Group #11935600 — subgroups

Subgroups — C₅×#12880 #11935600

Order 1280.

322 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 182 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×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₅×#1726	C₂	1	1	yes	maximal, characteristic
3	C₅×#1374	C₂	1	4	yes	maximal
4	C₂²×C₅×C₁₆	C₂²	1	4	yes	—
5	C₂×C₅×#97	C₄	1	2	yes	—
6	C₂×C₅×#97	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	C₅×#376	C₄	1	1	yes	characteristic
10	C₅×C₄⋊C₁₆	—	2	4	no	—
11	#12880	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	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×C₅×C₁₆	—	2	4	no	—
18	C₂×C₅×C₁₆	—	2	8	no	—
19	C₅×#97	—	2	4	no	—
20	C₅×#97	—	2	2	no	—
21	C₄×C₅×C₈	—	2	4	no	—
22	C₄×C₅×C₈	D₄	1	2	yes	—
23	C₄×C₅×C₈	Q₈	1	2	yes	—
24	C₅×#95	C₈	1	4	yes	—
25	C₂×C₄⋊C₁₆	C₂×C₅	1	2	yes	—
26	#1726	C₂×C₅	1	1	yes	characteristic
27	#1374	C₂×C₅	1	4	yes	—
28	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
29	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
30	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₅×C₈	—	2	2	no	—
32	C₂×C₅×C₈	—	2	2	no	—
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
35	C₂×C₅×C₈	M₁₆	1	4	yes	—
36	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
37	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₅×C₈	#41	1	4	yes	—
39	C₄²×C₅	—	2	2	no	—
40	C₄²×C₅	—	2	2	no	—
41	C₄²×C₅	C₄⋊C₄	1	2	yes	—
42	C₄²×C₅	M₁₆	1	2	yes	—
43	C₅×C₁₆	—	4	4	no	—
44	C₂²×C₁₆	C₂²×C₅	1	4	yes	—
45	C₂×#97	C₄×C₅	1	2	yes	—
46	C₂×#97	C₄×C₅	1	1	yes	characteristic
47	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
48	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
49	#376	C₄×C₅	1	1	yes	characteristic
50	C₄⋊C₁₆	—	2	4	no	—
51	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₅	—	2	4	no	—
53	C₂×C₄×C₅	—	2	4	no	—
54	C₂×C₄×C₅	—	2	8	no	—
55	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
56	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₅	#117	1	2	yes	—
58	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
59	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
60	C₅×C₈	—	2	2	no	—
61	C₅×C₈	—	2	4	no	—
62	C₅×C₈	#124	1	2	yes	—
63	C₅×C₈	#125	1	2	yes	—
64	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
65	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
66	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
67	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
68	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
69	C₂×C₁₆	—	2	4	no	—
70	C₂×C₁₆	—	2	8	no	—
71	#97	—	2	4	no	—
72	#97	—	2	2	no	—
73	C₄×C₈	—	2	4	no	—
74	C₄×C₈	C₅×D₄	1	2	yes	—
75	C₄×C₈	C₅×Q₈	1	2	yes	—
76	#95	C₅×C₈	1	4	yes	—
77	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
78	C₂²×C₅	#431	1	2	yes	—
79	C₂²×C₅	#504	1	4	yes	—
80	C₄×C₅	—	2	4	no	—
81	C₄×C₅	—	4	4	no	—
82	C₄×C₅	#382	1	1	yes	characteristic
83	C₄×C₅	#423	1	1	yes	characteristic
84	C₄×C₅	#432	1	2	yes	—
85	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
86	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
87	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
92	C₂×C₈	C₅×M₁₆	1	4	yes	—
93	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
94	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
95	C₂×C₈	C₅×#41	1	4	yes	—
96	C₄²	—	2	2	no	—
97	C₄²	—	2	2	no	—
98	C₄²	C₅×C₄⋊C₄	1	2	yes	—
99	C₄²	C₅×M₁₆	1	2	yes	—
100	C₁₆	—	4	4	no	—
101	C₂×C₅	#1831	1	1	yes	characteristic
102	C₂×C₅	#2151	1	2	yes	—
103	C₂×C₅	#2164	1	4	yes	—
104	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	8	no	—
108	C₂×C₄	C₅×C₄⋊C₈	1	4	yes	—
109	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄	C₅×#117	1	2	yes	—
111	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
112	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	2	4	no	—
115	C₈	C₅×#124	1	2	yes	—
116	C₈	C₅×#125	1	2	yes	—
117	C₅	#12880	1	1	yes	characteristic, direct product factor, Sylow
118	C₂²	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
119	C₂²	C₅×#431	1	2	yes	—
120	C₂²	C₅×#504	1	4	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₅×#382	1	1	yes	characteristic
124	C₄	C₅×#423	1	1	yes	characteristic
125	C₄	C₅×#432	1	2	yes	—
126	C₂	C₅×#1831	1	1	yes	characteristic
127	C₂	C₅×#2151	1	2	yes	—
128	C₂	C₅×#2164	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₄⋊C₁₆

