Subgroups — C₇×#60854 #13238070

Order 1792.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 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
2	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3240	C₂	1	4	yes	maximal, complemented
4	C₇×#3239	C₂	1	2	yes	maximal, complemented
5	C₇×#3238	C₂	1	2	yes	maximal, complemented
6	C₇×#3237	C₂	1	2	yes	maximal, complemented
7	C₇×#3236	C₂	1	2	yes	maximal, complemented
8	C₇×#3235	C₂	1	2	yes	maximal, complemented
9	C₇×#3234	C₂	1	2	yes	maximal, complemented
10	C₇×#3162	C₂	1	2	yes	maximal, complemented
11	C₇×#3135	C₂	1	2	yes	maximal, complemented
12	C₇×#3091	C₂	1	4	yes	maximal, complemented
13	C₇×#3076	C₂	1	4	yes	maximal, complemented
14	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#533	—	2	1	no	—
16	C₇×#533	—	2	1	no	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	—	2	1	no	—
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	2	yes	—
23	C₇×#533	C₂²	1	2	yes	—
24	C₇×#533	C₂²	1	2	yes	—
25	C₇×#533	C₂²	1	2	yes	—
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	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
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	C₂×C₇×#125	C₂²	1	2	yes	—
38	C₇×#525	—	2	1	no	—
39	C₇×#525	—	2	1	no	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
43	C₄×C₇×#41	—	2	1	no	—
44	C₄×C₇×#41	—	2	1	no	—
45	C₄×C₇×#41	C₂²	1	2	yes	—
46	C₂×C₄×C₇×Q₈	—	2	1	no	—
47	C₂×C₄×C₇×Q₈	—	2	1	no	—
48	C₂×C₇×#117	C₂²	1	2	yes	—
49	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#501	C₂²	1	4	yes	complemented
52	C₇×#501	C₂²	1	4	yes	complemented
53	C₇×#501	C₂²	1	4	yes	complemented
54	C₇×#491	C₂²	1	4	yes	complemented
55	C₇×#490	C₂²	1	4	yes	complemented
56	C₇×#489	C₂²	1	4	yes	complemented
57	C₇×#489	C₂²	1	4	yes	complemented
58	C₇×#485	C₂²	1	8	yes	—
59	C₇×#484	C₂²	1	4	yes	—
60	C₇×#483	C₂²	1	4	yes	—
61	C₇×#482	C₂²	1	8	yes	—
62	C₇×#481	C₂²	1	4	yes	—
63	C₇×#480	C₂²	1	4	yes	—
64	C₇×#479	C₂²	1	8	yes	complemented
65	C₇×#478	C₂²	1	8	yes	complemented
66	C₇×#477	C₂²	1	4	yes	complemented
67	C₇×#476	C₂²	1	4	yes	complemented
68	C₇×#475	C₂²	1	4	yes	complemented
69	C₇×#474	C₂²	1	4	yes	complemented
70	C₇×#432	C₂²	1	2	yes	—
71	C₇×#432	C₂²	1	2	yes	—
72	C₇×#432	C₂²	1	2	yes	—
73	C₇×#432	C₂²	1	2	yes	—
74	C₇×#427	C₂²	1	8	yes	—
75	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
76	C₇×#416	C₂²	1	8	yes	—
77	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
78	C₂×C₇×#97	C₂²	1	2	yes	—
79	#60854	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	1	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	C₂³	1	2	yes	—
83	C₂²×C₇×Q₈	—	2	1	no	—
84	C₂²×C₇×Q₈	—	2	1	no	—
85	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	4	yes	—
89	C₇×C₄⋊Q₈	—	2	1	no	—
90	C₇×C₄⋊Q₈	—	2	1	no	—
91	C₇×C₄⋊Q₈	—	2	1	no	—
92	C₇×C₄⋊Q₈	—	2	1	no	—
93	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₇×#127	C₂³	1	1	yes	characteristic
101	C₇×#126	—	2	2	no	—
102	C₇×#126	—	2	2	no	—
103	C₇×#125	—	2	2	no	—
104	C₇×#125	—	2	2	no	—
105	C₇×#125	—	2	1	no	—
106	C₇×#125	—	2	1	no	—
107	C₇×#125	C₂³	1	4	yes	—
108	C₇×#125	C₂³	1	4	yes	—
109	C₇×#125	C₂³	1	2	yes	—
110	C₇×#124	—	2	1	no	—
111	C₇×#124	—	2	1	no	—
112	C₇×#124	C₂³	1	2	yes	—
113	C₇×#123	—	2	2	no	—
114	C₇×#123	—	2	2	no	—
