Group #13097941 — subgroups

Subgroups — #13097941

Order 1600.

201 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 79 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×C₄⋊Dic₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#87718	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#95	C₂	1	1	yes	maximal, characteristic
4	#11716379	C₂	1	2	yes	maximal
5	#11716379	C₂	1	2	yes	maximal
6	C₂²×C₄×C₂₅	C₂²	1	2	yes	—
7	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
8	C₂²×Dic₂₅	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₅	C₂²	1	2	yes	—
10	C₂²×Dic₂₅	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₂₅	—	2	2	no	—
12	#87718	—	2	2	no	—
13	#64948	—	5	1	no	maximal
14	C₂³×C₂₅	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₂₅	—	2	2	no	—
16	C₂×C₄×C₂₅	—	2	2	no	—
17	C₂×C₄×C₂₅	—	2	2	no	—
18	C₂×C₄×C₂₅	—	2	2	no	—
19	C₂×C₄×C₂₅	D₄	1	2	yes	—
20	C₂×Dic₂₅	—	2	1	no	—
21	C₂×Dic₂₅	—	2	1	no	—
22	C₂×Dic₂₅	—	2	1	no	—
23	C₂×Dic₂₅	—	2	2	no	—
24	C₂×Dic₂₅	—	2	2	no	—
25	C₂×Dic₂₅	—	2	4	no	—
26	C₂×Dic₂₅	Q₈	1	2	yes	—
27	C₂×C₄⋊Dic₅	—	5	1	no	—
28	C₂×#683	—	5	1	no	—
29	C₅×#95	D₅	1	1	yes	characteristic
30	#3963	—	5	2	no	—
31	#3963	—	5	2	no	—
32	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₂₅	#41	1	2	yes	—
35	C₂²×C₂₅	#41	1	1	yes	characteristic
36	C₂²×C₂₅	#41	1	2	yes	—
37	C₄×C₂₅	—	2	2	no	—
38	C₄×C₂₅	—	4	2	no	—
39	Dic₂₅	—	2	2	no	—
40	Dic₂₅	—	4	1	no	—
41	Dic₂₅	—	4	2	no	—
42	C₂²×C₄×C₅	C₂×D₅	1	2	yes	—
43	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
44	C₂²×Dic₅	—	5	1	no	—
45	C₂²×Dic₅	—	5	1	no	—
46	C₂²×Dic₅	—	5	2	no	—
47	C₄⋊Dic₅	—	10	2	no	—
48	#683	—	10	2	no	—
49	#400	—	25	1	no	Sylow
50	C₂×C₂₅	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂×C₂₅	#123	1	1	yes	characteristic
52	C₂×C₂₅	#124	1	1	yes	characteristic
53	C₂×C₂₅	#125	1	2	yes	—
54	C₂×C₂₅	#126	1	2	yes	—
55	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
56	C₂×C₄×C₅	—	2	2	no	—
57	C₂×C₄×C₅	—	2	2	no	—
58	C₂×C₄×C₅	—	2	2	no	—
59	C₂×C₄×C₅	—	2	2	no	—
60	C₂×C₄×C₅	D₂₀	1	2	yes	—
61	C₂×Dic₅	—	5	2	no	—
62	C₂×Dic₅	—	10	1	no	—
63	C₂×Dic₅	—	10	1	no	—
64	C₂×Dic₅	—	10	1	no	—
65	C₂×Dic₅	—	10	2	no	—
66	C₂×Dic₅	—	10	4	no	—
67	C₂×Dic₅	—	10	2	no	—
68	C₂×C₄⋊C₄	—	25	1	no	—
69	C₂×C₄⋊C₄	—	25	1	no	—
70	#95	—	25	2	no	—
71	#95	—	25	2	no	—
72	#95	D₂₅	1	1	yes	characteristic
73	C₂₅	#400	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₅	C₂×D₂₀	1	1	yes	characteristic
75	C₂²×C₅	#709	1	2	yes	—
76	C₂²×C₅	#711	1	1	yes	characteristic
77	C₂²×C₅	#711	1	2	yes	—
78	C₂²×C₅	Q₈×D₅	1	1	yes	characteristic
79	C₄×C₅	—	2	2	no	—
80	C₄×C₅	—	4	2	no	—
81	Dic₅	—	10	2	no	—
82	Dic₅	—	20	2	no	—
83	Dic₅	—	20	1	no	—
84	C₂²×C₄	—	25	1	no	—
85	C₂²×C₄	—	25	2	no	—
86	C₂²×C₄	—	25	1	no	—
87	C₂²×C₄	C₂×D₂₅	1	2	yes	—
88	C₂²×C₄	C₂×D₂₅	1	1	yes	characteristic
89	C₄⋊C₄	—	50	2	no	—
90	C₄⋊C₄	—	50	2	no	—
91	C₂×C₅	#4021	1	1	yes	characteristic
92	C₂×C₅	#4025	1	2	yes	—
93	C₂×C₅	#4032	1	1	yes	characteristic
94	C₂×C₅	#4035	1	2	yes	—
95	C₂×C₅	#4043	1	1	yes	characteristic
96	C₂³	C₂²×D₂₅	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	25	2	no	—
102	C₂×C₄	—	50	1	no	—
103	C₂×C₄	—	50	1	no	—
104	C₂×C₄	—	50	2	no	—
105	C₂×C₄	—	50	1	no	—
106	C₂×C₄	—	50	4	no	—
107	C₂×C₄	—	50	2	no	—
108	C₂×C₄	D₁₀₀	1	2	yes	—
109	C₅	#64948	1	1	yes	characteristic
110	C₂²	C₂×D₁₀₀	1	1	yes	characteristic
111	C₂²	#87744	1	2	yes	—
112	C₂²	#87746	1	1	yes	characteristic
113	C₂²	#87746	1	2	yes	—
114	C₂²	Q₈×D₂₅	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	4	2	no	—
117	C₄	—	50	2	no	—
118	C₄	—	100	2	no	—
119	C₄	—	100	1	no	—
120	C₂	#11716437	1	1	yes	characteristic
121	C₂	#11716441	1	2	yes	—
122	C₂	#11716448	1	1	yes	characteristic
123	C₂	#11716451	1	2	yes	—
124	C₂	#11716459	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Dic₂₅

