Subgroups — C₇×#60324 #13237540

Order 1792.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3481	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2978	C₂	1	2	yes	maximal, complemented
9	C₇×#2976	C₂	1	2	yes	maximal, complemented
10	C₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2973	C₂	1	2	yes	maximal, complemented
13	C₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2967	C₂	1	2	yes	maximal, complemented
16	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×D₄×M₁₆	C₂	1	2	yes	maximal, complemented
20	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	2	yes	maximal, complemented
22	C₇×#2930	C₂	1	2	yes	maximal, complemented
23	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#131	C₂²	1	2	yes	complemented
25	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
26	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
27	C₇×#559	C₄	1	1	yes	characteristic
28	C₇×#554	C₄	1	1	yes	characteristic
29	C₇×#554	C₄	1	1	yes	characteristic
30	C₇×#553	C₄	1	1	yes	characteristic
31	C₇×#553	C₄	1	1	yes	characteristic
32	C₇×#553	C₄	1	2	yes	—
33	C₇×#551	C₄	1	2	yes	—
34	C₇×#551	C₄	1	2	yes	—
35	C₇×#546	C₄	1	2	yes	—
36	C₇×#546	C₄	1	1	yes	characteristic
37	C₇×#546	C₄	1	1	yes	characteristic
38	C₇×D₄²	C₄	1	1	yes	characteristic
39	C₇×#532	C₂²	1	1	yes	characteristic
40	C₇×#529	C₂²	1	1	yes	characteristic
41	C₇×#529	C₂²	1	2	yes	—
42	C₇×#529	C₂²	1	1	yes	characteristic
43	C₇×#525	C₂²	1	2	yes	—
44	C₇×#525	C₂²	1	2	yes	—
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₄×C₇×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₇×#446	C₂²	1	1	yes	characteristic, complemented
51	C₇×#446	C₂²	1	1	yes	characteristic, complemented
52	C₇×#446	C₂²	1	1	yes	characteristic, complemented
53	C₇×#446	C₂²	1	2	yes	complemented
54	C₇×#446	C₂²	1	1	yes	characteristic, complemented
55	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₇×#436	C₂²	1	1	yes	characteristic
58	C₇×#436	C₂²	1	1	yes	characteristic
59	C₇×#436	C₂²	1	1	yes	characteristic
60	C₇×#436	C₂²	1	1	yes	characteristic
61	C₇×#436	C₂²	1	2	yes	complemented
62	C₇×#436	C₂²	1	1	yes	characteristic, complemented
63	C₇×#436	C₂²	1	2	yes	complemented
64	C₇×#436	C₂²	1	1	yes	characteristic, complemented
65	C₇×#436	C₂²	1	1	yes	characteristic, complemented
66	C₇×#436	C₂²	1	2	yes	complemented
67	C₇×#436	C₂²	1	2	yes	complemented
68	C₇×#436	C₂²	1	2	yes	complemented
69	C₇×#436	C₂²	1	2	yes	complemented
70	C₇×#436	C₂²	1	1	yes	characteristic, complemented
71	C₇×#436	C₂²	1	1	yes	characteristic, complemented
72	C₇×#436	C₂²	1	1	yes	characteristic, complemented
73	C₇×#436	C₂²	1	2	yes	complemented
74	C₇×#436	C₂²	1	2	yes	complemented
75	C₇×#435	C₂²	1	1	yes	characteristic
76	C₇×#435	C₂²	1	2	yes	—
77	C₇×#435	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
83	C₇×#435	C₂²	1	2	yes	complemented
84	C₇×#435	C₂²	1	2	yes	complemented
85	C₇×#435	C₂²	1	2	yes	complemented
86	C₇×#435	C₂²	1	2	yes	complemented
87	C₇×#435	C₂²	1	2	yes	complemented
88	C₇×#435	C₂²	1	2	yes	complemented
89	C₇×#435	C₂²	1	2	yes	complemented
90	C₇×#435	C₂²	1	1	yes	characteristic, complemented
91	C₇×#435	C₂²	1	2	yes	complemented
92	C₇×#435	C₂²	1	2	yes	complemented
93	C₇×#435	C₂²	1	2	yes	complemented
94	C₇×#435	C₂²	1	2	yes	complemented
95	C₇×C₈×D₄	C₂²	1	2	yes	complemented
96	C₇×C₈×D₄	C₂²	1	2	yes	complemented
97	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
98	C₇×C₈×D₄	C₂²	1	2	yes	complemented
99	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
100	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
101	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
102	C₇×#433	C₂²	1	2	yes	complemented
103	C₇×#433	C₂²	1	2	yes	complemented
104	C₇×#433	C₂²	1	2	yes	complemented
105	C₇×#433	C₂²	1	2	yes	complemented
106	C₇×#432	C₂²	1	1	yes	characteristic, complemented
107	C₇×#432	C₂²	1	2	yes	complemented
108	C₇×#432	C₂²	1	2	yes	complemented
109	C₇×#432	C₂²	1	1	yes	characteristic, complemented
110	C₇×#431	C₂²	1	1	yes	characteristic, complemented
111	C₇×#431	C₂²	1	1	yes	characteristic, complemented
112	C₇×#431	C₂²	1	1	yes	characteristic, complemented
113	C₇×#431	C₂²	1	1	yes	characteristic, complemented
114	C₇×#424	C₂²	1	2	yes	complemented
115	C₇×#424	C₂²	1	2	yes	complemented
116	C₇×#423	C₂²	1	2	yes	complemented
117	C₇×#423	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
120	C₇×#408	C₂²	1	2	yes	complemented
121	C₇×#408	C₂²	1	2	yes	complemented
122	C₇×#408	C₂²	1	2	yes	complemented
123	C₇×#407	C₂²	1	2	yes	complemented
124	C₇×#407	C₂²	1	2	yes	complemented
125	C₇×#407	C₂²	1	2	yes	complemented
126	C₇×#407	C₂²	1	2	yes	complemented
127	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
128	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
129	C₇×#405	C₂²	1	2	yes	complemented
130	C₇×#405	C₂²	1	2	yes	complemented
131	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
135	#60324	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
141	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
142	C₂³×C₄×C₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	2	yes	—
144	C₇×#131	—	4	4	no	—
