Subgroups — C₇×#60219 #13237435

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3480	C₂	1	1	yes	maximal, characteristic
2	C₇×#2970	C₂	1	2	yes	maximal, complemented
3	C₇×#2969	C₂	1	2	yes	maximal, complemented
4	C₇×#2968	C₂	1	4	yes	maximal, complemented
5	C₇×#2967	C₂	1	4	yes	maximal, complemented
6	C₇×#2966	C₂	1	2	yes	maximal, complemented
7	C₇×#2965	C₂	1	2	yes	maximal, complemented
8	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2935	C₂	1	2	yes	maximal, complemented
12	C₇×#2932	C₂	1	2	yes	maximal, complemented
13	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2925	C₂	1	2	yes	maximal, complemented
16	C₇×#2875	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#131	C₂²	1	2	yes	—
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂×C₇×#131	C₂²	1	1	yes	characteristic
21	C₂×C₇×#131	C₂²	1	2	yes	—
22	C₇×#559	C₄	1	1	yes	characteristic
23	C₇×#559	C₄	1	2	yes	—
24	C₇×#557	C₄	1	1	yes	characteristic
25	C₇×#556	C₄	1	1	yes	characteristic
26	C₇×#556	C₄	1	2	yes	—
27	C₇×#553	C₄	1	2	yes	—
28	C₇×#553	C₄	1	4	yes	—
29	C₇×#550	C₄	1	1	yes	characteristic
30	C₇×#548	C₄	1	2	yes	—
31	C₇×#532	C₂²	1	1	yes	characteristic
32	C₇×#532	C₂²	1	2	yes	—
33	C₇×#529	C₂²	1	2	yes	—
34	C₇×#529	C₂²	1	4	yes	—
35	C₄×C₇×#41	C₂²	1	2	yes	—
36	C₄×C₇×#41	C₂²	1	1	yes	characteristic
37	C₄×C₇×#41	C₂²	1	2	yes	—
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	C₇×#446	C₂²	1	1	yes	characteristic
40	C₇×#446	C₂²	1	1	yes	characteristic
41	C₇×#446	C₂²	1	2	yes	—
42	C₇×#446	C₂²	1	2	yes	—
43	C₇×#446	C₂²	1	1	yes	characteristic
44	C₇×#446	C₂²	1	1	yes	characteristic
45	C₇×#446	C₂²	1	2	yes	—
46	C₇×#446	C₂²	1	4	yes	—
47	C₇×C₈×Q₈	C₂²	1	2	yes	—
48	C₇×#436	C₂²	1	2	yes	—
49	C₇×#436	C₂²	1	2	yes	—
50	C₇×#436	C₂²	1	2	yes	—
51	C₇×#436	C₂²	1	4	yes	—
52	C₇×#435	C₂²	1	4	yes	—
53	C₇×#435	C₂²	1	4	yes	—
54	C₇×#435	C₂²	1	4	yes	—
55	C₇×#435	C₂²	1	4	yes	—
56	C₇×#435	C₂²	1	4	yes	—
57	C₇×#435	C₂²	1	4	yes	—
58	C₇×#435	C₂²	1	4	yes	—
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×#433	C₂²	1	4	yes	—
64	C₇×#433	C₂²	1	4	yes	—
65	C₇×#433	C₂²	1	4	yes	—
66	C₇×#432	C₂²	1	2	yes	—
67	C₇×#432	C₂²	1	4	yes	—
68	C₇×#431	C₂²	1	4	yes	—
69	C₇×#431	C₂²	1	2	yes	—
70	C₇×#423	C₂²	1	1	yes	characteristic
71	C₇×#423	C₂²	1	2	yes	—
72	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
73	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
74	C₇×#408	C₂²	1	2	yes	—
75	C₇×#408	C₂²	1	2	yes	—
76	C₇×#408	C₂²	1	2	yes	—
77	C₇×#405	C₂²	1	1	yes	characteristic
78	C₇×#405	C₂²	1	2	yes	—
79	C₇×#405	C₂²	1	4	yes	—
80	C₇×#405	C₂²	1	2	yes	—
81	C₇×#405	C₂²	1	2	yes	—
82	C₇×#405	C₂²	1	4	yes	—
83	C₇×#405	C₂²	1	1	yes	characteristic
84	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
85	C₄×C₇×M₁₆	C₂²	1	2	yes	—
86	C₄×C₇×M₁₆	C₂²	1	4	yes	—
87	C₄×C₇×M₁₆	C₂²	1	2	yes	—
88	C₂×C₇×#97	C₂²	1	2	yes	—
89	C₂×C₇×#97	C₂²	1	4	yes	—
90	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
92	#60219	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₇×#41	C₂×C₄	1	2	yes	—
94	C₂×C₇×#41	C₂³	1	1	yes	characteristic
95	C₂×C₇×#41	C₂³	1	2	yes	—
96	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
97	C₇×#131	—	2	4	no	—
98	C₇×#131	—	2	8	no	—
99	C₇×#131	—	2	8	no	—
100	C₇×#131	—	2	4	no	—
