Group #11935238 — subgroups

Subgroups — C₅×#12518 #11935238

Order 1280.

330 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2248	C₂	1	2	yes	maximal, complemented
2	C₅×#2247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2246	C₂	1	1	yes	maximal, characteristic
4	C₅×#1709	C₂	1	2	yes	maximal, complemented
5	C₅×C₈×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Q₃₂	—	2	2	no	—
7	C₂×C₅×SD₃₂	—	2	4	no	—
8	C₂×C₅×D₁₆	—	2	2	no	—
9	C₅×#494	C₂²	1	2	yes	—
10	C₅×#493	C₂²	1	2	yes	—
11	C₅×#486	—	2	4	no	—
12	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
13	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
14	C₅×C₈²	C₂²	1	1	yes	characteristic
15	#12518	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₅×Q₁₆	—	2	2	no	—
17	C₂×C₅×Q₁₆	—	2	2	no	—
18	C₂×C₅×D₈	—	2	2	no	—
19	C₂×C₅×D₈	—	2	2	no	—
20	C₅×C₄⋊Q₈	—	2	2	no	—
21	C₅×#127	—	2	2	no	—
22	C₅×Q₃₂	—	4	4	no	—
23	C₅×SD₃₂	—	4	8	no	—
24	C₅×D₁₆	—	4	4	no	—
25	C₂×C₅×C₁₆	D₄	1	2	yes	—
26	C₂×C₅×C₁₆	D₄	1	2	yes	—
27	C₅×#102	—	4	8	no	—
28	C₄×C₅×C₈	D₄	1	2	yes	—
29	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
30	#2248	C₂×C₅	1	2	yes	complemented
31	#2247	C₂×C₅	1	1	yes	characteristic, complemented
32	#2246	C₂×C₅	1	1	yes	characteristic
33	#1709	C₂×C₅	1	2	yes	complemented
34	C₈×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
35	C₂×C₅×Q₈	—	4	2	no	—
36	C₂×C₅×D₄	—	4	2	no	—
37	C₂×C₅×D₄	—	4	4	no	—
38	C₅×Q₁₆	—	4	4	no	—
39	C₅×Q₁₆	—	4	4	no	—
40	C₅×D₈	—	4	4	no	—
41	C₅×D₈	—	4	4	no	—
42	C₂×C₅×C₈	D₈	1	4	yes	—
43	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
44	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
45	C₅×C₄⋊C₄	—	4	4	no	—
46	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
47	C₅×C₁₆	D₈	1	4	yes	—
48	C₅×C₁₆	D₈	1	4	yes	—
49	C₂×Q₃₂	—	2	2	no	—
50	C₂×SD₃₂	—	2	4	no	—
51	C₂×D₁₆	—	2	2	no	—
52	#494	C₂²×C₅	1	2	yes	—
53	#493	C₂²×C₅	1	2	yes	—
54	#486	—	2	4	no	—
55	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
56	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
57	C₈²	C₂²×C₅	1	1	yes	characteristic
58	C₂³×C₅	—	8	2	no	—
