Subgroups — C₇×#60275 #13237491

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 772 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×#2995	C₂	1	4	yes	maximal, complemented
3	C₇×#2994	C₂	1	2	yes	maximal, complemented
4	C₇×#2993	C₂	1	2	yes	maximal, complemented
5	C₇×#2992	C₂	1	4	yes	maximal, complemented
6	C₇×#2990	C₂	1	2	yes	maximal, complemented
7	C₇×#2989	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×#2923	C₂	1	2	yes	maximal, complemented
15	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2906	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#131	C₂²	1	2	yes	—
19	C₂×C₇×#131	C₂²	1	2	yes	—
20	C₂×C₇×#131	C₂²	1	2	yes	—
21	C₇×#559	C₄	1	1	yes	characteristic
22	C₇×#559	C₄	1	2	yes	—
23	C₇×#557	C₄	1	1	yes	characteristic
24	C₇×#556	C₄	1	1	yes	characteristic
25	C₇×#556	C₄	1	2	yes	—
26	C₇×#553	C₄	1	2	yes	—
27	C₇×#553	C₄	1	4	yes	—
28	C₇×#550	C₄	1	1	yes	characteristic
29	C₇×#548	C₄	1	2	yes	—
30	C₇×#532	C₂²	1	1	yes	characteristic
31	C₇×#532	C₂²	1	2	yes	—
32	C₇×#529	C₂²	1	4	yes	—
33	C₇×#529	C₂²	1	2	yes	—
34	C₄×C₇×#41	C₂²	1	2	yes	—
35	C₄×C₇×#41	C₂²	1	1	yes	characteristic
36	C₄×C₇×#41	C₂²	1	2	yes	—
37	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
38	C₇×#446	C₂²	1	1	yes	characteristic
39	C₇×#446	C₂²	1	1	yes	characteristic
40	C₇×#446	C₂²	1	2	yes	—
41	C₇×#446	C₂²	1	1	yes	characteristic
42	C₇×#446	C₂²	1	1	yes	characteristic
43	C₇×#446	C₂²	1	2	yes	—
44	C₇×#446	C₂²	1	2	yes	—
45	C₇×#446	C₂²	1	4	yes	—
46	C₇×C₈×Q₈	C₂²	1	2	yes	—
47	C₇×#436	C₂²	1	2	yes	—
48	C₇×#436	C₂²	1	2	yes	—
49	C₇×#436	C₂²	1	2	yes	—
50	C₇×#436	C₂²	1	4	yes	—
51	C₇×#435	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×C₈×D₄	C₂²	1	2	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×#433	C₂²	1	2	yes	—
63	C₇×#433	C₂²	1	2	yes	—
64	C₇×#433	C₂²	1	4	yes	—
65	C₇×#433	C₂²	1	4	yes	—
66	C₇×#432	C₂²	1	4	yes	—
67	C₇×#432	C₂²	1	4	yes	—
68	C₇×#431	C₂²	1	2	yes	—
69	C₇×#431	C₂²	1	2	yes	—
70	C₇×#424	C₂²	1	1	yes	characteristic
71	C₇×#424	C₂²	1	2	yes	—
72	C₇×#424	C₂²	1	4	yes	—
73	C₇×#424	C₂²	1	4	yes	—
74	C₇×#424	C₂²	1	4	yes	—
75	C₇×#424	C₂²	1	1	yes	characteristic
76	C₇×#423	C₂²	1	1	yes	characteristic
77	C₇×#423	C₂²	1	2	yes	—
78	C₇×#423	C₂²	1	4	yes	—
79	C₇×#423	C₂²	1	2	yes	—
80	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
81	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
83	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
84	C₇×#408	C₂²	1	1	yes	characteristic
85	C₇×#408	C₂²	1	1	yes	characteristic
86	C₇×#408	C₂²	1	2	yes	—
87	C₇×#408	C₂²	1	2	yes	—
88	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
89	C₄×C₇×M₁₆	C₂²	1	2	yes	—
90	C₂×C₇×#97	C₂²	1	2	yes	—
91	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
92	#60275	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	—	4	4	no	—
98	C₇×#131	—	4	4	no	—
99	C₇×#131	—	4	4	no	—
100	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
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	C₂×C₇×M₁₆	C₂³	1	4	yes	—
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	4	yes	—
111	C₂²×C₇×C₈	C₂³	1	4	yes	—
112	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
114	C₇×#127	C₂×C₄	1	1	yes	characteristic
115	C₇×#127	C₂×C₄	1	2	yes	—
116	C₇×#126	C₂×C₄	1	4	yes	—
117	C₇×#126	C₂×C₄	1	4	yes	—
118	C₇×#126	C₂×C₄	1	4	yes	—
119	C₇×#125	C₂×C₄	1	4	yes	—
120	C₇×#125	C₂×C₄	1	2	yes	—
121	C₇×#124	C₂×C₄	1	2	yes	—
122	C₇×#124	C₂×C₄	1	4	yes	—
123	C₇×#124	C₂×C₄	1	2	yes	—