101	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₇×M₁₆	C₂³	1	2	yes	—
103	C₂×C₇×M₁₆	C₂³	1	2	yes	—
104	C₂×C₇×M₁₆	C₂³	1	4	yes	—
105	C₂×C₇×M₁₆	C₂³	1	4	yes	—
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	2	yes	—
110	C₂²×C₇×C₈	C₂³	1	2	yes	—
111	C₂²×C₇×C₈	C₂³	1	2	yes	—
112	C₂²×C₇×C₈	C₂³	1	4	yes	—
113	C₂²×C₇×C₈	C₂³	1	4	yes	—
114	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
117	C₇×#127	C₂×C₄	1	1	yes	characteristic
118	C₇×#127	C₂×C₄	1	2	yes	—
119	C₇×#126	C₂×C₄	1	4	yes	—
120	C₇×#126	C₂×C₄	1	4	yes	—
121	C₇×#126	C₂×C₄	1	4	yes	—
122	C₇×#125	C₂×C₄	1	2	yes	—
123	C₇×#125	C₂×C₄	1	4	yes	—
124	C₇×#124	C₂×C₄	1	2	yes	—
125	C₇×#124	C₂×C₄	1	4	yes	—
126	C₇×#124	C₂×C₄	1	2	yes	—
127	C₇×#124	C₂×C₄	1	2	yes	—
128	C₇×#124	C₂×C₄	1	2	yes	—
129	C₇×#123	C₂×C₄	1	4	yes	—
130	C₇×#123	C₂×C₄	1	4	yes	—
131	C₇×#123	C₂×C₄	1	4	yes	—
132	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
133	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
134	C₇×#121	C₂×C₄	1	2	yes	—
135	C₇×#121	C₂×C₄	1	4	yes	—
136	C₇×#121	C₂×C₄	1	2	yes	—
137	C₇×#121	C₂×C₄	1	4	yes	—
138	C₇×#121	C₂×C₄	1	2	yes	—
139	C₇×#121	C₂×C₄	1	4	yes	—
140	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
142	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
143	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
144	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
145	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
146	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
147	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
148	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
149	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
150	C₄×C₇×Q₈	C₂³	1	2	yes	—
151	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
152	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
153	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
154	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
155	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
156	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
157	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
158	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
159	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
160	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
161	C₄×C₇×D₄	C₂³	1	2	yes	—
162	C₄×C₇×D₄	C₂³	1	4	yes	—
163	C₄×C₇×D₄	C₂³	1	4	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₇×#117	C₂×C₄	1	2	yes	—
166	C₇×#117	C₂×C₄	1	4	yes	—
167	C₇×#117	C₂³	1	1	yes	characteristic
168	C₇×#117	C₂³	1	2	yes	—
169	C₇×#117	C₂³	1	4	yes	—
170	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
171	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
172	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₇	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	1	yes	characteristic
179	C₇×C₄⋊C₈	C₂³	1	2	yes	—
180	C₇×C₄⋊C₈	C₂³	1	2	yes	—
181	C₇×C₄⋊C₈	C₂³	1	2	yes	—
182	C₇×C₄⋊C₈	C₂³	1	2	yes	—
183	C₇×C₄⋊C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊C₈	C₂³	1	4	yes	—
185	C₇×C₄⋊C₈	C₂³	1	2	yes	—
186	C₇×C₄⋊C₈	C₂³	1	4	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	4	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₇×#97	C₂³	1	2	yes	—
195	C₇×#97	C₂³	1	2	yes	—
196	C₇×#97	C₂³	1	4	yes	—
