Group #13098540 — subgroups

Subgroups — C₂₅×#391 #13098540

Order 1600.

279 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 279 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₂²×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic
4	C₂₅×#95	C₂	1	4	yes	maximal
5	C₂×Q₈×C₂₅	—	2	2	no	—
6	C₂×Q₈×C₂₅	—	2	2	no	—
7	C₂×Q₈×C₂₅	C₄	1	4	yes	complemented
8	C₂²×C₄×C₂₅	C₂²	1	2	yes	—
9	C₂²×C₄×C₂₅	C₂²	1	2	yes	—
10	C₂²×C₄×C₂₅	C₂²	1	2	yes	—
11	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₅	—	2	2	no	—
13	C₄²×C₂₅	—	2	2	no	—
14	C₅×#391	C₅	1	1	yes	maximal, characteristic
15	C₂³×C₂₅	C₂³	1	1	yes	characteristic
16	Q₈×C₂₅	—	2	8	no	—
17	C₂×C₄×C₂₅	—	2	2	no	—
18	C₂×C₄×C₂₅	—	2	2	no	—
19	C₂×C₄×C₂₅	—	2	2	no	—
20	C₂×C₄×C₂₅	—	2	2	no	—
21	C₂×C₄×C₂₅	—	2	2	no	—
22	C₂×C₄×C₂₅	—	2	4	no	—
23	C₂×C₄×C₂₅	C₂×C₄	1	4	yes	—
24	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₅	D₄	1	2	yes	—
26	C₂×C₄×C₂₅	D₄	1	2	yes	—
27	C₂×C₄×C₂₅	Q₈	1	4	yes	complemented
28	C₂²×C₅×Q₈	C₂×C₅	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
30	C₂×C₄²×C₅	C₂×C₅	1	1	yes	characteristic
31	C₅×#95	C₂×C₅	1	4	yes	—
32	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₂₅	C₂×Q₈	1	2	yes	—
36	C₂²×C₂₅	#41	1	2	yes	—
37	C₄×C₂₅	—	2	4	no	—
38	C₄×C₂₅	—	2	4	no	—
39	C₄×C₂₅	—	4	2	no	—
40	C₄×C₂₅	C₂²⋊C₄	1	4	yes	—
41	C₂×C₅×Q₈	—	2	2	no	—
42	C₂×C₅×Q₈	—	2	2	no	—
43	C₂×C₅×Q₈	C₄×C₅	1	4	yes	—
44	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
45	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
46	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
47	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
48	C₅×C₄⋊C₄	—	2	2	no	—
49	C₄²×C₅	—	2	2	no	—
50	#391	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₂₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₂₅	C₄×Q₈	1	2	yes	—
53	C₂×C₂₅	C₂²⋊Q₈	1	2	yes	—
54	C₂×C₂₅	#124	1	1	yes	characteristic
55	C₂×C₂₅	C₄⋊Q₈	1	1	yes	characteristic
56	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
57	C₅×Q₈	—	2	8	no	—
58	C₂×C₄×C₅	—	2	2	no	—
59	C₂×C₄×C₅	—	2	2	no	—
60	C₂×C₄×C₅	—	2	2	no	—
61	C₂×C₄×C₅	—	2	2	no	—
62	C₂×C₄×C₅	—	2	2	no	—
63	C₂×C₄×C₅	—	2	4	no	—
64	C₂×C₄×C₅	C₂×C₄×C₅	1	4	yes	—
65	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
66	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
67	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
68	C₂×C₄×C₅	C₅×Q₈	1	4	yes	—
69	C₂²×Q₈	C₂×C₂₅	1	1	yes	characteristic
70	C₂×C₄⋊C₄	C₂×C₂₅	1	1	yes	characteristic
71	C₂×C₄²	C₂×C₂₅	1	1	yes	characteristic
72	#95	C₂×C₂₅	1	4	yes	—
73	C₂₅	#391	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
75	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
76	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
77	C₂²×C₅	C₂×C₅×Q₈	1	2	yes	—
78	C₂²×C₅	C₅×#41	1	2	yes	—
79	C₄×C₅	—	2	4	no	—
80	C₄×C₅	—	2	4	no	—
81	C₄×C₅	—	4	2	no	—
82	C₄×C₅	C₅×C₂²⋊C₄	1	4	yes	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	—	2	2	no	—
85	C₂×Q₈	C₄×C₂₅	1	4	yes	complemented
86	C₂²×C₄	C₂²×C₂₅	1	2	yes	—
87	C₂²×C₄	C₂²×C₂₅	1	2	yes	—
88	C₂²×C₄	C₂²×C₂₅	1	2	yes	—
89	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
90	C₄⋊C₄	—	2	2	no	—
91	C₄²	—	2	2	no	—
92	C₂×C₅	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₅	C₄×C₅×Q₈	1	2	yes	—
94	C₂×C₅	C₅×C₂²⋊Q₈	1	2	yes	—
95	C₂×C₅	C₅×#124	1	1	yes	characteristic
96	C₂×C₅	C₅×C₄⋊Q₈	1	1	yes	characteristic
97	C₂³	C₂³×C₂₅	1	1	yes	characteristic
98	Q₈	—	2	8	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	C₂×C₄×C₂₅	1	4	yes	—
106	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
107	C₂×C₄	D₄×C₂₅	1	2	yes	—
108	C₂×C₄	D₄×C₂₅	1	2	yes	—
109	C₂×C₄	Q₈×C₂₅	1	4	yes	complemented
110	C₅	C₅×#391	1	1	yes	characteristic
111	C₂²	C₂²×C₄×C₂₅	1	1	yes	characteristic
112	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
113	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
114	C₂²	C₂×Q₈×C₂₅	1	2	yes	—
115	C₂²	#41×C₂₅	1	2	yes	—
116	C₄	—	2	4	no	—
117	C₄	—	2	4	no	—
118	C₄	—	4	2	no	—
119	C₄	C₂²⋊C₄×C₂₅	1	4	yes	—
120	C₂	C₂×C₂²⋊C₄×C₂₅	1	1	yes	characteristic
121	C₂	C₄×Q₈×C₂₅	1	2	yes	—
122	C₂	C₂₅×C₂²⋊Q₈	1	2	yes	—
123	C₂	C₂₅×#124	1	1	yes	characteristic
124	C₂	C₂₅×C₄⋊Q₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₈×C₂₅

