Subgroups — C₇×#60273 #13237489

Order 1792.

1826 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	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×#2993	C₂	1	4	yes	maximal, complemented
6	C₇×#2991	C₂	1	2	yes	maximal, complemented
7	C₇×#2989	C₂	1	2	yes	maximal, complemented
8	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2933	C₂	1	2	yes	maximal, complemented
12	C₇×#2930	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2924	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×#2905	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#131	C₂²	1	2	yes	—
19	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
20	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
21	C₇×#556	C₄	1	1	yes	characteristic
22	C₇×#555	C₄	1	1	yes	characteristic
23	C₇×#554	C₄	1	1	yes	characteristic
24	C₇×#553	C₄	1	2	yes	—
25	C₇×#552	C₄	1	2	yes	—
26	C₇×#552	C₄	1	2	yes	—
27	C₇×#551	C₄	1	4	yes	—
28	C₇×#547	C₄	1	1	yes	characteristic
29	C₇×#546	C₄	1	2	yes	—
30	C₇×#533	C₂²	1	1	yes	characteristic
31	C₇×#529	C₂²	1	2	yes	—
32	C₇×#529	C₂²	1	4	yes	—
33	C₇×#525	C₂²	1	2	yes	—
34	C₄×C₇×#41	C₂²	1	2	yes	—
35	C₄×C₇×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₇×#117	C₂²	1	2	yes	—
38	C₇×#446	C₂²	1	2	yes	complemented
39	C₇×#446	C₂²	1	2	yes	complemented
40	C₇×#446	C₂²	1	2	yes	complemented
41	C₇×#446	C₂²	1	4	yes	complemented
42	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
43	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
44	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
45	C₇×#436	C₂²	1	1	yes	characteristic
46	C₇×#436	C₂²	1	1	yes	characteristic
47	C₇×#436	C₂²	1	1	yes	characteristic
48	C₇×#436	C₂²	1	2	yes	—
49	C₇×#436	C₂²	1	1	yes	characteristic
50	C₇×#436	C₂²	1	2	yes	—
51	C₇×#436	C₂²	1	2	yes	—
52	C₇×#436	C₂²	1	4	yes	complemented
53	C₇×#436	C₂²	1	4	yes	complemented
54	C₇×#436	C₂²	1	4	yes	complemented
55	C₇×#435	C₂²	1	4	yes	—
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×#435	C₂²	1	4	yes	complemented
60	C₇×C₈×D₄	C₂²	1	2	yes	—
61	C₇×C₈×D₄	C₂²	1	4	yes	complemented
62	C₇×#433	C₂²	1	2	yes	complemented
63	C₇×#433	C₂²	1	2	yes	complemented
64	C₇×#433	C₂²	1	4	yes	complemented
65	C₇×#433	C₂²	1	4	yes	complemented
66	C₇×#432	C₂²	1	4	yes	complemented
67	C₇×#431	C₂²	1	2	yes	complemented
68	C₇×#431	C₂²	1	2	yes	complemented
69	C₇×#431	C₂²	1	4	yes	complemented
70	C₇×#424	C₂²	1	1	yes	characteristic
71	C₇×#424	C₂²	1	2	yes	—
72	C₇×#424	C₂²	1	2	yes	—
73	C₇×#424	C₂²	1	2	yes	—
74	C₇×#424	C₂²	1	1	yes	characteristic
75	C₇×#424	C₂²	1	4	yes	complemented
76	C₇×#424	C₂²	1	4	yes	complemented
77	C₇×#424	C₂²	1	4	yes	complemented
78	C₇×#423	C₂²	1	1	yes	characteristic
79	C₇×#423	C₂²	1	4	yes	complemented
80	C₇×#423	C₂²	1	4	yes	complemented
81	C₇×#423	C₂²	1	2	yes	complemented
82	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
84	C₇×#408	C₂²	1	1	yes	characteristic
85	C₇×#408	C₂²	1	1	yes	characteristic
86	C₇×#407	C₂²	1	2	yes	—
87	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
88	C₇×#405	C₂²	1	2	yes	—
89	C₇×#405	C₂²	1	2	yes	—
90	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
92	#60273	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	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
96	C₂³×C₄×C₇	C₂³	1	2	yes	—
97	C₇×#131	—	4	4	no	—
98	C₂×C₇×M₁₆	—	4	4	no	—
99	C₂×C₇×M₁₆	—	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	2	yes	—
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	4	yes	—
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂×C₇×M₁₆	C₂³	1	2	yes	—
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
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×#125	C₂×C₄	1	2	yes	—
