Subgroups — C₇×#60268 #13237484

Order 1792.

1908 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₇×#2994	C₂	1	4	yes	maximal, complemented
3	C₇×#2993	C₂	1	4	yes	maximal, complemented
4	C₇×#2991	C₂	1	2	yes	maximal, complemented
5	C₇×#2990	C₂	1	2	yes	maximal, complemented
6	C₇×#2989	C₂	1	2	yes	maximal, complemented
7	C₇×#2988	C₂	1	2	yes	maximal, complemented
8	C₇×#2960	C₂	1	2	yes	maximal, complemented
9	C₇×#2933	C₂	1	4	yes	maximal, complemented
10	C₇×#2931	C₂	1	2	yes	maximal, complemented
11	C₇×#2925	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2906	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#131	C₂²	1	4	yes	—
16	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
17	C₇×#533	C₄	1	1	yes	characteristic
18	C₇×#533	C₄	1	1	yes	characteristic
19	C₇×#533	C₂²	1	1	yes	characteristic
20	C₇×#532	C₄	1	1	yes	characteristic
21	C₇×#532	C₄	1	1	yes	characteristic
22	C₇×#532	C₂²	1	1	yes	characteristic
23	C₇×#529	C₄	1	2	yes	—
24	C₇×#529	C₄	1	2	yes	—
25	C₇×#529	C₄	1	2	yes	—
26	C₇×#529	C₄	1	2	yes	—
27	C₇×#529	C₂²	1	2	yes	—
28	C₇×#529	C₂²	1	2	yes	—
29	C₇×#525	C₄	1	2	yes	—
30	C₇×#525	C₄	1	2	yes	—
31	C₇×#525	C₂²	1	2	yes	—
32	C₄×C₇×#41	C₂²	1	2	yes	—
33	C₄×C₇×#41	C₂²	1	2	yes	—
34	C₄×C₇×#41	C₂²	1	2	yes	—
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₇×#446	C₂²	1	4	yes	complemented
37	C₇×#446	C₂²	1	4	yes	complemented
38	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
39	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
40	C₇×#436	C₂²	1	8	yes	—
41	C₇×#436	C₂²	1	4	yes	complemented
42	C₇×#436	C₂²	1	4	yes	complemented
43	C₇×#435	C₂²	1	8	yes	—
44	C₇×#435	C₂²	1	8	yes	—
45	C₇×C₈×D₄	C₂²	1	8	yes	—
46	C₇×C₈×D₄	C₂²	1	4	yes	complemented
47	C₇×C₈×D₄	C₂²	1	4	yes	complemented
48	C₇×#433	C₂²	1	8	yes	complemented
49	C₇×#432	C₂²	1	4	yes	complemented
50	C₇×#431	C₂²	1	1	yes	characteristic
51	C₇×#431	C₂²	1	1	yes	characteristic
52	C₇×#431	C₂²	1	1	yes	characteristic
53	C₇×#431	C₂²	1	1	yes	characteristic
54	C₇×#431	C₂²	1	2	yes	—
55	C₇×#431	C₂²	1	2	yes	—
56	C₇×#431	C₂²	1	4	yes	complemented
57	C₇×#424	C₂²	1	4	yes	—
58	C₇×#424	C₂²	1	8	yes	complemented
59	C₇×#423	C₂²	1	2	yes	—
60	C₇×#423	C₂²	1	2	yes	—
61	C₇×#423	C₂²	1	2	yes	—
62	C₇×#423	C₂²	1	2	yes	—
63	C₇×#423	C₂²	1	4	yes	complemented
64	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
65	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
66	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	complemented
69	C₇×#408	C₂²	1	4	yes	—
70	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
71	C₇×#405	C₂²	1	4	yes	—
72	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
73	#60268	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂×C₇×#41	C₂×C₄	1	2	yes	—
75	C₂×C₇×#41	C₂×C₄	1	2	yes	—
76	C₂×C₇×#41	C₂³	1	2	yes	—
77	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₇×#131	—	4	8	no	—
81	C₂×C₇×M₁₆	—	4	4	no	—
82	C₂×C₇×M₁₆	C₂³	1	4	yes	—
83	C₂×C₇×M₁₆	C₂³	1	4	yes	—
84	C₂×C₇×M₁₆	C₂³	1	8	yes	—
85	C₂²×C₇×C₈	C₂³	1	2	yes	—
86	C₂²×C₇×C₈	C₂³	1	2	yes	—
87	C₂²×C₇×C₈	C₂³	1	4	yes	—
88	C₂²×C₇×C₈	C₂³	1	8	yes	—
89	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
90	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
91	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
92	C₇×#127	C₂×C₄	1	1	yes	characteristic
93	C₇×#126	C₂×C₄	1	4	yes	—
94	C₇×#126	C₂×C₄	1	4	yes	—
95	C₇×#125	C₂×C₄	1	2	yes	—
96	C₇×#125	C₂×C₄	1	2	yes	—
97	C₇×#125	C₂×C₄	1	2	yes	—
98	C₇×#124	C₂×C₄	1	2	yes	—
99	C₇×#124	C₂×C₄	1	2	yes	—
100	C₇×#124	C₂×C₄	1	2	yes	—
101	C₇×#123	C₂×C₄	1	4	yes	—
102	C₇×#123	C₂×C₄	1	4	yes	—
103	C₇×#123	C₂×C₄	1	4	yes	—
104	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
105	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
106	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
107	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
108	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
109	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
110	C₇×#121	C₂×C₄	1	2	yes	—
