Subgroups — C₇×#60917 #13238133

Order 1792.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3256	C₂	1	4	yes	maximal, complemented
4	C₇×#3252	C₂	1	2	yes	maximal, complemented
5	C₇×#3251	C₂	1	2	yes	maximal, complemented
6	C₇×#3250	C₂	1	4	yes	maximal, complemented
7	C₇×#3248	C₂	1	2	yes	maximal, complemented
8	C₇×#3247	C₂	1	2	yes	maximal, complemented
9	C₇×#3080	C₂	1	2	yes	maximal, complemented
10	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3056	C₂	1	2	yes	maximal, complemented
13	C₇×#3055	C₂	1	2	yes	maximal, complemented
14	C₇×#3040	C₂	1	2	yes	maximal, complemented
15	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
21	C₇×#533	C₂²	1	1	yes	characteristic
22	C₇×#533	C₂²	1	1	yes	characteristic, complemented
23	C₇×#533	C₂²	1	1	yes	characteristic, complemented
24	C₇×#532	C₂²	1	1	yes	characteristic
25	C₇×#532	C₂²	1	1	yes	characteristic, complemented
26	C₇×#532	C₂²	1	1	yes	characteristic, complemented
27	C₇×#529	—	2	1	no	—
28	C₇×#529	—	2	1	no	—
29	C₇×#529	—	2	1	no	—
30	C₇×#529	—	2	1	no	—
31	C₇×#529	—	2	1	no	—
32	C₇×#529	—	2	1	no	—
33	C₇×#529	—	2	1	no	—
34	C₇×#529	—	2	1	no	—
35	C₇×#529	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	complemented
40	C₇×#529	C₂²	1	2	yes	complemented
41	C₂×C₇×#126	—	2	1	no	—
42	C₂×C₇×#125	C₂²	1	1	yes	characteristic
43	C₂×C₇×#124	C₂²	1	1	yes	characteristic
44	C₇×#525	—	2	1	no	—
45	C₇×#525	—	2	1	no	—
46	C₇×#525	C₂²	1	2	yes	—
47	C₂×C₇×#123	—	2	1	no	—
48	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#121	C₂²	1	1	yes	characteristic
50	C₄×C₇×#41	—	2	1	no	—
51	C₄×C₇×#41	—	2	1	no	—
52	C₄×C₇×#41	C₂²	1	2	yes	—
53	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₇×D₄	—	2	1	no	—
55	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
56	C₂×C₇×#117	—	2	1	no	—
57	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
58	C₇×#479	C₂²	1	4	yes	complemented
59	C₇×#479	C₂²	1	4	yes	complemented
60	C₇×#479	C₂²	1	4	yes	complemented
61	C₇×#478	C₂²	1	4	yes	complemented
62	C₇×#478	C₂²	1	4	yes	complemented
63	C₇×#478	C₂²	1	4	yes	complemented
64	C₇×#477	C₂²	1	2	yes	complemented
65	C₇×#476	C₂²	1	2	yes	complemented
66	C₇×#475	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#470	C₂²	1	4	yes	complemented
69	C₇×#469	C₂²	1	4	yes	—
70	C₇×#468	C₂²	1	4	yes	—
71	C₇×#468	C₂²	1	4	yes	complemented
72	C₇×#467	C₂²	1	4	yes	complemented
73	C₇×#466	C₂²	1	4	yes	—
74	C₇×#465	C₂²	1	4	yes	—
75	C₇×#465	C₂²	1	4	yes	complemented
76	C₇×#464	C₂²	1	4	yes	complemented
77	C₇×#464	C₂²	1	4	yes	complemented
78	C₇×#464	C₂²	1	4	yes	complemented
79	C₇×#463	C₂²	1	4	yes	complemented
80	C₇×#463	C₂²	1	4	yes	complemented
81	C₇×#463	C₂²	1	4	yes	complemented
82	C₇×#462	C₂²	1	2	yes	complemented
83	C₇×#461	C₂²	1	2	yes	complemented
84	C₇×#460	C₂²	1	2	yes	complemented
85	C₇×#459	C₂²	1	2	yes	complemented
86	C₇×#428	C₂²	1	2	yes	—
87	C₇×#428	C₂²	1	2	yes	—
88	C₇×#423	C₂²	1	1	yes	characteristic
89	C₇×#423	C₂²	1	1	yes	characteristic
90	C₇×#423	C₂²	1	2	yes	—
91	C₇×#423	C₂²	1	2	yes	complemented
92	C₇×#423	C₂²	1	2	yes	complemented
93	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
94	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
95	C₇×#419	C₂²	1	2	yes	—
96	C₇×#418	C₂²	1	2	yes	—
