Group #11746931 — subgroups

Subgroups — #11746931

Order 960.

180 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 64 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	#91759	C₂	1	1	yes	maximal, characteristic
2	C₅×#869	C₂	1	1	yes	maximal, characteristic
3	C₃×#3935	C₂	1	1	yes	maximal, characteristic
4	#90973	C₂	1	4	yes	maximal
5	#65371	—	3	1	no	maximal, Hall
6	C₂×C₅×Dic₆	C₂²	1	2	yes	—
7	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₅	C₂²	1	2	yes	—
9	#6712	—	2	2	no	—
10	C₅×C₄⋊Dic₃	—	2	2	no	—
11	C₂×C₃×#168	C₂²	1	2	yes	—
12	#4703	—	5	1	no	maximal, Hall
13	C₅×C₄⋊Q₈	—	3	1	no	—
14	#4016	—	3	1	no	—
15	#3967	—	3	4	no	—
16	#3935	D₃	1	1	yes	characteristic
17	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
18	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₅	—	2	2	no	—
20	C₂×C₅×Dic₃	—	2	2	no	—
21	C₅×Dic₆	—	2	4	no	—
22	C₃×#168	—	2	2	no	—
23	#870	—	5	1	no	—
24	#869	D₅	1	1	yes	characteristic
25	C₃×#97	—	5	1	no	—
26	#816	—	5	4	no	—
27	C₂×C₅×Q₈	—	3	2	no	—
28	C₅×C₄⋊C₄	—	6	2	no	—
29	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
30	C₄⋊Dic₅	—	3	2	no	—
31	#683	—	6	2	no	—
32	C₂×#168	C₂×D₃	1	2	yes	—
33	#491	—	15	1	no	Sylow
34	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄×C₅	—	2	2	no	—
36	C₃×C₄×C₅	#41	1	2	yes	—
37	Dic₁₅	—	4	2	no	—
38	C₅×Dic₃	—	4	2	no	—
39	C₂×Dic₆	C₂×D₅	1	2	yes	—
40	C₂×C₃×C₈	—	5	2	no	—
41	C₃×C₄²	C₂×D₅	1	1	yes	characteristic
42	C₄⋊Dic₃	—	2	2	no	—
43	C₄⋊Dic₃	—	5	2	no	—
44	Dic₃⋊C₄	—	10	2	no	—
45	C₅×Q₈	—	6	4	no	—
46	C₂×C₄×C₅	—	6	2	no	—
47	C₂×C₄×C₅	D₁₂	1	2	yes	—
48	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
49	C₂×Dic₅	—	6	2	no	—
50	#168	—	2	2	no	—
51	C₄⋊Q₈	—	3	1	no	—
52	#125	—	15	1	no	—
53	#103	—	15	4	no	—
54	#97	—	5	1	no	—
55	C₂×C₃×C₅	#124	1	1	yes	characteristic
56	C₂×C₃×C₅	#137	1	2	yes	—
57	C₂×C₃×C₄	C₂²⋊D₅	1	2	yes	—
58	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
59	C₂×Dic₃	—	2	2	no	—
60	C₂×Dic₃	—	10	2	no	—
61	Dic₆	—	2	4	no	—
62	C₃×C₈	—	10	2	no	—
63	C₂²×C₅	C₂×D₁₂	1	1	yes	characteristic
64	C₄×C₅	—	2	2	no	—
65	C₄×C₅	—	12	2	no	—
66	C₄×C₅	#235	1	2	yes	—
67	Dic₅	—	12	2	no	—
68	C₂×Q₈	—	3	2	no	—
69	C₂×C₈	—	5	2	no	—
70	C₄⋊C₄	—	6	2	no	—
71	C₄⋊C₄	—	15	2	no	—
72	C₄⋊C₄	—	30	2	no	—
73	C₄²	D₃×D₅	1	1	yes	characteristic
74	C₃×C₅	#491	1	1	yes	characteristic, complemented, Hall
75	C₂²×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
76	C₃×C₄	—	2	2	no	—
77	C₃×C₄	#711	1	2	yes	—
78	Dic₃	—	4	2	no	—
79	Dic₃	—	20	2	no	—
80	C₂×C₅	#875	1	1	yes	characteristic
81	C₂×C₅	#909	1	2	yes	—
82	Q₈	—	6	4	no	—
83	C₂×C₄	—	6	2	no	—
84	C₂×C₄	—	30	2	no	—
85	C₂×C₄	#1203	1	2	yes	—
86	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
87	C₈	—	10	2	no	—
88	C₂×C₃	#4082	1	1	yes	characteristic
89	C₂×C₃	#4088	1	2	yes	—
90	C₅	#4703	1	1	yes	characteristic, complemented, Sylow
91	C₂²	C₂×#1203	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	12	2	no	—
94	C₄	—	60	2	no	—
95	C₄	#6772	1	2	yes	—
96	C₃	#65371	1	1	yes	characteristic, complemented, Sylow
97	C₂	#91321	1	2	yes	—
98	C₂	#91373	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#91759

