Subgroups — C₄×#63304 #11764830

Order 1120.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#63304	C₂	1	2	yes	maximal
3	C₄×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₅×Dic₇	C₂	1	2	yes	maximal, complemented
6	C₂²×D₃₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₅	C₂²	1	1	yes	characteristic
9	C₄×D₃₅	C₄	1	4	yes	complemented
10	C₂×C₇×Dic₅	C₂²	1	2	yes	—
11	C₂×C₅×Dic₇	C₂²	1	2	yes	—
12	#63304	C₄	1	8	yes	direct product factor
13	C₄²×D₇	—	5	1	no	maximal, Hall
14	C₄²×D₅	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
16	C₂×D₃₅	C₂×C₄	1	4	yes	—
17	C₂×D₃₅	C₂×C₄	1	2	yes	—
18	C₄×C₅×C₇	C₂×C₄	1	2	yes	complemented
19	Dic₃₅	C₂×C₄	1	2	yes	complemented
20	C₅×Dic₇	C₂×C₄	1	4	yes	complemented
21	C₇×Dic₅	C₂×C₄	1	4	yes	complemented
22	C₂×C₄×D₇	—	5	1	no	—
23	C₂×C₄×D₇	—	5	2	no	—
24	C₄²×C₇	—	5	1	no	—
25	C₄×Dic₇	—	5	2	no	—
26	C₄×Dic₇	D₅	1	1	yes	characteristic, complemented
27	C₂×C₄×D₅	—	7	1	no	—
28	C₂×C₄×D₅	—	7	2	no	—
29	C₄²×C₅	—	7	1	no	—
30	C₄×Dic₅	—	7	2	no	—
31	C₄×Dic₅	D₇	1	1	yes	characteristic, complemented
32	C₂×C₅×C₇	C₂²×C₄	1	2	yes	—
33	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
34	D₃₅	C₄²	1	4	yes	complemented
35	C₂²×D₇	—	5	1	no	—
36	C₂×C₄×C₇	—	5	2	no	—
37	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
38	C₂×Dic₇	—	5	1	no	—
39	C₂×Dic₇	C₂×D₅	1	2	yes	—
40	C₄×D₇	—	5	4	no	—
41	C₄×D₇	—	5	8	no	—
42	C₂²×D₅	—	7	1	no	—
43	C₂×C₄×C₅	—	7	2	no	—
44	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
45	C₂×Dic₅	—	7	1	no	—
46	C₂×Dic₅	C₂×D₇	1	2	yes	—
47	C₄×D₅	—	7	4	no	—
48	C₄×D₅	—	7	8	no	—
49	C₅×C₇	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
50	C₂×C₄²	—	35	1	no	Sylow
51	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
52	C₂×D₇	—	5	4	no	—
53	C₂×D₇	—	5	2	no	—
54	C₄×C₇	—	5	4	no	—
55	C₄×C₇	C₄×D₅	1	2	yes	complemented
56	Dic₇	—	5	2	no	—
57	Dic₇	C₄×D₅	1	4	yes	complemented
58	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
59	C₂×D₅	—	7	4	no	—
60	C₂×D₅	—	7	2	no	—
61	C₄×C₅	—	7	4	no	—
62	C₄×C₅	C₄×D₇	1	2	yes	complemented
63	Dic₅	—	7	2	no	—
64	Dic₅	C₄×D₇	1	4	yes	complemented
65	C₂²×C₄	—	35	2	no	—
66	C₂²×C₄	—	35	1	no	—
67	C₄²	—	5	1	no	—
68	C₄²	—	7	1	no	—
69	C₄²	—	35	2	no	—
70	C₂×C₇	C₂×C₄×D₅	1	2	yes	—
71	C₂×C₇	C₂×C₄×D₅	1	1	yes	characteristic
72	D₇	—	5	4	no	—
73	C₂×C₅	C₂×C₄×D₇	1	2	yes	—
74	C₂×C₅	C₂×C₄×D₇	1	1	yes	characteristic
75	D₅	—	7	4	no	—
76	C₂³	—	35	1	no	—
77	C₂×C₄	—	5	2	no	—
78	C₂×C₄	—	7	2	no	—
79	C₂×C₄	—	35	8	no	—
80	C₂×C₄	—	35	1	no	—
81	C₂×C₄	—	35	4	no	—
82	C₂×C₄	D₅×D₇	1	1	yes	characteristic
83	C₇	C₄²×D₅	1	1	yes	characteristic, complemented, Sylow
84	C₅	C₄²×D₇	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	35	4	no	—
86	C₂²	—	35	2	no	—
87	C₂²	C₂×D₅×D₇	1	1	yes	characteristic
88	C₄	—	5	4	no	—
89	C₄	—	7	4	no	—
90	C₄	—	35	2	no	—
91	C₄	#63304	1	2	yes	direct product factor
92	C₂	—	35	4	no	—
93	C₂	C₄×D₅×D₇	1	2	yes	—
94	C₂	C₂×#63304	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₅×D₇
commutator, hypocenter	C₅×C₇	C₂×C₄²
Frattini	C₂²	C₂×D₅×D₇
Fitting	C₂×C₄×C₅×C₇	C₂²
socle, cosocle	C₂²×C₅×C₇	C₂³
prime radical	C₂²×D₃₅	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₇×Dic₅	C₂	semidirect
4. C₄×C₅×Dic₇	C₂	semidirect
5. Dic₅×Dic₇	C₂	semidirect
9. C₄×D₃₅	C₄	semidirect
12. #63304	C₄	direct (N × H)
18. C₄×C₅×C₇	C₂×C₄	semidirect
19. Dic₃₅	C₂×C₄	semidirect
20. C₅×Dic₇	C₂×C₄	semidirect
21. C₇×Dic₅	C₂×C₄	semidirect
26. C₄×Dic₇	D₅	semidirect
31. C₄×Dic₅	D₇	semidirect
34. D₃₅	C₄²	semidirect
49. C₅×C₇	C₂×C₄²	semidirect
55. C₄×C₇	C₄×D₅	semidirect
57. Dic₇	C₄×D₅	semidirect
62. C₄×C₅	C₄×D₇	semidirect
64. Dic₅	C₄×D₇	semidirect
83. C₇	C₄²×D₅	semidirect
84. C₅	C₄²×D₇	semidirect
91. C₄	#63304	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃₅	2
C₂×#63304	2
C₄×C₇×Dic₅	2
C₄×C₅×Dic₇	2
Dic₅×Dic₇	2
C₄²×D₇	5
C₄²×D₅	7

Subgroups — C4×#63304 #11764830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63304 #11764830