Subgroups — C₇×#60327 #13237543

Order 1792.

1812 conjugacy classes of subgroups.

The subgroup lattice has 1022 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×#2995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2994	C₂	1	2	yes	maximal, complemented
5	C₇×#2992	C₂	1	2	yes	maximal, complemented
6	C₇×#2981	C₂	1	2	yes	maximal, complemented
7	C₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2977	C₂	1	2	yes	maximal, complemented
9	C₇×#2976	C₂	1	2	yes	maximal, complemented
10	C₇×#2976	C₂	1	2	yes	maximal, complemented
11	C₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₇×#2967	C₂	1	2	yes	maximal, complemented
13	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2935	C₂	1	2	yes	maximal, complemented
16	C₇×#2933	C₂	1	2	yes	maximal, complemented
17	C₇×#2933	C₂	1	2	yes	maximal, complemented
18	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2930	C₂	1	2	yes	maximal, complemented
20	C₂×C₇×#131	C₂²	1	2	yes	—
21	C₂×C₇×#131	C₂²	1	1	yes	characteristic
22	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
24	C₇×#563	C₄	1	1	yes	characteristic
25	C₇×#563	C₄	1	2	yes	—
26	C₇×#562	C₄	1	1	yes	characteristic
27	C₇×#562	C₄	1	2	yes	—
28	C₇×#562	C₄	1	2	yes	—
29	C₇×#562	C₄	1	1	yes	characteristic
30	C₇×H(3,𝔽₄)	C₄	1	1	yes	characteristic
31	C₇×#560	C₄	1	2	yes	—
32	C₇×#560	C₄	1	2	yes	—
33	C₇×#560	C₄	1	2	yes	—
34	C₇×#532	C₂²	1	1	yes	characteristic
35	C₇×#532	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	1	yes	characteristic
37	C₇×#529	C₂²	1	1	yes	characteristic
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₇×#525	C₂²	1	2	yes	—
42	C₇×#525	C₂²	1	2	yes	—
43	C₇×#446	C₂²	1	1	yes	characteristic, complemented
44	C₇×#446	C₂²	1	1	yes	characteristic, complemented
45	C₇×#446	C₂²	1	2	yes	complemented
46	C₇×#446	C₂²	1	2	yes	complemented
47	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×#436	C₂²	1	1	yes	characteristic
50	C₇×#436	C₂²	1	2	yes	—
51	C₇×#436	C₂²	1	2	yes	—
52	C₇×#436	C₂²	1	1	yes	characteristic
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	—
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	—
64	C₇×#435	C₂²	1	2	yes	—
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	1	yes	characteristic
78	C₇×C₈×D₄	C₂²	1	2	yes	—
79	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
80	C₇×C₈×D₄	C₂²	1	2	yes	—
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×C₈×D₄	C₂²	1	2	yes	complemented
85	C₇×C₈×D₄	C₂²	1	2	yes	complemented
86	C₇×C₈×D₄	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×#433	C₂²	1	2	yes	complemented
91	C₇×#433	C₂²	1	2	yes	complemented
92	C₇×#433	C₂²	1	2	yes	complemented
93	C₇×#432	C₂²	1	1	yes	characteristic, complemented
94	C₇×#432	C₂²	1	1	yes	characteristic, complemented
95	C₇×#432	C₂²	1	2	yes	complemented
96	C₇×#431	C₂²	1	2	yes	complemented
97	C₇×#424	C₂²	1	2	yes	complemented
98	C₇×#424	C₂²	1	2	yes	complemented
99	C₇×#424	C₂²	1	2	yes	complemented
100	C₇×#423	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
102	C₇×#408	C₂²	1	2	yes	—
103	C₇×#408	C₂²	1	1	yes	characteristic
104	C₇×#408	C₂²	1	2	yes	—
105	C₇×#408	C₂²	1	2	yes	—
106	C₇×#408	C₂²	1	2	yes	—
107	C₇×#408	C₂²	1	1	yes	characteristic, complemented
108	C₇×#408	C₂²	1	2	yes	complemented
109	C₇×#407	C₂²	1	2	yes	complemented
110	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
112	C₇×#405	C₂²	1	2	yes	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×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
117	#60327	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂×C₇×#41	C₂³	1	2	yes	—
119	C₂×C₇×#41	C₂³	1	1	yes	characteristic
120	C₂×C₇×#41	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	2	yes	—
122	C₇×#131	—	4	4	no	—
123	C₇×#131	—	4	2	no	—
124	C₇×#131	—	4	2	no	—
125	C₂×C₇×M₁₆	—	4	4	no	—
126	C₂×C₇×M₁₆	C₂³	1	2	yes	—
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	2	yes	—
131	C₂×C₇×M₁₆	C₂³	1	2	yes	—
132	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₇×M₁₆	C₂³	1	2	yes	—
134	C₂×C₇×M₁₆	C₂³	1	2	yes	—
135	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
136	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
137	C₂²×C₇×C₈	C₂³	1	2	yes	—
138	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₇×C₈	C₂³	1	2	yes	—
