Subgroups — D₇×#4130 #72218426

Order 2240.

660 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅×D₇	C₂	1	1	yes	maximal, characteristic
2	#11765360	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#4130	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₂²⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
5	#11765326	C₂	1	2	yes	maximal, complemented
6	D₇×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	C₄×D₇×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	#11765312	C₂	1	2	yes	maximal, complemented
9	#11765311	C₂	1	2	yes	maximal, complemented
10	C₂²×D₅×D₇	C₂²	1	1	yes	characteristic
11	C₂×D₇×AGL(1,𝔽₅)	C₂²	1	4	yes	—
12	C₂×C₄×D₃₅	C₄	1	1	yes	characteristic, complemented
13	C₂×C₄×C₇×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₇	C₄	1	1	yes	characteristic, complemented
15	C₂×#63304	C₄	1	1	yes	characteristic, complemented
16	C₂×D₅×Dic₇	C₂²	1	1	yes	characteristic
17	C₂×D₇×Dic₅	C₄	1	1	yes	characteristic, complemented
18	C₄×D₅×D₇	C₄	1	1	yes	characteristic, complemented
19	C₄×D₅×D₇	C₄	1	1	yes	characteristic, complemented
20	C₄×D₅×D₇	C₄	1	1	yes	characteristic, complemented
21	C₄×D₅×D₇	C₄	1	1	yes	characteristic, complemented
22	C₄×D₅×D₇	C₂²	1	1	yes	characteristic
23	C₄×D₅×D₇	C₂²	1	1	yes	characteristic
24	C₄×D₅×D₇	C₂²	1	1	yes	characteristic
25	C₄×D₅×D₇	C₂²	1	1	yes	characteristic
26	C₂²⋊(C₇⋊AGL(1,𝔽₅))	C₂²	1	2	yes	—
27	C₄⋊(C₇⋊AGL(1,𝔽₅))	C₂²	1	2	yes	complemented
28	C₄×C₇⋊AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
29	C₇×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
30	C₇×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
31	C₄×C₇×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
32	Dic₇⋊AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
33	(C₂×D₇)⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
34	AGL(1,𝔽₅)×Dic₇	C₂²	1	4	yes	complemented
35	D₇×#117	—	5	1	no	maximal, Hall
36	C₂×#4130	—	7	1	no	maximal, Hall
37	C₂²×D₃₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₇×D₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×D₇	C₂×C₄	1	1	yes	characteristic
40	C₂×D₅×D₇	—	2	4	no	—
41	C₂×D₅×D₇	C₂×C₄	1	1	yes	characteristic
42	C₂×D₅×D₇	C₂×C₄	1	1	yes	characteristic
43	C₂×D₅×D₇	C₂³	1	1	yes	characteristic
44	C₂×D₅×D₇	C₂³	1	1	yes	characteristic
45	C₂×C₇⋊AGL(1,𝔽₅)	C₂³	1	4	yes	—
