Subgroups — C₇×#60272 #13237488

Order 1792.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 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	2	yes	maximal, complemented
3	C₇×#2995	C₂	1	2	yes	maximal, complemented
4	C₇×#2994	C₂	1	2	yes	maximal, complemented
5	C₇×#2993	C₂	1	2	yes	maximal, complemented
6	C₇×#2992	C₂	1	2	yes	maximal, complemented
7	C₇×#2992	C₂	1	2	yes	maximal, complemented
8	C₇×#2990	C₂	1	2	yes	maximal, complemented
9	C₇×#2989	C₂	1	2	yes	maximal, complemented
10	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2905	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#131	C₂²	1	1	yes	characteristic
25	C₂×C₇×#131	C₂²	1	1	yes	characteristic
26	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
29	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#556	C₄	1	1	yes	characteristic
31	C₇×#555	C₄	1	1	yes	characteristic
32	C₇×#554	C₄	1	1	yes	characteristic
33	C₇×#553	C₄	1	1	yes	characteristic
34	C₇×#553	C₄	1	1	yes	characteristic
35	C₇×#552	C₄	1	1	yes	characteristic
36	C₇×#552	C₄	1	1	yes	characteristic
37	C₇×#552	C₄	1	2	yes	—
38	C₇×#551	C₄	1	2	yes	—
39	C₇×#551	C₄	1	2	yes	—
40	C₇×#547	C₄	1	1	yes	characteristic
41	C₇×#546	C₄	1	2	yes	—
42	C₇×#533	C₂²	1	1	yes	characteristic
43	C₇×#529	C₂²	1	2	yes	—
44	C₇×#529	C₂²	1	2	yes	—
45	C₇×#529	C₂²	1	2	yes	—
46	C₇×#525	C₂²	1	1	yes	characteristic
47	C₇×#525	C₂²	1	1	yes	characteristic
48	C₄×C₇×#41	C₂²	1	2	yes	—
49	C₄×C₇×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₇×#117	C₂²	1	1	yes	characteristic
52	C₂×C₇×#117	C₂²	1	1	yes	characteristic
53	C₇×#446	C₂²	1	2	yes	complemented
54	C₇×#446	C₂²	1	2	yes	complemented
55	C₇×#446	C₂²	1	2	yes	complemented
56	C₇×#446	C₂²	1	2	yes	complemented
57	C₇×#446	C₂²	1	2	yes	complemented
58	C₇×#446	C₂²	1	2	yes	complemented
59	C₇×#446	C₂²	1	2	yes	complemented
60	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
61	C₇×#436	C₂²	1	2	yes	—
62	C₇×#436	C₂²	1	2	yes	complemented
63	C₇×#436	C₂²	1	2	yes	complemented
64	C₇×#436	C₂²	1	2	yes	complemented
65	C₇×#436	C₂²	1	2	yes	complemented
66	C₇×#435	C₂²	1	1	yes	characteristic
67	C₇×#435	C₂²	1	1	yes	characteristic
68	C₇×#435	C₂²	1	1	yes	characteristic
69	C₇×#435	C₂²	1	1	yes	characteristic
70	C₇×#435	C₂²	1	1	yes	characteristic
71	C₇×#435	C₂²	1	1	yes	characteristic
72	C₇×#435	C₂²	1	1	yes	characteristic
73	C₇×#435	C₂²	1	1	yes	characteristic
74	C₇×#435	C₂²	1	2	yes	—
75	C₇×#435	C₂²	1	2	yes	—
76	C₇×#435	C₂²	1	2	yes	complemented
77	C₇×#435	C₂²	1	2	yes	complemented
78	C₇×#435	C₂²	1	2	yes	complemented
79	C₇×#435	C₂²	1	2	yes	complemented
80	C₇×#435	C₂²	1	2	yes	complemented
81	C₇×#435	C₂²	1	2	yes	complemented
82	C₇×#435	C₂²	1	2	yes	complemented
83	C₇×#435	C₂²	1	2	yes	complemented
84	C₇×C₈×D₄	C₂²	1	2	yes	—
85	C₇×C₈×D₄	C₂²	1	2	yes	complemented
86	C₇×C₈×D₄	C₂²	1	2	yes	complemented
87	C₇×C₈×D₄	C₂²	1	2	yes	complemented
88	C₇×C₈×D₄	C₂²	1	2	yes	complemented
89	C₇×#433	C₂²	1	2	yes	complemented
90	C₇×#433	C₂²	1	2	yes	complemented
91	C₇×#433	C₂²	1	2	yes	complemented
92	C₇×#433	C₂²	1	2	yes	complemented
93	C₇×#433	C₂²	1	2	yes	complemented
94	C₇×#433	C₂²	1	2	yes	complemented
95	C₇×#432	C₂²	1	2	yes	complemented
96	C₇×#432	C₂²	1	2	yes	complemented
97	C₇×#432	C₂²	1	2	yes	complemented
98	C₇×#432	C₂²	1	2	yes	complemented
99	C₇×#431	C₂²	1	2	yes	complemented
100	C₇×#431	C₂²	1	2	yes	complemented
101	C₇×#424	C₂²	1	1	yes	characteristic
102	C₇×#424	C₂²	1	1	yes	characteristic
103	C₇×#424	C₂²	1	1	yes	characteristic
104	C₇×#424	C₂²	1	1	yes	characteristic
105	C₇×#424	C₂²	1	1	yes	characteristic
106	C₇×#424	C₂²	1	1	yes	characteristic
107	C₇×#424	C₂²	1	1	yes	characteristic
108	C₇×#424	C₂²	1	1	yes	characteristic
109	C₇×#424	C₂²	1	2	yes	complemented
110	C₇×#424	C₂²	1	2	yes	complemented
111	C₇×#424	C₂²	1	2	yes	complemented
112	C₇×#424	C₂²	1	2	yes	complemented
113	C₇×#424	C₂²	1	2	yes	complemented
114	C₇×#424	C₂²	1	2	yes	complemented
115	C₇×#423	C₂²	1	1	yes	characteristic
116	C₇×#423	C₂²	1	2	yes	complemented
117	C₇×#423	C₂²	1	2	yes	complemented
118	C₇×#423	C₂²	1	2	yes	complemented
119	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
120	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
121	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
122	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
123	C₇×#408	C₂²	1	1	yes	characteristic
124	C₇×#408	C₂²	1	1	yes	characteristic
125	C₇×#407	C₂²	1	1	yes	characteristic
126	C₇×#407	C₂²	1	1	yes	characteristic
127	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
128	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
129	C₇×#405	C₂²	1	1	yes	characteristic
130	C₇×#405	C₂²	1	1	yes	characteristic
131	C₇×#405	C₂²	1	1	yes	characteristic
132	C₇×#405	C₂²	1	1	yes	characteristic
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
134	C₂×C₇×#97	C₂²	1	1	yes	characteristic
135	#60272	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂×C₄	1	2	yes	—
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₇×#131	—	4	2	no	—
142	C₇×#131	—	4	2	no	—
143	C₂×C₇×M₁₆	—	4	2	no	—
144	C₂×C₇×M₁₆	—	4	2	no	—
145	C₂×C₇×M₁₆	—	4	2	no	—
146	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×M₁₆	C₂³	1	2	yes	—
153	C₂×C₇×M₁₆	C₂³	1	2	yes	—
154	C₂×C₇×M₁₆	C₂³	1	2	yes	—
155	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₇×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₇×C₈	—	4	2	no	—
159	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
164	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
