Subgroups — C₇×#60797 #13238013

Order 1792.

2062 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3225	C₂	1	4	yes	maximal, complemented
4	C₇×#3224	C₂	1	4	yes	maximal, complemented
5	C₇×#3223	C₂	1	2	yes	maximal, complemented
6	C₇×#3222	C₂	1	2	yes	maximal, complemented
7	C₇×#3221	C₂	1	2	yes	maximal, complemented
8	C₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₇×#3150	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3035	C₂	1	4	yes	maximal, complemented
14	C₇×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	2	yes	—
17	C₂×C₇×#135	C₂²	1	4	yes	complemented
18	C₂×C₇×#135	C₂²	1	4	yes	complemented
19	C₇×#542	C₂²	1	4	yes	complemented
20	C₇×#541	C₂²	1	2	yes	complemented
21	C₇×#540	C₂²	1	2	yes	complemented
22	C₇×#539	—	2	2	no	—
23	C₇×#538	—	2	2	no	—
24	C₇×#537	—	2	2	no	—
25	C₇×#536	C₂²	1	2	yes	—
26	C₇×#536	C₂²	1	2	yes	—
27	C₇×#535	C₂²	1	2	yes	—
28	C₇×#535	C₂²	1	2	yes	—
29	C₇×#534	—	2	2	no	—
30	C₇×#533	C₂²	1	1	yes	characteristic, complemented
31	C₇×#532	C₂²	1	2	yes	—
32	C₇×#532	C₂²	1	1	yes	characteristic
33	C₇×#532	C₂²	1	1	yes	characteristic
34	C₇×#532	C₂²	1	1	yes	characteristic, complemented
35	C₇×#529	—	2	4	no	—
36	C₇×#525	—	2	4	no	—
37	C₇×#525	C₂²	1	2	yes	—
38	C₄×C₇×#41	C₂²	1	2	yes	complemented
39	C₂×C₇×#117	C₂²	1	1	yes	characteristic
40	C₇×#497	C₂²	1	2	yes	complemented
41	C₇×#497	C₂²	1	2	yes	complemented
42	C₇×#496	C₂²	1	2	yes	complemented
43	C₇×#496	C₂²	1	2	yes	complemented
44	C₇×#495	C₂²	1	4	yes	complemented
45	C₇×#494	C₂²	1	1	yes	characteristic, complemented
46	C₇×#493	C₂²	1	1	yes	characteristic, complemented
47	C₇×#492	C₂²	1	1	yes	characteristic, complemented
48	C₇×#492	C₂²	1	1	yes	characteristic, complemented
49	C₇×#491	C₂²	1	2	yes	complemented
50	C₇×#490	C₂²	1	2	yes	complemented
51	C₇×#489	C₂²	1	4	yes	complemented
52	C₇×#488	C₂²	1	2	yes	complemented
53	C₇×#488	C₂²	1	2	yes	complemented
54	C₇×#487	C₂²	1	2	yes	complemented
55	C₇×#486	C₂²	1	2	yes	complemented
56	C₇×#464	C₂²	1	4	yes	complemented
57	C₇×#464	C₂²	1	4	yes	complemented
58	C₇×#463	C₂²	1	4	yes	complemented
59	C₇×#463	C₂²	1	4	yes	complemented
60	C₇×#462	C₂²	1	4	yes	complemented
61	C₇×#461	C₂²	1	4	yes	complemented
62	C₇×#460	C₂²	1	4	yes	complemented
63	C₇×#459	C₂²	1	4	yes	complemented
64	C₇×#452	C₂²	1	4	yes	—
65	C₇×#452	C₂²	1	4	yes	—
66	C₇×#451	C₂²	1	4	yes	complemented
67	C₇×#450	C₂²	1	4	yes	complemented
68	C₇×#449	C₂²	1	4	yes	—
69	C₇×#449	C₂²	1	4	yes	—
70	C₇×#448	C₂²	1	4	yes	complemented
71	C₇×#447	C₂²	1	4	yes	complemented
72	C₇×#433	C₂²	1	2	yes	complemented
73	C₇×#433	C₂²	1	2	yes	complemented
74	C₇×#433	C₂²	1	4	yes	complemented
75	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
76	C₇×#416	C₂²	1	4	yes	complemented
77	C₇×#416	C₂²	1	4	yes	complemented
78	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
79	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
