Subgroups — C₇×#60953 #13238169

Order 1792.

1824 conjugacy classes of subgroups.

The subgroup lattice has 984 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	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3252	C₂	1	2	yes	maximal, complemented
4	C₇×#3251	C₂	1	2	yes	maximal, complemented
5	C₇×#3240	C₂	1	2	yes	maximal, complemented
6	C₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3235	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3219	C₂	1	2	yes	maximal, complemented
9	C₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3197	C₂	1	4	yes	maximal, complemented
12	C₇×#3172	C₂	1	2	yes	maximal, complemented
13	C₇×#3171	C₂	1	2	yes	maximal, complemented
14	C₇×#3107	C₂	1	2	yes	maximal, complemented
15	C₇×#3106	C₂	1	2	yes	maximal, complemented
16	C₇×#3102	C₂	1	4	yes	maximal, complemented
17	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#533	C₂²	1	1	yes	characteristic
19	C₇×#533	C₂²	1	1	yes	characteristic
20	C₇×#533	C₂²	1	1	yes	characteristic
21	C₇×#533	C₂²	1	1	yes	characteristic
22	C₇×#533	C₂²	1	1	yes	characteristic
23	C₇×#533	C₂²	1	1	yes	characteristic
24	C₇×#532	C₂²	1	1	yes	characteristic
25	C₇×#532	C₂²	1	1	yes	characteristic
26	C₇×#532	C₂²	1	1	yes	characteristic
27	C₇×#532	C₂²	1	1	yes	characteristic
28	C₇×#532	C₂²	1	1	yes	characteristic
29	C₇×#532	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
36	C₇×#529	—	2	1	no	—
37	C₇×#529	—	2	1	no	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	—
40	C₇×#529	C₂²	1	2	yes	—
41	C₇×#529	C₂²	1	2	yes	—
42	C₇×#525	—	2	1	no	—
43	C₇×#525	—	2	1	no	—
44	C₇×#525	—	2	1	no	—
45	C₇×#525	—	2	1	no	—
46	C₇×#525	C₂²	1	2	yes	—
47	C₇×#525	C₂²	1	2	yes	—
48	C₄×C₇×#41	—	2	1	no	—
49	C₄×C₇×#41	—	2	1	no	—
50	C₄×C₇×#41	—	2	1	no	—
51	C₄×C₇×#41	—	2	1	no	—
52	C₄×C₇×#41	C₂²	1	2	yes	—
53	C₄×C₇×#41	C₂²	1	2	yes	—
54	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
55	C₇×#501	C₂²	1	2	yes	complemented
56	C₇×#501	C₂²	1	2	yes	complemented
57	C₇×#497	C₂²	1	2	yes	complemented
58	C₇×#496	C₂²	1	2	yes	complemented
59	C₇×#491	C₂²	1	2	yes	complemented
60	C₇×#490	C₂²	1	2	yes	complemented
61	C₇×#489	C₂²	1	2	yes	complemented
62	C₇×#489	C₂²	1	2	yes	complemented
63	C₇×#485	C₂²	1	4	yes	—
64	C₇×#485	C₂²	1	4	yes	—
65	C₇×#482	C₂²	1	4	yes	—
66	C₇×#482	C₂²	1	4	yes	—
67	C₇×#479	C₂²	1	4	yes	complemented
68	C₇×#478	C₂²	1	4	yes	complemented
69	C₇×#477	C₂²	1	2	yes	complemented
70	C₇×#476	C₂²	1	2	yes	complemented
71	C₇×#475	C₂²	1	2	yes	complemented
72	C₇×#474	C₂²	1	2	yes	complemented
73	C₇×#470	C₂²	1	4	yes	—
74	C₇×#469	C₂²	1	4	yes	—
75	C₇×#468	C₂²	1	4	yes	—
76	C₇×#468	C₂²	1	4	yes	—
77	C₇×#464	C₂²	1	4	yes	complemented
78	C₇×#463	C₂²	1	4	yes	complemented
79	C₇×#462	C₂²	1	2	yes	complemented
80	C₇×#461	C₂²	1	2	yes	complemented
81	C₇×#460	C₂²	1	2	yes	complemented
82	C₇×#459	C₂²	1	2	yes	complemented
83	C₇×#452	C₂²	1	4	yes	—
84	C₇×#452	C₂²	1	4	yes	—
85	C₇×#449	C₂²	1	4	yes	—
86	C₇×#449	C₂²	1	4	yes	—
87	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
