Subgroups — C₇×#60235 #13237451

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3449	C₂	1	1	yes	maximal, characteristic
2	C₇×#2981	C₂	1	4	yes	maximal, complemented
3	C₇×#2980	C₂	1	2	yes	maximal, complemented
4	C₇×#2979	C₂	1	2	yes	maximal, complemented
5	C₇×#2978	C₂	1	2	yes	maximal, complemented
6	C₇×#2977	C₂	1	2	yes	maximal, complemented
7	C₇×#2976	C₂	1	4	yes	maximal, complemented
8	C₇×#2933	C₂	1	2	yes	maximal, complemented
9	C₇×#2933	C₂	1	2	yes	maximal, complemented
10	C₇×#2930	C₂	1	2	yes	maximal, complemented
11	C₇×#2929	C₂	1	2	yes	maximal, complemented
12	C₇×#2924	C₂	1	2	yes	maximal, complemented
13	C₇×#2880	C₂	1	2	yes	maximal, complemented
14	C₇×#2879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂×C₇×#131	C₂²	1	2	yes	—
19	C₂×C₇×#131	C₂²	1	2	yes	—
20	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
24	C₇×#537	C₄	1	2	yes	—
25	C₇×#537	C₄	1	2	yes	—
26	C₇×#536	C₄	1	1	yes	characteristic
27	C₇×#536	C₄	1	1	yes	characteristic
28	C₇×#536	C₄	1	2	yes	—
29	C₇×#535	C₄	1	2	yes	—
30	C₇×#535	C₄	1	1	yes	characteristic
31	C₇×#535	C₄	1	1	yes	characteristic
32	C₇×#534	C₄	1	2	yes	—
33	C₇×#534	C₄	1	2	yes	—
34	C₇×#532	C₂²	1	2	yes	—
35	C₇×#532	C₂²	1	2	yes	—
36	C₇×#525	C₂²	1	2	yes	—
37	C₇×#525	C₂²	1	2	yes	—
38	C₇×#525	C₂²	1	2	yes	—
39	C₇×#525	C₂²	1	2	yes	—
40	C₂×C₇×#117	C₂²	1	1	yes	characteristic
41	C₇×#436	C₂²	1	4	yes	complemented
42	C₇×#436	C₂²	1	4	yes	complemented
43	C₇×#436	C₂²	1	4	yes	complemented
44	C₇×#436	C₂²	1	4	yes	complemented
45	C₇×#435	C₂²	1	4	yes	complemented
46	C₇×#435	C₂²	1	4	yes	complemented
47	C₇×#435	C₂²	1	4	yes	complemented
48	C₇×#435	C₂²	1	4	yes	complemented
49	C₇×#435	C₂²	1	4	yes	complemented
50	C₇×#435	C₂²	1	4	yes	complemented
51	C₇×#435	C₂²	1	4	yes	complemented
52	C₇×#435	C₂²	1	4	yes	complemented
53	C₇×C₈×D₄	C₂²	1	4	yes	complemented
54	C₇×C₈×D₄	C₂²	1	4	yes	complemented
55	C₇×C₈×D₄	C₂²	1	4	yes	complemented
56	C₇×C₈×D₄	C₂²	1	4	yes	complemented
57	C₇×#433	C₂²	1	4	yes	complemented
58	C₇×#433	C₂²	1	4	yes	complemented
59	C₇×#432	C₂²	1	4	yes	complemented
60	C₇×#431	C₂²	1	4	yes	complemented
61	C₇×#424	C₂²	1	2	yes	complemented
62	C₇×#424	C₂²	1	2	yes	complemented
63	C₇×#408	C₂²	1	2	yes	—
64	C₇×#408	C₂²	1	2	yes	—
65	C₇×#408	C₂²	1	2	yes	—
66	C₇×#408	C₂²	1	2	yes	—
67	C₇×#408	C₂²	1	1	yes	characteristic
68	C₇×#408	C₂²	1	2	yes	—
69	C₇×#408	C₂²	1	1	yes	characteristic
70	C₇×#408	C₂²	1	1	yes	characteristic, complemented
71	C₇×#408	C₂²	1	2	yes	complemented
72	C₇×#408	C₂²	1	4	yes	complemented
73	C₇×#408	C₂²	1	1	yes	characteristic, complemented
74	C₇×#408	C₂²	1	4	yes	complemented
75	C₇×#408	C₂²	1	2	yes	complemented
76	C₇×#408	C₂²	1	2	yes	complemented
77	C₇×#407	C₂²	1	2	yes	—
78	C₇×#407	C₂²	1	2	yes	complemented
79	C₇×#407	C₂²	1	4	yes	complemented
80	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
81	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
82	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
83	C₇×#405	C₂²	1	2	yes	complemented
84	C₇×#405	C₂²	1	2	yes	complemented
85	#60235	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂×C₇×#41	—	4	2	no	—
87	C₂×C₇×#41	—	4	2	no	—
88	C₂×C₇×#41	—	4	2	no	—
89	C₂×C₇×#41	—	4	2	no	—
90	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
91	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
92	C₂×C₇×#41	C₂×C₄	1	2	yes	—
93	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×#41	C₂×C₄	1	2	yes	—
96	C₂×C₇×#41	C₂³	1	2	yes	—
97	C₂×C₇×#41	C₂³	1	1	yes	characteristic
98	C₂×C₇×#41	C₂³	1	1	yes	characteristic
99	C₂×C₇×#41	C₂³	1	1	yes	characteristic
100	C₂×C₇×#41	C₂³	1	1	yes	characteristic
101	C₂×C₇×#41	C₂³	1	2	yes	—
102	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
106	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
107	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
109	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	C₂³	1	2	yes	—
113	C₇×#131	—	4	4	no	—
114	C₇×#131	—	4	4	no	—
115	C₂×C₇×M₁₆	—	4	2	no	—
116	C₂×C₇×M₁₆	—	4	2	no	—
117	C₂×C₇×M₁₆	—	4	2	no	—