C₂

yes

maximal, characteristic

C₅×#869

C₂

yes

maximal, characteristic

C₃×#3935

C₂

yes

maximal, characteristic

#90973

C₂

yes

maximal

#65371

—

maximal, Hall

C₂×C₅×Dic₆

C₂²

yes

—

C₃×C₄²×C₅

C₂²

yes

characteristic

C₄⋊Dic₁₅

C₂²

yes

—

#6712

—

C₅×C₄⋊Dic₃

—

C₂×C₃×#168

C₂²

yes

—

#4703

—

maximal, Hall

C₅×C₄⋊Q₈

—

#4016

—

#3967

—

#3935

D₃

yes

characteristic

C₂×C₃×C₄×C₅

D₄

yes

—

C₂×C₃×C₄×C₅

C₂³

yes

characteristic

C₂×Dic₁₅

—

C₂×C₅×Dic₃

—

C₅×Dic₆

—

C₃×#168

—

#870

—

#869

D₅

yes

characteristic

C₃×#97

—

#816

—

C₂×C₅×Q₈

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×D₃

yes

characteristic

C₄⋊Dic₅

—

#683

—

C₂×#168

C₂×D₃

yes

—

#491

—

Sylow

C₂²×C₃×C₅

C₂×D₄

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

#41

yes

—

Dic₁₅

—

C₅×Dic₃

—

C₂×Dic₆

C₂×D₅

yes

—

C₂×C₃×C₈

—

C₃×C₄²

C₂×D₅

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

D₁₂

yes

—

C₂×C₄×C₅

C₂²×D₃

yes

characteristic

C₂×Dic₅

—

#168

—

C₄⋊Q₈

—

#125

—

#103

—

#97

—

C₂×C₃×C₅

#124

yes

characteristic

C₂×C₃×C₅

#137

yes

—

C₂×C₃×C₄

C₂²⋊D₅

yes

—

C₂×C₃×C₄

C₂²×D₅

yes

characteristic

C₂×Dic₃

—

C₂×Dic₃

—

Dic₆

—

C₃×C₈

—

C₂²×C₅

C₂×D₁₂

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#235

yes

—

Dic₅

—

C₂×Q₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₃×D₅

yes

characteristic

C₃×C₅

#491

yes

characteristic, complemented, Hall

C₂²×C₃

C₂×C₂²⋊D₅

yes

characteristic

C₃×C₄

—

C₃×C₄

#711

yes

—

Dic₃

—

Dic₃

—

C₂×C₅

#875

yes

characteristic

C₂×C₅

#909

yes

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#1203

yes

—

C₂×C₄

C₂×D₃×D₅

yes

characteristic

C₈

—

C₂×C₃

#4082

yes

characteristic

C₂×C₃

#4088

yes

—

C₅

#4703

yes

characteristic, complemented, Sylow

C₂²

C₂×#1203

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#6772

yes

—

C₃

#65371

yes

characteristic, complemented, Sylow

C₂

#91321

yes

—

C₂

#91373

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#1203
commutator, cosocle	C₂×C₃×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂×D₃×D₅
Fitting	C₃×C₄²×C₅	C₂²
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₄²	D₃×D₅
hypocenter	C₃×C₅	#491
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄²

subgroup

G/H

center

C₂²

C₂×#1203

commutator, cosocle

C₂×C₃×C₄×C₅

C₂³

Frattini

C₂×C₄

C₂×D₃×D₅

Fitting

C₃×C₄²×C₅

C₂²

socle, prime radical

C₂²×C₃×C₅

C₂×D₄

hypercenter

C₄²

D₃×D₅

hypocenter

C₃×C₅

#491

LCS

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₄²

N	H ≅ G/N	type
74. C₃×C₅	#491	semidirect
90. C₅	#4703	semidirect
96. C₃	#65371	semidirect

H ≅ G/N

type

74. C₃×C₅

#491

semidirect

90. C₅

#4703

semidirect

96. C₃

#65371

semidirect

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

subgroup	index
#91759	2
C₅×#869	2
C₃×#3935	2
#90973	2
#65371	3
#4703	5

subgroup

index

Subgroups — #11746931

Conjugacy classes of subgroups

Complements

Maximal subgroups