145	C₂×C₇×M₁₆	—	4	4	no	—
146	C₂×C₇×M₁₆	—	4	4	no	—
147	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×M₁₆	C₂³	1	2	yes	—
149	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×M₁₆	C₂³	1	2	yes	—
151	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×M₁₆	C₂³	1	2	yes	—
153	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₇×M₁₆	C₂³	1	2	yes	—
155	C₂×C₇×M₁₆	C₂³	1	2	yes	—
156	C₂×C₇×M₁₆	C₂³	1	2	yes	—
157	C₂×C₇×M₁₆	C₂³	1	2	yes	—
158	C₂×C₇×M₁₆	C₂³	1	2	yes	—
159	C₂×C₇×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₇×C₈	C₂³	1	2	yes	—
162	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₇×C₈	C₂³	1	2	yes	—
164	C₂²×C₇×C₈	C₂³	1	2	yes	—
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	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
169	C₇×#127	C₂×C₄	1	1	yes	characteristic
170	C₇×#126	C₂×C₄	1	2	yes	—
171	C₇×#126	C₂×C₄	1	2	yes	—
172	C₇×#126	C₂×C₄	1	2	yes	—
173	C₇×#126	C₂×C₄	1	2	yes	—
174	C₇×#125	C₂×C₄	1	1	yes	characteristic
175	C₇×#125	C₂×C₄	1	2	yes	—
176	C₇×#125	C₂×C₄	1	1	yes	characteristic
177	C₇×#124	C₂×C₄	1	1	yes	characteristic
178	C₇×#124	C₂×C₄	1	1	yes	characteristic
179	C₇×#124	C₂×C₄	1	2	yes	—
180	C₇×#124	C₂×C₄	1	2	yes	—
181	C₇×#123	C₂×C₄	1	2	yes	—
182	C₇×#123	C₂×C₄	1	2	yes	—
183	C₇×#123	C₂×C₄	1	2	yes	—
184	C₇×#123	C₂×C₄	1	2	yes	—
185	C₇×#123	C₂×C₄	1	2	yes	—
186	C₇×#123	C₂×C₄	1	2	yes	—
187	C₇×#123	C₂×C₄	1	2	yes	—
188	C₇×#123	C₂×C₄	1	2	yes	—
189	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
193	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
194	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
195	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
196	C₇×#121	C₂×C₄	1	2	yes	—
197	C₇×#121	C₂×C₄	1	2	yes	—
198	C₇×#121	C₂×C₄	1	2	yes	—
199	C₇×#121	C₂×C₄	1	2	yes	—
200	C₇×#121	C₂×C₄	1	1	yes	characteristic
201	C₇×#121	C₂×C₄	1	1	yes	characteristic
202	C₇×#121	C₂×C₄	1	2	yes	—
203	C₇×#121	C₂×C₄	1	1	yes	characteristic
204	C₇×#121	C₂×C₄	1	1	yes	characteristic
205	C₇×#121	C₂×C₄	1	2	yes	—
206	C₇×#120	C₂×C₄	1	2	yes	—
207	C₇×#120	C₂×C₄	1	2	yes	—
208	C₇×#120	C₂×C₄	1	2	yes	—
209	C₇×#120	C₂×C₄	1	2	yes	—
210	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
211	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
212	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
213	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
214	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
215	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
216	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
217	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
218	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
219	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
220	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
221	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
222	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
226	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
227	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
228	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
229	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
230	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
231	C₄×C₇×D₄	C₂³	1	2	yes	—
232	C₄×C₇×D₄	C₂³	1	2	yes	—
233	C₄×C₇×D₄	C₂³	1	2	yes	—
234	C₄×C₇×D₄	C₂³	1	2	yes	—
235	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
236	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
237	C₄×C₇×D₄	C₂³	1	2	yes	—
238	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
239	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
240	C₄×C₇×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
245	C₇×#117	C₂×C₄	1	1	yes	characteristic
246	C₇×#117	C₂³	1	2	yes	—
247	C₇×#117	C₂³	1	2	yes	—
248	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
249	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
250	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
251	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
252	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
253	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
254	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
255	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₇	C₂³	1	2	yes	—
258	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
259	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₇×C₄⋊C₈	C₂³	1	2	yes	—
263	C₇×C₄⋊C₈	C₂³	1	2	yes	—
264	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₇×C₄⋊C₈	C₂³	1	2	yes	—
266	C₇×C₄⋊C₈	C₂³	1	2	yes	—
267	C₇×C₄⋊C₈	C₂³	1	2	yes	—
268	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₇×C₄⋊C₈	C₂³	1	2	yes	—
271	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₇×C₄⋊C₈	C₂³	1	2	yes	—
276	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
289	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
290	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
291	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
292	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
293	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
294	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