140	C₂²×C₇×C₈	C₂³	1	2	yes	—
141	C₂²×C₇×C₈	C₂³	1	2	yes	—
142	C₂²×C₇×C₈	C₂³	1	2	yes	—
143	C₂²×C₇×C₈	C₂³	1	2	yes	—
144	C₂²×C₇×C₈	C₂³	1	2	yes	—
145	C₂²×C₇×C₈	C₂³	1	2	yes	—
146	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
147	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
148	C₇×#127	C₂×C₄	1	1	yes	characteristic
149	C₇×#127	C₂×C₄	1	2	yes	—
150	C₇×#126	C₂×C₄	1	2	yes	—
151	C₇×#126	C₂×C₄	1	2	yes	—
152	C₇×#126	C₂×C₄	1	2	yes	—
153	C₇×#126	C₂×C₄	1	2	yes	—
154	C₇×#126	C₂×C₄	1	2	yes	—
155	C₇×#126	C₂×C₄	1	2	yes	—
156	C₇×#125	C₂×C₄	1	1	yes	characteristic
157	C₇×#125	C₂×C₄	1	1	yes	characteristic
158	C₇×#125	C₂×C₄	1	2	yes	—
159	C₇×#125	C₂×C₄	1	2	yes	—
160	C₇×#124	C₂×C₄	1	1	yes	characteristic
161	C₇×#124	C₂×C₄	1	1	yes	characteristic
162	C₇×#124	C₂×C₄	1	2	yes	—
163	C₇×#124	C₂×C₄	1	2	yes	—
164	C₇×#124	C₂×C₄	1	1	yes	characteristic
165	C₇×#124	C₂×C₄	1	2	yes	—
166	C₇×#124	C₂×C₄	1	1	yes	characteristic
167	C₇×#124	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×#123	C₂×C₄	1	2	yes	—
179	C₇×#123	C₂×C₄	1	2	yes	—
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	2	yes	—
183	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
187	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
188	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₇×#121	C₂×C₄	1	2	yes	—
191	C₇×#121	C₂×C₄	1	2	yes	—
192	C₇×#121	C₂×C₄	1	2	yes	—
193	C₇×#121	C₂×C₄	1	2	yes	—
194	C₇×#121	C₂×C₄	1	2	yes	—
195	C₇×#121	C₂×C₄	1	2	yes	—
196	C₇×#121	C₂×C₄	1	1	yes	characteristic
197	C₇×#121	C₂×C₄	1	1	yes	characteristic
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×#120	C₂×C₄	1	2	yes	—
207	C₇×#120	C₂×C₄	1	2	yes	—
208	C₇×#120	C₂×C₄	1	2	yes	—
209	C₇×#120	C₂×C₄	1	2	yes	—
210	C₇×#120	C₂×C₄	1	2	yes	—
211	C₇×#120	C₂×C₄	1	2	yes	—
212	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
213	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
214	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
215	C₄×C₇×D₄	C₂³	1	2	yes	—
216	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
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	C₄×C₇×D₄	C₂³	1	2	yes	—
223	C₄×C₇×D₄	C₂³	1	2	yes	—
224	C₇×#117	C₂³	1	2	yes	—
225	C₇×#117	C₂³	1	2	yes	—
226	C₇×#117	C₂³	1	2	yes	—
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	2	yes	—
229	C₇×C₄⋊C₈	C₂³	1	2	yes	—
230	C₇×C₄⋊C₈	C₂³	1	2	yes	—
231	C₇×C₄⋊C₈	C₂³	1	2	yes	—
232	C₇×C₄⋊C₈	C₂³	1	2	yes	—
233	C₇×C₄⋊C₈	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	1	yes	characteristic
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
239	C₇×C₄⋊C₈	C₂³	1	2	yes	—
240	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
241	C₇×C₄⋊C₈	C₂³	1	2	yes	—
242	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
243	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₇×C₂²⋊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×#97	C₂³	1	2	yes	—
262	C₇×#97	C₂³	1	2	yes	—
263	C₇×#97	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	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
268	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
269	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
270	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
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	#3529	C₂×C₇	1	1	yes	characteristic
276	#2995	C₂×C₇	1	1	yes	characteristic, complemented
277	#2995	C₂×C₇	1	1	yes	characteristic, complemented
278	#2994	C₂×C₇	1	2	yes	complemented
279	#2992	C₂×C₇	1	2	yes	complemented
280	#2981	C₂×C₇	1	2	yes	complemented
281	#2980	C₂×C₇	1	1	yes	characteristic, complemented
282	#2977	C₂×C₇	1	2	yes	complemented
283	#2976	C₂×C₇	1	2	yes	complemented
284	#2976	C₂×C₇	1	2	yes	complemented
285	#2969	C₂×C₇	1	2	yes	complemented
286	#2967	C₂×C₇	1	2	yes	complemented
287	#2966	C₂×C₇	1	1	yes	characteristic, complemented
288	#2966	C₂×C₇	1	1	yes	characteristic, complemented
289	#2935	C₂×C₇	1	2	yes	complemented
290	#2933	C₂×C₇	1	2	yes	complemented
291	#2933	C₂×C₇	1	2	yes	complemented
292	#2931	C₂×C₇	1	1	yes	characteristic, complemented
293	#2930	C₂×C₇	1	2	yes	complemented
294	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
295	C₇×#41	—	4	2	no	—
296	C₇×#41	—	4	1	no	—