115	C₇×#123	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	2	no	—
117	C₇×C₂²⋊Q₈	—	2	2	no	—
118	C₇×C₂²⋊Q₈	—	2	2	no	—
119	C₇×C₂²⋊Q₈	—	2	2	no	—
120	C₇×C₂²⋊Q₈	—	2	2	no	—
121	C₇×C₂²⋊Q₈	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	1	no	—
125	C₇×C₂²⋊Q₈	—	2	1	no	—
126	C₇×C₂²⋊Q₈	—	2	1	no	—
127	C₇×C₂²⋊Q₈	—	2	1	no	—
128	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₇×#121	—	2	1	no	—
131	C₇×#121	—	2	1	no	—
132	C₇×#121	—	2	1	no	—
133	C₇×#121	—	2	1	no	—
134	C₇×#121	C₂³	1	2	yes	—
135	C₇×#121	C₂³	1	2	yes	—
136	C₇×#120	—	2	2	no	—
137	C₄×C₇×Q₈	—	2	2	no	—
138	C₄×C₇×Q₈	—	2	2	no	—
139	C₄×C₇×Q₈	—	2	2	no	—
140	C₄×C₇×Q₈	—	2	2	no	—
141	C₄×C₇×Q₈	—	2	2	no	—
142	C₄×C₇×Q₈	—	2	2	no	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	—	2	2	no	—
145	C₄×C₇×Q₈	—	2	1	no	—
146	C₄×C₇×Q₈	—	2	1	no	—
147	C₄×C₇×Q₈	—	2	1	no	—
148	C₄×C₇×Q₈	—	2	1	no	—
149	C₄×C₇×Q₈	C₂³	1	2	yes	—
150	C₄×C₇×Q₈	C₂³	1	2	yes	—
151	C₄×C₇×D₄	—	2	2	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	—	2	2	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	1	no	—
158	C₄×C₇×D₄	—	2	1	no	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	C₂³	1	2	yes	—
162	C₄×C₇×D₄	C₂³	1	2	yes	—
163	C₇×#117	—	2	2	no	—
164	C₇×#117	—	2	2	no	—
165	C₇×#117	—	2	1	no	—
166	C₇×#117	—	2	1	no	—
167	C₇×#117	—	2	2	no	—
168	C₇×#117	—	2	2	no	—
169	C₇×#117	—	2	2	no	—
170	C₇×#117	C₂³	1	4	yes	—
171	C₇×#117	C₂³	1	4	yes	—
172	C₇×#117	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	—	2	2	no	—
174	C₂×C₇×C₄⋊C₄	—	2	2	no	—
175	C₂×C₇×C₄⋊C₄	—	2	1	no	—
176	C₂×C₇×C₄⋊C₄	—	2	1	no	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
180	C₂×C₄²×C₇	—	2	2	no	—
181	C₂×C₄²×C₇	—	2	2	no	—
182	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
183	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₇×#107	C₂³	1	8	yes	—
195	C₇×#107	C₂³	1	8	yes	—
196	C₇×#106	C₂³	1	8	yes	—
197	C₇×#106	C₂³	1	8	yes	—
198	C₇×C₄⋊C₈	C₂³	1	4	yes	—
199	C₇×C₄⋊C₈	C₂³	1	4	yes	—
200	C₇×#103	C₂³	1	8	yes	—
201	C₇×#103	C₂³	1	8	yes	—
202	C₇×#102	C₂³	1	8	yes	—
203	C₇×#102	C₂³	1	8	yes	—
204	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₇×#97	C₂³	1	4	yes	—
207	C₇×#97	C₂³	1	4	yes	—
208	#3444	C₂×C₇	1	1	yes	characteristic
209	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
210	#3240	C₂×C₇	1	4	yes	complemented
211	#3239	C₂×C₇	1	2	yes	complemented
212	#3238	C₂×C₇	1	2	yes	complemented
213	#3237	C₂×C₇	1	2	yes	complemented
214	#3236	C₂×C₇	1	2	yes	complemented
215	#3235	C₂×C₇	1	2	yes	complemented
216	#3234	C₂×C₇	1	2	yes	complemented
217	#3162	C₂×C₇	1	2	yes	complemented
218	#3135	C₂×C₇	1	2	yes	complemented
219	#3091	C₂×C₇	1	4	yes	complemented
220	#3076	C₂×C₇	1	4	yes	complemented
221	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
222	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
223	C₇×#41	—	2	8	no	—
224	C₇×#41	—	4	4	no	—
225	C₇×#41	—	4	4	no	—
226	C₂×C₇×Q₈	—	2	1	no	—
227	C₂×C₇×Q₈	—	2	1	no	—
228	C₂×C₇×Q₈	—	2	2	no	—
229	C₂×C₇×Q₈	—	2	2	no	—
230	C₂×C₇×Q₈	—	2	2	no	—
231	C₂×C₇×Q₈	—	2	2	no	—
232	C₂×C₇×Q₈	—	4	4	no	—
233	C₂×C₇×Q₈	—	4	4	no	—
234	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
235	C₂×C₇×D₄	—	2	2	no	—
236	C₂×C₇×D₄	—	2	2	no	—
237	C₂×C₇×D₄	—	2	2	no	—
238	C₂×C₇×D₄	—	2	1	no	—
239	C₂×C₇×D₄	—	2	1	no	—
