Subgroups — C₇×#60315 #13237531

Order 1792.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3529	C₂	1	1	yes	maximal, characteristic
2	C₇×#2994	C₂	1	2	yes	maximal, complemented
3	C₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₇×#2992	C₂	1	2	yes	maximal, complemented
5	C₇×#2981	C₂	1	2	yes	maximal, complemented
6	C₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2978	C₂	1	2	yes	maximal, complemented
9	C₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2976	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×#2935	C₂	1	2	yes	maximal, complemented
15	C₇×#2933	C₂	1	2	yes	maximal, complemented
16	C₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2929	C₂	1	2	yes	maximal, complemented
20	C₂×C₇×#131	C₂²	1	1	yes	characteristic
21	C₂×C₇×#131	C₂²	1	2	yes	—
22	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₇×#563	C₄	1	2	yes	—
26	C₇×#563	C₄	1	1	yes	characteristic
27	C₇×#562	C₄	1	2	yes	—
28	C₇×#562	C₄	1	2	yes	—
29	C₇×#562	C₄	1	2	yes	—
30	C₇×H(3,𝔽₄)	C₄	1	1	yes	characteristic
31	C₇×#560	C₄	1	2	yes	—
32	C₇×#560	C₄	1	1	yes	characteristic
33	C₇×#560	C₄	1	2	yes	—
34	C₇×#560	C₄	1	1	yes	characteristic
35	C₇×#532	C₂²	1	1	yes	characteristic
36	C₇×#532	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	—
40	C₇×#525	C₂²	1	1	yes	characteristic
41	C₇×#525	C₂²	1	2	yes	—
42	C₇×#525	C₂²	1	1	yes	characteristic
43	C₇×#525	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	—
49	C₇×#436	C₂²	1	2	yes	—
50	C₇×#436	C₂²	1	2	yes	—
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×#435	C₂²	1	2	yes	—
58	C₇×#435	C₂²	1	2	yes	—
59	C₇×#435	C₂²	1	2	yes	—
60	C₇×#435	C₂²	1	2	yes	—
61	C₇×#435	C₂²	1	2	yes	—
62	C₇×#435	C₂²	1	2	yes	—
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×C₈×D₄	C₂²	1	2	yes	—
76	C₇×C₈×D₄	C₂²	1	2	yes	—
77	C₇×C₈×D₄	C₂²	1	2	yes	—
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	2	yes	complemented
94	C₇×#424	C₂²	1	1	yes	characteristic, complemented
95	C₇×#424	C₂²	1	1	yes	characteristic, complemented
96	C₇×#424	C₂²	1	2	yes	complemented
97	C₇×#423	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
99	C₇×#408	C₂²	1	2	yes	—
100	C₇×#408	C₂²	1	1	yes	characteristic
101	C₇×#408	C₂²	1	1	yes	characteristic
102	C₇×#408	C₂²	1	1	yes	characteristic
103	C₇×#408	C₂²	1	2	yes	—
104	C₇×#408	C₂²	1	2	yes	—
105	C₇×#408	C₂²	1	1	yes	characteristic, complemented
106	C₇×#408	C₂²	1	2	yes	complemented
107	C₇×#407	C₂²	1	2	yes	complemented
108	C₇×#407	C₂²	1	1	yes	characteristic, complemented
109	C₇×#407	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	2	yes	complemented
113	C₇×#405	C₂²	1	1	yes	characteristic, 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	#60315	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	2	yes	—
120	C₂×C₇×#41	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₇×#131	—	4	2	no	—
124	C₇×#131	—	4	4	no	—
125	C₇×#131	—	4	2	no	—
126	C₂×C₇×M₁₆	—	4	2	no	—
127	C₂×C₇×M₁₆	C₂³	1	2	yes	—
128	C₂×C₇×M₁₆	C₂³	1	2	yes	—
129	C₂×C₇×M₁₆	C₂³	1	2	yes	—
130	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₇×M₁₆	C₂³	1	2	yes	—
132	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
134	C₂×C₇×M₁₆	C₂³	1	2	yes	—
135	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
136	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
137	C₂×C₇×M₁₆	C₂³	1	2	yes	—
138	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
139	C₂²×C₇×C₈	—	4	2	no	—
140	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₇×C₈	C₂³	1	2	yes	—
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	2	yes	—