97	C₇×#417	C₂²	1	2	yes	—
98	C₇×#417	C₂²	1	2	yes	—
99	#60917	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×C₇×#41	—	2	1	no	—
101	C₂×C₇×#41	—	2	1	no	—
102	C₂×C₇×#41	C₂³	1	2	yes	—
103	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×D₄	—	2	1	no	—
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	—	2	1	no	—
107	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
109	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
110	C₇×#137	—	4	4	no	—
111	C₇×AGL(1,ℤ/8)	—	4	4	no	—
112	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₇×D₈	C₂³	1	4	yes	—
116	C₂×C₇×M₁₆	—	4	4	no	—
117	C₂×C₇×M₁₆	C₂³	1	2	yes	—
118	C₂×C₇×M₁₆	C₂³	1	2	yes	—
119	C₂×C₇×M₁₆	C₂³	1	4	yes	—
120	C₂²×C₇×C₈	C₂³	1	4	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₇×#127	C₂³	1	1	yes	characteristic
125	C₇×#126	—	2	2	no	—
126	C₇×#126	—	2	2	no	—
127	C₇×#126	—	2	2	no	—
128	C₇×#126	—	2	2	no	—
129	C₇×#126	—	2	2	no	—
130	C₇×#126	—	2	2	no	—
131	C₇×#125	—	2	1	no	—
132	C₇×#125	—	2	1	no	—
133	C₇×#125	—	2	1	no	—
134	C₇×#125	—	2	1	no	—
135	C₇×#125	C₂³	1	2	yes	—
136	C₇×#125	C₂³	1	2	yes	—
137	C₇×#125	C₂³	1	2	yes	—
138	C₇×#124	—	2	1	no	—
139	C₇×#124	—	2	1	no	—
140	C₇×#124	—	2	1	no	—
141	C₇×#124	—	2	1	no	—
142	C₇×#124	C₂³	1	2	yes	—
143	C₇×#124	C₂³	1	2	yes	—
144	C₇×#124	C₂³	1	2	yes	—
145	C₇×#123	—	2	2	no	—
146	C₇×#123	—	2	2	no	—
147	C₇×#123	—	2	2	no	—
148	C₇×#123	—	2	2	no	—
149	C₇×#123	—	2	2	no	—
150	C₇×#123	—	2	2	no	—
151	C₇×#123	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	1	no	—
153	C₇×C₂²⋊Q₈	—	2	1	no	—
154	C₇×C₂²⋊Q₈	—	2	1	no	—
155	C₇×C₂²⋊Q₈	—	2	1	no	—
156	C₇×C₂²⋊Q₈	—	2	1	no	—
157	C₇×C₂²⋊Q₈	—	2	1	no	—
158	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
162	C₇×#121	—	2	1	no	—
163	C₇×#121	—	2	1	no	—
164	C₇×#121	—	2	1	no	—
165	C₇×#121	—	2	1	no	—
166	C₇×#121	—	2	1	no	—
167	C₇×#121	—	2	1	no	—
168	C₇×#121	C₂³	1	2	yes	—
169	C₇×#121	C₂³	1	2	yes	—
170	C₇×#121	C₂³	1	2	yes	—
171	C₇×#121	C₂³	1	2	yes	—
172	C₇×#120	—	2	2	no	—
173	C₄×C₇×Q₈	—	2	1	no	—
174	C₄×C₇×Q₈	—	2	1	no	—
175	C₄×C₇×Q₈	—	2	1	no	—
176	C₄×C₇×Q₈	—	2	1	no	—
177	C₄×C₇×Q₈	—	2	1	no	—
178	C₄×C₇×Q₈	—	2	1	no	—
179	C₄×C₇×Q₈	C₂³	1	2	yes	—
180	C₄×C₇×Q₈	C₂³	1	2	yes	—
181	C₄×C₇×Q₈	C₂³	1	2	yes	—
182	C₄×C₇×Q₈	C₂³	1	2	yes	—
183	C₄×C₇×D₄	—	2	2	no	—
184	C₄×C₇×D₄	—	2	2	no	—
185	C₄×C₇×D₄	—	2	2	no	—
186	C₄×C₇×D₄	—	2	2	no	—
187	C₄×C₇×D₄	—	2	2	no	—
188	C₄×C₇×D₄	—	2	2	no	—
189	C₄×C₇×D₄	—	2	2	no	—
190	C₄×C₇×D₄	—	2	2	no	—
191	C₄×C₇×D₄	—	2	2	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	—	2	1	no	—
194	C₄×C₇×D₄	—	2	1	no	—
195	C₄×C₇×D₄	—	2	1	no	—
196	C₄×C₇×D₄	—	2	1	no	—
197	C₄×C₇×D₄	—	2	1	no	—
198	C₄×C₇×D₄	—	2	1	no	—
199	C₄×C₇×D₄	C₂³	1	2	yes	—
200	C₄×C₇×D₄	C₂³	1	2	yes	—
201	C₄×C₇×D₄	C₂³	1	2	yes	—
202	C₄×C₇×D₄	C₂³	1	2	yes	—
203	C₇×#117	—	2	1	no	—
204	C₇×#117	—	2	1	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	—	2	2	no	—
208	C₇×#117	—	2	2	no	—
209	C₇×#117	—	2	2	no	—
210	C₇×#117	—	2	2	no	—
211	C₇×#117	—	2	2	no	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₂×C₇×C₄⋊C₄	—	2	1	no	—
214	C₂×C₇×C₄⋊C₄	—	2	1	no	—
215	C₂×C₇×C₄⋊C₄	—	2	1	no	—
216	C₂×C₇×C₄⋊C₄	—	2	1	no	—
217	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₄²×C₇	—	2	1	no	—
225	C₂×C₄²×C₇	—	2	2	no	—
