Group #11751466 — subgroups

Subgroups — C₃×C₅×#491 #11751466

Order 960.

180 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 100 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	C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#103	C₂	1	4	yes	maximal
4	C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
5	C₅×#491	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×Q₈	C₂²	1	2	yes	—
7	C₂×C₃×C₅×C₈	C₂²	1	2	yes	—
8	C₃×C₅×C₄⋊C₄	—	2	2	no	—
9	C₃×C₅×C₄⋊C₄	—	2	2	no	—
10	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₃×#491	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
14	C₅×#125	C₂×C₃	1	1	yes	characteristic
15	C₅×#103	C₂×C₃	1	4	yes	—
16	C₅×#97	C₂×C₃	1	1	yes	characteristic
17	C₃×C₅×Q₈	—	2	4	no	—
18	C₂×C₃×C₄×C₅	—	2	2	no	—
19	C₂×C₃×C₄×C₅	—	2	2	no	—
20	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
21	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₃×C₅×C₈	—	2	2	no	—
23	C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
24	C₃×#125	C₂×C₅	1	1	yes	characteristic
25	C₃×#103	C₂×C₅	1	4	yes	—
26	C₃×#97	C₂×C₅	1	1	yes	characteristic
27	C₂×C₅×Q₈	C₂²×C₃	1	2	yes	—
28	C₂×C₅×C₈	C₂²×C₃	1	2	yes	—
29	C₅×C₄⋊C₄	—	2	2	no	—
30	C₅×C₄⋊C₄	—	2	2	no	—
31	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
32	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
33	#491	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄×C₅	—	2	2	no	—
36	C₃×C₄×C₅	—	4	2	no	—
37	C₃×C₄×C₅	—	4	2	no	—
38	C₃×C₄×C₅	#41	1	2	yes	—
39	C₂×C₃×Q₈	C₂²×C₅	1	2	yes	—
40	C₂×C₃×C₈	C₂²×C₅	1	2	yes	—
41	C₃×C₄⋊C₄	—	2	2	no	—
42	C₃×C₄⋊C₄	—	2	2	no	—
43	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
44	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
45	C₅×Q₈	—	2	4	no	—
46	C₂×C₄×C₅	—	2	2	no	—
47	C₂×C₄×C₅	—	2	2	no	—
48	C₂×C₄×C₅	C₃×D₄	1	2	yes	—
49	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
50	C₅×C₈	—	2	2	no	—
51	C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
52	#125	C₂×C₃×C₅	1	1	yes	characteristic
53	#103	C₂×C₃×C₅	1	4	yes	—
54	#97	C₂×C₃×C₅	1	1	yes	characteristic
55	C₂×C₃×C₅	#124	1	1	yes	characteristic
56	C₂×C₃×C₅	#137	1	2	yes	—
57	C₃×Q₈	—	2	4	no	—
58	C₂×C₃×C₄	—	2	2	no	—
59	C₂×C₃×C₄	—	2	2	no	—
60	C₂×C₃×C₄	C₅×D₄	1	2	yes	—
61	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
62	C₃×C₈	—	2	2	no	—
63	C₂²×C₅	C₂×C₃×D₄	1	1	yes	characteristic
64	C₄×C₅	—	2	2	no	—
65	C₄×C₅	—	4	2	no	—
66	C₄×C₅	—	4	2	no	—
67	C₄×C₅	C₃×#41	1	2	yes	—
68	C₂×Q₈	C₂²×C₃×C₅	1	2	yes	—
69	C₂×C₈	C₂²×C₃×C₅	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
73	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
74	C₃×C₅	#491	1	1	yes	characteristic, direct product factor, Hall
75	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
76	C₃×C₄	—	2	2	no	—
77	C₃×C₄	—	4	2	no	—
78	C₃×C₄	—	4	2	no	—
79	C₃×C₄	C₅×#41	1	2	yes	—
80	C₂×C₅	C₃×#124	1	1	yes	characteristic
81	C₂×C₅	C₃×#137	1	2	yes	—
82	Q₈	—	2	4	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	C₃×C₅×D₄	1	2	yes	—
86	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
87	C₈	—	2	2	no	—
88	C₂×C₃	C₅×#124	1	1	yes	characteristic
89	C₂×C₃	C₅×#137	1	2	yes	—
90	C₅	C₃×#491	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	C₂×C₃×C₅×D₄	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	4	2	no	—
94	C₄	—	4	2	no	—
95	C₄	C₃×C₅×#41	1	2	yes	—
96	C₃	C₅×#491	1	1	yes	characteristic, direct product factor, Sylow
97	C₂	C₃×C₅×#124	1	1	yes	characteristic
98	C₂	C₃×C₅×#137	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₃×C₅×#125