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₂₅

C₂

yes

maximal, characteristic

C₂×C₄²×C₂₅

C₂

yes

maximal, characteristic

C₂₅×#95

C₂

yes

maximal

C₂×Q₈×C₂₅

—

C₂×Q₈×C₂₅

—

C₂×Q₈×C₂₅

C₄

yes

complemented

C₂²×C₄×C₂₅

C₂²

yes

—

C₂²×C₄×C₂₅

C₂²

yes

—

C₂²×C₄×C₂₅

C₂²

yes

—

C₂²×C₄×C₂₅

C₂²

yes

characteristic

C₄⋊C₄×C₂₅

—

C₄²×C₂₅

—

C₅×#391

C₅

yes

maximal, characteristic

C₂³×C₂₅

C₂³

yes

characteristic

Q₈×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

—

C₂×C₄×C₂₅

C₂×C₄

yes

—

C₂×C₄×C₂₅

C₂×C₄

yes

—

C₂×C₄×C₂₅

D₄

yes

—

C₂×C₄×C₂₅

D₄

yes

—

C₂×C₄×C₂₅

Q₈

yes

complemented

C₂²×C₅×Q₈

C₂×C₅

yes

characteristic

C₂×C₅×C₄⋊C₄

C₂×C₅

yes

characteristic

C₂×C₄²×C₅

C₂×C₅

yes

characteristic

C₅×#95

C₂×C₅

yes

—

C₂²×C₂₅

C₂²×C₄

yes

characteristic

C₂²×C₂₅

C₂×D₄

yes

characteristic

C₂²×C₂₅

C₂×D₄

yes

characteristic

C₂²×C₂₅

C₂×Q₈

yes

—

C₂²×C₂₅

#41

yes

—

C₄×C₂₅

—

C₄×C₂₅

—

C₄×C₂₅

—

C₄×C₂₅

C₂²⋊C₄

yes

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

C₄×C₅

yes

—

C₂²×C₄×C₅

C₂²×C₅

yes

—

C₂²×C₄×C₅

C₂²×C₅

yes

—

C₂²×C₄×C₅

C₂²×C₅

yes

—

C₂²×C₄×C₅

C₂²×C₅

yes

characteristic

C₅×C₄⋊C₄

—

C₄²×C₅

—

#391

C₂₅

yes

characteristic, direct product factor, Sylow

C₂×C₂₅

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₂₅

C₄×Q₈

yes

—

C₂×C₂₅

C₂²⋊Q₈

yes

—

C₂×C₂₅

#124

yes

characteristic

C₂×C₂₅

C₄⋊Q₈

yes

characteristic

C₂³×C₅

yes

characteristic

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

C₅×D₄

yes

—

C₂×C₄×C₅

C₅×D₄

yes

—

C₂×C₄×C₅

C₅×Q₈

yes

—

C₂²×Q₈

C₂×C₂₅

yes

characteristic

C₂×C₄⋊C₄

C₂×C₂₅

yes

characteristic

C₂×C₄²

C₂×C₂₅

yes

characteristic

#95

C₂×C₂₅

yes

—

C₂₅

#391

yes

characteristic, direct product factor, Sylow

C₂²×C₅

C₂²×C₄×C₅

yes

characteristic

C₂²×C₅

C₂×C₅×D₄

yes

characteristic

C₂²×C₅

C₂×C₅×D₄

yes

characteristic

C₂²×C₅

C₂×C₅×Q₈

yes

—

C₂²×C₅

C₅×#41

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₅×C₂²⋊C₄

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄×C₂₅

