Group #11935603 — subgroups

Subgroups — C₅×#12883 #11935603

Order 1280.

342 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 174 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×#2150	C₂	1	2	yes	maximal
2	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#1376	C₂	1	4	yes	maximal
4	C₂×C₅×M₃₂	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×C₄⋊C₁₆	—	2	4	no	—
11	#12883	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
14	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₅	—	2	2	no	—
16	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
18	C₅×M₃₂	—	2	8	no	—
19	C₂×C₅×C₁₆	—	2	4	no	—
20	C₄×C₅×C₈	—	2	4	no	—
21	C₄×C₅×C₈	—	2	4	no	—
22	C₄×C₅×C₈	C₈	1	2	yes	—
23	C₄×C₅×C₈	C₈	1	2	yes	—
24	C₄×C₅×C₈	D₄	1	2	yes	—
25	C₄×C₅×C₈	Q₈	1	2	yes	—
26	#2150	C₂×C₅	1	2	yes	—
27	C₄²×C₈	C₂×C₅	1	1	yes	characteristic
28	#1376	C₂×C₅	1	4	yes	—
29	C₂²×C₄×C₅	—	2	2	no	—
30	C₂²×C₄×C₅	M₁₆	1	2	yes	—
31	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₅×C₈	—	2	2	no	—
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	—	2	2	no	—
35	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
36	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
37	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
38	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₅×C₈	#41	1	4	yes	—
40	C₄²×C₅	—	2	8	no	—
41	C₄²×C₅	—	2	2	no	—
42	C₄²×C₅	C₄⋊C₄	1	2	yes	—
43	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
44	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
45	C₄²×C₅	M₁₆	1	4	yes	—
46	C₅×C₁₆	—	4	4	no	—
47	C₂×M₃₂	C₂²×C₅	1	4	yes	—
48	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
49	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
50	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
51	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
52	C₄³	C₄×C₅	1	1	yes	characteristic
53	C₄⋊C₁₆	—	2	4	no	—
54	C₂³×C₅	C₂×M₁₆	1	1	yes	characteristic
55	C₂×C₄×C₅	—	2	8	no	—
56	C₂×C₄×C₅	—	2	4	no	—
57	C₂×C₄×C₅	—	2	4	no	—
58	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
59	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
60	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₅	#117	1	2	yes	—
62	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
63	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
64	C₅×C₈	—	2	2	no	—
65	C₅×C₈	—	2	4	no	—
66	C₅×C₈	#124	1	2	yes	—
67	C₅×C₈	#125	1	2	yes	—
68	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
69	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
70	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
71	C₂×C₄²	—	2	2	no	—
72	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
73	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
74	M₃₂	—	2	8	no	—
75	C₂×C₁₆	—	2	4	no	—
76	C₄×C₈	—	2	4	no	—
77	C₄×C₈	—	2	4	no	—
78	C₄×C₈	C₅×C₈	1	2	yes	—
79	C₄×C₈	C₅×C₈	1	2	yes	—
80	C₄×C₈	C₅×D₄	1	2	yes	—
81	C₄×C₈	C₅×Q₈	1	2	yes	—
82	C₂²×C₅	—	2	2	no	—
83	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
84	C₂²×C₅	#432	1	2	yes	—
85	C₄×C₅	—	2	8	no	—
86	C₄×C₅	—	2	2	no	—
87	C₄×C₅	#364	1	4	yes	—
88	C₄×C₅	#382	1	1	yes	characteristic
89	C₄×C₅	#423	1	1	yes	characteristic
90	C₄×C₅	#431	1	2	yes	—
91	C₂²×C₄	—	2	2	no	—
92	C₂²×C₄	C₅×M₁₆	1	2	yes	—
93	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
98	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
99	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
100	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
101	C₂×C₈	C₅×#41	1	4	yes	—
102	C₄²	—	2	8	no	—
103	C₄²	—	2	2	no	—
104	C₄²	C₅×C₄⋊C₄	1	2	yes	—
105	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
106	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
107	C₄²	C₅×M₁₆	1	4	yes	—
108	C₁₆	—	4	4	no	—
109	C₂×C₅	—	2	2	no	—
110	C₂×C₅	#1831	1	1	yes	characteristic
111	C₂×C₅	C₂×#364	1	2	yes	—
112	C₂³	C₂×C₅×M₁₆	1	1	yes	characteristic
113	C₂×C₄	—	2	8	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	C₅×C₄⋊C₈	1	2	yes	—
117	C₂×C₄	C₅×C₄⋊C₈	1	2	yes	—
118	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄	C₅×#117	1	2	yes	—
120	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
121	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
122	C₈	—	2	2	no	—
123	C₈	—	2	4	no	—
124	C₈	C₅×#124	1	2	yes	—
125	C₈	C₅×#125	1	2	yes	—
126	C₅	#12883	1	1	yes	characteristic, direct product factor, Sylow
127	C₂²	—	2	2	no	—
128	C₂²	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
129	C₂²	C₅×#432	1	2	yes	—
130	C₄	—	2	8	no	—
131	C₄	—	2	2	no	—
132	C₄	C₅×#364	1	4	yes	—
133	C₄	C₅×#382	1	1	yes	characteristic
134	C₄	C₅×#423	1	1	yes	characteristic
135	C₄	C₅×#431	1	2	yes	—
136	C₂	—	2	2	no	—
137	C₂	C₅×#1831	1	1	yes	characteristic
138	C₂	C₂×C₅×#364	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2150

