yes	maximal, complemented
5	C₇×#2978	C₂	1	2	yes	maximal, complemented
6	C₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2976	C₂	1	2	yes	maximal, complemented
9	C₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2974	C₂	1	2	yes	maximal, complemented
11	C₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₇×#2968	C₂	1	2	yes	maximal, complemented
13	C₇×#2967	C₂	1	2	yes	maximal, complemented
14	C₇×D₄×M₁₆	C₂	1	2	yes	maximal, complemented
15	C₇×#2933	C₂	1	2	yes	maximal, complemented
16	C₇×#2930	C₂	1	2	yes	maximal, complemented
17	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
24	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₇×#543	C₄	1	1	yes	characteristic
26	C₇×#539	C₄	1	1	yes	characteristic
27	C₇×#539	C₄	1	1	yes	characteristic
28	C₇×#539	C₄	1	2	yes	—
29	C₇×#539	C₄	1	2	yes	—
30	C₇×#538	C₄	1	2	yes	—
31	C₇×#538	C₄	1	2	yes	—
32	C₇×#538	C₄	1	2	yes	—
33	C₇×#534	C₄	1	1	yes	characteristic
34	C₇×#534	C₄	1	2	yes	—
35	C₇×#529	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#525	C₂²	1	1	yes	characteristic
39	C₇×#525	C₂²	1	1	yes	characteristic
40	C₇×#525	C₂²	1	2	yes	—
41	C₇×#525	C₂²	1	2	yes	—
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
44	C₇×#446	C₂²	1	2	yes	complemented
45	C₇×#446	C₂²	1	2	yes	complemented
46	C₇×#446	C₂²	1	2	yes	complemented
47	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
48	C₇×#436	C₂²	1	2	yes	complemented
49	C₇×#436	C₂²	1	2	yes	complemented
50	C₇×#436	C₂²	1	2	yes	complemented
51	C₇×#436	C₂²	1	2	yes	complemented
52	C₇×#436	C₂²	1	2	yes	complemented
53	C₇×#436	C₂²	1	2	yes	complemented
54	C₇×#436	C₂²	1	2	yes	complemented
55	C₇×#436	C₂²	1	2	yes	complemented
56	C₇×#436	C₂²	1	2	yes	complemented
57	C₇×#436	C₂²	1	2	yes	complemented
58	C₇×#436	C₂²	1	2	yes	complemented
59	C₇×#435	C₂²	1	2	yes	complemented
60	C₇×#435	C₂²	1	2	yes	complemented
61	C₇×#435	C₂²	1	2	yes	complemented
62	C₇×#435	C₂²	1	2	yes	complemented
63	C₇×#435	C₂²	1	2	yes	complemented
64	C₇×#435	C₂²	1	2	yes	complemented
65	C₇×#435	C₂²	1	2	yes	complemented
66	C₇×#435	C₂²	1	2	yes	complemented
67	C₇×#435	C₂²	1	2	yes	complemented
68	C₇×#435	C₂²	1	2	yes	complemented
69	C₇×#435	C₂²	1	2	yes	complemented
70	C₇×#435	C₂²	1	2	yes	complemented
71	C₇×#435	C₂²	1	2	yes	complemented
72	C₇×#435	C₂²	1	2	yes	complemented
73	C₇×#435	C₂²	1	2	yes	complemented
74	C₇×#435	C₂²	1	2	yes	complemented
75	C₇×#435	C₂²	1	2	yes	complemented
76	C₇×#435	C₂²	1	2	yes	complemented
77	C₇×C₈×D₄	C₂²	1	2	yes	complemented
78	C₇×C₈×D₄	C₂²	1	2	yes	complemented
79	C₇×C₈×D₄	C₂²	1	2	yes	complemented
80	C₇×C₈×D₄	C₂²	1	2	yes	complemented
81	C₇×C₈×D₄	C₂²	1	2	yes	complemented
82	C₇×C₈×D₄	C₂²	1	2	yes	complemented
83	C₇×C₈×D₄	C₂²	1	2	yes	complemented
84	C₇×#433	C₂²	1	2	yes	complemented
85	C₇×#433	C₂²	1	2	yes	complemented
86	C₇×#433	C₂²	1	2	yes	complemented
87	C₇×#433	C₂²	1	2	yes	complemented
88	C₇×#433	C₂²	1	2	yes	complemented
89	C₇×#433	C₂²	1	2	yes	complemented
90	C₇×#432	C₂²	1	2	yes	complemented
91	C₇×#431	C₂²	1	2	yes	complemented
92	C₇×#431	C₂²	1	2	yes	complemented
93	C₇×#424	C₂²	1	1	yes	characteristic, complemented
94	C₇×#424	C₂²	1	1	yes	characteristic, complemented
95	C₇×#424	C₂²	1	2	yes	complemented
96	C₇×#424	C₂²	1	2	yes	complemented
97	C₇×#423	C₂²	1	2	yes	complemented
98	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	C₇×#408	C₂²	1	1	yes	characteristic, complemented
100	C₇×#408	C₂²	1	1	yes	characteristic, complemented
101	C₇×#408	C₂²	1	2	yes	complemented
102	C₇×#408	C₂²	1	2	yes	complemented
103	C₇×#407	C₂²	1	2	yes	—
104	C₇×#407	C₂²	1	1	yes	characteristic, complemented
105	C₇×#407	C₂²	1	1	yes	characteristic, complemented
106	C₇×#407	C₂²	1	2	yes	complemented
107	C₇×#407	C₂²	1	2	yes	complemented
108	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₇×#405	C₂²	1	1	yes	characteristic, complemented
112	C₇×#405	C₂²	1	1	yes	characteristic, complemented
113	C₇×#405	C₂²	1	2	yes	complemented
114	C₇×#405	C₂²	1	2	yes	complemented
115	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
116	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
117	#60313	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂×C₇×#41	C₂³	1	1	yes	characteristic
119	C₂×C₇×#41	C₂³	1	1	yes	characteristic
120	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
121	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₇	C₂³	1	2	yes	—
125	C₇×#131	—	4	2	no	—
126	C₇×#131	—	4	2	no	—
127	C₂×C₇×M₁₆	—	4	2	no	—
128	C₂×C₇×M₁₆	—	4	4	no	—
129	C₂×C₇×M₁₆	C₂³	1	2	yes	—
130	C₂×C₇×M₁₆	C₂³	1	2	yes	—
131	C₂×C₇×M₁₆	C₂³	1	2	yes	—
132	C₂×C₇×M₁₆	C₂³	1	2	yes	—
133	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
134	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
135	C₂×C₇×M₁₆	C₂³	1	2	yes	—
136	C₂×C₇×M₁₆	C₂³	1	2	yes	—
137	C₂×C₇×M₁₆	C₂³	1	2	yes	—
138	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₇×M₁₆	C₂³	1	2	yes	—
141	C₂²×C₇×C₈	—	4	2	no	—
142	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₂²×C₇×C₈	C₂³	1	2	yes	—