118	C₂×C₇×M₁₆	C₂³	1	2	yes	—
119	C₂×C₇×M₁₆	C₂³	1	2	yes	—
120	C₂×C₇×M₁₆	C₂³	1	4	yes	—
121	C₂×C₇×M₁₆	C₂³	1	4	yes	—
122	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×M₁₆	C₂³	1	2	yes	—
124	C₂×C₇×M₁₆	C₂³	1	2	yes	—
125	C₂×C₇×M₁₆	C₂³	1	2	yes	—
126	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
127	C₂²×C₇×C₈	—	4	2	no	—
128	C₂²×C₇×C₈	C₂³	1	2	yes	—
129	C₂²×C₇×C₈	C₂³	1	2	yes	—
130	C₂²×C₇×C₈	C₂³	1	4	yes	—
131	C₂²×C₇×C₈	C₂³	1	4	yes	—
132	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
133	C₂²×C₇×C₈	C₂³	1	2	yes	—
134	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
135	C₂²×C₇×C₈	C₂³	1	2	yes	—
136	C₂²×C₇×C₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
139	C₇×#127	C₂×C₄	1	2	yes	—
140	C₇×#127	C₂×C₄	1	2	yes	—
141	C₇×#124	C₂×C₄	1	2	yes	—
142	C₇×#124	C₂×C₄	1	2	yes	—
143	C₇×#124	C₂×C₄	1	2	yes	—
144	C₇×#124	C₂×C₄	1	2	yes	—
145	C₇×#123	C₂×C₄	1	4	yes	—
146	C₇×#123	C₂×C₄	1	4	yes	—
147	C₇×#123	C₂×C₄	1	2	yes	—
148	C₇×#123	C₂×C₄	1	2	yes	—
149	C₇×#123	C₂×C₄	1	2	yes	—
150	C₇×#123	C₂×C₄	1	2	yes	—
151	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
152	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
153	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
154	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
155	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
156	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
157	C₇×#121	C₂×C₄	1	2	yes	—
158	C₇×#121	C₂×C₄	1	2	yes	—
159	C₇×#121	C₂×C₄	1	2	yes	—
160	C₇×#121	C₂×C₄	1	2	yes	—
161	C₇×#121	C₂×C₄	1	4	yes	—
162	C₇×#121	C₂×C₄	1	4	yes	—
163	C₇×#121	C₂×C₄	1	4	yes	—
164	C₇×#121	C₂×C₄	1	4	yes	—
165	C₇×#121	C₂×C₄	1	4	yes	—
166	C₇×#121	C₂×C₄	1	4	yes	—
167	C₇×#120	C₂×C₄	1	4	yes	—
168	C₇×#120	C₂×C₄	1	4	yes	—
169	C₇×#120	C₂×C₄	1	2	yes	—
170	C₇×#120	C₂×C₄	1	2	yes	—
171	C₇×#120	C₂×C₄	1	2	yes	—
172	C₇×#120	C₂×C₄	1	2	yes	—
173	C₄×C₇×D₄	C₂³	1	4	yes	—
174	C₄×C₇×D₄	C₂³	1	4	yes	—
175	C₄×C₇×D₄	C₂³	1	4	yes	—
176	C₄×C₇×D₄	C₂³	1	4	yes	—
177	C₇×#117	C₂×C₄	1	1	yes	characteristic
178	C₇×#117	C₂×C₄	1	1	yes	characteristic
179	C₇×#117	C₂×C₄	1	2	yes	—
180	C₇×#117	C₂³	1	2	yes	—
181	C₇×#117	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
184	C₂×C₄²×C₇	C₂³	1	2	yes	—
185	C₇×C₄⋊C₈	C₂³	1	4	yes	—
186	C₇×C₄⋊C₈	C₂³	1	4	yes	—
187	C₇×C₄⋊C₈	C₂³	1	4	yes	—
188	C₇×C₄⋊C₈	C₂³	1	4	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
198	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
200	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
201	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
202	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
203	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₇×#97	C₂³	1	4	yes	—
206	C₇×#97	C₂³	1	4	yes	—
207	C₄×C₇×C₈	C₂³	1	4	yes	—
208	C₄×C₇×C₈	C₂³	1	4	yes	—
209	#3449	C₂×C₇	1	1	yes	characteristic
210	#2981	C₂×C₇	1	4	yes	complemented
211	#2980	C₂×C₇	1	2	yes	complemented
212	#2979	C₂×C₇	1	2	yes	complemented
213	#2978	C₂×C₇	1	2	yes	complemented
214	#2977	C₂×C₇	1	2	yes	complemented
215	#2976	C₂×C₇	1	4	yes	complemented
216	#2933	C₂×C₇	1	2	yes	complemented
217	#2933	C₂×C₇	1	2	yes	complemented
218	#2930	C₂×C₇	1	2	yes	complemented
219	#2929	C₂×C₇	1	2	yes	complemented
220	#2924	C₂×C₇	1	2	yes	complemented
221	#2880	C₂×C₇	1	2	yes	complemented
222	#2879	C₂×C₇	1	1	yes	characteristic, complemented
223	C₂×#408	C₂×C₇	1	1	yes	characteristic, complemented
224	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
225	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
226	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
227	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
228	C₇×#41	—	2	4	no	—
229	C₇×#41	—	2	4	no	—
230	C₇×#41	—	4	2	no	—
231	C₇×#41	—	4	2	no	—
232	C₇×#41	—	4	2	no	—
233	C₇×#41	—	4	2	no	—
234	C₇×#41	—	4	1	no	—
235	C₇×#41	—	4	1	no	—
236	C₇×#41	—	4	1	no	—
237	C₇×#41	—	4	1	no	—
238	C₇×#41	—	4	1	no	—
239	C₇×#41	—	4	1	no	—
240	C₇×#41	—	4	2	no	—
241	C₇×#41	—	4	2	no	—
242	C₇×#41	—	4	1	no	—
243	C₇×#41	—	4	1	no	—
244	C₇×#41	—	4	4	no	—