147	C₂²×C₇×C₈	C₂³	1	2	yes	—
148	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₇×C₈	C₂³	1	2	yes	—
150	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×C₈	C₂³	1	2	yes	—
152	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
153	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
154	C₇×#127	C₂×C₄	1	1	yes	characteristic
155	C₇×#127	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×#126	C₂×C₄	1	2	yes	—
161	C₇×#126	C₂×C₄	1	2	yes	—
162	C₇×#125	C₂×C₄	1	2	yes	—
163	C₇×#125	C₂×C₄	1	2	yes	—
164	C₇×#125	C₂×C₄	1	2	yes	—
165	C₇×#124	C₂×C₄	1	2	yes	—
166	C₇×#124	C₂×C₄	1	2	yes	—
167	C₇×#124	C₂×C₄	1	2	yes	—
168	C₇×#124	C₂×C₄	1	1	yes	characteristic
169	C₇×#124	C₂×C₄	1	2	yes	—
170	C₇×#124	C₂×C₄	1	1	yes	characteristic
171	C₇×#124	C₂×C₄	1	2	yes	—
172	C₇×#123	C₂×C₄	1	1	yes	characteristic
173	C₇×#123	C₂×C₄	1	2	yes	—
174	C₇×#123	C₂×C₄	1	1	yes	characteristic
175	C₇×#123	C₂×C₄	1	2	yes	—
176	C₇×#123	C₂×C₄	1	1	yes	characteristic
177	C₇×#123	C₂×C₄	1	2	yes	—
178	C₇×#123	C₂×C₄	1	1	yes	characteristic
179	C₇×#123	C₂×C₄	1	2	yes	—
180	C₇×#123	C₂×C₄	1	2	yes	—
181	C₇×#123	C₂×C₄	1	2	yes	—
182	C₇×#123	C₂×C₄	1	2	yes	—
183	C₇×#123	C₂×C₄	1	2	yes	—
184	C₇×#123	C₂×C₄	1	2	yes	—
185	C₇×#123	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×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
193	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
194	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
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×#121	C₂×C₄	1	2	yes	—
201	C₇×#121	C₂×C₄	1	2	yes	—
202	C₇×#121	C₂×C₄	1	2	yes	—
203	C₇×#121	C₂×C₄	1	2	yes	—
204	C₇×#121	C₂×C₄	1	2	yes	—
205	C₇×#121	C₂×C₄	1	2	yes	—
206	C₇×#121	C₂×C₄	1	2	yes	—
207	C₇×#121	C₂×C₄	1	2	yes	—
208	C₇×#121	C₂×C₄	1	2	yes	—
209	C₇×#121	C₂×C₄	1	2	yes	—
210	C₇×#120	C₂×C₄	1	1	yes	characteristic
211	C₇×#120	C₂×C₄	1	2	yes	—
212	C₇×#120	C₂×C₄	1	1	yes	characteristic
213	C₇×#120	C₂×C₄	1	2	yes	—
214	C₇×#120	C₂×C₄	1	1	yes	characteristic
215	C₇×#120	C₂×C₄	1	2	yes	—
216	C₇×#120	C₂×C₄	1	1	yes	characteristic
217	C₇×#120	C₂×C₄	1	2	yes	—
218	C₄×C₇×Q₈	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	C₄×C₇×D₄	C₂³	1	2	yes	—
223	C₄×C₇×D₄	C₂³	1	2	yes	—
224	C₄×C₇×D₄	C₂³	1	2	yes	—
225	C₄×C₇×D₄	C₂³	1	2	yes	—
226	C₄×C₇×D₄	C₂³	1	2	yes	—
227	C₄×C₇×D₄	C₂³	1	2	yes	—
228	C₇×#117	C₂³	1	1	yes	characteristic
229	C₇×#117	C₂³	1	2	yes	—
230	C₇×#117	C₂³	1	1	yes	characteristic
231	C₇×#117	C₂³	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	#3529	C₂×C₇	1	1	yes	characteristic
277	#2994	C₂×C₇	1	2	yes	complemented
278	#2993	C₂×C₇	1	2	yes	complemented
279	#2992	C₂×C₇	1	2	yes	complemented
280	#2981	C₂×C₇	1	2	yes	complemented
281	#2979	C₂×C₇	1	1	yes	characteristic, complemented
282	#2978	C₂×C₇	1	1	yes	characteristic, complemented
283	#2978	C₂×C₇	1	2	yes	complemented
284	#2977	C₂×C₇	1	1	yes	characteristic, complemented
285	#2976	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	#2935	C₂×C₇	1	2	yes	complemented
290	#2933	C₂×C₇	1	2	yes	complemented
291	#2932	C₂×C₇	1	1	yes	characteristic, complemented
292	#2930	C₂×C₇	1	1	yes	characteristic, complemented
293	#2929	C₂×C₇	1	1	yes	characteristic, complemented
294	#2929	C₂×C₇	1	2	yes	complemented
295	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
296	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
297	C₇×#41	—	4	1	no	—
298	C₇×#41	—	4	2	no	—
299	C₇×#41	—	4	1	no	—
300	C₇×#41	—	4	2	no	—
301	C₇×#41	—	4	1	no	—
302	C₇×#41	—	4	1	no	—
303	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