146	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
147	C₂²×C₇×C₈	C₂³	1	2	yes	—
148	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₇×C₈	C₂³	1	2	yes	—
151	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×C₈	C₂³	1	2	yes	—
154	C₇×#126	C₂×C₄	1	2	yes	—
155	C₇×#126	C₂×C₄	1	2	yes	—
156	C₇×#126	C₂×C₄	1	2	yes	—
157	C₇×#126	C₂×C₄	1	2	yes	—
158	C₇×#126	C₂×C₄	1	2	yes	—
159	C₇×#126	C₂×C₄	1	2	yes	—
160	C₇×#125	C₂×C₄	1	2	yes	—
161	C₇×#125	C₂×C₄	1	2	yes	—
162	C₇×#125	C₂×C₄	1	2	yes	—
163	C₇×#124	C₂×C₄	1	2	yes	—
164	C₇×#124	C₂×C₄	1	2	yes	—
165	C₇×#124	C₂×C₄	1	2	yes	—
166	C₇×#123	C₂×C₄	1	2	yes	—
167	C₇×#123	C₂×C₄	1	2	yes	—
168	C₇×#123	C₂×C₄	1	2	yes	—
169	C₇×#123	C₂×C₄	1	2	yes	—
170	C₇×#123	C₂×C₄	1	2	yes	—
171	C₇×#123	C₂×C₄	1	2	yes	—
172	C₇×#123	C₂×C₄	1	2	yes	—
173	C₇×#123	C₂×C₄	1	2	yes	—
174	C₇×#123	C₂×C₄	1	2	yes	—
175	C₇×#123	C₂×C₄	1	2	yes	—
176	C₇×#123	C₂×C₄	1	2	yes	—
177	C₇×#123	C₂×C₄	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
179	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
180	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
184	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₇×#121	C₂×C₄	1	1	yes	characteristic
190	C₇×#121	C₂×C₄	1	1	yes	characteristic
191	C₇×#121	C₂×C₄	1	2	yes	—
192	C₇×#121	C₂×C₄	1	2	yes	—
193	C₇×#121	C₂×C₄	1	1	yes	characteristic
194	C₇×#121	C₂×C₄	1	1	yes	characteristic
195	C₇×#121	C₂×C₄	1	2	yes	—
196	C₇×#121	C₂×C₄	1	2	yes	—
197	C₇×#121	C₂×C₄	1	2	yes	—
198	C₇×#121	C₂×C₄	1	2	yes	—
199	C₇×#121	C₂×C₄	1	2	yes	—
200	C₇×#120	C₂×C₄	1	2	yes	—
201	C₇×#120	C₂×C₄	1	2	yes	—
202	C₇×#120	C₂×C₄	1	2	yes	—
203	C₇×#120	C₂×C₄	1	2	yes	—
204	C₇×#120	C₂×C₄	1	2	yes	—
205	C₇×#120	C₂×C₄	1	2	yes	—
206	C₄×C₇×Q₈	C₂³	1	2	yes	—
207	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
208	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
209	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
210	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
211	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
212	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
213	C₄×C₇×D₄	C₂³	1	2	yes	—
214	C₄×C₇×D₄	C₂³	1	2	yes	—
215	C₄×C₇×D₄	C₂³	1	2	yes	—
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₄×C₇×D₄	C₂³	1	2	yes	—
218	C₄×C₇×D₄	C₂³	1	2	yes	—
219	C₄×C₇×D₄	C₂³	1	2	yes	—
220	C₄×C₇×D₄	C₂³	1	2	yes	—
221	C₄×C₇×D₄	C₂³	1	2	yes	—
222	C₇×#117	C₂³	1	1	yes	characteristic
223	C₇×#117	C₂³	1	1	yes	characteristic
224	C₇×#117	C₂³	1	2	yes	—
225	C₇×#117	C₂³	1	2	yes	—
226	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
227	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
228	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
229	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
230	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
231	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	2	yes	—
234	C₇×C₄⋊C₈	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	2	yes	—
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	2	yes	—
239	C₇×C₄⋊C₈	C₂³	1	2	yes	—
240	C₇×C₄⋊C₈	C₂³	1	2	yes	—
241	C₇×C₄⋊C₈	C₂³	1	2	yes	—
242	C₇×C₄⋊C₈	C₂³	1	2	yes	—
243	C₇×C₄⋊C₈	C₂³	1	2	yes	—
244	C₇×C₄⋊C₈	C₂³	1	2	yes	—
245	C₇×C₄⋊C₈	C₂³	1	2	yes	—
246	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₇×#97	C₂³	1	2	yes	—
265	C₇×#97	C₂³	1	2	yes	—
266	C₇×#97	C₂³	1	2	yes	—
267	C₇×#97	C₂³	1	2	yes	—
268	C₇×#97	C₂³	1	2	yes	—
269	C₇×#97	C₂³	1	2	yes	—
270	C₄×C₇×C₈	C₂³	1	2	yes	—
271	C₄×C₇×C₈	C₂³	1	2	yes	—
272	C₄×C₇×C₈	C₂³	1	2	yes	—
273	C₄×C₇×C₈	C₂³	1	2	yes	—
274	C₄×C₇×C₈	C₂³	1	2	yes	—
275	C₄×C₇×C₈	C₂³	1	2	yes	—
276	#3459	C₂×C₇	1	1	yes	characteristic
277	#2995	C₂×C₇	1	2	yes	complemented
278	#2994	C₂×C₇	1	2	yes	complemented
279	#2993	C₂×C₇	1	2	yes	complemented
280	#2978	C₂×C₇	1	2	yes	complemented
281	#2976	C₂×C₇	1	1	yes	characteristic, complemented
282	#2976	C₂×C₇	1	1	yes	characteristic, complemented
283	#2976	C₂×C₇	1	2	yes	complemented
284	#2975	C₂×C₇	1	1	yes	characteristic, complemented
285	#2974	C₂×C₇	1	2	yes	complemented
286	#2969	C₂×C₇	1	2	yes	complemented
287	#2968	C₂×C₇	1	2	yes	complemented
288	#2967	C₂×C₇	1	2	yes	complemented
289	D₄×M₁₆	C₂×C₇	1	2	yes	complemented
290	#2933	C₂×C₇	1	2	yes	complemented
291	#2930	C₂×C₇	1	2	yes	complemented
292	#2929	C₂×C₇	1	1	yes	characteristic, complemented
293	#2929	C₂×C₇	1	1	yes	characteristic, complemented
294	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
295	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
296	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
297	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
298	C₇×#41	—	4	1	no	—
299	C₇×#41	—	4	1	no	—
300	C₇×#41	—	4	1	no	—
301	C₇×#41	—	4	1	no	—
302	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
303	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
304	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
305	C₂×C₇×D₄	—	4	2	no	—
306	C₂×C₇×D₄	—	4	4	no	—
307	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