88	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
89	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
90	C₄×C₇×D₈	C₂²	1	4	yes	complemented
91	C₇×#432	C₂²	1	1	yes	characteristic
92	C₇×#432	C₂²	1	1	yes	characteristic
93	C₇×#432	C₂²	1	2	yes	—
94	C₇×#431	C₂²	1	2	yes	—
95	C₇×#431	C₂²	1	2	yes	—
96	C₇×#423	C₂²	1	2	yes	—
97	C₇×#407	C₂²	1	2	yes	—
98	C₄×C₇×M₁₆	C₂²	1	2	yes	—
99	#60953	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	—	2	1	no	—
103	C₂×C₇×#41	—	2	1	no	—
104	C₂×C₇×#41	C₂³	1	2	yes	—
105	C₂×C₇×#41	C₂³	1	2	yes	—
106	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
109	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
110	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₇×D₈	C₂³	1	4	yes	—
113	C₂×C₇×M₁₆	C₂³	1	4	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₇×#127	C₂³	1	1	yes	characteristic
121	C₇×#127	C₂³	1	1	yes	characteristic
122	C₇×#126	—	2	2	no	—
123	C₇×#126	—	2	2	no	—
124	C₇×#126	—	2	2	no	—
125	C₇×#126	—	2	2	no	—
126	C₇×#125	—	2	1	no	—
127	C₇×#125	—	2	1	no	—
128	C₇×#125	—	2	1	no	—
129	C₇×#125	—	2	1	no	—
130	C₇×#125	C₂³	1	2	yes	—
131	C₇×#125	C₂³	1	2	yes	—
132	C₇×#124	—	2	1	no	—
133	C₇×#124	—	2	1	no	—
134	C₇×#124	—	2	1	no	—
135	C₇×#124	—	2	1	no	—
136	C₇×#124	C₂³	1	2	yes	—
137	C₇×#124	C₂³	1	2	yes	—
138	C₇×#123	—	2	2	no	—
139	C₇×#123	—	2	2	no	—
140	C₇×#123	—	2	2	no	—
141	C₇×#123	—	2	2	no	—
142	C₇×#123	—	2	2	no	—
143	C₇×#123	—	2	2	no	—
144	C₇×C₂²⋊Q₈	—	2	1	no	—
145	C₇×C₂²⋊Q₈	—	2	1	no	—
146	C₇×C₂²⋊Q₈	—	2	1	no	—
147	C₇×C₂²⋊Q₈	—	2	1	no	—
148	C₇×C₂²⋊Q₈	—	2	1	no	—
149	C₇×C₂²⋊Q₈	—	2	1	no	—
150	C₇×C₂²⋊Q₈	—	2	1	no	—
151	C₇×C₂²⋊Q₈	—	2	1	no	—
152	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₇×#121	—	2	1	no	—
157	C₇×#121	—	2	1	no	—
158	C₇×#121	—	2	1	no	—
159	C₇×#121	—	2	1	no	—
160	C₇×#121	—	2	1	no	—
161	C₇×#121	—	2	1	no	—
162	C₇×#121	—	2	1	no	—
163	C₇×#121	—	2	1	no	—
164	C₇×#121	C₂³	1	2	yes	—
165	C₇×#121	C₂³	1	2	yes	—
166	C₇×#121	C₂³	1	2	yes	—
167	C₇×#121	C₂³	1	2	yes	—
168	C₇×#120	—	2	2	no	—
169	C₇×#120	—	2	2	no	—
170	C₄×C₇×Q₈	—	2	1	no	—
171	C₄×C₇×Q₈	—	2	1	no	—
172	C₄×C₇×Q₈	—	2	1	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	C₂³	1	2	yes	—
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×D₄	—	2	2	no	—
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	2	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	—	2	1	no	—
200	C₄×C₇×D₄	—	2	1	no	—
201	C₄×C₇×D₄	—	2	1	no	—
202	C₄×C₇×D₄	C₂³	1	2	yes	—
203	C₄×C₇×D₄	C₂³	1	2	yes	—
204	C₄×C₇×D₄	C₂³	1	2	yes	—
205	C₄×C₇×D₄	C₂³	1	2	yes	—
206	C₇×#117	—	2	1	no	—
207	C₇×#117	—	2	1	no	—
208	C₇×#117	—	2	1	no	—
209	C₇×#117	—	2	1	no	—
210	C₇×#117	—	2	2	no	—
211	C₇×#117	—	2	2	no	—
212	C₇×#117	—	2	2	no	—
213	C₇×#117	—	2	2	no	—
214	C₇×#117	—	2	2	no	—
215	C₇×#117	—	2	2	no	—
216	C₇×#117	C₂³	1	2	yes	—
217	C₇×#117	C₂³	1	2	yes	—
218	C₂×C₄²×C₇	—	2	2	no	—
219	C₂×C₄²×C₇	—	2	2	no	—
220	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
221	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₇×#107	C₂³	1	4	yes	—