297	C₇×#97	C₂³	1	1	yes	characteristic
298	C₇×#97	C₂³	1	1	yes	characteristic
299	C₇×#97	C₂³	1	2	yes	—
300	C₇×#97	C₂³	1	1	yes	characteristic
301	C₇×#97	C₂³	1	1	yes	characteristic
302	C₇×#97	C₂³	1	2	yes	—
303	C₇×#97	C₂³	1	2	yes	—
304	C₇×#97	C₂³	1	2	yes	—
305	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
307	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
308	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₇×C₈	C₂³	1	2	yes	—
310	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	2	yes	—
314	#3481	C₂×C₇	1	1	yes	characteristic
315	#2995	C₂×C₇	1	2	yes	complemented
316	#2994	C₂×C₇	1	1	yes	characteristic, complemented
317	#2993	C₂×C₇	1	1	yes	characteristic, complemented
318	#2990	C₂×C₇	1	1	yes	characteristic, complemented
319	#2989	C₂×C₇	1	1	yes	characteristic, complemented
320	#2981	C₂×C₇	1	1	yes	characteristic, complemented
321	#2978	C₂×C₇	1	2	yes	complemented
322	#2976	C₂×C₇	1	2	yes	complemented
323	#2975	C₂×C₇	1	1	yes	characteristic, complemented
324	#2974	C₂×C₇	1	1	yes	characteristic, complemented
325	#2973	C₂×C₇	1	2	yes	complemented
326	#2971	C₂×C₇	1	1	yes	characteristic, complemented
327	#2969	C₂×C₇	1	1	yes	characteristic, complemented
328	#2967	C₂×C₇	1	2	yes	complemented
329	#2966	C₂×C₇	1	1	yes	characteristic, complemented
330	#2965	C₂×C₇	1	1	yes	characteristic, complemented
331	#2935	C₂×C₇	1	1	yes	characteristic, complemented
332	D₄×M₁₆	C₂×C₇	1	2	yes	complemented
333	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
334	#2933	C₂×C₇	1	2	yes	complemented
335	#2930	C₂×C₇	1	2	yes	complemented
336	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
337	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
338	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
339	C₇×#41	—	4	2	no	—
340	C₇×#41	—	4	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
346	C₂×C₇×D₄	—	4	2	no	—
347	C₂×C₇×D₄	—	4	2	no	—
348	C₂×C₇×D₄	—	4	4	no	—
349	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
355	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
356	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
357	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
358	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
359	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
360	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
361	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
362	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
363	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₇	—	4	2	no	—
365	C₂²×C₄×C₇	—	4	2	no	—
366	C₂²×C₄×C₇	—	4	2	no	—
367	C₂²×C₄×C₇	—	4	2	no	—
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	1	yes	characteristic
372	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
373	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
374	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
375	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
376	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
378	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
379	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
380	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
381	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
382	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
388	C₇×M₁₆	—	2	2	no	—
389	C₇×M₁₆	—	2	4	no	—
390	C₇×M₁₆	—	2	4	no	—
391	C₇×M₁₆	—	2	2	no	—
392	C₇×M₁₆	—	4	2	no	—
393	C₇×M₁₆	—	4	2	no	—
394	C₇×M₁₆	—	4	2	no	—
395	C₇×M₁₆	—	4	2	no	—
396	C₇×M₁₆	—	4	1	no	—
397	C₇×M₁₆	—	4	2	no	—
398	C₇×M₁₆	—	4	2	no	—
399	C₇×M₁₆	—	4	1	no	—
400	C₇×M₁₆	—	4	2	no	—
401	C₂×C₇×C₈	—	2	2	no	—
402	C₂×C₇×C₈	—	2	4	no	—
403	C₂×C₇×C₈	—	4	2	no	—
404	C₂×C₇×C₈	—	4	1	no	—
405	C₂×C₇×C₈	—	4	2	no	—
406	C₂×C₇×C₈	—	4	2	no	—
407	C₂×C₇×C₈	—	4	2	no	—
408	C₂×C₇×C₈	—	4	2	no	—
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	1	yes	characteristic
414	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
415	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₇×C₈	C₂⁴	1	2	yes	—
418	C₂×C₇×C₈	C₂⁴	1	2	yes	—
419	C₂×C₇×C₈	C₂⁴	1	2	yes	—
420	C₂×C₇×C₈	C₂⁴	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	2	yes	—
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	2	yes	—
433	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
434	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
436	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
443	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
444	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
445	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
446	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
447	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
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	2	yes	—
455	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
456	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
457	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
458	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
459	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
460	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