308	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
309	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
310	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
311	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
312	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
313	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
314	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
315	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
316	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
317	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
318	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
319	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
320	C₂²×C₄×C₇	—	4	1	no	—
321	C₂²×C₄×C₇	—	4	1	no	—
322	C₂²×C₄×C₇	—	4	2	no	—
323	C₂²×C₄×C₇	—	4	1	no	—
324	C₂²×C₄×C₇	—	4	1	no	—
325	C₂²×C₄×C₇	—	4	2	no	—
326	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
328	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
330	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
331	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
333	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
337	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
344	C₇×M₁₆	—	2	4	no	—
345	C₇×M₁₆	—	2	4	no	—
346	C₇×M₁₆	—	4	2	no	—
347	C₇×M₁₆	—	4	2	no	—
348	C₇×M₁₆	—	4	2	no	—
349	C₇×M₁₆	—	4	2	no	—
350	C₇×M₁₆	—	4	1	no	—
351	C₇×M₁₆	—	4	2	no	—
352	C₇×M₁₆	—	4	1	no	—
353	C₇×M₁₆	—	4	2	no	—
354	C₇×M₁₆	—	4	1	no	—
355	C₇×M₁₆	—	4	1	no	—
356	C₂×C₇×C₈	—	2	2	no	—
357	C₂×C₇×C₈	—	2	2	no	—
358	C₂×C₇×C₈	—	2	2	no	—
359	C₂×C₇×C₈	—	2	4	no	—
360	C₂×C₇×C₈	—	4	1	no	—
361	C₂×C₇×C₈	—	4	1	no	—
362	C₂×C₇×C₈	—	4	1	no	—
363	C₂×C₇×C₈	—	4	1	no	—
364	C₂×C₇×C₈	—	4	2	no	—
365	C₂×C₇×C₈	—	4	1	no	—
366	C₂×C₇×C₈	—	4	2	no	—
367	C₂×C₇×C₈	—	4	2	no	—
368	C₂×C₇×C₈	C₂⁴	1	2	yes	—
369	C₂×C₇×C₈	C₂⁴	1	2	yes	—
370	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₇×C₈	C₂⁴	1	2	yes	—
372	C₂×C₇×C₈	C₂⁴	1	2	yes	—
373	C₂×C₇×C₈	C₂⁴	1	2	yes	—
374	C₂×C₇×C₈	C₂⁴	1	2	yes	—
375	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
378	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
379	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
380	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
382	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
384	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
387	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
388	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
389	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
390	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
391	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
393	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
394	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
396	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
398	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
399	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
400	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
401	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
402	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
403	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
404	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
405	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
406	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
407	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
408	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
409	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
410	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
411	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
412	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
413	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
414	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
415	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
417	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
419	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
420	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
421	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
422	C₄²×C₇	C₂²×C₄	1	2	yes	—
423	C₄²×C₇	C₂²×C₄	1	2	yes	—
424	C₄²×C₇	C₂²×C₄	1	2	yes	—
425	C₄²×C₇	C₂⁴	1	2	yes	—
426	C₄²×C₇	C₂⁴	1	2	yes	—
427	C₄²×C₇	C₂⁴	1	2	yes	—
428	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
429	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
430	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
431	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
432	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
433	#543	C₄×C₇	1	1	yes	characteristic
434	#539	C₄×C₇	1	1	yes	characteristic
435	#539	C₄×C₇	1	1	yes	characteristic
436	#539	C₄×C₇	1	2	yes	—
437	#539	C₄×C₇	1	2	yes	—
438	#538	C₄×C₇	1	2	yes	—
439	#538	C₄×C₇	1	2	yes	—
440	#538	C₄×C₇	1	2	yes	—
441	#534	C₄×C₇	1	1	yes	characteristic
442	#534	C₄×C₇	1	2	yes	—
443	#529	C₂²×C₇	1	2	yes	—
444	#529	C₂²×C₇	1	2	yes	—