122	C₇×#124	C₂×C₄	1	2	yes	—
123	C₇×#124	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×#123	C₂×C₄	1	4	yes	—
128	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
129	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
130	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
131	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
132	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
133	C₇×C₂²⋊Q₈	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	4	yes	—
137	C₇×#121	C₂×C₄	1	2	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	2	yes	—
141	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
142	C₄×C₇×Q₈	C₂³	1	2	yes	—
143	C₄×C₇×Q₈	C₂³	1	2	yes	—
144	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
145	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
146	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
151	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
152	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
153	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
154	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₄×C₇×D₄	C₂³	1	2	yes	—
156	C₄×C₇×D₄	C₂³	1	4	yes	—
157	C₄×C₇×D₄	C₂³	1	4	yes	—
158	C₇×#117	C₂×C₄	1	4	yes	—
159	C₇×#117	C₂×C₄	1	2	yes	—
160	C₇×#117	C₂×C₄	1	2	yes	—
161	C₇×#117	C₂×C₄	1	4	yes	—
162	C₇×#117	C₂×C₄	1	2	yes	—
163	C₇×#117	C₂³	1	1	yes	characteristic
164	C₇×#117	C₂³	1	2	yes	—
165	C₇×#117	C₂³	1	4	yes	—
166	C₇×#117	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
170	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
172	C₂×C₄²×C₇	C₂³	1	4	yes	—
173	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	2	yes	—
175	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
181	C₇×C₄⋊C₈	C₂³	1	2	yes	—
182	C₇×C₄⋊C₈	C₂³	1	2	yes	—
183	C₇×C₄⋊C₈	C₂³	1	4	yes	—
184	C₇×C₄⋊C₈	C₂³	1	4	yes	—
185	C₇×C₄⋊C₈	C₂³	1	4	yes	—
186	C₇×C₄⋊C₈	C₂³	1	4	yes	—
187	C₇×C₄⋊C₈	C₂³	1	4	yes	—
188	C₇×C₄⋊C₈	C₂³	1	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	2	yes	—
197	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
198	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
199	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
200	C₇×#97	C₂³	1	2	yes	—
201	C₇×#97	C₂³	1	4	yes	—
202	C₇×#97	C₂³	1	4	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	1	yes	characteristic
206	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
207	C₄×C₇×C₈	C₂³	1	2	yes	—
208	C₄×C₇×C₈	C₂³	1	4	yes	—
209	C₄×C₇×C₈	C₂³	1	4	yes	—
210	#3475	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	#2993	C₂×C₇	1	4	yes	complemented
215	#2991	C₂×C₇	1	2	yes	complemented
216	#2989	C₂×C₇	1	2	yes	complemented
217	#2962	C₂×C₇	1	1	yes	characteristic, complemented
218	#2960	C₂×C₇	1	1	yes	characteristic, complemented
219	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
220	#2933	C₂×C₇	1	2	yes	complemented
221	#2930	C₂×C₇	1	2	yes	complemented
222	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
223	#2924	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	#2905	C₂×C₇	1	2	yes	complemented
227	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
228	C₇×#41	—	2	2	no	—
229	C₇×#41	—	2	2	no	—
230	C₇×#41	—	4	4	no	—
231	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
233	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
234	C₂×C₇×D₄	—	4	2	no	—
235	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
237	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
240	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
241	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
246	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