46	C₂×C₇×AGL(1,𝔽₅)	C₂³	1	4	yes	—
47	D₇×AGL(1,𝔽₅)	—	2	8	no	—
48	C₂×C₄×C₅×C₇	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×Dic₃₅	C₂×C₄	1	1	yes	characteristic, complemented
50	C₄×D₃₅	C₂×C₄	1	1	yes	characteristic
51	C₄×D₃₅	C₂×C₄	1	1	yes	characteristic
52	C₄×D₃₅	C₂×C₄	1	1	yes	characteristic, complemented
53	C₄×D₃₅	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂×C₇×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
55	C₄×C₇×D₅	C₂×C₄	1	1	yes	characteristic, complemented
56	C₄×C₇×D₅	C₂×C₄	1	1	yes	characteristic, complemented
57	C₄×C₇×D₅	C₂³	1	1	yes	characteristic
58	C₄×C₇×D₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×Dic₇	C₂×C₄	1	1	yes	characteristic, complemented
60	C₄×C₅×D₇	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×D₇	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×D₇	C₂×C₄	1	1	yes	characteristic, complemented
63	C₄×C₅×D₇	C₂×C₄	1	1	yes	characteristic, complemented
64	#63304	C₂×C₄	1	1	yes	characteristic
65	#63304	C₂×C₄	1	1	yes	characteristic
66	#63304	C₂×C₄	1	1	yes	characteristic, complemented
67	#63304	C₂×C₄	1	1	yes	characteristic, complemented
68	D₅×Dic₇	C₂×C₄	1	1	yes	characteristic, complemented
69	D₅×Dic₇	C₂×C₄	1	1	yes	characteristic, complemented
70	D₅×Dic₇	C₂³	1	1	yes	characteristic
71	D₅×Dic₇	C₂³	1	1	yes	characteristic
72	D₇×Dic₅	C₂×C₄	1	1	yes	characteristic
73	D₇×Dic₅	C₂×C₄	1	1	yes	characteristic
74	D₇×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
75	D₇×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂²×C₄×D₇	—	5	1	no	—
77	C₇×#117	—	5	1	no	—
78	#6489	—	5	1	no	—
79	#6455	—	5	2	no	—
80	D₇×C₄⋊C₄	—	5	2	no	—
81	D₇×C₂²⋊C₄	—	5	2	no	—
82	#6440	—	5	2	no	—
83	#6435	—	5	2	no	—
84	C₄²×D₇	—	5	2	no	—
85	C₂²×C₄×D₅	—	7	1	no	—
86	C₂×C₂²⋊AGL(1,𝔽₅)	—	7	2	no	—
87	#4130	—	7	1	no	—
88	#4130	—	7	2	no	—
89	#4130	—	7	2	no	—
90	#4130	—	7	2	no	—
91	#4130	D₇	1	1	yes	characteristic, direct product factor
92	C₂×C₄⋊AGL(1,𝔽₅)	—	7	2	no	—
93	C₂×C₄×AGL(1,𝔽₅)	—	7	2	no	—
94	C₂²×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
95	C₂×D₃₅	—	2	2	no	—
96	C₂×D₃₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×D₃₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₇×D₅	—	2	2	no	—
99	C₂×C₇×D₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₇×D₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×D₇	—	2	2	no	—
