Subgroups — C₇×#60321 #13237537

Order 1792.

1894 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3460	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×#2989	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2981	C₂	1	2	yes	maximal, complemented
7	C₇×#2979	C₂	1	2	yes	maximal, complemented
8	C₇×#2977	C₂	1	4	yes	maximal, complemented
9	C₇×#2972	C₂	1	1	yes	maximal, characteristic, 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×#2935	C₂	1	2	yes	maximal, complemented
15	C₇×#2933	C₂	1	4	yes	maximal, complemented
16	C₇×#2931	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#131	C₂²	1	4	yes	complemented
19	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
20	C₇×#544	C₄	1	1	yes	characteristic
21	C₇×#542	C₄	1	2	yes	—
22	C₇×#542	C₄	1	2	yes	—
23	C₇×#540	C₄	1	2	yes	—
24	C₇×#540	C₄	1	2	yes	—
25	C₇×#538	C₄	1	4	yes	—
26	C₇×#537	C₄	1	1	yes	characteristic
27	C₇×#535	C₄	1	1	yes	characteristic
28	C₇×#535	C₄	1	1	yes	characteristic
29	C₇×#532	C₂²	1	2	yes	—
30	C₇×#532	C₂²	1	2	yes	—
31	C₇×#529	C₂²	1	2	yes	—
32	C₇×#529	C₂²	1	2	yes	—
33	C₇×#525	C₂²	1	4	yes	—
34	C₄×C₇×#41	C₂²	1	1	yes	characteristic
35	C₄×C₇×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
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	2	yes	—
44	C₇×#436	C₂²	1	2	yes	—
45	C₇×#436	C₂²	1	2	yes	—
46	C₇×#436	C₂²	1	2	yes	—
47	C₇×#436	C₂²	1	1	yes	characteristic, complemented
48	C₇×#436	C₂²	1	4	yes	complemented
49	C₇×#436	C₂²	1	4	yes	complemented
50	C₇×#436	C₂²	1	2	yes	complemented
51	C₇×#436	C₂²	1	1	yes	characteristic, complemented
52	C₇×#435	C₂²	1	2	yes	—
53	C₇×#435	C₂²	1	4	yes	—
54	C₇×#435	C₂²	1	2	yes	—
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	4	yes	complemented
59	C₇×C₈×D₄	C₂²	1	2	yes	—
60	C₇×C₈×D₄	C₂²	1	2	yes	—
61	C₇×C₈×D₄	C₂²	1	4	yes	—
62	C₇×C₈×D₄	C₂²	1	2	yes	—
63	C₇×C₈×D₄	C₂²	1	2	yes	—
64	C₇×C₈×D₄	C₂²	1	2	yes	—
65	C₇×C₈×D₄	C₂²	1	2	yes	—
66	C₇×C₈×D₄	C₂²	1	4	yes	complemented
67	C₇×C₈×D₄	C₂²	1	2	yes	complemented
68	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
69	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
70	C₇×C₈×D₄	C₂²	1	4	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	1	yes	characteristic
75	C₇×#431	C₂²	1	1	yes	characteristic
76	C₇×#431	C₂²	1	2	yes	complemented
77	C₇×#431	C₂²	1	2	yes	complemented
78	C₇×#431	C₂²	1	2	yes	complemented
79	C₇×#424	C₂²	1	4	yes	complemented
80	C₇×#423	C₂²	1	2	yes	complemented
81	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
83	C₇×#408	C₂²	1	4	yes	complemented
84	C₇×#408	C₂²	1	4	yes	complemented
85	C₇×#408	C₂²	1	4	yes	complemented
86	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
87	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
88	C₇×#405	C₂²	1	4	yes	complemented
89	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
90	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
92	#60321	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	4	yes	—
96	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	2	yes	—
98	C₇×#131	—	4	8	no	—
99	C₂×C₇×M₁₆	—	4	4	no	—
100	C₂×C₇×M₁₆	C₂³	1	2	yes	—
101	C₂×C₇×M₁₆	C₂³	1	4	yes	—
102	C₂×C₇×M₁₆	C₂³	1	2	yes	—
103	C₂×C₇×M₁₆	C₂³	1	4	yes	—
104	C₂×C₇×M₁₆	C₂³	1	4	yes	—
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	2	yes	—
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	2	yes	—
109	C₂²×C₇×C₈	C₂³	1	4	yes	—
110	C₂²×C₇×C₈	C₂³	1	2	yes	—
111	C₂²×C₇×C₈	C₂³	1	4	yes	—
112	C₂²×C₇×C₈	C₂³	1	4	yes	—
113	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
114	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
115	C₇×#127	C₂×C₄	1	2	yes	—
116	C₇×#127	C₂×C₄	1	2	yes	—
117	C₇×#126	C₂×C₄	1	4	yes	—
118	C₇×#126	C₂×C₄	1	4	yes	—
119	C₇×#125	C₂×C₄	1	2	yes	—