197	C₇×#97	C₂³	1	4	yes	—
198	C₇×#97	C₂³	1	2	yes	—
199	C₇×#97	C₂³	1	2	yes	—
200	C₇×#97	C₂³	1	2	yes	—
201	C₇×#97	C₂³	1	2	yes	—
202	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
203	C₄×C₇×C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
208	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
209	C₄×C₇×C₈	C₂³	1	4	yes	—
210	C₄×C₇×C₈	C₂³	1	4	yes	—
211	#3480	C₂×C₇	1	1	yes	characteristic
212	#2970	C₂×C₇	1	2	yes	complemented
213	#2969	C₂×C₇	1	2	yes	complemented
214	#2968	C₂×C₇	1	4	yes	complemented
215	#2967	C₂×C₇	1	4	yes	complemented
216	#2966	C₂×C₇	1	2	yes	complemented
217	#2965	C₂×C₇	1	2	yes	complemented
218	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
219	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
220	#2935	C₂×C₇	1	1	yes	characteristic, complemented
221	#2935	C₂×C₇	1	2	yes	complemented
222	#2932	C₂×C₇	1	2	yes	complemented
223	#2931	C₂×C₇	1	1	yes	characteristic, complemented
224	#2925	C₂×C₇	1	1	yes	characteristic, complemented
225	#2925	C₂×C₇	1	2	yes	complemented
226	#2875	C₂×C₇	1	2	yes	complemented
227	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
228	C₇×#41	—	2	2	no	—
229	C₇×#41	—	2	4	no	—
230	C₇×#41	—	2	4	no	—
231	C₇×#41	—	2	2	no	—
232	C₇×#41	—	4	4	no	—
233	C₂×C₇×Q₈	—	4	2	no	—
234	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
237	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
239	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
240	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
241	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
242	C₂×C₇×D₄	C₂²×C₄	1	2	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	4	yes	—
246	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
247	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
249	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
251	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
252	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
254	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
258	C₇×M₁₆	—	2	2	no	—
259	C₇×M₁₆	—	2	4	no	—
260	C₇×M₁₆	—	2	4	no	—
261	C₇×M₁₆	—	2	8	no	—
262	C₇×M₁₆	—	2	4	no	—
263	C₇×M₁₆	—	2	8	no	—
264	C₇×M₁₆	#41	1	4	yes	complemented
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	4	no	—
267	C₂×C₇×C₈	—	2	4	no	—
268	C₂×C₇×C₈	—	2	8	no	—
269	C₂×C₇×C₈	—	2	8	no	—
270	C₂×C₇×C₈	—	2	4	no	—
271	C₂×C₇×C₈	#41	1	4	yes	complemented
272	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×C₈	C₂⁴	1	2	yes	—
275	C₂×C₇×C₈	C₂⁴	1	2	yes	—
276	C₂×C₇×C₈	C₂⁴	1	4	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₂×C₇×C₈	C₂⁴	1	2	yes	—
279	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
280	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
281	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
282	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
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	4	yes	—
289	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
290	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
292	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
293	C₇×C₄⋊C₄	C₂²×C₄	1	4	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×C₄⋊C₄	C₂²×C₄	1	2	yes	—
298	C₇×C₂²⋊C₄	C₂²×C₄	1	4	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	2	yes	—