247	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	4	yes	—
251	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	2	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	2	no	—
261	C₇×M₁₆	—	4	2	no	—
262	C₇×M₁₆	—	4	2	no	—
263	C₇×M₁₆	—	4	2	no	—
264	C₇×M₁₆	—	4	4	no	—
265	C₇×M₁₆	—	4	4	no	—
266	C₂×C₇×C₈	—	2	2	no	—
267	C₂×C₇×C₈	—	2	4	no	—
268	C₂×C₇×C₈	—	2	2	no	—
269	C₂×C₇×C₈	—	4	4	no	—
270	C₂×C₇×C₈	—	4	4	no	—
271	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
272	C₂×C₇×C₈	C₂⁴	1	2	yes	—
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₂×C₇×C₈	C₂⁴	1	4	yes	—
279	C₂×C₇×C₈	C₂⁴	1	2	yes	—
280	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
281	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
285	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
286	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
287	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
288	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	4	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	4	yes	—
295	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
296	C₇×C₄⋊C₄	C₂²×C₄	1	2	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	2	yes	—
303	C₇×C₂²⋊C₄	C₂²×C₄	1	2	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	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	4	yes	—
312	C₄²×C₇	C₂²×C₄	1	4	yes	—
313	C₄²×C₇	C₂²×C₄	1	2	yes	—
314	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
315	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
316	C₄²×C₇	C₂²×C₄	1	2	yes	—
317	C₄²×C₇	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇	C₂⁴	1	1	yes	characteristic
319	C₄²×C₇	C₂⁴	1	4	yes	—
320	C₄²×C₇	C₂⁴	1	2	yes	—
321	C₂×#131	C₂²×C₇	1	2	yes	—
322	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
323	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
324	#556	C₄×C₇	1	1	yes	characteristic
325	#555	C₄×C₇	1	1	yes	characteristic
326	#554	C₄×C₇	1	1	yes	characteristic
327	#553	C₄×C₇	1	2	yes	—
328	#552	C₄×C₇	1	2	yes	—
329	#552	C₄×C₇	1	2	yes	—
330	#551	C₄×C₇	1	4	yes	—
331	#547	C₄×C₇	1	1	yes	characteristic
332	#546	C₄×C₇	1	2	yes	—
333	#533	C₂²×C₇	1	1	yes	characteristic
334	#529	C₂²×C₇	1	2	yes	—
335	#529	C₂²×C₇	1	4	yes	—
336	#525	C₂²×C₇	1	2	yes	—
337	C₄×#41	C₂²×C₇	1	2	yes	—
338	C₄×#41	C₂²×C₇	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
340	C₂×#117	C₂²×C₇	1	2	yes	—
341	#446	C₂²×C₇	1	2	yes	complemented
342	#446	C₂²×C₇	1	2	yes	complemented
343	#446	C₂²×C₇	1	2	yes	complemented
344	#446	C₂²×C₇	1	4	yes	complemented
345	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
346	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
347	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
348	#436	C₂²×C₇	1	1	yes	characteristic
349	#436	C₂²×C₇	1	1	yes	characteristic
350	#436	C₂²×C₇	1	1	yes	characteristic
351	#436	C₂²×C₇	1	2	yes	—
352	#436	C₂²×C₇	1	1	yes	characteristic
353	#436	C₂²×C₇	1	2	yes	—
354	#436	C₂²×C₇	1	2	yes	—
355	#436	C₂²×C₇	1	4	yes	complemented
356	#436	C₂²×C₇	1	4	yes	complemented
357	#436	C₂²×C₇	1	4	yes	complemented
358	#435	C₂²×C₇	1	4	yes	—
359	#435	C₂²×C₇	1	4	yes	complemented
360	#435	C₂²×C₇	1	4	yes	complemented
361	#435	C₂²×C₇	1	4	yes	complemented
362	#435	C₂²×C₇	1	4	yes	complemented
363	C₈×D₄	C₂²×C₇	1	2	yes	—
364	C₈×D₄	C₂²×C₇	1	4	yes	complemented
365	#433	C₂²×C₇	1	2	yes	complemented
366	#433	C₂²×C₇	1	2	yes	complemented
367	#433	C₂²×C₇	1	4	yes	complemented
368	#433	C₂²×C₇	1	4	yes	complemented
369	#432	C₂²×C₇	1	4	yes	complemented
370	#431	C₂²×C₇	1	2	yes	complemented
371	#431	C₂²×C₇	1	2	yes	complemented
372	#431	C₂²×C₇	1	4	yes	complemented