120	C₇×#125	C₂×C₄	1	2	yes	—
121	C₇×#124	C₂×C₄	1	2	yes	—
122	C₇×#124	C₂×C₄	1	2	yes	—
123	C₇×#124	C₂×C₄	1	4	yes	—
124	C₇×#124	C₂×C₄	1	4	yes	—
125	C₇×#123	C₂×C₄	1	4	yes	—
126	C₇×#123	C₂×C₄	1	4	yes	—
127	C₇×#123	C₂×C₄	1	4	yes	—
128	C₇×#123	C₂×C₄	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
130	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
131	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
132	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
133	C₇×#121	C₂×C₄	1	4	yes	—
134	C₇×#121	C₂×C₄	1	4	yes	—
135	C₇×#121	C₂×C₄	1	2	yes	—
136	C₇×#121	C₂×C₄	1	2	yes	—
137	C₇×#121	C₂×C₄	1	2	yes	—
138	C₇×#121	C₂×C₄	1	2	yes	—
139	C₇×#121	C₂×C₄	1	2	yes	—
140	C₇×#121	C₂×C₄	1	2	yes	—
141	C₇×#121	C₂×C₄	1	4	yes	—
142	C₇×#121	C₂×C₄	1	4	yes	—
143	C₇×#120	C₂×C₄	1	4	yes	—
144	C₇×#120	C₂×C₄	1	4	yes	—
145	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
146	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
147	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
148	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
149	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
150	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
151	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
152	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
153	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
154	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
155	C₄×C₇×D₄	C₂³	1	2	yes	—
156	C₄×C₇×D₄	C₂³	1	2	yes	—
157	C₄×C₇×D₄	C₂³	1	2	yes	—
158	C₄×C₇×D₄	C₂³	1	2	yes	—
159	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
160	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
161	C₄×C₇×D₄	C₂³	1	4	yes	—
162	C₄×C₇×D₄	C₂³	1	4	yes	—
163	C₇×#117	C₂×C₄	1	1	yes	characteristic
164	C₇×#117	C₂×C₄	1	1	yes	characteristic
165	C₇×#117	C₂×C₄	1	2	yes	—
166	C₇×#117	C₂×C₄	1	2	yes	—
167	C₇×#117	C₂³	1	4	yes	—
168	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
169	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
170	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₇	C₂³	1	2	yes	—
173	C₇×C₄⋊C₈	C₂³	1	2	yes	—
174	C₇×C₄⋊C₈	C₂³	1	2	yes	—
175	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₈	C₂³	1	4	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	4	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	2	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	4	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	1	yes	characteristic
203	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
204	C₄×C₇×C₈	C₂³	1	2	yes	—
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	#3460	C₂×C₇	1	1	yes	characteristic
210	#2994	C₂×C₇	1	2	yes	complemented
211	#2993	C₂×C₇	1	2	yes	complemented
212	#2989	C₂×C₇	1	1	yes	characteristic, complemented
213	#2988	C₂×C₇	1	1	yes	characteristic, complemented
214	#2981	C₂×C₇	1	2	yes	complemented
215	#2979	C₂×C₇	1	2	yes	complemented
216	#2977	C₂×C₇	1	4	yes	complemented
217	#2972	C₂×C₇	1	1	yes	characteristic, 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	#2935	C₂×C₇	1	2	yes	complemented
223	#2933	C₂×C₇	1	4	yes	complemented
224	#2931	C₂×C₇	1	2	yes	complemented
225	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
226	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
227	C₇×#41	—	2	4	no	—
228	C₇×#41	—	2	4	no	—
229	C₇×#41	—	4	4	no	—
230	C₇×#41	—	4	4	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	4	yes	—
234	C₂×C₇×D₄	—	2	4	no	—
235	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
236	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
237	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
238	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
239	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