165	C₂²×C₇×C₈	C₂³	1	2	yes	—
166	C₂²×C₇×C₈	C₂³	1	2	yes	—
167	C₂²×C₇×C₈	C₂³	1	2	yes	—
168	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
169	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
170	C₂²×C₇×C₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
172	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
173	C₇×#126	C₂×C₄	1	2	yes	—
174	C₇×#126	C₂×C₄	1	2	yes	—
175	C₇×#126	C₂×C₄	1	2	yes	—
176	C₇×#126	C₂×C₄	1	2	yes	—
177	C₇×#126	C₂×C₄	1	2	yes	—
178	C₇×#126	C₂×C₄	1	2	yes	—
179	C₇×#125	C₂×C₄	1	2	yes	—
180	C₇×#125	C₂×C₄	1	2	yes	—
181	C₇×#125	C₂×C₄	1	2	yes	—
182	C₇×#125	C₂×C₄	1	1	yes	characteristic
183	C₇×#125	C₂×C₄	1	1	yes	characteristic
184	C₇×#124	C₂×C₄	1	2	yes	—
185	C₇×#124	C₂×C₄	1	2	yes	—
186	C₇×#124	C₂×C₄	1	2	yes	—
187	C₇×#123	C₂×C₄	1	2	yes	—
188	C₇×#123	C₂×C₄	1	2	yes	—
189	C₇×#123	C₂×C₄	1	2	yes	—
190	C₇×#123	C₂×C₄	1	2	yes	—
191	C₇×#123	C₂×C₄	1	2	yes	—
192	C₇×#123	C₂×C₄	1	2	yes	—
193	C₇×#123	C₂×C₄	1	2	yes	—
194	C₇×#123	C₂×C₄	1	2	yes	—
195	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
196	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
197	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
198	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
199	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
200	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
201	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
202	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
204	C₇×#121	C₂×C₄	1	1	yes	characteristic
205	C₇×#121	C₂×C₄	1	1	yes	characteristic
206	C₇×#121	C₂×C₄	1	1	yes	characteristic
207	C₇×#121	C₂×C₄	1	1	yes	characteristic
208	C₇×#121	C₂×C₄	1	2	yes	—
209	C₇×#121	C₂×C₄	1	2	yes	—
210	C₇×#121	C₂×C₄	1	2	yes	—
211	C₇×#120	C₂×C₄	1	2	yes	—
212	C₇×#120	C₂×C₄	1	2	yes	—
213	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
214	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
215	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	2	yes	—
218	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
219	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
220	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
221	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
222	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
223	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
224	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
225	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
226	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
227	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
228	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
229	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
230	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
231	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
232	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
233	C₄×C₇×D₄	C₂³	1	2	yes	—
234	C₄×C₇×D₄	C₂³	1	2	yes	—
235	C₄×C₇×D₄	C₂³	1	2	yes	—
236	C₄×C₇×D₄	C₂³	1	2	yes	—
237	C₇×#117	C₂×C₄	1	2	yes	—
238	C₇×#117	C₂×C₄	1	2	yes	—
239	C₇×#117	C₂×C₄	1	1	yes	characteristic
240	C₇×#117	C₂×C₄	1	1	yes	characteristic
241	C₇×#117	C₂×C₄	1	1	yes	characteristic
242	C₇×#117	C₂×C₄	1	1	yes	characteristic
243	C₇×#117	C₂×C₄	1	2	yes	—
244	C₇×#117	C₂×C₄	1	2	yes	—
245	C₇×#117	C₂×C₄	1	2	yes	—
246	C₇×#117	C₂³	1	1	yes	characteristic
247	C₇×#117	C₂³	1	1	yes	characteristic
248	C₇×#117	C₂³	1	1	yes	characteristic
249	C₇×#117	C₂³	1	2	yes	—
250	C₇×#117	C₂³	1	2	yes	—
251	C₇×#117	C₂³	1	2	yes	—
252	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
253	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
254	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
255	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
256	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
257	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
258	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
259	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
260	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
261	C₂×C₄²×C₇	C₂³	1	2	yes	—
262	C₂×C₄²×C₇	C₂³	1	2	yes	—
263	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₇	C₂³	1	2	yes	—
265	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₇×C₄⋊C₈	C₂³	1	2	yes	—
270	C₇×C₄⋊C₈	C₂³	1	2	yes	—
271	C₇×C₄⋊C₈	C₂³	1	2	yes	—
272	C₇×C₄⋊C₈	C₂³	1	2	yes	—
273	C₇×C₄⋊C₈	C₂³	1	2	yes	—
274	C₇×C₄⋊C₈	C₂³	1	2	yes	—
275	C₇×C₄⋊C₈	C₂³	1	2	yes	—
276	C₇×C₄⋊C₈	C₂³	1	2	yes	—
277	C₇×C₄⋊C₈	C₂³	1	2	yes	—
278	C₇×C₄⋊C₈	C₂³	1	2	yes	—
279	C₇×C₄⋊C₈	C₂³	1	2	yes	—
280	C₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
296	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
297	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
298	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
299	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
300	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
301	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
302	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₇×#97	C₂³	1	1	yes	characteristic
304	C₇×#97	C₂³	1	1	yes	characteristic
305	C₇×#97	C₂³	1	1	yes	characteristic
306	C₇×#97	C₂³	1	1	yes	characteristic
307	C₇×#97	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	2	yes	—
309	C₇×#97	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	2	yes	—
311	C₇×#97	C₂³	1	2	yes	—
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	2	yes	—