373	#424	C₂²×C₇	1	1	yes	characteristic
374	#424	C₂²×C₇	1	2	yes	—
375	#424	C₂²×C₇	1	2	yes	—
376	#424	C₂²×C₇	1	2	yes	—
377	#424	C₂²×C₇	1	1	yes	characteristic
378	#424	C₂²×C₇	1	4	yes	complemented
379	#424	C₂²×C₇	1	4	yes	complemented
380	#424	C₂²×C₇	1	4	yes	complemented
381	#423	C₂²×C₇	1	1	yes	characteristic
382	#423	C₂²×C₇	1	4	yes	complemented
383	#423	C₂²×C₇	1	4	yes	complemented
384	#423	C₂²×C₇	1	2	yes	complemented
385	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
387	#408	C₂²×C₇	1	1	yes	characteristic
388	#408	C₂²×C₇	1	1	yes	characteristic
389	#407	C₂²×C₇	1	2	yes	—
390	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
391	#405	C₂²×C₇	1	2	yes	—
392	#405	C₂²×C₇	1	2	yes	—
393	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
394	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
395	C₂³×C₇	—	2	4	no	—
396	C₂³×C₇	—	4	2	no	—
397	C₂³×C₇	—	4	2	no	—
398	C₂³×C₇	C₂³×C₄	1	2	yes	—
399	C₂³×C₇	C₂³×C₄	1	2	yes	—
400	C₂³×C₇	C₂³×C₄	1	2	yes	—
401	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
402	C₇×Q₈	—	2	2	no	—
403	C₇×Q₈	—	2	4	no	—
404	C₇×Q₈	—	4	2	no	—
405	C₇×D₄	—	2	4	no	—
406	C₇×D₄	—	2	2	no	—
407	C₇×D₄	—	2	2	no	—
408	C₇×D₄	—	2	2	no	—
409	C₇×D₄	—	4	2	no	—
410	C₇×D₄	—	4	4	no	—
411	C₇×D₄	—	4	4	no	—
412	C₂×C₄×C₇	—	2	4	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	4	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	4	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	4	2	no	—
424	C₂×C₄×C₇	—	4	4	no	—
425	C₂×C₄×C₇	—	4	1	no	—
426	C₂×C₄×C₇	—	4	4	no	—
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	1	yes	characteristic
430	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
433	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
434	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
435	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
437	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
438	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
439	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
441	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
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	C₇×C₈	—	2	2	no	—
447	C₇×C₈	—	2	4	no	—
448	C₇×C₈	—	2	1	no	—
449	C₇×C₈	—	2	1	no	—
450	C₇×C₈	—	2	2	no	—
451	C₂×#41	C₂×C₄×C₇	1	2	yes	—
452	C₂×#41	C₂³×C₇	1	1	yes	characteristic
453	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₇	1	2	yes	—
455	#131	—	4	4	no	—
456	C₂×M₁₆	—	4	4	no	—
457	C₂×M₁₆	—	4	4	no	—
458	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₇	1	2	yes	—
460	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
461	C₂×M₁₆	C₂³×C₇	1	4	yes	—
462	C₂×M₁₆	C₂³×C₇	1	2	yes	—
463	C₂×M₁₆	C₂³×C₇	1	2	yes	—
464	C₂×M₁₆	C₂³×C₇	1	2	yes	—
465	C₂×M₁₆	C₂³×C₇	1	2	yes	—
466	C₂×M₁₆	C₂³×C₇	1	4	yes	—
467	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
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	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
473	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
474	#126	C₂×C₄×C₇	1	4	yes	—
475	#126	C₂×C₄×C₇	1	4	yes	—
476	#126	C₂×C₄×C₇	1	4	yes	—
477	#125	C₂×C₄×C₇	1	4	yes	—
478	#125	C₂×C₄×C₇	1	2	yes	—
479	#125	C₂×C₄×C₇	1	2	yes	—
480	#124	C₂×C₄×C₇	1	2	yes	—
481	#124	C₂×C₄×C₇	1	4	yes	—
482	#123	C₂×C₄×C₇	1	4	yes	—
483	#123	C₂×C₄×C₇	1	4	yes	—
484	#123	C₂×C₄×C₇	1	4	yes	—
485	#123	C₂×C₄×C₇	1	4	yes	—
486	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
487	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
488	C₂²⋊Q₈	C₂×C₄×C₇	1	2	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	2	yes	—
493	#121	C₂×C₄×C₇	1	2	yes	—
494	#121	C₂×C₄×C₇	1	4	yes	—