C₂

yes

maximal, characteristic

C₃×C₅×#103

C₂

yes

maximal

C₃×C₅×#97

C₂

yes

maximal, characteristic

C₅×#491

C₃

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₅×Q₈

C₂²

yes

—

C₂×C₃×C₅×C₈

C₂²

yes

—

C₃×C₅×C₄⋊C₄

—

C₃×C₅×C₄⋊C₄

—

C₃×C₅×C₄⋊C₄

C₂²

yes

—

C₃×C₄²×C₅

C₂²

yes

characteristic

C₃×#491

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₄⋊Q₈

C₂×C₃

yes

characteristic

C₅×#125

C₂×C₃

yes

characteristic

C₅×#103

C₂×C₃

yes

—

C₅×#97

C₂×C₃

yes

characteristic

C₃×C₅×Q₈

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

D₄

yes

—

C₂×C₃×C₄×C₅

C₂³

yes

characteristic

C₃×C₅×C₈

—

C₃×C₄⋊Q₈

C₂×C₅

yes

characteristic

C₃×#125

C₂×C₅

yes

characteristic

C₃×#103

C₂×C₅

yes

—

C₃×#97

C₂×C₅

yes

characteristic

C₂×C₅×Q₈

C₂²×C₃

yes

—

C₂×C₅×C₈

C₂²×C₃

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

C₂²×C₃

yes

—

C₄²×C₅

C₂²×C₃

yes

characteristic

#491

C₃×C₅

yes

characteristic, direct product factor, Sylow

C₂²×C₃×C₅

C₂×D₄

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

#41

yes

—

C₂×C₃×Q₈

C₂²×C₅

yes

—

C₂×C₃×C₈

C₂²×C₅

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

C₂²×C₅

yes

—

C₃×C₄²

C₂²×C₅

yes

characteristic

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₃×D₄

yes

—

C₂×C₄×C₅

C₂³×C₃

yes

characteristic

C₅×C₈

—

C₄⋊Q₈

C₂×C₃×C₅

yes

characteristic

#125

C₂×C₃×C₅

yes

characteristic

#103

C₂×C₃×C₅

yes

—

#97

C₂×C₃×C₅

yes

C₂×C₃×C₅

yes

C₂×C₃×C₅

yes

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₅×D₄

yes

—

C₂×C₃×C₄

C₂³×C₅

yes

characteristic

C₃×C₈

—

C₂²×C₅

C₂×C₃×D₄

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₃×#41

yes

—

C₂×Q₈

C₂²×C₃×C₅

yes

—

C₂×C₈

C₂²×C₃×C₅

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×C₃×C₅

yes

—

C₄²

C₂²×C₃×C₅

yes

characteristic

C₃×C₅

#491

yes

characteristic, direct product factor, Hall

C₂²×C₃

C₂×C₅×D₄

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₅×#41

yes

—

C₂×C₅

C₃×#124

yes

characteristic

C₂×C₅

C₃×#137

yes

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₃×C₅×D₄

yes

—

C₂×C₄

C₂³×C₃×C₅

yes

characteristic

C₈

—

C₂×C₃

C₅×#124

yes

characteristic

C₂×C₃

C₅×#137

yes

—

C₅

C₃×#491

yes

characteristic, direct product factor, Sylow

C₂²

C₂×C₃×C₅×D₄

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₃×C₅×#41

yes

—

C₃

C₅×#491

yes

characteristic, direct product factor, Sylow

C₂

C₃×C₅×#124

yes

characteristic

C₂

C₃×C₅×#137

yes

—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₃×C₅

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂³×C₃×C₅

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

N	H ≅ G/N	type
5. C₅×#491	C₃	direct (N × H)
12. C₃×#491	C₅	direct (N × H)
33. #491	C₃×C₅	direct (N × H)
74. C₃×C₅	#491	direct (N × H)
90. C₅	C₃×#491	direct (N × H)
96. C₃	C₅×#491	direct (N × H)

H ≅ G/N

type

5. C₅×#491

C₃

direct (N × H)

12. C₃×#491

C₅

direct (N × H)

33. #491

C₃×C₅

direct (N × H)

74. C₃×C₅

#491

direct (N × H)

90. C₅

C₃×#491

direct (N × H)

96. C₃

C₅×#491

direct (N × H)

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

subgroup	index
C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#125	2
C₃×C₅×#103	2
C₃×C₅×#97	2
C₅×#491	3
C₃×#491	5

subgroup

index

C₃×C₅×C₄⋊Q₈

C₃×C₅×#125

C₃×C₅×#103

C₃×C₅×#97

C₅×#491

C₃×#491

Subgroups — C₃×C₅×#491 #11751466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×C5×#491 #11751466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#491 #11751466