233	C₇×#107	C₂³	1	4	yes	—
234	C₇×#106	C₂³	1	4	yes	—
235	C₇×#106	C₂³	1	4	yes	—
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	4	yes	—
239	C₇×#103	C₂³	1	4	yes	—
240	C₇×#103	C₂³	1	4	yes	—
241	C₇×#103	C₂³	1	4	yes	—
242	C₇×#103	C₂³	1	4	yes	—
243	C₇×#102	C₂³	1	4	yes	—
244	C₇×#102	C₂³	1	4	yes	—
245	C₇×#102	C₂³	1	4	yes	—
246	C₇×#102	C₂³	1	4	yes	—
247	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
249	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₇×#97	C₂³	1	2	yes	—
251	C₇×#97	C₂³	1	2	yes	—
252	C₄×C₇×C₈	C₂³	1	4	yes	—
253	#3444	C₂×C₇	1	1	yes	characteristic, complemented
254	#3444	C₂×C₇	1	1	yes	characteristic, complemented
255	#3252	C₂×C₇	1	2	yes	complemented
256	#3251	C₂×C₇	1	2	yes	complemented
257	#3240	C₂×C₇	1	2	yes	complemented
258	#3237	C₂×C₇	1	1	yes	characteristic, complemented
259	#3235	C₂×C₇	1	1	yes	characteristic, complemented
260	#3219	C₂×C₇	1	2	yes	complemented
261	#3216	C₂×C₇	1	1	yes	characteristic, complemented
262	#3214	C₂×C₇	1	1	yes	characteristic, complemented
263	#3197	C₂×C₇	1	4	yes	complemented
264	#3172	C₂×C₇	1	2	yes	complemented
265	#3171	C₂×C₇	1	2	yes	complemented
266	#3107	C₂×C₇	1	2	yes	complemented
267	#3106	C₂×C₇	1	2	yes	complemented
268	#3102	C₂×C₇	1	4	yes	complemented
269	#2920	C₂×C₇	1	1	yes	characteristic, complemented
270	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
271	C₇×#41	—	4	2	no	—
272	C₇×#41	—	4	4	no	—
273	C₇×#41	—	4	2	no	—
274	C₇×#41	—	4	4	no	—
275	C₇×#41	—	4	4	no	—
276	C₇×#41	—	4	4	no	—
277	C₇×#41	—	4	4	no	—
278	C₂×C₇×Q₈	—	2	1	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	C₂⁴	1	2	yes	—
283	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
284	C₂×C₇×D₄	—	2	2	no	—
285	C₂×C₇×D₄	—	2	2	no	—
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	1	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	C₂⁴	1	2	yes	—
295	C₂×C₇×D₄	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	—	2	2	no	—
297	C₂²×C₄×C₇	—	2	2	no	—
298	C₂²×C₄×C₇	—	2	2	no	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	4	2	no	—
303	C₂²×C₄×C₇	—	4	2	no	—
304	C₂²×C₄×C₇	—	4	2	no	—
305	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₇×Q₁₆	—	4	4	no	—
324	C₇×SD₁₆	—	4	4	no	—
325	C₇×SD₁₆	—	4	4	no	—
326	C₇×D₈	—	4	4	no	—
327	C₇×M₁₆	—	4	4	no	—
328	C₂×C₇×C₈	C₂⁴	1	4	yes	—
329	C₂×C₇×C₈	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	—	2	1	no	—
331	C₇×C₄⋊C₄	—	2	1	no	—
332	C₇×C₄⋊C₄	—	2	1	no	—
333	C₇×C₄⋊C₄	—	2	1	no	—
334	C₇×C₄⋊C₄	—	2	1	no	—
335	C₇×C₄⋊C₄	—	2	1	no	—
336	C₇×C₄⋊C₄	—	2	1	no	—
337	C₇×C₄⋊C₄	—	2	1	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
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	2	no	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
351	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
352	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
353	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
354	C₇×C₂²⋊C₄	—	2	2	no	—
355	C₇×C₂²⋊C₄	—	2	2	no	—