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	C₄×C₇×C₈	C₂³	1	2	yes	—
317	#3475	C₂×C₇	1	1	yes	characteristic
318	#2995	C₂×C₇	1	2	yes	complemented
319	#2995	C₂×C₇	1	2	yes	complemented
320	#2994	C₂×C₇	1	2	yes	complemented
321	#2993	C₂×C₇	1	2	yes	complemented
322	#2992	C₂×C₇	1	2	yes	complemented
323	#2992	C₂×C₇	1	2	yes	complemented
324	#2990	C₂×C₇	1	2	yes	complemented
325	#2989	C₂×C₇	1	2	yes	complemented
326	#2962	C₂×C₇	1	1	yes	characteristic, complemented
327	#2961	C₂×C₇	1	1	yes	characteristic, complemented
328	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
329	#2933	C₂×C₇	1	1	yes	characteristic, complemented
330	#2933	C₂×C₇	1	1	yes	characteristic, complemented
331	#2930	C₂×C₇	1	1	yes	characteristic, complemented
332	#2929	C₂×C₇	1	1	yes	characteristic, complemented
333	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
334	#2924	C₂×C₇	1	1	yes	characteristic, complemented
335	#2924	C₂×C₇	1	1	yes	characteristic, complemented
336	#2923	C₂×C₇	1	1	yes	characteristic, complemented
337	#2906	C₂×C₇	1	1	yes	characteristic, complemented
338	#2905	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
340	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
341	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
342	C₇×#41	—	2	2	no	—
343	C₇×#41	—	2	2	no	—
344	C₇×#41	—	4	4	no	—
345	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
347	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
348	C₂×C₇×D₄	—	4	2	no	—
349	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
351	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
353	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
354	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
355	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
356	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
357	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
358	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
359	C₂²×C₄×C₇	—	2	2	no	—
360	C₂²×C₄×C₇	—	2	2	no	—
361	C₂²×C₄×C₇	—	2	2	no	—
362	C₂²×C₄×C₇	—	2	2	no	—
363	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
365	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
366	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
367	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
368	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
369	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
371	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
372	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
373	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
374	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
375	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
376	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
383	C₇×M₁₆	—	2	2	no	—
384	C₇×M₁₆	—	2	2	no	—
385	C₇×M₁₆	—	2	2	no	—
386	C₇×M₁₆	—	2	2	no	—
387	C₇×M₁₆	—	4	1	no	—
388	C₇×M₁₆	—	4	1	no	—
389	C₇×M₁₆	—	4	1	no	—
390	C₇×M₁₆	—	4	1	no	—
391	C₇×M₁₆	—	4	2	no	—
392	C₇×M₁₆	—	4	2	no	—
393	C₇×M₁₆	—	4	2	no	—
394	C₇×M₁₆	—	4	2	no	—
395	C₂×C₇×C₈	—	2	2	no	—
396	C₂×C₇×C₈	—	2	2	no	—
397	C₂×C₇×C₈	—	2	2	no	—
398	C₂×C₇×C₈	—	2	2	no	—
399	C₂×C₇×C₈	—	4	1	no	—
400	C₂×C₇×C₈	—	4	1	no	—
401	C₂×C₇×C₈	—	4	1	no	—
402	C₂×C₇×C₈	—	4	1	no	—
403	C₂×C₇×C₈	—	4	2	no	—
404	C₂×C₇×C₈	—	4	2	no	—
405	C₂×C₇×C₈	—	4	2	no	—
406	C₂×C₇×C₈	—	4	2	no	—
407	C₂×C₇×C₈	C₂⁴	1	2	yes	—
408	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₇×C₈	C₂⁴	1	2	yes	—
413	C₂×C₇×C₈	C₂⁴	1	2	yes	—
414	C₂×C₇×C₈	C₂⁴	1	2	yes	—
415	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
419	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
420	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
422	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
423	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
424	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
426	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
427	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
428	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
429	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
430	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
431	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
432	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
433	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
434	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
435	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
437	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
438	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
439	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
440	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
441	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
442	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
443	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
444	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
445	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
446	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
447	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
448	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
449	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
450	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
451	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
452	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
453	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