124	C₇×#124	C₂×C₄	1	2	yes	—
125	C₇×#124	C₂×C₄	1	2	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	2	yes	—
130	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
131	C₇×#121	C₂×C₄	1	2	yes	—
132	C₇×#121	C₂×C₄	1	4	yes	—
133	C₇×#121	C₂×C₄	1	2	yes	—
134	C₇×#121	C₂×C₄	1	4	yes	—
135	C₇×#121	C₂×C₄	1	2	yes	—
136	C₇×#121	C₂×C₄	1	4	yes	—
137	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
138	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
139	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
140	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
144	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
145	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
146	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
147	C₄×C₇×Q₈	C₂³	1	2	yes	—
148	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
149	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	4	yes	—
154	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
155	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
156	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
157	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
158	C₄×C₇×D₄	C₂³	1	2	yes	—
159	C₄×C₇×D₄	C₂³	1	4	yes	—
160	C₄×C₇×D₄	C₂³	1	2	yes	—
161	C₄×C₇×D₄	C₂³	1	4	yes	—
162	C₇×#117	C₂×C₄	1	2	yes	—
163	C₇×#117	C₂×C₄	1	4	yes	—
164	C₇×#117	C₂³	1	1	yes	characteristic
165	C₇×#117	C₂³	1	2	yes	—
166	C₇×#117	C₂³	1	4	yes	—
167	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
169	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₇	C₂³	1	4	yes	—
173	C₇×C₄⋊C₈	C₂³	1	2	yes	—
174	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₇×C₄⋊C₈	C₂³	1	2	yes	—
176	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₈	C₂³	1	2	yes	—
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×C₄⋊C₈	C₂³	1	4	yes	—
180	C₇×C₄⋊C₈	C₂³	1	4	yes	—
181	C₇×C₄⋊C₈	C₂³	1	4	yes	—
182	C₇×C₄⋊C₈	C₂³	1	2	yes	—
183	C₇×C₄⋊C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊C₈	C₂³	1	2	yes	—
185	C₇×C₄⋊C₈	C₂³	1	2	yes	—
186	C₇×C₄⋊C₈	C₂³	1	2	yes	—
187	C₇×C₄⋊C₈	C₂³	1	4	yes	—
188	C₇×C₄⋊C₈	C₂³	1	2	yes	—
189	C₇×C₄⋊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	2	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₇×C₂²⋊C₈	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	C₇×#97	C₂³	1	4	yes	—
203	C₇×#97	C₂³	1	2	yes	—
204	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
205	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
206	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
207	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
208	C₄×C₇×C₈	C₂³	1	2	yes	—
209	C₄×C₇×C₈	C₂³	1	4	yes	—
210	#3480	C₂×C₇	1	1	yes	characteristic
211	#2995	C₂×C₇	1	4	yes	complemented
212	#2994	C₂×C₇	1	2	yes	complemented
213	#2993	C₂×C₇	1	2	yes	complemented
214	#2992	C₂×C₇	1	4	yes	complemented
215	#2990	C₂×C₇	1	2	yes	complemented
216	#2989	C₂×C₇	1	2	yes	complemented
217	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
218	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
219	#2935	C₂×C₇	1	1	yes	characteristic, complemented
220	#2935	C₂×C₇	1	2	yes	complemented
221	#2932	C₂×C₇	1	2	yes	complemented
222	#2931	C₂×C₇	1	1	yes	characteristic, complemented
223	#2923	C₂×C₇	1	2	yes	complemented
224	#2922	C₂×C₇	1	1	yes	characteristic, complemented
225	#2906	C₂×C₇	1	1	yes	characteristic, complemented
226	#2906	C₂×C₇	1	2	yes	complemented
227	C₇×#41	—	2	4	no	—
228	C₇×#41	—	2	2	no	—