81	#60797	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₇×#41	—	2	2	no	—
83	C₂×C₇×#41	—	2	2	no	—
84	C₂×C₇×#41	—	4	8	no	—
85	C₂×C₇×#41	C₂³	1	2	yes	—
86	C₂×C₇×#41	C₂³	1	2	yes	—
87	C₂×C₇×#41	C₂³	1	2	yes	—
88	C₂×C₇×#41	C₂³	1	2	yes	—
89	C₂×C₇×#41	C₂³	1	2	yes	—
90	C₂²×C₇×Q₈	C₂³	1	2	yes	—
91	C₂²×C₇×D₄	—	2	2	no	—
92	C₂²×C₇×D₄	C₂³	1	2	yes	—
93	C₂³×C₄×C₇	—	2	2	no	—
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₇×#135	—	4	8	no	—
96	C₇×#135	—	4	8	no	—
97	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₇×D₈	C₂³	1	4	yes	—
104	C₂×C₇×D₈	C₂³	1	4	yes	—
105	C₂²×C₇×C₈	C₂³	1	2	yes	—
106	C₂²×C₇×C₈	C₂³	1	2	yes	—
107	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₇×#127	C₂³	1	1	yes	characteristic
113	C₇×#127	C₂³	1	1	yes	characteristic
114	C₇×#127	C₂³	1	1	yes	characteristic
115	C₇×#127	C₂³	1	2	yes	—
116	C₇×#126	—	2	4	no	—
117	C₇×#126	—	2	4	no	—
118	C₇×#125	—	2	4	no	—
119	C₇×#125	C₂³	1	2	yes	—
120	C₇×#124	—	2	4	no	—
121	C₇×#124	C₂³	1	2	yes	—
122	C₇×#124	C₂³	1	2	yes	—
123	C₇×#124	C₂³	1	2	yes	—
124	C₇×#124	C₂³	1	2	yes	—
125	C₇×#124	C₂³	1	2	yes	—
126	C₇×#123	—	2	2	no	—
127	C₇×#123	—	2	4	no	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	4	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₇×C₂²⋊Q₈	—	2	4	no	—
135	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₇×#121	—	2	4	no	—
137	C₇×#121	—	2	2	no	—
138	C₇×#121	—	2	2	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	4	no	—
141	C₇×#121	—	2	4	no	—
142	C₇×#121	—	2	4	no	—
143	C₇×#121	C₂³	1	4	yes	—
144	C₇×#120	—	2	2	no	—
145	C₇×#120	—	2	4	no	—
146	C₇×#120	—	2	4	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	C₂³	1	4	yes	—
149	C₄×C₇×D₄	—	2	4	no	—
150	C₄×C₇×D₄	—	2	4	no	—
151	C₄×C₇×D₄	—	2	4	no	—
152	C₄×C₇×D₄	—	2	2	no	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	C₂³	1	4	yes	—
156	C₇×#117	—	2	2	no	—
157	C₇×#117	D₄	1	4	yes	—
158	C₇×#117	C₂³	1	2	yes	—
159	C₇×#117	C₂³	1	2	yes	—
160	C₇×#117	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
162	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
163	C₂×C₄²×C₇	—	2	2	no	—
164	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊C₈	C₂³	1	4	yes	—
167	C₇×C₄⋊C₈	C₂³	1	4	yes	—
168	C₇×#103	C₂³	1	4	yes	—
169	C₇×#103	C₂³	1	4	yes	—
170	C₇×#103	C₂³	1	4	yes	—
171	C₇×#103	C₂³	1	4	yes	—
172	C₇×#102	C₂³	1	4	yes	—
173	C₇×#102	C₂³	1	4	yes	—
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₇×#97	C₂³	1	2	yes	—
179	C₇×#97	C₂³	1	2	yes	—
180	C₄×C₇×C₈	C₂³	1	2	yes	—
181	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
182	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
183	#3455	C₂×C₇	1	1	yes	characteristic, complemented
184	#3449	C₂×C₇	1	1	yes	characteristic, complemented
185	#3225	C₂×C₇	1	4	yes	complemented
186	#3224	C₂×C₇	1	4	yes	complemented
187	#3223	C₂×C₇	1	2	yes	complemented
188	#3222	C₂×C₇	1	2	yes	complemented