495	#121	C₂×C₄×C₇	1	2	yes	—
496	#120	C₂×C₄×C₇	1	4	yes	—
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	1	yes	characteristic
500	C₄×Q₈	C₂³×C₇	1	2	yes	—
501	C₄×Q₈	C₂³×C₇	1	2	yes	—
502	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
503	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
504	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
505	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
506	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
507	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
508	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
509	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
510	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
511	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
512	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
513	C₄×D₄	C₂³×C₇	1	2	yes	—
514	C₄×D₄	C₂³×C₇	1	4	yes	—
515	C₄×D₄	C₂³×C₇	1	4	yes	—
516	#117	C₂×C₄×C₇	1	4	yes	—
517	#117	C₂×C₄×C₇	1	2	yes	—
518	#117	C₂×C₄×C₇	1	2	yes	—
519	#117	C₂×C₄×C₇	1	4	yes	—
520	#117	C₂×C₄×C₇	1	2	yes	—
521	#117	C₂³×C₇	1	1	yes	characteristic
522	#117	C₂³×C₇	1	2	yes	—
523	#117	C₂³×C₇	1	4	yes	—
524	#117	C₂³×C₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
530	C₂×C₄²	C₂³×C₇	1	4	yes	—
531	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
532	C₂×C₄²	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	4	yes	—
538	C₄⋊C₈	C₂³×C₇	1	2	yes	—
539	C₄⋊C₈	C₂³×C₇	1	2	yes	—
540	C₄⋊C₈	C₂³×C₇	1	2	yes	—
541	C₄⋊C₈	C₂³×C₇	1	4	yes	—
542	C₄⋊C₈	C₂³×C₇	1	4	yes	—
543	C₄⋊C₈	C₂³×C₇	1	4	yes	—
544	C₄⋊C₈	C₂³×C₇	1	4	yes	—
545	C₄⋊C₈	C₂³×C₇	1	4	yes	—
546	C₄⋊C₈	C₂³×C₇	1	2	yes	—
547	C₄⋊C₈	C₂³×C₇	1	2	yes	—
548	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
549	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
550	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
551	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₇	1	2	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	4	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	1	yes	characteristic
564	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₇	1	2	yes	—
566	C₄×C₈	C₂³×C₇	1	4	yes	—
567	C₄×C₈	C₂³×C₇	1	4	yes	—
568	C₂²×C₇	—	2	1	no	—
569	C₂²×C₇	—	2	1	no	—
570	C₂²×C₇	—	2	2	no	—
571	C₂²×C₇	—	2	2	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	2	no	—
577	C₂²×C₇	—	2	2	no	—
578	C₂²×C₇	—	2	2	no	—
579	C₂²×C₇	—	8	4	no	—
580	C₂²×C₇	#520	1	2	yes	—
581	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
582	C₄×C₇	—	2	2	no	—
583	C₄×C₇	—	2	2	no	—
584	C₄×C₇	—	2	2	no	—
585	C₄×C₇	—	2	2	no	—
586	C₄×C₇	—	2	1	no	—
587	C₄×C₇	—	2	4	no	—
588	C₄×C₇	—	2	1	no	—
589	C₄×C₇	—	2	2	no	—
590	C₄×C₇	—	2	4	no	—
591	C₄×C₇	—	2	1	no	—
592	C₄×C₇	#520	1	2	yes	—
593	C₄×C₇	#568	1	2	yes	—
594	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
595	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
596	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
597	#41	—	2	2	no	—
598	#41	—	2	2	no	—
599	#41	—	4	4	no	—
600	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
601	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
602	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
605	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
606	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
607	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
608	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
609	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
610	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
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	2	yes	—
617	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