111	C₇×#121	C₂×C₄	1	2	yes	—
112	C₇×#121	C₂×C₄	1	2	yes	—
113	C₇×#121	C₂×C₄	1	2	yes	—
114	C₇×#121	C₂×C₄	1	2	yes	—
115	C₇×#121	C₂×C₄	1	2	yes	—
116	C₇×#120	C₂×C₄	1	4	yes	—
117	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
118	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
119	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
120	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
121	C₄×C₇×Q₈	C₂³	1	2	yes	—
122	C₄×C₇×Q₈	C₂³	1	2	yes	—
123	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
124	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
125	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
126	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
127	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
128	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
129	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
130	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
131	C₄×C₇×D₄	C₂³	1	4	yes	—
132	C₄×C₇×D₄	C₂³	1	4	yes	—
133	C₄×C₇×D₄	C₂³	1	2	yes	—
134	C₄×C₇×D₄	C₂³	1	2	yes	—
135	C₇×#117	C₂×C₄	1	2	yes	—
136	C₇×#117	C₂×C₄	1	2	yes	—
137	C₇×#117	C₂×C₄	1	4	yes	—
138	C₇×#117	C₂×C₄	1	4	yes	—
139	C₇×#117	C₂³	1	2	yes	—
140	C₇×#117	C₂³	1	4	yes	—
141	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
143	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
144	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
145	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
146	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
147	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₇	C₂³	1	4	yes	—
154	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₇×C₄⋊C₈	C₂³	1	4	yes	—
156	C₇×C₄⋊C₈	C₂³	1	4	yes	—
157	C₇×C₄⋊C₈	C₂³	1	4	yes	—
158	C₇×C₄⋊C₈	C₂³	1	4	yes	—
159	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊C₈	C₂³	1	2	yes	—
161	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊C₈	C₂³	1	2	yes	—
164	C₇×C₄⋊C₈	C₂³	1	8	yes	—
165	C₇×C₄⋊C₈	C₂³	1	8	yes	—
166	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
167	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
168	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
169	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
170	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
171	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
172	C₇×#97	C₂³	1	8	yes	—
173	C₄×C₇×C₈	C₂³	1	2	yes	—
174	C₄×C₇×C₈	C₂³	1	2	yes	—
175	C₄×C₇×C₈	C₂³	1	2	yes	—
176	C₄×C₇×C₈	C₂³	1	2	yes	—
177	C₄×C₇×C₈	C₂³	1	8	yes	—
178	#3444	C₂×C₇	1	1	yes	characteristic
179	#2994	C₂×C₇	1	4	yes	complemented
180	#2993	C₂×C₇	1	4	yes	complemented
181	#2991	C₂×C₇	1	2	yes	complemented
182	#2990	C₂×C₇	1	2	yes	complemented
183	#2989	C₂×C₇	1	2	yes	complemented
184	#2988	C₂×C₇	1	2	yes	complemented
185	#2960	C₂×C₇	1	2	yes	complemented
186	#2933	C₂×C₇	1	4	yes	complemented
187	#2931	C₂×C₇	1	2	yes	complemented
188	#2925	C₂×C₇	1	2	yes	complemented
189	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
190	#2906	C₂×C₇	1	2	yes	complemented
191	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
193	C₇×#41	—	2	8	no	—
194	C₇×#41	—	2	4	no	—
195	C₇×#41	—	2	4	no	—
196	C₇×#41	—	4	4	no	—
197	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
198	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
199	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
200	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
201	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
202	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
203	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
204	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
205	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₇	—	2	4	no	—
207	C₂²×C₄×C₇	—	2	2	no	—
208	C₂²×C₄×C₇	—	2	2	no	—
209	C₂²×C₄×C₇	—	4	2	no	—
210	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
222	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
226	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