445	#529	C₂²×C₇	1	2	yes	—
446	#525	C₂²×C₇	1	1	yes	characteristic
447	#525	C₂²×C₇	1	1	yes	characteristic
448	#525	C₂²×C₇	1	2	yes	—
449	#525	C₂²×C₇	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
452	#446	C₂²×C₇	1	2	yes	complemented
453	#446	C₂²×C₇	1	2	yes	complemented
454	#446	C₂²×C₇	1	2	yes	complemented
455	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
456	#436	C₂²×C₇	1	2	yes	complemented
457	#436	C₂²×C₇	1	2	yes	complemented
458	#436	C₂²×C₇	1	2	yes	complemented
459	#436	C₂²×C₇	1	2	yes	complemented
460	#436	C₂²×C₇	1	2	yes	complemented
461	#436	C₂²×C₇	1	2	yes	complemented
462	#436	C₂²×C₇	1	2	yes	complemented
463	#436	C₂²×C₇	1	2	yes	complemented
464	#436	C₂²×C₇	1	2	yes	complemented
465	#436	C₂²×C₇	1	2	yes	complemented
466	#436	C₂²×C₇	1	2	yes	complemented
467	#435	C₂²×C₇	1	2	yes	complemented
468	#435	C₂²×C₇	1	2	yes	complemented
469	#435	C₂²×C₇	1	2	yes	complemented
470	#435	C₂²×C₇	1	2	yes	complemented
471	#435	C₂²×C₇	1	2	yes	complemented
472	#435	C₂²×C₇	1	2	yes	complemented
473	#435	C₂²×C₇	1	2	yes	complemented
474	#435	C₂²×C₇	1	2	yes	complemented
475	#435	C₂²×C₇	1	2	yes	complemented
476	#435	C₂²×C₇	1	2	yes	complemented
477	#435	C₂²×C₇	1	2	yes	complemented
478	#435	C₂²×C₇	1	2	yes	complemented
479	#435	C₂²×C₇	1	2	yes	complemented
480	#435	C₂²×C₇	1	2	yes	complemented
481	#435	C₂²×C₇	1	2	yes	complemented
482	#435	C₂²×C₇	1	2	yes	complemented
483	#435	C₂²×C₇	1	2	yes	complemented
484	#435	C₂²×C₇	1	2	yes	complemented
485	C₈×D₄	C₂²×C₇	1	2	yes	complemented
486	C₈×D₄	C₂²×C₇	1	2	yes	complemented
487	C₈×D₄	C₂²×C₇	1	2	yes	complemented
488	C₈×D₄	C₂²×C₇	1	2	yes	complemented
489	C₈×D₄	C₂²×C₇	1	2	yes	complemented
490	C₈×D₄	C₂²×C₇	1	2	yes	complemented
491	C₈×D₄	C₂²×C₇	1	2	yes	complemented
492	#433	C₂²×C₇	1	2	yes	complemented
493	#433	C₂²×C₇	1	2	yes	complemented
494	#433	C₂²×C₇	1	2	yes	complemented
495	#433	C₂²×C₇	1	2	yes	complemented
496	#433	C₂²×C₇	1	2	yes	complemented
497	#433	C₂²×C₇	1	2	yes	complemented
498	#432	C₂²×C₇	1	2	yes	complemented
499	#431	C₂²×C₇	1	2	yes	complemented
500	#431	C₂²×C₇	1	2	yes	complemented
501	#424	C₂²×C₇	1	1	yes	characteristic, complemented
502	#424	C₂²×C₇	1	1	yes	characteristic, complemented
503	#424	C₂²×C₇	1	2	yes	complemented
504	#424	C₂²×C₇	1	2	yes	complemented
505	#423	C₂²×C₇	1	2	yes	complemented
506	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
507	#408	C₂²×C₇	1	1	yes	characteristic, complemented
508	#408	C₂²×C₇	1	1	yes	characteristic, complemented
509	#408	C₂²×C₇	1	2	yes	complemented
510	#408	C₂²×C₇	1	2	yes	complemented
511	#407	C₂²×C₇	1	2	yes	—
512	#407	C₂²×C₇	1	1	yes	characteristic, complemented
513	#407	C₂²×C₇	1	1	yes	characteristic, complemented
514	#407	C₂²×C₇	1	2	yes	complemented
515	#407	C₂²×C₇	1	2	yes	complemented
516	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
517	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
518	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
519	#405	C₂²×C₇	1	1	yes	characteristic, complemented
520	#405	C₂²×C₇	1	1	yes	characteristic, complemented
521	#405	C₂²×C₇	1	2	yes	complemented
522	#405	C₂²×C₇	1	2	yes	complemented
523	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
524	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
525	C₂³×C₇	—	2	2	no	—
526	C₂³×C₇	—	2	2	no	—
527	C₂³×C₇	—	4	1	no	—
528	C₂³×C₇	—	4	1	no	—
529	C₂³×C₇	—	4	1	no	—
530	C₂³×C₇	—	4	2	no	—
531	C₂³×C₇	—	4	2	no	—
532	C₂³×C₇	—	4	1	no	—
533	C₂³×C₇	—	4	2	no	—
534	C₂³×C₇	C₂³×C₄	1	2	yes	—
535	C₂³×C₇	C₂³×C₄	1	2	yes	—
536	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
537	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
538	C₂³×C₇	C₂³×C₄	1	2	yes	—
539	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
540	C₇×Q₈	—	4	2	no	—
541	C₇×Q₈	—	4	1	no	—
542	C₇×Q₈	—	4	1	no	—
543	C₇×D₄	—	2	4	no	—
544	C₇×D₄	—	2	4	no	—
545	C₇×D₄	—	4	2	no	—
546	C₇×D₄	—	4	2	no	—
547	C₇×D₄	—	4	2	no	—
548	C₇×D₄	—	4	2	no	—
549	C₇×D₄	—	4	2	no	—
550	C₇×D₄	—	4	2	no	—
551	C₇×D₄	—	4	2	no	—
552	C₇×D₄	—	4	2	no	—
553	C₇×D₄	—	4	1	no	—
554	C₇×D₄	—	4	1	no	—
555	C₇×D₄	—	4	2	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	2	1	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	2	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	2	no	—
563	C₂×C₄×C₇	—	2	1	no	—
564	C₂×C₄×C₇	—	2	2	no	—
565	C₂×C₄×C₇	—	2	2	no	—
566	C₂×C₄×C₇	—	2	1	no	—
567	C₂×C₄×C₇	—	2	1	no	—
568	C₂×C₄×C₇	—	2	2	no	—
569	C₂×C₄×C₇	—	4	1	no	—
570	C₂×C₄×C₇	—	4	2	no	—
571	C₂×C₄×C₇	—	4	1	no	—
572	C₂×C₄×C₇	—	4	1	no	—
573	C₂×C₄×C₇	—	4	2	no	—
574	C₂×C₄×C₇	—	4	2	no	—
575	C₂×C₄×C₇	—	4	1	no	—
576	C₂×C₄×C₇	—	4	2	no	—
577	C₂×C₄×C₇	—	4	1	no	—
578	C₂×C₄×C₇	—	4	2	no	—
579	C₂×C₄×C₇	—	4	2	no	—
580	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
585	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
586	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
587	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
589	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
