Subgroups — C₇×#60323 #13237539

Order 1792.

1940 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3481	C₂	1	1	yes	maximal, characteristic
2	C₇×#2994	C₂	1	2	yes	maximal, complemented
3	C₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2976	C₂	1	4	yes	maximal, complemented
8	C₇×#2974	C₂	1	2	yes	maximal, complemented
9	C₇×#2972	C₂	1	2	yes	maximal, complemented
10	C₇×#2969	C₂	1	2	yes	maximal, complemented
11	C₇×#2966	C₂	1	2	yes	maximal, complemented
12	C₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×D₄×M₁₆	C₂	1	2	yes	maximal, complemented
15	C₇×#2933	C₂	1	4	yes	maximal, complemented
16	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#436	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#131	C₂²	1	2	yes	complemented
19	C₂²×C₇×M₁₆	C₂²	1	4	yes	complemented
20	C₇×#559	C₄	1	1	yes	characteristic
21	C₇×#554	C₄	1	1	yes	characteristic
22	C₇×#554	C₄	1	1	yes	characteristic
23	C₇×#553	C₄	1	2	yes	—
24	C₇×#553	C₄	1	2	yes	—
25	C₇×#551	C₄	1	4	yes	—
26	C₇×#546	C₄	1	2	yes	—
27	C₇×#546	C₄	1	2	yes	—
28	C₇×D₄²	C₄	1	1	yes	characteristic
29	C₇×#532	C₂²	1	1	yes	characteristic
30	C₇×#529	C₂²	1	2	yes	—
31	C₇×#529	C₂²	1	2	yes	—
32	C₇×#525	C₂²	1	4	yes	—
33	C₄×C₇×#41	C₂²	1	1	yes	characteristic
34	C₄×C₇×#41	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
36	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
37	C₇×#446	C₂²	1	1	yes	characteristic, complemented
38	C₇×#446	C₂²	1	1	yes	characteristic, complemented
39	C₇×#446	C₂²	1	2	yes	complemented
40	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
43	C₇×#436	C₂²	1	1	yes	characteristic
44	C₇×#436	C₂²	1	2	yes	—
45	C₇×#436	C₂²	1	1	yes	characteristic
46	C₇×#436	C₂²	1	2	yes	complemented
47	C₇×#436	C₂²	1	4	yes	complemented
48	C₇×#436	C₂²	1	4	yes	complemented
49	C₇×#436	C₂²	1	2	yes	complemented
50	C₇×#436	C₂²	1	2	yes	complemented
51	C₇×#436	C₂²	1	4	yes	complemented
52	C₇×#436	C₂²	1	2	yes	complemented
53	C₇×#435	C₂²	1	2	yes	complemented
54	C₇×#435	C₂²	1	4	yes	complemented
55	C₇×#435	C₂²	1	4	yes	complemented
56	C₇×#435	C₂²	1	4	yes	complemented
57	C₇×#435	C₂²	1	4	yes	complemented
58	C₇×#435	C₂²	1	2	yes	complemented
59	C₇×#435	C₂²	1	4	yes	complemented
60	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
61	C₇×C₈×D₄	C₂²	1	2	yes	—
62	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
63	C₇×C₈×D₄	C₂²	1	2	yes	complemented
64	C₇×C₈×D₄	C₂²	1	2	yes	complemented
65	C₇×C₈×D₄	C₂²	1	2	yes	complemented
66	C₇×C₈×D₄	C₂²	1	4	yes	complemented
67	C₇×C₈×D₄	C₂²	1	2	yes	complemented
68	C₇×C₈×D₄	C₂²	1	4	yes	complemented
69	C₇×C₈×D₄	C₂²	1	2	yes	complemented
70	C₇×C₈×D₄	C₂²	1	2	yes	complemented
71	C₇×#433	C₂²	1	4	yes	complemented
72	C₇×#433	C₂²	1	4	yes	complemented
73	C₇×#432	C₂²	1	2	yes	complemented
74	C₇×#431	C₂²	1	2	yes	complemented
75	C₇×#431	C₂²	1	1	yes	characteristic, complemented
76	C₇×#431	C₂²	1	2	yes	complemented
77	C₇×#431	C₂²	1	1	yes	characteristic, complemented
78	C₇×#431	C₂²	1	2	yes	complemented
79	C₇×#424	C₂²	1	4	yes	complemented
80	C₇×#423	C₂²	1	1	yes	characteristic, complemented
81	C₇×#423	C₂²	1	2	yes	complemented
82	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
83	C₇×#408	C₂²	1	2	yes	complemented
84	C₇×#408	C₂²	1	4	yes	complemented
85	C₇×#407	C₂²	1	4	yes	complemented
86	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
87	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
88	C₇×#405	C₂²	1	4	yes	complemented
89	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
90	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
91	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
92	#60323	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×#41	C₂³	1	2	yes	—
96	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
97	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
98	C₂³×C₄×C₇	C₂³	1	4	yes	—
99	C₇×#131	—	4	4	no	—
100	C₂×C₇×M₁₆	—	4	8	no	—
101	C₂×C₇×M₁₆	C₂³	1	2	yes	—
102	C₂×C₇×M₁₆	C₂³	1	4	yes	—