245	C₇×#41	—	4	4	no	—
246	C₂×C₇×Q₈	—	4	2	no	—
247	C₂×C₇×Q₈	—	4	2	no	—
248	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
249	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
254	C₂×C₇×D₄	—	4	2	no	—
255	C₂×C₇×D₄	—	4	2	no	—
256	C₂×C₇×D₄	—	4	2	no	—
257	C₂×C₇×D₄	—	4	2	no	—
258	C₂×C₇×D₄	—	4	4	no	—
259	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
260	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
261	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
262	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
263	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
264	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
265	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
266	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
267	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
268	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
269	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
270	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
271	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
272	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
273	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
274	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
275	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
276	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
277	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
278	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	4	2	no	—
286	C₂²×C₄×C₇	—	4	2	no	—
287	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
290	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
297	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
298	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₇×M₁₆	—	2	4	no	—
308	C₇×M₁₆	—	2	4	no	—
309	C₇×M₁₆	—	4	1	no	—
310	C₇×M₁₆	—	4	2	no	—
311	C₇×M₁₆	—	4	1	no	—
312	C₇×M₁₆	—	4	2	no	—
313	C₇×M₁₆	—	4	2	no	—
314	C₇×M₁₆	—	4	4	no	—
315	C₇×M₁₆	—	4	4	no	—
316	C₂×C₇×C₈	—	2	4	no	—
317	C₂×C₇×C₈	—	2	4	no	—
318	C₂×C₇×C₈	—	4	1	no	—
319	C₂×C₇×C₈	—	4	2	no	—
320	C₂×C₇×C₈	—	4	1	no	—
321	C₂×C₇×C₈	—	4	2	no	—
322	C₂×C₇×C₈	—	4	2	no	—
323	C₂×C₇×C₈	—	4	4	no	—
324	C₂×C₇×C₈	—	4	4	no	—
325	C₂×C₇×C₈	C₂⁴	1	2	yes	—
326	C₂×C₇×C₈	C₂⁴	1	2	yes	—
327	C₂×C₇×C₈	C₂⁴	1	4	yes	—
328	C₂×C₇×C₈	C₂⁴	1	4	yes	—
329	C₂×C₇×C₈	C₂⁴	1	2	yes	—
330	C₂×C₇×C₈	C₂⁴	1	2	yes	—
331	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
332	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
333	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
334	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
335	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
336	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
337	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
338	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
339	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
340	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
341	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
342	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
343	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
344	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
345	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
346	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
347	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
348	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
349	C₄²×C₇	C₂²×C₄	1	2	yes	—
350	C₄²×C₇	C₂²×C₄	1	2	yes	—
351	C₄²×C₇	C₂⁴	1	4	yes	—
352	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
353	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
354	C₂×#131	C₂²×C₇	1	2	yes	—
355	C₂×#131	C₂²×C₇	1	2	yes	—
356	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
357	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
360	#537	C₄×C₇	1	2	yes	—
361	#537	C₄×C₇	1	2	yes	—
362	#536	C₄×C₇	1	1	yes	characteristic
363	#536	C₄×C₇	1	1	yes	characteristic
364	#536	C₄×C₇	1	2	yes	—
365	#535	C₄×C₇	1	2	yes	—