189	#3221	C₂×C₇	1	2	yes	complemented
190	#3220	C₂×C₇	1	2	yes	complemented
191	#3150	C₂×C₇	1	1	yes	characteristic, complemented
192	#3147	C₂×C₇	1	1	yes	characteristic, complemented
193	#3135	C₂×C₇	1	1	yes	characteristic, complemented
194	#3131	C₂×C₇	1	1	yes	characteristic, complemented
195	#3035	C₂×C₇	1	4	yes	complemented
196	#3002	C₂×C₇	1	4	yes	complemented
197	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂⁴×C₇	—	2	2	no	—
199	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
200	C₇×#41	—	2	8	no	—
201	C₇×#41	—	2	8	no	—
202	C₇×#41	—	2	8	no	—
203	C₇×#41	—	4	4	no	—
204	C₇×#41	—	4	4	no	—
205	C₇×#41	—	4	8	no	—
206	C₇×#41	—	4	8	no	—
207	C₂×C₇×Q₈	—	2	2	no	—
208	C₂×C₇×Q₈	—	2	2	no	—
209	C₂×C₇×Q₈	—	4	4	no	—
210	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
211	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
212	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
213	C₂×C₇×D₄	—	2	2	no	—
214	C₂×C₇×D₄	—	2	2	no	—
215	C₂×C₇×D₄	—	2	2	no	—
216	C₂×C₇×D₄	—	2	2	no	—
217	C₂×C₇×D₄	—	2	2	no	—
218	C₂×C₇×D₄	—	2	4	no	—
219	C₂×C₇×D₄	—	2	2	no	—
220	C₂×C₇×D₄	—	2	4	no	—
221	C₂×C₇×D₄	—	2	2	no	—
222	C₂×C₇×D₄	—	2	2	no	—
223	C₂×C₇×D₄	—	2	2	no	—
224	C₂×C₇×D₄	—	4	4	no	—
225	C₂×C₇×D₄	—	4	8	no	—
226	C₂×C₇×D₄	C₂⁴	1	2	yes	—
227	C₂×C₇×D₄	C₂⁴	1	2	yes	—
228	C₂×C₇×D₄	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇	—	2	4	no	—
230	C₂²×C₄×C₇	—	2	2	no	—
231	C₂²×C₄×C₇	—	2	2	no	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	4	no	—
237	C₂²×C₄×C₇	—	4	8	no	—
238	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
244	C₇×Q₁₆	—	4	4	no	—
245	C₇×Q₁₆	—	4	4	no	—
246	C₇×SD₁₆	—	4	4	no	—
247	C₇×SD₁₆	—	4	4	no	—
248	C₇×SD₁₆	—	4	4	no	—
249	C₇×SD₁₆	—	4	4	no	—
250	C₇×D₈	—	4	4	no	—
251	C₇×D₈	—	4	4	no	—
252	C₂×C₇×C₈	—	2	4	no	—
253	C₂×C₇×C₈	—	2	4	no	—
254	C₂×C₇×C₈	C₂⁴	1	2	yes	—
255	C₂×C₇×C₈	C₂⁴	1	2	yes	—
256	C₂×C₇×C₈	C₂⁴	1	4	yes	—
257	C₇×C₄⋊C₄	—	2	4	no	—
258	C₇×C₄⋊C₄	—	2	4	no	—
259	C₇×C₄⋊C₄	—	2	2	no	—
260	C₇×C₄⋊C₄	—	2	2	no	—
261	C₇×C₄⋊C₄	—	2	2	no	—
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	2	no	—
265	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
266	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
267	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
268	C₇×C₂²⋊C₄	—	2	2	no	—
269	C₇×C₂²⋊C₄	—	2	4	no	—
270	C₇×C₂²⋊C₄	—	2	4	no	—
271	C₇×C₂²⋊C₄	—	2	4	no	—
272	C₇×C₂²⋊C₄	—	2	4	no	—
273	C₇×C₂²⋊C₄	—	2	4	no	—
274	C₇×C₂²⋊C₄	—	2	4	no	—
275	C₇×C₂²⋊C₄	—	2	4	no	—
276	C₇×C₂²⋊C₄	—	2	4	no	—
277	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
278	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
279	C₄²×C₇	—	2	4	no	—
280	C₄²×C₇	—	2	2	no	—
281	C₄²×C₇	C₂×D₄	1	2	yes	—
282	C₄²×C₇	C₂×D₄	1	2	yes	—
283	C₄²×C₇	C₂⁴	1	1	yes	characteristic
284	C₄²×C₇	C₂⁴	1	1	yes	characteristic
285	C₄²×C₇	C₂⁴	1	2	yes	—
286	C₂²×#41	C₂²×C₇	1	2	yes	—