103	C₂×C₇×M₁₆	C₂³	1	2	yes	—
104	C₂×C₇×M₁₆	C₂³	1	4	yes	—
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	4	yes	—
107	C₂²×C₇×C₈	C₂³	1	2	yes	—
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	2	yes	—
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	4	yes	—
112	C₂²×C₇×C₈	C₂³	1	4	yes	—
113	C₂²×C₇×C₈	C₂³	1	4	yes	—
114	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₇×#127	C₂×C₄	1	1	yes	characteristic
116	C₇×#126	C₂×C₄	1	4	yes	—
117	C₇×#126	C₂×C₄	1	4	yes	—
118	C₇×#125	C₂×C₄	1	2	yes	—
119	C₇×#125	C₂×C₄	1	2	yes	—
120	C₇×#124	C₂×C₄	1	2	yes	—
121	C₇×#124	C₂×C₄	1	2	yes	—
122	C₇×#124	C₂×C₄	1	2	yes	—
123	C₇×#123	C₂×C₄	1	4	yes	—
124	C₇×#123	C₂×C₄	1	4	yes	—
125	C₇×#123	C₂×C₄	1	4	yes	—
126	C₇×#123	C₂×C₄	1	4	yes	—
127	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
128	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
130	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
131	C₇×#121	C₂×C₄	1	4	yes	—
132	C₇×#121	C₂×C₄	1	4	yes	—
133	C₇×#121	C₂×C₄	1	2	yes	—
134	C₇×#121	C₂×C₄	1	2	yes	—
135	C₇×#121	C₂×C₄	1	2	yes	—
136	C₇×#121	C₂×C₄	1	2	yes	—
137	C₇×#120	C₂×C₄	1	4	yes	—
138	C₇×#120	C₂×C₄	1	4	yes	—
139	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
142	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
143	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
144	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
145	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
146	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
147	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
148	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
149	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
151	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
152	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
153	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
154	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₄×C₇×D₄	C₂³	1	4	yes	—
156	C₄×C₇×D₄	C₂³	1	4	yes	—
157	C₄×C₇×D₄	C₂³	1	2	yes	—
158	C₄×C₇×D₄	C₂³	1	2	yes	—
159	C₄×C₇×D₄	C₂³	1	2	yes	—
160	C₄×C₇×D₄	C₂³	1	2	yes	—
161	C₇×#117	C₂×C₄	1	2	yes	—
162	C₇×#117	C₂×C₄	1	2	yes	—
163	C₇×#117	C₂×C₄	1	1	yes	characteristic
164	C₇×#117	C₂×C₄	1	1	yes	characteristic
165	C₇×#117	C₂³	1	4	yes	—
166	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
170	C₂×C₄²×C₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
174	C₇×C₄⋊C₈	C₂³	1	2	yes	—
175	C₇×C₄⋊C₈	C₂³	1	4	yes	—
176	C₇×C₄⋊C₈	C₂³	1	2	yes	—
177	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
178	C₇×C₄⋊C₈	C₂³	1	4	yes	—
179	C₇×C₄⋊C₈	C₂³	1	2	yes	—
180	C₇×C₄⋊C₈	C₂³	1	2	yes	—
181	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
182	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
183	C₇×C₄⋊C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊C₈	C₂³	1	2	yes	—
185	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
186	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
188	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₇×#97	C₂³	1	2	yes	—
198	C₇×#97	C₂³	1	2	yes	—
199	C₇×#97	C₂³	1	4	yes	—
200	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
202	C₄×C₇×C₈	C₂³	1	2	yes	—
203	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
204	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
205	C₄×C₇×C₈	C₂³	1	2	yes	—
206	C₄×C₇×C₈	C₂³	1	2	yes	—
207	C₄×C₇×C₈	C₂³	1	2	yes	—
208	C₄×C₇×C₈	C₂³	1	4	yes	—
209	#3481	C₂×C₇	1	1	yes	characteristic
210	#2994	C₂×C₇	1	2	yes	complemented
211	#2993	C₂×C₇	1	2	yes	complemented
212	#2991	C₂×C₇	1	1	yes	characteristic, complemented
213	#2990	C₂×C₇	1	1	yes	characteristic, complemented
214	#2979	C₂×C₇	1	1	yes	characteristic, complemented
215	#2976	C₂×C₇	1	4	yes	complemented
216	#2974	C₂×C₇	1	2	yes	complemented
217	#2972	C₂×C₇	1	2	yes	complemented
218	#2969	C₂×C₇	1	2	yes	complemented
219	#2966	C₂×C₇	1	2	yes	complemented
220	#2965	C₂×C₇	1	1	yes	characteristic, complemented
221	C₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