240	C₂×C₇×D₄	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇	—	2	4	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	2	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	2	no	—
247	C₂²×C₄×C₇	—	4	2	no	—
248	C₂²×C₄×C₇	—	4	2	no	—
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₇×C₈	—	2	8	no	—
268	C₂×C₇×C₈	C₂⁴	1	8	yes	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	4	no	—
272	C₇×C₄⋊C₄	—	2	4	no	—
273	C₇×C₄⋊C₄	—	2	2	no	—
274	C₇×C₄⋊C₄	—	2	2	no	—
275	C₇×C₄⋊C₄	—	2	2	no	—
276	C₇×C₄⋊C₄	—	2	2	no	—
277	C₇×C₄⋊C₄	—	2	2	no	—
278	C₇×C₄⋊C₄	—	2	2	no	—
279	C₇×C₄⋊C₄	—	2	1	no	—
280	C₇×C₄⋊C₄	—	2	1	no	—
281	C₇×C₄⋊C₄	—	2	1	no	—
282	C₇×C₄⋊C₄	—	2	1	no	—
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	—	2	2	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	2	no	—
296	C₇×C₂²⋊C₄	—	2	2	no	—
297	C₇×C₂²⋊C₄	—	2	2	no	—
298	C₇×C₂²⋊C₄	—	2	2	no	—
299	C₇×C₂²⋊C₄	—	2	2	no	—
300	C₇×C₂²⋊C₄	—	2	2	no	—
301	C₇×C₂²⋊C₄	—	2	2	no	—
302	C₇×C₂²⋊C₄	—	2	2	no	—
303	C₇×C₂²⋊C₄	—	2	2	no	—
304	C₄²×C₇	—	2	2	no	—
305	C₄²×C₇	—	2	2	no	—
306	C₄²×C₇	—	2	4	no	—
307	C₄²×C₇	—	2	2	no	—
308	C₄²×C₇	—	2	4	no	—
309	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂⁴	1	1	yes	characteristic
322	C₄²×C₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	1	yes	characteristic
324	C₄²×C₇	C₂⁴	1	1	yes	characteristic
325	#533	—	2	1	no	—
326	#533	—	2	1	no	—
327	#533	—	2	1	no	—
328	#533	—	2	1	no	—
329	#533	C₂²×C₇	1	1	yes	characteristic
330	#533	C₂²×C₇	1	1	yes	characteristic
331	#533	C₂²×C₇	1	2	yes	—
332	#533	C₂²×C₇	1	2	yes	—
333	#533	C₂²×C₇	1	1	yes	characteristic
334	#533	C₂²×C₇	1	2	yes	—
335	#533	C₂²×C₇	1	2	yes	—
336	#532	C₂²×C₇	1	1	yes	characteristic
337	#532	C₂²×C₇	1	1	yes	characteristic
338	#532	C₂²×C₇	1	1	yes	characteristic
339	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
340	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
341	#529	—	2	1	no	—
342	#529	—	2	1	no	—
343	#529	—	2	1	no	—
344	#529	—	2	1	no	—
345	#529	C₂²×C₇	1	2	yes	—
346	#529	C₂²×C₇	1	2	yes	—
347	C₂×#125	C₂²×C₇	1	2	yes	—
348	#525	—	2	1	no	—
349	#525	—	2	1	no	—
350	#525	C₂²×C₇	1	2	yes	—
351	C₂×C₂²⋊Q₈	—	2	1	no	—
352	C₂×C₂²⋊Q₈	—	2	1	no	—
353	C₄×#41	—	2	1	no	—
354	C₄×#41	—	2	1	no	—
355	C₄×#41	C₂²×C₇	1	2	yes	—
356	C₂×C₄×Q₈	—	2	1	no	—
357	C₂×C₄×Q₈	—	2	1	no	—
358	C₂×#117	C₂²×C₇	1	2	yes	—
359	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
360	#501	C₂²×C₇	1	4	yes	complemented
361	#501	C₂²×C₇	1	4	yes	complemented
362	#501	C₂²×C₇	1	4	yes	complemented
363	#501	C₂²×C₇	1	4	yes	complemented
364	#491	C₂²×C₇	1	4	yes	complemented
365	#490	C₂²×C₇	1	4	yes	complemented
366	#489	C₂²×C₇	1	4	yes	complemented
367	#489	C₂²×C₇	1	4	yes	complemented
368	#485	C₂²×C₇	1	8	yes	—
369	#484	C₂²×C₇	1	4	yes	—
370	#483	C₂²×C₇	1	4	yes	—
371	#482	C₂²×C₇	1	8	yes	—
372	#481	C₂²×C₇	1	4	yes	—
373	#480	C₂²×C₇	1	4	yes	—
374	#479	C₂²×C₇	1	8	yes	complemented
375	#478	C₂²×C₇	1	8	yes	complemented
376	#477	C₂²×C₇	1	4	yes	complemented
377	#476	C₂²×C₇	1	4	yes	complemented
378	#475	C₂²×C₇	1	4	yes	complemented
379	#474	C₂²×C₇	1	4	yes	complemented
380	#432	C₂²×C₇	1	2	yes	—
381	#432	C₂²×C₇	1	2	yes	—
382	#432	C₂²×C₇	1	2	yes	—
383	#432	C₂²×C₇	1	2	yes	—
384	#427	C₂²×C₇	1	8	yes	—
385	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
386	#416	C₂²×C₇	1	8	yes	—
387	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