356	C₇×C₂²⋊C₄	—	2	2	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	2	no	—
361	C₇×C₂²⋊C₄	—	2	2	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
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	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	2	2	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	2	no	—
377	C₄²×C₇	—	2	2	no	—
378	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₇	C₂⁴	1	1	yes	characteristic
391	C₄²×C₇	C₂⁴	1	1	yes	characteristic
392	C₄²×C₇	C₂⁴	1	1	yes	characteristic
393	C₄²×C₇	C₂⁴	1	1	yes	characteristic
394	#533	C₂²×C₇	1	1	yes	characteristic
395	#533	C₂²×C₇	1	1	yes	characteristic
396	#533	C₂²×C₇	1	1	yes	characteristic
397	#533	C₂²×C₇	1	1	yes	characteristic
398	#533	C₂²×C₇	1	1	yes	characteristic
399	#533	C₂²×C₇	1	1	yes	characteristic
400	#532	C₂²×C₇	1	1	yes	characteristic
401	#532	C₂²×C₇	1	1	yes	characteristic
402	#532	C₂²×C₇	1	1	yes	characteristic
403	#532	C₂²×C₇	1	1	yes	characteristic
404	#532	C₂²×C₇	1	1	yes	characteristic
405	#532	C₂²×C₇	1	1	yes	characteristic
406	#529	—	2	1	no	—
407	#529	—	2	1	no	—
408	#529	—	2	1	no	—
409	#529	—	2	1	no	—
410	#529	—	2	1	no	—
411	#529	—	2	1	no	—
412	#529	—	2	1	no	—
413	#529	—	2	1	no	—
414	#529	C₂²×C₇	1	2	yes	—
415	#529	C₂²×C₇	1	2	yes	—
416	#529	C₂²×C₇	1	2	yes	—
417	#529	C₂²×C₇	1	2	yes	—
418	#525	—	2	1	no	—
419	#525	—	2	1	no	—
420	#525	—	2	1	no	—
421	#525	—	2	1	no	—
422	#525	C₂²×C₇	1	2	yes	—
423	#525	C₂²×C₇	1	2	yes	—
424	C₄×#41	—	2	1	no	—
425	C₄×#41	—	2	1	no	—
426	C₄×#41	—	2	1	no	—
427	C₄×#41	—	2	1	no	—
428	C₄×#41	C₂²×C₇	1	2	yes	—
429	C₄×#41	C₂²×C₇	1	2	yes	—
430	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
431	#501	C₂²×C₇	1	2	yes	complemented
432	#501	C₂²×C₇	1	2	yes	complemented
433	#497	C₂²×C₇	1	2	yes	complemented
434	#496	C₂²×C₇	1	2	yes	complemented
435	#491	C₂²×C₇	1	2	yes	complemented
436	#490	C₂²×C₇	1	2	yes	complemented
437	#489	C₂²×C₇	1	2	yes	complemented
438	#489	C₂²×C₇	1	2	yes	complemented
439	#485	C₂²×C₇	1	4	yes	—
440	#485	C₂²×C₇	1	4	yes	—
441	#482	C₂²×C₇	1	4	yes	—
442	#482	C₂²×C₇	1	4	yes	—
443	#479	C₂²×C₇	1	4	yes	complemented
444	#478	C₂²×C₇	1	4	yes	complemented
445	#477	C₂²×C₇	1	2	yes	complemented
446	#476	C₂²×C₇	1	2	yes	complemented
447	#475	C₂²×C₇	1	2	yes	complemented
448	#474	C₂²×C₇	1	2	yes	complemented
449	#470	C₂²×C₇	1	4	yes	—
450	#469	C₂²×C₇	1	4	yes	—
451	#468	C₂²×C₇	1	4	yes	—
452	#468	C₂²×C₇	1	4	yes	—
453	#464	C₂²×C₇	1	4	yes	complemented
454	#463	C₂²×C₇	1	4	yes	complemented
455	#462	C₂²×C₇	1	2	yes	complemented
456	#461	C₂²×C₇	1	2	yes	complemented
457	#460	C₂²×C₇	1	2	yes	complemented
458	#459	C₂²×C₇	1	2	yes	complemented
459	#452	C₂²×C₇	1	4	yes	—
460	#452	C₂²×C₇	1	4	yes	—
461	#449	C₂²×C₇	1	4	yes	—
462	#449	C₂²×C₇	1	4	yes	—
463	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
464	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
465	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
466	C₄×D₈	C₂²×C₇	1	4	yes	complemented
467	#432	C₂²×C₇	1	1	yes	characteristic