229	C₇×#41	—	2	2	no	—
230	C₇×#41	—	2	4	no	—
231	C₇×#41	—	4	4	no	—
232	C₂×C₇×Q₈	—	4	2	no	—
233	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
234	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
236	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
238	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
239	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
240	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
242	C₂×C₇×D₄	C₂²×C₄	1	2	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	2	yes	—
246	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
248	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
252	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
253	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
257	C₇×M₁₆	—	2	2	no	—
258	C₇×M₁₆	—	2	4	no	—
259	C₇×M₁₆	—	2	2	no	—
260	C₇×M₁₆	—	4	4	no	—
261	C₇×M₁₆	—	4	4	no	—
262	C₇×M₁₆	—	4	4	no	—
263	C₂×C₇×C₈	—	2	2	no	—
264	C₂×C₇×C₈	—	2	4	no	—
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	4	4	no	—
267	C₂×C₇×C₈	—	4	4	no	—
268	C₂×C₇×C₈	—	4	4	no	—
269	C₂×C₇×C₈	C₂⁴	1	2	yes	—
270	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
271	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
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	4	yes	—
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
279	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
280	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
281	C₇×C₄⋊C₄	C₂²×C₄	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	2	yes	—
285	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
286	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
287	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
288	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
289	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
290	C₇×C₄⋊C₄	C₂²×C₄	1	4	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	2	yes	—
294	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
295	C₇×C₂²⋊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	4	yes	—
301	C₇×C₂²⋊C₄	C₂²×C₄	1	2	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	4	yes	—
306	C₄²×C₇	C₂²×C₄	1	2	yes	—
307	C₄²×C₇	C₂²×C₄	1	4	yes	—
308	C₄²×C₇	C₂²×C₄	1	4	yes	—
309	C₄²×C₇	C₂²×C₄	1	2	yes	—
310	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
311	C₄²×C₇	C₂²×C₄	1	2	yes	—
312	C₄²×C₇	C₂²×C₄	1	2	yes	—
313	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
314	C₄²×C₇	C₂⁴	1	1	yes	characteristic
315	C₄²×C₇	C₂⁴	1	1	yes	characteristic
316	C₄²×C₇	C₂⁴	1	2	yes	—
317	C₄²×C₇	C₂⁴	1	2	yes	—
318	C₄²×C₇	C₂⁴	1	2	yes	—
319	C₂×#131	C₂²×C₇	1	2	yes	—
320	C₂×#131	C₂²×C₇	1	2	yes	—
321	C₂×#131	C₂²×C₇	1	2	yes	—
322	#559	C₄×C₇	1	1	yes	characteristic
323	#559	C₄×C₇	1	2	yes	—
324	#557	C₄×C₇	1	1	yes	characteristic
325	#556	C₄×C₇	1	1	yes	characteristic
326	#556	C₄×C₇	1	2	yes	—
327	#553	C₄×C₇	1	2	yes	—
328	#553	C₄×C₇	1	4	yes	—
329	#550	C₄×C₇	1	1	yes	characteristic
330	#548	C₄×C₇	1	2	yes	—
331	#532	C₂²×C₇	1	1	yes	characteristic
332	#532	C₂²×C₇	1	2	yes	—
333	#529	C₂²×C₇	1	4	yes	—
334	#529	C₂²×C₇	1	2	yes	—
335	C₄×#41	C₂²×C₇	1	2	yes	—
336	C₄×#41	C₂²×C₇	1	1	yes	characteristic
337	C₄×#41	C₂²×C₇	1	2	yes	—
338	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
339	#446	C₂²×C₇	1	1	yes	characteristic
340	#446	C₂²×C₇	1	1	yes	characteristic
341	#446	C₂²×C₇	1	2	yes	—
342	#446	C₂²×C₇	1	1	yes	characteristic
343	#446	C₂²×C₇	1	1	yes	characteristic