366	#535	C₄×C₇	1	1	yes	characteristic
367	#535	C₄×C₇	1	1	yes	characteristic
368	#534	C₄×C₇	1	2	yes	—
369	#534	C₄×C₇	1	2	yes	—
370	#532	C₂²×C₇	1	2	yes	—
371	#532	C₂²×C₇	1	2	yes	—
372	#525	C₂²×C₇	1	2	yes	—
373	#525	C₂²×C₇	1	2	yes	—
374	#525	C₂²×C₇	1	2	yes	—
375	#525	C₂²×C₇	1	2	yes	—
376	C₂×#117	C₂²×C₇	1	1	yes	characteristic
377	#436	C₂²×C₇	1	4	yes	complemented
378	#436	C₂²×C₇	1	4	yes	complemented
379	#436	C₂²×C₇	1	4	yes	complemented
380	#436	C₂²×C₇	1	4	yes	complemented
381	#435	C₂²×C₇	1	4	yes	complemented
382	#435	C₂²×C₇	1	4	yes	complemented
383	#435	C₂²×C₇	1	4	yes	complemented
384	#435	C₂²×C₇	1	4	yes	complemented
385	#435	C₂²×C₇	1	4	yes	complemented
386	#435	C₂²×C₇	1	4	yes	complemented
387	#435	C₂²×C₇	1	4	yes	complemented
388	#435	C₂²×C₇	1	4	yes	complemented
389	C₈×D₄	C₂²×C₇	1	4	yes	complemented
390	C₈×D₄	C₂²×C₇	1	4	yes	complemented
391	C₈×D₄	C₂²×C₇	1	4	yes	complemented
392	C₈×D₄	C₂²×C₇	1	4	yes	complemented
393	#433	C₂²×C₇	1	4	yes	complemented
394	#433	C₂²×C₇	1	4	yes	complemented
395	#432	C₂²×C₇	1	4	yes	complemented
396	#431	C₂²×C₇	1	4	yes	complemented
397	#424	C₂²×C₇	1	2	yes	complemented
398	#424	C₂²×C₇	1	2	yes	complemented
399	#408	C₂²×C₇	1	2	yes	—
400	#408	C₂²×C₇	1	1	yes	characteristic
401	#408	C₂²×C₇	1	1	yes	characteristic
402	#408	C₂²×C₇	1	2	yes	—
403	#408	C₂²×C₇	1	2	yes	—
404	#408	C₂²×C₇	1	2	yes	—
405	#408	C₂²×C₇	1	2	yes	—
406	#408	C₂²×C₇	1	1	yes	characteristic, complemented
407	#408	C₂²×C₇	1	1	yes	characteristic, complemented
408	#408	C₂²×C₇	1	2	yes	complemented
409	#408	C₂²×C₇	1	2	yes	complemented
410	#408	C₂²×C₇	1	2	yes	complemented
411	#408	C₂²×C₇	1	4	yes	complemented
412	#408	C₂²×C₇	1	4	yes	complemented
413	#407	C₂²×C₇	1	2	yes	—
414	#407	C₂²×C₇	1	2	yes	complemented
415	#407	C₂²×C₇	1	4	yes	complemented
416	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
417	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
418	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	complemented
419	#405	C₂²×C₇	1	2	yes	complemented
420	#405	C₂²×C₇	1	2	yes	complemented
421	C₂³×C₇	—	2	2	no	—
422	C₂³×C₇	—	2	2	no	—
423	C₂³×C₇	—	2	2	no	—
424	C₂³×C₇	—	4	2	no	—
425	C₂³×C₇	—	4	2	no	—
426	C₂³×C₇	—	4	2	no	—
427	C₂³×C₇	—	4	2	no	—
428	C₂³×C₇	—	4	4	no	—
429	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
430	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
431	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
432	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
433	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
434	C₂³×C₇	C₂³×C₄	1	4	yes	—
435	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
436	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
437	C₇×Q₈	—	2	4	no	—
438	C₇×Q₈	—	4	1	no	—
439	C₇×Q₈	—	4	1	no	—
440	C₇×Q₈	—	4	1	no	—
441	C₇×Q₈	—	4	1	no	—
442	C₇×Q₈	—	4	2	no	—
443	C₇×D₄	—	2	8	no	—
444	C₇×D₄	—	2	4	no	—
445	C₇×D₄	—	4	1	no	—
446	C₇×D₄	—	4	1	no	—
447	C₇×D₄	—	4	1	no	—
448	C₇×D₄	—	4	1	no	—
449	C₇×D₄	—	4	2	no	—
450	C₇×D₄	—	4	1	no	—
451	C₇×D₄	—	4	1	no	—
452	C₇×D₄	—	4	1	no	—
453	C₇×D₄	—	4	1	no	—
454	C₇×D₄	—	4	1	no	—
455	C₇×D₄	—	4	1	no	—
456	C₇×D₄	—	4	1	no	—
457	C₇×D₄	—	4	1	no	—
458	C₇×D₄	—	4	4	no	—
459	C₇×D₄	—	4	4	no	—
460	C₇×D₄	—	4	4	no	—
461	C₇×D₄	—	4	4	no	—
462	C₇×D₄	—	4	4	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	1	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	4	no	—
477	C₂×C₄×C₇	—	2	4	no	—
478	C₂×C₄×C₇	—	2	1	no	—
479	C₂×C₄×C₇	—	2	1	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	1	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	1	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	4	2	no	—
487	C₂×C₄×C₇	—	4	4	no	—
488	C₂×C₄×C₇	—	4	4	no	—
489	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
491	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
492	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
497	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
499	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
500	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