304	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
305	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
306	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
318	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
319	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
320	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
321	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
322	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
323	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₇	—	4	1	no	—
325	C₂²×C₄×C₇	—	4	1	no	—
326	C₂²×C₄×C₇	—	4	1	no	—
327	C₂²×C₄×C₇	—	4	1	no	—
328	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	2	yes	—
332	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
334	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₇×M₁₆	—	2	4	no	—
342	C₇×M₁₆	—	2	4	no	—
343	C₇×M₁₆	—	4	2	no	—
344	C₇×M₁₆	—	4	2	no	—
345	C₇×M₁₆	—	4	1	no	—
346	C₇×M₁₆	—	4	2	no	—
347	C₇×M₁₆	—	4	1	no	—
348	C₇×M₁₆	—	4	1	no	—
349	C₇×M₁₆	—	4	1	no	—
350	C₇×M₁₆	—	4	1	no	—
351	C₇×M₁₆	—	4	2	no	—
352	C₇×M₁₆	—	4	1	no	—
353	C₂×C₇×C₈	—	2	4	no	—
354	C₂×C₇×C₈	—	2	2	no	—
355	C₂×C₇×C₈	—	2	2	no	—
356	C₂×C₇×C₈	—	2	2	no	—
357	C₂×C₇×C₈	—	4	1	no	—
358	C₂×C₇×C₈	—	4	2	no	—
359	C₂×C₇×C₈	—	4	1	no	—
360	C₂×C₇×C₈	—	4	2	no	—
361	C₂×C₇×C₈	—	4	1	no	—
362	C₂×C₇×C₈	—	4	2	no	—
363	C₂×C₇×C₈	—	4	2	no	—
364	C₂×C₇×C₈	—	4	2	no	—
365	C₂×C₇×C₈	C₂⁴	1	2	yes	—
366	C₂×C₇×C₈	C₂⁴	1	2	yes	—
367	C₂×C₇×C₈	C₂⁴	1	2	yes	—
368	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₇×C₈	C₂⁴	1	2	yes	—
370	C₂×C₇×C₈	C₂⁴	1	2	yes	—
371	C₂×C₇×C₈	C₂⁴	1	2	yes	—
372	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
375	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
376	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
377	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	2	yes	—
385	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	2	yes	—
391	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
392	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
393	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
394	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
399	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
420	C₄²×C₇	C₂²×C₄	1	2	yes	—
421	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
422	C₄²×C₇	C₂²×C₄	1	2	yes	—
423	C₄²×C₇	C₂⁴	1	2	yes	—
424	C₄²×C₇	C₂⁴	1	2	yes	—
425	C₄²×C₇	C₂⁴	1	2	yes	—
426	C₂×#131	C₂²×C₇	1	1	yes	characteristic
427	C₂×#131	C₂²×C₇	1	2	yes	—
428	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
429	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
430	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
431	#563	C₄×C₇	1	2	yes	—
432	#563	C₄×C₇	1	1	yes	characteristic
433	#562	C₄×C₇	1	2	yes	—
434	#562	C₄×C₇	1	2	yes	—
435	#562	C₄×C₇	1	2	yes	—
436	H(3,𝔽₄)	C₄×C₇	1	1	yes	characteristic
437	#560	C₄×C₇	1	2	yes	—
438	#560	C₄×C₇	1	1	yes	characteristic
439	#560	C₄×C₇	1	2	yes	—
440	#560	C₄×C₇	1	1	yes	characteristic
441	#532	C₂²×C₇	1	1	yes	characteristic
442	#532	C₂²×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	2	yes	—
448	#525	C₂²×C₇	1	1	yes	characteristic
449	#525	C₂²×C₇	1	2	yes	—
450	#446	C₂²×C₇	1	2	yes	complemented
451	#446	C₂²×C₇	1	2	yes	complemented
452	#446	C₂²×C₇	1	2	yes	complemented
453	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
454	#436	C₂²×C₇	1	2	yes	—
455	#436	C₂²×C₇	1	2	yes	—
456	#436	C₂²×C₇	1	2	yes	—
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	#435	C₂²×C₇	1	2	yes	—
464	#435	C₂²×C₇	1	2	yes	—
465	#435	C₂²×C₇	1	2	yes	—
466	#435	C₂²×C₇	1	2	yes	—