287	C₂×#135	C₂²×C₇	1	4	yes	complemented
288	C₂×#135	C₂²×C₇	1	4	yes	complemented
289	#542	C₂²×C₇	1	4	yes	complemented
290	#541	C₂²×C₇	1	2	yes	complemented
291	#540	C₂²×C₇	1	2	yes	complemented
292	#539	—	2	2	no	—
293	#538	—	2	2	no	—
294	#537	—	2	2	no	—
295	#536	C₂²×C₇	1	2	yes	—
296	#536	C₂²×C₇	1	2	yes	—
297	#535	C₂²×C₇	1	2	yes	—
298	#535	C₂²×C₇	1	2	yes	—
299	#534	—	2	2	no	—
300	#533	C₂²×C₇	1	1	yes	characteristic, complemented
301	#532	C₂²×C₇	1	1	yes	characteristic
302	#532	C₂²×C₇	1	1	yes	characteristic
303	#532	C₂²×C₇	1	2	yes	—
304	#532	C₂²×C₇	1	1	yes	characteristic, complemented
305	#529	—	2	4	no	—
306	#525	—	2	4	no	—
307	#525	C₂²×C₇	1	2	yes	—
308	C₄×#41	C₂²×C₇	1	2	yes	complemented
309	C₂×#117	C₂²×C₇	1	1	yes	characteristic
310	#497	C₂²×C₇	1	2	yes	complemented
311	#497	C₂²×C₇	1	2	yes	complemented
312	#496	C₂²×C₇	1	2	yes	complemented
313	#496	C₂²×C₇	1	2	yes	complemented
314	#495	C₂²×C₇	1	4	yes	complemented
315	#494	C₂²×C₇	1	1	yes	characteristic, complemented
316	#493	C₂²×C₇	1	1	yes	characteristic, complemented
317	#492	C₂²×C₇	1	1	yes	characteristic, complemented
318	#492	C₂²×C₇	1	1	yes	characteristic, complemented
319	#491	C₂²×C₇	1	2	yes	complemented
320	#490	C₂²×C₇	1	2	yes	complemented
321	#489	C₂²×C₇	1	4	yes	complemented
322	#488	C₂²×C₇	1	2	yes	complemented
323	#488	C₂²×C₇	1	2	yes	complemented
324	#487	C₂²×C₇	1	2	yes	complemented
325	#486	C₂²×C₇	1	2	yes	complemented
326	#464	C₂²×C₇	1	4	yes	complemented
327	#464	C₂²×C₇	1	4	yes	complemented
328	#463	C₂²×C₇	1	4	yes	complemented
329	#463	C₂²×C₇	1	4	yes	complemented
330	#462	C₂²×C₇	1	4	yes	complemented
331	#461	C₂²×C₇	1	4	yes	complemented
332	#460	C₂²×C₇	1	4	yes	complemented
333	#459	C₂²×C₇	1	4	yes	complemented
334	#452	C₂²×C₇	1	4	yes	—
335	#452	C₂²×C₇	1	4	yes	—
336	#451	C₂²×C₇	1	4	yes	complemented
337	#450	C₂²×C₇	1	4	yes	complemented
338	#449	C₂²×C₇	1	4	yes	—
339	#449	C₂²×C₇	1	4	yes	—
340	#448	C₂²×C₇	1	4	yes	complemented
341	#447	C₂²×C₇	1	4	yes	complemented
342	#433	C₂²×C₇	1	2	yes	complemented
343	#433	C₂²×C₇	1	2	yes	complemented
344	#433	C₂²×C₇	1	4	yes	complemented
345	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
346	#416	C₂²×C₇	1	4	yes	complemented
347	#416	C₂²×C₇	1	4	yes	complemented
348	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
349	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
351	C₂³×C₇	—	2	2	no	—
352	C₂³×C₇	—	2	2	no	—
353	C₂³×C₇	—	2	2	no	—
354	C₂³×C₇	—	2	2	no	—
355	C₂³×C₇	—	4	2	no	—
356	C₂³×C₇	—	4	4	no	—
357	C₂³×C₇	—	8	4	no	—
358	C₂³×C₇	C₂²×D₄	1	2	yes	—
359	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
360	C₇×Q₈	—	2	4	no	—
361	C₇×Q₈	—	2	4	no	—
362	C₇×Q₈	—	2	4	no	—
363	C₇×Q₈	—	4	4	no	—
364	C₇×Q₈	—	8	2	no	—
365	C₇×D₄	—	2	4	no	—
366	C₇×D₄	—	2	4	no	—
367	C₇×D₄	—	2	4	no	—
368	C₇×D₄	—	4	4	no	—
369	C₇×D₄	—	4	4	no	—
370	C₇×D₄	—	4	4	no	—
371	C₇×D₄	—	4	4	no	—