297	C₇×#41	—	4	1	no	—
298	C₇×#41	—	4	1	no	—
299	C₇×#41	—	4	2	no	—
300	C₇×#41	—	4	1	no	—
301	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
302	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
306	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
307	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
308	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
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	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
321	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
322	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
323	C₂²×C₄×C₇	—	4	2	no	—
324	C₂²×C₄×C₇	—	4	2	no	—
325	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	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	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₇×M₁₆	—	2	4	no	—
338	C₇×M₁₆	—	2	4	no	—
339	C₇×M₁₆	—	2	4	no	—
340	C₇×M₁₆	—	4	2	no	—
341	C₇×M₁₆	—	4	2	no	—
342	C₇×M₁₆	—	4	2	no	—
343	C₇×M₁₆	—	4	2	no	—
344	C₇×M₁₆	—	4	2	no	—
345	C₇×M₁₆	—	4	1	no	—
346	C₇×M₁₆	—	4	1	no	—
347	C₂×C₇×C₈	—	2	4	no	—
348	C₂×C₇×C₈	—	2	2	no	—
349	C₂×C₇×C₈	—	4	2	no	—
350	C₂×C₇×C₈	—	4	1	no	—
351	C₂×C₇×C₈	—	4	2	no	—
352	C₂×C₇×C₈	—	4	2	no	—
353	C₂×C₇×C₈	—	4	2	no	—
354	C₂×C₇×C₈	—	4	2	no	—
355	C₂×C₇×C₈	—	4	2	no	—
356	C₂×C₇×C₈	—	4	2	no	—
357	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×C₈	C₂⁴	1	2	yes	—
360	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₇×C₈	C₂⁴	1	2	yes	—
362	C₂×C₇×C₈	C₂⁴	1	2	yes	—
363	C₂×C₇×C₈	C₂⁴	1	2	yes	—
364	C₂×C₇×C₈	C₂⁴	1	2	yes	—
365	C₂×C₇×C₈	C₂⁴	1	2	yes	—
366	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
367	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
368	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
369	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
370	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
371	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
372	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
373	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
374	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
380	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
382	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
385	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
387	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
388	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
389	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
390	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
391	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
392	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
393	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
394	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
396	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₂²⋊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	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
412	C₄²×C₇	C₂²×C₄	1	2	yes	—
413	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
414	C₄²×C₇	C₂²×C₄	1	2	yes	—
415	C₄²×C₇	C₂⁴	1	1	yes	characteristic
416	C₄²×C₇	C₂⁴	1	1	yes	characteristic
417	C₄²×C₇	C₂⁴	1	2	yes	—
418	C₄²×C₇	C₂⁴	1	2	yes	—
419	C₂×#131	C₂²×C₇	1	2	yes	—
420	C₂×#131	C₂²×C₇	1	1	yes	characteristic
421	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
422	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
423	#563	C₄×C₇	1	1	yes	characteristic
424	#563	C₄×C₇	1	2	yes	—
425	#562	C₄×C₇	1	1	yes	characteristic
426	#562	C₄×C₇	1	2	yes	—
427	#562	C₄×C₇	1	2	yes	—
428	#562	C₄×C₇	1	1	yes	characteristic
429	H(3,𝔽₄)	C₄×C₇	1	1	yes	characteristic
430	#560	C₄×C₇	1	2	yes	—
431	#560	C₄×C₇	1	2	yes	—
432	#560	C₄×C₇	1	2	yes	—
433	#532	C₂²×C₇	1	1	yes	characteristic
434	#532	C₂²×C₇	1	2	yes	—
435	#529	C₂²×C₇	1	1	yes	characteristic
436	#529	C₂²×C₇	1	1	yes	characteristic
437	#529	C₂²×C₇	1	2	yes	—
438	#529	C₂²×C₇	1	2	yes	—
439	#525	C₂²×C₇	1	2	yes	—
440	#525	C₂²×C₇	1	2	yes	—
441	#525	C₂²×C₇	1	2	yes	—
442	#446	C₂²×C₇	1	1	yes	characteristic, complemented
443	#446	C₂²×C₇	1	1	yes	characteristic, complemented
444	#446	C₂²×C₇	1	2	yes	complemented
445	#446	C₂²×C₇	1	2	yes	complemented
446	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