242	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
243	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
244	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
245	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
246	C₂²×C₄×C₇	—	4	2	no	—
247	C₂²×C₄×C₇	—	4	2	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	1	yes	characteristic
251	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
252	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
256	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
260	C₇×M₁₆	—	2	8	no	—
261	C₇×M₁₆	—	2	4	no	—
262	C₇×M₁₆	—	4	4	no	—
263	C₇×M₁₆	—	4	2	no	—
264	C₇×M₁₆	—	4	4	no	—
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	4	no	—
267	C₂×C₇×C₈	—	4	2	no	—
268	C₂×C₇×C₈	—	4	4	no	—
269	C₂×C₇×C₈	—	4	1	no	—
270	C₂×C₇×C₈	—	4	2	no	—
271	C₂×C₇×C₈	—	4	4	no	—
272	C₂×C₇×C₈	—	4	4	no	—
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×C₈	C₂⁴	1	2	yes	—
275	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	4	yes	—
281	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
282	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
283	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
284	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
285	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
286	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
287	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
288	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
289	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
290	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
291	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
292	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
293	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
294	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
295	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
296	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
297	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
298	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
299	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
300	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
301	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
302	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
303	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
304	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
305	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
306	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
307	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
308	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
309	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
310	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
317	C₄²×C₇	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇	C₂⁴	1	2	yes	—
319	C₄²×C₇	C₂⁴	1	2	yes	—
320	C₂×#131	C₂²×C₇	1	4	yes	complemented
321	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
322	#544	C₄×C₇	1	1	yes	characteristic
323	#542	C₄×C₇	1	2	yes	—
324	#542	C₄×C₇	1	2	yes	—
325	#540	C₄×C₇	1	2	yes	—
326	#540	C₄×C₇	1	2	yes	—
327	#538	C₄×C₇	1	4	yes	—
328	#537	C₄×C₇	1	1	yes	characteristic
329	#535	C₄×C₇	1	1	yes	characteristic
330	#535	C₄×C₇	1	1	yes	characteristic
331	#532	C₂²×C₇	1	2	yes	—
332	#532	C₂²×C₇	1	2	yes	—
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	1	yes	characteristic
339	#446	C₂²×C₇	1	1	yes	characteristic, complemented
340	#446	C₂²×C₇	1	1	yes	characteristic, complemented
341	#446	C₂²×C₇	1	2	yes	complemented
342	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
343	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
345	#436	C₂²×C₇	1	2	yes	—