C₂

yes

maximal

C₅×#1726

C₂

yes

maximal, characteristic

C₅×#1374

C₂

yes

maximal

C₂²×C₅×C₁₆

C₂²

yes

—

C₂×C₅×#97

C₄

yes

—

C₂×C₅×#97

C₄

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#376

C₄

yes

characteristic

C₅×C₄⋊C₁₆

—

#12880

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×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

—

C₅×#97

—

C₅×#97

—

C₄×C₅×C₈

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

C₅×#95

C₈

yes

—

C₂×C₄⋊C₁₆

C₂×C₅

yes

—

#1726

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

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

M₁₆

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

M₁₆

yes

—

C₅×C₁₆

—

C₂²×C₁₆

C₂²×C₅

yes

—

C₂×#97

C₄×C₅

yes

—

C₂×#97

C₄×C₅

yes

characteristic

C₂×C₄×C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#376

C₄×C₅

yes

characteristic

C₄⋊C₁₆

—

C₂³×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄⋊C₈

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₂×C₄×C₅

C₂×M₁₆

yes

characteristic

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×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₅×D₄

yes

—

C₄×C₈

C₅×Q₈

yes

—

#95

C₅×C₈

yes

—

C₂²×C₅

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₅

#431

yes

—

C₂²×C₅

#504

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

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

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×M₁₆

yes

—

C₂×C₈

C₂×C₅×D₄

yes

characteristic

C₂×C₈

C₂×C₅×Q₈

yes

characteristic

C₂×C₈

C₅×#41

yes

—

C₄²

—

C₄²

—

C₄²

C₅×C₄⋊C₄

yes

—

C₄²

C₅×M₁₆

yes

—

100

C₁₆

—

101

C₂×C₅

#1831

yes

characteristic

102

C₂×C₅

#2151

yes

—

103

C₂×C₅

#2164

yes

—

104

C₂³

C₂²×C₅×C₈

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₅×C₄⋊C₈

yes

—

109

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

110

C₂×C₄

C₅×#117

yes

—

111

C₂×C₄

C₂×C₅×M₁₆

yes

—

112

C₂×C₄

C₂×C₅×M₁₆

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

C₅×#124

yes

—

116

C₈

C₅×#125

yes

—

117

C₅

#12880

yes

characteristic, direct product factor, Sylow

118

C₂²

C₂×C₅×C₄⋊C₈

yes

characteristic

119

C₂²

C₅×#431

yes

—

120

C₂²

C₅×#504

yes

—

121

C₄

—

122

C₄

—

123

C₄

C₅×#382

yes

characteristic

124

C₄

C₅×#423

yes

characteristic

125

C₄

C₅×#432

yes

—

126

C₂

C₅×#1831

yes

characteristic

127

C₂

C₅×#2151

yes

—

128

C₂

C₅×#2164

yes

—

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

subgroup

G/H

center

C₂²×C₅×C₈

C₂³

commutator

C₂³

C₂²×C₅×C₈

Frattini, cosocle

C₂²×C₈

C₂³×C₅

socle, prime radical

C₂³×C₅

C₂²×C₈

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂²×C₅×C₈ ◁ G

N	H ≅ G/N	type
11. #12880	C₅	direct (N × H)
117. C₅	#12880	direct (N × H)

H ≅ G/N

type

11. #12880

C₅

direct (N × H)

117. C₅

#12880

direct (N × H)

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

subgroup	index
C₂×C₅×C₄⋊C₁₆	2
C₅×#1726	2
C₅×#1374	2
#12880	5

subgroup

index

C₂×C₅×C₄⋊C₁₆

C₅×#1726

C₅×#1374

#12880

Subgroups — C₅×#12880 #11935600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12880 #11935600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12880 #11935600