Group #11750814 — subgroups

Subgroups — #11750814

Order 960.

220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#91763	C₂	1	1	yes	maximal, characteristic
2	#91759	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	#91105	C₂	1	4	yes	maximal, complemented
5	#65002	—	3	1	no	maximal, Hall
6	C₂×D₆₀	—	2	2	no	—
7	C₂×D₆₀	C₂²	1	2	yes	—
8	C₂×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₅	C₂²	1	2	yes	—
11	#6712	—	2	2	no	—
12	#4713	—	5	1	no	maximal, Hall
13	#4020	—	3	1	no	—
14	#4016	—	3	1	no	—
15	C₅×#97	D₃	1	1	yes	characteristic, complemented
16	#3953	—	3	4	no	—
17	C₂²×D₁₅	—	2	2	no	—
18	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
19	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₅	—	2	2	no	—
21	D₆₀	—	2	4	no	—
22	D₆₀	—	4	4	no	—
23	C₃×C₅×C₈	—	2	2	no	—
24	#874	—	5	1	no	—
25	#870	—	5	1	no	—
26	C₃×#97	D₅	1	1	yes	characteristic, complemented
27	#821	—	5	4	no	—
28	C₂×D₂₀	—	3	2	no	—
29	C₂×D₂₀	—	6	2	no	—
30	C₂×C₅×C₈	C₂×D₃	1	2	yes	—
31	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
32	C₄⋊Dic₅	—	3	2	no	—
33	#683	—	6	2	no	—
34	#490	—	15	1	no	Sylow
35	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×D₁₅	—	4	2	no	—
37	C₂×D₁₅	—	4	4	no	—
38	C₃×C₄×C₅	—	2	2	no	—
39	C₃×C₄×C₅	#41	1	2	yes	—
40	Dic₁₅	—	4	2	no	—
41	C₂×D₁₂	—	5	2	no	—
42	C₂×D₁₂	—	10	2	no	—
43	C₂×C₃×C₈	C₂×D₅	1	2	yes	—
44	C₃×C₄²	C₂×D₅	1	1	yes	characteristic
45	C₄⋊Dic₃	—	5	2	no	—
46	Dic₃⋊C₄	—	10	2	no	—
47	C₂²×D₅	—	6	2	no	—
48	C₂×C₄×C₅	D₁₂	1	2	yes	—
49	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
50	C₂×Dic₅	—	6	2	no	—
51	D₂₀	—	6	4	no	—
52	D₂₀	—	12	4	no	—
53	C₅×C₈	—	2	2	no	—
54	#127	—	15	1	no	—
55	#125	—	15	1	no	—
56	#102	—	15	4	no	—
57	#97	D₁₅	1	1	yes	characteristic, complemented
58	C₂×C₃×C₅	#124	1	1	yes	characteristic
59	C₂×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
60	D₁₅	—	8	2	no	—
61	C₂²×D₃	—	10	2	no	—
62	C₂×C₃×C₄	D₂₀	1	2	yes	—
63	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
64	C₂×Dic₃	—	10	2	no	—
65	D₁₂	—	10	4	no	—
66	D₁₂	—	20	4	no	—
67	C₃×C₈	—	2	2	no	—
68	C₂²×C₅	C₂×D₁₂	1	1	yes	characteristic
69	C₂×D₅	—	12	2	no	—
70	C₂×D₅	—	12	4	no	—
71	C₄×C₅	—	2	2	no	—
72	C₄×C₅	#235	1	2	yes	—
73	Dic₅	—	12	2	no	—
74	C₂×D₄	—	15	2	no	—
75	C₂×D₄	—	30	2	no	—
76	C₂×C₈	C₂×D₁₅	1	2	yes	—
77	C₄⋊C₄	—	15	2	no	—
78	C₄⋊C₄	—	30	2	no	—
79	C₄²	C₂×D₁₅	1	1	yes	characteristic
80	C₃×C₅	#490	1	1	yes	characteristic, complemented, Hall
81	C₂²×C₃	C₂×D₂₀	1	1	yes	characteristic
82	C₂×D₃	—	20	2	no	—
83	C₂×D₃	—	20	4	no	—
84	C₃×C₄	—	2	2	no	—
85	C₃×C₄	#709	1	2	yes	—
86	Dic₃	—	20	2	no	—
87	C₂×C₅	#875	1	1	yes	characteristic
88	C₂×C₅	#908	1	2	yes	—
89	D₅	—	24	2	no	—
90	C₂³	—	30	2	no	—
91	D₄	—	30	4	no	—
92	D₄	—	60	4	no	—
93	C₂×C₄	—	30	2	no	—
94	C₂×C₄	D₆₀	1	2	yes	—
95	C₂×C₄	C₂²×D₁₅	1	1	yes	characteristic
96	C₈	—	2	2	no	—
97	C₂×C₃	#4021	1	1	yes	characteristic
98	C₂×C₃	#4054	1	2	yes	—
99	D₃	—	40	2	no	—
100	C₅	#4713	1	1	yes	characteristic, complemented, Sylow
101	C₂²	—	60	2	no	—
102	C₂²	—	60	4	no	—
103	C₂²	C₂×D₆₀	1	1	yes	characteristic
104	C₄	—	2	2	no	—
105	C₄	—	60	2	no	—
106	C₄	#6817	1	2	yes	—
107	C₃	#65002	1	1	yes	characteristic, complemented, Sylow
108	C₂	—	120	2	no	—
109	C₂	#91764	1	1	yes	characteristic
110	C₂	#91797	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#91763