344	#446	C₂²×C₇	1	2	yes	—
345	#446	C₂²×C₇	1	2	yes	—
346	#446	C₂²×C₇	1	4	yes	—
347	C₈×Q₈	C₂²×C₇	1	2	yes	—
348	#436	C₂²×C₇	1	2	yes	—
349	#436	C₂²×C₇	1	2	yes	—
350	#436	C₂²×C₇	1	2	yes	—
351	#436	C₂²×C₇	1	4	yes	—
352	#435	C₂²×C₇	1	4	yes	—
353	#435	C₂²×C₇	1	4	yes	—
354	#435	C₂²×C₇	1	4	yes	—
355	#435	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	C₈×D₄	C₂²×C₇	1	2	yes	—
360	C₈×D₄	C₂²×C₇	1	2	yes	—
361	C₈×D₄	C₂²×C₇	1	2	yes	—
362	C₈×D₄	C₂²×C₇	1	4	yes	—
363	#433	C₂²×C₇	1	2	yes	—
364	#433	C₂²×C₇	1	2	yes	—
365	#433	C₂²×C₇	1	4	yes	—
366	#433	C₂²×C₇	1	4	yes	—
367	#432	C₂²×C₇	1	4	yes	—
368	#432	C₂²×C₇	1	4	yes	—
369	#431	C₂²×C₇	1	2	yes	—
370	#431	C₂²×C₇	1	2	yes	—
371	#424	C₂²×C₇	1	1	yes	characteristic
372	#424	C₂²×C₇	1	2	yes	—
373	#424	C₂²×C₇	1	4	yes	—
374	#424	C₂²×C₇	1	4	yes	—
375	#424	C₂²×C₇	1	4	yes	—
376	#424	C₂²×C₇	1	1	yes	characteristic
377	#423	C₂²×C₇	1	1	yes	characteristic
378	#423	C₂²×C₇	1	2	yes	—
379	#423	C₂²×C₇	1	4	yes	—
380	#423	C₂²×C₇	1	2	yes	—
381	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
382	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
384	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
385	#408	C₂²×C₇	1	1	yes	characteristic
386	#408	C₂²×C₇	1	1	yes	characteristic
387	#408	C₂²×C₇	1	2	yes	—
388	#408	C₂²×C₇	1	2	yes	—
389	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
390	C₄×M₁₆	C₂²×C₇	1	2	yes	—
391	C₂×#97	C₂²×C₇	1	2	yes	—
392	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
393	C₂³×C₇	C₂³×C₄	1	2	yes	—
394	C₂³×C₇	C₂³×C₄	1	4	yes	—
395	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
396	C₇×Q₈	—	2	2	no	—
397	C₇×Q₈	—	2	4	no	—
398	C₇×Q₈	—	2	2	no	—
399	C₇×Q₈	—	2	2	no	—
400	C₇×Q₈	—	4	2	no	—
401	C₇×D₄	—	2	4	no	—
402	C₇×D₄	—	2	8	no	—
403	C₇×D₄	—	2	2	no	—
404	C₇×D₄	—	2	4	no	—
405	C₇×D₄	—	2	4	no	—
406	C₇×D₄	—	4	4	no	—
407	C₇×D₄	—	4	2	no	—
408	C₇×D₄	—	4	4	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	4	no	—
411	C₂×C₄×C₇	—	2	4	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	4	no	—
415	C₂×C₄×C₇	—	4	2	no	—
416	C₂×C₄×C₇	—	4	4	no	—
417	C₂×C₄×C₇	—	4	1	no	—
418	C₂×C₄×C₇	—	4	2	no	—
419	C₂×C₄×C₇	—	4	2	no	—
420	C₂×C₄×C₇	—	4	4	no	—
421	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
423	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
427	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
428	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
429	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
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	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
436	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
437	C₇×C₈	—	2	1	no	—
438	C₇×C₈	—	2	2	no	—
439	C₇×C₈	—	2	2	no	—
440	C₇×C₈	—	2	1	no	—
441	C₇×C₈	—	2	4	no	—
442	C₇×C₈	—	2	2	no	—
443	C₇×C₈	—	2	1	no	—
444	C₇×C₈	—	2	1	no	—
445	C₇×C₈	—	2	2	no	—
446	C₂×#41	C₂×C₄×C₇	1	2	yes	—
447	C₂×#41	C₂³×C₇	1	1	yes	characteristic
448	C₂×#41	C₂³×C₇	1	2	yes	—
449	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
450	#131	—	4	4	no	—
451	#131	—	4	4	no	—
452	#131	—	4	4	no	—
453	C₂×M₁₆	C₂³×C₇	1	2	yes	—
454	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
455	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
456	C₂×M₁₆	C₂³×C₇	1	4	yes	—
457	C₂×M₁₆	C₂³×C₇	1	4	yes	—
458	C₂×M₁₆	C₂³×C₇	1	4	yes	—
459	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₇	1	2	yes	—
461	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₇	1	4	yes	—