372	C₇×D₄	—	4	4	no	—
373	C₇×D₄	—	4	4	no	—
374	C₇×D₄	—	8	4	no	—
375	C₇×D₄	—	8	2	no	—
376	C₇×D₄	—	8	2	no	—
377	C₇×D₄	—	8	2	no	—
378	C₇×D₄	—	8	4	no	—
379	C₂×C₄×C₇	—	2	2	no	—
380	C₂×C₄×C₇	—	2	4	no	—
381	C₂×C₄×C₇	—	2	4	no	—
382	C₂×C₄×C₇	—	2	2	no	—
383	C₂×C₄×C₇	—	2	4	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	4	2	no	—
387	C₂×C₄×C₇	—	4	2	no	—
388	C₂×C₄×C₇	—	4	4	no	—
389	C₂×C₄×C₇	—	4	4	no	—
390	C₂×C₄×C₇	—	4	4	no	—
391	C₂×C₄×C₇	—	4	4	no	—
392	C₂×C₄×C₇	—	4	4	no	—
393	C₂×C₄×C₇	—	4	4	no	—
394	C₂×C₄×C₇	—	8	4	no	—
395	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
396	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
401	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
402	C₇×C₈	—	2	2	no	—
403	C₇×C₈	—	2	4	no	—
404	C₇×C₈	—	2	2	no	—
405	C₂×#41	—	2	2	no	—
406	C₂×#41	—	2	2	no	—
407	C₂×#41	—	4	8	no	—
408	C₂×#41	C₂³×C₇	1	2	yes	—
409	C₂×#41	C₂³×C₇	1	2	yes	—
410	C₂×#41	C₂³×C₇	1	2	yes	—
411	C₂×#41	C₂³×C₇	1	2	yes	—
412	C₂×#41	C₂³×C₇	1	2	yes	—
413	C₂²×Q₈	C₂³×C₇	1	2	yes	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	C₂³×C₇	1	2	yes	—
416	C₂³×C₄	—	2	2	no	—
417	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
418	#135	—	4	8	no	—
419	#135	—	4	8	no	—
420	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
421	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
422	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
423	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
424	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
425	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
426	C₂×D₈	C₂³×C₇	1	4	yes	—
427	C₂×D₈	C₂³×C₇	1	4	yes	—
428	C₂²×C₈	C₂³×C₇	1	2	yes	—
429	C₂²×C₈	C₂³×C₇	1	2	yes	—
430	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
431	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
432	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
433	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
434	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
435	#127	C₂³×C₇	1	2	yes	—
436	#127	C₂³×C₇	1	1	yes	characteristic
437	#127	C₂³×C₇	1	1	yes	characteristic
438	#127	C₂³×C₇	1	1	yes	characteristic
439	#126	—	2	4	no	—
440	#126	—	2	4	no	—
441	#125	—	2	4	no	—
442	#125	C₂³×C₇	1	2	yes	—
443	#124	—	2	4	no	—
444	#124	C₂³×C₇	1	2	yes	—
445	#124	C₂³×C₇	1	2	yes	—
446	#124	C₂³×C₇	1	2	yes	—
447	#124	C₂³×C₇	1	2	yes	—
448	#124	C₂³×C₇	1	2	yes	—
449	#123	—	2	2	no	—
450	#123	—	2	4	no	—
451	#123	—	2	4	no	—
452	#123	—	2	4	no	—
453	#123	—	2	4	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	—	2	4	no	—
457	C₂²⋊Q₈	—	2	4	no	—
458	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
459	#121	—	2	4	no	—
460	#121	—	2	2	no	—
461	#121	—	2	2	no	—
462	#121	—	2	2	no	—
463	#121	—	2	4	no	—
464	#121	—	2	4	no	—
465	#121	—	2	4	no	—
466	#121	C₂³×C₇	1	4	yes	—
467	#120	—	2	2	no	—
468	#120	—	2	4	no	—