461	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
468	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
469	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
470	C₄²×C₇	C₂²×C₄	1	2	yes	—
471	C₄²×C₇	C₂²×C₄	1	2	yes	—
472	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
473	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
474	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
475	C₄²×C₇	C₂⁴	1	1	yes	characteristic
476	C₄²×C₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₇	C₂⁴	1	2	yes	—
478	C₄²×C₇	C₂⁴	1	1	yes	characteristic
479	C₄²×C₇	C₂⁴	1	1	yes	characteristic
480	C₂×#131	C₂²×C₇	1	2	yes	complemented
481	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
482	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
483	#559	C₄×C₇	1	1	yes	characteristic
484	#554	C₄×C₇	1	1	yes	characteristic
485	#554	C₄×C₇	1	1	yes	characteristic
486	#553	C₄×C₇	1	1	yes	characteristic
487	#553	C₄×C₇	1	1	yes	characteristic
488	#553	C₄×C₇	1	2	yes	—
489	#551	C₄×C₇	1	2	yes	—
490	#551	C₄×C₇	1	2	yes	—
491	#546	C₄×C₇	1	2	yes	—
492	#546	C₄×C₇	1	1	yes	characteristic
493	#546	C₄×C₇	1	1	yes	characteristic
494	D₄²	C₄×C₇	1	1	yes	characteristic
495	#532	C₂²×C₇	1	1	yes	characteristic
496	#529	C₂²×C₇	1	1	yes	characteristic
497	#529	C₂²×C₇	1	2	yes	—
498	#529	C₂²×C₇	1	1	yes	characteristic
499	#525	C₂²×C₇	1	2	yes	—
500	#525	C₂²×C₇	1	2	yes	—
501	C₄×#41	C₂²×C₇	1	1	yes	characteristic
502	C₄×#41	C₂²×C₇	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
506	#446	C₂²×C₇	1	1	yes	characteristic, complemented
507	#446	C₂²×C₇	1	1	yes	characteristic, complemented
508	#446	C₂²×C₇	1	1	yes	characteristic, complemented
509	#446	C₂²×C₇	1	2	yes	complemented
510	#446	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
512	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
513	#436	C₂²×C₇	1	1	yes	characteristic
514	#436	C₂²×C₇	1	1	yes	characteristic
515	#436	C₂²×C₇	1	1	yes	characteristic
516	#436	C₂²×C₇	1	1	yes	characteristic
517	#436	C₂²×C₇	1	2	yes	complemented
518	#436	C₂²×C₇	1	1	yes	characteristic, complemented
519	#436	C₂²×C₇	1	2	yes	complemented
520	#436	C₂²×C₇	1	1	yes	characteristic, complemented
521	#436	C₂²×C₇	1	1	yes	characteristic, 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	#436	C₂²×C₇	1	2	yes	complemented
526	#436	C₂²×C₇	1	1	yes	characteristic, complemented
527	#436	C₂²×C₇	1	1	yes	characteristic, complemented
528	#436	C₂²×C₇	1	1	yes	characteristic, complemented
529	#436	C₂²×C₇	1	2	yes	complemented
530	#436	C₂²×C₇	1	2	yes	complemented
531	#435	C₂²×C₇	1	1	yes	characteristic
532	#435	C₂²×C₇	1	2	yes	—
533	#435	C₂²×C₇	1	1	yes	characteristic
534	#435	C₂²×C₇	1	2	yes	complemented
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	1	yes	characteristic, 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	#435	C₂²×C₇	1	2	yes	complemented
544	#435	C₂²×C₇	1	2	yes	complemented
545	#435	C₂²×C₇	1	2	yes	complemented
546	#435	C₂²×C₇	1	1	yes	characteristic, complemented
547	#435	C₂²×C₇	1	2	yes	complemented
548	#435	C₂²×C₇	1	2	yes	complemented
549	#435	C₂²×C₇	1	2	yes	complemented
550	#435	C₂²×C₇	1	2	yes	complemented
551	C₈×D₄	C₂²×C₇	1	2	yes	complemented
552	C₈×D₄	C₂²×C₇	1	2	yes	complemented
553	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
554	C₈×D₄	C₂²×C₇	1	2	yes	complemented
555	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
556	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
557	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
558	#433	C₂²×C₇	1	2	yes	complemented
559	#433	C₂²×C₇	1	2	yes	complemented
560	#433	C₂²×C₇	1	2	yes	complemented
561	#433	C₂²×C₇	1	2	yes	complemented
562	#432	C₂²×C₇	1	1	yes	characteristic, complemented
563	#432	C₂²×C₇	1	2	yes	complemented
564	#432	C₂²×C₇	1	2	yes	complemented
565	#432	C₂²×C₇	1	1	yes	characteristic, complemented
566	#431	C₂²×C₇	1	1	yes	characteristic, complemented
567	#431	C₂²×C₇	1	1	yes	characteristic, complemented
568	#431	C₂²×C₇	1	1	yes	characteristic, complemented
569	#431	C₂²×C₇	1	1	yes	characteristic, complemented
570	#424	C₂²×C₇	1	2	yes	complemented
571	#424	C₂²×C₇	1	2	yes	complemented
572	#423	C₂²×C₇	1	2	yes	complemented
573	#423	C₂²×C₇	1	1	yes	characteristic, complemented
574	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
575	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
576	#408	C₂²×C₇	1	2	yes	complemented
577	#408	C₂²×C₇	1	2	yes	complemented
578	#408	C₂²×C₇	1	2	yes	complemented
579	#407	C₂²×C₇	1	2	yes	complemented
580	#407	C₂²×C₇	1	2	yes	complemented
581	#407	C₂²×C₇	1	2	yes	complemented
582	#407	C₂²×C₇	1	2	yes	complemented
583	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
584	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
585	#405	C₂²×C₇	1	2	yes	complemented
586	#405	C₂²×C₇	1	2	yes	complemented
587	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
588	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
589	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
590	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
591	C₂³×C₇	—	2	4	no	—
592	C₂³×C₇	—	4	2	no	—
593	C₂³×C₇	—	4	2	no	—