222	D₄×M₁₆	C₂×C₇	1	2	yes	complemented
223	#2933	C₂×C₇	1	4	yes	complemented
224	#2931	C₂×C₇	1	1	yes	characteristic, complemented
225	C₂×#436	C₂×C₇	1	2	yes	complemented
226	C₂⁴×C₇	C₂²×C₄	1	4	yes	—
227	C₇×#41	—	2	4	no	—
228	C₇×#41	—	4	2	no	—
229	C₇×#41	—	4	2	no	—
230	C₇×#41	—	4	2	no	—
231	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
234	C₂×C₇×D₄	—	2	8	no	—
235	C₂×C₇×D₄	—	4	4	no	—
236	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
238	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
239	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
240	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
241	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
242	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
243	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
244	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
245	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	—	4	4	no	—
247	C₂²×C₄×C₇	—	4	4	no	—
248	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
249	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
250	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
251	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
254	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
255	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
256	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
261	C₇×M₁₆	—	2	4	no	—
262	C₇×M₁₆	—	2	8	no	—
263	C₇×M₁₆	—	4	4	no	—
264	C₇×M₁₆	—	4	4	no	—
265	C₇×M₁₆	—	4	2	no	—
266	C₇×M₁₆	—	4	2	no	—
267	C₂×C₇×C₈	—	2	4	no	—
268	C₂×C₇×C₈	—	2	2	no	—
269	C₂×C₇×C₈	—	4	2	no	—
270	C₂×C₇×C₈	—	4	4	no	—
271	C₂×C₇×C₈	—	4	1	no	—
272	C₂×C₇×C₈	—	4	4	no	—
273	C₂×C₇×C₈	—	4	4	no	—
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	C₂⁴	1	2	yes	—
276	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
277	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
278	C₂×C₇×C₈	C₂⁴	1	2	yes	—
279	C₂×C₇×C₈	C₂⁴	1	2	yes	—
280	C₂×C₇×C₈	C₂⁴	1	2	yes	—
281	C₂×C₇×C₈	C₂⁴	1	4	yes	—
282	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
283	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
284	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
285	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
286	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
287	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
288	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
289	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
290	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
292	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
293	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
294	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
295	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
296	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
297	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
298	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
299	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
300	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
301	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
302	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
303	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
304	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
305	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
306	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
307	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
308	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
309	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
310	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
311	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
312	C₄²×C₇	C₂²×C₄	1	2	yes	—
313	C₄²×C₇	C₂²×C₄	1	2	yes	—
314	C₄²×C₇	C₂²×C₄	1	2	yes	—
315	C₄²×C₇	C₂²×C₄	1	2	yes	—
316	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