226	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
231	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
238	C₇×#107	C₂³	1	4	yes	—
239	C₇×#107	C₂³	1	4	yes	—
240	C₇×#106	C₂³	1	4	yes	—
241	C₇×#106	C₂³	1	4	yes	—
242	C₇×C₄⋊C₈	C₂³	1	2	yes	—
243	C₇×C₄⋊C₈	C₂³	1	2	yes	—
244	C₇×C₄⋊C₈	C₂³	1	2	yes	—
245	C₇×C₄⋊C₈	C₂³	1	4	yes	—
246	C₇×C₄⋊C₈	C₂³	1	4	yes	—
247	C₇×C₄⋊C₈	C₂³	1	2	yes	—
248	C₇×#103	C₂³	1	4	yes	—
249	C₇×#103	C₂³	1	4	yes	—
250	C₇×#103	C₂³	1	4	yes	—
251	C₇×#103	C₂³	1	4	yes	—
252	C₇×#102	C₂³	1	4	yes	—
253	C₇×#102	C₂³	1	4	yes	—
254	C₇×#102	C₂³	1	4	yes	—
255	C₇×#102	C₂³	1	4	yes	—
256	#3444	C₂×C₇	1	1	yes	characteristic, complemented
257	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
258	#3256	C₂×C₇	1	4	yes	complemented
259	#3252	C₂×C₇	1	2	yes	complemented
260	#3251	C₂×C₇	1	2	yes	complemented
261	#3250	C₂×C₇	1	4	yes	complemented
262	#3248	C₂×C₇	1	2	yes	complemented
263	#3247	C₂×C₇	1	2	yes	complemented
264	#3080	C₂×C₇	1	2	yes	complemented
265	#3078	C₂×C₇	1	1	yes	characteristic, complemented
266	#3077	C₂×C₇	1	1	yes	characteristic, complemented
267	#3056	C₂×C₇	1	2	yes	complemented
268	#3055	C₂×C₇	1	2	yes	complemented
269	#3040	C₂×C₇	1	2	yes	complemented
270	#3037	C₂×C₇	1	1	yes	characteristic, complemented
271	#3036	C₂×C₇	1	1	yes	characteristic, complemented
272	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
273	C₂⁴×C₇	—	2	1	no	—
274	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
275	C₇×#41	—	2	4	no	—
276	C₇×#41	—	2	4	no	—
277	C₇×#41	—	4	4	no	—
278	C₇×#41	—	4	4	no	—
279	C₂×C₇×Q₈	—	2	1	no	—
280	C₂×C₇×Q₈	—	2	1	no	—
281	C₂×C₇×Q₈	—	2	1	no	—
282	C₂×C₇×Q₈	—	2	2	no	—
283	C₂×C₇×Q₈	—	2	2	no	—
284	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
285	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	2	2	no	—
288	C₂×C₇×D₄	—	2	2	no	—
289	C₂×C₇×D₄	—	2	2	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	1	no	—
292	C₂×C₇×D₄	—	2	1	no	—
293	C₂×C₇×D₄	—	2	1	no	—
294	C₂×C₇×D₄	—	2	2	no	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	4	4	no	—
297	C₂×C₇×D₄	C₂⁴	1	2	yes	—
298	C₂×C₇×D₄	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	1	no	—
302	C₂²×C₄×C₇	—	2	1	no	—
303	C₂²×C₄×C₇	—	2	1	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	4	2	no	—
310	C₂²×C₄×C₇	—	4	2	no	—
311	C₂²×C₄×C₇	—	4	4	no	—
312	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
330	C₇×Q₁₆	—	4	4	no	—
331	C₇×SD₁₆	—	4	4	no	—
332	C₇×SD₁₆	—	4	4	no	—
333	C₇×D₈	—	4	4	no	—
334	C₇×M₁₆	—	2	4	no	—
335	C₇×M₁₆	—	2	4	no	—
336	C₇×M₁₆	—	4	4	no	—
337	C₂×C₇×C₈	—	4	4	no	—
338	C₂×C₇×C₈	C₂⁴	1	4	yes	—
339	C₂×C₇×C₈	C₂⁴	1	4	yes	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	1	no	—
349	C₇×C₄⋊C₄	—	2	1	no	—
350	C₇×C₄⋊C₄	—	2	1	no	—
351	C₇×C₄⋊C₄	—	2	1	no	—
352	C₇×C₄⋊C₄	—	2	1	no	—
353	C₇×C₄⋊C₄	—	2	1	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
362	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₇×C₂²⋊C₄	—	2	2	no	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
368	C₇×C₂²⋊C₄	—	2	2	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇	C₂⁴	1	1	yes	characteristic
401	C₄²×C₇	C₂⁴	1	1	yes	characteristic
402	C₄²×C₇	C₂⁴	1	1	yes	characteristic
403	C₄²×C₇	C₂⁴	1	1	yes	characteristic
404	C₂×#137	C₂²×C₇	1	2	yes	—