346	#436	C₂²×C₇	1	2	yes	—
347	#436	C₂²×C₇	1	2	yes	—
348	#436	C₂²×C₇	1	2	yes	—
349	#436	C₂²×C₇	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
354	#435	C₂²×C₇	1	2	yes	—
355	#435	C₂²×C₇	1	4	yes	—
356	#435	C₂²×C₇	1	2	yes	—
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	C₈×D₄	C₂²×C₇	1	2	yes	—
362	C₈×D₄	C₂²×C₇	1	2	yes	—
363	C₈×D₄	C₂²×C₇	1	4	yes	—
364	C₈×D₄	C₂²×C₇	1	2	yes	—
365	C₈×D₄	C₂²×C₇	1	2	yes	—
366	C₈×D₄	C₂²×C₇	1	2	yes	—
367	C₈×D₄	C₂²×C₇	1	2	yes	—
368	C₈×D₄	C₂²×C₇	1	4	yes	complemented
369	C₈×D₄	C₂²×C₇	1	2	yes	complemented
370	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
371	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
372	C₈×D₄	C₂²×C₇	1	4	yes	complemented
373	#433	C₂²×C₇	1	4	yes	complemented
374	#433	C₂²×C₇	1	4	yes	complemented
375	#432	C₂²×C₇	1	2	yes	complemented
376	#431	C₂²×C₇	1	1	yes	characteristic
377	#431	C₂²×C₇	1	1	yes	characteristic
378	#431	C₂²×C₇	1	2	yes	complemented
379	#431	C₂²×C₇	1	2	yes	complemented
380	#431	C₂²×C₇	1	2	yes	complemented
381	#424	C₂²×C₇	1	4	yes	complemented
382	#423	C₂²×C₇	1	2	yes	complemented
383	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
385	#408	C₂²×C₇	1	4	yes	complemented
386	#408	C₂²×C₇	1	4	yes	complemented
387	#408	C₂²×C₇	1	4	yes	complemented
388	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
389	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
390	#405	C₂²×C₇	1	4	yes	complemented
391	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
392	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
394	C₂³×C₇	—	2	4	no	—
395	C₂³×C₇	—	4	2	no	—
396	C₂³×C₇	—	4	2	no	—
397	C₂³×C₇	C₂³×C₄	1	4	yes	—
398	C₂³×C₇	C₂³×C₄	1	2	yes	—
399	C₂³×C₇	C₂³×C₄	1	2	yes	—
400	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
401	C₇×Q₈	—	2	2	no	—
402	C₇×Q₈	—	2	2	no	—
403	C₇×Q₈	—	4	4	no	—
404	C₇×D₄	—	2	4	no	—
405	C₇×D₄	—	2	4	no	—
406	C₇×D₄	—	2	4	no	—
407	C₇×D₄	—	2	4	no	—
408	C₇×D₄	—	2	2	no	—
409	C₇×D₄	—	2	2	no	—
410	C₇×D₄	—	4	4	no	—
411	C₇×D₄	—	4	4	no	—
412	C₇×D₄	—	4	4	no	—
413	C₇×D₄	—	4	4	no	—
414	C₇×D₄	—	4	4	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	2	4	no	—
417	C₂×C₄×C₇	—	2	1	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	4	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	—	4	4	no	—
426	C₂×C₄×C₇	—	4	2	no	—
427	C₂×C₄×C₇	—	4	1	no	—
428	C₂×C₄×C₇	—	4	2	no	—
429	C₂×C₄×C₇	—	4	2	no	—
430	C₂×C₄×C₇	#131	1	4	yes	complemented
431	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
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	2	yes	—
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	4	yes	—
441	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
444	C₇×C₈	—	2	2	no	—
445	C₇×C₈	—	2	1	no	—
446	C₇×C₈	—	2	4	no	—
447	C₇×C₈	—	2	2	no	—
448	C₇×C₈	—	2	1	no	—
449	C₇×C₈	—	2	2	no	—
450	C₇×C₈	—	2	2	no	—
451	C₇×C₈	—	2	1	no	—
452	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
453	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
454	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
455	C₂×#41	C₂³×C₇	1	4	yes	—
456	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₇	1	2	yes	—
458	#131	—	4	8	no	—
459	C₂×M₁₆	—	4	4	no	—
460	C₂×M₁₆	C₂³×C₇	1	4	yes	—
461	C₂×M₁₆	C₂³×C₇	1	2	yes	—
462	C₂×M₁₆	C₂³×C₇	1	4	yes	—
463	C₂×M₁₆	C₂³×C₇	1	4	yes	—
464	C₂×M₁₆	C₂³×C₇	1	2	yes	—
465	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₇	1	2	yes	—
467	C₂²×C₈	C₂³×C₇	1	2	yes	—
468	C₂²×C₈	C₂³×C₇	1	4	yes	—
469	C₂²×C₈	C₂³×C₇	1	4	yes	—
470	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₇	1	2	yes	—
472	C₂²×C₈	C₂³×C₇	1	4	yes	—
473	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
474	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
475	#127	C₂×C₄×C₇	1	2	yes	—
476	#127	C₂×C₄×C₇	1	2	yes	—