447	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
448	#436	C₂²×C₇	1	1	yes	characteristic
449	#436	C₂²×C₇	1	2	yes	—
450	#436	C₂²×C₇	1	2	yes	—
451	#436	C₂²×C₇	1	1	yes	characteristic
452	#436	C₂²×C₇	1	2	yes	complemented
453	#436	C₂²×C₇	1	2	yes	complemented
454	#436	C₂²×C₇	1	2	yes	complemented
455	#436	C₂²×C₇	1	2	yes	complemented
456	#436	C₂²×C₇	1	2	yes	complemented
457	#436	C₂²×C₇	1	2	yes	complemented
458	#435	C₂²×C₇	1	2	yes	—
459	#435	C₂²×C₇	1	2	yes	—
460	#435	C₂²×C₇	1	2	yes	—
461	#435	C₂²×C₇	1	2	yes	—
462	#435	C₂²×C₇	1	2	yes	—
463	#435	C₂²×C₇	1	2	yes	—
464	#435	C₂²×C₇	1	2	yes	complemented
465	#435	C₂²×C₇	1	2	yes	complemented
466	#435	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	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
477	C₈×D₄	C₂²×C₇	1	2	yes	—
478	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
479	C₈×D₄	C₂²×C₇	1	2	yes	—
480	C₈×D₄	C₂²×C₇	1	2	yes	complemented
481	C₈×D₄	C₂²×C₇	1	2	yes	complemented
482	C₈×D₄	C₂²×C₇	1	2	yes	complemented
483	C₈×D₄	C₂²×C₇	1	2	yes	complemented
484	C₈×D₄	C₂²×C₇	1	2	yes	complemented
485	C₈×D₄	C₂²×C₇	1	2	yes	complemented
486	#433	C₂²×C₇	1	2	yes	complemented
487	#433	C₂²×C₇	1	2	yes	complemented
488	#433	C₂²×C₇	1	2	yes	complemented
489	#433	C₂²×C₇	1	2	yes	complemented
490	#433	C₂²×C₇	1	2	yes	complemented
491	#433	C₂²×C₇	1	2	yes	complemented
492	#432	C₂²×C₇	1	1	yes	characteristic, complemented
493	#432	C₂²×C₇	1	1	yes	characteristic, complemented
494	#432	C₂²×C₇	1	2	yes	complemented
495	#431	C₂²×C₇	1	2	yes	complemented
496	#424	C₂²×C₇	1	2	yes	complemented
497	#424	C₂²×C₇	1	2	yes	complemented
498	#424	C₂²×C₇	1	2	yes	complemented
499	#423	C₂²×C₇	1	1	yes	characteristic, complemented
500	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
501	#408	C₂²×C₇	1	2	yes	—
502	#408	C₂²×C₇	1	1	yes	characteristic
503	#408	C₂²×C₇	1	2	yes	—
504	#408	C₂²×C₇	1	2	yes	—
505	#408	C₂²×C₇	1	2	yes	—
506	#408	C₂²×C₇	1	1	yes	characteristic, complemented
507	#408	C₂²×C₇	1	2	yes	complemented
508	#407	C₂²×C₇	1	2	yes	complemented
509	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
510	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
511	#405	C₂²×C₇	1	2	yes	complemented
512	#405	C₂²×C₇	1	2	yes	complemented
513	#405	C₂²×C₇	1	2	yes	complemented
514	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
515	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₂³×C₇	—	4	2	no	—
517	C₂³×C₇	—	4	2	no	—
518	C₂³×C₇	—	4	2	no	—
519	C₂³×C₇	C₂³×C₄	1	2	yes	—
520	C₂³×C₇	C₂³×C₄	1	2	yes	—
521	C₂³×C₇	C₂³×C₄	1	2	yes	—
522	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
523	C₂³×C₇	C₂³×C₄	1	2	yes	—
524	C₇×Q₈	—	4	1	no	—
525	C₇×Q₈	—	4	1	no	—
526	C₇×Q₈	—	4	2	no	—
527	C₇×Q₈	—	4	1	no	—
528	C₇×Q₈	—	4	1	no	—
529	C₇×D₄	—	4	2	no	—
530	C₇×D₄	—	4	2	no	—
531	C₇×D₄	—	4	2	no	—
532	C₇×D₄	—	4	2	no	—
533	C₇×D₄	—	4	2	no	—
534	C₇×D₄	—	4	2	no	—
535	C₇×D₄	—	4	1	no	—
536	C₇×D₄	—	4	2	no	—
537	C₇×D₄	—	4	1	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	1	no	—
543	C₇×D₄	—	4	2	no	—
544	C₇×D₄	—	4	1	no	—
545	C₇×D₄	—	4	2	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	4	2	no	—
557	C₂×C₄×C₇	—	4	2	no	—
558	C₂×C₄×C₇	—	4	2	no	—
559	C₂×C₄×C₇	—	4	1	no	—
560	C₂×C₄×C₇	—	4	1	no	—
561	C₂×C₄×C₇	—	4	2	no	—
562	C₂×C₄×C₇	—	4	2	no	—
563	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
564	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
565	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
566	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
567	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
568	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
569	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
570	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
571	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
572	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
577	C₇×C₈	—	2	1	no	—
578	C₇×C₈	—	2	2	no	—
579	C₇×C₈	—	2	2	no	—
580	C₇×C₈	—	2	2	no	—
581	C₇×C₈	—	2	2	no	—
582	C₇×C₈	—	2	1	no	—
583	C₇×C₈	—	2	2	no	—
584	C₇×C₈	—	2	1	no	—
585	C₇×C₈	—	2	2	no	—
586	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
587	C₂×#41	C₂³×C₇	1	2	yes	—
588	C₂×#41	C₂³×C₇	1	1	yes	characteristic