405	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
406	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
407	#533	C₂²×C₇	1	1	yes	characteristic
408	#533	C₂²×C₇	1	1	yes	characteristic, complemented
409	#533	C₂²×C₇	1	1	yes	characteristic, complemented
410	#532	C₂²×C₇	1	1	yes	characteristic
411	#532	C₂²×C₇	1	1	yes	characteristic, complemented
412	#532	C₂²×C₇	1	1	yes	characteristic, complemented
413	#529	—	2	1	no	—
414	#529	—	2	1	no	—
415	#529	—	2	1	no	—
416	#529	—	2	1	no	—
417	#529	—	2	1	no	—
418	#529	—	2	1	no	—
419	#529	—	2	1	no	—
420	#529	—	2	1	no	—
421	#529	C₂²×C₇	1	2	yes	—
422	#529	C₂²×C₇	1	2	yes	—
423	#529	C₂²×C₇	1	2	yes	—
424	#529	C₂²×C₇	1	2	yes	—
425	#529	C₂²×C₇	1	2	yes	complemented
426	#529	C₂²×C₇	1	2	yes	complemented
427	C₂×#126	—	2	1	no	—
428	C₂×#125	C₂²×C₇	1	1	yes	characteristic
429	C₂×#124	C₂²×C₇	1	1	yes	characteristic
430	#525	—	2	1	no	—
431	#525	—	2	1	no	—
432	#525	C₂²×C₇	1	2	yes	—
433	C₂×#123	—	2	1	no	—
434	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
435	C₂×#121	C₂²×C₇	1	1	yes	characteristic
436	C₄×#41	—	2	1	no	—
437	C₄×#41	—	2	1	no	—
438	C₄×#41	C₂²×C₇	1	2	yes	—
439	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
440	C₂×C₄×D₄	—	2	1	no	—
441	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
442	C₂×#117	—	2	1	no	—
443	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
444	#479	C₂²×C₇	1	4	yes	complemented
445	#479	C₂²×C₇	1	4	yes	complemented
446	#479	C₂²×C₇	1	4	yes	complemented
447	#478	C₂²×C₇	1	4	yes	complemented
448	#478	C₂²×C₇	1	4	yes	complemented
449	#478	C₂²×C₇	1	4	yes	complemented
450	#477	C₂²×C₇	1	2	yes	complemented
451	#476	C₂²×C₇	1	2	yes	complemented
452	#475	C₂²×C₇	1	2	yes	complemented
453	#474	C₂²×C₇	1	2	yes	complemented
454	#470	C₂²×C₇	1	4	yes	complemented
455	#469	C₂²×C₇	1	4	yes	—
456	#468	C₂²×C₇	1	4	yes	—
457	#468	C₂²×C₇	1	4	yes	complemented
458	#467	C₂²×C₇	1	4	yes	complemented
459	#466	C₂²×C₇	1	4	yes	—
460	#465	C₂²×C₇	1	4	yes	—
461	#465	C₂²×C₇	1	4	yes	complemented
462	#464	C₂²×C₇	1	4	yes	complemented
463	#464	C₂²×C₇	1	4	yes	complemented
464	#464	C₂²×C₇	1	4	yes	complemented
465	#463	C₂²×C₇	1	4	yes	complemented
466	#463	C₂²×C₇	1	4	yes	complemented
467	#463	C₂²×C₇	1	4	yes	complemented
468	#462	C₂²×C₇	1	2	yes	complemented
469	#461	C₂²×C₇	1	2	yes	complemented
470	#460	C₂²×C₇	1	2	yes	complemented
471	#459	C₂²×C₇	1	2	yes	complemented
472	#428	C₂²×C₇	1	2	yes	—
473	#428	C₂²×C₇	1	2	yes	—
474	#423	C₂²×C₇	1	1	yes	characteristic
475	#423	C₂²×C₇	1	1	yes	characteristic
476	#423	C₂²×C₇	1	2	yes	—
477	#423	C₂²×C₇	1	2	yes	complemented
478	#423	C₂²×C₇	1	2	yes	complemented
479	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
480	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
481	#419	C₂²×C₇	1	2	yes	—
482	#418	C₂²×C₇	1	2	yes	—
483	#417	C₂²×C₇	1	2	yes	—
484	#417	C₂²×C₇	1	2	yes	—
485	C₂³×C₇	—	2	2	no	—
486	C₂³×C₇	—	2	2	no	—
487	C₂³×C₇	—	2	2	no	—
488	C₂³×C₇	—	2	2	no	—
489	C₂³×C₇	—	4	1	no	—
490	C₂³×C₇	—	4	2	no	—
491	C₂³×C₇	—	4	2	no	—
492	C₂³×C₇	—	4	2	no	—
493	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
494	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
495	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
496	C₇×Q₈	—	2	2	no	—