594	C₂³×C₇	—	4	2	no	—
595	C₂³×C₇	—	4	2	no	—
596	C₂³×C₇	—	4	2	no	—
597	C₂³×C₇	C₂³×C₄	1	2	yes	—
598	C₂³×C₇	C₂³×C₄	1	2	yes	—
599	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
600	C₂³×C₇	C₂³×C₄	1	2	yes	—
601	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
602	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	4	2	no	—
605	C₇×Q₈	—	4	1	no	—
606	C₇×D₄	—	2	2	no	—
607	C₇×D₄	—	2	4	no	—
608	C₇×D₄	—	2	2	no	—
609	C₇×D₄	—	2	2	no	—
610	C₇×D₄	—	2	2	no	—
611	C₇×D₄	—	2	2	no	—
612	C₇×D₄	—	4	2	no	—
613	C₇×D₄	—	4	2	no	—
614	C₇×D₄	—	4	2	no	—
615	C₇×D₄	—	4	2	no	—
616	C₇×D₄	—	4	2	no	—
617	C₇×D₄	—	4	2	no	—
618	C₇×D₄	—	4	2	no	—
619	C₇×D₄	—	4	1	no	—
620	C₇×D₄	—	4	2	no	—
621	C₂×C₄×C₇	—	2	2	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	1	no	—
626	C₂×C₄×C₇	—	2	2	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	2	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	2	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	2	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	2	no	—
635	C₂×C₄×C₇	—	2	2	no	—
636	C₂×C₄×C₇	—	2	1	no	—
637	C₂×C₄×C₇	—	4	2	no	—
638	C₂×C₄×C₇	—	4	2	no	—
639	C₂×C₄×C₇	—	4	2	no	—
640	C₂×C₄×C₇	—	4	2	no	—
641	C₂×C₄×C₇	—	4	2	no	—
642	C₂×C₄×C₇	—	4	2	no	—
643	C₂×C₄×C₇	—	4	2	no	—
644	C₂×C₄×C₇	—	4	1	no	—
645	C₂×C₄×C₇	—	4	1	no	—
646	C₂×C₄×C₇	—	4	2	no	—
647	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
648	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
649	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
650	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
651	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
652	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
653	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
654	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
655	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
657	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
658	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
660	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
661	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
662	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
664	C₇×C₈	—	2	2	no	—
665	C₇×C₈	—	2	1	no	—
666	C₇×C₈	—	2	2	no	—
667	C₇×C₈	—	2	1	no	—
668	C₇×C₈	—	2	2	no	—
669	C₇×C₈	—	2	1	no	—
670	C₇×C₈	—	2	1	no	—
671	C₇×C₈	—	2	2	no	—
672	C₇×C₈	—	2	1	no	—
673	C₇×C₈	—	2	1	no	—
674	C₇×C₈	—	2	1	no	—
675	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
676	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
677	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
678	C₂×#41	C₂³×C₇	1	2	yes	—
679	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
680	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
681	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
682	C₂³×C₄	C₂³×C₇	1	2	yes	—
683	C₂³×C₄	C₂³×C₇	1	2	yes	—
684	#131	—	4	4	no	—
685	C₂×M₁₆	—	4	4	no	—
686	C₂×M₁₆	—	4	4	no	—
687	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
688	C₂×M₁₆	C₂³×C₇	1	2	yes	—
689	C₂×M₁₆	C₂³×C₇	1	2	yes	—
690	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₇	1	2	yes	—
692	C₂×M₁₆	C₂³×C₇	1	2	yes	—
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	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₇	1	2	yes	—
698	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
699	C₂×M₁₆	C₂³×C₇	1	2	yes	—
700	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₇	1	2	yes	—
702	C₂²×C₈	C₂³×C₇	1	2	yes	—
703	C₂²×C₈	C₂³×C₇	1	2	yes	—
704	C₂²×C₈	C₂³×C₇	1	2	yes	—
705	C₂²×C₈	C₂³×C₇	1	2	yes	—
706	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
707	C₂²×C₈	C₂³×C₇	1	2	yes	—
708	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
709	#127	C₂×C₄×C₇	1	1	yes	characteristic
710	#126	C₂×C₄×C₇	1	2	yes	—
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	#125	C₂×C₄×C₇	1	1	yes	characteristic
715	#125	C₂×C₄×C₇	1	2	yes	—
716	#125	C₂×C₄×C₇	1	1	yes	characteristic
717	#124	C₂×C₄×C₇	1	1	yes	characteristic
718	#124	C₂×C₄×C₇	1	1	yes	characteristic
719	#124	C₂×C₄×C₇	1	2	yes	—
720	#124	C₂×C₄×C₇	1	2	yes	—
721	#123	C₂×C₄×C₇	1	2	yes	—
722	#123	C₂×C₄×C₇	1	2	yes	—
723	#123	C₂×C₄×C₇	1	2	yes	—
724	#123	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	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
730	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
731	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
732	C₂²⋊Q₈	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	2	yes	—
736	#121	C₂×C₄×C₇	1	2	yes	—
737	#121	C₂×C₄×C₇	1	2	yes	—
738	#121	C₂×C₄×C₇	1	2	yes	—
739	#121	C₂×C₄×C₇	1	2	yes	—
740	#121	C₂×C₄×C₇	1	1	yes	characteristic
741	#121	C₂×C₄×C₇	1	1	yes	characteristic
742	#121	C₂×C₄×C₇	1	2	yes	—
743	#121	C₂×C₄×C₇	1	1	yes	characteristic
744	#121	C₂×C₄×C₇	1	1	yes	characteristic
745	#121	C₂×C₄×C₇	1	2	yes	—
746	#120	C₂×C₄×C₇	1	2	yes	—
747	#120	C₂×C₄×C₇	1	2	yes	—
748	#120	C₂×C₄×C₇	1	2	yes	—
749	#120	C₂×C₄×C₇	1	2	yes	—
750	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
751	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
753	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