454	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
455	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
456	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
457	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
458	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
459	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
460	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
461	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
462	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
463	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
464	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
465	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
466	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
467	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
468	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
469	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
470	C₄²×C₇	C₂²×C₄	1	2	yes	—
471	C₄²×C₇	C₂²×C₄	1	2	yes	—
472	C₄²×C₇	C₂²×C₄	1	2	yes	—
473	C₄²×C₇	C₂²×C₄	1	2	yes	—
474	C₄²×C₇	C₂²×C₄	1	2	yes	—
475	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
476	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
477	C₄²×C₇	C₂²×C₄	1	2	yes	—
478	C₄²×C₇	C₂⁴	1	1	yes	characteristic
479	C₄²×C₇	C₂⁴	1	2	yes	—
480	C₄²×C₇	C₂⁴	1	2	yes	—
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₄²×C₇	C₂⁴	1	2	yes	—
483	C₂×#131	C₂²×C₇	1	1	yes	characteristic
484	C₂×#131	C₂²×C₇	1	1	yes	characteristic
485	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
486	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
487	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
488	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
489	#556	C₄×C₇	1	1	yes	characteristic
490	#555	C₄×C₇	1	1	yes	characteristic
491	#554	C₄×C₇	1	1	yes	characteristic
492	#553	C₄×C₇	1	1	yes	characteristic
493	#553	C₄×C₇	1	1	yes	characteristic
494	#552	C₄×C₇	1	1	yes	characteristic
495	#552	C₄×C₇	1	1	yes	characteristic
496	#552	C₄×C₇	1	2	yes	—
497	#551	C₄×C₇	1	2	yes	—
498	#551	C₄×C₇	1	2	yes	—
499	#547	C₄×C₇	1	1	yes	characteristic
500	#546	C₄×C₇	1	2	yes	—
501	#533	C₂²×C₇	1	1	yes	characteristic
502	#529	C₂²×C₇	1	2	yes	—
503	#529	C₂²×C₇	1	2	yes	—
504	#529	C₂²×C₇	1	2	yes	—
505	#525	C₂²×C₇	1	1	yes	characteristic
506	#525	C₂²×C₇	1	1	yes	characteristic
507	C₄×#41	C₂²×C₇	1	2	yes	—
508	C₄×#41	C₂²×C₇	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
510	C₂×#117	C₂²×C₇	1	1	yes	characteristic
511	C₂×#117	C₂²×C₇	1	1	yes	characteristic
512	#446	C₂²×C₇	1	2	yes	complemented
513	#446	C₂²×C₇	1	2	yes	complemented
514	#446	C₂²×C₇	1	2	yes	complemented
515	#446	C₂²×C₇	1	2	yes	complemented
516	#446	C₂²×C₇	1	2	yes	complemented
517	#446	C₂²×C₇	1	2	yes	complemented
518	#446	C₂²×C₇	1	2	yes	complemented
519	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
520	#436	C₂²×C₇	1	2	yes	—
521	#436	C₂²×C₇	1	2	yes	complemented
522	#436	C₂²×C₇	1	2	yes	complemented
523	#436	C₂²×C₇	1	2	yes	complemented
524	#436	C₂²×C₇	1	2	yes	complemented
525	#435	C₂²×C₇	1	1	yes	characteristic
526	#435	C₂²×C₇	1	1	yes	characteristic
527	#435	C₂²×C₇	1	1	yes	characteristic
528	#435	C₂²×C₇	1	1	yes	characteristic
529	#435	C₂²×C₇	1	1	yes	characteristic
530	#435	C₂²×C₇	1	1	yes	characteristic
531	#435	C₂²×C₇	1	1	yes	characteristic
532	#435	C₂²×C₇	1	1	yes	characteristic
533	#435	C₂²×C₇	1	2	yes	—
534	#435	C₂²×C₇	1	2	yes	—
535	#435	C₂²×C₇	1	2	yes	complemented
536	#435	C₂²×C₇	1	2	yes	complemented
537	#435	C₂²×C₇	1	2	yes	complemented
538	#435	C₂²×C₇	1	2	yes	complemented
539	#435	C₂²×C₇	1	2	yes	complemented
540	#435	C₂²×C₇	1	2	yes	complemented
541	#435	C₂²×C₇	1	2	yes	complemented
542	#435	C₂²×C₇	1	2	yes	complemented
543	C₈×D₄	C₂²×C₇	1	2	yes	—
544	C₈×D₄	C₂²×C₇	1	2	yes	complemented
545	C₈×D₄	C₂²×C₇	1	2	yes	complemented
546	C₈×D₄	C₂²×C₇	1	2	yes	complemented
547	C₈×D₄	C₂²×C₇	1	2	yes	complemented
548	#433	C₂²×C₇	1	2	yes	complemented
549	#433	C₂²×C₇	1	2	yes	complemented
550	#433	C₂²×C₇	1	2	yes	complemented
551	#433	C₂²×C₇	1	2	yes	complemented
552	#433	C₂²×C₇	1	2	yes	complemented
553	#433	C₂²×C₇	1	2	yes	complemented
554	#432	C₂²×C₇	1	2	yes	complemented
555	#432	C₂²×C₇	1	2	yes	complemented
556	#432	C₂²×C₇	1	2	yes	complemented
557	#432	C₂²×C₇	1	2	yes	complemented
558	#431	C₂²×C₇	1	2	yes	complemented
559	#431	C₂²×C₇	1	2	yes	complemented
560	#424	C₂²×C₇	1	1	yes	characteristic
561	#424	C₂²×C₇	1	1	yes	characteristic
562	#424	C₂²×C₇	1	1	yes	characteristic
563	#424	C₂²×C₇	1	1	yes	characteristic
564	#424	C₂²×C₇	1	1	yes	characteristic
565	#424	C₂²×C₇	1	1	yes	characteristic
566	#424	C₂²×C₇	1	1	yes	characteristic
567	#424	C₂²×C₇	1	1	yes	characteristic
568	#424	C₂²×C₇	1	2	yes	complemented
569	#424	C₂²×C₇	1	2	yes	complemented
570	#424	C₂²×C₇	1	2	yes	complemented
571	#424	C₂²×C₇	1	2	yes	complemented
572	#424	C₂²×C₇	1	2	yes	complemented
573	#424	C₂²×C₇	1	2	yes	complemented
574	#423	C₂²×C₇	1	1	yes	characteristic
575	#423	C₂²×C₇	1	2	yes	complemented
576	#423	C₂²×C₇	1	2	yes	complemented
577	#423	C₂²×C₇	1	2	yes	complemented
578	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
579	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
580	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
581	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
582	#408	C₂²×C₇	1	1	yes	characteristic
583	#408	C₂²×C₇	1	1	yes	characteristic
584	#407	C₂²×C₇	1	1	yes	characteristic