C₂

yes

maximal, characteristic

C₂×#87718

C₂

yes

maximal, characteristic

C₂₅×#95

C₂

yes

maximal, characteristic

#11716379

C₂

yes

maximal

#11716379

C₂

yes

maximal

C₂²×C₄×C₂₅

C₂²

yes

—

C₂²×C₄×C₂₅

C₂²

yes

characteristic

C₂²×Dic₂₅

C₂²

yes

characteristic

C₂²×Dic₂₅

C₂²

yes

—

C₂²×Dic₂₅

C₂²

yes

characteristic

C₄⋊Dic₂₅

—

#87718

—

#64948

—

maximal

C₂³×C₂₅

C₂³

yes

characteristic

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

D₄

yes

—

C₂×Dic₂₅

—

C₂×Dic₂₅

—

C₂×Dic₂₅

—

C₂×Dic₂₅

—

C₂×Dic₂₅

—

C₂×Dic₂₅

—

C₂×Dic₂₅

Q₈

yes

—

C₂×C₄⋊Dic₅

—

C₂×#683

—

C₅×#95

D₅

yes

characteristic

#3963

—

#3963

—

C₂²×C₂₅

C₂×D₄

yes

characteristic

C₂²×C₂₅

C₂×Q₈

yes

characteristic

C₂²×C₂₅

#41

yes

—

C₂²×C₂₅

#41

yes

characteristic

C₂²×C₂₅

#41

yes

—

C₄×C₂₅

—

C₄×C₂₅

—

Dic₂₅

—

Dic₂₅

—

Dic₂₅

—

C₂²×C₄×C₅

C₂×D₅

yes

—

C₂²×C₄×C₅

C₂×D₅

yes

characteristic

C₂²×Dic₅

—

C₂²×Dic₅

—

C₂²×Dic₅

—

C₄⋊Dic₅

—

#683

—

#400

—

Sylow

C₂×C₂₅

C₂²⋊Q₈

yes

C₂×C₂₅

yes

C₂×C₂₅

yes

C₂×C₂₅

yes

—

C₂×C₂₅

#126

yes

—

C₂³×C₅

C₂²×D₅

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

D₂₀

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

#95

—

#95

—

#95

D₂₅

yes

characteristic

C₂₅

#400

yes

characteristic, complemented, Sylow

C₂²×C₅

C₂×D₂₀

yes

characteristic

C₂²×C₅

#709

yes

—

C₂²×C₅

#711

yes

characteristic

C₂²×C₅

#711

yes

—

C₂²×C₅

Q₈×D₅

yes

characteristic

C₄×C₅

—

C₄×C₅

—

Dic₅

—

Dic₅

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₅

yes

—

C₂²×C₄

C₂×D₂₅

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂×C₅

#4021

yes

characteristic

C₂×C₅

#4025

yes

—

C₂×C₅

#4032

yes

characteristic

C₂×C₅

#4035

yes

—

C₂×C₅

#4043

yes

characteristic

C₂³

C₂²×D₂₅

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

D₁₀₀

yes

—

109

C₅

#64948

yes

characteristic

110

C₂²

C₂×D₁₀₀

yes

characteristic

111

C₂²

#87744

yes

—

112

C₂²

#87746

yes

characteristic

113

C₂²

#87746

yes

—

114

C₂²

Q₈×D₂₅

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

100

—

119

C₄

—

100

—

120

C₂

#11716437

yes

characteristic

121

C₂

#11716441

yes

—

122

C₂

#11716448

yes

characteristic

123

C₂

#11716451

yes

—

124

C₂

#11716459

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂³×C₂₅	C₂³
Frattini, socle, prime radical	C₂³×C₅	C₂²×D₅
Fitting	C₂₅×#95	C₂
hypercenter	#95	D₂₅
hypocenter	C₂₅	#400
LCS	G ▷ C₂³×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center

C₂³

C₂²×D₂₅

commutator, cosocle

C₂³×C₂₅

C₂³

Frattini, socle, prime radical

C₂³×C₅

C₂²×D₅

Fitting

C₂₅×#95

C₂

D₂₅

C₂₅

G ▷ C₂³×C₂₅ ▷ C₂₅

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
73. C₂₅	#400	semidirect

H ≅ G/N

type

73. C₂₅

#400

semidirect

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

subgroup	index
C₂×C₄⋊Dic₂₅	2
C₂×#87718	2
C₂₅×#95	2
#11716379	2
#64948	5

subgroup

index

C₂×C₄⋊Dic₂₅

C₂×#87718

C₂₅×#95

#11716379

#64948

Subgroups — #13097941

Conjugacy classes of subgroups

Complements

Maximal subgroups