317	C₄²×C₇	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇	C₂⁴	1	1	yes	characteristic
319	C₄²×C₇	C₂⁴	1	2	yes	—
320	C₄²×C₇	C₂⁴	1	2	yes	—
321	C₂×#131	C₂²×C₇	1	2	yes	complemented
322	C₂²×M₁₆	C₂²×C₇	1	4	yes	complemented
323	#559	C₄×C₇	1	1	yes	characteristic
324	#554	C₄×C₇	1	1	yes	characteristic
325	#554	C₄×C₇	1	1	yes	characteristic
326	#553	C₄×C₇	1	2	yes	—
327	#553	C₄×C₇	1	2	yes	—
328	#551	C₄×C₇	1	4	yes	—
329	#546	C₄×C₇	1	2	yes	—
330	#546	C₄×C₇	1	2	yes	—
331	D₄²	C₄×C₇	1	1	yes	characteristic
332	#532	C₂²×C₇	1	1	yes	characteristic
333	#529	C₂²×C₇	1	2	yes	—
334	#529	C₂²×C₇	1	2	yes	—
335	#525	C₂²×C₇	1	4	yes	—
336	C₄×#41	C₂²×C₇	1	1	yes	characteristic
337	C₄×#41	C₂²×C₇	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
339	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
340	#446	C₂²×C₇	1	1	yes	characteristic, complemented
341	#446	C₂²×C₇	1	1	yes	characteristic, complemented
342	#446	C₂²×C₇	1	2	yes	complemented
343	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
345	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
346	#436	C₂²×C₇	1	1	yes	characteristic
347	#436	C₂²×C₇	1	2	yes	—
348	#436	C₂²×C₇	1	1	yes	characteristic
349	#436	C₂²×C₇	1	2	yes	complemented
350	#436	C₂²×C₇	1	4	yes	complemented
351	#436	C₂²×C₇	1	4	yes	complemented
352	#436	C₂²×C₇	1	2	yes	complemented
353	#436	C₂²×C₇	1	2	yes	complemented
354	#436	C₂²×C₇	1	4	yes	complemented
355	#436	C₂²×C₇	1	2	yes	complemented
356	#435	C₂²×C₇	1	2	yes	complemented
357	#435	C₂²×C₇	1	4	yes	complemented
358	#435	C₂²×C₇	1	4	yes	complemented
359	#435	C₂²×C₇	1	4	yes	complemented
360	#435	C₂²×C₇	1	4	yes	complemented
361	#435	C₂²×C₇	1	2	yes	complemented
362	#435	C₂²×C₇	1	4	yes	complemented
363	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
364	C₈×D₄	C₂²×C₇	1	2	yes	—
365	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
366	C₈×D₄	C₂²×C₇	1	2	yes	complemented
367	C₈×D₄	C₂²×C₇	1	2	yes	complemented
368	C₈×D₄	C₂²×C₇	1	2	yes	complemented
369	C₈×D₄	C₂²×C₇	1	4	yes	complemented
370	C₈×D₄	C₂²×C₇	1	2	yes	complemented
371	C₈×D₄	C₂²×C₇	1	4	yes	complemented
372	C₈×D₄	C₂²×C₇	1	2	yes	complemented
373	C₈×D₄	C₂²×C₇	1	2	yes	complemented
374	#433	C₂²×C₇	1	4	yes	complemented
375	#433	C₂²×C₇	1	4	yes	complemented
376	#432	C₂²×C₇	1	2	yes	complemented
377	#431	C₂²×C₇	1	2	yes	complemented
378	#431	C₂²×C₇	1	1	yes	characteristic, complemented
379	#431	C₂²×C₇	1	2	yes	complemented
380	#431	C₂²×C₇	1	1	yes	characteristic, complemented
381	#431	C₂²×C₇	1	2	yes	complemented
382	#424	C₂²×C₇	1	4	yes	complemented
383	#423	C₂²×C₇	1	1	yes	characteristic, complemented
384	#423	C₂²×C₇	1	2	yes	complemented
385	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
386	#408	C₂²×C₇	1	2	yes	complemented
387	#408	C₂²×C₇	1	4	yes	complemented
388	#407	C₂²×C₇	1	4	yes	complemented
389	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	complemented
390	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	complemented
391	#405	C₂²×C₇	1	4	yes	complemented
392	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
393	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
394	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
395	C₂³×C₇	—	2	8	no	—
396	C₂³×C₇	—	4	4	no	—
397	C₂³×C₇	—	4	4	no	—
398	C₂³×C₇	C₂³×C₄	1	4	yes	—
399	C₂³×C₇	C₂³×C₄	1	2	yes	—
400	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
401	C₂³×C₇	C₂³×C₄	1	2	yes	—
402	C₇×Q₈	—	2	2	no	—
403	C₇×Q₈	—	2	2	no	—
404	C₇×Q₈	—	4	2	no	—
405	C₇×D₄	—	2	8	no	—
406	C₇×D₄	—	2	4	no	—
407	C₇×D₄	—	2	4	no	—
408	C₇×D₄	—	2	2	no	—
409	C₇×D₄	—	2	4	no	—
410	C₇×D₄	—	4	4	no	—
411	C₇×D₄	—	4	4	no	—
412	C₇×D₄	—	4	2	no	—
413	C₇×D₄	—	4	2	no	—
414	C₇×D₄	#131	1	4	yes	complemented
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	2	4	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	4	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	1	no	—
422	C₂×C₄×C₇	—	2	4	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	4	no	—