59	C₅×Q₈	—	8	2	no	—
60	C₅×Q₈	—	8	2	no	—
61	C₅×D₄	—	8	2	no	—
62	C₅×D₄	—	8	2	no	—
63	C₅×D₄	—	8	8	no	—
64	C₂×C₄×C₅	—	8	2	no	—
65	C₂×C₄×C₅	#127	1	1	yes	characteristic
66	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
67	C₅×C₈	—	2	4	no	—
68	C₅×C₈	C₂×D₈	1	2	yes	—
69	C₅×C₈	C₂×D₈	1	2	yes	—
70	C₂×Q₁₆	—	2	2	no	—
71	C₂×Q₁₆	—	2	2	no	—
72	C₂×D₈	—	2	2	no	—
73	C₂×D₈	—	2	2	no	—
74	C₄⋊Q₈	—	2	2	no	—
75	#127	—	2	2	no	—
76	Q₃₂	—	4	4	no	—
77	SD₃₂	—	4	8	no	—
78	D₁₆	—	4	4	no	—
79	C₂×C₁₆	C₅×D₄	1	2	yes	—
80	C₂×C₁₆	C₅×D₄	1	2	yes	—
81	#102	—	4	8	no	—
82	C₄×C₈	C₅×D₄	1	2	yes	—
83	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
84	C₂²×C₅	—	16	2	no	—
85	C₂²×C₅	—	16	4	no	—
86	C₂²×C₅	#493	1	1	yes	characteristic
87	C₄×C₅	—	16	2	no	—
88	C₄×C₅	#493	1	1	yes	characteristic
89	C₄×C₅	#493	1	1	yes	characteristic
90	C₄×C₅	#508	1	4	yes	—
91	C₂×Q₈	—	4	2	no	—
92	C₂×D₄	—	4	2	no	—
93	C₂×D₄	—	4	4	no	—
94	Q₁₆	—	4	4	no	—
95	Q₁₆	—	4	4	no	—
96	D₈	—	4	4	no	—
97	D₈	—	4	4	no	—
98	C₂×C₈	C₅×D₈	1	4	yes	—
99	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
100	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
101	C₄⋊C₄	—	4	4	no	—
102	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
103	C₁₆	C₅×D₈	1	4	yes	—
104	C₁₆	C₅×D₈	1	4	yes	—
105	C₂×C₅	—	32	2	no	—
106	C₂×C₅	#1712	1	1	yes	characteristic
107	C₂×C₅	#2249	1	2	yes	—
108	C₂³	—	8	2	no	—
109	Q₈	—	8	2	no	—
110	Q₈	—	8	2	no	—
111	D₄	—	8	2	no	—
112	D₄	—	8	2	no	—
113	D₄	—	8	8	no	—
114	C₂×C₄	—	8	2	no	—
115	C₂×C₄	C₅×#127	1	1	yes	characteristic
116	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
117	C₈	—	2	4	no	—
118	C₈	C₂×C₅×D₈	1	2	yes	—
119	C₈	C₂×C₅×D₈	1	2	yes	—
120	C₅	#12518	1	1	yes	characteristic, direct product factor, Sylow
121	C₂²	—	16	2	no	—
122	C₂²	—	16	4	no	—
123	C₂²	C₅×#493	1	1	yes	characteristic
124	C₄	—	16	2	no	—
125	C₄	C₅×#493	1	1	yes	characteristic
126	C₄	C₅×#493	1	1	yes	characteristic
127	C₄	C₅×#508	1	4	yes	—
128	C₂	—	32	2	no	—
129	C₂	C₅×#1712	1	1	yes	characteristic
130	C₂	C₅×#2249	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2248