589	C₂×#41	C₂³×C₇	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₇	1	2	yes	—
591	#131	—	4	4	no	—
592	#131	—	4	2	no	—
593	#131	—	4	2	no	—
594	C₂×M₁₆	—	4	4	no	—
595	C₂×M₁₆	C₂³×C₇	1	2	yes	—
596	C₂×M₁₆	C₂³×C₇	1	2	yes	—
597	C₂×M₁₆	C₂³×C₇	1	2	yes	—
598	C₂×M₁₆	C₂³×C₇	1	2	yes	—
599	C₂×M₁₆	C₂³×C₇	1	2	yes	—
600	C₂×M₁₆	C₂³×C₇	1	2	yes	—
601	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
602	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₇	1	2	yes	—
604	C₂×M₁₆	C₂³×C₇	1	2	yes	—
605	C₂²×C₈	C₂³×C₇	1	2	yes	—
606	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
607	C₂²×C₈	C₂³×C₇	1	2	yes	—
608	C₂²×C₈	C₂³×C₇	1	2	yes	—
609	C₂²×C₈	C₂³×C₇	1	2	yes	—
610	C₂²×C₈	C₂³×C₇	1	2	yes	—
611	C₂²×C₈	C₂³×C₇	1	2	yes	—
612	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
613	C₂²×C₈	C₂³×C₇	1	2	yes	—
614	C₂²×C₈	C₂³×C₇	1	2	yes	—
615	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
616	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
617	#127	C₂×C₄×C₇	1	1	yes	characteristic
618	#127	C₂×C₄×C₇	1	2	yes	—
619	#126	C₂×C₄×C₇	1	2	yes	—
620	#126	C₂×C₄×C₇	1	2	yes	—
621	#126	C₂×C₄×C₇	1	2	yes	—
622	#126	C₂×C₄×C₇	1	2	yes	—
623	#126	C₂×C₄×C₇	1	2	yes	—
624	#126	C₂×C₄×C₇	1	2	yes	—
625	#125	C₂×C₄×C₇	1	1	yes	characteristic
626	#125	C₂×C₄×C₇	1	1	yes	characteristic
627	#125	C₂×C₄×C₇	1	2	yes	—
628	#125	C₂×C₄×C₇	1	2	yes	—
629	#124	C₂×C₄×C₇	1	1	yes	characteristic
630	#124	C₂×C₄×C₇	1	1	yes	characteristic
631	#124	C₂×C₄×C₇	1	2	yes	—
632	#124	C₂×C₄×C₇	1	2	yes	—
633	#124	C₂×C₄×C₇	1	1	yes	characteristic
634	#124	C₂×C₄×C₇	1	2	yes	—
635	#124	C₂×C₄×C₇	1	1	yes	characteristic
636	#124	C₂×C₄×C₇	1	2	yes	—
637	#123	C₂×C₄×C₇	1	2	yes	—
638	#123	C₂×C₄×C₇	1	2	yes	—
639	#123	C₂×C₄×C₇	1	2	yes	—
640	#123	C₂×C₄×C₇	1	2	yes	—
641	#123	C₂×C₄×C₇	1	2	yes	—
642	#123	C₂×C₄×C₇	1	2	yes	—
643	#123	C₂×C₄×C₇	1	2	yes	—
644	#123	C₂×C₄×C₇	1	2	yes	—
645	#123	C₂×C₄×C₇	1	2	yes	—
646	#123	C₂×C₄×C₇	1	2	yes	—
647	#123	C₂×C₄×C₇	1	2	yes	—
648	#123	C₂×C₄×C₇	1	2	yes	—
649	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
650	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
651	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
652	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
653	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
654	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
655	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
656	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
657	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
658	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
659	#121	C₂×C₄×C₇	1	2	yes	—
660	#121	C₂×C₄×C₇	1	2	yes	—
661	#121	C₂×C₄×C₇	1	2	yes	—
662	#121	C₂×C₄×C₇	1	2	yes	—
663	#121	C₂×C₄×C₇	1	2	yes	—
664	#121	C₂×C₄×C₇	1	2	yes	—
665	#121	C₂×C₄×C₇	1	1	yes	characteristic
666	#121	C₂×C₄×C₇	1	1	yes	characteristic
667	#121	C₂×C₄×C₇	1	2	yes	—
668	#121	C₂×C₄×C₇	1	2	yes	—
669	#121	C₂×C₄×C₇	1	2	yes	—
670	#121	C₂×C₄×C₇	1	2	yes	—
671	#121	C₂×C₄×C₇	1	2	yes	—
672	#121	C₂×C₄×C₇	1	2	yes	—
673	#121	C₂×C₄×C₇	1	2	yes	—
674	#121	C₂×C₄×C₇	1	2	yes	—
675	#120	C₂×C₄×C₇	1	2	yes	—
676	#120	C₂×C₄×C₇	1	2	yes	—
677	#120	C₂×C₄×C₇	1	2	yes	—
678	#120	C₂×C₄×C₇	1	2	yes	—
679	#120	C₂×C₄×C₇	1	2	yes	—
680	#120	C₂×C₄×C₇	1	2	yes	—
681	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
682	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
683	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
684	C₄×D₄	C₂³×C₇	1	2	yes	—
685	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₇	1	2	yes	—
687	C₄×D₄	C₂³×C₇	1	2	yes	—
688	C₄×D₄	C₂³×C₇	1	2	yes	—
689	C₄×D₄	C₂³×C₇	1	2	yes	—
690	C₄×D₄	C₂³×C₇	1	2	yes	—
691	C₄×D₄	C₂³×C₇	1	2	yes	—
692	C₄×D₄	C₂³×C₇	1	2	yes	—
693	#117	C₂³×C₇	1	2	yes	—
694	#117	C₂³×C₇	1	2	yes	—
695	#117	C₂³×C₇	1	2	yes	—
696	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₇	1	2	yes	—
698	C₄⋊C₈	C₂³×C₇	1	2	yes	—
699	C₄⋊C₈	C₂³×C₇	1	2	yes	—
700	C₄⋊C₈	C₂³×C₇	1	2	yes	—
701	C₄⋊C₈	C₂³×C₇	1	2	yes	—
702	C₄⋊C₈	C₂³×C₇	1	2	yes	—
703	C₄⋊C₈	C₂³×C₇	1	2	yes	—
704	C₄⋊C₈	C₂³×C₇	1	2	yes	—
705	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
706	C₄⋊C₈	C₂³×C₇	1	2	yes	—
707	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