467	#435	C₂²×C₇	1	2	yes	—
468	#435	C₂²×C₇	1	2	yes	—
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	C₈×D₄	C₂²×C₇	1	2	yes	—
482	C₈×D₄	C₂²×C₇	1	2	yes	—
483	C₈×D₄	C₂²×C₇	1	2	yes	—
484	C₈×D₄	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	#433	C₂²×C₇	1	2	yes	complemented
491	#433	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	#432	C₂²×C₇	1	2	yes	complemented
497	#431	C₂²×C₇	1	2	yes	complemented
498	#431	C₂²×C₇	1	2	yes	complemented
499	#424	C₂²×C₇	1	2	yes	complemented
500	#424	C₂²×C₇	1	1	yes	characteristic, complemented
501	#424	C₂²×C₇	1	1	yes	characteristic, complemented
502	#424	C₂²×C₇	1	2	yes	complemented
503	#423	C₂²×C₇	1	1	yes	characteristic, complemented
504	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
505	#408	C₂²×C₇	1	2	yes	—
506	#408	C₂²×C₇	1	1	yes	characteristic
507	#408	C₂²×C₇	1	1	yes	characteristic
508	#408	C₂²×C₇	1	1	yes	characteristic
509	#408	C₂²×C₇	1	2	yes	—
510	#408	C₂²×C₇	1	2	yes	—
511	#408	C₂²×C₇	1	1	yes	characteristic, complemented
512	#408	C₂²×C₇	1	2	yes	complemented
513	#407	C₂²×C₇	1	2	yes	complemented
514	#407	C₂²×C₇	1	1	yes	characteristic, complemented
515	#407	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
517	#405	C₂²×C₇	1	1	yes	characteristic, complemented
518	#405	C₂²×C₇	1	2	yes	complemented
519	#405	C₂²×C₇	1	1	yes	characteristic, complemented
520	#405	C₂²×C₇	1	2	yes	complemented
521	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
522	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
523	C₂³×C₇	—	4	1	no	—
524	C₂³×C₇	—	4	2	no	—
525	C₂³×C₇	—	4	1	no	—
526	C₂³×C₇	—	4	2	no	—
527	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
528	C₂³×C₇	C₂³×C₄	1	2	yes	—
529	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
530	C₂³×C₇	C₂³×C₄	1	2	yes	—
531	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
532	C₂³×C₇	C₂³×C₄	1	2	yes	—
533	C₇×Q₈	—	4	2	no	—
534	C₇×Q₈	—	4	1	no	—
535	C₇×Q₈	—	4	2	no	—
536	C₇×Q₈	—	4	1	no	—
537	C₇×D₄	—	4	2	no	—
538	C₇×D₄	—	4	2	no	—
539	C₇×D₄	—	4	2	no	—
540	C₇×D₄	—	4	2	no	—
541	C₇×D₄	—	4	2	no	—
542	C₇×D₄	—	4	2	no	—
543	C₇×D₄	—	4	2	no	—
544	C₇×D₄	—	4	2	no	—
545	C₇×D₄	—	4	2	no	—
546	C₇×D₄	—	4	1	no	—
547	C₇×D₄	—	4	1	no	—
548	C₇×D₄	—	4	2	no	—
549	C₇×D₄	—	4	2	no	—
550	C₇×D₄	—	4	1	no	—
551	C₇×D₄	—	4	2	no	—
552	C₇×D₄	—	4	1	no	—
553	C₇×D₄	—	4	2	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	1	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	2	2	no	—
560	C₂×C₄×C₇	—	2	2	no	—
561	C₂×C₄×C₇	—	2	1	no	—
562	C₂×C₄×C₇	—	2	2	no	—
563	C₂×C₄×C₇	—	2	1	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	2	no	—
566	C₂×C₄×C₇	—	4	1	no	—
567	C₂×C₄×C₇	—	4	2	no	—
568	C₂×C₄×C₇	—	4	2	no	—
569	C₂×C₄×C₇	—	4	1	no	—
570	C₂×C₄×C₇	—	4	2	no	—
571	C₂×C₄×C₇	—	4	2	no	—
572	C₂×C₄×C₇	—	4	2	no	—
573	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
574	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
577	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
578	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
579	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
580	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
582	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
583	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
585	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
586	C₇×C₈	—	2	2	no	—
587	C₇×C₈	—	2	1	no	—
588	C₇×C₈	—	2	1	no	—
589	C₇×C₈	—	2	1	no	—
590	C₇×C₈	—	2	2	no	—
591	C₇×C₈	—	2	2	no	—
592	C₇×C₈	—	2	2	no	—
593	C₇×C₈	—	2	2	no	—
594	C₇×C₈	—	2	2	no	—
595	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