102	C₂×C₅×D₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₅×D₇	C₂²×C₄	1	1	yes	characteristic
104	D₅×D₇	—	2	2	no	—
105	D₅×D₇	—	2	2	no	—
106	D₅×D₇	—	2	2	no	—
107	D₅×D₇	#41	1	4	yes	—
108	C₇⋊AGL(1,𝔽₅)	—	2	4	no	—
109	C₇×AGL(1,𝔽₅)	—	2	4	no	—
110	C₄×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₄×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
112	Dic₃₅	C₂²×C₄	1	1	yes	characteristic
113	Dic₃₅	C₂²×C₄	1	1	yes	characteristic
114	C₅×Dic₇	C₂²×C₄	1	1	yes	characteristic
115	C₅×Dic₇	C₂²×C₄	1	1	yes	characteristic
116	C₇×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₇×Dic₅	C₂²×C₄	1	1	yes	characteristic
118	C₂³×D₇	—	5	1	no	—
119	C₂²×C₄×C₇	—	5	1	no	—
120	C₂²×Dic₇	—	5	1	no	—
121	C₂×C₄×D₇	—	5	1	no	—
122	C₂×C₄×D₇	—	5	1	no	—
123	C₂×C₄×D₇	—	5	1	no	—
124	C₂×C₄×D₇	—	5	1	no	—
125	C₂×C₄×D₇	—	5	1	no	—
126	C₂×C₄×D₇	—	5	1	no	—
127	C₂×C₄×D₇	—	5	1	no	—
128	C₂×C₄×D₇	—	5	1	no	—
129	C₂×C₄×D₇	—	5	1	no	—
130	C₂×C₄×D₇	—	5	1	no	—
131	C₂×C₄×D₇	—	5	1	no	—
132	C₂×C₄×D₇	—	5	4	no	—
133	C₂×C₄×D₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
134	C₇×C₄⋊C₄	—	5	2	no	—
135	C₇×C₂²⋊C₄	—	5	2	no	—
136	C₄²×C₇	—	5	2	no	—
137	C₂²⋊Dic₇	—	5	2	no	—
138	(C₂×D₇)⋊C₄	—	5	4	no	—
139	C₄⋊Dic₇	—	5	2	no	—
140	Dic₇⋊C₄	—	5	4	no	—
141	C₄×Dic₇	—	5	4	no	—
142	C₄×Dic₇	—	5	2	no	—
143	C₂³×D₅	—	7	1	no	—
144	C₂²×AGL(1,𝔽₅)	—	7	4	no	—
145	C₂²×C₄×C₅	—	7	1	no	—
146	C₂²×Dic₅	—	7	1	no	—
147	C₂×C₄×D₅	—	7	1	no	—
148	C₂×C₄×D₅	—	7	1	no	—
149	C₂×C₄×D₅	—	7	1	no	—
150	C₂×C₄×D₅	—	7	1	no	—
151	C₂×C₄×D₅	—	7	1	no	—
152	C₂×C₄×D₅	—	7	1	no	—
153	C₂×C₄×D₅	—	7	1	no	—
154	C₂×C₄×D₅	—	7	1	no	—
155	C₂×C₄×D₅	—	7	1	no	—
156	C₂×C₄×D₅	—	7	1	no	—
157	C₂×C₄×D₅	—	7	1	no	—
158	C₂×C₄×D₅	C₂×D₇	1	1	yes	characteristic
159	C₂²⋊AGL(1,𝔽₅)	—	7	2	no	—
160	C₂²⋊AGL(1,𝔽₅)	—	7	4	no	—
161	C₂²⋊AGL(1,𝔽₅)	C₂×D₇	1	2	yes	—
162	C₄⋊AGL(1,𝔽₅)	—	7	4	no	—
163	C₄⋊AGL(1,𝔽₅)	—	7	2	no	—
164	C₄⋊AGL(1,𝔽₅)	C₂×D₇	1	2	yes	complemented
165	C₄×AGL(1,𝔽₅)	—	7	4	no	—
166	C₄×AGL(1,𝔽₅)	—	7	2	no	—
167	C₄×AGL(1,𝔽₅)	C₂×D₇	1	2	yes	complemented
168	C₂×C₅×C₇	—	2	1	no	—
169	C₂×C₅×C₇	C₂³×C₄	1	1	yes	characteristic
170	D₃₅	—	2	1	no	—
171	D₃₅	#117	1	2	yes	complemented
172	C₅×D₇	—	2	1	no	—
173	C₅×D₇	#117	1	2	yes	complemented
174	C₇×D₅	—	2	1	no	—
175	C₇×D₅	C₂×#41	1	2	yes	—
176	C₂×#117	—	35	1	no	Sylow