708	C₄⋊C₈	C₂³×C₇	1	2	yes	—
709	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
710	C₄⋊C₈	C₂³×C₇	1	2	yes	—
711	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
712	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
717	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
723	C₂²⋊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	#97	C₂³×C₇	1	2	yes	—
731	#97	C₂³×C₇	1	2	yes	—
732	#97	C₂³×C₇	1	2	yes	—
733	#97	C₂³×C₇	1	2	yes	—
734	#97	C₂³×C₇	1	2	yes	—
735	#97	C₂³×C₇	1	2	yes	—
736	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
737	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
738	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
739	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₇	1	2	yes	—
741	C₄×C₈	C₂³×C₇	1	2	yes	—
742	C₄×C₈	C₂³×C₇	1	2	yes	—
743	C₄×C₈	C₂³×C₇	1	2	yes	—
744	C₂²×C₇	—	2	2	no	—
745	C₂²×C₇	—	2	2	no	—
746	C₂²×C₇	—	2	2	no	—
747	C₂²×C₇	—	2	1	no	—
748	C₂²×C₇	—	2	2	no	—
749	C₂²×C₇	—	2	1	no	—
750	C₂²×C₇	—	2	1	no	—
751	C₂²×C₇	—	2	2	no	—
752	C₂²×C₇	—	2	2	no	—
753	C₂²×C₇	—	2	2	no	—
754	C₂²×C₇	—	2	2	no	—
755	C₂²×C₇	—	2	2	no	—
756	C₂²×C₇	—	2	2	no	—
757	C₂²×C₇	—	2	2	no	—
758	C₂²×C₇	—	2	2	no	—
759	C₂²×C₇	—	8	4	no	—
760	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
761	C₄×C₇	—	2	2	no	—
762	C₄×C₇	—	2	2	no	—
763	C₄×C₇	—	2	2	no	—
764	C₄×C₇	—	2	1	no	—
765	C₄×C₇	—	2	2	no	—
766	C₄×C₇	—	2	1	no	—
767	C₄×C₇	—	2	1	no	—
768	C₄×C₇	—	2	2	no	—
769	C₄×C₇	—	2	2	no	—
770	C₄×C₇	—	2	1	no	—
771	C₄×C₇	—	2	1	no	—
772	C₄×C₇	—	2	2	no	—
773	C₄×C₇	—	2	2	no	—
774	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
775	C₄×C₇	#585	1	1	yes	characteristic
776	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
777	#41	—	4	2	no	—
778	#41	—	4	1	no	—
779	#41	—	4	1	no	—
780	#41	—	4	1	no	—
781	#41	—	4	2	no	—
782	#41	—	4	1	no	—
783	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
784	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
785	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
786	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
787	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
788	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
789	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
790	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
791	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
792	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
793	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
794	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
795	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
796	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
797	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
798	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
799	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	1	yes	characteristic
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
808	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
809	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
810	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
811	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
812	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
813	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
819	M₁₆	—	2	4	no	—
820	M₁₆	—	2	4	no	—
821	M₁₆	—	2	4	no	—
822	M₁₆	—	4	2	no	—
823	M₁₆	—	4	2	no	—
824	M₁₆	—	4	2	no	—
825	M₁₆	—	4	2	no	—
826	M₁₆	—	4	2	no	—
827	M₁₆	—	4	1	no	—
828	M₁₆	—	4	1	no	—
829	C₂×C₈	—	2	4	no	—
830	C₂×C₈	—	2	2	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	—	4	1	no	—
833	C₂×C₈	—	4	2	no	—
834	C₂×C₈	—	4	2	no	—
835	C₂×C₈	—	4	2	no	—
836	C₂×C₈	—	4	2	no	—
837	C₂×C₈	—	4	2	no	—
838	C₂×C₈	—	4	2	no	—
839	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
840	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
841	C₂×C₈	C₂⁴×C₇	1	2	yes	—
842	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
843	C₂×C₈	C₂⁴×C₇	1	2	yes	—
844	C₂×C₈	C₂⁴×C₇	1	2	yes	—
845	C₂×C₈	C₂⁴×C₇	1	2	yes	—
846	C₂×C₈	C₂⁴×C₇	1	2	yes	—
847	C₂×C₈	C₂⁴×C₇	1	2	yes	—
848	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
849	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