501	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
502	C₇×C₈	—	2	2	no	—
503	C₇×C₈	—	2	2	no	—
504	C₇×C₈	—	2	2	no	—
505	C₇×C₈	—	2	2	no	—
506	C₇×C₈	—	2	4	no	—
507	C₇×C₈	—	2	4	no	—
508	C₂×#41	—	4	2	no	—
509	C₂×#41	—	4	2	no	—
510	C₂×#41	—	4	2	no	—
511	C₂×#41	—	4	2	no	—
512	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
513	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
514	C₂×#41	C₂×C₄×C₇	1	2	yes	—
515	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
516	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
517	C₂×#41	C₂×C₄×C₇	1	2	yes	—
518	C₂×#41	C₂³×C₇	1	2	yes	—
519	C₂×#41	C₂³×C₇	1	1	yes	characteristic
520	C₂×#41	C₂³×C₇	1	1	yes	characteristic
521	C₂×#41	C₂³×C₇	1	1	yes	characteristic
522	C₂×#41	C₂³×C₇	1	2	yes	—
523	C₂×#41	C₂³×C₇	1	1	yes	characteristic
524	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
525	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
526	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
527	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
528	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
529	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
530	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₇	1	2	yes	—
535	#131	—	4	4	no	—
536	#131	—	4	4	no	—
537	C₂×M₁₆	—	4	2	no	—
538	C₂×M₁₆	—	4	2	no	—
539	C₂×M₁₆	—	4	2	no	—
540	C₂×M₁₆	C₂³×C₇	1	2	yes	—
541	C₂×M₁₆	C₂³×C₇	1	2	yes	—
542	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
543	C₂×M₁₆	C₂³×C₇	1	2	yes	—
544	C₂×M₁₆	C₂³×C₇	1	2	yes	—
545	C₂×M₁₆	C₂³×C₇	1	2	yes	—
546	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
547	C₂×M₁₆	C₂³×C₇	1	4	yes	—
548	C₂×M₁₆	C₂³×C₇	1	4	yes	—
549	C₂²×C₈	—	4	2	no	—
550	C₂²×C₈	C₂³×C₇	1	2	yes	—
551	C₂²×C₈	C₂³×C₇	1	2	yes	—
552	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
553	C₂²×C₈	C₂³×C₇	1	2	yes	—
554	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₇	1	2	yes	—
556	C₂²×C₈	C₂³×C₇	1	2	yes	—
557	C₂²×C₈	C₂³×C₇	1	4	yes	—
558	C₂²×C₈	C₂³×C₇	1	4	yes	—
559	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
560	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
561	#127	C₂×C₄×C₇	1	2	yes	—
562	#127	C₂×C₄×C₇	1	2	yes	—
563	#124	C₂×C₄×C₇	1	2	yes	—
564	#124	C₂×C₄×C₇	1	2	yes	—
565	#124	C₂×C₄×C₇	1	2	yes	—
566	#124	C₂×C₄×C₇	1	2	yes	—
567	#123	C₂×C₄×C₇	1	4	yes	—
568	#123	C₂×C₄×C₇	1	4	yes	—
569	#123	C₂×C₄×C₇	1	2	yes	—
570	#123	C₂×C₄×C₇	1	2	yes	—
571	#123	C₂×C₄×C₇	1	2	yes	—
572	#123	C₂×C₄×C₇	1	2	yes	—
573	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
574	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
575	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
576	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
577	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
578	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
579	#121	C₂×C₄×C₇	1	2	yes	—
580	#121	C₂×C₄×C₇	1	2	yes	—
581	#121	C₂×C₄×C₇	1	2	yes	—
582	#121	C₂×C₄×C₇	1	2	yes	—
583	#121	C₂×C₄×C₇	1	4	yes	—
584	#121	C₂×C₄×C₇	1	4	yes	—
585	#121	C₂×C₄×C₇	1	4	yes	—
586	#121	C₂×C₄×C₇	1	4	yes	—
587	#121	C₂×C₄×C₇	1	4	yes	—
588	#121	C₂×C₄×C₇	1	4	yes	—
589	#120	C₂×C₄×C₇	1	4	yes	—
590	#120	C₂×C₄×C₇	1	4	yes	—
591	#120	C₂×C₄×C₇	1	2	yes	—
592	#120	C₂×C₄×C₇	1	2	yes	—
593	#120	C₂×C₄×C₇	1	2	yes	—
594	#120	C₂×C₄×C₇	1	2	yes	—
595	C₄×D₄	C₂³×C₇	1	4	yes	—
596	C₄×D₄	C₂³×C₇	1	4	yes	—
597	C₄×D₄	C₂³×C₇	1	4	yes	—
598	C₄×D₄	C₂³×C₇	1	4	yes	—
599	#117	C₂×C₄×C₇	1	1	yes	characteristic
600	#117	C₂×C₄×C₇	1	1	yes	characteristic
601	#117	C₂×C₄×C₇	1	2	yes	—
602	#117	C₂³×C₇	1	2	yes	—
603	#117	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
606	C₂×C₄²	C₂³×C₇	1	2	yes	—
607	C₄⋊C₈	C₂³×C₇	1	4	yes	—
608	C₄⋊C₈	C₂³×C₇	1	4	yes	—
609	C₄⋊C₈	C₂³×C₇	1	4	yes	—
610	C₄⋊C₈	C₂³×C₇	1	4	yes	—
611	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
613	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
614	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
615	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