468	#432	C₂²×C₇	1	1	yes	characteristic
469	#432	C₂²×C₇	1	2	yes	—
470	#431	C₂²×C₇	1	2	yes	—
471	#431	C₂²×C₇	1	2	yes	—
472	#423	C₂²×C₇	1	2	yes	—
473	#407	C₂²×C₇	1	2	yes	—
474	C₄×M₁₆	C₂²×C₇	1	2	yes	—
475	C₂³×C₇	—	2	2	no	—
476	C₂³×C₇	—	2	2	no	—
477	C₂³×C₇	—	4	1	no	—
478	C₂³×C₇	—	4	1	no	—
479	C₂³×C₇	—	4	1	no	—
480	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
483	C₇×Q₈	—	2	2	no	—
484	C₇×Q₈	—	2	4	no	—
485	C₇×Q₈	—	2	2	no	—
486	C₇×Q₈	—	4	2	no	—
487	C₇×Q₈	—	4	2	no	—
488	C₇×Q₈	—	4	2	no	—
489	C₇×Q₈	—	4	2	no	—
490	C₇×D₄	—	2	2	no	—
491	C₇×D₄	—	2	4	no	—
492	C₇×D₄	—	2	2	no	—
493	C₇×D₄	—	4	2	no	—
494	C₇×D₄	—	4	2	no	—
495	C₇×D₄	—	4	2	no	—
496	C₇×D₄	—	4	4	no	—
497	C₇×D₄	—	4	4	no	—
498	C₇×D₄	—	4	4	no	—
499	C₇×D₄	—	4	4	no	—
500	C₇×D₄	—	4	4	no	—
501	C₇×D₄	—	4	4	no	—
502	C₇×D₄	—	4	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	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	—	4	1	no	—
519	C₂×C₄×C₇	—	4	1	no	—
520	C₂×C₄×C₇	—	4	1	no	—
521	C₂×C₄×C₇	—	4	1	no	—
522	C₂×C₄×C₇	—	4	1	no	—
523	C₂×C₄×C₇	—	4	1	no	—
524	C₂×C₄×C₇	—	4	1	no	—
525	C₂×C₄×C₇	—	4	1	no	—
526	C₂×C₄×C₇	—	4	1	no	—
527	C₂×C₄×C₇	—	4	4	no	—
528	C₂×C₄×C₇	—	4	4	no	—
529	C₂×C₄×C₇	—	4	4	no	—
530	C₂×C₄×C₇	—	4	4	no	—
531	C₂×C₄×C₇	—	4	4	no	—
532	C₂×C₄×C₇	—	4	4	no	—
533	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
545	C₇×C₈	—	2	4	no	—
546	C₇×C₈	—	2	4	no	—
547	C₂×#41	—	2	1	no	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	2	1	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	C₂³×C₇	1	2	yes	—
552	C₂×#41	C₂³×C₇	1	2	yes	—
553	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
554	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
559	C₂×D₈	C₂³×C₇	1	4	yes	—
560	C₂×M₁₆	C₂³×C₇	1	4	yes	—
561	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
567	#127	C₂³×C₇	1	1	yes	characteristic
568	#127	C₂³×C₇	1	1	yes	characteristic
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#126	—	2	2	no	—
573	#125	—	2	1	no	—
574	#125	—	2	1	no	—
575	#125	—	2	1	no	—
576	#125	—	2	1	no	—
577	#125	C₂³×C₇	1	2	yes	—
578	#125	C₂³×C₇	1	2	yes	—
579	#124	—	2	1	no	—
580	#124	—	2	1	no	—
581	#124	—	2	1	no	—
582	#124	—	2	1	no	—
583	#124	C₂³×C₇	1	2	yes	—
584	#124	C₂³×C₇	1	2	yes	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
603	#121	—	2	1	no	—
604	#121	—	2	1	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#121	—	2	1	no	—
611	#121	C₂³×C₇	1	2	yes	—
612	#121	C₂³×C₇	1	2	yes	—
613	#121	C₂³×C₇	1	2	yes	—
614	#121	C₂³×C₇	1	2	yes	—
615	#120	—	2	2	no	—
616	#120	—	2	2	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	—	2	1	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	—	2	1	no	—
625	C₄×Q₈	C₂³×C₇	1	2	yes	—
626	C₄×Q₈	C₂³×C₇	1	2	yes	—
627	C₄×Q₈	C₂³×C₇	1	2	yes	—
628	C₄×Q₈	C₂³×C₇	1	2	yes	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	C₂³×C₇	1	2	yes	—
650	C₄×D₄	C₂³×C₇	1	2	yes	—
651	C₄×D₄	C₂³×C₇	1	2	yes	—
652	C₄×D₄	C₂³×C₇	1	2	yes	—
653	#117	—	2	1	no	—
654	#117	—	2	1	no	—
655	#117	—	2	1	no	—
656	#117	—	2	1	no	—
657	#117	—	2	2	no	—