497	C₇×Q₈	—	2	2	no	—
498	C₇×Q₈	—	2	2	no	—
499	C₇×Q₈	—	2	2	no	—
500	C₇×Q₈	—	4	2	no	—
501	C₇×Q₈	—	4	2	no	—
502	C₇×Q₈	—	4	2	no	—
503	C₇×D₄	—	2	2	no	—
504	C₇×D₄	—	2	2	no	—
505	C₇×D₄	—	2	2	no	—
506	C₇×D₄	—	2	2	no	—
507	C₇×D₄	—	4	2	no	—
508	C₇×D₄	—	4	4	no	—
509	C₇×D₄	—	4	4	no	—
510	C₇×D₄	—	4	4	no	—
511	C₇×D₄	—	4	4	no	—
512	C₇×D₄	—	4	4	no	—
513	C₇×D₄	—	4	2	no	—
514	C₇×D₄	—	4	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	4	1	no	—
534	C₂×C₄×C₇	—	4	1	no	—
535	C₂×C₄×C₇	—	4	1	no	—
536	C₂×C₄×C₇	—	4	1	no	—
537	C₂×C₄×C₇	—	4	1	no	—
538	C₂×C₄×C₇	—	4	1	no	—
539	C₂×C₄×C₇	—	4	1	no	—
540	C₂×C₄×C₇	—	4	4	no	—
541	C₂×C₄×C₇	—	4	4	no	—
542	C₂×C₄×C₇	—	4	4	no	—
543	C₂×C₄×C₇	—	4	2	no	—
544	C₂×C₄×C₇	—	4	2	no	—
545	C₂×C₄×C₇	—	4	2	no	—
546	C₂×C₄×C₇	—	4	4	no	—
547	C₂×C₄×C₇	—	4	4	no	—
548	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
560	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
561	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
562	C₇×C₈	—	2	4	no	—
563	C₇×C₈	—	2	4	no	—
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	C₂³×C₇	1	2	yes	—
567	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
572	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
574	#137	—	4	4	no	—
575	AGL(1,ℤ/8)	—	4	4	no	—
576	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
579	C₂×D₈	C₂³×C₇	1	4	yes	—
580	C₂×M₁₆	—	4	4	no	—
581	C₂×M₁₆	C₂³×C₇	1	2	yes	—
582	C₂×M₁₆	C₂³×C₇	1	2	yes	—
583	C₂×M₁₆	C₂³×C₇	1	4	yes	—
584	C₂²×C₈	C₂³×C₇	1	4	yes	—
585	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
586	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
587	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
588	#127	C₂³×C₇	1	1	yes	characteristic
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#125	—	2	1	no	—
596	#125	—	2	1	no	—
597	#125	—	2	1	no	—
598	#125	—	2	1	no	—
599	#125	C₂³×C₇	1	2	yes	—
600	#125	C₂³×C₇	1	2	yes	—
601	#125	C₂³×C₇	1	2	yes	—
602	#124	—	2	1	no	—
603	#124	—	2	1	no	—
604	#124	—	2	1	no	—
605	#124	—	2	1	no	—
606	#124	C₂³×C₇	1	2	yes	—
607	#124	C₂³×C₇	1	2	yes	—
608	#124	C₂³×C₇	1	2	yes	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	1	no	—
622	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	1	no	—
629	#121	—	2	1	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	C₂³×C₇	1	2	yes	—
633	#121	C₂³×C₇	1	2	yes	—
634	#121	C₂³×C₇	1	2	yes	—
635	#121	C₂³×C₇	1	2	yes	—
636	#120	—	2	2	no	—
637	C₄×Q₈	—	2	1	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	1	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	C₂³×C₇	1	2	yes	—
644	C₄×Q₈	C₂³×C₇	1	2	yes	—
645	C₄×Q₈	C₂³×C₇	1	2	yes	—
646	C₄×Q₈	C₂³×C₇	1	2	yes	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	C₂³×C₇	1	2	yes	—
664	C₄×D₄	C₂³×C₇	1	2	yes	—
665	C₄×D₄	C₂³×C₇	1	2	yes	—
666	C₄×D₄	C₂³×C₇	1	2	yes	—
667	#117	—	2	1	no	—
668	#117	—	2	1	no	—
669	#117	—	2	2	no	—
670	#117	—	2	2	no	—
671	#117	—	2	2	no	—
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	C₂³×C₇	1	2	yes	—
677	C₂×C₄⋊C₄	—	2	1	no	—
678	C₂×C₄⋊C₄	—	2	1	no	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	—	2	1	no	—
681	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	2	no	—
690	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
691	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