426	C₂×C₄×C₇	—	2	1	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	4	4	no	—
429	C₂×C₄×C₇	—	4	4	no	—
430	C₂×C₄×C₇	—	4	4	no	—
431	C₂×C₄×C₇	—	4	2	no	—
432	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
433	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
434	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
437	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
438	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
440	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
441	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
442	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
445	C₇×C₈	—	2	1	no	—
446	C₇×C₈	—	2	2	no	—
447	C₇×C₈	—	2	2	no	—
448	C₇×C₈	—	2	4	no	—
449	C₇×C₈	—	2	1	no	—
450	C₇×C₈	—	2	2	no	—
451	C₇×C₈	—	2	2	no	—
452	C₇×C₈	—	2	1	no	—
453	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
454	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
455	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
456	C₂×#41	C₂³×C₇	1	2	yes	—
457	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
458	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
459	C₂³×C₄	C₂³×C₇	1	4	yes	—
460	#131	—	4	4	no	—
461	C₂×M₁₆	—	4	8	no	—
462	C₂×M₁₆	C₂³×C₇	1	2	yes	—
463	C₂×M₁₆	C₂³×C₇	1	4	yes	—
464	C₂×M₁₆	C₂³×C₇	1	4	yes	—
465	C₂×M₁₆	C₂³×C₇	1	4	yes	—
466	C₂×M₁₆	C₂³×C₇	1	2	yes	—
467	C₂×M₁₆	C₂³×C₇	1	2	yes	—
468	C₂²×C₈	C₂³×C₇	1	2	yes	—
469	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₇	1	4	yes	—
471	C₂²×C₈	C₂³×C₇	1	4	yes	—
472	C₂²×C₈	C₂³×C₇	1	2	yes	—
473	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₇	1	4	yes	—
475	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
476	#127	C₂×C₄×C₇	1	1	yes	characteristic
477	#126	C₂×C₄×C₇	1	4	yes	—
478	#126	C₂×C₄×C₇	1	4	yes	—
479	#125	C₂×C₄×C₇	1	2	yes	—
480	#125	C₂×C₄×C₇	1	2	yes	—
481	#124	C₂×C₄×C₇	1	2	yes	—
482	#124	C₂×C₄×C₇	1	2	yes	—
483	#124	C₂×C₄×C₇	1	2	yes	—
484	#123	C₂×C₄×C₇	1	4	yes	—
485	#123	C₂×C₄×C₇	1	4	yes	—
486	#123	C₂×C₄×C₇	1	4	yes	—
487	#123	C₂×C₄×C₇	1	4	yes	—
488	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
489	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
490	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
491	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
492	#121	C₂×C₄×C₇	1	4	yes	—
493	#121	C₂×C₄×C₇	1	4	yes	—
494	#121	C₂×C₄×C₇	1	2	yes	—
495	#121	C₂×C₄×C₇	1	2	yes	—
496	#121	C₂×C₄×C₇	1	2	yes	—
497	#121	C₂×C₄×C₇	1	2	yes	—
498	#120	C₂×C₄×C₇	1	4	yes	—
499	#120	C₂×C₄×C₇	1	4	yes	—
500	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
501	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
502	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
503	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
504	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
505	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
506	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
507	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
508	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
509	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
510	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
511	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
512	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
513	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
514	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
515	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
516	C₄×D₄	C₂³×C₇	1	4	yes	—
517	C₄×D₄	C₂³×C₇	1	4	yes	—
518	C₄×D₄	C₂³×C₇	1	2	yes	—
519	C₄×D₄	C₂³×C₇	1	2	yes	—
520	C₄×D₄	C₂³×C₇	1	2	yes	—
521	C₄×D₄	C₂³×C₇	1	2	yes	—
522	#117	C₂×C₄×C₇	1	2	yes	—
523	#117	C₂×C₄×C₇	1	2	yes	—
524	#117	C₂×C₄×C₇	1	1	yes	characteristic
525	#117	C₂×C₄×C₇	1	1	yes	characteristic
526	#117	C₂³×C₇	1	4	yes	—
527	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
528	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
531	C₂×C₄²	C₂³×C₇	1	2	yes	—
