Group #11935311 — subgroups

Subgroups — C₅×#12591 #11935311

Order 1280.

390 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 254 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	C₂×C₅×#346	C₂	1	2	yes	maximal
2	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#1374	C₂	1	4	yes	maximal
4	C₂²×C₅×C₁₆	C₂²	1	4	yes	—
5	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
6	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₄³×C₅	C₄	1	1	yes	characteristic
10	C₅×#346	C₄	1	8	yes	complemented
11	#12591	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
13	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₅	C₈	1	4	yes	—
16	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂×C₅×C₁₆	—	2	8	no	—
19	C₂×C₅×C₁₆	C₂×C₄	1	8	yes	—
20	C₄×C₅×C₈	—	2	4	no	—
21	C₄×C₅×C₈	—	2	4	no	—
22	C₄×C₅×C₈	C₈	1	4	yes	—
23	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
24	C₂×#346	C₂×C₅	1	2	yes	—
25	C₄²×C₈	C₂×C₅	1	1	yes	characteristic
26	#1374	C₂×C₅	1	4	yes	—
27	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
28	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
29	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₅×C₈	—	2	2	no	—
31	C₂×C₅×C₈	—	2	2	no	—
32	C₂×C₅×C₈	C₄²	1	2	yes	—
33	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
34	C₂×C₅×C₈	M₁₆	1	4	yes	—
35	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
36	C₂×C₅×C₈	#41	1	4	yes	—
37	C₄²×C₅	—	2	8	no	—
38	C₄²×C₅	—	2	2	no	—
39	C₄²×C₅	—	2	2	no	—
40	C₄²×C₅	C₄²	1	2	yes	—
41	C₄²×C₅	C₂×C₈	1	2	yes	—
42	C₅×C₁₆	—	2	8	no	—
43	C₂²×C₁₆	C₂²×C₅	1	4	yes	—
44	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
45	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
46	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
47	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
48	C₄³	C₄×C₅	1	1	yes	characteristic
49	#346	C₄×C₅	1	8	yes	complemented
50	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
51	C₂×C₄×C₅	—	2	4	no	—
52	C₂×C₄×C₅	—	2	4	no	—
53	C₂×C₄×C₅	—	2	4	no	—
54	C₂×C₄×C₅	C₄×C₈	1	4	yes	—
55	C₂×C₄×C₅	M₃₂	1	8	yes	—
56	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₅	#117	1	2	yes	—
58	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
60	C₅×C₈	—	2	4	no	—
61	C₅×C₈	#97	1	4	yes	—
62	C₅×C₈	#117	1	4	yes	—
63	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
64	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
65	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
66	C₂×C₄²	C₅×C₈	1	4	yes	—
67	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
68	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
69	C₂×C₁₆	—	2	8	no	—
70	C₂×C₁₆	C₂×C₄×C₅	1	8	yes	—
71	C₄×C₈	—	2	4	no	—
72	C₄×C₈	—	2	4	no	—
73	C₄×C₈	C₅×C₈	1	4	yes	—
74	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
75	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
76	C₂²×C₅	#431	1	2	yes	—
77	C₂²×C₅	C₂×M₃₂	1	4	yes	—
78	C₄×C₅	—	2	4	no	—
79	C₄×C₅	—	2	8	no	—
80	C₄×C₅	#376	1	1	yes	characteristic
81	C₄×C₅	C₂×#97	1	1	yes	characteristic
82	C₄×C₅	#431	1	2	yes	—
83	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
84	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
85	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	C₄²×C₅	1	2	yes	—
89	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
90	C₂×C₈	C₅×M₁₆	1	4	yes	—
91	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
92	C₂×C₈	C₅×#41	1	4	yes	—
93	C₄²	—	2	2	no	—
94	C₄²	—	2	2	no	—
95	C₄²	—	2	8	no	—
96	C₄²	C₄²×C₅	1	2	yes	—
97	C₄²	C₂×C₅×C₈	1	2	yes	—
98	C₁₆	—	2	8	no	—
99	C₂×C₅	#1744	1	1	yes	characteristic
100	C₂×C₅	C₄×M₃₂	1	2	yes	—
101	C₂×C₅	#2163	1	4	yes	—
102	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	C₄×C₅×C₈	1	4	yes	—
107	C₂×C₄	C₅×M₃₂	1	8	yes	—
108	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
109	C₂×C₄	C₅×#117	1	2	yes	—
110	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
111	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
112	C₈	—	2	4	no	—
113	C₈	C₅×#97	1	4	yes	—
114	C₈	C₅×#117	1	4	yes	—
115	C₅	#12591	1	1	yes	characteristic, direct product factor, Sylow
116	C₂²	C₂×C₄×C₅×C₈	1	1	yes	characteristic
117	C₂²	C₅×#431	1	2	yes	—
118	C₂²	C₂×C₅×M₃₂	1	4	yes	—
119	C₄	—	2	4	no	—
120	C₄	—	2	8	no	—
121	C₄	C₅×#376	1	1	yes	characteristic
122	C₄	C₂×C₅×#97	1	1	yes	characteristic
123	C₄	C₅×#431	1	2	yes	—
124	C₂	C₅×#1744	1	1	yes	characteristic
125	C₂	C₄×C₅×M₃₂	1	2	yes	—
126	C₂	C₅×#2163	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#346