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	4	yes	—
484	#124	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	#123	C₂×C₄×C₇	1	4	yes	—
489	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
490	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
491	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
492	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
493	#121	C₂×C₄×C₇	1	4	yes	—
494	#121	C₂×C₄×C₇	1	4	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	#121	C₂×C₄×C₇	1	2	yes	—
499	#121	C₂×C₄×C₇	1	2	yes	—
500	#121	C₂×C₄×C₇	1	2	yes	—
501	#121	C₂×C₄×C₇	1	4	yes	—
502	#121	C₂×C₄×C₇	1	4	yes	—
503	#120	C₂×C₄×C₇	1	4	yes	—
504	#120	C₂×C₄×C₇	1	4	yes	—
505	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
506	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
507	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
508	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
509	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
510	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
511	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
512	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
513	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
514	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
515	C₄×D₄	C₂³×C₇	1	2	yes	—
516	C₄×D₄	C₂³×C₇	1	2	yes	—
517	C₄×D₄	C₂³×C₇	1	2	yes	—
518	C₄×D₄	C₂³×C₇	1	2	yes	—
519	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
520	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
521	C₄×D₄	C₂³×C₇	1	4	yes	—
522	C₄×D₄	C₂³×C₇	1	4	yes	—
523	#117	C₂×C₄×C₇	1	1	yes	characteristic
524	#117	C₂×C₄×C₇	1	1	yes	characteristic
525	#117	C₂×C₄×C₇	1	2	yes	—
526	#117	C₂×C₄×C₇	1	2	yes	—
527	#117	C₂³×C₇	1	4	yes	—
528	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
530	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₇	1	2	yes	—
532	C₂×C₄²	C₂³×C₇	1	2	yes	—
533	C₄⋊C₈	C₂³×C₇	1	2	yes	—
534	C₄⋊C₈	C₂³×C₇	1	2	yes	—
535	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
536	C₄⋊C₈	C₂³×C₇	1	4	yes	—
537	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₇	1	4	yes	—
539	C₄⋊C₈	C₂³×C₇	1	2	yes	—
540	C₄⋊C₈	C₂³×C₇	1	2	yes	—
541	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₇	1	2	yes	—
544	C₄⋊C₈	C₂³×C₇	1	2	yes	—
545	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
546	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
547	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
549	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
556	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
557	#97	C₂³×C₇	1	2	yes	—
558	#97	C₂³×C₇	1	2	yes	—
559	#97	C₂³×C₇	1	4	yes	—
560	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×C₈	C₂³×C₇	1	2	yes	—
565	C₄×C₈	C₂³×C₇	1	2	yes	—
566	C₄×C₈	C₂³×C₇	1	2	yes	—
567	C₄×C₈	C₂³×C₇	1	2	yes	—
568	C₄×C₈	C₂³×C₇	1	4	yes	—
569	C₂²×C₇	—	2	1	no	—
570	C₂²×C₇	—	2	1	no	—
571	C₂²×C₇	—	2	4	no	—
572	C₂²×C₇	—	2	2	no	—
573	C₂²×C₇	—	2	2	no	—
574	C₂²×C₇	—	2	2	no	—
575	C₂²×C₇	—	2	2	no	—
576	C₂²×C₇	—	2	4	no	—
577	C₂²×C₇	—	2	2	no	—
578	C₂²×C₇	—	2	2	no	—
579	C₂²×C₇	—	2	4	no	—
580	C₂²×C₇	—	8	4	no	—
581	C₂²×C₇	C₂×#131	1	2	yes	—
582	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
583	C₄×C₇	—	2	1	no	—
584	C₄×C₇	—	2	4	no	—
585	C₄×C₇	—	2	2	no	—
586	C₄×C₇	—	2	2	no	—
587	C₄×C₇	—	2	2	no	—
588	C₄×C₇	—	2	2	no	—
589	C₄×C₇	—	2	1	no	—
590	C₄×C₇	—	2	1	no	—
591	C₄×C₇	—	2	2	no	—
592	C₄×C₇	—	2	2	no	—
593	C₄×C₇	C₂×#131	1	2	yes	—
594	C₄×C₇	C₂×#131	1	2	yes	—
595	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	C₄×C₇	#585	1	1	yes	characteristic
597	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
598	#41	—	2	4	no	—
599	#41	—	2	4	no	—
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