618	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
619	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
620	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
621	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	M₁₆	—	2	2	no	—
629	M₁₆	—	4	2	no	—
630	M₁₆	—	4	2	no	—
631	M₁₆	—	4	2	no	—
632	M₁₆	—	4	2	no	—
633	M₁₆	—	4	4	no	—
634	M₁₆	—	4	4	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	—	4	4	no	—
639	C₂×C₈	—	4	4	no	—
640	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₇	1	2	yes	—
642	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
643	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
644	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
645	C₂×C₈	C₂⁴×C₇	1	2	yes	—
646	C₂×C₈	C₂⁴×C₇	1	2	yes	—
647	C₂×C₈	C₂⁴×C₇	1	4	yes	—
648	C₂×C₈	C₂⁴×C₇	1	2	yes	—
649	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
650	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
651	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
652	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
653	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
654	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
655	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
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	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	2	yes	—
666	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
667	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
668	C₂²⋊C₄	C₂²×C₄×C₇	1	4	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	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	4	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
680	C₄²	C₂²×C₄×C₇	1	4	yes	—
681	C₄²	C₂²×C₄×C₇	1	4	yes	—
682	C₄²	C₂²×C₄×C₇	1	2	yes	—
683	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
684	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
685	C₄²	C₂²×C₄×C₇	1	2	yes	—
686	C₄²	C₂⁴×C₇	1	1	yes	characteristic
687	C₄²	C₂⁴×C₇	1	1	yes	characteristic
688	C₄²	C₂⁴×C₇	1	4	yes	—
689	C₄²	C₂⁴×C₇	1	2	yes	—
690	C₂×C₇	—	2	2	no	—
691	C₂×C₇	—	4	2	no	—
692	C₂×C₇	—	4	2	no	—
693	C₂×C₇	—	4	2	no	—
694	C₂×C₇	C₂×#520	1	1	yes	characteristic
695	C₂×C₇	C₂×#568	1	1	yes	characteristic
696	C₂×C₇	#3573	1	1	yes	characteristic
697	C₂³	—	2	4	no	—
698	C₂³	—	4	2	no	—
699	C₂³	—	4	2	no	—
700	C₂³	C₂³×C₄×C₇	1	2	yes	—
701	C₂³	C₂³×C₄×C₇	1	2	yes	—
702	C₂³	C₂³×C₄×C₇	1	2	yes	—
703	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	4	no	—
706	Q₈	—	4	2	no	—
707	D₄	—	2	4	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
730	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
731	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
732	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
733	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
734	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
735	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
736	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
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	1	yes	characteristic
740	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
741	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
742	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
743	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
744	C₈	—	2	2	no	—
745	C₈	—	2	1	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	4	no	—
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	2	no	—
753	C₇	#60273	1	1	yes	characteristic, direct product factor, Sylow
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₇×#520	1	2	yes	—