585	#407	C₂²×C₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
587	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
588	#405	C₂²×C₇	1	1	yes	characteristic
589	#405	C₂²×C₇	1	1	yes	characteristic
590	#405	C₂²×C₇	1	1	yes	characteristic
591	#405	C₂²×C₇	1	1	yes	characteristic
592	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
593	C₂×#97	C₂²×C₇	1	1	yes	characteristic
594	C₂³×C₇	—	2	2	no	—
595	C₂³×C₇	—	2	2	no	—
596	C₂³×C₇	—	2	2	no	—
597	C₂³×C₇	—	4	1	no	—
598	C₂³×C₇	—	4	1	no	—
599	C₂³×C₇	—	4	1	no	—
600	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
601	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
602	C₂³×C₇	C₂³×C₄	1	2	yes	—
603	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
604	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
605	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
606	C₇×Q₈	—	2	2	no	—
607	C₇×Q₈	—	4	2	no	—
608	C₇×Q₈	—	4	2	no	—
609	C₇×D₄	—	2	4	no	—
610	C₇×D₄	—	2	2	no	—
611	C₇×D₄	—	2	2	no	—
612	C₇×D₄	—	2	4	no	—
613	C₇×D₄	—	2	2	no	—
614	C₇×D₄	—	4	1	no	—
615	C₇×D₄	—	4	1	no	—
616	C₇×D₄	—	4	2	no	—
617	C₇×D₄	—	4	2	no	—
618	C₇×D₄	—	4	2	no	—
619	C₂×C₄×C₇	—	2	2	no	—
620	C₂×C₄×C₇	—	2	2	no	—
621	C₂×C₄×C₇	—	2	4	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	2	no	—
624	C₂×C₄×C₇	—	2	2	no	—
625	C₂×C₄×C₇	—	2	2	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	2	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	2	no	—
636	C₂×C₄×C₇	—	4	2	no	—
637	C₂×C₄×C₇	—	4	2	no	—
638	C₂×C₄×C₇	—	4	2	no	—
639	C₂×C₄×C₇	—	4	1	no	—
640	C₂×C₄×C₇	—	4	1	no	—
641	C₂×C₄×C₇	—	4	2	no	—
642	C₂×C₄×C₇	—	4	2	no	—
643	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
644	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
645	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
646	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
647	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
648	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
649	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
650	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
651	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
652	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
653	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
654	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
655	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
657	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
658	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
659	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
660	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
661	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
662	C₇×C₈	—	2	1	no	—
663	C₇×C₈	—	2	1	no	—
664	C₇×C₈	—	2	1	no	—
665	C₇×C₈	—	2	1	no	—
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	—	2	1	no	—
668	C₇×C₈	—	2	2	no	—
669	C₇×C₈	—	2	2	no	—
670	C₇×C₈	—	2	2	no	—
671	C₇×C₈	—	2	1	no	—
672	C₇×C₈	—	2	1	no	—
673	C₇×C₈	—	2	2	no	—
674	C₂×#41	C₂×C₄×C₇	1	2	yes	—
675	C₂×#41	C₂³×C₇	1	1	yes	characteristic
676	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
679	#131	—	4	2	no	—
680	#131	—	4	2	no	—
681	C₂×M₁₆	—	4	2	no	—
682	C₂×M₁₆	—	4	2	no	—
683	C₂×M₁₆	—	4	2	no	—
684	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
688	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
689	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₇	1	2	yes	—
691	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
692	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
693	C₂×M₁₆	C₂³×C₇	1	2	yes	—
694	C₂×M₁₆	C₂³×C₇	1	2	yes	—
695	C₂×M₁₆	C₂³×C₇	1	2	yes	—
696	C₂²×C₈	—	4	2	no	—
697	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
698	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
699	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
700	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
702	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
703	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
704	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
705	C₂²×C₈	C₂³×C₇	1	2	yes	—
706	C₂²×C₈	C₂³×C₇	1	2	yes	—
707	C₂²×C₈	C₂³×C₇	1	2	yes	—
708	C₂²×C₈	C₂³×C₇	1	2	yes	—
709	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
710	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
711	#126	C₂×C₄×C₇	1	2	yes	—
712	#126	C₂×C₄×C₇	1	2	yes	—
713	#126	C₂×C₄×C₇	1	2	yes	—
714	#126	C₂×C₄×C₇	1	2	yes	—
715	#126	C₂×C₄×C₇	1	2	yes	—
716	#126	C₂×C₄×C₇	1	2	yes	—
717	#125	C₂×C₄×C₇	1	2	yes	—
718	#125	C₂×C₄×C₇	1	2	yes	—
719	#125	C₂×C₄×C₇	1	2	yes	—
720	#125	C₂×C₄×C₇	1	1	yes	characteristic
721	#125	C₂×C₄×C₇	1	1	yes	characteristic
722	#124	C₂×C₄×C₇	1	2	yes	—
723	#124	C₂×C₄×C₇	1	2	yes	—
724	#124	C₂×C₄×C₇	1	2	yes	—
725	#123	C₂×C₄×C₇	1	2	yes	—
726	#123	C₂×C₄×C₇	1	2	yes	—
727	#123	C₂×C₄×C₇	1	2	yes	—
728	#123	C₂×C₄×C₇	1	2	yes	—
729	#123	C₂×C₄×C₇	1	2	yes	—
730	#123	C₂×C₄×C₇	1	2	yes	—
731	#123	C₂×C₄×C₇	1	2	yes	—
732	#123	C₂×C₄×C₇	1	2	yes	—
733	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
734	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
735	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
736	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
737	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
738	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
739	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
740	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