302	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
303	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
304	C₇×C₂²⋊C₄	C₂²×C₄	1	2	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	C₄²×C₇	C₂²×C₄	1	2	yes	—
310	C₄²×C₇	C₂²×C₄	1	4	yes	—
311	C₄²×C₇	C₂²×C₄	1	4	yes	—
312	C₄²×C₇	C₂²×C₄	1	2	yes	—
313	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
318	C₄²×C₇	C₂⁴	1	1	yes	characteristic
319	C₄²×C₇	C₂⁴	1	1	yes	characteristic
320	C₄²×C₇	C₂⁴	1	2	yes	—
321	C₄²×C₇	C₂⁴	1	2	yes	—
322	C₂×#131	C₂²×C₇	1	1	yes	characteristic
323	C₂×#131	C₂²×C₇	1	1	yes	characteristic
324	C₂×#131	C₂²×C₇	1	2	yes	—
325	C₂×#131	C₂²×C₇	1	2	yes	—
326	#559	C₄×C₇	1	1	yes	characteristic
327	#559	C₄×C₇	1	2	yes	—
328	#557	C₄×C₇	1	1	yes	characteristic
329	#556	C₄×C₇	1	1	yes	characteristic
330	#556	C₄×C₇	1	2	yes	—
331	#553	C₄×C₇	1	2	yes	—
332	#553	C₄×C₇	1	4	yes	—
333	#550	C₄×C₇	1	1	yes	characteristic
334	#548	C₄×C₇	1	2	yes	—
335	#532	C₂²×C₇	1	1	yes	characteristic
336	#532	C₂²×C₇	1	2	yes	—
337	#529	C₂²×C₇	1	2	yes	—
338	#529	C₂²×C₇	1	4	yes	—
339	C₄×#41	C₂²×C₇	1	2	yes	—
340	C₄×#41	C₂²×C₇	1	1	yes	characteristic
341	C₄×#41	C₂²×C₇	1	2	yes	—
342	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
343	#446	C₂²×C₇	1	1	yes	characteristic
344	#446	C₂²×C₇	1	1	yes	characteristic
345	#446	C₂²×C₇	1	2	yes	—
346	#446	C₂²×C₇	1	2	yes	—
347	#446	C₂²×C₇	1	1	yes	characteristic
348	#446	C₂²×C₇	1	1	yes	characteristic
349	#446	C₂²×C₇	1	2	yes	—
350	#446	C₂²×C₇	1	4	yes	—
351	C₈×Q₈	C₂²×C₇	1	2	yes	—
352	#436	C₂²×C₇	1	2	yes	—
353	#436	C₂²×C₇	1	2	yes	—
354	#436	C₂²×C₇	1	2	yes	—
355	#436	C₂²×C₇	1	4	yes	—
356	#435	C₂²×C₇	1	4	yes	—
357	#435	C₂²×C₇	1	4	yes	—
358	#435	C₂²×C₇	1	4	yes	—
359	#435	C₂²×C₇	1	4	yes	—
360	#435	C₂²×C₇	1	4	yes	—
361	#435	C₂²×C₇	1	4	yes	—
362	#435	C₂²×C₇	1	4	yes	—
363	C₈×D₄	C₂²×C₇	1	2	yes	—
364	C₈×D₄	C₂²×C₇	1	2	yes	—
365	C₈×D₄	C₂²×C₇	1	4	yes	—
366	C₈×D₄	C₂²×C₇	1	2	yes	—
367	#433	C₂²×C₇	1	4	yes	—
368	#433	C₂²×C₇	1	4	yes	—
369	#433	C₂²×C₇	1	4	yes	—
370	#432	C₂²×C₇	1	2	yes	—
371	#432	C₂²×C₇	1	4	yes	—
372	#431	C₂²×C₇	1	4	yes	—
373	#431	C₂²×C₇	1	2	yes	—
374	#423	C₂²×C₇	1	1	yes	characteristic
375	#423	C₂²×C₇	1	2	yes	—
376	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
377	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
378	#408	C₂²×C₇	1	2	yes	—
379	#408	C₂²×C₇	1	2	yes	—
380	#408	C₂²×C₇	1	2	yes	—
381	#405	C₂²×C₇	1	1	yes	characteristic
382	#405	C₂²×C₇	1	1	yes	characteristic
383	#405	C₂²×C₇	1	2	yes	—
384	#405	C₂²×C₇	1	2	yes	—
385	#405	C₂²×C₇	1	2	yes	—
386	#405	C₂²×C₇	1	4	yes	—
387	#405	C₂²×C₇	1	4	yes	—
388	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
389	C₄×M₁₆	C₂²×C₇	1	2	yes	—
390	C₄×M₁₆	C₂²×C₇	1	2	yes	—
391	C₄×M₁₆	C₂²×C₇	1	4	yes	—
392	C₂×#97	C₂²×C₇	1	2	yes	—
393	C₂×#97	C₂²×C₇	1	4	yes	—
394	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
395	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
396	C₂³×C₇	C₂³×C₄	1	2	yes	—
397	C₂³×C₇	C₂³×C₄	1	4	yes	—
398	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
399	C₇×Q₈	—	2	2	no	—
400	C₇×Q₈	—	2	4	no	—
401	C₇×Q₈	—	2	2	no	—
402	C₇×Q₈	—	2	2	no	—
403	C₇×Q₈	—	4	2	no	—
404	C₇×D₄	—	2	4	no	—
405	C₇×D₄	—	2	8	no	—
406	C₇×D₄	—	2	2	no	—
407	C₇×D₄	—	2	4	no	—