231	C₇×M₁₆	—	2	8	no	—
232	C₇×M₁₆	—	4	4	no	—
233	C₇×M₁₆	—	4	8	no	—
234	C₂×C₇×C₈	—	2	4	no	—
235	C₂×C₇×C₈	—	2	4	no	—
236	C₂×C₇×C₈	—	4	4	no	—
237	C₂×C₇×C₈	—	4	8	no	—
238	C₂×C₇×C₈	C₂⁴	1	2	yes	—
239	C₂×C₇×C₈	C₂⁴	1	2	yes	—
240	C₂×C₇×C₈	C₂⁴	1	2	yes	—
241	C₂×C₇×C₈	C₂⁴	1	2	yes	—
242	C₂×C₇×C₈	C₂⁴	1	8	yes	—
243	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
244	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
245	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
246	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
247	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
248	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
249	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
250	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
251	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
252	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
253	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
254	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
255	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
256	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
257	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
258	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
259	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
260	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
261	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
262	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
263	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
264	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
265	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
266	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
267	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
268	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
269	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
270	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
271	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
272	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
273	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
274	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
275	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
276	C₄²×C₇	C₂²×C₄	1	4	yes	—
277	C₄²×C₇	C₂²×C₄	1	4	yes	—
278	C₄²×C₇	C₂⁴	1	1	yes	characteristic
279	C₄²×C₇	C₂⁴	1	1	yes	characteristic
280	C₄²×C₇	C₂⁴	1	4	yes	—
281	C₄²×C₇	C₂⁴	1	1	yes	characteristic
282	C₄²×C₇	C₂⁴	1	1	yes	characteristic
283	C₂×#131	C₂²×C₇	1	4	yes	—
284	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
285	#533	C₄×C₇	1	1	yes	characteristic
286	#533	C₄×C₇	1	1	yes	characteristic
287	#533	C₂²×C₇	1	1	yes	characteristic
288	#532	C₄×C₇	1	1	yes	characteristic
289	#532	C₄×C₇	1	1	yes	characteristic
290	#532	C₂²×C₇	1	1	yes	characteristic
291	#529	C₄×C₇	1	2	yes	—
292	#529	C₄×C₇	1	2	yes	—
293	#529	C₄×C₇	1	2	yes	—
294	#529	C₄×C₇	1	2	yes	—
295	#529	C₂²×C₇	1	2	yes	—
296	#529	C₂²×C₇	1	2	yes	—
297	#525	C₄×C₇	1	2	yes	—
298	#525	C₄×C₇	1	2	yes	—
299	#525	C₂²×C₇	1	2	yes	—
300	C₄×#41	C₂²×C₇	1	2	yes	—
301	C₄×#41	C₂²×C₇	1	2	yes	—
302	C₄×#41	C₂²×C₇	1	2	yes	—
303	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
304	#446	C₂²×C₇	1	4	yes	complemented
305	#446	C₂²×C₇	1	4	yes	complemented
306	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
307	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
308	#436	C₂²×C₇	1	8	yes	—
309	#436	C₂²×C₇	1	4	yes	complemented
310	#436	C₂²×C₇	1	4	yes	complemented
311	#435	C₂²×C₇	1	8	yes	—
312	#435	C₂²×C₇	1	8	yes	—
313	C₈×D₄	C₂²×C₇	1	8	yes	—
314	C₈×D₄	C₂²×C₇	1	4	yes	complemented
315	C₈×D₄	C₂²×C₇	1	4	yes	complemented
316	#433	C₂²×C₇	1	8	yes	complemented
317	#432	C₂²×C₇	1	4	yes	complemented
318	#431	C₂²×C₇	1	1	yes	characteristic
319	#431	C₂²×C₇	1	1	yes	characteristic
320	#431	C₂²×C₇	1	1	yes	characteristic
321	#431	C₂²×C₇	1	1	yes	characteristic
322	#431	C₂²×C₇	1	2	yes	—
323	#431	C₂²×C₇	1	2	yes	—