463	C₂²×C₈	C₂³×C₇	1	4	yes	—
464	C₂²×C₈	C₂³×C₇	1	4	yes	—
465	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
466	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
467	#127	C₂×C₄×C₇	1	1	yes	characteristic
468	#127	C₂×C₄×C₇	1	2	yes	—
469	#126	C₂×C₄×C₇	1	4	yes	—
470	#126	C₂×C₄×C₇	1	4	yes	—
471	#126	C₂×C₄×C₇	1	4	yes	—
472	#125	C₂×C₄×C₇	1	4	yes	—
473	#125	C₂×C₄×C₇	1	2	yes	—
474	#124	C₂×C₄×C₇	1	2	yes	—
475	#124	C₂×C₄×C₇	1	4	yes	—
476	#124	C₂×C₄×C₇	1	2	yes	—
477	#124	C₂×C₄×C₇	1	2	yes	—
478	#124	C₂×C₄×C₇	1	2	yes	—
479	#123	C₂×C₄×C₇	1	4	yes	—
480	#123	C₂×C₄×C₇	1	4	yes	—
481	#123	C₂×C₄×C₇	1	4	yes	—
482	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
483	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
484	#121	C₂×C₄×C₇	1	2	yes	—
485	#121	C₂×C₄×C₇	1	4	yes	—
486	#121	C₂×C₄×C₇	1	2	yes	—
487	#121	C₂×C₄×C₇	1	4	yes	—
488	#121	C₂×C₄×C₇	1	2	yes	—
489	#121	C₂×C₄×C₇	1	4	yes	—
490	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
491	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
492	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
493	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
494	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
495	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
496	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
497	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
498	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
499	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
500	C₄×Q₈	C₂³×C₇	1	2	yes	—
501	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
502	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
503	C₄×D₄	C₂×C₄×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	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	C₂³×C₇	1	2	yes	—
512	C₄×D₄	C₂³×C₇	1	4	yes	—
513	C₄×D₄	C₂³×C₇	1	2	yes	—
514	C₄×D₄	C₂³×C₇	1	4	yes	—
515	#117	C₂×C₄×C₇	1	2	yes	—
516	#117	C₂×C₄×C₇	1	4	yes	—
517	#117	C₂³×C₇	1	1	yes	characteristic
518	#117	C₂³×C₇	1	2	yes	—
519	#117	C₂³×C₇	1	4	yes	—
520	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
522	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₇	1	2	yes	—
524	C₂×C₄²	C₂³×C₇	1	2	yes	—
525	C₂×C₄²	C₂³×C₇	1	4	yes	—
526	C₄⋊C₈	C₂³×C₇	1	2	yes	—
527	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₇	1	2	yes	—
529	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
530	C₄⋊C₈	C₂³×C₇	1	2	yes	—
531	C₄⋊C₈	C₂³×C₇	1	2	yes	—
532	C₄⋊C₈	C₂³×C₇	1	4	yes	—
533	C₄⋊C₈	C₂³×C₇	1	4	yes	—
534	C₄⋊C₈	C₂³×C₇	1	4	yes	—
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	2	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
544	C₂²⋊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	#97	C₂³×C₇	1	2	yes	—
552	#97	C₂³×C₇	1	2	yes	—
553	#97	C₂³×C₇	1	2	yes	—
554	#97	C₂³×C₇	1	2	yes	—
555	#97	C₂³×C₇	1	4	yes	—
556	#97	C₂³×C₇	1	2	yes	—
557	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₇	1	2	yes	—
562	C₄×C₈	C₂³×C₇	1	4	yes	—
563	C₂²×C₇	—	2	1	no	—
564	C₂²×C₇	—	2	1	no	—
565	C₂²×C₇	—	2	2	no	—
566	C₂²×C₇	—	2	4	no	—
567	C₂²×C₇	—	2	2	no	—
568	C₂²×C₇	—	2	4	no	—
569	C₂²×C₇	—	2	2	no	—
570	C₂²×C₇	—	2	4	no	—
571	C₂²×C₇	#520	1	2	yes	—
572	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
573	C₄×C₇	—	2	4	no	—
574	C₄×C₇	—	2	2	no	—
575	C₄×C₇	—	2	2	no	—
576	C₄×C₇	—	2	1	no	—
577	C₄×C₇	—	2	2	no	—
578	C₄×C₇	—	2	2	no	—
579	C₄×C₇	—	2	2	no	—
580	C₄×C₇	—	2	1	no	—
581	C₄×C₇	—	2	2	no	—
582	C₄×C₇	—	2	1	no	—