754	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
755	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
756	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
757	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
758	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
759	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
760	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
761	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
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	1	yes	characteristic
765	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
766	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
767	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
768	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
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	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₇	1	2	yes	—
778	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₇	1	2	yes	—
781	#117	C₂×C₄×C₇	1	1	yes	characteristic
782	#117	C₂×C₄×C₇	1	1	yes	characteristic
783	#117	C₂×C₄×C₇	1	2	yes	—
784	#117	C₂×C₄×C₇	1	1	yes	characteristic
785	#117	C₂×C₄×C₇	1	1	yes	characteristic
786	#117	C₂³×C₇	1	2	yes	—
787	#117	C₂³×C₇	1	2	yes	—
788	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
795	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₇	1	2	yes	—
798	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
799	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
800	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
802	C₄⋊C₈	C₂³×C₇	1	2	yes	—
803	C₄⋊C₈	C₂³×C₇	1	2	yes	—
804	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₇	1	2	yes	—
806	C₄⋊C₈	C₂³×C₇	1	2	yes	—
807	C₄⋊C₈	C₂³×C₇	1	2	yes	—
808	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₇	1	2	yes	—
811	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₇	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
817	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
821	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
822	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
823	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
826	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
827	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
828	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
833	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
835	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
836	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
837	#97	C₂³×C₇	1	1	yes	characteristic
838	#97	C₂³×C₇	1	1	yes	characteristic
839	#97	C₂³×C₇	1	2	yes	—
840	#97	C₂³×C₇	1	1	yes	characteristic
841	#97	C₂³×C₇	1	1	yes	characteristic
842	#97	C₂³×C₇	1	2	yes	—
843	#97	C₂³×C₇	1	2	yes	—
844	#97	C₂³×C₇	1	2	yes	—
845	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₇	1	2	yes	—
850	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₇	1	2	yes	—
853	C₄×C₈	C₂³×C₇	1	2	yes	—
854	C₂²×C₇	—	2	1	no	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	1	no	—
857	C₂²×C₇	—	2	2	no	—
858	C₂²×C₇	—	2	2	no	—
859	C₂²×C₇	—	2	2	no	—
860	C₂²×C₇	—	2	1	no	—
861	C₂²×C₇	—	2	1	no	—
862	C₂²×C₇	—	2	1	no	—
863	C₂²×C₇	—	2	1	no	—
864	C₂²×C₇	—	2	2	no	—
865	C₂²×C₇	—	2	1	no	—
866	C₂²×C₇	—	2	2	no	—
867	C₂²×C₇	—	2	2	no	—
868	C₂²×C₇	—	2	2	no	—
869	C₂²×C₇	—	2	2	no	—
870	C₂²×C₇	—	2	2	no	—
871	C₂²×C₇	—	8	4	no	—
872	C₂²×C₇	—	8	4	no	—
873	C₂²×C₇	#568	1	2	yes	—
874	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
875	C₄×C₇	—	2	1	no	—
876	C₄×C₇	—	2	2	no	—
877	C₄×C₇	—	2	1	no	—
878	C₄×C₇	—	2	2	no	—
879	C₄×C₇	—	2	2	no	—
880	C₄×C₇	—	2	1	no	—
881	C₄×C₇	—	2	1	no	—
882	C₄×C₇	—	2	1	no	—
883	C₄×C₇	—	2	1	no	—
884	C₄×C₇	—	2	1	no	—
885	C₄×C₇	—	2	1	no	—
886	C₄×C₇	—	2	1	no	—
887	C₄×C₇	—	2	2	no	—
888	C₄×C₇	—	2	1	no	—
889	C₄×C₇	—	2	2	no	—
890	C₄×C₇	#568	1	2	yes	—
891	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
892	C₄×C₇	#585	1	1	yes	characteristic
893	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
894	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
895	#41	—	4	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
900	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
901	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	4	no	—
905	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
906	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	1	yes	characteristic
912	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
913	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
914	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
915	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
916	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
917	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
918	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
925	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
926	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
927	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	C₂²×C₄×C₇	1	1	yes	characteristic
932	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
933	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