388	C₂×#97	C₂²×C₇	1	2	yes	—
389	C₂³×C₇	—	2	2	no	—
390	C₂³×C₇	—	2	2	no	—
391	C₂³×C₇	—	2	2	no	—
392	C₂³×C₇	—	4	1	no	—
393	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₇×Q₈	—	2	4	no	—
397	C₇×Q₈	—	4	4	no	—
398	C₇×Q₈	—	4	4	no	—
399	C₇×Q₈	—	4	4	no	—
400	C₇×Q₈	—	4	2	no	—
401	C₇×Q₈	—	4	2	no	—
402	C₇×Q₈	—	4	4	no	—
403	C₇×D₄	—	2	4	no	—
404	C₇×D₄	—	4	2	no	—
405	C₇×D₄	—	4	2	no	—
406	C₇×D₄	—	4	4	no	—
407	C₇×D₄	—	4	4	no	—
408	C₇×D₄	—	4	4	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	4	no	—
423	C₂×C₄×C₇	—	2	4	no	—
424	C₂×C₄×C₇	—	4	1	no	—
425	C₂×C₄×C₇	—	4	1	no	—
426	C₂×C₄×C₇	—	4	1	no	—
427	C₂×C₄×C₇	—	4	1	no	—
428	C₂×C₄×C₇	—	4	1	no	—
429	C₂×C₄×C₇	—	4	1	no	—
430	C₂×C₄×C₇	—	4	1	no	—
431	C₂×C₄×C₇	—	4	4	no	—
432	C₂×C₄×C₇	—	4	4	no	—
433	C₂×C₄×C₇	—	4	4	no	—
434	C₂×C₄×C₇	—	4	4	no	—
435	C₂×C₄×C₇	—	4	4	no	—
436	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
448	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
449	C₇×C₈	—	2	8	no	—
450	C₂×#41	—	2	1	no	—
451	C₂×#41	—	2	1	no	—
452	C₂×#41	C₂³×C₇	1	2	yes	—
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	—	2	1	no	—
455	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
456	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₇	1	4	yes	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
470	#127	C₂³×C₇	1	1	yes	characteristic
471	#126	—	2	2	no	—
472	#126	—	2	2	no	—
473	#125	—	2	2	no	—
474	#125	—	2	2	no	—
475	#125	—	2	1	no	—
476	#125	—	2	1	no	—
477	#125	C₂³×C₇	1	4	yes	—
478	#125	C₂³×C₇	1	4	yes	—
479	#125	C₂³×C₇	1	2	yes	—
480	#124	—	2	1	no	—
481	#124	—	2	1	no	—
482	#124	C₂³×C₇	1	2	yes	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	—	2	1	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
499	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	C₂³×C₇	1	2	yes	—
505	#121	C₂³×C₇	1	2	yes	—
506	#120	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	C₂³×C₇	1	2	yes	—
520	C₄×Q₈	C₂³×C₇	1	2	yes	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	C₂³×C₇	1	2	yes	—
532	C₄×D₄	C₂³×C₇	1	2	yes	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	2	1	no	—
536	#117	—	2	1	no	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	C₂³×C₇	1	4	yes	—
541	#117	C₂³×C₇	1	4	yes	—
542	#117	C₂³×C₇	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₄²	—	2	2	no	—
551	C₂×C₄²	—	2	2	no	—
552	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
553	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
554	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
555	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
556	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
557	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
564	#107	C₂³×C₇	1	8	yes	—
565	#107	C₂³×C₇	1	8	yes	—
566	#106	C₂³×C₇	1	8	yes	—
567	#106	C₂³×C₇	1	8	yes	—
568	C₄⋊C₈	C₂³×C₇	1	4	yes	—
569	C₄⋊C₈	C₂³×C₇	1	4	yes	—
570	#103	C₂³×C₇	1	8	yes	—
571	#103	C₂³×C₇	1	8	yes	—
572	#102	C₂³×C₇	1	8	yes	—
573	#102	C₂³×C₇	1	8	yes	—
574	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
576	#97	C₂³×C₇	1	4	yes	—
577	#97	C₂³×C₇	1	4	yes	—
578	C₂²×C₇	—	2	1	no	—
579	C₂²×C₇	—	2	1	no	—
580	C₂²×C₇	—	2	1	no	—
581	C₂²×C₇	—	2	1	no	—
582	C₂²×C₇	—	2	1	no	—
583	C₂²×C₇	—	2	1	no	—
584	C₂²×C₇	—	2	1	no	—
585	C₂²×C₇	—	4	4	no	—