324	#431	C₂²×C₇	1	4	yes	complemented
325	#424	C₂²×C₇	1	4	yes	—
326	#424	C₂²×C₇	1	8	yes	complemented
327	#423	C₂²×C₇	1	2	yes	—
328	#423	C₂²×C₇	1	2	yes	—
329	#423	C₂²×C₇	1	2	yes	—
330	#423	C₂²×C₇	1	2	yes	—
331	#423	C₂²×C₇	1	4	yes	complemented
332	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
333	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
334	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
335	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	complemented
337	#408	C₂²×C₇	1	4	yes	—
338	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
339	#405	C₂²×C₇	1	4	yes	—
340	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
341	C₂³×C₇	—	2	2	no	—
342	C₂³×C₇	—	2	2	no	—
343	C₂³×C₇	—	4	1	no	—
344	C₂³×C₇	C₂³×C₄	1	4	yes	—
345	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
346	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
347	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
348	C₇×Q₈	—	2	4	no	—
349	C₇×Q₈	—	2	4	no	—
350	C₇×Q₈	—	2	4	no	—
351	C₇×D₄	—	2	8	no	—
352	C₇×D₄	—	2	8	no	—
353	C₇×D₄	—	2	4	no	—
354	C₇×D₄	—	2	4	no	—
355	C₇×D₄	—	2	4	no	—
356	C₇×D₄	—	4	4	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	2	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	2	no	—
364	C₂×C₄×C₇	—	2	2	no	—
365	C₂×C₄×C₇	—	2	8	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	2	4	no	—
371	C₂×C₄×C₇	—	2	1	no	—
372	C₂×C₄×C₇	—	2	1	no	—
373	C₂×C₄×C₇	—	2	1	no	—
374	C₂×C₄×C₇	—	2	4	no	—
375	C₂×C₄×C₇	—	4	1	no	—
376	C₂×C₄×C₇	—	4	1	no	—
377	C₂×C₄×C₇	—	4	1	no	—
378	C₂×C₄×C₇	—	4	4	no	—
379	C₂×C₄×C₇	#131	1	4	yes	complemented
380	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
381	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
382	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
383	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
384	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
385	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
386	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
387	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
388	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
389	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
390	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
391	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
392	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
393	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
394	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
396	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
397	C₇×C₈	—	2	2	no	—
398	C₇×C₈	—	2	2	no	—
399	C₇×C₈	—	2	8	no	—
400	C₇×C₈	—	2	2	no	—
401	C₇×C₈	—	2	2	no	—
402	C₂×#41	C₂×C₄×C₇	1	2	yes	—
403	C₂×#41	C₂×C₄×C₇	1	2	yes	—
404	C₂×#41	C₂³×C₇	1	2	yes	—
405	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
406	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
408	#131	—	4	8	no	—
409	C₂×M₁₆	—	4	4	no	—
410	C₂×M₁₆	C₂³×C₇	1	4	yes	—
411	C₂×M₁₆	C₂³×C₇	1	4	yes	—
412	C₂×M₁₆	C₂³×C₇	1	8	yes	—
413	C₂²×C₈	C₂³×C₇	1	2	yes	—
414	C₂²×C₈	C₂³×C₇	1	2	yes	—
415	C₂²×C₈	C₂³×C₇	1	4	yes	—
416	C₂²×C₈	C₂³×C₇	1	8	yes	—
417	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
418	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
419	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
420	#127	C₂×C₄×C₇	1	1	yes	characteristic
421	#126	C₂×C₄×C₇	1	4	yes	—
422	#126	C₂×C₄×C₇	1	4	yes	—
423	#125	C₂×C₄×C₇	1	2	yes	—
424	#125	C₂×C₄×C₇	1	2	yes	—
425	#125	C₂×C₄×C₇	1	2	yes	—
426	#124	C₂×C₄×C₇	1	2	yes	—
427	#124	C₂×C₄×C₇	1	2	yes	—
428	#124	C₂×C₄×C₇	1	2	yes	—
429	#123	C₂×C₄×C₇	1	4	yes	—
430	#123	C₂×C₄×C₇	1	4	yes	—
431	#123	C₂×C₄×C₇	1	4	yes	—
432	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
433	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
434	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
435	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
436	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