741	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
742	#121	C₂×C₄×C₇	1	1	yes	characteristic
743	#121	C₂×C₄×C₇	1	1	yes	characteristic
744	#121	C₂×C₄×C₇	1	1	yes	characteristic
745	#121	C₂×C₄×C₇	1	1	yes	characteristic
746	#121	C₂×C₄×C₇	1	2	yes	—
747	#121	C₂×C₄×C₇	1	2	yes	—
748	#121	C₂×C₄×C₇	1	2	yes	—
749	#120	C₂×C₄×C₇	1	2	yes	—
750	#120	C₂×C₄×C₇	1	2	yes	—
751	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
752	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
753	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₇	1	2	yes	—
755	C₄×Q₈	C₂³×C₇	1	2	yes	—
756	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
757	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
758	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
759	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
760	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
761	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
762	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
763	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
764	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
765	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
766	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
767	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₇	1	2	yes	—
772	C₄×D₄	C₂³×C₇	1	2	yes	—
773	C₄×D₄	C₂³×C₇	1	2	yes	—
774	C₄×D₄	C₂³×C₇	1	2	yes	—
775	#117	C₂×C₄×C₇	1	2	yes	—
776	#117	C₂×C₄×C₇	1	2	yes	—
777	#117	C₂×C₄×C₇	1	1	yes	characteristic
778	#117	C₂×C₄×C₇	1	1	yes	characteristic
779	#117	C₂×C₄×C₇	1	1	yes	characteristic
780	#117	C₂×C₄×C₇	1	1	yes	characteristic
781	#117	C₂×C₄×C₇	1	2	yes	—
782	#117	C₂×C₄×C₇	1	2	yes	—
783	#117	C₂×C₄×C₇	1	2	yes	—
784	#117	C₂³×C₇	1	1	yes	characteristic
785	#117	C₂³×C₇	1	1	yes	characteristic
786	#117	C₂³×C₇	1	1	yes	characteristic
787	#117	C₂³×C₇	1	2	yes	—
788	#117	C₂³×C₇	1	2	yes	—
789	#117	C₂³×C₇	1	2	yes	—
790	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
798	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₇	1	2	yes	—
800	C₂×C₄²	C₂³×C₇	1	2	yes	—
801	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₇	1	2	yes	—
803	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
804	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₇	1	2	yes	—
808	C₄⋊C₈	C₂³×C₇	1	2	yes	—
809	C₄⋊C₈	C₂³×C₇	1	2	yes	—
810	C₄⋊C₈	C₂³×C₇	1	2	yes	—
811	C₄⋊C₈	C₂³×C₇	1	2	yes	—
812	C₄⋊C₈	C₂³×C₇	1	2	yes	—
813	C₄⋊C₈	C₂³×C₇	1	2	yes	—
814	C₄⋊C₈	C₂³×C₇	1	2	yes	—
815	C₄⋊C₈	C₂³×C₇	1	2	yes	—
816	C₄⋊C₈	C₂³×C₇	1	2	yes	—
817	C₄⋊C₈	C₂³×C₇	1	2	yes	—
818	C₄⋊C₈	C₂³×C₇	1	2	yes	—
819	C₄⋊C₈	C₂³×C₇	1	2	yes	—
820	C₄⋊C₈	C₂³×C₇	1	2	yes	—
821	C₄⋊C₈	C₂³×C₇	1	2	yes	—
822	C₄⋊C₈	C₂³×C₇	1	2	yes	—
823	C₄⋊C₈	C₂³×C₇	1	2	yes	—
824	C₄⋊C₈	C₂³×C₇	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
826	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
827	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
828	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
829	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
830	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
831	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
835	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
841	#97	C₂³×C₇	1	1	yes	characteristic
842	#97	C₂³×C₇	1	1	yes	characteristic
843	#97	C₂³×C₇	1	1	yes	characteristic
844	#97	C₂³×C₇	1	1	yes	characteristic
845	#97	C₂³×C₇	1	2	yes	—
846	#97	C₂³×C₇	1	2	yes	—
847	#97	C₂³×C₇	1	2	yes	—
848	#97	C₂³×C₇	1	2	yes	—
849	#97	C₂³×C₇	1	2	yes	—
850	C₄×C₈	C₂³×C₇	1	2	yes	—
851	C₄×C₈	C₂³×C₇	1	2	yes	—
852	C₄×C₈	C₂³×C₇	1	2	yes	—
853	C₄×C₈	C₂³×C₇	1	2	yes	—
854	C₄×C₈	C₂³×C₇	1	2	yes	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	1	no	—
857	C₂²×C₇	—	2	1	no	—
858	C₂²×C₇	—	2	1	no	—
859	C₂²×C₇	—	2	1	no	—
860	C₂²×C₇	—	2	1	no	—
861	C₂²×C₇	—	2	1	no	—
862	C₂²×C₇	—	2	2	no	—
863	C₂²×C₇	—	2	1	no	—
864	C₂²×C₇	—	2	2	no	—
865	C₂²×C₇	—	2	1	no	—
866	C₂²×C₇	—	2	1	no	—
867	C₂²×C₇	—	2	1	no	—
868	C₂²×C₇	—	2	2	no	—
869	C₂²×C₇	—	2	1	no	—
870	C₂²×C₇	—	2	1	no	—
871	C₂²×C₇	—	4	4	no	—
872	C₂²×C₇	—	8	2	no	—
873	C₂²×C₇	#520	1	2	yes	—
874	C₂²×C₇	#568	1	2	yes	—
875	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
876	C₄×C₇	—	2	1	no	—
877	C₄×C₇	—	2	1	no	—
878	C₄×C₇	—	2	1	no	—
879	C₄×C₇	—	2	1	no	—
880	C₄×C₇	—	2	2	no	—
881	C₄×C₇	—	2	2	no	—
882	C₄×C₇	—	2	2	no	—
883	C₄×C₇	—	2	1	no	—
884	C₄×C₇	—	2	1	no	—
885	C₄×C₇	—	2	2	no	—
886	C₄×C₇	—	2	1	no	—
887	C₄×C₇	—	2	2	no	—
888	C₄×C₇	—	2	2	no	—
889	C₄×C₇	—	2	2	no	—
890	C₄×C₇	—	2	1	no	—
891	C₄×C₇	#520	1	2	yes	—
892	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
893	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
894	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
895	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
896	#41	—	2	2	no	—
897	#41	—	2	2	no	—
898	#41	—	4	4	no	—
899	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
900	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
901	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
904	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
905	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
906	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
907	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
908	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
909	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
910	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
911	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