603	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
604	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
607	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
608	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
609	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
610	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
611	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
612	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
613	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
614	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
615	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
616	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
620	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
621	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
623	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
624	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
625	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
626	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
631	M₁₆	—	2	8	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	4	4	no	—
634	M₁₆	—	4	2	no	—
635	M₁₆	—	4	4	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	—	4	2	no	—
639	C₂×C₈	—	4	4	no	—
640	C₂×C₈	—	4	1	no	—
641	C₂×C₈	—	4	2	no	—
642	C₂×C₈	—	4	4	no	—
643	C₂×C₈	—	4	4	no	—
644	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
645	C₂×C₈	C₂⁴×C₇	1	2	yes	—
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	2	yes	—
650	C₂×C₈	C₂⁴×C₇	1	2	yes	—
651	C₂×C₈	C₂⁴×C₇	1	4	yes	—
652	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
653	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
654	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
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	1	yes	characteristic
660	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
661	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
662	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
663	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
664	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
665	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
666	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
667	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
668	C₂²⋊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	2	yes	—
672	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
673	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
674	C₂²⋊C₄	C₂²×C₄×C₇	1	2	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	4	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
681	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
682	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
683	C₄²	C₂²×C₄×C₇	1	2	yes	—
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	C₂⁴×C₇	1	1	yes	characteristic
688	C₄²	C₂⁴×C₇	1	1	yes	characteristic
689	C₄²	C₂⁴×C₇	1	2	yes	—
690	C₄²	C₂⁴×C₇	1	2	yes	—
691	C₂×C₇	—	2	2	no	—
692	C₂×C₇	—	4	2	no	—
693	C₂×C₇	—	4	2	no	—
694	C₂×C₇	—	4	4	no	—
695	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₇	C₂²×#131	1	1	yes	characteristic
697	C₂×C₇	#3573	1	1	yes	characteristic
698	C₂³	—	2	4	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	C₂³×C₄×C₇	1	4	yes	—
702	C₂³	C₂³×C₄×C₇	1	2	yes	—
703	C₂³	C₂³×C₄×C₇	1	2	yes	—
704	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	4	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	C₇×#131	1	4	yes	complemented
735	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
736	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
737	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
738	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