437	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
438	#121	C₂×C₄×C₇	1	2	yes	—
439	#121	C₂×C₄×C₇	1	2	yes	—
440	#121	C₂×C₄×C₇	1	2	yes	—
441	#121	C₂×C₄×C₇	1	2	yes	—
442	#121	C₂×C₄×C₇	1	2	yes	—
443	#121	C₂×C₄×C₇	1	2	yes	—
444	#120	C₂×C₄×C₇	1	4	yes	—
445	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
446	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
447	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
448	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
449	C₄×Q₈	C₂³×C₇	1	2	yes	—
450	C₄×Q₈	C₂³×C₇	1	2	yes	—
451	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
452	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
453	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
454	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
455	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
456	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
457	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
458	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
459	C₄×D₄	C₂³×C₇	1	4	yes	—
460	C₄×D₄	C₂³×C₇	1	4	yes	—
461	C₄×D₄	C₂³×C₇	1	2	yes	—
462	C₄×D₄	C₂³×C₇	1	2	yes	—
463	#117	C₂×C₄×C₇	1	2	yes	—
464	#117	C₂×C₄×C₇	1	2	yes	—
465	#117	C₂×C₄×C₇	1	4	yes	—
466	#117	C₂×C₄×C₇	1	4	yes	—
467	#117	C₂³×C₇	1	2	yes	—
468	#117	C₂³×C₇	1	4	yes	—
469	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
470	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
471	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
472	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
473	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
474	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₇	1	4	yes	—
476	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
482	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
483	C₄⋊C₈	C₂³×C₇	1	4	yes	—
484	C₄⋊C₈	C₂³×C₇	1	4	yes	—
485	C₄⋊C₈	C₂³×C₇	1	4	yes	—
486	C₄⋊C₈	C₂³×C₇	1	4	yes	—
487	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
488	C₄⋊C₈	C₂³×C₇	1	2	yes	—
489	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
490	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
491	C₄⋊C₈	C₂³×C₇	1	2	yes	—
492	C₄⋊C₈	C₂³×C₇	1	8	yes	—
493	C₄⋊C₈	C₂³×C₇	1	8	yes	—
494	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
495	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
496	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
497	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
498	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
499	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
500	#97	C₂³×C₇	1	8	yes	—
501	C₄×C₈	C₂³×C₇	1	2	yes	—
502	C₄×C₈	C₂³×C₇	1	2	yes	—
503	C₄×C₈	C₂³×C₇	1	2	yes	—
504	C₄×C₈	C₂³×C₇	1	2	yes	—
505	C₄×C₈	C₂³×C₇	1	8	yes	—
506	C₂²×C₇	—	2	1	no	—
507	C₂²×C₇	—	2	1	no	—
508	C₂²×C₇	—	2	1	no	—
509	C₂²×C₇	—	2	1	no	—
510	C₂²×C₇	—	2	1	no	—
511	C₂²×C₇	—	2	4	no	—
512	C₂²×C₇	—	2	1	no	—
513	C₂²×C₇	—	2	4	no	—
514	C₂²×C₇	—	2	1	no	—
515	C₂²×C₇	—	2	4	no	—
516	C₂²×C₇	—	4	4	no	—
517	C₂²×C₇	#520	1	2	yes	—
518	C₂²×C₇	C₂×#131	1	2	yes	—
519	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
520	C₄×C₇	—	2	1	no	—
521	C₄×C₇	—	2	1	no	—
522	C₄×C₇	—	2	4	no	—
523	C₄×C₇	—	2	1	no	—
524	C₄×C₇	—	2	1	no	—
525	C₄×C₇	—	2	4	no	—
526	C₄×C₇	—	2	1	no	—
527	C₄×C₇	—	2	1	no	—
528	C₄×C₇	—	2	1	no	—
529	C₄×C₇	—	2	4	no	—
530	C₄×C₇	#520	1	2	yes	—
531	C₄×C₇	C₂×#131	1	2	yes	—
532	C₄×C₇	C₂×#131	1	2	yes	—
533	C₄×C₇	#568	1	2	yes	—
534	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
535	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
537	#41	—	2	8	no	—
538	#41	—	2	4	no	—
539	#41	—	2	4	no	—
540	#41	—	4	4	no	—
541	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
542	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
543	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
544	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
545	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
546	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