590	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
592	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
593	C₇×C₈	—	2	1	no	—
594	C₇×C₈	—	2	1	no	—
595	C₇×C₈	—	2	1	no	—
596	C₇×C₈	—	2	2	no	—
597	C₇×C₈	—	2	2	no	—
598	C₇×C₈	—	2	2	no	—
599	C₇×C₈	—	2	2	no	—
600	C₇×C₈	—	2	2	no	—
601	C₇×C₈	—	2	2	no	—
602	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
603	C₂×#41	C₂³×C₇	1	1	yes	characteristic
604	C₂×#41	C₂³×C₇	1	1	yes	characteristic
605	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
606	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
607	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₇	1	2	yes	—
610	#131	—	4	2	no	—
611	#131	—	4	2	no	—
612	C₂×M₁₆	—	4	2	no	—
613	C₂×M₁₆	—	4	4	no	—
614	C₂×M₁₆	C₂³×C₇	1	2	yes	—
615	C₂×M₁₆	C₂³×C₇	1	2	yes	—
616	C₂×M₁₆	C₂³×C₇	1	2	yes	—
617	C₂×M₁₆	C₂³×C₇	1	2	yes	—
618	C₂×M₁₆	C₂³×C₇	1	2	yes	—
619	C₂×M₁₆	C₂³×C₇	1	2	yes	—
620	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
622	C₂×M₁₆	C₂³×C₇	1	2	yes	—
623	C₂×M₁₆	C₂³×C₇	1	2	yes	—
624	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
625	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
626	C₂²×C₈	—	4	2	no	—
627	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
628	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
629	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
630	C₂²×C₈	C₂³×C₇	1	2	yes	—
631	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
632	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
633	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
634	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
635	C₂²×C₈	C₂³×C₇	1	2	yes	—
636	C₂²×C₈	C₂³×C₇	1	2	yes	—
637	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
638	C₂²×C₈	C₂³×C₇	1	2	yes	—
639	#126	C₂×C₄×C₇	1	2	yes	—
640	#126	C₂×C₄×C₇	1	2	yes	—
641	#126	C₂×C₄×C₇	1	2	yes	—
642	#126	C₂×C₄×C₇	1	2	yes	—
643	#126	C₂×C₄×C₇	1	2	yes	—
644	#126	C₂×C₄×C₇	1	2	yes	—
645	#125	C₂×C₄×C₇	1	2	yes	—
646	#125	C₂×C₄×C₇	1	2	yes	—
647	#125	C₂×C₄×C₇	1	2	yes	—
648	#124	C₂×C₄×C₇	1	2	yes	—
649	#124	C₂×C₄×C₇	1	2	yes	—
650	#124	C₂×C₄×C₇	1	2	yes	—
651	#123	C₂×C₄×C₇	1	2	yes	—
652	#123	C₂×C₄×C₇	1	2	yes	—
653	#123	C₂×C₄×C₇	1	2	yes	—
654	#123	C₂×C₄×C₇	1	2	yes	—
655	#123	C₂×C₄×C₇	1	2	yes	—
656	#123	C₂×C₄×C₇	1	2	yes	—
657	#123	C₂×C₄×C₇	1	2	yes	—
658	#123	C₂×C₄×C₇	1	2	yes	—
659	#123	C₂×C₄×C₇	1	2	yes	—
660	#123	C₂×C₄×C₇	1	2	yes	—
661	#123	C₂×C₄×C₇	1	2	yes	—
662	#123	C₂×C₄×C₇	1	2	yes	—
663	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
664	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
665	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
666	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
667	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
668	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
669	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
670	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
671	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
672	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
673	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
674	#121	C₂×C₄×C₇	1	1	yes	characteristic
675	#121	C₂×C₄×C₇	1	1	yes	characteristic
676	#121	C₂×C₄×C₇	1	2	yes	—
677	#121	C₂×C₄×C₇	1	2	yes	—
678	#121	C₂×C₄×C₇	1	1	yes	characteristic
679	#121	C₂×C₄×C₇	1	1	yes	characteristic
680	#121	C₂×C₄×C₇	1	2	yes	—
681	#121	C₂×C₄×C₇	1	2	yes	—
682	#121	C₂×C₄×C₇	1	2	yes	—
683	#121	C₂×C₄×C₇	1	2	yes	—
684	#121	C₂×C₄×C₇	1	2	yes	—
685	#120	C₂×C₄×C₇	1	2	yes	—
686	#120	C₂×C₄×C₇	1	2	yes	—
687	#120	C₂×C₄×C₇	1	2	yes	—
688	#120	C₂×C₄×C₇	1	2	yes	—
689	#120	C₂×C₄×C₇	1	2	yes	—
690	#120	C₂×C₄×C₇	1	2	yes	—
691	C₄×Q₈	C₂³×C₇	1	2	yes	—
692	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
693	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
694	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
695	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
696	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
697	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
698	C₄×D₄	C₂³×C₇	1	2	yes	—
699	C₄×D₄	C₂³×C₇	1	2	yes	—
700	C₄×D₄	C₂³×C₇	1	2	yes	—
701	C₄×D₄	C₂³×C₇	1	2	yes	—
702	C₄×D₄	C₂³×C₇	1	2	yes	—
703	C₄×D₄	C₂³×C₇	1	2	yes	—
704	C₄×D₄	C₂³×C₇	1	2	yes	—
705	C₄×D₄	C₂³×C₇	1	2	yes	—
706	C₄×D₄	C₂³×C₇	1	2	yes	—
707	#117	C₂³×C₇	1	1	yes	characteristic
708	#117	C₂³×C₇	1	1	yes	characteristic
709	#117	C₂³×C₇	1	2	yes	—
710	#117	C₂³×C₇	1	2	yes	—
711	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
717	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₇	1	2	yes	—
719	C₄⋊C₈	C₂³×C₇	1	2	yes	—
720	C₄⋊C₈	C₂³×C₇	1	2	yes	—
721	C₄⋊C₈	C₂³×C₇	1	2	yes	—
722	C₄⋊C₈	C₂³×C₇	1	2	yes	—
723	C₄⋊C₈	C₂³×C₇	1	2	yes	—
724	C₄⋊C₈	C₂³×C₇	1	2	yes	—
725	C₄⋊C₈	C₂³×C₇	1	2	yes	—
726	C₄⋊C₈	C₂³×C₇	1	2	yes	—
727	C₄⋊C₈	C₂³×C₇	1	2	yes	—
728	C₄⋊C₈	C₂³×C₇	1	2	yes	—
729	C₄⋊C₈	C₂³×C₇	1	2	yes	—
730	C₄⋊C₈	C₂³×C₇	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
741	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