586	C₂²×C₇	—	4	2	no	—
587	C₂²×C₇	—	4	2	no	—
588	C₂²×C₇	—	4	2	no	—
589	C₂²×C₇	#536	1	2	yes	—
590	C₂²×C₇	#575	1	2	yes	—
591	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
592	C₄×C₇	—	2	1	no	—
593	C₄×C₇	—	2	1	no	—
594	C₄×C₇	—	2	1	no	—
595	C₄×C₇	—	2	1	no	—
596	C₄×C₇	—	2	1	no	—
597	C₄×C₇	—	2	1	no	—
598	C₄×C₇	—	2	1	no	—
599	C₄×C₇	—	2	1	no	—
600	C₄×C₇	—	2	1	no	—
601	C₄×C₇	—	4	2	no	—
602	C₄×C₇	—	4	2	no	—
603	C₄×C₇	—	4	2	no	—
604	C₄×C₇	—	4	4	no	—
605	C₄×C₇	—	4	4	no	—
606	C₄×C₇	#536	1	2	yes	—
607	C₄×C₇	#575	1	2	yes	—
608	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
609	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
610	#41	—	2	8	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	4	4	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	C₂⁴×C₇	1	2	yes	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
637	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
638	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
639	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
640	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
643	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
644	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
645	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
646	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
647	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
648	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
649	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
650	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
654	C₂×C₈	—	2	8	no	—
655	C₂×C₈	C₂⁴×C₇	1	8	yes	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
677	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
678	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	4	no	—
696	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
697	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
698	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
699	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
700	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
701	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
702	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
703	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
704	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
705	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
706	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
707	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
708	C₄²	C₂⁴×C₇	1	1	yes	characteristic
709	C₄²	C₂⁴×C₇	1	1	yes	characteristic
710	C₄²	C₂⁴×C₇	1	1	yes	characteristic
711	C₄²	C₂⁴×C₇	1	1	yes	characteristic
712	C₂×C₇	—	2	2	no	—
713	C₂×C₇	—	2	2	no	—
714	C₂×C₇	—	4	1	no	—
715	C₂×C₇	—	8	2	no	—
716	C₂×C₇	C₂×#536	1	1	yes	characteristic
717	C₂×C₇	C₂×#575	1	1	yes	characteristic
718	C₂×C₇	C₂×#575	1	1	yes	characteristic
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	4	1	no	—
723	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
724	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
725	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
726	Q₈	—	2	4	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	4	no	—
729	Q₈	—	4	4	no	—
730	Q₈	—	4	2	no	—
731	Q₈	—	4	2	no	—