177	C₂³×C₇	—	5	1	no	—
178	C₂²×D₇	—	5	1	no	—
179	C₂²×D₇	—	5	1	no	—
180	C₂²×D₇	—	5	1	no	—
181	C₂²×D₇	—	5	1	no	—
182	C₂²×D₇	—	5	1	no	—
183	C₂²×D₇	—	10	4	no	—
184	C₂²×D₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
185	C₂×C₄×C₇	—	5	1	no	—
186	C₂×C₄×C₇	—	5	1	no	—
187	C₂×C₄×C₇	—	5	1	no	—
188	C₂×C₄×C₇	—	5	1	no	—
189	C₂×C₄×C₇	—	5	1	no	—
190	C₂×C₄×C₇	—	5	4	no	—
191	C₂×C₄×C₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
192	C₂×Dic₇	—	5	1	no	—
193	C₂×Dic₇	—	5	1	no	—
194	C₂×Dic₇	—	5	1	no	—
195	C₂×Dic₇	—	5	1	no	—
196	C₂×Dic₇	—	5	1	no	—
197	C₂×Dic₇	—	5	4	no	—
198	C₂×Dic₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
199	C₄×D₇	—	5	1	no	—
200	C₄×D₇	—	5	1	no	—
201	C₄×D₇	—	5	1	no	—
202	C₄×D₇	—	5	1	no	—
203	C₄×D₇	—	5	1	no	—
204	C₄×D₇	—	5	1	no	—
205	C₄×D₇	—	5	1	no	—
206	C₄×D₇	—	5	1	no	—
207	C₄×D₇	—	5	1	no	—
208	C₄×D₇	—	5	1	no	—
209	C₄×D₇	—	5	1	no	—
210	C₄×D₇	—	5	1	no	—
211	C₄×D₇	—	10	8	no	—
212	C₄×D₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
213	C₄×D₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
214	C₄×D₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
215	C₄×D₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
216	C₂³×C₅	—	7	1	no	—
217	C₂²×D₅	—	7	1	no	—
218	C₂²×D₅	—	7	1	no	—
219	C₂²×D₅	—	7	1	no	—
220	C₂²×D₅	—	7	1	no	—
221	C₂²×D₅	—	7	1	no	—
222	C₂²×D₅	—	14	4	no	—
223	C₂²×D₅	C₂²×D₇	1	1	yes	characteristic
224	C₂×AGL(1,𝔽₅)	—	7	4	no	—
225	C₂×AGL(1,𝔽₅)	—	14	8	no	—
226	C₂×AGL(1,𝔽₅)	C₂²×D₇	1	4	yes	—
227	C₂×C₄×C₅	—	7	1	no	—
228	C₂×C₄×C₅	—	7	1	no	—
229	C₂×C₄×C₅	—	7	1	no	—
230	C₂×C₄×C₅	—	7	1	no	—
231	C₂×C₄×C₅	—	7	1	no	—
232	C₂×C₄×C₅	C₄×D₇	1	1	yes	characteristic, complemented
233	C₂×Dic₅	—	7	1	no	—
234	C₂×Dic₅	—	7	1	no	—
235	C₂×Dic₅	—	7	1	no	—
236	C₂×Dic₅	—	7	1	no	—
237	C₂×Dic₅	—	7	1	no	—
238	C₂×Dic₅	C₄×D₇	1	1	yes	characteristic, complemented
239	C₄×D₅	—	7	1	no	—
240	C₄×D₅	—	7	1	no	—
241	C₄×D₅	—	7	1	no	—
242	C₄×D₅	—	7	1	no	—
243	C₄×D₅	—	7	1	no	—
244	C₄×D₅	—	7	1	no	—
245	C₄×D₅	—	7	1	no	—
246	C₄×D₅	—	7	1	no	—
247	C₄×D₅	—	7	1	no	—
248	C₄×D₅	—	7	1	no	—
249	C₄×D₅	—	7	1	no	—
250	C₄×D₅	—	7	1	no	—
251	C₄×D₅	C₄×D₇	1	1	yes	characteristic, complemented
252	C₄×D₅	C₄×D₇	1	1	yes	characteristic, complemented
253	C₄×D₅	C₂²×D₇	1	1	yes	characteristic
254	C₄×D₅	C₂²×D₇	1	1	yes	characteristic