547	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
548	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
549	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
557	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
558	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
559	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
562	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
563	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
564	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
565	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
566	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
567	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
569	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
570	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
575	M₁₆	—	2	8	no	—
576	M₁₆	—	4	4	no	—
577	M₁₆	—	4	8	no	—
578	C₂×C₈	—	2	4	no	—
579	C₂×C₈	—	2	4	no	—
580	C₂×C₈	—	4	4	no	—
581	C₂×C₈	—	4	8	no	—
582	C₂×C₈	C₂⁴×C₇	1	2	yes	—
583	C₂×C₈	C₂⁴×C₇	1	2	yes	—
584	C₂×C₈	C₂⁴×C₇	1	2	yes	—
585	C₂×C₈	C₂⁴×C₇	1	2	yes	—
586	C₂×C₈	C₂⁴×C₇	1	8	yes	—
587	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
588	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
589	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
590	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
591	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
592	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
593	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
594	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
595	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
596	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
597	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
598	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
599	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
600	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
601	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
602	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
603	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
604	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
605	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
606	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
607	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
608	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
609	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
610	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
611	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
612	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
613	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
614	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
615	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
616	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
617	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
618	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
619	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
620	C₄²	C₂²×C₄×C₇	1	4	yes	—
621	C₄²	C₂²×C₄×C₇	1	4	yes	—
622	C₄²	C₂⁴×C₇	1	1	yes	characteristic
623	C₄²	C₂⁴×C₇	1	1	yes	characteristic
624	C₄²	C₂⁴×C₇	1	4	yes	—
625	C₄²	C₂⁴×C₇	1	1	yes	characteristic
626	C₄²	C₂⁴×C₇	1	1	yes	characteristic
627	C₂×C₇	—	2	2	no	—
628	C₂×C₇	—	2	2	no	—
629	C₂×C₇	—	4	4	no	—
630	C₂×C₇	—	4	1	no	—
631	C₂×C₇	C₂×#520	1	1	yes	characteristic
632	C₂×C₇	C₂²×#131	1	1	yes	characteristic
633	C₂×C₇	C₂×#568	1	1	yes	characteristic
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	4	1	no	—
637	C₂³	C₂³×C₄×C₇	1	4	yes	—
638	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
639	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
640	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
641	Q₈	—	2	4	no	—
642	Q₈	—	2	4	no	—
643	Q₈	—	2	4	no	—
644	D₄	—	2	8	no	—
645	D₄	—	2	8	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	4	no	—
648	D₄	—	2	4	no	—