583	C₄×C₇	—	2	2	no	—
584	C₄×C₇	#520	1	2	yes	—
585	C₄×C₇	#568	1	2	yes	—
586	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
588	#41	—	2	4	no	—
589	#41	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	4	no	—
592	#41	—	4	4	no	—
593	C₂×Q₈	—	4	2	no	—
594	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
595	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
596	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
597	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
598	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
599	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
600	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
601	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
602	C₂×D₄	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	4	yes	—
606	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
607	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
608	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
609	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
610	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
611	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
612	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
613	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
614	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	M₁₆	—	2	4	no	—
619	M₁₆	—	2	2	no	—
620	M₁₆	—	2	2	no	—
621	M₁₆	—	4	4	no	—
622	M₁₆	—	4	4	no	—
623	M₁₆	—	4	4	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	4	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	4	4	no	—
628	C₂×C₈	—	4	4	no	—
629	C₂×C₈	—	4	4	no	—
630	C₂×C₈	C₂⁴×C₇	1	2	yes	—
631	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
634	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
635	C₂×C₈	C₂⁴×C₇	1	2	yes	—
636	C₂×C₈	C₂⁴×C₇	1	4	yes	—
637	C₂×C₈	C₂⁴×C₇	1	2	yes	—
638	C₂×C₈	C₂⁴×C₇	1	2	yes	—
639	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
640	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
641	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
642	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
643	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
644	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
645	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
646	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
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	1	yes	characteristic
650	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
651	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
652	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
653	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
654	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
655	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
656	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
657	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
658	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
659	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
660	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
661	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
662	C₂²⋊C₄	C₂²×C₄×C₇	1	2	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	4	yes	—
666	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
667	C₄²	C₂²×C₄×C₇	1	2	yes	—
668	C₄²	C₂²×C₄×C₇	1	4	yes	—
669	C₄²	C₂²×C₄×C₇	1	4	yes	—
670	C₄²	C₂²×C₄×C₇	1	2	yes	—