616	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
617	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
618	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
619	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
620	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
621	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
622	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
623	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
624	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
625	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
627	#97	C₂³×C₇	1	4	yes	—
628	#97	C₂³×C₇	1	4	yes	—
629	C₄×C₈	C₂³×C₇	1	4	yes	—
630	C₄×C₈	C₂³×C₇	1	4	yes	—
631	C₂²×C₇	—	2	2	no	—
632	C₂²×C₇	—	2	1	no	—
633	C₂²×C₇	—	2	1	no	—
634	C₂²×C₇	—	2	1	no	—
635	C₂²×C₇	—	2	1	no	—
636	C₂²×C₇	—	2	1	no	—
637	C₂²×C₇	—	2	1	no	—
638	C₂²×C₇	—	2	4	no	—
639	C₂²×C₇	—	2	2	no	—
640	C₂²×C₇	—	2	2	no	—
641	C₂²×C₇	—	2	2	no	—
642	C₂²×C₇	—	2	2	no	—
643	C₂²×C₇	—	2	2	no	—
644	C₂²×C₇	—	2	4	no	—
645	C₂²×C₇	—	2	4	no	—
646	C₂²×C₇	—	2	2	no	—
647	C₂²×C₇	—	4	4	no	—
648	C₂²×C₇	—	8	2	no	—
649	C₂²×C₇	—	8	2	no	—
650	C₂²×C₇	—	8	4	no	—
651	C₂²×C₇	#518	1	2	yes	—
652	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
653	C₄×C₇	—	2	1	no	—
654	C₄×C₇	—	2	1	no	—
655	C₄×C₇	—	2	1	no	—
656	C₄×C₇	—	2	1	no	—
657	C₄×C₇	—	2	1	no	—
658	C₄×C₇	—	2	1	no	—
659	C₄×C₇	—	2	4	no	—
660	C₄×C₇	—	2	4	no	—
661	C₄×C₇	—	2	4	no	—
662	C₄×C₇	#518	1	2	yes	—
663	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
664	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
666	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
667	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
668	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	4	2	no	—
672	#41	—	4	2	no	—
673	#41	—	4	2	no	—
674	#41	—	4	2	no	—
675	#41	—	4	1	no	—
676	#41	—	4	1	no	—
677	#41	—	4	1	no	—
678	#41	—	4	1	no	—
679	#41	—	4	1	no	—
680	#41	—	4	1	no	—
681	#41	—	4	2	no	—
682	#41	—	4	2	no	—
683	#41	—	4	1	no	—
684	#41	—	4	1	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
690	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
691	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
692	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
693	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
694	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
701	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
702	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
703	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
704	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
705	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
706	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
707	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
708	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
709	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
710	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
711	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
712	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
713	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
714	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
715	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
716	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
717	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
718	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
719	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
729	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
730	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
731	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
732	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
733	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
734	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
735	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
736	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
737	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