408	C₇×D₄	—	2	4	no	—
409	C₇×D₄	—	4	4	no	—
410	C₇×D₄	—	4	2	no	—
411	C₇×D₄	—	4	4	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	2	no	—
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	—	4	2	no	—
419	C₂×C₄×C₇	—	4	4	no	—
420	C₂×C₄×C₇	—	4	1	no	—
421	C₂×C₄×C₇	—	4	2	no	—
422	C₂×C₄×C₇	—	4	2	no	—
423	C₂×C₄×C₇	—	4	4	no	—
424	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
426	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
427	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
428	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
431	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
432	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
433	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
434	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
435	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
437	C₂×C₄×C₇	C₂×#41	1	2	yes	—
438	C₂×C₄×C₇	C₂×#41	1	2	yes	—
439	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
440	C₇×C₈	—	2	1	no	—
441	C₇×C₈	—	2	2	no	—
442	C₇×C₈	—	2	1	no	—
443	C₇×C₈	—	2	2	no	—
444	C₇×C₈	—	2	4	no	—
445	C₇×C₈	—	2	2	no	—
446	C₇×C₈	C₂×#41	1	2	yes	—
447	C₇×C₈	C₂×#41	1	4	yes	—
448	C₇×C₈	C₂×#41	1	2	yes	—
449	C₂×#41	C₂×C₄×C₇	1	2	yes	—
450	C₂×#41	C₂³×C₇	1	1	yes	characteristic
451	C₂×#41	C₂³×C₇	1	2	yes	—
452	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
453	#131	—	2	4	no	—
454	#131	—	2	8	no	—
455	#131	—	2	4	no	—
456	#131	—	2	8	no	—
457	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
458	C₂×M₁₆	C₂³×C₇	1	2	yes	—
459	C₂×M₁₆	C₂³×C₇	1	2	yes	—
460	C₂×M₁₆	C₂³×C₇	1	2	yes	—
461	C₂×M₁₆	C₂³×C₇	1	4	yes	—
462	C₂×M₁₆	C₂³×C₇	1	4	yes	—
463	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₇	1	2	yes	—
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	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
472	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
473	#127	C₂×C₄×C₇	1	1	yes	characteristic
474	#127	C₂×C₄×C₇	1	2	yes	—
475	#126	C₂×C₄×C₇	1	4	yes	—
476	#126	C₂×C₄×C₇	1	4	yes	—
477	#126	C₂×C₄×C₇	1	4	yes	—
478	#125	C₂×C₄×C₇	1	2	yes	—
479	#125	C₂×C₄×C₇	1	4	yes	—
480	#124	C₂×C₄×C₇	1	2	yes	—
481	#124	C₂×C₄×C₇	1	4	yes	—
482	#124	C₂×C₄×C₇	1	2	yes	—
483	#124	C₂×C₄×C₇	1	2	yes	—
484	#124	C₂×C₄×C₇	1	2	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	2	yes	—
489	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
490	#121	C₂×C₄×C₇	1	2	yes	—
491	#121	C₂×C₄×C₇	1	4	yes	—
492	#121	C₂×C₄×C₇	1	2	yes	—
493	#121	C₂×C₄×C₇	1	4	yes	—
494	#121	C₂×C₄×C₇	1	2	yes	—
495	#121	C₂×C₄×C₇	1	4	yes	—
496	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
497	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
498	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
499	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
500	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
501	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
502	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
503	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
504	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
505	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₇	1	2	yes	—
507	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