658	#117	—	2	2	no	—
659	#117	—	2	2	no	—
660	#117	—	2	2	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	C₂³×C₇	1	2	yes	—
664	#117	C₂³×C₇	1	2	yes	—
665	C₂×C₄²	—	2	2	no	—
666	C₂×C₄²	—	2	2	no	—
667	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
668	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
671	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
679	#107	C₂³×C₇	1	4	yes	—
680	#107	C₂³×C₇	1	4	yes	—
681	#106	C₂³×C₇	1	4	yes	—
682	#106	C₂³×C₇	1	4	yes	—
683	C₄⋊C₈	C₂³×C₇	1	2	yes	—
684	C₄⋊C₈	C₂³×C₇	1	2	yes	—
685	C₄⋊C₈	C₂³×C₇	1	4	yes	—
686	#103	C₂³×C₇	1	4	yes	—
687	#103	C₂³×C₇	1	4	yes	—
688	#103	C₂³×C₇	1	4	yes	—
689	#103	C₂³×C₇	1	4	yes	—
690	#102	C₂³×C₇	1	4	yes	—
691	#102	C₂³×C₇	1	4	yes	—
692	#102	C₂³×C₇	1	4	yes	—
693	#102	C₂³×C₇	1	4	yes	—
694	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
695	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
696	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
697	#97	C₂³×C₇	1	2	yes	—
698	#97	C₂³×C₇	1	2	yes	—
699	C₄×C₈	C₂³×C₇	1	4	yes	—
700	C₂²×C₇	—	2	1	no	—
701	C₂²×C₇	—	2	1	no	—
702	C₂²×C₇	—	2	1	no	—
703	C₂²×C₇	—	2	1	no	—
704	C₂²×C₇	—	2	1	no	—
705	C₂²×C₇	—	2	1	no	—
706	C₂²×C₇	—	2	1	no	—
707	C₂²×C₇	—	2	1	no	—
708	C₂²×C₇	—	2	1	no	—
709	C₂²×C₇	—	4	4	no	—
710	C₂²×C₇	—	4	2	no	—
711	C₂²×C₇	—	4	2	no	—
712	C₂²×C₇	—	4	2	no	—
713	C₂²×C₇	—	4	2	no	—
714	C₂²×C₇	—	4	2	no	—
715	C₂²×C₇	—	4	2	no	—
716	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
717	C₄×C₇	—	2	1	no	—
718	C₄×C₇	—	2	1	no	—
719	C₄×C₇	—	2	1	no	—
720	C₄×C₇	—	2	1	no	—
721	C₄×C₇	—	2	1	no	—
722	C₄×C₇	—	2	1	no	—
723	C₄×C₇	—	2	1	no	—
724	C₄×C₇	—	2	1	no	—
725	C₄×C₇	—	2	1	no	—
726	C₄×C₇	—	4	2	no	—
727	C₄×C₇	—	4	2	no	—
728	C₄×C₇	—	4	2	no	—
729	C₄×C₇	—	4	2	no	—
730	C₄×C₇	—	4	2	no	—
731	C₄×C₇	—	4	2	no	—
732	C₄×C₇	#575	1	2	yes	—
733	C₄×C₇	#575	1	2	yes	—
734	C₄×C₇	#585	1	2	yes	—
735	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
736	#41	—	4	2	no	—
737	#41	—	4	4	no	—
738	#41	—	4	2	no	—
739	#41	—	4	4	no	—
740	#41	—	4	4	no	—
741	#41	—	4	4	no	—
742	#41	—	4	4	no	—
743	C₂×Q₈	—	2	1	no	—
744	C₂×Q₈	—	2	1	no	—
745	C₂×Q₈	—	2	1	no	—
746	C₂×Q₈	—	2	1	no	—
747	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
748	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	1	no	—
758	C₂×D₄	—	2	1	no	—
759	C₂×D₄	C₂⁴×C₇	1	2	yes	—
760	C₂×D₄	C₂⁴×C₇	1	2	yes	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
771	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
772	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
773	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
774	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
775	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
776	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
777	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
778	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
779	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
780	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