767	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
768	C₄	—	2	2	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	4	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	2	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	C₇×#520	1	2	yes	—
779	C₄	C₇×#568	1	2	yes	—
780	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
781	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
782	C₂	—	2	2	no	—
783	C₂	—	4	2	no	—
784	C₂	—	4	2	no	—
785	C₂	—	4	2	no	—
786	C₂	C₂×C₇×#520	1	1	yes	characteristic
787	C₂	C₂×C₇×#568	1	1	yes	characteristic
788	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×#3475	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×#2993	C₂	semidirect
6. C₇×#2991	C₂	semidirect
7. C₇×#2989	C₂	semidirect
8. C₇×#2962	C₂	semidirect
9. C₇×#2960	C₂	semidirect
10. C₇×D₄×M₁₆	C₂	semidirect
11. C₇×#2933	C₂	semidirect
12. C₇×#2930	C₂	semidirect
13. C₂×C₇×#436	C₂	semidirect
14. C₇×#2924	C₂	semidirect
15. C₇×#2922	C₂	semidirect
16. C₇×#2906	C₂	semidirect
17. C₇×#2905	C₂	semidirect
38. C₇×#446	C₂²	semidirect
39. C₇×#446	C₂²	semidirect
40. C₇×#446	C₂²	semidirect
41. C₇×#446	C₂²	semidirect
42. C₇×C₈×Q₈	C₂²	semidirect
43. C₇×C₈×Q₈	C₂²	semidirect
44. C₇×C₈×Q₈	C₂²	semidirect
52. C₇×#436	C₂²	semidirect
53. C₇×#436	C₂²	semidirect
54. C₇×#436	C₂²	semidirect
56. C₇×#435	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
58. C₇×#435	C₂²	semidirect
59. C₇×#435	C₂²	semidirect
61. C₇×C₈×D₄	C₂²	semidirect
62. C₇×#433	C₂²	semidirect
63. C₇×#433	C₂²	semidirect
64. C₇×#433	C₂²	semidirect
65. C₇×#433	C₂²	semidirect
66. C₇×#432	C₂²	semidirect
67. C₇×#431	C₂²	semidirect
68. C₇×#431	C₂²	semidirect
69. C₇×#431	C₂²	semidirect
75. C₇×#424	C₂²	semidirect
76. C₇×#424	C₂²	semidirect
77. C₇×#424	C₂²	semidirect
79. C₇×#423	C₂²	semidirect
80. C₇×#423	C₂²	semidirect
81. C₇×#423	C₂²	semidirect
83. C₂×C₇×C₄⋊C₈	C₂²	semidirect
92. #60273	C₇	direct (N × H)
211. #2995	C₂×C₇	semidirect
212. #2994	C₂×C₇	semidirect
213. #2993	C₂×C₇	semidirect
214. #2993	C₂×C₇	semidirect
215. #2991	C₂×C₇	semidirect
216. #2989	C₂×C₇	semidirect
217. #2962	C₂×C₇	semidirect
218. #2960	C₂×C₇	semidirect
219. D₄×M₁₆	C₂×C₇	semidirect
220. #2933	C₂×C₇	semidirect
221. #2930	C₂×C₇	semidirect
222. C₂×#436	C₂×C₇	semidirect
223. #2924	C₂×C₇	semidirect
224. #2922	C₂×C₇	semidirect
225. #2906	C₂×C₇	semidirect
226. #2905	C₂×C₇	semidirect
341. #446	C₂²×C₇	semidirect
342. #446	C₂²×C₇	semidirect
343. #446	C₂²×C₇	semidirect
344. #446	C₂²×C₇	semidirect
345. C₈×Q₈	C₂²×C₇	semidirect
346. C₈×Q₈	C₂²×C₇	semidirect
347. C₈×Q₈	C₂²×C₇	semidirect
355. #436	C₂²×C₇	semidirect
356. #436	C₂²×C₇	semidirect
357. #436	C₂²×C₇	semidirect
359. #435	C₂²×C₇	semidirect
360. #435	C₂²×C₇	semidirect
361. #435	C₂²×C₇	semidirect
362. #435	C₂²×C₇	semidirect
364. C₈×D₄	C₂²×C₇	semidirect
365. #433	C₂²×C₇	semidirect
366. #433	C₂²×C₇	semidirect
367. #433	C₂²×C₇	semidirect
368. #433	C₂²×C₇	semidirect
369. #432	C₂²×C₇	semidirect
370. #431	C₂²×C₇	semidirect
371. #431	C₂²×C₇	semidirect
372. #431	C₂²×C₇	semidirect
378. #424	C₂²×C₇	semidirect
379. #424	C₂²×C₇	semidirect
380. #424	C₂²×C₇	semidirect
382. #423	C₂²×C₇	semidirect
383. #423	C₂²×C₇	semidirect
384. #423	C₂²×C₇	semidirect
386. C₂×C₄⋊C₈	C₂²×C₇	semidirect
753. C₇	#60273	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×#3475	2
C₇×#2995	2
C₇×#2994	2
C₇×#2993	2
C₇×#2991	2
C₇×#2989	2
C₇×#2962	2
C₇×#2960	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2930	2
C₂×C₇×#436	2
C₇×#2924	2
C₇×#2922	2
C₇×#2906	2
C₇×#2905	2
#60273	7

Subgroups — C7×#60273 #13237489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60273 #13237489