742	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
743	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
744	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
745	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
746	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
749	#97	C₂³×C₇	1	2	yes	—
750	#97	C₂³×C₇	1	2	yes	—
751	#97	C₂³×C₇	1	2	yes	—
752	#97	C₂³×C₇	1	2	yes	—
753	#97	C₂³×C₇	1	2	yes	—
754	#97	C₂³×C₇	1	2	yes	—
755	C₄×C₈	C₂³×C₇	1	2	yes	—
756	C₄×C₈	C₂³×C₇	1	2	yes	—
757	C₄×C₈	C₂³×C₇	1	2	yes	—
758	C₄×C₈	C₂³×C₇	1	2	yes	—
759	C₄×C₈	C₂³×C₇	1	2	yes	—
760	C₄×C₈	C₂³×C₇	1	2	yes	—
761	C₂²×C₇	—	2	1	no	—
762	C₂²×C₇	—	2	1	no	—
763	C₂²×C₇	—	2	2	no	—
764	C₂²×C₇	—	2	1	no	—
765	C₂²×C₇	—	2	1	no	—
766	C₂²×C₇	—	2	2	no	—
767	C₂²×C₇	—	2	2	no	—
768	C₂²×C₇	—	2	2	no	—
769	C₂²×C₇	—	2	2	no	—
770	C₂²×C₇	—	2	2	no	—
771	C₂²×C₇	—	2	1	no	—
772	C₂²×C₇	—	2	1	no	—
773	C₂²×C₇	—	2	2	no	—
774	C₂²×C₇	—	2	1	no	—
775	C₂²×C₇	—	2	1	no	—
776	C₂²×C₇	—	2	2	no	—
777	C₂²×C₇	—	2	2	no	—
778	C₂²×C₇	—	4	4	no	—
779	C₂²×C₇	—	8	2	no	—
780	C₂²×C₇	—	8	4	no	—
781	C₂²×C₇	#568	1	2	yes	—
782	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
783	C₄×C₇	—	2	1	no	—
784	C₄×C₇	—	2	2	no	—
785	C₄×C₇	—	2	1	no	—
786	C₄×C₇	—	2	1	no	—
787	C₄×C₇	—	2	2	no	—
788	C₄×C₇	—	2	2	no	—
789	C₄×C₇	—	2	2	no	—
790	C₄×C₇	—	2	2	no	—
791	C₄×C₇	—	2	2	no	—
792	C₄×C₇	—	2	2	no	—
793	C₄×C₇	—	2	2	no	—
794	C₄×C₇	—	2	2	no	—
795	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
796	C₄×C₇	#585	1	1	yes	characteristic
797	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
798	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
799	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
800	#41	—	4	1	no	—
801	#41	—	4	1	no	—
802	#41	—	4	1	no	—
803	#41	—	4	1	no	—
804	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
805	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
806	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
807	C₂×D₄	—	4	2	no	—
808	C₂×D₄	—	4	4	no	—
809	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
810	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
811	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
812	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
813	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
814	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
815	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
816	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
817	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
818	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
819	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
820	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
821	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
822	C₂²×C₄	—	4	1	no	—
823	C₂²×C₄	—	4	1	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	1	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
829	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
830	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
831	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
832	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
833	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
834	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
835	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
836	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
837	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
838	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
839	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
846	M₁₆	—	2	4	no	—
847	M₁₆	—	2	4	no	—
848	M₁₆	—	4	2	no	—
849	M₁₆	—	4	2	no	—
850	M₁₆	—	4	2	no	—
851	M₁₆	—	4	2	no	—
852	M₁₆	—	4	1	no	—
853	M₁₆	—	4	2	no	—
854	M₁₆	—	4	1	no	—
855	M₁₆	—	4	2	no	—
856	M₁₆	—	4	1	no	—
857	M₁₆	—	4	1	no	—
858	C₂×C₈	—	2	2	no	—
859	C₂×C₈	—	2	2	no	—
860	C₂×C₈	—	2	2	no	—
861	C₂×C₈	—	2	4	no	—
862	C₂×C₈	—	4	1	no	—
863	C₂×C₈	—	4	1	no	—
864	C₂×C₈	—	4	1	no	—
865	C₂×C₈	—	4	1	no	—
866	C₂×C₈	—	4	2	no	—
867	C₂×C₈	—	4	1	no	—
868	C₂×C₈	—	4	2	no	—
869	C₂×C₈	—	4	2	no	—
870	C₂×C₈	C₂⁴×C₇	1	2	yes	—
871	C₂×C₈	C₂⁴×C₇	1	2	yes	—
872	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₇	1	2	yes	—
874	C₂×C₈	C₂⁴×C₇	1	2	yes	—
875	C₂×C₈	C₂⁴×C₇	1	2	yes	—
876	C₂×C₈	C₂⁴×C₇	1	2	yes	—
877	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
880	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
881	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
882	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
883	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
884	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
885	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
886	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
887	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
888	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
889	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
890	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