781	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
782	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
783	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
784	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
788	Q₁₆	—	4	4	no	—
789	SD₁₆	—	4	4	no	—
790	SD₁₆	—	4	4	no	—
791	D₈	—	4	4	no	—
792	M₁₆	—	4	4	no	—
793	C₂×C₈	C₂⁴×C₇	1	4	yes	—
794	C₂×C₈	C₂⁴×C₇	1	4	yes	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
844	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
845	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
846	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
847	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
848	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
849	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
850	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
851	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
852	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
853	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
854	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
855	C₄²	C₂⁴×C₇	1	1	yes	characteristic
856	C₄²	C₂⁴×C₇	1	1	yes	characteristic
857	C₄²	C₂⁴×C₇	1	1	yes	characteristic
858	C₄²	C₂⁴×C₇	1	1	yes	characteristic
859	C₂×C₇	—	4	1	no	—
860	C₂×C₇	—	4	1	no	—
861	C₂×C₇	—	4	1	no	—
862	C₂×C₇	—	8	2	no	—
863	C₂×C₇	—	8	2	no	—
864	C₂×C₇	#3449	1	1	yes	characteristic
865	C₂×C₇	C₂×#575	1	1	yes	characteristic
866	C₂×C₇	C₂×#575	1	1	yes	characteristic
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	4	1	no	—
871	C₂³	—	4	1	no	—
872	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
873	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
874	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
875	Q₈	—	2	2	no	—
876	Q₈	—	2	4	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	4	2	no	—
879	Q₈	—	4	2	no	—
880	Q₈	—	4	2	no	—
881	Q₈	—	4	2	no	—
882	D₄	—	2	2	no	—
883	D₄	—	2	4	no	—
884	D₄	—	2	2	no	—
885	D₄	—	4	2	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	2	no	—
888	D₄	—	4	4	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
926	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
927	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
928	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
929	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
930	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
931	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
932	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
933	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
934	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
935	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
936	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
937	C₈	—	2	4	no	—
938	C₈	—	2	4	no	—
939	C₇	#60953	1	1	yes	characteristic, direct product factor, Sylow
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	4	4	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	C₇×#575	1	2	yes	—