692	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
693	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
694	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
695	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
702	#107	C₂³×C₇	1	4	yes	—
703	#107	C₂³×C₇	1	4	yes	—
704	#106	C₂³×C₇	1	4	yes	—
705	#106	C₂³×C₇	1	4	yes	—
706	C₄⋊C₈	C₂³×C₇	1	2	yes	—
707	C₄⋊C₈	C₂³×C₇	1	2	yes	—
708	C₄⋊C₈	C₂³×C₇	1	2	yes	—
709	C₄⋊C₈	C₂³×C₇	1	4	yes	—
710	C₄⋊C₈	C₂³×C₇	1	4	yes	—
711	C₄⋊C₈	C₂³×C₇	1	2	yes	—
712	#103	C₂³×C₇	1	4	yes	—
713	#103	C₂³×C₇	1	4	yes	—
714	#103	C₂³×C₇	1	4	yes	—
715	#103	C₂³×C₇	1	4	yes	—
716	#102	C₂³×C₇	1	4	yes	—
717	#102	C₂³×C₇	1	4	yes	—
718	#102	C₂³×C₇	1	4	yes	—
719	#102	C₂³×C₇	1	4	yes	—
720	C₂²×C₇	—	2	1	no	—
721	C₂²×C₇	—	2	1	no	—
722	C₂²×C₇	—	2	1	no	—
723	C₂²×C₇	—	2	1	no	—
724	C₂²×C₇	—	2	1	no	—
725	C₂²×C₇	—	2	1	no	—
726	C₂²×C₇	—	2	1	no	—
727	C₂²×C₇	—	4	4	no	—
728	C₂²×C₇	—	4	2	no	—
729	C₂²×C₇	—	4	2	no	—
730	C₂²×C₇	—	4	2	no	—
731	C₂²×C₇	—	4	2	no	—
732	C₂²×C₇	—	4	2	no	—
733	C₂²×C₇	—	4	2	no	—
734	C₂²×C₇	—	8	4	no	—
735	C₂²×C₇	#537	1	2	yes	—
736	C₂²×C₇	#575	1	2	yes	—
737	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
738	C₄×C₇	—	2	1	no	—
739	C₄×C₇	—	2	1	no	—
740	C₄×C₇	—	2	1	no	—
741	C₄×C₇	—	2	1	no	—
742	C₄×C₇	—	2	1	no	—
743	C₄×C₇	—	2	1	no	—
744	C₄×C₇	—	2	1	no	—
745	C₄×C₇	—	2	1	no	—
746	C₄×C₇	—	2	1	no	—
747	C₄×C₇	—	4	2	no	—
748	C₄×C₇	—	4	2	no	—
749	C₄×C₇	—	4	2	no	—
750	C₄×C₇	—	4	2	no	—
751	C₄×C₇	—	4	2	no	—
752	C₄×C₇	—	4	2	no	—
753	C₄×C₇	#537	1	2	yes	—
754	C₄×C₇	#575	1	2	yes	—
755	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
756	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
757	C₂⁴	—	2	1	no	—
758	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
759	#41	—	2	4	no	—
760	#41	—	2	4	no	—
761	#41	—	4	4	no	—
762	#41	—	4	4	no	—
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
769	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	4	4	no	—
781	C₂×D₄	C₂⁴×C₇	1	2	yes	—
782	C₂×D₄	C₂⁴×C₇	1	2	yes	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	—	4	4	no	—
796	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
797	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
798	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
799	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
800	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
801	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
802	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
803	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
804	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
805	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
806	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
807	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
808	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
809	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
810	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
814	Q₁₆	—	4	4	no	—
815	SD₁₆	—	4	4	no	—
816	SD₁₆	—	4	4	no	—
817	D₈	—	4	4	no	—
818	M₁₆	—	2	4	no	—
819	M₁₆	—	2	4	no	—
820	M₁₆	—	4	4	no	—
821	C₂×C₈	—	4	4	no	—
822	C₂×C₈	C₂⁴×C₇	1	4	yes	—
823	C₂×C₈	C₂⁴×C₇	1	4	yes	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