891	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
892	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
893	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
894	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
895	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
896	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
897	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
898	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
899	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
912	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
913	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
914	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
915	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
916	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
917	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
918	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
919	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
920	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
921	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
922	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
923	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
924	C₄²	C₂²×C₄×C₇	1	2	yes	—
925	C₄²	C₂²×C₄×C₇	1	2	yes	—
926	C₄²	C₂²×C₄×C₇	1	2	yes	—
927	C₄²	C₂⁴×C₇	1	2	yes	—
928	C₄²	C₂⁴×C₇	1	2	yes	—
929	C₄²	C₂⁴×C₇	1	2	yes	—
930	C₂×C₇	—	2	2	no	—
931	C₂×C₇	—	4	1	no	—
932	C₂×C₇	—	4	1	no	—
933	C₂×C₇	—	4	2	no	—
934	C₂×C₇	—	4	2	no	—
935	C₂×C₇	—	4	2	no	—
936	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
937	C₂×C₇	C₂×#568	1	1	yes	characteristic
938	C₂×C₇	#3573	1	1	yes	characteristic
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	4	1	no	—
942	C₂³	—	4	1	no	—
943	C₂³	—	4	1	no	—
944	C₂³	—	4	2	no	—
945	C₂³	—	4	2	no	—
946	C₂³	—	4	1	no	—
947	C₂³	—	4	2	no	—
948	C₂³	C₂³×C₄×C₇	1	2	yes	—
949	C₂³	C₂³×C₄×C₇	1	2	yes	—
950	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
951	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
952	C₂³	C₂³×C₄×C₇	1	2	yes	—
953	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
954	Q₈	—	4	2	no	—
955	Q₈	—	4	1	no	—
956	Q₈	—	4	1	no	—
957	D₄	—	2	4	no	—
958	D₄	—	2	4	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	2	no	—
963	D₄	—	4	2	no	—
964	D₄	—	4	2	no	—
965	D₄	—	4	2	no	—
966	D₄	—	4	2	no	—
967	D₄	—	4	1	no	—
968	D₄	—	4	1	no	—
969	D₄	—	4	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	4	1	no	—
984	C₂×C₄	—	4	2	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	4	2	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	1	no	—
990	C₂×C₄	—	4	2	no	—
991	C₂×C₄	—	4	1	no	—
992	C₂×C₄	—	4	2	no	—
993	C₂×C₄	—	4	2	no	—
994	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
995	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
996	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1001	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1002	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1003	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1004	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1005	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1006	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1007	C₈	—	2	1	no	—
1008	C₈	—	2	1	no	—
1009	C₈	—	2	1	no	—
1010	C₈	—	2	2	no	—
1011	C₈	—	2	2	no	—
1012	C₈	—	2	2	no	—
1013	C₈	—	2	2	no	—
1014	C₈	—	2	2	no	—
1015	C₈	—	2	2	no	—
1016	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
1017	C₇	#60313	1	1	yes	characteristic, direct product factor, Sylow
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	4	4	no	—
1036	C₂²	—	8	2	no	—
1037	C₂²	—	8	4	no	—
1038	C₂²	C₇×#568	1	2	yes	—
1039	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1053	C₄	C₇×#585	1	1	yes	characteristic
1054	C₂	—	2	2	no	—
1055	C₂	—	4	1	no	—
1056	C₂	—	4	1	no	—
1057	C₂	—	4	2	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1061	C₂	C₂×C₇×#568	1	1	yes	characteristic
1062	C₂	C₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₇×#3459	C₂
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
2. C₇×#2995	C₂	semidirect
3. C₇×#2994	C₂	semidirect
4. C₇×#2993	C₂	semidirect
5. C₇×#2978	C₂	semidirect
6. C₇×#2976	C₂	semidirect
7. C₇×#2976	C₂	semidirect
8. C₇×#2976	C₂	semidirect
9. C₇×#2975	C₂	semidirect
10. C₇×#2974	C₂	semidirect
11. C₇×#2969	C₂	semidirect
12. C₇×#2968	C₂	semidirect
13. C₇×#2967	C₂	semidirect
14. C₇×D₄×M₁₆	C₂	semidirect
15. C₇×#2933	C₂	semidirect
16. C₇×#2930	C₂	semidirect
17. C₇×#2929	C₂	semidirect
18. C₇×#2929	C₂	semidirect
19. C₂×C₇×#435	C₂	semidirect
20. C₂×C₇×#131	C₂²	semidirect
21. C₂×C₇×#131	C₂²	semidirect
23. C₂²×C₇×M₁₆	C₂²	semidirect
24. C₂³×C₇×C₈	C₂²	semidirect
44. C₇×#446	C₂²	semidirect
45. C₇×#446	C₂²	semidirect
46. C₇×#446	C₂²	semidirect
47. C₇×C₈×Q₈	C₂²	semidirect
48. C₇×#436	C₂²	semidirect
49. C₇×#436	C₂²	semidirect
50. C₇×#436	C₂²	semidirect
51. C₇×#436	C₂²	semidirect
52. C₇×#436	C₂²	semidirect