850	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
851	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
852	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
853	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
854	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
855	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
856	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
857	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
858	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
859	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
860	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
861	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
862	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
863	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
864	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
865	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
866	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
867	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
868	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
869	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
870	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
871	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
872	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
873	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
874	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
875	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
876	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
877	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
883	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
891	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
893	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
894	C₄²	C₂²×C₄×C₇	1	2	yes	—
895	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
896	C₄²	C₂²×C₄×C₇	1	2	yes	—
897	C₄²	C₂⁴×C₇	1	1	yes	characteristic
898	C₄²	C₂⁴×C₇	1	1	yes	characteristic
899	C₄²	C₂⁴×C₇	1	2	yes	—
900	C₄²	C₂⁴×C₇	1	2	yes	—
901	C₂×C₇	—	4	1	no	—
902	C₂×C₇	—	4	2	no	—
903	C₂×C₇	—	4	2	no	—
904	C₂×C₇	—	4	2	no	—
905	C₂×C₇	—	4	2	no	—
906	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂×C₇	#3573	1	1	yes	characteristic
908	C₂×C₇	#3573	1	1	yes	characteristic
909	C₂³	—	4	2	no	—
910	C₂³	—	4	2	no	—
911	C₂³	—	4	2	no	—
912	C₂³	C₂³×C₄×C₇	1	2	yes	—
913	C₂³	C₂³×C₄×C₇	1	2	yes	—
914	C₂³	C₂³×C₄×C₇	1	2	yes	—
915	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
916	C₂³	C₂³×C₄×C₇	1	2	yes	—
917	Q₈	—	4	1	no	—
918	Q₈	—	4	1	no	—
919	Q₈	—	4	2	no	—
920	Q₈	—	4	1	no	—
921	Q₈	—	4	1	no	—
922	D₄	—	4	2	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	2	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	2	no	—
933	D₄	—	4	2	no	—
934	D₄	—	4	2	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	1	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
957	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
958	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
959	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
960	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
961	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
962	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
963	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
964	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
965	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
966	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
968	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
969	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
970	C₈	—	2	1	no	—
971	C₈	—	2	2	no	—
972	C₈	—	2	2	no	—
973	C₈	—	2	2	no	—
974	C₈	—	2	2	no	—
975	C₈	—	2	1	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	1	no	—
978	C₈	—	2	2	no	—
979	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
980	C₇	#60327	1	1	yes	characteristic, direct product factor, Sylow
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	8	4	no	—
997	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₄	C₇×#585	1	1	yes	characteristic
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	4	2	no	—
1016	C₂	—	4	1	no	—
