Group #11746925 — subgroups

Subgroups — #11746925

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	C₅×#870	C₂	1	1	yes	maximal, characteristic
2	C₃×#4015	C₂	1	1	yes	maximal, characteristic
3	#91087	C₂	1	1	yes	maximal, characteristic
4	#90970	C₂	1	4	yes	maximal
5	#65358	—	3	1	no	maximal, Hall
6	C₂×C₃×Dic₁₀	C₂²	1	2	yes	—
7	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊#168	C₂²	1	2	yes	—
9	C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
10	C₅×Dic₃⋊C₄	—	2	2	no	—
11	C₃×C₄⋊Dic₅	—	2	2	no	—
12	#5082	—	5	1	no	maximal, Hall
13	C₅×#125	—	3	1	no	—
14	#4015	D₃	1	1	yes	characteristic
15	#3942	—	3	4	no	—
16	#3935	—	3	1	no	—
17	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
18	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×C₅×Dic₃	—	2	2	no	—
20	C₂×C₃×Dic₅	—	2	2	no	—
21	C₃×Dic₁₀	—	2	4	no	—
22	C₃⋊#168	—	2	2	no	—
23	C₃×C₄⋊Q₈	—	5	1	no	—
24	#870	D₅	1	1	yes	characteristic
25	#835	—	5	4	no	—
26	#803	—	5	1	no	—
27	C₂×Dic₁₀	C₂×D₃	1	2	yes	—
28	C₅×C₄⋊C₄	—	3	2	no	—
29	C₅×C₄⋊C₄	—	6	2	no	—
30	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
31	C₄⋊Dic₅	—	2	2	no	—
32	C₂×#168	—	3	2	no	—
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	C₃×Dic₅	—	4	2	no	—
38	C₅×Dic₃	—	4	2	no	—
39	C₂×C₃×Q₈	—	5	2	no	—
40	C₃×C₄⋊C₄	—	10	2	no	—
41	C₃×C₄²	C₂×D₅	1	1	yes	characteristic
42	C₄⋊Dic₃	C₂×D₅	1	2	yes	—
43	Dic₃⋊C₄	—	2	2	no	—
44	C₂×C₃⋊C₈	—	5	2	no	—
45	C₂×C₄×C₅	—	6	2	no	—
46	C₂×C₄×C₅	#67	1	2	yes	—
47	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
48	C₂×Dic₅	—	2	2	no	—
49	Dic₁₀	—	2	4	no	—
50	#168	—	6	2	no	—
51	C₄⋊Q₈	—	5	1	no	—
52	#125	—	3	1	no	—
53	#103	—	15	4	no	—
54	#97	—	15	1	no	—
55	C₂×C₃×C₅	#124	1	1	yes	characteristic
56	C₂×C₃×C₅	#137	1	2	yes	—
57	C₃×Q₈	—	10	4	no	—
58	C₂×C₃×C₄	—	10	2	no	—
59	C₂×C₃×C₄	C₂²⋊D₅	1	2	yes	—
60	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
61	C₂×Dic₃	—	2	2	no	—
62	C₃⋊C₈	—	10	2	no	—
63	C₂²×C₅	C₂×#67	1	1	yes	characteristic
64	C₄×C₅	—	2	2	no	—
65	C₄×C₅	—	12	2	no	—
66	C₄×C₅	#237	1	2	yes	—
67	Dic₅	—	4	2	no	—
68	C₂×Q₈	—	5	2	no	—
69	C₂×C₈	—	15	2	no	—
70	C₄⋊C₄	—	3	2	no	—
71	C₄⋊C₄	—	6	2	no	—
72	C₄⋊C₄	—	10	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	—	20	2	no	—
78	C₃×C₄	#713	1	2	yes	—
79	Dic₃	—	4	2	no	—
80	C₂×C₅	#936	1	1	yes	characteristic
81	C₂×C₅	#942	1	2	yes	—
82	Q₈	—	10	4	no	—
83	C₂×C₄	—	6	2	no	—
84	C₂×C₄	—	10	2	no	—
85	C₂×C₄	#1201	1	2	yes	—
86	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
87	C₈	—	30	2	no	—
88	C₂×C₃	#4093	1	1	yes	characteristic
89	C₂×C₃	#4097	1	2	yes	—
90	C₅	#5082	1	1	yes	characteristic, complemented, Sylow
91	C₂²	C₂×#1201	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	12	2	no	—
94	C₄	—	20	2	no	—
95	C₄	#6766	1	2	yes	—
96	C₃	#65358	1	1	yes	characteristic, complemented, Sylow
97	C₂	#91309	1	2	yes	—
98	C₂	#91368	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#870