255	C₅×C₇	C₂×#117	1	1	yes	characteristic, complemented, Hall
256	C₂³×C₄	—	35	1	no	—
257	#117	—	5	1	no	—
258	#117	—	35	2	no	—
259	#117	—	35	2	no	—
260	#117	—	35	2	no	—
261	#117	—	35	1	no	—
262	C₂×C₄⋊C₄	—	35	2	no	—
263	C₂×C₂²⋊C₄	—	35	2	no	—
264	C₂×C₄²	—	35	2	no	—
265	C₂²×C₇	—	5	1	no	—
266	C₂²×C₇	—	5	1	no	—
267	C₂²×C₇	—	10	2	no	—
268	C₂²×C₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
269	C₂×D₇	—	2	2	no	—
270	C₂×D₇	—	5	1	no	—
271	C₂×D₇	—	5	4	no	—
272	C₂×D₇	—	5	1	no	—
273	C₂×D₇	—	10	2	no	—
274	C₂×D₇	—	10	2	no	—
275	C₂×D₇	—	10	2	no	—
276	C₂×D₇	—	10	2	no	—
277	C₂×D₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
278	C₂×D₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
279	C₄×C₇	—	5	1	no	—
280	C₄×C₇	—	5	1	no	—
281	C₄×C₇	—	10	4	no	—
282	C₄×C₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
283	C₄×C₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
284	Dic₇	—	5	1	no	—
285	Dic₇	—	5	1	no	—
286	Dic₇	—	10	4	no	—
287	Dic₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
288	Dic₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₂²×C₅	—	7	1	no	—
290	C₂²×C₅	—	7	1	no	—
291	C₂²×C₅	—	14	2	no	—
292	C₂²×C₅	C₂×C₄×D₇	1	1	yes	characteristic
293	C₂×D₅	—	2	2	no	—
294	C₂×D₅	—	7	1	no	—
295	C₂×D₅	—	7	4	no	—
296	C₂×D₅	—	7	1	no	—
297	C₂×D₅	—	14	2	no	—
298	C₂×D₅	—	14	2	no	—
299	C₂×D₅	—	14	2	no	—
300	C₂×D₅	—	14	2	no	—
301	C₂×D₅	C₂×C₄×D₇	1	1	yes	characteristic
302	C₂×D₅	C₂³×D₇	1	1	yes	characteristic
303	AGL(1,𝔽₅)	—	2	4	no	—
304	AGL(1,𝔽₅)	—	14	4	no	—
305	C₄×C₅	—	7	1	no	—
306	C₄×C₅	—	7	1	no	—
307	C₄×C₅	C₂×C₄×D₇	1	1	yes	characteristic
308	C₄×C₅	C₂×C₄×D₇	1	1	yes	characteristic
309	Dic₅	—	7	1	no	—
310	Dic₅	—	7	1	no	—
311	Dic₅	C₂×C₄×D₇	1	1	yes	characteristic
312	Dic₅	C₂×C₄×D₇	1	1	yes	characteristic
313	C₂⁴	—	35	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	7	1	no	—
316	C₂²×C₄	—	35	1	no	—
317	C₂²×C₄	—	35	1	no	—
318	C₂²×C₄	—	35	1	no	—
319	C₂²×C₄	—	35	1	no	—
320	C₂²×C₄	—	35	1	no	—
321	C₂²×C₄	—	35	1	no	—
322	C₂²×C₄	—	35	1	no	—
323	C₂²×C₄	—	35	1	no	—
324	C₂²×C₄	—	35	1	no	—
325	C₂²×C₄	—	35	1	no	—
326	C₂²×C₄	—	35	4	no	—
327	C₂²×C₄	—	35	1	no	—
328	C₂²×C₄	—	35	1	no	—
329	C₄⋊C₄	—	5	2	no	—
330	C₄⋊C₄	—	35	4	no	—
331	C₄⋊C₄	—	35	2	no	—
332	C₂²⋊C₄	—	5	2	no	—
333	C₂²⋊C₄	—	35	4	no	—
334	C₂²⋊C₄	—	35	2	no	—
335	C₄²	—	5	2	no	—