649	D₄	—	4	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	8	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	C₇×#131	1	4	yes	complemented
673	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
674	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
675	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
676	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
677	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
678	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
679	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
680	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
681	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
682	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
683	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
684	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
685	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
686	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
687	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
688	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
689	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
690	C₈	—	2	2	no	—
691	C₈	—	2	2	no	—
692	C₈	—	2	8	no	—
693	C₈	—	2	2	no	—
694	C₈	—	2	2	no	—
695	C₇	#60268	1	1	yes	characteristic, direct product factor, Sylow
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	C₇×#520	1	2	yes	—
708	C₂²	C₂×C₇×#131	1	2	yes	—
709	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	4	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	4	no	—
720	C₄	C₇×#520	1	2	yes	—
721	C₄	C₂×C₇×#131	1	2	yes	—
722	C₄	C₂×C₇×#131	1	2	yes	—
723	C₄	C₇×#568	1	2	yes	—
724	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
725	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
726	C₂	—	2	2	no	—
727	C₂	—	2	2	no	—
728	C₂	—	4	1	no	—
729	C₂	—	4	4	no	—
730	C₂	C₂×C₇×#520	1	1	yes	characteristic
731	C₂	C₂²×C₇×#131	1	1	yes	characteristic
732	C₂	C₂×C₇×#568	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×#3444	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×#2991	C₂	semidirect
5. C₇×#2990	C₂	semidirect
6. C₇×#2989	C₂	semidirect
7. C₇×#2988	C₂	semidirect
8. C₇×#2960	C₂	semidirect
9. C₇×#2933	C₂	semidirect
10. C₇×#2931	C₂	semidirect
11. C₇×#2925	C₂	semidirect
12. C₂×C₇×#431	C₂	semidirect
13. C₇×#2906	C₂	semidirect
14. C₂×C₇×#423	C₂	semidirect
36. C₇×#446	C₂²	semidirect
37. C₇×#446	C₂²	semidirect
38. C₇×C₈×Q₈	C₂²	semidirect
39. C₇×C₈×Q₈	C₂²	semidirect
41. C₇×#436	C₂²	semidirect
42. C₇×#436	C₂²	semidirect
46. C₇×C₈×D₄	C₂²	semidirect
47. C₇×C₈×D₄	C₂²	semidirect
48. C₇×#433	C₂²	semidirect
49. C₇×#432	C₂²	semidirect
56. C₇×#431	C₂²	semidirect
58. C₇×#424	C₂²	semidirect
63. C₇×#423	C₂²	semidirect
68. C₂×C₇×C₄⋊C₈	C₂²	semidirect
73. #60268	C₇	direct (N × H)
179. #2994	C₂×C₇	semidirect
180. #2993	C₂×C₇	semidirect
181. #2991	C₂×C₇	semidirect
182. #2990	C₂×C₇	semidirect
183. #2989	C₂×C₇	semidirect
184. #2988	C₂×C₇	semidirect
185. #2960	C₂×C₇	semidirect
186. #2933	C₂×C₇	semidirect
187. #2931	C₂×C₇	semidirect
188. #2925	C₂×C₇	semidirect
189. C₂×#431	C₂×C₇	semidirect
190. #2906	C₂×C₇	semidirect
191. C₂×#423	C₂×C₇	semidirect
304. #446	C₂²×C₇	semidirect
305. #446	C₂²×C₇	semidirect
306. C₈×Q₈	C₂²×C₇	semidirect
307. C₈×Q₈	C₂²×C₇	semidirect
309. #436	C₂²×C₇	semidirect
310. #436	C₂²×C₇	semidirect
314. C₈×D₄	C₂²×C₇	semidirect
315. C₈×D₄	C₂²×C₇	semidirect
316. #433	C₂²×C₇	semidirect
317. #432	C₂²×C₇	semidirect
324. #431	C₂²×C₇	semidirect
326. #424	C₂²×C₇	semidirect
331. #423	C₂²×C₇	semidirect
336. C₂×C₄⋊C₈	C₂²×C₇	semidirect
379. C₂×C₄×C₇	#131	semidirect
672. C₂×C₄	C₇×#131	semidirect
695. C₇	#60268	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×#3444	2
C₇×#2994	2
C₇×#2993	2
C₇×#2991	2
C₇×#2990	2
C₇×#2989	2
C₇×#2988	2
C₇×#2960	2
C₇×#2933	2
C₇×#2931	2
C₇×#2925	2
C₂×C₇×#431	2
C₇×#2906	2
C₂×C₇×#423	2
#60268	7

Subgroups — C7×#60268 #13237484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60268 #13237484