C₂

yes

maximal, characteristic

C₃×#4015

C₂

yes

maximal, characteristic

#91087

C₂

yes

maximal, characteristic

#90970

C₂

yes

maximal

#65358

—

maximal, Hall

C₂×C₃×Dic₁₀

C₂²

yes

—

C₃×C₄²×C₅

C₂²

yes

characteristic

C₂×C₃⋊#168

C₂²

yes

—

C₅×C₄⋊Dic₃

C₂²

yes

—

C₅×Dic₃⋊C₄

—

C₃×C₄⋊Dic₅

—

—

—

D₃

yes

characteristic

#3942

—

#3935

—

C₂×C₃×C₄×C₅

D₄

yes

—

C₂×C₃×C₄×C₅

C₂³

yes

characteristic

C₂×C₅×Dic₃

—

C₂×C₃×Dic₅

—

C₃×Dic₁₀

—

C₃⋊#168

—

C₃×C₄⋊Q₈

—

#870

D₅

yes

characteristic

#835

—

#803

—

C₂×Dic₁₀

C₂×D₃

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×D₃

yes

characteristic

C₄⋊Dic₅

—

C₂×#168

—

#491

—

Sylow

C₂²×C₃×C₅

C₂×D₄

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

#41

yes

—

C₃×Dic₅

—

C₅×Dic₃

—

C₂×C₃×Q₈

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂×D₅

yes

characteristic

C₄⋊Dic₃

C₂×D₅

yes

—

Dic₃⋊C₄

—

C₂×C₃⋊C₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#67

yes

—

C₂×C₄×C₅

C₂²×D₃

yes

characteristic

C₂×Dic₅

—

Dic₁₀

—

#168

—

C₄⋊Q₈

—

#125

—

#103

—

#97

—

C₂×C₃×C₅

#124

yes

characteristic

C₂×C₃×C₅

#137

yes

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²⋊D₅

yes

—

C₂×C₃×C₄

C₂²×D₅

yes

characteristic

C₂×Dic₃

—

C₃⋊C₈

—

C₂²×C₅

C₂×#67

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#237

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

—

C₃×C₄

#713

yes

—

Dic₃

—

C₂×C₅

#936

yes

characteristic

C₂×C₅

#942

yes

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#1201

yes

—

C₂×C₄

C₂×D₃×D₅

yes

characteristic

C₈

—

C₂×C₃

#4093

yes

characteristic

C₂×C₃

#4097

yes

—

C₅

#5082

yes

characteristic, complemented, Sylow

C₂²

C₂×#1201

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#6766

yes

—

C₃

#65358

yes

characteristic, complemented, Sylow

C₂

#91309

yes

—

C₂

#91368

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#1201
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×#1201

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	#5082	semidirect
96. C₃	#65358	semidirect

H ≅ G/N

type

74. C₃×C₅

#491

semidirect

90. C₅

#5082

semidirect

96. C₃

#65358

semidirect

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

subgroup	index
C₅×#870	2
C₃×#4015	2
#91087	2
#90970	2
#65358	3
#5082	5

subgroup

index

Subgroups — #11746925

Conjugacy classes of subgroups

Complements

Maximal subgroups