732	Q₈	—	4	4	no	—
733	D₄	—	2	4	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
769	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
770	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
771	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
772	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
773	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
774	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
775	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
776	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
777	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
778	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
779	C₈	—	2	8	no	—
780	C₇	#60854	1	1	yes	characteristic, direct product factor, Sylow
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	C₇×#536	1	2	yes	—
793	C₂²	C₇×#575	1	2	yes	—
794	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	4	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	2	no	—
809	C₄	C₇×#536	1	2	yes	—
810	C₄	C₇×#575	1	2	yes	—
811	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	4	1	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×C₇×#536	1	1	yes	characteristic
817	C₂	C₂×C₇×#575	1	1	yes	characteristic
818	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
prime radical	C₇×#3444	C₂
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
2. C₂×C₇×#533	C₂	semidirect
3. C₇×#3240	C₂	semidirect
4. C₇×#3239	C₂	semidirect
5. C₇×#3238	C₂	semidirect
6. C₇×#3237	C₂	semidirect
7. C₇×#3236	C₂	semidirect
8. C₇×#3235	C₂	semidirect
9. C₇×#3234	C₂	semidirect
10. C₇×#3162	C₂	semidirect
11. C₇×#3135	C₂	semidirect
12. C₇×#3091	C₂	semidirect
13. C₇×#3076	C₂	semidirect
14. C₂×C₇×#432	C₂	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#501	C₂²	semidirect
52. C₇×#501	C₂²	semidirect
53. C₇×#501	C₂²	semidirect
54. C₇×#491	C₂²	semidirect
55. C₇×#490	C₂²	semidirect
56. C₇×#489	C₂²	semidirect
57. C₇×#489	C₂²	semidirect
64. C₇×#479	C₂²	semidirect
65. C₇×#478	C₂²	semidirect
66. C₇×#477	C₂²	semidirect
67. C₇×#476	C₂²	semidirect
68. C₇×#475	C₂²	semidirect
69. C₇×#474	C₂²	semidirect
79. #60854	C₇	direct (N × H)
209. C₂×#533	C₂×C₇	semidirect
210. #3240	C₂×C₇	semidirect
211. #3239	C₂×C₇	semidirect
212. #3238	C₂×C₇	semidirect
213. #3237	C₂×C₇	semidirect
214. #3236	C₂×C₇	semidirect
215. #3235	C₂×C₇	semidirect
216. #3234	C₂×C₇	semidirect
217. #3162	C₂×C₇	semidirect
218. #3135	C₂×C₇	semidirect
219. #3091	C₂×C₇	semidirect
220. #3076	C₂×C₇	semidirect
221. C₂×#432	C₂×C₇	semidirect
360. #501	C₂²×C₇	semidirect
361. #501	C₂²×C₇	semidirect
362. #501	C₂²×C₇	semidirect
363. #501	C₂²×C₇	semidirect
364. #491	C₂²×C₇	semidirect
365. #490	C₂²×C₇	semidirect
366. #489	C₂²×C₇	semidirect
367. #489	C₂²×C₇	semidirect
374. #479	C₂²×C₇	semidirect
375. #478	C₂²×C₇	semidirect
376. #477	C₂²×C₇	semidirect
377. #476	C₂²×C₇	semidirect
378. #475	C₂²×C₇	semidirect
379. #474	C₂²×C₇	semidirect
780. C₇	#60854	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×#533	2
C₇×#3240	2
C₇×#3239	2
C₇×#3238	2
C₇×#3237	2
C₇×#3236	2
C₇×#3235	2
C₇×#3234	2
C₇×#3162	2
C₇×#3135	2
C₇×#3091	2
C₇×#3076	2
C₂×C₇×#432	2
#60854	7

Subgroups — C7×#60854 #13238070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60854 #13238070