596	C₂×#41	C₂³×C₇	1	1	yes	characteristic
597	C₂×#41	C₂³×C₇	1	2	yes	—
598	C₂×#41	C₂³×C₇	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
601	#131	—	4	2	no	—
602	#131	—	4	4	no	—
603	#131	—	4	2	no	—
604	C₂×M₁₆	—	4	2	no	—
605	C₂×M₁₆	C₂³×C₇	1	2	yes	—
606	C₂×M₁₆	C₂³×C₇	1	2	yes	—
607	C₂×M₁₆	C₂³×C₇	1	2	yes	—
608	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
609	C₂×M₁₆	C₂³×C₇	1	2	yes	—
610	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₇	1	2	yes	—
614	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₇	1	2	yes	—
616	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
617	C₂²×C₈	—	4	2	no	—
618	C₂²×C₈	C₂³×C₇	1	2	yes	—
619	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
620	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₇	1	2	yes	—
624	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₇	1	2	yes	—
626	C₂²×C₈	C₂³×C₇	1	2	yes	—
627	C₂²×C₈	C₂³×C₇	1	2	yes	—
628	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
629	C₂²×C₈	C₂³×C₇	1	2	yes	—
630	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
631	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
632	#127	C₂×C₄×C₇	1	1	yes	characteristic
633	#127	C₂×C₄×C₇	1	2	yes	—
634	#126	C₂×C₄×C₇	1	2	yes	—
635	#126	C₂×C₄×C₇	1	2	yes	—
636	#126	C₂×C₄×C₇	1	2	yes	—
637	#126	C₂×C₄×C₇	1	2	yes	—
638	#126	C₂×C₄×C₇	1	2	yes	—
639	#126	C₂×C₄×C₇	1	2	yes	—
640	#125	C₂×C₄×C₇	1	2	yes	—
641	#125	C₂×C₄×C₇	1	2	yes	—
642	#125	C₂×C₄×C₇	1	2	yes	—
643	#124	C₂×C₄×C₇	1	2	yes	—
644	#124	C₂×C₄×C₇	1	2	yes	—
645	#124	C₂×C₄×C₇	1	2	yes	—
646	#124	C₂×C₄×C₇	1	1	yes	characteristic
647	#124	C₂×C₄×C₇	1	2	yes	—
648	#124	C₂×C₄×C₇	1	1	yes	characteristic
649	#124	C₂×C₄×C₇	1	2	yes	—
650	#123	C₂×C₄×C₇	1	1	yes	characteristic
651	#123	C₂×C₄×C₇	1	2	yes	—
652	#123	C₂×C₄×C₇	1	1	yes	characteristic
653	#123	C₂×C₄×C₇	1	2	yes	—
654	#123	C₂×C₄×C₇	1	1	yes	characteristic
655	#123	C₂×C₄×C₇	1	2	yes	—
656	#123	C₂×C₄×C₇	1	1	yes	characteristic
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	#123	C₂×C₄×C₇	1	2	yes	—
664	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
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	2	yes	—
668	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
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	#121	C₂×C₄×C₇	1	2	yes	—
674	#121	C₂×C₄×C₇	1	2	yes	—
675	#121	C₂×C₄×C₇	1	2	yes	—
676	#121	C₂×C₄×C₇	1	2	yes	—
677	#121	C₂×C₄×C₇	1	2	yes	—
678	#121	C₂×C₄×C₇	1	2	yes	—
679	#121	C₂×C₄×C₇	1	2	yes	—
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	#121	C₂×C₄×C₇	1	2	yes	—
686	#121	C₂×C₄×C₇	1	2	yes	—
687	#121	C₂×C₄×C₇	1	2	yes	—
688	#120	C₂×C₄×C₇	1	1	yes	characteristic
689	#120	C₂×C₄×C₇	1	2	yes	—
690	#120	C₂×C₄×C₇	1	1	yes	characteristic
691	#120	C₂×C₄×C₇	1	2	yes	—
692	#120	C₂×C₄×C₇	1	1	yes	characteristic
693	#120	C₂×C₄×C₇	1	2	yes	—
694	#120	C₂×C₄×C₇	1	1	yes	characteristic
695	#120	C₂×C₄×C₇	1	2	yes	—
696	C₄×Q₈	C₂³×C₇	1	2	yes	—
697	C₄×D₄	C₂³×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	#117	C₂³×C₇	1	1	yes	characteristic
707	#117	C₂³×C₇	1	2	yes	—
708	#117	C₂³×C₇	1	1	yes	characteristic
709	#117	C₂³×C₇	1	2	yes	—
710	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₇	1	2	yes	—
712	C₄⋊C₈	C₂³×C₇	1	2	yes	—
713	C₄⋊C₈	C₂³×C₇	1	2	yes	—
714	C₄⋊C₈	C₂³×C₇	1	2	yes	—
715	C₄⋊C₈	C₂³×C₇	1	2	yes	—
716	C₄⋊C₈	C₂³×C₇	1	2	yes	—
717	C₄⋊C₈	C₂³×C₇	1	2	yes	—
718	C₄⋊C₈	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	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
730	C₂²⋊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	#97	C₂³×C₇	1	2	yes	—