C₂

yes

maximal

C₄²×C₅×C₈

C₂

yes

maximal, characteristic

C₅×#1376

C₂

yes

maximal

C₂×C₅×M₃₂

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×C₄⋊C₁₆

—

#12883

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂³

yes

characteristic

C₂×C₄²×C₅

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₅×M₃₂

—

C₂×C₅×C₁₆

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

C₈

yes

—

C₄×C₅×C₈

C₈

yes

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

#2150

C₂×C₅

yes

—

C₄²×C₈

C₂×C₅

yes

characteristic

#1376

C₂×C₅

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

M₁₆

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₂×C₈

yes

—

C₂×C₅×C₈

C₂×D₄

yes

characteristic

C₂×C₅×C₈

C₂×Q₈

yes

characteristic

C₂×C₅×C₈

#41

yes

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

C₄⋊C₄

yes

—

C₄²×C₅

C₂×C₈

yes

characteristic

C₄²×C₅

C₂×C₈

yes

characteristic

C₄²×C₅

M₁₆

yes

—

C₅×C₁₆

—

C₂×M₃₂

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

C₄⋊C₁₆

—

C₂³×C₅

C₂×M₁₆

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄⋊C₈

yes

—

C₂×C₄×C₅

C₄⋊C₈

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#124

yes

—

C₅×C₈

#125

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂³×C₅

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₅×C₈

yes

—

C₄×C₈

C₅×C₈

yes

—

C₄×C₈

C₅×D₄

yes

—

C₄×C₈

C₅×Q₈

yes

—

C₂²×C₅

—

C₂²×C₅

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₅

#432

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#364

yes

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

yes

—

C₂²×C₄

—

C₂²×C₄

C₅×M₁₆

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₂×C₅×C₈

yes

—

C₂×C₈

C₂×C₅×D₄

yes

characteristic

100

C₂×C₈

C₂×C₅×Q₈

yes

characteristic

101

C₂×C₈

C₅×#41

yes

—

102

C₄²

—

103

C₄²

—

104

C₄²

C₅×C₄⋊C₄

yes

—

105

C₄²

C₂×C₅×C₈

yes

characteristic

106

C₄²

C₂×C₅×C₈

yes

characteristic

107

C₄²

C₅×M₁₆

yes

—

108

C₁₆

—

109

C₂×C₅

—

110

C₂×C₅

#1831

yes

characteristic

111

C₂×C₅

C₂×#364

yes

—

112

C₂³

C₂×C₅×M₁₆

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₅×C₄⋊C₈

yes

—

117

C₂×C₄

C₅×C₄⋊C₈

yes

—

118

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

119

C₂×C₄

C₅×#117

yes

—

120

C₂×C₄

C₂²×C₅×C₈

yes

characteristic

121

C₂×C₄

C₂×C₅×M₁₆

yes

—

122

C₈

—

123

C₈

—

124

C₈

C₅×#124

yes

—

125

C₈

C₅×#125

yes

—

126

C₅

#12883

yes

characteristic, direct product factor, Sylow

127

C₂²

—

128

C₂²

C₂×C₅×C₄⋊C₈

yes

characteristic

129

C₂²

C₅×#432

yes

—

130

C₄

—

131

C₄

—

132

C₄

C₅×#364

yes

—

133

C₄

C₅×#382

yes

characteristic

134

C₄

C₅×#423

yes

characteristic

135

C₄

C₅×#431

yes

—

136

C₂

—

137

C₂

C₅×#1831

yes

characteristic

138

C₂

C₂×C₅×#364

yes

—

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₂×C₄	C₂²×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×C₄⋊C₈
prime radical	C₂³×C₅	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

subgroup

G/H

center

C₂×C₅×C₈

C₂×D₄

commutator

C₂×C₄

C₂²×C₅×C₈

Frattini, cosocle

C₂²×C₈

C₂³×C₅

socle

C₂²×C₅

C₂×C₄⋊C₈

prime radical

C₂³×C₅

C₂×M₁₆

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

N	H ≅ G/N	type
11. #12883	C₅	direct (N × H)
126. C₅	#12883	direct (N × H)

H ≅ G/N

type

11. #12883

C₅

direct (N × H)

126. C₅

#12883

direct (N × H)

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

subgroup	index
C₅×#2150	2
C₄²×C₅×C₈	2
C₅×#1376	2
#12883	5

subgroup

index

C₅×#2150

C₄²×C₅×C₈

C₅×#1376

#12883

Subgroups — C₅×#12883 #11935603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12883 #11935603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12883 #11935603