469	#120	—	2	4	no	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	C₂³×C₇	1	4	yes	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	C₂³×C₇	1	4	yes	—
479	#117	—	2	2	no	—
480	#117	C₇×D₄	1	4	yes	—
481	#117	C₂³×C₇	1	2	yes	—
482	#117	C₂³×C₇	1	2	yes	—
483	#117	C₂³×C₇	1	2	yes	—
484	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
485	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
486	C₂×C₄²	—	2	2	no	—
487	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
489	C₄⋊C₈	C₂³×C₇	1	4	yes	—
490	C₄⋊C₈	C₂³×C₇	1	4	yes	—
491	#103	C₂³×C₇	1	4	yes	—
492	#103	C₂³×C₇	1	4	yes	—
493	#103	C₂³×C₇	1	4	yes	—
494	#103	C₂³×C₇	1	4	yes	—
495	#102	C₂³×C₇	1	4	yes	—
496	#102	C₂³×C₇	1	4	yes	—
497	#102	C₂³×C₇	1	4	yes	—
498	#102	C₂³×C₇	1	4	yes	—
499	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
500	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
501	#97	C₂³×C₇	1	2	yes	—
502	#97	C₂³×C₇	1	2	yes	—
503	C₄×C₈	C₂³×C₇	1	2	yes	—
504	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
505	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
506	C₂²×C₇	—	2	2	no	—
507	C₂²×C₇	—	2	4	no	—
508	C₂²×C₇	—	2	2	no	—
509	C₂²×C₇	—	4	4	no	—
510	C₂²×C₇	—	4	4	no	—
511	C₂²×C₇	—	4	4	no	—
512	C₂²×C₇	—	4	2	no	—
513	C₂²×C₇	—	4	2	no	—
514	C₂²×C₇	—	4	2	no	—
515	C₂²×C₇	—	8	2	no	—
516	C₂²×C₇	—	8	8	no	—
517	C₂²×C₇	#535	1	2	yes	—
518	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₇	—	2	4	no	—
520	C₄×C₇	—	2	2	no	—
521	C₄×C₇	—	2	2	no	—
522	C₄×C₇	—	2	2	no	—
523	C₄×C₇	—	4	4	no	—
524	C₄×C₇	—	4	2	no	—
525	C₄×C₇	—	4	2	no	—
526	C₄×C₇	—	4	2	no	—
527	C₄×C₇	#535	1	2	yes	—
528	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
531	#41	—	2	8	no	—
532	#41	—	2	8	no	—
533	#41	—	2	8	no	—
534	#41	—	4	4	no	—
535	#41	—	4	4	no	—
536	#41	—	4	8	no	—
537	#41	—	4	8	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
542	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
543	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	8	no	—
557	C₂×D₄	C₂⁴×C₇	1	2	yes	—
558	C₂×D₄	C₂⁴×C₇	1	2	yes	—
559	C₂×D₄	C₂⁴×C₇	1	2	yes	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	4	8	no	—
569	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
570	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
571	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
572	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
575	Q₁₆	—	4	4	no	—
576	Q₁₆	—	4	4	no	—
577	SD₁₆	—	4	4	no	—
578	SD₁₆	—	4	4	no	—
579	SD₁₆	—	4	4	no	—
580	SD₁₆	—	4	4	no	—
581	D₈	—	4	4	no	—
582	D₈	—	4	4	no	—
583	C₂×C₈	—	2	4	no	—
584	C₂×C₈	—	2	4	no	—
585	C₂×C₈	C₂⁴×C₇	1	2	yes	—
586	C₂×C₈	C₂⁴×C₇	1	2	yes	—
587	C₂×C₈	C₂⁴×C₇	1	4	yes	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
597	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
598	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
609	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	4	no	—