1017	C₂	—	4	2	no	—
1018	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1019	C₂	C₇×#3573	1	1	yes	characteristic
1020	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×#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×#2995	C₂	semidirect
3. C₇×#2995	C₂	semidirect
4. C₇×#2994	C₂	semidirect
5. C₇×#2992	C₂	semidirect
6. C₇×#2981	C₂	semidirect
7. C₇×#2980	C₂	semidirect
8. C₇×#2977	C₂	semidirect
9. C₇×#2976	C₂	semidirect
10. C₇×#2976	C₂	semidirect
11. C₇×#2969	C₂	semidirect
12. C₇×#2967	C₂	semidirect
13. C₇×#2966	C₂	semidirect
14. C₇×#2966	C₂	semidirect
15. C₇×#2935	C₂	semidirect
16. C₇×#2933	C₂	semidirect
17. C₇×#2933	C₂	semidirect
18. C₇×#2931	C₂	semidirect
19. C₇×#2930	C₂	semidirect
22. C₂×C₇×#131	C₂²	semidirect
23. C₂²×C₇×M₁₆	C₂²	semidirect
43. C₇×#446	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×C₈×Q₈	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
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
81. C₇×C₈×D₄	C₂²	semidirect
82. C₇×C₈×D₄	C₂²	semidirect
83. C₇×C₈×D₄	C₂²	semidirect
84. C₇×C₈×D₄	C₂²	semidirect
85. C₇×C₈×D₄	C₂²	semidirect
86. C₇×C₈×D₄	C₂²	semidirect
87. C₇×#433	C₂²	semidirect
88. C₇×#433	C₂²	semidirect
89. C₇×#433	C₂²	semidirect
90. C₇×#433	C₂²	semidirect
91. C₇×#433	C₂²	semidirect
92. C₇×#433	C₂²	semidirect
93. C₇×#432	C₂²	semidirect
94. C₇×#432	C₂²	semidirect
95. C₇×#432	C₂²	semidirect
96. C₇×#431	C₂²	semidirect
97. C₇×#424	C₂²	semidirect
98. C₇×#424	C₂²	semidirect
99. C₇×#424	C₂²	semidirect
100. C₇×#423	C₂²	semidirect
101. C₂×C₇×C₄⋊C₈	C₂²	semidirect
107. C₇×#408	C₂²	semidirect
108. C₇×#408	C₂²	semidirect
109. C₇×#407	C₂²	semidirect
110. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
111. C₂×C₇×C₂²⋊C₈	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×C₄×C₇×C₈	C₂²	semidirect
117. #60327	C₇	direct (N × H)
276. #2995	C₂×C₇	semidirect
277. #2995	C₂×C₇	semidirect
278. #2994	C₂×C₇	semidirect
279. #2992	C₂×C₇	semidirect
280. #2981	C₂×C₇	semidirect
281. #2980	C₂×C₇	semidirect
282. #2977	C₂×C₇	semidirect
283. #2976	C₂×C₇	semidirect
284. #2976	C₂×C₇	semidirect
285. #2969	C₂×C₇	semidirect
286. #2967	C₂×C₇	semidirect
287. #2966	C₂×C₇	semidirect
288. #2966	C₂×C₇	semidirect
289. #2935	C₂×C₇	semidirect
290. #2933	C₂×C₇	semidirect
291. #2933	C₂×C₇	semidirect
292. #2931	C₂×C₇	semidirect
293. #2930	C₂×C₇	semidirect
421. C₂×#131	C₂²×C₇	semidirect
422. C₂²×M₁₆	C₂²×C₇	semidirect
442. #446	C₂²×C₇	semidirect
443. #446	C₂²×C₇	semidirect
444. #446	C₂²×C₇	semidirect
445. #446	C₂²×C₇	semidirect
446. C₈×Q₈	C₂²×C₇	semidirect
447. C₈×Q₈	C₂²×C₇	semidirect
452. #436	C₂²×C₇	semidirect
453. #436	C₂²×C₇	semidirect
454. #436	C₂²×C₇	semidirect
455. #436	C₂²×C₇	semidirect
456. #436	C₂²×C₇	semidirect
457. #436	C₂²×C₇	semidirect
464. #435	C₂²×C₇	semidirect
465. #435	C₂²×C₇	semidirect
466. #435	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
480. C₈×D₄	C₂²×C₇	semidirect
481. C₈×D₄	C₂²×C₇	semidirect
482. C₈×D₄	C₂²×C₇	semidirect
483. C₈×D₄	C₂²×C₇	semidirect
484. C₈×D₄	C₂²×C₇	semidirect
485. C₈×D₄	C₂²×C₇	semidirect
486. #433	C₂²×C₇	semidirect
487. #433	C₂²×C₇	semidirect
488. #433	C₂²×C₇	semidirect
489. #433	C₂²×C₇	semidirect
490. #433	C₂²×C₇	semidirect
491. #433	C₂²×C₇	semidirect
492. #432	C₂²×C₇	semidirect
493. #432	C₂²×C₇	semidirect
494. #432	C₂²×C₇	semidirect
495. #431	C₂²×C₇	semidirect
496. #424	C₂²×C₇	semidirect
497. #424	C₂²×C₇	semidirect
498. #424	C₂²×C₇	semidirect
499. #423	C₂²×C₇	semidirect
500. C₂×C₄⋊C₈	C₂²×C₇	semidirect
506. #408	C₂²×C₇	semidirect
507. #408	C₂²×C₇	semidirect
508. #407	C₂²×C₇	semidirect
509. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
510. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
511. #405	C₂²×C₇	semidirect
512. #405	C₂²×C₇	semidirect
513. #405	C₂²×C₇	semidirect
514. C₄×M₁₆	C₂²×C₇	semidirect
515. C₂×C₄×C₈	C₂²×C₇	semidirect
980. C₇	#60327	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×#2995	2
C₇×#2994	2
C₇×#2992	2
C₇×#2981	2
C₇×#2980	2
C₇×#2977	2
C₇×#2976	2
C₇×#2969	2
C₇×#2967	2
C₇×#2966	2
C₇×#2935	2
C₇×#2933	2
C₇×#2931	2
C₇×#2930	2
#60327	7

Subgroups — C7×#60327 #13237543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60327 #13237543