508	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
509	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
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	4	yes	—
513	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
514	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
515	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
516	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
517	C₄×D₄	C₂³×C₇	1	2	yes	—
518	C₄×D₄	C₂³×C₇	1	4	yes	—
519	C₄×D₄	C₂³×C₇	1	4	yes	—
520	C₄×D₄	C₂³×C₇	1	2	yes	—
521	#117	C₂×C₄×C₇	1	2	yes	—
522	#117	C₂×C₄×C₇	1	4	yes	—
523	#117	C₂³×C₇	1	1	yes	characteristic
524	#117	C₂³×C₇	1	2	yes	—
525	#117	C₂³×C₇	1	4	yes	—
526	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
528	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₇	1	2	yes	—
530	C₂×C₄²	C₂³×C₇	1	2	yes	—
531	C₂×C₄²	C₂³×C₇	1	4	yes	—
532	C₄⋊C₈	C₂³×C₇	1	2	yes	—
533	C₄⋊C₈	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	2	yes	—
537	C₄⋊C₈	C₂³×C₇	1	2	yes	—
538	C₄⋊C₈	C₂³×C₇	1	2	yes	—
539	C₄⋊C₈	C₂³×C₇	1	2	yes	—
540	C₄⋊C₈	C₂³×C₇	1	4	yes	—
541	C₄⋊C₈	C₂³×C₇	1	2	yes	—
542	C₄⋊C₈	C₂³×C₇	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
546	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
547	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
549	#97	C₂³×C₇	1	2	yes	—
550	#97	C₂³×C₇	1	2	yes	—
551	#97	C₂³×C₇	1	2	yes	—
552	#97	C₂³×C₇	1	4	yes	—
553	#97	C₂³×C₇	1	4	yes	—
554	#97	C₂³×C₇	1	2	yes	—
555	#97	C₂³×C₇	1	2	yes	—
556	#97	C₂³×C₇	1	2	yes	—
557	#97	C₂³×C₇	1	2	yes	—
558	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₇	1	2	yes	—
560	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₇	1	2	yes	—
562	C₄×C₈	C₂³×C₇	1	2	yes	—
563	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₇	1	4	yes	—
566	C₄×C₈	C₂³×C₇	1	4	yes	—
567	C₂²×C₇	—	2	1	no	—
568	C₂²×C₇	—	2	1	no	—
569	C₂²×C₇	—	2	2	no	—
570	C₂²×C₇	—	2	4	no	—
571	C₂²×C₇	—	2	2	no	—
572	C₂²×C₇	—	2	4	no	—
573	C₂²×C₇	—	2	2	no	—
574	C₂²×C₇	—	2	4	no	—
575	C₂²×C₇	C₄×#41	1	2	yes	—
576	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
577	C₄×C₇	—	2	2	no	—
578	C₄×C₇	—	2	4	no	—
579	C₄×C₇	—	2	2	no	—
580	C₄×C₇	—	2	1	no	—
581	C₄×C₇	—	2	2	no	—
582	C₄×C₇	—	2	2	no	—
583	C₄×C₇	—	2	2	no	—
584	C₄×C₇	—	2	1	no	—
585	C₄×C₇	—	2	2	no	—
586	C₄×C₇	—	2	1	no	—
587	C₄×C₇	—	2	2	no	—
588	C₄×C₇	C₄×#41	1	2	yes	—
589	C₄×C₇	#568	1	2	yes	—
590	C₄×C₇	C₂²×#41	1	1	yes	characteristic
591	C₄×C₇	C₂²×#41	1	1	yes	characteristic
592	#41	—	2	2	no	—
593	#41	—	2	4	no	—
594	#41	—	2	2	no	—
595	#41	—	2	4	no	—
596	#41	—	4	4	no	—
597	C₂×Q₈	—	4	2	no	—
598	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
599	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
600	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
601	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
602	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
603	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
604	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
605	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	4	yes	—
609	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
610	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
611	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
612	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