934	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
935	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
936	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
937	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
944	M₁₆	—	2	2	no	—
945	M₁₆	—	2	4	no	—
946	M₁₆	—	2	4	no	—
947	M₁₆	—	2	2	no	—
948	M₁₆	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	M₁₆	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	M₁₆	—	4	1	no	—
953	M₁₆	—	4	2	no	—
954	M₁₆	—	4	2	no	—
955	M₁₆	—	4	1	no	—
956	M₁₆	—	4	2	no	—
957	C₂×C₈	—	2	2	no	—
958	C₂×C₈	—	2	4	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	—	4	1	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	—	4	2	no	—
963	C₂×C₈	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
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	C₂×C₈	C₂⁴×C₇	1	2	yes	—
974	C₂×C₈	C₂⁴×C₇	1	2	yes	—
975	C₂×C₈	C₂⁴×C₇	1	2	yes	—
976	C₂×C₈	C₂⁴×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	2	yes	—
980	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	2	yes	—
985	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
986	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
989	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
1009	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1011	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
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	1	yes	characteristic
1016	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
1017	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1024	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1025	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1026	C₄²	C₂²×C₄×C₇	1	2	yes	—
1027	C₄²	C₂²×C₄×C₇	1	2	yes	—
1028	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1029	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1030	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₇	1	2	yes	—
1034	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1036	C₂×C₇	—	2	2	no	—
1037	C₂×C₇	—	4	1	no	—
1038	C₂×C₇	—	4	2	no	—
1039	C₂×C₇	—	4	2	no	—
1040	C₂×C₇	—	4	1	no	—
1041	C₂×C₇	—	4	2	no	—
1042	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1043	C₂×C₇	C₂×#568	1	1	yes	characteristic
1044	C₂×C₇	C₂×#568	1	1	yes	characteristic
1045	C₂³	—	2	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	4	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	C₂³×C₄×C₇	1	2	yes	—
1052	C₂³	C₂³×C₄×C₇	1	2	yes	—
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	Q₈	—	2	2	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	4	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1102	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1103	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1104	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1105	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
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	2	yes	—
1111	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1112	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1113	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1114	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1115	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1116	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1117	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
1130	C₇	#60324	1	1	yes	characteristic, direct product factor, Sylow
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	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	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	8	4	no	—
1149	C₂²	—	8	4	no	—
1150	C₂²	C₇×#568	1	2	yes	—
1151	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	C₇×#568	1	2	yes	—
1168	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1169	C₄	C₇×#585	1	1	yes	characteristic
1170	C₂	—	2	2	no	—
1171	C₂	—	4	1	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₂	C₂×C₇×#568	1	1	yes	characteristic
1178	C₂	C₂×C₇×#568	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×#3481	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×#2990	C₂	semidirect
6. C₇×#2989	C₂	semidirect
7. C₇×#2981	C₂	semidirect
8. C₇×#2978	C₂	semidirect
9. C₇×#2976	C₂	semidirect
10. C₇×#2975	C₂	semidirect
11. C₇×#2974	C₂	semidirect
12. C₇×#2973	C₂	semidirect
13. C₇×#2971	C₂	semidirect
14. C₇×#2969	C₂	semidirect
15. C₇×#2967	C₂	semidirect
16. C₇×#2966	C₂	semidirect
17. C₇×#2965	C₂	semidirect
18. C₇×#2935	C₂	semidirect
19. C₇×D₄×M₁₆	C₂	semidirect
20. C₇×D₄×M₁₆	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2930	C₂	semidirect
23. C₂×C₇×#436	C₂	semidirect
24. C₂×C₇×#131	C₂²	semidirect
25. C₂²×C₇×M₁₆	C₂²	semidirect
26. C₂²×C₇×M₁₆	C₂²	semidirect
50. C₇×#446	C₂²	semidirect
51. C₇×#446	C₂²	semidirect
52. C₇×#446	C₂²	semidirect
53. C₇×#446	C₂²	semidirect
54. C₇×#446	C₂²	semidirect
55. C₇×C₈×Q₈	C₂²	semidirect
56. C₇×C₈×Q₈	C₂²	semidirect
61. C₇×#436	C₂²	semidirect
62. C₇×#436	C₂²	semidirect
63. C₇×#436	C₂²	semidirect
64. C₇×#436	C₂²	semidirect
65. C₇×#436	C₂²	semidirect
66. C₇×#436	C₂²	semidirect
67. C₇×#436	C₂²	semidirect
68. C₇×#436	C₂²	semidirect