532	C₂×C₄²	C₂³×C₇	1	2	yes	—
533	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
534	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
535	C₄⋊C₈	C₂³×C₇	1	2	yes	—
536	C₄⋊C₈	C₂³×C₇	1	4	yes	—
537	C₄⋊C₈	C₂³×C₇	1	2	yes	—
538	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₇	1	4	yes	—
540	C₄⋊C₈	C₂³×C₇	1	2	yes	—
541	C₄⋊C₈	C₂³×C₇	1	2	yes	—
542	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₇	1	2	yes	—
545	C₄⋊C₈	C₂³×C₇	1	2	yes	—
546	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
547	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
548	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
549	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
555	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
558	#97	C₂³×C₇	1	2	yes	—
559	#97	C₂³×C₇	1	2	yes	—
560	#97	C₂³×C₇	1	4	yes	—
561	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₇	1	2	yes	—
564	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₇	1	2	yes	—
567	C₄×C₈	C₂³×C₇	1	2	yes	—
568	C₄×C₈	C₂³×C₇	1	2	yes	—
569	C₄×C₈	C₂³×C₇	1	4	yes	—
570	C₂²×C₇	—	2	2	no	—
571	C₂²×C₇	—	2	2	no	—
572	C₂²×C₇	—	2	2	no	—
573	C₂²×C₇	—	2	4	no	—
574	C₂²×C₇	—	2	1	no	—
575	C₂²×C₇	—	2	1	no	—
576	C₂²×C₇	—	2	2	no	—
577	C₂²×C₇	—	2	4	no	—
578	C₂²×C₇	—	2	1	no	—
579	C₂²×C₇	—	2	2	no	—
580	C₂²×C₇	—	2	4	no	—
581	C₂²×C₇	—	8	8	no	—
582	C₂²×C₇	C₂×#131	1	4	yes	—
583	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
584	C₄×C₇	—	2	2	no	—
585	C₄×C₇	—	2	2	no	—
586	C₄×C₇	—	2	4	no	—
587	C₄×C₇	—	2	1	no	—
588	C₄×C₇	—	2	1	no	—
589	C₄×C₇	—	2	2	no	—
590	C₄×C₇	—	2	2	no	—
591	C₄×C₇	—	2	1	no	—
592	C₄×C₇	—	2	2	no	—
593	C₄×C₇	—	2	2	no	—
594	C₄×C₇	C₂×#131	1	2	yes	—
595	C₄×C₇	#568	1	2	yes	—
596	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄×C₇	#585	1	1	yes	characteristic
598	C₂⁴	C₂²×C₄×C₇	1	4	yes	—
599	#41	—	2	4	no	—
600	#41	—	4	2	no	—
601	#41	—	4	2	no	—
602	#41	—	4	2	no	—
603	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
604	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
605	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
606	C₂×D₄	—	2	8	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
609	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
610	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
611	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
612	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
613	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
614	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
615	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
616	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
617	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
621	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
622	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
623	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
624	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
625	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
626	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
627	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
628	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
633	M₁₆	—	2	4	no	—
634	M₁₆	—	2	8	no	—
635	M₁₆	—	4	4	no	—
636	M₁₆	—	4	4	no	—
637	M₁₆	—	4	2	no	—
638	M₁₆	—	4	2	no	—
639	C₂×C₈	—	2	4	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	4	2	no	—
642	C₂×C₈	—	4	4	no	—
643	C₂×C₈	—	4	1	no	—
644	C₂×C₈	—	4	4	no	—
645	C₂×C₈	—	4	4	no	—
646	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
647	C₂×C₈	C₂⁴×C₇	1	2	yes	—
648	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
649	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
650	C₂×C₈	C₂⁴×C₇	1	2	yes	—
651	C₂×C₈	C₂⁴×C₇	1	2	yes	—
652	C₂×C₈	C₂⁴×C₇	1	2	yes	—
653	C₂×C₈	C₂⁴×C₇	1	4	yes	—
654	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
655	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
656	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