612	C₄²	C₂×C₇×D₄	1	2	yes	—
613	C₄²	C₂×C₇×D₄	1	2	yes	—
614	C₄²	C₂⁴×C₇	1	1	yes	characteristic
615	C₄²	C₂⁴×C₇	1	1	yes	characteristic
616	C₄²	C₂⁴×C₇	1	2	yes	—
617	C₂×C₇	—	2	2	no	—
618	C₂×C₇	—	4	2	no	—
619	C₂×C₇	—	8	2	no	—
620	C₂×C₇	—	8	2	no	—
621	C₂×C₇	—	8	2	no	—
622	C₂×C₇	C₂×#535	1	1	yes	characteristic
623	C₂×C₇	#3584	1	2	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	4	no	—
630	C₂³	—	8	4	no	—
631	C₂³	C₂²×C₇×D₄	1	2	yes	—
632	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
633	Q₈	—	2	4	no	—
634	Q₈	—	2	4	no	—
635	Q₈	—	2	4	no	—
636	Q₈	—	4	4	no	—
637	Q₈	—	8	2	no	—
638	D₄	—	2	4	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	4	no	—
641	D₄	—	4	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	8	4	no	—
648	D₄	—	8	2	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	8	4	no	—
668	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
669	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
670	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
671	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
672	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
673	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
674	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
675	C₈	—	2	2	no	—
676	C₈	—	2	4	no	—
677	C₈	—	2	2	no	—
678	C₇	#60797	1	1	yes	characteristic, direct product factor, Sylow
679	C₂²	—	2	2	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	8	no	—
690	C₂²	C₇×#535	1	2	yes	—
691	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
692	C₄	—	2	4	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	2	no	—
700	C₄	C₇×#535	1	2	yes	—
701	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
702	C₂	—	2	2	no	—
703	C₂	—	4	2	no	—
704	C₂	—	8	2	no	—
705	C₂	—	8	2	no	—
706	C₂	—	8	2	no	—
707	C₂	C₂×C₇×#535	1	1	yes	characteristic
708	C₂	C₇×#3584	1	2	yes	—

	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 ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3455	C₂	semidirect
2. C₇×#3449	C₂	semidirect
3. C₇×#3225	C₂	semidirect
4. C₇×#3224	C₂	semidirect
5. C₇×#3223	C₂	semidirect
6. C₇×#3222	C₂	semidirect
7. C₇×#3221	C₂	semidirect
8. C₇×#3220	C₂	semidirect
9. C₇×#3150	C₂	semidirect
10. C₇×#3147	C₂	semidirect
11. C₇×#3135	C₂	semidirect
12. C₇×#3131	C₂	semidirect
13. C₇×#3035	C₂	semidirect
14. C₇×#3002	C₂	semidirect
15. C₂×C₇×#433	C₂	semidirect
17. C₂×C₇×#135	C₂²	semidirect
18. C₂×C₇×#135	C₂²	semidirect
19. C₇×#542	C₂²	semidirect
20. C₇×#541	C₂²	semidirect
21. C₇×#540	C₂²	semidirect
30. C₇×#533	C₂²	semidirect
34. C₇×#532	C₂²	semidirect
38. C₄×C₇×#41	C₂²	semidirect
40. C₇×#497	C₂²	semidirect
41. C₇×#497	C₂²	semidirect
42. C₇×#496	C₂²	semidirect
43. C₇×#496	C₂²	semidirect
44. C₇×#495	C₂²	semidirect
45. C₇×#494	C₂²	semidirect
46. C₇×#493	C₂²	semidirect
47. C₇×#492	C₂²	semidirect
48. C₇×#492	C₂²	semidirect