912	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
918	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
919	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
920	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
921	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
922	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
923	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
924	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
925	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
926	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
927	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
928	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
929	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
930	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
937	M₁₆	—	2	2	no	—
938	M₁₆	—	2	2	no	—
939	M₁₆	—	2	2	no	—
940	M₁₆	—	2	2	no	—
941	M₁₆	—	4	1	no	—
942	M₁₆	—	4	1	no	—
943	M₁₆	—	4	1	no	—
944	M₁₆	—	4	1	no	—
945	M₁₆	—	4	2	no	—
946	M₁₆	—	4	2	no	—
947	M₁₆	—	4	2	no	—
948	M₁₆	—	4	2	no	—
949	C₂×C₈	—	2	2	no	—
950	C₂×C₈	—	2	2	no	—
951	C₂×C₈	—	2	2	no	—
952	C₂×C₈	—	2	2	no	—
953	C₂×C₈	—	4	1	no	—
954	C₂×C₈	—	4	1	no	—
955	C₂×C₈	—	4	1	no	—
956	C₂×C₈	—	4	1	no	—
957	C₂×C₈	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	C₂⁴×C₇	1	2	yes	—
962	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₇	1	2	yes	—
967	C₂×C₈	C₂⁴×C₇	1	2	yes	—
968	C₂×C₈	C₂⁴×C₇	1	2	yes	—
969	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
979	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
980	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
981	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
982	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
983	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
984	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
988	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
989	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
990	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
991	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
992	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
995	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
996	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
997	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
998	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
999	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1000	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1001	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1002	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1003	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1004	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1005	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1006	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1007	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1008	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1009	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1010	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1012	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1013	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1019	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1020	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1021	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1022	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1023	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1024	C₄²	C₂²×C₄×C₇	1	2	yes	—
1025	C₄²	C₂²×C₄×C₇	1	2	yes	—
1026	C₄²	C₂²×C₄×C₇	1	2	yes	—
1027	C₄²	C₂²×C₄×C₇	1	2	yes	—
1028	C₄²	C₂²×C₄×C₇	1	2	yes	—
1029	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1030	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1031	C₄²	C₂²×C₄×C₇	1	2	yes	—
1032	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₇	1	2	yes	—
1034	C₄²	C₂⁴×C₇	1	2	yes	—
1035	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₇	1	2	yes	—
1037	C₂×C₇	—	2	2	no	—
1038	C₂×C₇	—	2	2	no	—
1039	C₂×C₇	—	4	2	no	—
1040	C₂×C₇	—	4	1	no	—
1041	C₂×C₇	—	4	1	no	—
1042	C₂×C₇	—	4	1	no	—
1043	C₂×C₇	C₂×#520	1	1	yes	characteristic
1044	C₂×C₇	C₂×#568	1	1	yes	characteristic
1045	C₂×C₇	#3573	1	1	yes	characteristic
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
1053	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
1054	C₂³	C₂³×C₄×C₇	1	2	yes	—
1055	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
1056	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
1057	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
1058	Q₈	—	2	2	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	4	2	no	—
1061	D₄	—	2	4	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	4	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	4	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1096	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1097	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1098	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1099	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1100	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1101	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1102	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1103	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1104	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1105	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1106	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1107	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1108	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1109	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1110	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1111	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1112	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1113	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	2	no	—