657	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
658	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
659	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
660	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
661	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
662	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
664	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
665	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
666	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
668	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
669	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
670	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
671	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
672	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
673	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
674	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
683	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
684	C₄²	C₂²×C₄×C₇	1	2	yes	—
685	C₄²	C₂²×C₄×C₇	1	2	yes	—
686	C₄²	C₂²×C₄×C₇	1	2	yes	—
687	C₄²	C₂²×C₄×C₇	1	2	yes	—
688	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
689	C₄²	C₂⁴×C₇	1	1	yes	characteristic
690	C₄²	C₂⁴×C₇	1	1	yes	characteristic
691	C₄²	C₂⁴×C₇	1	2	yes	—
692	C₄²	C₂⁴×C₇	1	2	yes	—
693	C₂×C₇	—	2	4	no	—
694	C₂×C₇	—	4	1	no	—
695	C₂×C₇	—	4	4	no	—
696	C₂×C₇	—	4	2	no	—
697	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂×C₇	C₂²×#131	1	1	yes	characteristic
699	C₂×C₇	C₂×#568	1	1	yes	characteristic
700	C₂³	—	2	8	no	—
701	C₂³	—	4	4	no	—
702	C₂³	—	4	4	no	—
703	C₂³	C₂³×C₄×C₇	1	4	yes	—
704	C₂³	C₂³×C₄×C₇	1	2	yes	—
705	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
706	C₂³	C₂³×C₄×C₇	1	2	yes	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	2	no	—
710	D₄	—	2	8	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	2	no	—
719	D₄	C₇×#131	1	4	yes	complemented
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
738	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
740	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
741	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
742	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
743	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
744	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
745	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
746	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
747	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
748	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
749	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
750	C₈	—	2	1	no	—
751	C₈	—	2	2	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	4	no	—
754	C₈	—	2	1	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₈	—	2	1	no	—
758	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
759	C₇	#60323	1	1	yes	characteristic, direct product factor, Sylow
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	8	8	no	—
772	C₂²	C₂×C₇×#131	1	4	yes	—
773	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	1	no	—
784	C₄	C₂×C₇×#131	1	2	yes	—
785	C₄	C₇×#568	1	2	yes	—
786	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
787	C₄	C₇×#585	1	1	yes	characteristic
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	4	1	no	—
792	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
793	C₂	C₂²×C₇×#131	1	1	yes	characteristic
794	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×#3481	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×#2979	C₂	semidirect
7. C₇×#2976	C₂	semidirect
8. C₇×#2974	C₂	semidirect
9. C₇×#2972	C₂	semidirect
10. C₇×#2969	C₂	semidirect
11. C₇×#2966	C₂	semidirect
12. C₇×#2965	C₂	semidirect
13. C₇×C₈×#41	C₂	semidirect
14. C₇×D₄×M₁₆	C₂	semidirect
15. C₇×#2933	C₂	semidirect
16. C₇×#2931	C₂	semidirect
17. C₂×C₇×#436	C₂	semidirect
18. C₂×C₇×#131	C₂²	semidirect
19. C₂²×C₇×M₁₆	C₂²	semidirect
37. C₇×#446	C₂²	semidirect