336	C₄²	—	35	2	no	—
337	C₄²	—	35	4	no	—
338	C₂×C₇	—	2	1	no	—
339	C₂×C₇	—	5	2	no	—
340	C₂×C₇	—	10	1	no	—
341	C₂×C₇	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
342	D₇	—	2	1	no	—
343	D₇	—	5	2	no	—
344	D₇	—	10	1	no	—
345	D₇	#4130	1	2	yes	direct product factor
346	C₂×C₅	—	2	1	no	—
347	C₂×C₅	—	7	2	no	—
348	C₂×C₅	—	14	1	no	—
349	C₂×C₅	C₂²×C₄×D₇	1	1	yes	characteristic
350	D₅	—	2	1	no	—
351	D₅	—	7	2	no	—
352	D₅	—	14	1	no	—
353	D₅	D₇×#41	1	2	yes	—
354	C₂³	—	5	1	no	—
355	C₂³	—	7	1	no	—
356	C₂³	—	35	1	no	—
357	C₂³	—	35	1	no	—
358	C₂³	—	35	1	no	—
359	C₂³	—	35	1	no	—
360	C₂³	—	35	1	no	—
361	C₂³	—	70	4	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	5	1	no	—
364	C₂×C₄	—	5	1	no	—
365	C₂×C₄	—	5	1	no	—
366	C₂×C₄	—	5	1	no	—
367	C₂×C₄	—	5	4	no	—
368	C₂×C₄	—	7	1	no	—
369	C₂×C₄	—	7	1	no	—
370	C₂×C₄	—	7	1	no	—
371	C₂×C₄	—	7	1	no	—
372	C₂×C₄	—	7	1	no	—
373	C₂×C₄	—	35	1	no	—
374	C₂×C₄	—	35	1	no	—
375	C₂×C₄	—	35	1	no	—
376	C₂×C₄	—	35	1	no	—
377	C₂×C₄	—	35	1	no	—
378	C₂×C₄	—	35	1	no	—
379	C₂×C₄	—	35	1	no	—
380	C₂×C₄	—	35	1	no	—
381	C₂×C₄	—	35	1	no	—
382	C₂×C₄	—	35	1	no	—
383	C₂×C₄	—	35	1	no	—
384	C₂×C₄	—	35	1	no	—
385	C₂×C₄	—	35	1	no	—
386	C₂×C₄	—	35	1	no	—
387	C₂×C₄	—	35	1	no	—
388	C₂×C₄	—	35	1	no	—
389	C₂×C₄	—	35	1	no	—
390	C₂×C₄	—	35	4	no	—
391	C₂×C₄	—	70	8	no	—
392	C₂×C₄	D₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
393	C₇	C₂×#4130	1	1	yes	characteristic, complemented, Sylow
394	C₅	D₇×#117	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	5	1	no	—
396	C₂²	—	5	1	no	—
397	C₂²	—	7	1	no	—
398	C₂²	—	7	1	no	—
399	C₂²	—	10	2	no	—
400	C₂²	—	14	2	no	—
401	C₂²	—	35	4	no	—
402	C₂²	—	35	1	no	—
403	C₂²	—	35	1	no	—
404	C₂²	—	70	2	no	—
405	C₂²	—	70	2	no	—
406	C₂²	—	70	2	no	—
407	C₂²	—	70	2	no	—
408	C₂²	C₂×D₇×AGL(1,𝔽₅)	1	1	yes	characteristic
409	C₄	—	5	1	no	—
410	C₄	—	5	1	no	—
411	C₄	—	7	1	no	—
412	C₄	—	7	1	no	—
413	C₄	—	10	4	no	—
414	C₄	—	35	1	no	—
415	C₄	—	35	1	no	—
416	C₄	—	70	4	no	—
417	C₄	C₂×D₇×AGL(1,𝔽₅)	1	1	yes	characteristic
418	C₄	C₂×D₇×AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	5	2	no	—
421	C₂	—	7	2	no	—
422	C₂	—	10	1	no	—
423	C₂	—	14	1	no	—
424	C₂	—	35	2	no	—
425	C₂	—	70	1	no	—
426	C₂	C₂²×D₇×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₇×AGL(1,𝔽₅)
commutator, socle	C₂×C₅×C₇	C₂³×C₄