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	2	yes	—
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	4	yes	—
745	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
746	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
747	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
748	C₈	—	2	2	no	—
749	C₈	—	2	1	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	2	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₈	—	2	1	no	—
756	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
757	C₇	#60321	1	1	yes	characteristic, direct product factor, Sylow
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	8	4	no	—
770	C₂²	C₂×C₇×#131	1	2	yes	—
771	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	1	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	C₂×C₇×#131	1	2	yes	—
783	C₄	C₂×C₇×#131	1	2	yes	—
784	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
785	C₄	C₇×#585	1	1	yes	characteristic
786	C₂	—	2	2	no	—
787	C₂	—	4	4	no	—
788	C₂	—	4	2	no	—
789	C₂	—	4	2	no	—
790	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
791	C₂	C₂²×C₇×#131	1	1	yes	characteristic
792	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×#3460	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×#2989	C₂	semidirect
5. C₇×#2988	C₂	semidirect
6. C₇×#2981	C₂	semidirect
7. C₇×#2979	C₂	semidirect
8. C₇×#2977	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×#2935	C₂	semidirect
15. C₇×#2933	C₂	semidirect
16. C₇×#2931	C₂	semidirect
17. C₂×C₇×#436	C₂	semidirect
18. C₂×C₇×#131	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
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
55. C₇×#435	C₂²	semidirect
56. C₇×#435	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
58. C₇×#435	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
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
82. C₂×C₇×C₄⋊C₈	C₂²	semidirect
83. C₇×#408	C₂²	semidirect
84. C₇×#408	C₂²	semidirect
85. C₇×#408	C₂²	semidirect
88. C₇×#405	C₂²	semidirect
89. C₄×C₇×M₁₆	C₂²	semidirect
91. C₂×C₄×C₇×C₈	C₂²	semidirect
92. #60321	C₇	direct (N × H)
210. #2994	C₂×C₇	semidirect
211. #2993	C₂×C₇	semidirect
212. #2989	C₂×C₇	semidirect
213. #2988	C₂×C₇	semidirect
214. #2981	C₂×C₇	semidirect
215. #2979	C₂×C₇	semidirect
216. #2977	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. #2935	C₂×C₇	semidirect
223. #2933	C₂×C₇	semidirect
224. #2931	C₂×C₇	semidirect
225. C₂×#436	C₂×C₇	semidirect
320. C₂×#131	C₂²×C₇	semidirect
339. #446	C₂²×C₇	semidirect
340. #446	C₂²×C₇	semidirect
341. #446	C₂²×C₇	semidirect
342. C₈×Q₈	C₂²×C₇	semidirect
343. C₈×Q₈	C₂²×C₇	semidirect
344. 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
357. #435	C₂²×C₇	semidirect
358. #435	C₂²×C₇	semidirect
359. #435	C₂²×C₇	semidirect
360. #435	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. #433	C₂²×C₇	semidirect
374. #433	C₂²×C₇	semidirect
375. #432	C₂²×C₇	semidirect
378. #431	C₂²×C₇	semidirect
379. #431	C₂²×C₇	semidirect
380. #431	C₂²×C₇	semidirect
381. #424	C₂²×C₇	semidirect
382. #423	C₂²×C₇	semidirect
384. C₂×C₄⋊C₈	C₂²×C₇	semidirect
385. #408	C₂²×C₇	semidirect
386. #408	C₂²×C₇	semidirect
387. #408	C₂²×C₇	semidirect
390. #405	C₂²×C₇	semidirect
391. C₄×M₁₆	C₂²×C₇	semidirect
393. C₂×C₄×C₈	C₂²×C₇	semidirect
430. C₂×C₄×C₇	#131	semidirect
734. C₂×C₄	C₇×#131	semidirect
757. C₇	#60321	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×#3460	2
C₇×#2994	2
C₇×#2993	2
C₇×#2989	2
C₇×#2988	2
C₇×#2981	2
C₇×#2979	2
C₇×#2977	2
C₇×#2972	2
C₇×#2969	2
C₇×#2966	2
C₇×#2965	2
C₇×C₈×#41	2
C₇×#2935	2
C₇×#2933	2
C₇×#2931	2
C₂×C₇×#436	2
#60321	7

Subgroups — C7×#60321 #13237537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60321 #13237537