38. C₇×#446	C₂²	semidirect
39. C₇×#446	C₂²	semidirect
40. C₇×C₈×Q₈	C₂²	semidirect
41. C₇×C₈×Q₈	C₂²	semidirect
42. C₇×C₈×Q₈	C₂²	semidirect
46. C₇×#436	C₂²	semidirect
47. C₇×#436	C₂²	semidirect
48. C₇×#436	C₂²	semidirect
49. C₇×#436	C₂²	semidirect
50. C₇×#436	C₂²	semidirect
51. C₇×#436	C₂²	semidirect
52. C₇×#436	C₂²	semidirect
53. C₇×#435	C₂²	semidirect
54. C₇×#435	C₂²	semidirect
55. C₇×#435	C₂²	semidirect
56. C₇×#435	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
58. C₇×#435	C₂²	semidirect
59. C₇×#435	C₂²	semidirect
63. C₇×C₈×D₄	C₂²	semidirect
64. C₇×C₈×D₄	C₂²	semidirect
65. C₇×C₈×D₄	C₂²	semidirect
66. C₇×C₈×D₄	C₂²	semidirect
67. C₇×C₈×D₄	C₂²	semidirect
68. C₇×C₈×D₄	C₂²	semidirect
69. C₇×C₈×D₄	C₂²	semidirect
70. C₇×C₈×D₄	C₂²	semidirect
71. C₇×#433	C₂²	semidirect
72. C₇×#433	C₂²	semidirect
73. C₇×#432	C₂²	semidirect
74. C₇×#431	C₂²	semidirect
75. C₇×#431	C₂²	semidirect
76. C₇×#431	C₂²	semidirect
77. C₇×#431	C₂²	semidirect
78. C₇×#431	C₂²	semidirect
79. C₇×#424	C₂²	semidirect
80. C₇×#423	C₂²	semidirect
81. C₇×#423	C₂²	semidirect
82. C₂×C₇×C₄⋊C₈	C₂²	semidirect
83. C₇×#408	C₂²	semidirect
84. C₇×#408	C₂²	semidirect
85. C₇×#407	C₂²	semidirect
86. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
87. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
88. C₇×#405	C₂²	semidirect
89. C₄×C₇×M₁₆	C₂²	semidirect
90. C₂×C₄×C₇×C₈	C₂²	semidirect
91. C₂×C₄×C₇×C₈	C₂²	semidirect
92. #60323	C₇	direct (N × H)
210. #2994	C₂×C₇	semidirect
211. #2993	C₂×C₇	semidirect
212. #2991	C₂×C₇	semidirect
213. #2990	C₂×C₇	semidirect
214. #2979	C₂×C₇	semidirect
215. #2976	C₂×C₇	semidirect
216. #2974	C₂×C₇	semidirect
217. #2972	C₂×C₇	semidirect
218. #2969	C₂×C₇	semidirect
219. #2966	C₂×C₇	semidirect
220. #2965	C₂×C₇	semidirect
221. C₈×#41	C₂×C₇	semidirect
222. D₄×M₁₆	C₂×C₇	semidirect
223. #2933	C₂×C₇	semidirect
224. #2931	C₂×C₇	semidirect
225. C₂×#436	C₂×C₇	semidirect
321. C₂×#131	C₂²×C₇	semidirect
322. C₂²×M₁₆	C₂²×C₇	semidirect
340. #446	C₂²×C₇	semidirect
341. #446	C₂²×C₇	semidirect
342. #446	C₂²×C₇	semidirect
343. C₈×Q₈	C₂²×C₇	semidirect
344. C₈×Q₈	C₂²×C₇	semidirect
345. C₈×Q₈	C₂²×C₇	semidirect
349. #436	C₂²×C₇	semidirect
350. #436	C₂²×C₇	semidirect
351. #436	C₂²×C₇	semidirect
352. #436	C₂²×C₇	semidirect
353. #436	C₂²×C₇	semidirect
354. #436	C₂²×C₇	semidirect
355. #436	C₂²×C₇	semidirect
356. #435	C₂²×C₇	semidirect
357. #435	C₂²×C₇	semidirect
358. #435	C₂²×C₇	semidirect
359. #435	C₂²×C₇	semidirect
360. #435	C₂²×C₇	semidirect
361. #435	C₂²×C₇	semidirect
362. #435	C₂²×C₇	semidirect
366. C₈×D₄	C₂²×C₇	semidirect
367. C₈×D₄	C₂²×C₇	semidirect
368. C₈×D₄	C₂²×C₇	semidirect
369. C₈×D₄	C₂²×C₇	semidirect
370. C₈×D₄	C₂²×C₇	semidirect
371. C₈×D₄	C₂²×C₇	semidirect
372. C₈×D₄	C₂²×C₇	semidirect
373. C₈×D₄	C₂²×C₇	semidirect
374. #433	C₂²×C₇	semidirect
375. #433	C₂²×C₇	semidirect
376. #432	C₂²×C₇	semidirect
377. #431	C₂²×C₇	semidirect
378. #431	C₂²×C₇	semidirect
379. #431	C₂²×C₇	semidirect
380. #431	C₂²×C₇	semidirect
381. #431	C₂²×C₇	semidirect
382. #424	C₂²×C₇	semidirect
383. #423	C₂²×C₇	semidirect
384. #423	C₂²×C₇	semidirect
385. C₂×C₄⋊C₈	C₂²×C₇	semidirect
386. #408	C₂²×C₇	semidirect
387. #408	C₂²×C₇	semidirect
388. #407	C₂²×C₇	semidirect
389. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
390. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
391. #405	C₂²×C₇	semidirect
392. C₄×M₁₆	C₂²×C₇	semidirect
393. C₂×C₄×C₈	C₂²×C₇	semidirect
394. C₂×C₄×C₈	C₂²×C₇	semidirect
414. C₇×D₄	#131	semidirect
719. D₄	C₇×#131	semidirect
759. C₇	#60323	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×#3481	2
C₇×#2994	2
C₇×#2993	2
C₇×#2991	2
C₇×#2990	2
C₇×#2979	2
C₇×#2976	2
C₇×#2974	2
C₇×#2972	2
C₇×#2969	2
C₇×#2966	2
C₇×#2965	2
C₇×C₈×#41	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2931	2
C₂×C₇×#436	2
#60323	7

Subgroups — C7×#60323 #13237539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60323 #13237539