Group #11931543 — subgroups

Subgroups — C₅×#8823 #11931543

Order 1280.

354 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 214 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×#1848	C₂	1	2	yes	maximal
2	C₅×#1567	C₂	1	4	yes	maximal
3	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#108	—	2	4	no	—
5	C₅×#423	C₂²	1	4	yes	—
6	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
8	C₅×#335	—	2	8	no	—
9	C₅×C₈²	C₄	1	1	yes	characteristic
10	C₅×C₈²	C₄	1	2	yes	—
11	C₅×C₈²	C₄	1	1	yes	characteristic
12	#8823	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₅×M₁₆	—	2	4	no	—
14	C₂²×C₅×C₈	D₄	1	2	yes	—
15	C₂²×C₅×C₈	Q₈	1	4	yes	—
16	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
17	C₅×#108	—	4	8	no	—
18	C₅×C₄⋊C₈	—	2	8	no	—
19	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
20	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
23	C₄×C₅×C₈	D₄	1	4	yes	—
24	C₄×C₅×C₈	Q₈	1	2	yes	—
25	#1848	C₂×C₅	1	2	yes	—
26	#1567	C₂×C₅	1	4	yes	—
27	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
28	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
30	C₅×M₁₆	—	4	8	no	—
31	C₂×C₅×C₈	—	2	8	no	—
32	C₂×C₅×C₈	—	4	4	no	—
33	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
34	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
35	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
36	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
37	C₂×C₅×C₈	D₈	1	4	yes	—
38	C₂×C₅×C₈	Q₁₆	1	4	yes	—
39	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₅	C₂×D₄	1	2	yes	—
41	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
42	C₂×#108	—	2	4	no	—
43	#423	C₂²×C₅	1	4	yes	—
44	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
45	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
46	#335	—	2	8	no	—
47	C₈²	C₄×C₅	1	1	yes	characteristic
48	C₈²	C₄×C₅	1	2	yes	—
49	C₈²	C₄×C₅	1	1	yes	characteristic
50	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₄×C₅	—	2	4	no	—
52	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
54	C₂×C₄×C₅	#127	1	1	yes	characteristic
55	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
56	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
57	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
58	C₅×C₈	—	2	4	no	—
59	C₅×C₈	—	8	4	no	—
60	C₅×C₈	#107	1	4	yes	—
61	C₅×C₈	#107	1	4	yes	—
62	C₅×C₈	#108	1	8	yes	complemented
63	C₂×M₁₆	—	2	4	no	—
64	C₂²×C₈	C₅×D₄	1	2	yes	—
65	C₂²×C₈	C₅×Q₈	1	4	yes	—
66	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
67	#108	—	4	8	no	—
68	C₄⋊C₈	—	2	8	no	—
69	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
70	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
71	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
72	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
73	C₄×C₈	C₅×D₄	1	4	yes	—
74	C₄×C₈	C₅×Q₈	1	2	yes	—
75	C₂²×C₅	—	2	2	no	—
76	C₂²×C₅	#384	1	1	yes	characteristic
77	C₂²×C₅	#500	1	2	yes	—
78	C₄×C₅	—	2	2	no	—
79	C₄×C₅	C₂×#107	1	2	yes	—
80	C₄×C₅	C₂×#108	1	4	yes	—
81	C₄×C₅	#493	1	1	yes	characteristic
82	C₄×C₅	#494	1	1	yes	characteristic
83	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
84	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
85	M₁₆	—	4	8	no	—
86	C₂×C₈	—	2	8	no	—
87	C₂×C₈	—	4	4	no	—
88	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
89	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
90	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
91	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
92	C₂×C₈	C₅×D₈	1	4	yes	—
93	C₂×C₈	C₅×Q₁₆	1	4	yes	—
94	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
95	C₄²	C₂×C₅×D₄	1	2	yes	—
96	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
97	C₂×C₅	—	2	2	no	—
98	C₂×C₅	#1845	1	1	yes	characteristic
99	C₂×C₅	#1848	1	2	yes	—
100	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
104	C₂×C₄	C₅×#127	1	1	yes	characteristic
105	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
106	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
107	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
108	C₈	—	2	4	no	—
109	C₈	—	8	4	no	—
110	C₈	C₅×#107	1	4	yes	—
111	C₈	C₅×#107	1	4	yes	—
112	C₈	C₅×#108	1	8	yes	complemented
113	C₅	#8823	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	—	2	2	no	—
115	C₂²	C₅×#384	1	1	yes	characteristic
116	C₂²	C₅×#500	1	2	yes	—
117	C₄	—	2	2	no	—
118	C₄	C₂×C₅×#107	1	2	yes	—
119	C₄	C₂×C₅×#108	1	4	yes	—
120	C₄	C₅×#493	1	1	yes	characteristic
121	C₄	C₅×#494	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	C₅×#1845	1	1	yes	characteristic
124	C₂	C₅×#1848	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1848