1126	C₇	#60272	1	1	yes	characteristic, direct product factor, Sylow
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	4	no	—
1144	C₂²	—	8	2	no	—
1145	C₂²	C₇×#520	1	2	yes	—
1146	C₂²	C₇×#568	1	2	yes	—
1147	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	C₇×#520	1	2	yes	—
1164	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	4	2	no	—
1172	C₂	C₂×C₇×#520	1	1	yes	characteristic
1173	C₂	C₂×C₇×#568	1	1	yes	characteristic
1174	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×#2995	C₂	semidirect
4. C₇×#2994	C₂	semidirect
5. C₇×#2993	C₂	semidirect
6. C₇×#2992	C₂	semidirect
7. C₇×#2992	C₂	semidirect
8. C₇×#2990	C₂	semidirect
9. C₇×#2989	C₂	semidirect
10. C₇×#2962	C₂	semidirect
11. C₇×#2961	C₂	semidirect
12. C₇×D₄×M₁₆	C₂	semidirect
13. C₇×#2933	C₂	semidirect
14. C₇×#2933	C₂	semidirect
15. C₇×#2930	C₂	semidirect
16. C₇×#2929	C₂	semidirect
17. C₂×C₇×#435	C₂	semidirect
18. C₇×#2924	C₂	semidirect
19. C₇×#2924	C₂	semidirect
20. C₇×#2923	C₂	semidirect
21. C₇×#2906	C₂	semidirect
22. C₇×#2905	C₂	semidirect
23. C₂×C₇×#424	C₂	semidirect
53. C₇×#446	C₂²	semidirect
54. C₇×#446	C₂²	semidirect
55. C₇×#446	C₂²	semidirect
56. C₇×#446	C₂²	semidirect
57. C₇×#446	C₂²	semidirect
58. C₇×#446	C₂²	semidirect
59. C₇×#446	C₂²	semidirect
60. C₇×C₈×Q₈	C₂²	semidirect
62. C₇×#436	C₂²	semidirect
63. C₇×#436	C₂²	semidirect
64. C₇×#436	C₂²	semidirect
65. C₇×#436	C₂²	semidirect
76. C₇×#435	C₂²	semidirect
77. C₇×#435	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
79. C₇×#435	C₂²	semidirect
80. C₇×#435	C₂²	semidirect
81. C₇×#435	C₂²	semidirect
82. C₇×#435	C₂²	semidirect
83. C₇×#435	C₂²	semidirect
85. C₇×C₈×D₄	C₂²	semidirect
86. C₇×C₈×D₄	C₂²	semidirect
87. C₇×C₈×D₄	C₂²	semidirect
88. C₇×C₈×D₄	C₂²	semidirect
89. C₇×#433	C₂²	semidirect
90. C₇×#433	C₂²	semidirect
91. C₇×#433	C₂²	semidirect
92. C₇×#433	C₂²	semidirect
93. C₇×#433	C₂²	semidirect
94. C₇×#433	C₂²	semidirect
95. C₇×#432	C₂²	semidirect
96. C₇×#432	C₂²	semidirect
97. C₇×#432	C₂²	semidirect
98. C₇×#432	C₂²	semidirect
99. C₇×#431	C₂²	semidirect
100. C₇×#431	C₂²	semidirect
109. C₇×#424	C₂²	semidirect
110. C₇×#424	C₂²	semidirect
111. C₇×#424	C₂²	semidirect
112. C₇×#424	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
114. C₇×#424	C₂²	semidirect
116. C₇×#423	C₂²	semidirect
117. C₇×#423	C₂²	semidirect
118. C₇×#423	C₂²	semidirect
120. C₂×C₇×C₄⋊C₈	C₂²	semidirect
121. C₂×C₇×C₄⋊C₈	C₂²	semidirect
122. C₂×C₇×C₄⋊C₈	C₂²	semidirect
135. #60272	C₇	direct (N × H)
318. #2995	C₂×C₇	semidirect
319. #2995	C₂×C₇	semidirect
320. #2994	C₂×C₇	semidirect
321. #2993	C₂×C₇	semidirect
322. #2992	C₂×C₇	semidirect
323. #2992	C₂×C₇	semidirect
324. #2990	C₂×C₇	semidirect
325. #2989	C₂×C₇	semidirect
326. #2962	C₂×C₇	semidirect
327. #2961	C₂×C₇	semidirect
328. D₄×M₁₆	C₂×C₇	semidirect
329. #2933	C₂×C₇	semidirect
330. #2933	C₂×C₇	semidirect
331. #2930	C₂×C₇	semidirect
332. #2929	C₂×C₇	semidirect
333. C₂×#435	C₂×C₇	semidirect
334. #2924	C₂×C₇	semidirect
335. #2924	C₂×C₇	semidirect
336. #2923	C₂×C₇	semidirect
337. #2906	C₂×C₇	semidirect
338. #2905	C₂×C₇	semidirect
339. C₂×#424	C₂×C₇	semidirect
512. #446	C₂²×C₇	semidirect
513. #446	C₂²×C₇	semidirect
514. #446	C₂²×C₇	semidirect
515. #446	C₂²×C₇	semidirect
516. #446	C₂²×C₇	semidirect
517. #446	C₂²×C₇	semidirect
518. #446	C₂²×C₇	semidirect
519. C₈×Q₈	C₂²×C₇	semidirect
521. #436	C₂²×C₇	semidirect
522. #436	C₂²×C₇	semidirect
523. #436	C₂²×C₇	semidirect
524. #436	C₂²×C₇	semidirect
535. #435	C₂²×C₇	semidirect
536. #435	C₂²×C₇	semidirect
537. #435	C₂²×C₇	semidirect
538. #435	C₂²×C₇	semidirect
539. #435	C₂²×C₇	semidirect
540. #435	C₂²×C₇	semidirect
541. #435	C₂²×C₇	semidirect
542. #435	C₂²×C₇	semidirect
544. C₈×D₄	C₂²×C₇	semidirect
545. C₈×D₄	C₂²×C₇	semidirect
546. C₈×D₄	C₂²×C₇	semidirect
547. C₈×D₄	C₂²×C₇	semidirect
548. #433	C₂²×C₇	semidirect
549. #433	C₂²×C₇	semidirect
550. #433	C₂²×C₇	semidirect
551. #433	C₂²×C₇	semidirect
552. #433	C₂²×C₇	semidirect
553. #433	C₂²×C₇	semidirect
554. #432	C₂²×C₇	semidirect
555. #432	C₂²×C₇	semidirect
556. #432	C₂²×C₇	semidirect
557. #432	C₂²×C₇	semidirect
558. #431	C₂²×C₇	semidirect
559. #431	C₂²×C₇	semidirect
568. #424	C₂²×C₇	semidirect
569. #424	C₂²×C₇	semidirect
570. #424	C₂²×C₇	semidirect
571. #424	C₂²×C₇	semidirect
572. #424	C₂²×C₇	semidirect
573. #424	C₂²×C₇	semidirect
575. #423	C₂²×C₇	semidirect
576. #423	C₂²×C₇	semidirect
577. #423	C₂²×C₇	semidirect
579. C₂×C₄⋊C₈	C₂²×C₇	semidirect
580. C₂×C₄⋊C₈	C₂²×C₇	semidirect
581. C₂×C₄⋊C₈	C₂²×C₇	semidirect
1126. C₇	#60272	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×#2992	2
C₇×#2990	2
C₇×#2989	2
C₇×#2962	2
C₇×#2961	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2930	2
C₇×#2929	2
C₂×C₇×#435	2
C₇×#2924	2
C₇×#2923	2
C₇×#2906	2
C₇×#2905	2
C₂×C₇×#424	2
#60272	7

Subgroups — C7×#60272 #13237488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60272 #13237488