738	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
739	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
748	M₁₆	—	2	4	no	—
749	M₁₆	—	2	4	no	—
750	M₁₆	—	4	1	no	—
751	M₁₆	—	4	2	no	—
752	M₁₆	—	4	1	no	—
753	M₁₆	—	4	2	no	—
754	M₁₆	—	4	2	no	—
755	M₁₆	—	4	4	no	—
756	M₁₆	—	4	4	no	—
757	C₂×C₈	—	2	4	no	—
758	C₂×C₈	—	2	4	no	—
759	C₂×C₈	—	4	1	no	—
760	C₂×C₈	—	4	2	no	—
761	C₂×C₈	—	4	1	no	—
762	C₂×C₈	—	4	2	no	—
763	C₂×C₈	—	4	2	no	—
764	C₂×C₈	—	4	4	no	—
765	C₂×C₈	—	4	4	no	—
766	C₂×C₈	C₂⁴×C₇	1	2	yes	—
767	C₂×C₈	C₂⁴×C₇	1	2	yes	—
768	C₂×C₈	C₂⁴×C₇	1	4	yes	—
769	C₂×C₈	C₂⁴×C₇	1	4	yes	—
770	C₂×C₈	C₂⁴×C₇	1	2	yes	—
771	C₂×C₈	C₂⁴×C₇	1	2	yes	—
772	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
773	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
774	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
775	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
776	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
777	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
778	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
779	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
780	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
781	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
782	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
783	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
784	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
785	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
786	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
787	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
788	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
789	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
790	C₄²	C₂²×C₄×C₇	1	2	yes	—
791	C₄²	C₂²×C₄×C₇	1	2	yes	—
792	C₄²	C₂⁴×C₇	1	4	yes	—
793	C₂×C₇	—	2	2	no	—
794	C₂×C₇	—	4	1	no	—
795	C₂×C₇	—	4	1	no	—
796	C₂×C₇	—	4	1	no	—
797	C₂×C₇	—	4	1	no	—
798	C₂×C₇	—	4	1	no	—
799	C₂×C₇	—	4	4	no	—
800	C₂×C₇	—	4	1	no	—
801	C₂×C₇	C₂×#518	1	1	yes	characteristic
802	C₂×C₇	#3573	1	2	yes	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	2	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	4	no	—
811	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
812	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
813	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
814	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
815	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
816	C₂³	C₂³×C₄×C₇	1	4	yes	—
817	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
818	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	4	1	no	—
821	Q₈	—	4	1	no	—
822	Q₈	—	4	1	no	—
823	Q₈	—	4	1	no	—
824	Q₈	—	4	2	no	—
825	D₄	—	2	8	no	—
826	D₄	—	2	4	no	—
827	D₄	—	4	1	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	1	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
872	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
873	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
874	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
876	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
877	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
878	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
879	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
880	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
881	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
882	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
883	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
884	C₈	—	2	2	no	—
885	C₈	—	2	2	no	—
886	C₈	—	2	2	no	—
887	C₈	—	2	2	no	—
888	C₈	—	2	4	no	—
889	C₈	—	2	4	no	—
890	C₇	#60235	1	1	yes	characteristic, direct product factor, Sylow
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	8	2	no	—
909	C₂²	—	8	2	no	—
910	C₂²	—	8	4	no	—
911	C₂²	C₇×#518	1	2	yes	—
912	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
913	C₄	—	2	4	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	4	no	—