69. C₇×#436	C₂²	semidirect
70. C₇×#436	C₂²	semidirect
71. C₇×#436	C₂²	semidirect
72. C₇×#436	C₂²	semidirect
73. C₇×#436	C₂²	semidirect
74. C₇×#436	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
84. C₇×#435	C₂²	semidirect
85. C₇×#435	C₂²	semidirect
86. C₇×#435	C₂²	semidirect
87. C₇×#435	C₂²	semidirect
88. C₇×#435	C₂²	semidirect
89. C₇×#435	C₂²	semidirect
90. C₇×#435	C₂²	semidirect
91. C₇×#435	C₂²	semidirect
92. C₇×#435	C₂²	semidirect
93. C₇×#435	C₂²	semidirect
94. C₇×#435	C₂²	semidirect
95. C₇×C₈×D₄	C₂²	semidirect
96. C₇×C₈×D₄	C₂²	semidirect
97. C₇×C₈×D₄	C₂²	semidirect
98. C₇×C₈×D₄	C₂²	semidirect
99. C₇×C₈×D₄	C₂²	semidirect
100. C₇×C₈×D₄	C₂²	semidirect
101. C₇×C₈×D₄	C₂²	semidirect
102. C₇×#433	C₂²	semidirect
103. C₇×#433	C₂²	semidirect
104. C₇×#433	C₂²	semidirect
105. C₇×#433	C₂²	semidirect
106. C₇×#432	C₂²	semidirect
107. C₇×#432	C₂²	semidirect
108. C₇×#432	C₂²	semidirect
109. C₇×#432	C₂²	semidirect
110. C₇×#431	C₂²	semidirect
111. C₇×#431	C₂²	semidirect
112. C₇×#431	C₂²	semidirect
113. C₇×#431	C₂²	semidirect
114. C₇×#424	C₂²	semidirect
115. C₇×#424	C₂²	semidirect
116. C₇×#423	C₂²	semidirect
117. C₇×#423	C₂²	semidirect
118. C₂×C₇×C₄⋊C₈	C₂²	semidirect
119. C₂×C₇×C₄⋊C₈	C₂²	semidirect
120. C₇×#408	C₂²	semidirect
121. C₇×#408	C₂²	semidirect
122. C₇×#408	C₂²	semidirect
123. C₇×#407	C₂²	semidirect
124. C₇×#407	C₂²	semidirect
125. C₇×#407	C₂²	semidirect
126. C₇×#407	C₂²	semidirect
127. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
128. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
129. C₇×#405	C₂²	semidirect
130. C₇×#405	C₂²	semidirect
131. C₄×C₇×M₁₆	C₂²	semidirect
132. C₄×C₇×M₁₆	C₂²	semidirect
133. C₄×C₇×M₁₆	C₂²	semidirect
134. C₂×C₄×C₇×C₈	C₂²	semidirect
135. #60324	C₇	direct (N × H)
315. #2995	C₂×C₇	semidirect
316. #2994	C₂×C₇	semidirect
317. #2993	C₂×C₇	semidirect
318. #2990	C₂×C₇	semidirect
319. #2989	C₂×C₇	semidirect
320. #2981	C₂×C₇	semidirect
321. #2978	C₂×C₇	semidirect
322. #2976	C₂×C₇	semidirect
323. #2975	C₂×C₇	semidirect
324. #2974	C₂×C₇	semidirect
325. #2973	C₂×C₇	semidirect
326. #2971	C₂×C₇	semidirect
327. #2969	C₂×C₇	semidirect
328. #2967	C₂×C₇	semidirect
329. #2966	C₂×C₇	semidirect
330. #2965	C₂×C₇	semidirect
331. #2935	C₂×C₇	semidirect
332. D₄×M₁₆	C₂×C₇	semidirect
333. D₄×M₁₆	C₂×C₇	semidirect
334. #2933	C₂×C₇	semidirect
335. #2930	C₂×C₇	semidirect
336. C₂×#436	C₂×C₇	semidirect
480. C₂×#131	C₂²×C₇	semidirect
481. C₂²×M₁₆	C₂²×C₇	semidirect
482. C₂²×M₁₆	C₂²×C₇	semidirect
506. #446	C₂²×C₇	semidirect
507. #446	C₂²×C₇	semidirect
508. #446	C₂²×C₇	semidirect
509. #446	C₂²×C₇	semidirect
510. #446	C₂²×C₇	semidirect
511. C₈×Q₈	C₂²×C₇	semidirect
512. C₈×Q₈	C₂²×C₇	semidirect
517. #436	C₂²×C₇	semidirect
518. #436	C₂²×C₇	semidirect
519. #436	C₂²×C₇	semidirect
520. #436	C₂²×C₇	semidirect
521. #436	C₂²×C₇	semidirect
522. #436	C₂²×C₇	semidirect
523. #436	C₂²×C₇	semidirect
524. #436	C₂²×C₇	semidirect
525. #436	C₂²×C₇	semidirect
526. #436	C₂²×C₇	semidirect
527. #436	C₂²×C₇	semidirect
528. #436	C₂²×C₇	semidirect
529. #436	C₂²×C₇	semidirect
530. #436	C₂²×C₇	semidirect
534. #435	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
543. #435	C₂²×C₇	semidirect
544. #435	C₂²×C₇	semidirect
545. #435	C₂²×C₇	semidirect
546. #435	C₂²×C₇	semidirect
547. #435	C₂²×C₇	semidirect
548. #435	C₂²×C₇	semidirect
549. #435	C₂²×C₇	semidirect
550. #435	C₂²×C₇	semidirect
551. C₈×D₄	C₂²×C₇	semidirect
552. C₈×D₄	C₂²×C₇	semidirect
553. C₈×D₄	C₂²×C₇	semidirect
554. C₈×D₄	C₂²×C₇	semidirect
555. C₈×D₄	C₂²×C₇	semidirect
556. C₈×D₄	C₂²×C₇	semidirect
557. C₈×D₄	C₂²×C₇	semidirect
558. #433	C₂²×C₇	semidirect
559. #433	C₂²×C₇	semidirect
560. #433	C₂²×C₇	semidirect
561. #433	C₂²×C₇	semidirect
562. #432	C₂²×C₇	semidirect
563. #432	C₂²×C₇	semidirect
564. #432	C₂²×C₇	semidirect
565. #432	C₂²×C₇	semidirect
566. #431	C₂²×C₇	semidirect
567. #431	C₂²×C₇	semidirect
568. #431	C₂²×C₇	semidirect
569. #431	C₂²×C₇	semidirect
570. #424	C₂²×C₇	semidirect
571. #424	C₂²×C₇	semidirect
572. #423	C₂²×C₇	semidirect
573. #423	C₂²×C₇	semidirect
574. C₂×C₄⋊C₈	C₂²×C₇	semidirect
575. C₂×C₄⋊C₈	C₂²×C₇	semidirect
576. #408	C₂²×C₇	semidirect
577. #408	C₂²×C₇	semidirect
578. #408	C₂²×C₇	semidirect
579. #407	C₂²×C₇	semidirect
580. #407	C₂²×C₇	semidirect
581. #407	C₂²×C₇	semidirect
582. #407	C₂²×C₇	semidirect
583. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
584. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
585. #405	C₂²×C₇	semidirect
586. #405	C₂²×C₇	semidirect
587. C₄×M₁₆	C₂²×C₇	semidirect
588. C₄×M₁₆	C₂²×C₇	semidirect
589. C₄×M₁₆	C₂²×C₇	semidirect
590. C₂×C₄×C₈	C₂²×C₇	semidirect
1130. C₇	#60324	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×#3481	2
C₇×#2995	2
C₇×#2994	2
C₇×#2993	2
C₇×#2990	2
C₇×#2989	2
C₇×#2981	2
C₇×#2978	2
C₇×#2976	2
C₇×#2975	2
C₇×#2974	2
C₇×#2973	2
C₇×#2971	2
C₇×#2969	2
C₇×#2967	2
C₇×#2966	2
C₇×#2965	2
C₇×#2935	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2930	2
C₂×C₇×#436	2
#60324	7

Subgroups — C7×#60324 #13237540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60324 #13237540