743	#97	C₂³×C₇	1	2	yes	—
744	#97	C₂³×C₇	1	2	yes	—
745	#97	C₂³×C₇	1	2	yes	—
746	#97	C₂³×C₇	1	2	yes	—
747	#97	C₂³×C₇	1	2	yes	—
748	C₄×C₈	C₂³×C₇	1	2	yes	—
749	C₄×C₈	C₂³×C₇	1	2	yes	—
750	C₄×C₈	C₂³×C₇	1	2	yes	—
751	C₄×C₈	C₂³×C₇	1	2	yes	—
752	C₄×C₈	C₂³×C₇	1	2	yes	—
753	C₄×C₈	C₂³×C₇	1	2	yes	—
754	C₂²×C₇	—	2	2	no	—
755	C₂²×C₇	—	2	1	no	—
756	C₂²×C₇	—	2	1	no	—
757	C₂²×C₇	—	2	2	no	—
758	C₂²×C₇	—	2	1	no	—
759	C₂²×C₇	—	2	2	no	—
760	C₂²×C₇	—	2	2	no	—
761	C₂²×C₇	—	2	2	no	—
762	C₂²×C₇	—	2	2	no	—
763	C₂²×C₇	—	2	2	no	—
764	C₂²×C₇	—	2	2	no	—
765	C₂²×C₇	—	2	2	no	—
766	C₂²×C₇	—	2	2	no	—
767	C₂²×C₇	—	2	2	no	—
768	C₂²×C₇	—	2	2	no	—
769	C₂²×C₇	—	4	4	no	—
770	C₂²×C₇	—	8	2	no	—
771	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
772	C₄×C₇	—	2	2	no	—
773	C₄×C₇	—	2	1	no	—
774	C₄×C₇	—	2	1	no	—
775	C₄×C₇	—	2	2	no	—
776	C₄×C₇	—	2	1	no	—
777	C₄×C₇	—	2	2	no	—
778	C₄×C₇	—	2	2	no	—
779	C₄×C₇	—	2	2	no	—
780	C₄×C₇	—	2	2	no	—
781	C₄×C₇	—	2	2	no	—
782	C₄×C₇	—	2	2	no	—
783	C₄×C₇	—	2	2	no	—
784	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
785	C₄×C₇	#585	1	1	yes	characteristic
786	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
787	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
788	#41	—	4	1	no	—
789	#41	—	4	2	no	—
790	#41	—	4	1	no	—
791	#41	—	4	2	no	—
792	#41	—	4	1	no	—
793	#41	—	4	1	no	—
794	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
795	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
796	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
797	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
798	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
799	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
800	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
801	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
802	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
803	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
804	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
805	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
806	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
807	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
808	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
809	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
810	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
811	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	1	yes	characteristic
815	C₂²×C₄	—	4	1	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
820	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
821	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
822	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
823	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
824	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
825	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
832	M₁₆	—	2	4	no	—
833	M₁₆	—	2	4	no	—
834	M₁₆	—	4	2	no	—
835	M₁₆	—	4	2	no	—
836	M₁₆	—	4	1	no	—
837	M₁₆	—	4	2	no	—
838	M₁₆	—	4	1	no	—
839	M₁₆	—	4	1	no	—
840	M₁₆	—	4	1	no	—
841	M₁₆	—	4	1	no	—
842	M₁₆	—	4	2	no	—
843	M₁₆	—	4	1	no	—
844	C₂×C₈	—	2	4	no	—
845	C₂×C₈	—	2	2	no	—
846	C₂×C₈	—	2	2	no	—
847	C₂×C₈	—	2	2	no	—
848	C₂×C₈	—	4	1	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	—	4	1	no	—
851	C₂×C₈	—	4	2	no	—
852	C₂×C₈	—	4	1	no	—
853	C₂×C₈	—	4	2	no	—
854	C₂×C₈	—	4	2	no	—
855	C₂×C₈	—	4	2	no	—
856	C₂×C₈	C₂⁴×C₇	1	2	yes	—
857	C₂×C₈	C₂⁴×C₇	1	2	yes	—
858	C₂×C₈	C₂⁴×C₇	1	2	yes	—
859	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
860	C₂×C₈	C₂⁴×C₇	1	2	yes	—
