Subgroups — C₅×#6453 #11765048

Order 1120.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊Dic₇	C₂	1	2	yes	maximal
3	C₅×C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₇⋊C₄	C₂	1	2	yes	maximal
5	C₄×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
8	C₂×C₅×Dic₇	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₇	C₂²	1	1	yes	characteristic
10	C₂×C₅×Dic₇	C₂²	1	2	yes	—
11	#6453	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×#125	—	7	1	no	maximal, Hall
13	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
14	C₄×C₅×C₇	—	2	2	no	—
15	C₄×C₅×C₇	Q₈	1	2	yes	—
16	C₅×Dic₇	—	2	1	no	—
17	C₅×Dic₇	—	2	1	no	—
18	C₅×Dic₇	—	2	2	no	—
19	C₇×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
20	C₄⋊Dic₇	C₂×C₅	1	2	yes	—
21	C₄⋊Dic₇	C₂×C₅	1	1	yes	characteristic
22	Dic₇⋊C₄	C₂×C₅	1	2	yes	—
23	C₄×Dic₇	C₂×C₅	1	1	yes	characteristic
24	C₅×C₄⋊C₄	—	7	2	no	—
25	C₅×C₄⋊C₄	—	7	2	no	—
26	C₅×C₄⋊C₄	—	7	1	no	—
27	C₅×C₄⋊C₄	D₇	1	1	yes	characteristic
28	C₄²×C₅	—	7	1	no	—
29	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₅×C₇	#41	1	1	yes	characteristic
31	C₂×C₅×C₇	#41	1	1	yes	characteristic
32	C₂×C₄×C₇	C₂²×C₅	1	2	yes	—
33	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
34	C₂×Dic₇	C₂²×C₅	1	1	yes	characteristic
35	C₂×Dic₇	C₂²×C₅	1	1	yes	characteristic
36	C₂×Dic₇	C₂²×C₅	1	2	yes	—
37	C₂×C₄×C₅	—	7	1	no	—
38	C₂×C₄×C₅	—	7	1	no	—
39	C₂×C₄×C₅	—	7	2	no	—
40	C₂×C₄×C₅	C₂×D₇	1	2	yes	—
41	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
42	C₅×C₇	#125	1	1	yes	characteristic, complemented, Hall
43	#125	—	7	1	no	Sylow
44	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
45	C₄×C₇	—	2	2	no	—
46	C₄×C₇	C₅×Q₈	1	2	yes	—
47	Dic₇	—	2	1	no	—
48	Dic₇	—	2	1	no	—
49	Dic₇	—	2	2	no	—
50	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
51	C₄×C₅	—	2	2	no	—
52	C₄×C₅	—	14	1	no	—
53	C₄×C₅	—	14	1	no	—
54	C₄×C₅	—	14	2	no	—
55	C₄×C₅	Dic₁₄	1	2	yes	—
56	C₄⋊C₄	—	7	2	no	—
57	C₄⋊C₄	—	7	2	no	—
58	C₄⋊C₄	—	7	1	no	—
59	C₄⋊C₄	C₅×D₇	1	1	yes	characteristic
60	C₄²	—	7	1	no	—
61	C₂×C₇	C₂×C₅×Q₈	1	1	yes	characteristic
62	C₂×C₇	C₅×#41	1	1	yes	characteristic
63	C₂×C₇	C₅×#41	1	1	yes	characteristic
64	C₂×C₅	C₂×Dic₁₄	1	1	yes	characteristic
65	C₂×C₅	#1159	1	1	yes	characteristic
66	C₂×C₅	#1161	1	1	yes	characteristic
67	C₂×C₄	—	7	1	no	—
68	C₂×C₄	—	7	1	no	—
69	C₂×C₄	—	7	2	no	—
70	C₂×C₄	C₂×C₅×D₇	1	2	yes	—
71	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
72	C₇	C₅×#125	1	1	yes	characteristic, complemented, Sylow
73	C₅	#6453	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	14	1	no	—
77	C₄	—	14	1	no	—
78	C₄	—	14	2	no	—
79	C₄	C₅×Dic₁₄	1	2	yes	—
80	C₂	C₂×C₅×Dic₁₄	1	1	yes	characteristic
81	C₂	C₅×#1159	1	1	yes	characteristic
82	C₂	C₅×#1161	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting	C₅×C₇×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₅×C₇	C₂³
hypercenter	C₅×C₄⋊C₄	D₇
hypocenter	C₇	C₅×#125
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
11. #6453	C₅	direct (N × H)
42. C₅×C₇	#125	semidirect
72. C₇	C₅×#125	semidirect
73. C₅	#6453	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₄⋊C₄	2
C₅×C₄⋊Dic₇	2
C₅×Dic₇⋊C₄	2
C₄×C₅×Dic₇	2
#6453	5
C₅×#125	7

Subgroups — C5×#6453 #11765048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6453 #11765048