Frattini	C₂	C₂²×D₇×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₇	C₂×C₄
prime radical	C₂²×D₅×D₇	C₂²
cosocle	C₂×C₇×D₅	C₂⁴
hypercenter	C₂×C₄	D₇×AGL(1,𝔽₅)
hypocenter	C₅×C₇	C₂×#117
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #11765360	C₂	semidirect
3. C₇×#4130	C₂	semidirect
5. #11765326	C₂	semidirect
6. D₇×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
7. C₄×D₇×AGL(1,𝔽₅)	C₂	semidirect
8. #11765312	C₂	semidirect
9. #11765311	C₂	semidirect
12. C₂×C₄×D₃₅	C₄	semidirect
14. C₂×C₄×C₅×D₇	C₄	semidirect
15. C₂×#63304	C₄	semidirect
17. C₂×D₇×Dic₅	C₄	semidirect
18. C₄×D₅×D₇	C₄	semidirect
19. C₄×D₅×D₇	C₄	semidirect
20. C₄×D₅×D₇	C₄	semidirect
21. C₄×D₅×D₇	C₄	semidirect
27. C₄⋊(C₇⋊AGL(1,𝔽₅))	C₂²	semidirect
28. C₄×C₇⋊AGL(1,𝔽₅)	C₂²	semidirect
30. C₇×C₄⋊AGL(1,𝔽₅)	C₂²	semidirect
31. C₄×C₇×AGL(1,𝔽₅)	C₂²	semidirect
32. Dic₇⋊AGL(1,𝔽₅)	C₂²	semidirect
34. AGL(1,𝔽₅)×Dic₇	C₂²	semidirect
48. C₂×C₄×C₅×C₇	C₂×C₄	semidirect
49. C₂×Dic₃₅	C₂×C₄	semidirect
52. C₄×D₃₅	C₂×C₄	semidirect
53. C₄×D₃₅	C₂×C₄	semidirect
54. C₂×C₇×Dic₅	C₂×C₄	semidirect
55. C₄×C₇×D₅	C₂×C₄	semidirect
56. C₄×C₇×D₅	C₂×C₄	semidirect
59. C₂×C₅×Dic₇	C₂×C₄	semidirect
62. C₄×C₅×D₇	C₂×C₄	semidirect
63. C₄×C₅×D₇	C₂×C₄	semidirect
66. #63304	C₂×C₄	semidirect
67. #63304	C₂×C₄	semidirect
68. D₅×Dic₇	C₂×C₄	semidirect
69. D₅×Dic₇	C₂×C₄	semidirect
74. D₇×Dic₅	C₂×C₄	semidirect
75. D₇×Dic₅	C₂×C₄	semidirect
91. #4130	D₇	direct (N × H)
133. C₂×C₄×D₇	AGL(1,𝔽₅)	semidirect
164. C₄⋊AGL(1,𝔽₅)	C₂×D₇	semidirect
167. C₄×AGL(1,𝔽₅)	C₂×D₇	semidirect
171. D₃₅	#117	semidirect
173. C₅×D₇	#117	semidirect
191. C₂×C₄×C₇	C₂×AGL(1,𝔽₅)	semidirect
198. C₂×Dic₇	C₂×AGL(1,𝔽₅)	semidirect
214. C₄×D₇	C₂×AGL(1,𝔽₅)	semidirect
215. C₄×D₇	C₂×AGL(1,𝔽₅)	semidirect
232. C₂×C₄×C₅	C₄×D₇	semidirect
238. C₂×Dic₅	C₄×D₇	semidirect
251. C₄×D₅	C₄×D₇	semidirect
252. C₄×D₅	C₄×D₇	semidirect
255. C₅×C₇	C₂×#117	semidirect
345. D₇	#4130	direct (N × H)
392. C₂×C₄	D₇×AGL(1,𝔽₅)	semidirect
393. C₇	C₂×#4130	semidirect
394. C₅	D₇×#117	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×D₅×D₇	2
#11765360	2
C₇×#4130	2
D₇×C₂²⋊AGL(1,𝔽₅)	2
#11765326	2
D₇×C₄⋊AGL(1,𝔽₅)	2
C₄×D₇×AGL(1,𝔽₅)	2
#11765312	2
#11765311	2
D₇×#117	5
C₂×#4130	7

Subgroups — D7×#4130 #72218426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#4130 #72218426