613	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
614	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
615	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
616	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
617	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
618	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
622	M₁₆	—	2	2	no	—
623	M₁₆	—	2	4	no	—
624	M₁₆	—	2	4	no	—
625	M₁₆	—	2	4	no	—
626	M₁₆	—	2	8	no	—
627	M₁₆	—	2	8	no	—
628	M₁₆	C₇×#41	1	4	yes	complemented
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	4	no	—
631	C₂×C₈	—	2	4	no	—
632	C₂×C₈	—	2	8	no	—
633	C₂×C₈	—	2	8	no	—
634	C₂×C₈	—	2	4	no	—
635	C₂×C₈	C₇×#41	1	4	yes	complemented
636	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
637	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
638	C₂×C₈	C₂⁴×C₇	1	2	yes	—
639	C₂×C₈	C₂⁴×C₇	1	2	yes	—
640	C₂×C₈	C₂⁴×C₇	1	4	yes	—
641	C₂×C₈	C₂⁴×C₇	1	2	yes	—
642	C₂×C₈	C₂⁴×C₇	1	2	yes	—
643	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
644	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
645	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
646	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
647	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
648	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
649	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
650	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
651	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
652	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
653	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
654	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
655	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
656	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
657	C₄⋊C₄	C₂²×C₄×C₇	1	4	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	2	yes	—
662	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
663	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
664	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
665	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
666	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
667	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
668	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
669	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
670	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
671	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
672	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
673	C₄²	C₂²×C₄×C₇	1	2	yes	—
674	C₄²	C₂²×C₄×C₇	1	4	yes	—
675	C₄²	C₂²×C₄×C₇	1	4	yes	—
676	C₄²	C₂²×C₄×C₇	1	2	yes	—
677	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
678	C₄²	C₂²×C₄×C₇	1	2	yes	—
679	C₄²	C₂²×C₄×C₇	1	2	yes	—
680	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
681	C₄²	C₂⁴×C₇	1	2	yes	—
682	C₄²	C₂⁴×C₇	1	1	yes	characteristic
683	C₄²	C₂⁴×C₇	1	1	yes	characteristic
684	C₄²	C₂⁴×C₇	1	2	yes	—
685	C₄²	C₂⁴×C₇	1	2	yes	—
686	C₂×C₇	—	2	2	no	—
687	C₂×C₇	—	4	2	no	—
688	C₂×C₇	—	4	4	no	—
689	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
690	C₂×C₇	C₂×#568	1	1	yes	characteristic
691	C₂×C₇	#3573	1	1	yes	characteristic
692	C₂³	C₂³×C₄×C₇	1	2	yes	—