861	C₂×C₈	C₂⁴×C₇	1	2	yes	—
862	C₂×C₈	C₂⁴×C₇	1	2	yes	—
863	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
864	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
865	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
866	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
867	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
868	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
869	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
870	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
871	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
872	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
873	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
874	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
875	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
877	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
878	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
879	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
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	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
889	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
891	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
894	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
899	C₂²⋊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	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
911	C₄²	C₂²×C₄×C₇	1	2	yes	—
912	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
913	C₄²	C₂²×C₄×C₇	1	2	yes	—
914	C₄²	C₂⁴×C₇	1	2	yes	—
915	C₄²	C₂⁴×C₇	1	2	yes	—
916	C₄²	C₂⁴×C₇	1	2	yes	—
917	C₂×C₇	—	4	1	no	—
918	C₂×C₇	—	4	2	no	—
919	C₂×C₇	—	4	2	no	—
920	C₂×C₇	—	4	1	no	—
921	C₂×C₇	—	4	1	no	—
922	C₂×C₇	—	4	2	no	—
923	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
924	C₂×C₇	#3573	1	2	yes	—
925	C₂³	—	4	1	no	—
926	C₂³	—	4	2	no	—
927	C₂³	—	4	1	no	—
928	C₂³	—	4	2	no	—
929	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
930	C₂³	C₂³×C₄×C₇	1	2	yes	—
931	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
932	C₂³	C₂³×C₄×C₇	1	2	yes	—
933	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
934	C₂³	C₂³×C₄×C₇	1	2	yes	—
935	Q₈	—	4	2	no	—
936	Q₈	—	4	1	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	4	1	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	1	no	—
949	D₄	—	4	1	no	—
950	D₄	—	4	2	no	—
951	D₄	—	4	2	no	—
952	D₄	—	4	1	no	—
953	D₄	—	4	2	no	—
954	D₄	—	4	1	no	—
955	D₄	—	4	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	2	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	2	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
976	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
977	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
978	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
979	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
980	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
981	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
984	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
986	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
987	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
988	C₈	—	2	2	no	—
989	C₈	—	2	1	no	—
990	C₈	—	2	1	no	—
991	C₈	—	2	1	no	—
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₈	—	2	2	no	—
995	C₈	—	2	2	no	—
996	C₈	—	2	2	no	—
997	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
998	C₇	#60315	1	1	yes	characteristic, direct product factor, Sylow
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	8	2	no	—