C₂

yes

maximal

C₄²×C₅×C₈

C₂

yes

maximal, characteristic

C₅×#1374

C₂

yes

maximal

C₂²×C₅×C₁₆

C₂²

yes

—

C₂×C₄×C₅×C₈

C₄

yes

—

C₂×C₄×C₅×C₈

C₄

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₄³×C₅

C₄

yes

characteristic

C₅×#346

C₄

yes

complemented

#12591

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂³

yes

characteristic

C₂×C₄²×C₅

C₈

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

C₂×C₄

yes

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

C₈

yes

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₂×#346

C₂×C₅

yes

—

C₄²×C₈

C₂×C₅

yes

characteristic

#1374

C₂×C₅

yes

—

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄²

yes

—

C₂×C₅×C₈

C₂×C₈

yes

—

C₂×C₅×C₈

M₁₆

yes

—

C₂×C₅×C₈

C₂²×C₄

yes

—

C₂×C₅×C₈

#41

yes

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

C₄²

yes

—

C₄²×C₅

C₂×C₈

yes

—

C₅×C₁₆

—

C₂²×C₁₆

C₂²×C₅

yes

—

C₂×C₄×C₈

C₄×C₅

yes

—

C₂×C₄×C₈

C₄×C₅

yes

characteristic

C₂×C₄×C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

C₄³

C₄×C₅

yes

characteristic

#346

C₄×C₅

yes

complemented

C₂³×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄×C₈

yes

—

C₂×C₄×C₅

M₃₂

yes

—

C₂×C₄×C₅

C₂×C₄²

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₅×C₈

—

C₅×C₈

#97

yes

—

C₅×C₈

#117

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

C₂²×C₈

C₂³×C₅

yes

characteristic

C₂×C₄²

C₅×C₈

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₅

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₅×C₈

yes

—

C₄×C₈

C₂×C₄×C₅

yes

—

C₂²×C₅

C₂×C₄×C₈

yes

characteristic

C₂²×C₅

#431

yes

—

C₂²×C₅

C₂×M₃₂

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#376

yes

characteristic

C₄×C₅

C₂×#97

yes

characteristic

C₄×C₅

#431

yes

—

C₂²×C₄

C₂×C₅×C₈

yes

—

C₂²×C₄

C₂×C₅×C₈

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₅

yes

—

C₂×C₈

C₂×C₅×C₈

yes

—

C₂×C₈

C₅×M₁₆

yes

—

C₂×C₈

C₂²×C₄×C₅

yes

—

C₂×C₈

C₅×#41

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄²×C₅

yes

—

C₄²

C₂×C₅×C₈

yes

—

C₁₆

—

C₂×C₅

#1744

yes

characteristic

100

C₂×C₅

C₄×M₃₂

yes

—

101

C₂×C₅

#2163

yes

—

102

C₂³

C₂²×C₅×C₈

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₄×C₅×C₈

yes

—

107

C₂×C₄

C₅×M₃₂

yes

—

108

C₂×C₄

C₂×C₄²×C₅

yes

characteristic

109

C₂×C₄

C₅×#117

yes

—

110

C₂×C₄

C₂²×C₅×C₈

yes

characteristic

111

C₂×C₄

C₂×C₅×M₁₆

yes

—

112

C₈

—

113

C₈

C₅×#97

yes

—

114

C₈

C₅×#117

yes

—

115

C₅

#12591

yes

characteristic, direct product factor, Sylow

116

C₂²

C₂×C₄×C₅×C₈

yes

characteristic

117

C₂²

C₅×#431

yes

—

118

C₂²

C₂×C₅×M₃₂

yes

—

119

C₄

—

120

C₄

—

121

C₄

C₅×#376

yes

characteristic

122

C₄

C₂×C₅×#97

yes

characteristic

123

C₄

C₅×#431

yes

—

124

C₂

C₅×#1744

yes

characteristic

125

C₂

C₄×C₅×M₃₂

yes

—

126

C₂

C₅×#2163

yes

—

	subgroup	G/H
center	C₂²×C₅×C₈	C₂³
commutator	C₂²	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ G

subgroup

G/H

center

C₂²×C₅×C₈

C₂³

commutator

C₂²

C₂×C₄×C₅×C₈

Frattini, cosocle

C₂²×C₈

C₂³×C₅

socle, prime radical

C₂³×C₅

C₂²×C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅×C₈ ◁ G

N	H ≅ G/N	type
10. C₅×#346	C₄	semidirect
11. #12591	C₅	direct (N × H)
49. #346	C₄×C₅	semidirect
115. C₅	#12591	direct (N × H)

H ≅ G/N

type

10. C₅×#346

C₄

semidirect

11. #12591

C₅

direct (N × H)

49. #346

C₄×C₅

semidirect

115. C₅

#12591

direct (N × H)

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

subgroup	index
C₂×C₅×#346	2
C₄²×C₅×C₈	2
C₅×#1374	2
#12591	5

subgroup

index

C₂×C₅×#346

C₄²×C₅×C₈

C₅×#1374

#12591

Subgroups — C₅×#12591 #11935311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12591 #11935311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12591 #11935311