49. C₇×#491	C₂²	semidirect
50. C₇×#490	C₂²	semidirect
51. C₇×#489	C₂²	semidirect
52. C₇×#488	C₂²	semidirect
53. C₇×#488	C₂²	semidirect
54. C₇×#487	C₂²	semidirect
55. C₇×#486	C₂²	semidirect
56. C₇×#464	C₂²	semidirect
57. C₇×#464	C₂²	semidirect
58. C₇×#463	C₂²	semidirect
59. C₇×#463	C₂²	semidirect
60. C₇×#462	C₂²	semidirect
61. C₇×#461	C₂²	semidirect
62. C₇×#460	C₂²	semidirect
63. C₇×#459	C₂²	semidirect
66. C₇×#451	C₂²	semidirect
67. C₇×#450	C₂²	semidirect
70. C₇×#448	C₂²	semidirect
71. C₇×#447	C₂²	semidirect
72. C₇×#433	C₂²	semidirect
73. C₇×#433	C₂²	semidirect
74. C₇×#433	C₂²	semidirect
75. C₂×C₇×C₄⋊C₈	C₂²	semidirect
76. C₇×#416	C₂²	semidirect
77. C₇×#416	C₂²	semidirect
79. C₂×C₇×#97	C₂²	semidirect
80. C₂×C₄×C₇×C₈	C₂²	semidirect
81. #60797	C₇	direct (N × H)
183. #3455	C₂×C₇	semidirect
184. #3449	C₂×C₇	semidirect
185. #3225	C₂×C₇	semidirect
186. #3224	C₂×C₇	semidirect
187. #3223	C₂×C₇	semidirect
188. #3222	C₂×C₇	semidirect
189. #3221	C₂×C₇	semidirect
190. #3220	C₂×C₇	semidirect
191. #3150	C₂×C₇	semidirect
192. #3147	C₂×C₇	semidirect
193. #3135	C₂×C₇	semidirect
194. #3131	C₂×C₇	semidirect
195. #3035	C₂×C₇	semidirect
196. #3002	C₂×C₇	semidirect
197. C₂×#433	C₂×C₇	semidirect
287. C₂×#135	C₂²×C₇	semidirect
288. C₂×#135	C₂²×C₇	semidirect
289. #542	C₂²×C₇	semidirect
290. #541	C₂²×C₇	semidirect
291. #540	C₂²×C₇	semidirect
300. #533	C₂²×C₇	semidirect
304. #532	C₂²×C₇	semidirect
308. C₄×#41	C₂²×C₇	semidirect
310. #497	C₂²×C₇	semidirect
311. #497	C₂²×C₇	semidirect
312. #496	C₂²×C₇	semidirect
313. #496	C₂²×C₇	semidirect
314. #495	C₂²×C₇	semidirect
315. #494	C₂²×C₇	semidirect
316. #493	C₂²×C₇	semidirect
317. #492	C₂²×C₇	semidirect
318. #492	C₂²×C₇	semidirect
319. #491	C₂²×C₇	semidirect
320. #490	C₂²×C₇	semidirect
321. #489	C₂²×C₇	semidirect
322. #488	C₂²×C₇	semidirect
323. #488	C₂²×C₇	semidirect
324. #487	C₂²×C₇	semidirect
325. #486	C₂²×C₇	semidirect
326. #464	C₂²×C₇	semidirect
327. #464	C₂²×C₇	semidirect
328. #463	C₂²×C₇	semidirect
329. #463	C₂²×C₇	semidirect
330. #462	C₂²×C₇	semidirect
331. #461	C₂²×C₇	semidirect
332. #460	C₂²×C₇	semidirect
333. #459	C₂²×C₇	semidirect
336. #451	C₂²×C₇	semidirect
337. #450	C₂²×C₇	semidirect
340. #448	C₂²×C₇	semidirect
341. #447	C₂²×C₇	semidirect
342. #433	C₂²×C₇	semidirect
343. #433	C₂²×C₇	semidirect
344. #433	C₂²×C₇	semidirect
345. C₂×C₄⋊C₈	C₂²×C₇	semidirect
346. #416	C₂²×C₇	semidirect
347. #416	C₂²×C₇	semidirect
349. C₂×#97	C₂²×C₇	semidirect
350. C₂×C₄×C₈	C₂²×C₇	semidirect
678. C₇	#60797	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×#3455	2
C₇×#3449	2
C₇×#3225	2
C₇×#3224	2
C₇×#3223	2
C₇×#3222	2
C₇×#3221	2
C₇×#3220	2
C₇×#3150	2
C₇×#3147	2
C₇×#3135	2
C₇×#3131	2
C₇×#3035	2
C₇×#3002	2
C₂×C₇×#433	2
#60797	7

Subgroups — C7×#60797 #13238013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60797 #13238013