922	C₄	C₇×#518	1	2	yes	—
923	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
924	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
925	C₂	—	2	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	4	1	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	1	no	—
930	C₂	—	4	1	no	—
931	C₂	—	4	1	no	—
932	C₂	—	4	4	no	—
933	C₂	C₂×C₇×#518	1	1	yes	characteristic
934	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×#3449	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×#2981	C₂	semidirect
3. C₇×#2980	C₂	semidirect
4. C₇×#2979	C₂	semidirect
5. C₇×#2978	C₂	semidirect
6. C₇×#2977	C₂	semidirect
7. C₇×#2976	C₂	semidirect
8. C₇×#2933	C₂	semidirect
9. C₇×#2933	C₂	semidirect
10. C₇×#2930	C₂	semidirect
11. C₇×#2929	C₂	semidirect
12. C₇×#2924	C₂	semidirect
13. C₇×#2880	C₂	semidirect
14. C₇×#2879	C₂	semidirect
15. C₂×C₇×#408	C₂	semidirect
20. C₂²×C₇×M₁₆	C₂²	semidirect
21. C₂²×C₇×M₁₆	C₂²	semidirect
22. C₂²×C₇×M₁₆	C₂²	semidirect
23. C₂³×C₇×C₈	C₂²	semidirect
41. C₇×#436	C₂²	semidirect
42. C₇×#436	C₂²	semidirect
43. C₇×#436	C₂²	semidirect
44. C₇×#436	C₂²	semidirect
45. C₇×#435	C₂²	semidirect
46. C₇×#435	C₂²	semidirect
47. C₇×#435	C₂²	semidirect
48. C₇×#435	C₂²	semidirect
49. C₇×#435	C₂²	semidirect
50. C₇×#435	C₂²	semidirect
51. C₇×#435	C₂²	semidirect
52. C₇×#435	C₂²	semidirect
53. C₇×C₈×D₄	C₂²	semidirect
54. C₇×C₈×D₄	C₂²	semidirect
55. C₇×C₈×D₄	C₂²	semidirect
56. C₇×C₈×D₄	C₂²	semidirect
57. C₇×#433	C₂²	semidirect
58. C₇×#433	C₂²	semidirect
59. C₇×#432	C₂²	semidirect
60. C₇×#431	C₂²	semidirect
61. C₇×#424	C₂²	semidirect
62. C₇×#424	C₂²	semidirect
70. C₇×#408	C₂²	semidirect
71. C₇×#408	C₂²	semidirect
72. C₇×#408	C₂²	semidirect
73. C₇×#408	C₂²	semidirect
74. C₇×#408	C₂²	semidirect
75. C₇×#408	C₂²	semidirect
76. C₇×#408	C₂²	semidirect
78. C₇×#407	C₂²	semidirect
79. C₇×#407	C₂²	semidirect
81. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
82. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
83. C₇×#405	C₂²	semidirect
84. C₇×#405	C₂²	semidirect
85. #60235	C₇	direct (N × H)
210. #2981	C₂×C₇	semidirect
211. #2980	C₂×C₇	semidirect
212. #2979	C₂×C₇	semidirect
213. #2978	C₂×C₇	semidirect
214. #2977	C₂×C₇	semidirect
215. #2976	C₂×C₇	semidirect
216. #2933	C₂×C₇	semidirect
217. #2933	C₂×C₇	semidirect
218. #2930	C₂×C₇	semidirect
219. #2929	C₂×C₇	semidirect
220. #2924	C₂×C₇	semidirect
221. #2880	C₂×C₇	semidirect
222. #2879	C₂×C₇	semidirect
223. C₂×#408	C₂×C₇	semidirect
356. C₂²×M₁₆	C₂²×C₇	semidirect
357. C₂²×M₁₆	C₂²×C₇	semidirect
358. C₂²×M₁₆	C₂²×C₇	semidirect
359. C₂³×C₈	C₂²×C₇	semidirect
377. #436	C₂²×C₇	semidirect
378. #436	C₂²×C₇	semidirect
379. #436	C₂²×C₇	semidirect
380. #436	C₂²×C₇	semidirect
381. #435	C₂²×C₇	semidirect
382. #435	C₂²×C₇	semidirect
383. #435	C₂²×C₇	semidirect
384. #435	C₂²×C₇	semidirect
385. #435	C₂²×C₇	semidirect
386. #435	C₂²×C₇	semidirect
387. #435	C₂²×C₇	semidirect
388. #435	C₂²×C₇	semidirect
389. C₈×D₄	C₂²×C₇	semidirect
390. C₈×D₄	C₂²×C₇	semidirect
391. C₈×D₄	C₂²×C₇	semidirect
392. C₈×D₄	C₂²×C₇	semidirect
393. #433	C₂²×C₇	semidirect
394. #433	C₂²×C₇	semidirect
395. #432	C₂²×C₇	semidirect
396. #431	C₂²×C₇	semidirect
397. #424	C₂²×C₇	semidirect
398. #424	C₂²×C₇	semidirect
406. #408	C₂²×C₇	semidirect
407. #408	C₂²×C₇	semidirect
408. #408	C₂²×C₇	semidirect
409. #408	C₂²×C₇	semidirect
410. #408	C₂²×C₇	semidirect
411. #408	C₂²×C₇	semidirect
412. #408	C₂²×C₇	semidirect
414. #407	C₂²×C₇	semidirect
415. #407	C₂²×C₇	semidirect
417. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
418. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
419. #405	C₂²×C₇	semidirect
420. #405	C₂²×C₇	semidirect
890. C₇	#60235	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×#3449	2
C₇×#2981	2
C₇×#2980	2
C₇×#2979	2
C₇×#2978	2
C₇×#2977	2
C₇×#2976	2
C₇×#2933	2
C₇×#2930	2
C₇×#2929	2
C₇×#2924	2
C₇×#2880	2
C₇×#2879	2
C₂×C₇×#408	2
#60235	7

Subgroups — C7×#60235 #13237451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60235 #13237451