847	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
873	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
874	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
875	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
876	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
877	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
878	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
879	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
880	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
881	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
882	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
883	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
884	C₄²	C₂⁴×C₇	1	1	yes	characteristic
885	C₄²	C₂⁴×C₇	1	1	yes	characteristic
886	C₄²	C₂⁴×C₇	1	1	yes	characteristic
887	C₄²	C₂⁴×C₇	1	1	yes	characteristic
888	C₂×C₇	—	2	2	no	—
889	C₂×C₇	—	2	2	no	—
890	C₂×C₇	—	4	1	no	—
891	C₂×C₇	—	8	2	no	—
892	C₂×C₇	—	8	2	no	—
893	C₂×C₇	C₂×#537	1	1	yes	characteristic
894	C₂×C₇	C₂×#575	1	1	yes	characteristic
895	C₂×C₇	C₂×#575	1	1	yes	characteristic
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	2	no	—
904	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
905	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
906	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
907	Q₈	—	2	2	no	—
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	4	2	no	—
912	Q₈	—	4	2	no	—
913	Q₈	—	4	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	4	2	no	—
919	D₄	—	4	4	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	4	1	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
960	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
961	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
962	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
963	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
964	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
965	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
966	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
967	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
968	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
969	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
970	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
971	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
972	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
973	C₈	—	2	4	no	—
974	C₈	—	2	4	no	—
975	C₇	#60917	1	1	yes	characteristic, direct product factor, Sylow
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	4	4	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	8	4	no	—
991	C₂²	C₇×#537	1	2	yes	—
992	C₂²	C₇×#575	1	2	yes	—
993	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	C₇×#537	1	2	yes	—
1010	C₄	C₇×#575	1	2	yes	—
1011	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1013	C₂	—	2	2	no	—
1014	C₂	—	2	2	no	—
1015	C₂	—	4	1	no	—
1016	C₂	—	8	2	no	—
1017	C₂	—	8	2	no	—
1018	C₂	C₂×C₇×#537	1	1	yes	characteristic
1019	C₂	C₂×C₇×#575	1	1	yes	characteristic
1020	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3444	C₂	semidirect
2. C₂×C₇×#529	C₂	semidirect
3. C₇×#3256	C₂	semidirect