C₂

yes

maximal, characteristic

#91759

C₂

yes

maximal, characteristic, complemented

C₃×C₅×#97

C₂

yes

maximal, characteristic, complemented

#91105

C₂

yes

maximal, complemented

#65002

—

maximal, Hall

C₂×D₆₀

—

C₂×D₆₀

C₂²

yes

—

C₂×C₃×C₅×C₈

C₂²

yes

—

C₃×C₄²×C₅

C₂²

yes

characteristic

C₄⋊Dic₁₅

C₂²

yes

—

—

—

—

—

C₅×#97

D₃

yes

characteristic, complemented

#3953

—

C₂²×D₁₅

—

C₂×C₃×C₄×C₅

D₄

yes

—

C₂×C₃×C₄×C₅

C₂³

yes

characteristic

C₂×Dic₁₅

—

D₆₀

—

D₆₀

—

C₃×C₅×C₈

—

#874

—

#870

—

C₃×#97

D₅

yes

characteristic, complemented

#821

—

C₂×D₂₀

—

C₂×D₂₀

—

C₂×C₅×C₈

C₂×D₃

yes

—

C₄²×C₅

C₂×D₃

yes

characteristic

C₄⋊Dic₅

—

#683

—

#490

—

Sylow

C₂²×C₃×C₅

C₂×D₄

yes

characteristic

C₂×D₁₅

—

C₂×D₁₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

#41

yes

—

Dic₁₅

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×C₃×C₈

C₂×D₅

yes

—

C₃×C₄²

C₂×D₅

yes

characteristic

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₂²×D₅

—

C₂×C₄×C₅

D₁₂

yes

—

C₂×C₄×C₅

C₂²×D₃

yes

characteristic

C₂×Dic₅

—

D₂₀

—

D₂₀

—

C₅×C₈

—

—

—

—

D₁₅

yes

characteristic, complemented

C₂×C₃×C₅

#124

yes

characteristic

C₂×C₃×C₅

AGL(1,ℤ/8)

yes

—

D₁₅

—

C₂²×D₃

—

C₂×C₃×C₄

D₂₀

yes

—

C₂×C₃×C₄

C₂²×D₅

yes

characteristic

C₂×Dic₃

—

D₁₂

—

D₁₂

—

C₃×C₈

—

C₂²×C₅

C₂×D₁₂

yes

characteristic

C₂×D₅

—

C₂×D₅

—

C₄×C₅

—

C₄×C₅

#235

yes

—

Dic₅

—

C₂×D₄

—

C₂×D₄

—

C₂×C₈

C₂×D₁₅

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×D₁₅

yes

characteristic

C₃×C₅

#490

yes

characteristic, complemented, Hall

C₂²×C₃

C₂×D₂₀

yes

characteristic

C₂×D₃

—

C₂×D₃

—

C₃×C₄

—

C₃×C₄

#709

yes

—

Dic₃

—

C₂×C₅

#875

yes

characteristic

C₂×C₅

#908

yes

—

D₅

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

D₆₀

yes

—

C₂×C₄

C₂²×D₁₅

yes

characteristic

C₈

—

C₂×C₃

#4021

yes

characteristic

C₂×C₃

#4054

yes

—

D₃

—

100

C₅

#4713

yes

characteristic, complemented, Sylow

101

C₂²

—

102

C₂²

—

103

C₂²

C₂×D₆₀

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

#6817

yes

—

107

C₃

#65002

yes

characteristic, complemented, Sylow

108

C₂

—

120

—

109

C₂

#91764

yes

characteristic

110

C₂

#91797

yes

—

	subgroup	G/H
center	C₂²	C₂×D₆₀
commutator, cosocle	C₂×C₃×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#97	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	#91763	C₂
hypercenter	#97	D₁₅
hypocenter	C₃×C₅	#490
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×D₆₀

commutator, cosocle

C₂×C₃×C₄×C₅

C₂³

Frattini

C₂×C₄

C₂²×D₁₅

Fitting

C₃×C₅×#97

C₂

socle

C₂²×C₃×C₅

C₂×D₄

C₂

D₁₅

C₃×C₅

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
2. #91759	C₂	semidirect
3. C₃×C₅×#97	C₂	semidirect
4. #91105	C₂	semidirect
15. C₅×#97	D₃	semidirect
26. C₃×#97	D₅	semidirect
57. #97	D₁₅	semidirect
80. C₃×C₅	#490	semidirect
100. C₅	#4713	semidirect
107. C₃	#65002	semidirect

H ≅ G/N

type

2. #91759

C₂

semidirect

3. C₃×C₅×#97

C₂

semidirect

4. #91105

C₂

semidirect

15. C₅×#97

D₃

semidirect

26. C₃×#97

D₅

semidirect

57. #97

D₁₅

semidirect

80. C₃×C₅

#490

semidirect

100. C₅

#4713

semidirect

107. C₃

#65002

semidirect

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

subgroup	index
#91763	2
#91759	2
C₃×C₅×#97	2
#91105	2
#65002	3
#4713	5

subgroup

index

C₃×C₅×#97

Subgroups — #11750814

Conjugacy classes of subgroups

Complements

Maximal subgroups