973	C₄	C₇×#575	1	2	yes	—
974	C₄	C₇×#585	1	2	yes	—
975	C₂	—	4	1	no	—
976	C₂	—	4	1	no	—
977	C₂	—	4	1	no	—
978	C₂	—	8	2	no	—
979	C₂	—	8	2	no	—
980	C₂	C₇×#3449	1	1	yes	characteristic
981	C₂	C₂×C₇×#575	1	1	yes	characteristic
982	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₇×#3444	C₂	semidirect
3. C₇×#3252	C₂	semidirect
4. C₇×#3251	C₂	semidirect
5. C₇×#3240	C₂	semidirect
6. C₇×#3237	C₂	semidirect
7. C₇×#3235	C₂	semidirect
8. C₇×#3219	C₂	semidirect
9. C₇×#3216	C₂	semidirect
10. C₇×#3214	C₂	semidirect
11. C₇×#3197	C₂	semidirect
12. C₇×#3172	C₂	semidirect
13. C₇×#3171	C₂	semidirect
14. C₇×#3107	C₂	semidirect
15. C₇×#3106	C₂	semidirect
16. C₇×#3102	C₂	semidirect
17. C₇×#2920	C₂	semidirect
55. C₇×#501	C₂²	semidirect
56. C₇×#501	C₂²	semidirect
57. C₇×#497	C₂²	semidirect
58. C₇×#496	C₂²	semidirect
59. C₇×#491	C₂²	semidirect
60. C₇×#490	C₂²	semidirect
61. C₇×#489	C₂²	semidirect
62. C₇×#489	C₂²	semidirect
67. C₇×#479	C₂²	semidirect
68. C₇×#478	C₂²	semidirect
69. C₇×#477	C₂²	semidirect
70. C₇×#476	C₂²	semidirect
71. C₇×#475	C₂²	semidirect
72. C₇×#474	C₂²	semidirect
77. C₇×#464	C₂²	semidirect
78. C₇×#463	C₂²	semidirect
79. C₇×#462	C₂²	semidirect
80. C₇×#461	C₂²	semidirect
81. C₇×#460	C₂²	semidirect
82. C₇×#459	C₂²	semidirect
87. C₄×C₇×Q₁₆	C₂²	semidirect
88. C₄×C₇×SD₁₆	C₂²	semidirect
89. C₄×C₇×SD₁₆	C₂²	semidirect
90. C₄×C₇×D₈	C₂²	semidirect
99. #60953	C₇	direct (N × H)
253. #3444	C₂×C₇	semidirect
254. #3444	C₂×C₇	semidirect
255. #3252	C₂×C₇	semidirect
256. #3251	C₂×C₇	semidirect
257. #3240	C₂×C₇	semidirect
258. #3237	C₂×C₇	semidirect
259. #3235	C₂×C₇	semidirect
260. #3219	C₂×C₇	semidirect
261. #3216	C₂×C₇	semidirect
262. #3214	C₂×C₇	semidirect
263. #3197	C₂×C₇	semidirect
264. #3172	C₂×C₇	semidirect
265. #3171	C₂×C₇	semidirect
266. #3107	C₂×C₇	semidirect
267. #3106	C₂×C₇	semidirect
268. #3102	C₂×C₇	semidirect
269. #2920	C₂×C₇	semidirect
431. #501	C₂²×C₇	semidirect
432. #501	C₂²×C₇	semidirect
433. #497	C₂²×C₇	semidirect
434. #496	C₂²×C₇	semidirect
435. #491	C₂²×C₇	semidirect
436. #490	C₂²×C₇	semidirect
437. #489	C₂²×C₇	semidirect
438. #489	C₂²×C₇	semidirect
443. #479	C₂²×C₇	semidirect
444. #478	C₂²×C₇	semidirect
445. #477	C₂²×C₇	semidirect
446. #476	C₂²×C₇	semidirect
447. #475	C₂²×C₇	semidirect
448. #474	C₂²×C₇	semidirect
453. #464	C₂²×C₇	semidirect
454. #463	C₂²×C₇	semidirect
455. #462	C₂²×C₇	semidirect
456. #461	C₂²×C₇	semidirect
457. #460	C₂²×C₇	semidirect
458. #459	C₂²×C₇	semidirect
463. C₄×Q₁₆	C₂²×C₇	semidirect
464. C₄×SD₁₆	C₂²×C₇	semidirect
465. C₄×SD₁₆	C₂²×C₇	semidirect
466. C₄×D₈	C₂²×C₇	semidirect
939. C₇	#60953	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
C₇×#3252	2
C₇×#3251	2
C₇×#3240	2
C₇×#3237	2
C₇×#3235	2
C₇×#3219	2
C₇×#3216	2
C₇×#3214	2
C₇×#3197	2
C₇×#3172	2
C₇×#3171	2
C₇×#3107	2
C₇×#3106	2
C₇×#3102	2
C₇×#2920	2
#60953	7

Subgroups — C7×#60953 #13238169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60953 #13238169