4. C₇×#3252	C₂	semidirect
5. C₇×#3251	C₂	semidirect
6. C₇×#3250	C₂	semidirect
7. C₇×#3248	C₂	semidirect
8. C₇×#3247	C₂	semidirect
9. C₇×#3080	C₂	semidirect
10. C₇×#3078	C₂	semidirect
11. C₇×#3077	C₂	semidirect
12. C₇×#3056	C₂	semidirect
13. C₇×#3055	C₂	semidirect
14. C₇×#3040	C₂	semidirect
15. C₇×#3037	C₂	semidirect
16. C₇×#3036	C₂	semidirect
17. C₂×C₇×#423	C₂	semidirect
22. C₇×#533	C₂²	semidirect
23. C₇×#533	C₂²	semidirect
25. C₇×#532	C₂²	semidirect
26. C₇×#532	C₂²	semidirect
39. C₇×#529	C₂²	semidirect
40. C₇×#529	C₂²	semidirect
58. C₇×#479	C₂²	semidirect
59. C₇×#479	C₂²	semidirect
60. C₇×#479	C₂²	semidirect
61. C₇×#478	C₂²	semidirect
62. C₇×#478	C₂²	semidirect
63. C₇×#478	C₂²	semidirect
64. C₇×#477	C₂²	semidirect
65. C₇×#476	C₂²	semidirect
66. C₇×#475	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#470	C₂²	semidirect
71. C₇×#468	C₂²	semidirect
72. C₇×#467	C₂²	semidirect
75. C₇×#465	C₂²	semidirect
76. C₇×#464	C₂²	semidirect
77. C₇×#464	C₂²	semidirect
78. C₇×#464	C₂²	semidirect
79. C₇×#463	C₂²	semidirect
80. C₇×#463	C₂²	semidirect
81. C₇×#463	C₂²	semidirect
82. C₇×#462	C₂²	semidirect
83. C₇×#461	C₂²	semidirect
84. C₇×#460	C₂²	semidirect
85. C₇×#459	C₂²	semidirect
91. C₇×#423	C₂²	semidirect
92. C₇×#423	C₂²	semidirect
93. C₂×C₇×C₄⋊C₈	C₂²	semidirect
94. C₂×C₇×C₄⋊C₈	C₂²	semidirect
99. #60917	C₇	direct (N × H)
256. #3444	C₂×C₇	semidirect
257. C₂×#529	C₂×C₇	semidirect
258. #3256	C₂×C₇	semidirect
259. #3252	C₂×C₇	semidirect
260. #3251	C₂×C₇	semidirect
261. #3250	C₂×C₇	semidirect
262. #3248	C₂×C₇	semidirect
263. #3247	C₂×C₇	semidirect
264. #3080	C₂×C₇	semidirect
265. #3078	C₂×C₇	semidirect
266. #3077	C₂×C₇	semidirect
267. #3056	C₂×C₇	semidirect
268. #3055	C₂×C₇	semidirect
269. #3040	C₂×C₇	semidirect
270. #3037	C₂×C₇	semidirect
271. #3036	C₂×C₇	semidirect
272. C₂×#423	C₂×C₇	semidirect
408. #533	C₂²×C₇	semidirect
409. #533	C₂²×C₇	semidirect
411. #532	C₂²×C₇	semidirect
412. #532	C₂²×C₇	semidirect
425. #529	C₂²×C₇	semidirect
426. #529	C₂²×C₇	semidirect
444. #479	C₂²×C₇	semidirect
445. #479	C₂²×C₇	semidirect
446. #479	C₂²×C₇	semidirect
447. #478	C₂²×C₇	semidirect
448. #478	C₂²×C₇	semidirect
449. #478	C₂²×C₇	semidirect
450. #477	C₂²×C₇	semidirect
451. #476	C₂²×C₇	semidirect
452. #475	C₂²×C₇	semidirect
453. #474	C₂²×C₇	semidirect
454. #470	C₂²×C₇	semidirect
457. #468	C₂²×C₇	semidirect
458. #467	C₂²×C₇	semidirect
461. #465	C₂²×C₇	semidirect
462. #464	C₂²×C₇	semidirect
463. #464	C₂²×C₇	semidirect
464. #464	C₂²×C₇	semidirect
465. #463	C₂²×C₇	semidirect
466. #463	C₂²×C₇	semidirect
467. #463	C₂²×C₇	semidirect
468. #462	C₂²×C₇	semidirect
469. #461	C₂²×C₇	semidirect
470. #460	C₂²×C₇	semidirect
471. #459	C₂²×C₇	semidirect
477. #423	C₂²×C₇	semidirect
478. #423	C₂²×C₇	semidirect
479. C₂×C₄⋊C₈	C₂²×C₇	semidirect
480. C₂×C₄⋊C₈	C₂²×C₇	semidirect
975. C₇	#60917	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×#3444	2
C₂×C₇×#529	2
C₇×#3256	2
C₇×#3252	2
C₇×#3251	2
C₇×#3250	2
C₇×#3248	2
C₇×#3247	2
C₇×#3080	2
C₇×#3078	2
C₇×#3077	2
C₇×#3056	2
C₇×#3055	2
C₇×#3040	2
C₇×#3037	2
C₇×#3036	2
C₂×C₇×#423	2
#60917	7

Subgroups — C7×#60917 #13238133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60917 #13238133