Group #11931508 — subgroups

Subgroups — C₅×#8788 #11931508

Order 1280.

322 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 158 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×#1831	C₂	1	2	yes	maximal
2	C₅×#1744	C₂	1	1	yes	maximal, characteristic
3	C₅×#1277	C₂	1	4	yes	maximal
4	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
5	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
6	C₄³×C₅	C₂²	1	1	yes	characteristic
7	C₅×#336	—	2	4	no	—
8	C₅×#336	C₄	1	4	yes	—
9	#8788	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅×C₈	—	2	4	no	—
11	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₅	D₄	1	2	yes	—
14	C₂×C₄²×C₅	Q₈	1	2	yes	—
15	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
16	C₅×C₄⋊C₈	—	2	8	no	—
17	C₄×C₅×C₈	—	2	4	no	—
18	#1831	C₂×C₅	1	2	yes	—
19	#1744	C₂×C₅	1	1	yes	characteristic
20	#1277	C₂×C₅	1	4	yes	—
21	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
22	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
24	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₅×C₈	—	2	4	no	—
26	C₂×C₅×C₈	—	2	8	no	—
27	C₂×C₅×C₈	—	4	4	no	—
28	C₂×C₅×C₈	—	4	8	no	—
29	C₄²×C₅	—	2	4	no	—
30	C₄²×C₅	—	2	4	no	—
31	C₄²×C₅	—	4	2	no	—
32	C₄²×C₅	#41	1	4	yes	—
33	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
34	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
35	C₄³	C₂²×C₅	1	1	yes	characteristic
36	#336	—	2	4	no	—
37	#336	C₄×C₅	1	4	yes	—
38	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₅	—	2	2	no	—
40	C₂×C₄×C₅	—	2	4	no	—
41	C₂×C₄×C₅	—	2	4	no	—
42	C₂×C₄×C₅	—	2	4	no	—
43	C₂×C₄×C₅	#117	1	2	yes	—
44	C₂×C₄×C₅	#124	1	2	yes	—
45	C₂×C₄×C₅	#125	1	2	yes	—
46	C₂×C₄×C₅	#131	1	4	yes	—
47	C₂×C₄×C₅	#135	1	4	yes	—
48	C₅×C₈	—	4	4	no	—
49	C₅×C₈	—	8	4	no	—
50	C₂²×C₈	—	2	4	no	—
51	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
52	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
53	C₂×C₄²	C₅×D₄	1	2	yes	—
54	C₂×C₄²	C₅×Q₈	1	2	yes	—
55	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
56	C₄⋊C₈	—	2	8	no	—
57	C₄×C₈	—	2	4	no	—
58	C₂²×C₅	#382	1	1	yes	characteristic
59	C₂²×C₅	#424	1	2	yes	—
60	C₂²×C₅	#427	1	2	yes	—
61	C₂²×C₅	#430	1	2	yes	—
62	C₄×C₅	—	2	2	no	—
63	C₄×C₅	—	4	4	no	—
64	C₄×C₅	#433	1	4	yes	—
65	C₄×C₅	#488	1	4	yes	—
66	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
67	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
68	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
69	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
70	C₂×C₈	—	2	4	no	—
71	C₂×C₈	—	2	8	no	—
72	C₂×C₈	—	4	4	no	—
73	C₂×C₈	—	4	8	no	—
74	C₄²	—	2	4	no	—
75	C₄²	—	2	4	no	—
76	C₄²	—	4	2	no	—
77	C₄²	C₅×#41	1	4	yes	—
78	C₂×C₅	#1572	1	4	yes	—
79	C₂×C₅	#1832	1	1	yes	characteristic
80	C₂×C₅	#1835	1	1	yes	characteristic
81	C₂×C₅	#1838	1	1	yes	characteristic
82	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	C₅×#117	1	2	yes	—
88	C₂×C₄	C₅×#124	1	2	yes	—
89	C₂×C₄	C₅×#125	1	2	yes	—
90	C₂×C₄	C₅×#131	1	4	yes	—
91	C₂×C₄	C₅×#135	1	4	yes	—
92	C₈	—	4	4	no	—
93	C₈	—	8	4	no	—
94	C₅	#8788	1	1	yes	characteristic, direct product factor, Sylow
95	C₂²	C₅×#382	1	1	yes	characteristic
96	C₂²	C₅×#424	1	2	yes	—
97	C₂²	C₅×#427	1	2	yes	—
98	C₂²	C₅×#430	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	4	4	no	—
101	C₄	C₅×#433	1	4	yes	—
102	C₄	C₅×#488	1	4	yes	—
103	C₂	C₅×#1572	1	4	yes	—
104	C₂	C₅×#1832	1	1	yes	characteristic
105	C₂	C₅×#1835	1	1	yes	characteristic
106	C₂	C₅×#1838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1831