693	C₂³	C₂³×C₄×C₇	1	4	yes	—
694	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	4	2	no	—
700	D₄	—	2	4	no	—
701	D₄	—	2	8	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	4	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
721	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
722	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
723	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
724	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
726	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
727	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
728	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
729	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
730	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
731	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
732	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
733	C₂×C₄	C₂×C₇×#41	1	2	yes	—
734	C₂×C₄	C₂×C₇×#41	1	2	yes	—
735	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
736	C₈	—	2	1	no	—
737	C₈	—	2	2	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	4	no	—
741	C₈	—	2	2	no	—
742	C₈	C₂×C₇×#41	1	2	yes	—
743	C₈	C₂×C₇×#41	1	4	yes	—
744	C₈	C₂×C₇×#41	1	2	yes	—
745	C₇	#60219	1	1	yes	characteristic, direct product factor, Sylow
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	C₄×C₇×#41	1	2	yes	—
755	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	4	no	—
767	C₄	C₄×C₇×#41	1	2	yes	—
768	C₄	C₇×#568	1	2	yes	—
769	C₄	C₂²×C₇×#41	1	1	yes	characteristic
770	C₄	C₂²×C₇×#41	1	1	yes	characteristic
771	C₂	—	2	2	no	—
772	C₂	—	4	2	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
775	C₂	C₂×C₇×#568	1	1	yes	characteristic
776	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×#3480	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×#2970	C₂	semidirect
3. C₇×#2969	C₂	semidirect
4. C₇×#2968	C₂	semidirect
5. C₇×#2967	C₂	semidirect
6. C₇×#2966	C₂	semidirect
7. C₇×#2965	C₂	semidirect
8. C₇×Q₈×M₁₆	C₂	semidirect
9. C₂×C₇×#446	C₂	semidirect
10. C₇×#2935	C₂	semidirect
11. C₇×#2935	C₂	semidirect
12. C₇×#2932	C₂	semidirect
13. C₇×#2931	C₂	semidirect
14. C₇×#2925	C₂	semidirect
15. C₇×#2925	C₂	semidirect
16. C₇×#2875	C₂	semidirect
17. C₄×C₇×#131	C₂	semidirect
92. #60219	C₇	direct (N × H)
212. #2970	C₂×C₇	semidirect
213. #2969	C₂×C₇	semidirect
214. #2968	C₂×C₇	semidirect
215. #2967	C₂×C₇	semidirect
216. #2966	C₂×C₇	semidirect
217. #2965	C₂×C₇	semidirect
218. Q₈×M₁₆	C₂×C₇	semidirect
219. C₂×#446	C₂×C₇	semidirect
220. #2935	C₂×C₇	semidirect
221. #2935	C₂×C₇	semidirect
222. #2932	C₂×C₇	semidirect
223. #2931	C₂×C₇	semidirect
224. #2925	C₂×C₇	semidirect
225. #2925	C₂×C₇	semidirect
226. #2875	C₂×C₇	semidirect
227. C₄×#131	C₂×C₇	semidirect
264. C₇×M₁₆	#41	semidirect
271. C₂×C₇×C₈	#41	semidirect
628. M₁₆	C₇×#41	semidirect
635. C₂×C₈	C₇×#41	semidirect
745. C₇	#60219	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×#3480	2
C₇×#2970	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×#2966	2
C₇×#2965	2
C₇×Q₈×M₁₆	2
C₂×C₇×#446	2
C₇×#2935	2
C₇×#2932	2
C₇×#2931	2
C₇×#2925	2
C₇×#2875	2
C₄×C₇×#131	2
#60219	7

Subgroups — C7×#60219 #13237435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60219 #13237435