671	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
672	C₄²	C₂²×C₄×C₇	1	2	yes	—
673	C₄²	C₂²×C₄×C₇	1	2	yes	—
674	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
675	C₄²	C₂⁴×C₇	1	1	yes	characteristic
676	C₄²	C₂⁴×C₇	1	1	yes	characteristic
677	C₄²	C₂⁴×C₇	1	2	yes	—
678	C₄²	C₂⁴×C₇	1	2	yes	—
679	C₄²	C₂⁴×C₇	1	2	yes	—
680	C₂×C₇	—	2	2	no	—
681	C₂×C₇	—	4	2	no	—
682	C₂×C₇	—	4	4	no	—
683	C₂×C₇	C₂×#520	1	1	yes	characteristic
684	C₂×C₇	C₂×#568	1	1	yes	characteristic
685	C₂×C₇	#3573	1	1	yes	characteristic
686	C₂³	C₂³×C₄×C₇	1	2	yes	—
687	C₂³	C₂³×C₄×C₇	1	4	yes	—
688	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	4	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	4	2	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	8	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	4	no	—
698	D₄	—	2	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
715	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
716	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
717	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
718	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
719	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
720	C₂×C₄	C₂³×C₄×C₇	1	4	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	1	yes	characteristic
725	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
726	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
727	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
728	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
729	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
730	C₈	—	2	1	no	—
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	4	no	—
735	C₈	—	2	2	no	—
736	C₈	—	2	1	no	—
737	C₈	—	2	1	no	—
738	C₈	—	2	2	no	—
739	C₇	#60275	1	1	yes	characteristic, direct product factor, Sylow
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	C₇×#520	1	2	yes	—
749	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	2	no	—
761	C₄	C₇×#520	1	2	yes	—
762	C₄	C₇×#568	1	2	yes	—
763	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
764	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
765	C₂	—	2	2	no	—
766	C₂	—	4	2	no	—
767	C₂	—	4	4	no	—
768	C₂	C₂×C₇×#520	1	1	yes	characteristic
769	C₂	C₂×C₇×#568	1	1	yes	characteristic
770	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×#2995	C₂	semidirect
3. C₇×#2994	C₂	semidirect
4. C₇×#2993	C₂	semidirect
5. C₇×#2992	C₂	semidirect
6. C₇×#2990	C₂	semidirect
7. C₇×#2989	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×#2923	C₂	semidirect
15. C₇×#2922	C₂	semidirect
16. C₇×#2906	C₂	semidirect
17. C₇×#2906	C₂	semidirect
92. #60275	C₇	direct (N × H)
211. #2995	C₂×C₇	semidirect
212. #2994	C₂×C₇	semidirect
213. #2993	C₂×C₇	semidirect
214. #2992	C₂×C₇	semidirect
215. #2990	C₂×C₇	semidirect
216. #2989	C₂×C₇	semidirect
217. Q₈×M₁₆	C₂×C₇	semidirect
218. C₂×#446	C₂×C₇	semidirect
219. #2935	C₂×C₇	semidirect
220. #2935	C₂×C₇	semidirect
221. #2932	C₂×C₇	semidirect
222. #2931	C₂×C₇	semidirect
223. #2923	C₂×C₇	semidirect
224. #2922	C₂×C₇	semidirect
225. #2906	C₂×C₇	semidirect
226. #2906	C₂×C₇	semidirect
739. C₇	#60275	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×#2995	2
C₇×#2994	2
C₇×#2993	2
C₇×#2992	2
C₇×#2990	2
C₇×#2989	2
C₇×Q₈×M₁₆	2
C₂×C₇×#446	2
C₇×#2935	2
C₇×#2932	2
C₇×#2931	2
C₇×#2923	2
C₇×#2922	2
C₇×#2906	2
#60275	7

Subgroups — C7×#60275 #13237491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60275 #13237491