C₂

yes

maximal

C₅×#1744

C₂

yes

maximal, characteristic

C₅×#1277

C₂

yes

maximal

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

—

C₄³×C₅

C₂²

yes

characteristic

C₅×#336

—

C₅×#336

C₄

yes

—

#8788

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

—

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

D₄

yes

—

C₂×C₄²×C₅

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₄×C₅×C₈

—

#1831

C₂×C₅

yes

—

#1744

C₂×C₅

yes

characteristic

#1277

C₂×C₅

yes

—

C₂²×C₄×C₅

C₄⋊C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

#41

yes

—

C₂×C₄⋊C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

C₄³

C₂²×C₅

yes

characteristic

#336

—

#336

C₄×C₅

yes

—

C₂³×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#124

yes

—

C₂×C₄×C₅

#125

yes

—

C₂×C₄×C₅

#131

yes

—

C₂×C₄×C₅

#135

yes

—

C₅×C₈

—

C₅×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₅×D₄

yes

—

C₂×C₄²

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₂²×C₅

#382

yes

characteristic

C₂²×C₅

#424

yes

—

C₂²×C₅

#427

yes

—

C₂²×C₅

#430

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#433

yes

—

C₄×C₅

#488

yes

—

C₂²×C₄

C₅×C₄⋊C₄

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

C₂²×C₄

C₂×C₅×Q₈

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₅×#41

yes

—

C₂×C₅

#1572

yes

—

C₂×C₅

yes

C₂×C₅

yes

C₂×C₅

yes

C₂³

C₂×C₅×C₄⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₅×#117

yes

—

C₂×C₄

C₅×#124

yes

—

C₂×C₄

C₅×#125

yes

—

C₂×C₄

C₅×#131

yes

—

C₂×C₄

C₅×#135

yes

—

C₈

—

C₈

—

C₅

#8788

yes

characteristic, direct product factor, Sylow

C₂²

C₅×#382

yes

characteristic

C₂²

C₅×#424

yes

—

C₂²

C₅×#427

yes

—

C₂²

C₅×#430

yes

—

C₄

—

100

C₄

—

101

C₄

C₅×#433

yes

—

102

C₄

C₅×#488

yes

—

103

C₂

C₅×#1572

yes

—

104

C₂

C₅×#1832

yes

characteristic

105

C₂

C₅×#1835

yes

characteristic

106

C₂

C₅×#1838

yes

characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

subgroup

G/H

center

C₂²×C₄×C₅

C₂×D₄

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

socle, prime radical

C₂³×C₅

C₂×C₄⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

N	H ≅ G/N	type
9. #8788	C₅	direct (N × H)
94. C₅	#8788	direct (N × H)

H ≅ G/N

type

9. #8788

C₅

direct (N × H)

94. C₅

#8788

direct (N × H)

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

subgroup	index
C₅×#1831	2
C₅×#1744	2
C₅×#1277	2
#8788	5

subgroup

index

Subgroups — C₅×#8788 #11931508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8788 #11931508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8788 #11931508