1016	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	2	1	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	2	no	—
1029	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₄	C₇×#585	1	1	yes	characteristic
1031	C₂	—	4	1	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	2	no	—
1035	C₂	—	4	1	no	—
1036	C₂	—	4	2	no	—
1037	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂	C₇×#3573	1	2	yes	—

	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×#3529	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×#2994	C₂	semidirect
3. C₇×#2993	C₂	semidirect
4. C₇×#2992	C₂	semidirect
5. C₇×#2981	C₂	semidirect
6. C₇×#2979	C₂	semidirect
7. C₇×#2978	C₂	semidirect
8. C₇×#2978	C₂	semidirect
9. C₇×#2977	C₂	semidirect
10. C₇×#2976	C₂	semidirect
11. C₇×#2969	C₂	semidirect
12. C₇×#2968	C₂	semidirect
13. C₇×#2967	C₂	semidirect
14. C₇×#2935	C₂	semidirect
15. C₇×#2933	C₂	semidirect
16. C₇×#2932	C₂	semidirect
17. C₇×#2930	C₂	semidirect
18. C₇×#2929	C₂	semidirect
19. C₇×#2929	C₂	semidirect
22. 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
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
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
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
105. C₇×#408	C₂²	semidirect
106. C₇×#408	C₂²	semidirect
107. C₇×#407	C₂²	semidirect
108. C₇×#407	C₂²	semidirect
109. C₇×#407	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. #60315	C₇	direct (N × H)
277. #2994	C₂×C₇	semidirect
278. #2993	C₂×C₇	semidirect
279. #2992	C₂×C₇	semidirect
280. #2981	C₂×C₇	semidirect
281. #2979	C₂×C₇	semidirect
282. #2978	C₂×C₇	semidirect
283. #2978	C₂×C₇	semidirect
284. #2977	C₂×C₇	semidirect
285. #2976	C₂×C₇	semidirect
286. #2969	C₂×C₇	semidirect
287. #2968	C₂×C₇	semidirect
288. #2967	C₂×C₇	semidirect
289. #2935	C₂×C₇	semidirect
290. #2933	C₂×C₇	semidirect
291. #2932	C₂×C₇	semidirect
292. #2930	C₂×C₇	semidirect
293. #2929	C₂×C₇	semidirect
294. #2929	C₂×C₇	semidirect
428. C₂×#131	C₂²×C₇	semidirect
429. C₂²×M₁₆	C₂²×C₇	semidirect
430. C₂³×C₈	C₂²×C₇	semidirect
450. #446	C₂²×C₇	semidirect
451. #446	C₂²×C₇	semidirect
452. #446	C₂²×C₇	semidirect
453. C₈×Q₈	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
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
484. C₈×D₄	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. #433	C₂²×C₇	semidirect
491. #433	C₂²×C₇	semidirect
492. #433	C₂²×C₇	semidirect
493. #433	C₂²×C₇	semidirect
494. #433	C₂²×C₇	semidirect
495. #433	C₂²×C₇	semidirect
496. #432	C₂²×C₇	semidirect
497. #431	C₂²×C₇	semidirect
498. #431	C₂²×C₇	semidirect
499. #424	C₂²×C₇	semidirect
500. #424	C₂²×C₇	semidirect
501. #424	C₂²×C₇	semidirect
502. #424	C₂²×C₇	semidirect
503. #423	C₂²×C₇	semidirect
504. C₂×C₄⋊C₈	C₂²×C₇	semidirect
511. #408	C₂²×C₇	semidirect
512. #408	C₂²×C₇	semidirect
513. #407	C₂²×C₇	semidirect
514. #407	C₂²×C₇	semidirect
515. #407	C₂²×C₇	semidirect
516. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
517. #405	C₂²×C₇	semidirect
518. #405	C₂²×C₇	semidirect
519. #405	C₂²×C₇	semidirect
520. #405	C₂²×C₇	semidirect
521. C₄×M₁₆	C₂²×C₇	semidirect
522. C₂×#97	C₂²×C₇	semidirect
998. C₇	#60315	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×#3529	2
C₇×#2994	2
C₇×#2993	2
C₇×#2992	2
C₇×#2981	2
C₇×#2979	2
C₇×#2978	2
C₇×#2977	2
C₇×#2976	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×#2935	2
C₇×#2933	2
C₇×#2932	2
C₇×#2930	2
C₇×#2929	2
#60315	7

Subgroups — C7×#60315 #13237531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60315 #13237531