C₂

yes

maximal, complemented

C₅×#2247

C₂

yes

maximal, characteristic, complemented

C₅×#2246

C₂

yes

maximal, characteristic

C₅×#1709

C₂

yes

maximal, complemented

C₅×C₈×C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₅×Q₃₂

—

C₂×C₅×SD₃₂

—

C₂×C₅×D₁₆

—

C₅×#494

C₂²

yes

—

C₅×#493

C₂²

yes

—

C₅×#486

—

C₄×C₅×C₁₆

C₂²

yes

characteristic

C₄×C₅×C₁₆

C₂²

yes

characteristic

C₅×C₈²

C₂²

yes

characteristic

#12518

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

—

C₂×C₅×D₈

—

C₂×C₅×D₈

—

C₅×C₄⋊Q₈

—

C₅×#127

—

C₅×Q₃₂

—

C₅×SD₃₂

—

C₅×D₁₆

—

C₂×C₅×C₁₆

D₄

yes

—

C₂×C₅×C₁₆

D₄

yes

—

C₅×#102

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

C₂³

yes

characteristic

#2248

C₂×C₅

yes

complemented

#2247

C₂×C₅

yes

characteristic, complemented

#2246

C₂×C₅

yes

characteristic

#1709

C₂×C₅

yes

complemented

C₈×C₁₆

C₂×C₅

yes

characteristic, complemented

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₅×Q₁₆

—

C₅×Q₁₆

—

C₅×D₈

—

C₅×D₈

—

C₂×C₅×C₈

D₈

yes

—

C₂×C₅×C₈

C₂×D₄

yes

characteristic

C₂×C₅×C₈

C₂×D₄

yes

characteristic

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×D₄

yes

characteristic

C₅×C₁₆

D₈

yes

—

C₅×C₁₆

D₈

yes

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#494

C₂²×C₅

yes

—

#493

C₂²×C₅

yes

—

#486

—

C₄×C₁₆

C₂²×C₅

yes

characteristic

C₄×C₁₆

C₂²×C₅

yes

characteristic

C₈²

C₂²×C₅

yes

characteristic

C₂³×C₅

—

C₅×Q₈

—

C₅×Q₈

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#127

yes

characteristic

C₂×C₄×C₅

C₂×D₈

yes

—

C₅×C₈

—

C₅×C₈

C₂×D₈

yes

—

C₅×C₈

C₂×D₈

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₅×D₄

yes

—

C₂×C₁₆

C₅×D₄

yes

—

#102

—

C₄×C₈

C₅×D₄

yes

—

C₄×C₈

C₂³×C₅

yes

characteristic

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#493

yes

characteristic

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

yes

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

D₈

—

D₈

—

C₂×C₈

C₅×D₈

yes

—

C₂×C₈

C₂×C₅×D₄

yes

characteristic

100

C₂×C₈

C₂×C₅×D₄

yes

characteristic

101

C₄⋊C₄

—

102

C₄²

C₂×C₅×D₄

yes

characteristic

103

C₁₆

C₅×D₈

yes

—

104

C₁₆

C₅×D₈

yes

—

105

C₂×C₅

—

106

C₂×C₅

#1712

yes

characteristic

107

C₂×C₅

#2249

yes

—

108

C₂³

—

109

Q₈

—

110

Q₈

—

111

D₄

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

C₅×#127

yes

characteristic

116

C₂×C₄

C₂×C₅×D₈

yes

—

117

C₈

—

118

C₈

C₂×C₅×D₈

yes

—

119

C₈

C₂×C₅×D₈

yes

—

120

C₅

#12518

yes

characteristic, direct product factor, Sylow

121

C₂²

—

122

C₂²

—

123

C₂²

C₅×#493

yes

characteristic

124

C₄

—

125

C₄

C₅×#493

yes

characteristic

126

C₄

C₅×#493

yes

characteristic

127

C₄

C₅×#508

yes

—

128

C₂

—

129

C₂

C₅×#1712

yes

characteristic

130

C₂

C₅×#2249

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅
prime radical	C₅×#2246	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×C₈² ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#493

commutator, Frattini, cosocle

C₄×C₈

C₂³×C₅

prime radical

C₅×#2246

C₂

LCS

G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×C₈² ◁ G

N	H ≅ G/N	type
1. C₅×#2248	C₂	semidirect
2. C₅×#2247	C₂	semidirect
4. C₅×#1709	C₂	semidirect
5. C₅×C₈×C₁₆	C₂	semidirect
15. #12518	C₅	direct (N × H)
30. #2248	C₂×C₅	semidirect
31. #2247	C₂×C₅	semidirect
33. #1709	C₂×C₅	semidirect
34. C₈×C₁₆	C₂×C₅	semidirect
120. C₅	#12518	direct (N × H)

H ≅ G/N

type

1. C₅×#2248

C₂

semidirect

2. C₅×#2247

C₂

semidirect

4. C₅×#1709

C₂

semidirect

5. C₅×C₈×C₁₆

C₂

semidirect

15. #12518

C₅

direct (N × H)

30. #2248

C₂×C₅

semidirect

31. #2247

C₂×C₅

semidirect

33. #1709

C₂×C₅

semidirect

34. C₈×C₁₆

C₂×C₅

semidirect

120. C₅

#12518

direct (N × H)

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

subgroup	index
C₅×#2248	2
C₅×#2247	2
C₅×#2246	2
C₅×#1709	2
C₅×C₈×C₁₆	2
#12518	5

subgroup

index

C₅×C₈×C₁₆

Subgroups — C₅×#12518 #11935238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12518 #11935238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12518 #11935238