C₂

yes

maximal

C₅×#1567

C₂

yes

maximal

C₂×C₅×C₈²

C₂

yes

maximal, characteristic

C₂×C₅×#108

—

C₅×#423

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

—

C₅×#335

—

C₅×C₈²

C₄

yes

characteristic

C₅×C₈²

C₄

yes

—

C₅×C₈²

C₄

yes

characteristic

#8823

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

D₄

yes

—

C₂²×C₅×C₈

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#108

—

C₅×C₄⋊C₈

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

C₂×C₄

yes

characteristic

C₄×C₅×C₈

C₂×C₄

yes

characteristic

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

#1848

C₂×C₅

yes

—

#1567

C₂×C₅

yes

—

C₂×C₈²

C₂×C₅

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×Q₈

yes

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

D₈

yes

—

C₂×C₅×C₈

Q₁₆

yes

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₂×#108

—

#423

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#335

—

C₈²

C₄×C₅

yes

characteristic

C₈²

C₄×C₅

yes

—

C₈²

C₄×C₅

yes

characteristic

C₂³×C₅

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

#127

yes

characteristic

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₂×D₈

yes

—

C₂×C₄×C₅

C₂×Q₁₆

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#107

yes

—

C₅×C₈

#107

yes

—

C₅×C₈

#108

yes

complemented

C₂×M₁₆

—

C₂²×C₈

C₅×D₄

yes

—

C₂²×C₈

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₂×C₄×C₅

yes

characteristic

C₄×C₈

C₂×C₄×C₅

yes

characteristic

C₄×C₈

C₂×C₄×C₅

yes

—

C₄×C₈

C₅×D₄

yes

—

C₄×C₈

C₅×Q₈

yes

—

C₂²×C₅

—

C₂²×C₅

#384

yes

characteristic

C₂²×C₅

#500

yes

—

C₄×C₅

—

C₄×C₅

C₂×#107

yes

—

C₄×C₅

C₂×#108

yes

—

C₄×C₅

yes

C₄×C₅

yes

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

C₂²×C₄

C₂×C₅×Q₈

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×D₈

yes

—

C₂×C₈

C₅×Q₁₆

yes

—

C₄²

C₂²×C₄×C₅

yes

characteristic

C₄²

C₂×C₅×D₄

yes

—

C₄²

C₂×C₅×Q₈

yes

characteristic

C₂×C₅

—

C₂×C₅

#1845

yes

characteristic

C₂×C₅

#1848

yes

—

100

C₂³

C₅×C₄⋊Q₈

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

103

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

104

C₂×C₄

C₅×#127

yes

characteristic

105

C₂×C₄

C₅×C₄⋊Q₈

yes

—

106

C₂×C₄

C₂×C₅×D₈

yes

—

107

C₂×C₄

C₂×C₅×Q₁₆

yes

—

108

C₈

—

109

C₈

—

110

C₈

C₅×#107

yes

—

111

C₈

C₅×#107

yes

—

112

C₈

C₅×#108

yes

complemented

113

C₅

#8823

yes

characteristic, direct product factor, Sylow

114

C₂²

—

115

C₂²

C₅×#384

yes

characteristic

116

C₂²

C₅×#500

yes

—

117

C₄

—

118

C₄

C₂×C₅×#107

yes

—

119

C₄

C₂×C₅×#108

yes

—

120

C₄

C₅×#493

yes

characteristic

121

C₄

C₅×#494

yes

characteristic

122

C₂

—

123

C₂

C₅×#1845

yes

characteristic

124

C₂

C₅×#1848

yes

—

	subgroup	G/H
center	C₂×C₄×C₅	#127
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	#384
prime radical	C₂³×C₅	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center

C₂×C₄×C₅

#127

commutator

C₄²

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

socle

C₂²×C₅

#384

prime radical

C₂³×C₅

C₄⋊Q₈

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
12. #8823	C₅	direct (N × H)
62. C₅×C₈	#108	semidirect
112. C₈	C₅×#108	semidirect
113. C₅	#8823	direct (N × H)

H ≅ G/N

type

12. #8823

C₅

direct (N × H)

62. C₅×C₈

#108

semidirect

112. C₈

C₅×#108

semidirect

113. C₅

#8823

direct (N × H)

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

subgroup	index
C₅×#1848	2
C₅×#1567	2
C₂×C₅×C₈²	2
#8823	5

subgroup

index

C₅×#1848

C₅×#1567

C₂×C₅×C₈²

#8823

Subgroups — C₅×#8823 #11931543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8823 #11931543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8823 #11931543