53. C₇×#436	C₂²	semidirect
54. C₇×#436	C₂²	semidirect
55. C₇×#436	C₂²	semidirect
56. C₇×#436	C₂²	semidirect
57. C₇×#436	C₂²	semidirect
58. C₇×#436	C₂²	semidirect
59. C₇×#435	C₂²	semidirect
60. C₇×#435	C₂²	semidirect
61. C₇×#435	C₂²	semidirect
62. C₇×#435	C₂²	semidirect
63. C₇×#435	C₂²	semidirect
64. C₇×#435	C₂²	semidirect
65. C₇×#435	C₂²	semidirect
66. C₇×#435	C₂²	semidirect
67. C₇×#435	C₂²	semidirect
68. C₇×#435	C₂²	semidirect
69. C₇×#435	C₂²	semidirect
70. C₇×#435	C₂²	semidirect
71. C₇×#435	C₂²	semidirect
72. C₇×#435	C₂²	semidirect
73. C₇×#435	C₂²	semidirect
74. C₇×#435	C₂²	semidirect
75. C₇×#435	C₂²	semidirect
76. C₇×#435	C₂²	semidirect
77. C₇×C₈×D₄	C₂²	semidirect
78. C₇×C₈×D₄	C₂²	semidirect
79. C₇×C₈×D₄	C₂²	semidirect
80. C₇×C₈×D₄	C₂²	semidirect
81. C₇×C₈×D₄	C₂²	semidirect
82. C₇×C₈×D₄	C₂²	semidirect
83. C₇×C₈×D₄	C₂²	semidirect
84. C₇×#433	C₂²	semidirect
85. C₇×#433	C₂²	semidirect
86. C₇×#433	C₂²	semidirect
87. C₇×#433	C₂²	semidirect
88. C₇×#433	C₂²	semidirect
89. C₇×#433	C₂²	semidirect
90. C₇×#432	C₂²	semidirect
91. C₇×#431	C₂²	semidirect
92. C₇×#431	C₂²	semidirect
93. C₇×#424	C₂²	semidirect
94. C₇×#424	C₂²	semidirect
95. C₇×#424	C₂²	semidirect
96. C₇×#424	C₂²	semidirect
97. C₇×#423	C₂²	semidirect
98. C₂×C₇×C₄⋊C₈	C₂²	semidirect
99. C₇×#408	C₂²	semidirect
100. C₇×#408	C₂²	semidirect
101. C₇×#408	C₂²	semidirect
102. C₇×#408	C₂²	semidirect
104. C₇×#407	C₂²	semidirect
105. C₇×#407	C₂²	semidirect
106. C₇×#407	C₂²	semidirect
107. C₇×#407	C₂²	semidirect
109. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
110. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
111. C₇×#405	C₂²	semidirect
112. C₇×#405	C₂²	semidirect
113. C₇×#405	C₂²	semidirect
114. C₇×#405	C₂²	semidirect
115. C₄×C₇×M₁₆	C₂²	semidirect
116. C₂×C₇×#97	C₂²	semidirect
117. #60313	C₇	direct (N × H)
277. #2995	C₂×C₇	semidirect
278. #2994	C₂×C₇	semidirect
279. #2993	C₂×C₇	semidirect
280. #2978	C₂×C₇	semidirect
281. #2976	C₂×C₇	semidirect
282. #2976	C₂×C₇	semidirect
283. #2976	C₂×C₇	semidirect
284. #2975	C₂×C₇	semidirect
285. #2974	C₂×C₇	semidirect
286. #2969	C₂×C₇	semidirect
287. #2968	C₂×C₇	semidirect
288. #2967	C₂×C₇	semidirect
289. D₄×M₁₆	C₂×C₇	semidirect
290. #2933	C₂×C₇	semidirect
291. #2930	C₂×C₇	semidirect
292. #2929	C₂×C₇	semidirect
293. #2929	C₂×C₇	semidirect
294. C₂×#435	C₂×C₇	semidirect
428. C₂×#131	C₂²×C₇	semidirect
429. C₂×#131	C₂²×C₇	semidirect
431. C₂²×M₁₆	C₂²×C₇	semidirect
432. C₂³×C₈	C₂²×C₇	semidirect
452. #446	C₂²×C₇	semidirect
453. #446	C₂²×C₇	semidirect
454. #446	C₂²×C₇	semidirect
455. C₈×Q₈	C₂²×C₇	semidirect
456. #436	C₂²×C₇	semidirect
457. #436	C₂²×C₇	semidirect
458. #436	C₂²×C₇	semidirect
459. #436	C₂²×C₇	semidirect
460. #436	C₂²×C₇	semidirect
461. #436	C₂²×C₇	semidirect
462. #436	C₂²×C₇	semidirect
463. #436	C₂²×C₇	semidirect
464. #436	C₂²×C₇	semidirect
465. #436	C₂²×C₇	semidirect
466. #436	C₂²×C₇	semidirect
467. #435	C₂²×C₇	semidirect
468. #435	C₂²×C₇	semidirect
469. #435	C₂²×C₇	semidirect
470. #435	C₂²×C₇	semidirect
471. #435	C₂²×C₇	semidirect
472. #435	C₂²×C₇	semidirect
473. #435	C₂²×C₇	semidirect
474. #435	C₂²×C₇	semidirect
475. #435	C₂²×C₇	semidirect
476. #435	C₂²×C₇	semidirect
477. #435	C₂²×C₇	semidirect
478. #435	C₂²×C₇	semidirect
479. #435	C₂²×C₇	semidirect
480. #435	C₂²×C₇	semidirect
481. #435	C₂²×C₇	semidirect
482. #435	C₂²×C₇	semidirect
483. #435	C₂²×C₇	semidirect
484. #435	C₂²×C₇	semidirect
485. C₈×D₄	C₂²×C₇	semidirect
486. C₈×D₄	C₂²×C₇	semidirect
487. C₈×D₄	C₂²×C₇	semidirect
488. C₈×D₄	C₂²×C₇	semidirect
489. C₈×D₄	C₂²×C₇	semidirect
490. C₈×D₄	C₂²×C₇	semidirect
491. C₈×D₄	C₂²×C₇	semidirect
492. #433	C₂²×C₇	semidirect
493. #433	C₂²×C₇	semidirect
494. #433	C₂²×C₇	semidirect
495. #433	C₂²×C₇	semidirect
496. #433	C₂²×C₇	semidirect
497. #433	C₂²×C₇	semidirect
498. #432	C₂²×C₇	semidirect
499. #431	C₂²×C₇	semidirect
500. #431	C₂²×C₇	semidirect
501. #424	C₂²×C₇	semidirect
502. #424	C₂²×C₇	semidirect
503. #424	C₂²×C₇	semidirect
504. #424	C₂²×C₇	semidirect
505. #423	C₂²×C₇	semidirect
506. C₂×C₄⋊C₈	C₂²×C₇	semidirect
507. #408	C₂²×C₇	semidirect
508. #408	C₂²×C₇	semidirect
509. #408	C₂²×C₇	semidirect
510. #408	C₂²×C₇	semidirect
512. #407	C₂²×C₇	semidirect
513. #407	C₂²×C₇	semidirect
514. #407	C₂²×C₇	semidirect
515. #407	C₂²×C₇	semidirect
517. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
518. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
519. #405	C₂²×C₇	semidirect
520. #405	C₂²×C₇	semidirect
521. #405	C₂²×C₇	semidirect
522. #405	C₂²×C₇	semidirect
523. C₄×M₁₆	C₂²×C₇	semidirect
524. C₂×#97	C₂²×C₇	semidirect
1017. C₇	#60313	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×#3459	2
C₇×#2995	2
C₇×#2994	2
C₇×#2993	2
C₇×#2978	2
C₇×#2976	2
C₇×#2975	2
C₇×#2974	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2930	2
C₇×#2929	2
C₂×C₇×#435	2
#60313	7

Subgroups — C7×#60313 #13237529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60313 #13237529