yes

complemented

C₂²×C₄

C₂²×C₂₅

yes

—

C₂²×C₄

C₂²×C₂₅

yes

—

C₂²×C₄

C₂²×C₂₅

yes

—

C₂²×C₄

C₂²×C₂₅

yes

characteristic

C₄⋊C₄

—

C₄²

—

C₂×C₅

C₂×C₅×C₂²⋊C₄

yes

characteristic

C₂×C₅

C₄×C₅×Q₈

yes

—

C₂×C₅

C₅×C₂²⋊Q₈

yes

—

C₂×C₅

C₅×#124

yes

characteristic

C₂×C₅

C₅×C₄⋊Q₈

yes

characteristic

C₂³

C₂³×C₂₅

yes

characteristic

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×C₄×C₂₅

yes

—

106

C₂×C₄

C₂×C₄×C₂₅

yes

—

107

C₂×C₄

D₄×C₂₅

yes

—

108

C₂×C₄

D₄×C₂₅

yes

—

109

C₂×C₄

Q₈×C₂₅

yes

complemented

110

C₅

C₅×#391

yes

characteristic

111

C₂²

C₂²×C₄×C₂₅

yes

characteristic

112

C₂²

C₂×D₄×C₂₅

yes

characteristic

113

C₂²

C₂×D₄×C₂₅

yes

characteristic

114

C₂²

C₂×Q₈×C₂₅

yes

—

115

C₂²

#41×C₂₅

yes

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

C₂²⋊C₄×C₂₅

yes

—

120

C₂

C₂×C₂²⋊C₄×C₂₅

yes

characteristic

121

C₂

C₄×Q₈×C₂₅

yes

—

122

C₂

C₂₅×C₂²⋊Q₈

yes

—

123

C₂

C₂₅×#124

yes

characteristic

124

C₂

C₂₅×C₄⋊Q₈

yes

characteristic

	subgroup	G/H
center	C₂³×C₂₅	C₂³
commutator	C₂²	C₂²×C₄×C₂₅
Frattini, socle, prime radical, cosocle	C₂³×C₅	C₂³×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₅ ◁ G

subgroup

G/H

center

C₂³×C₂₅

C₂³

commutator

C₂²

C₂²×C₄×C₂₅

Frattini, socle, prime radical, cosocle

C₂³×C₅

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₂₅ ◁ G

N	H ≅ G/N	type
7. C₂×Q₈×C₂₅	C₄	semidirect
27. C₂×C₄×C₂₅	Q₈	semidirect
50. #391	C₂₅	direct (N × H)
73. C₂₅	#391	direct (N × H)
85. C₂×Q₈	C₄×C₂₅	semidirect
109. C₂×C₄	Q₈×C₂₅	semidirect

H ≅ G/N

type

7. C₂×Q₈×C₂₅

C₄

semidirect

27. C₂×C₄×C₂₅

Q₈

semidirect

50. #391

C₂₅

direct (N × H)

73. C₂₅

#391

direct (N × H)

85. C₂×Q₈

C₄×C₂₅

semidirect

109. C₂×C₄

Q₈×C₂₅

semidirect

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

subgroup	index
C₂²×Q₈×C₂₅	2
C₂×C₄⋊C₄×C₂₅	2
C₂×C₄²×C₂₅	2
C₂₅×#95	2
C₅×#391	5

subgroup

index

C₂²×Q₈×C₂₅

C₂×C₄⋊C₄×C₂₅

C₂×C₄²×C₂₅

C₂₅×#95

C₅×#391

Subgroups — C₂₅×#391 #13098540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C25×#391 #13098540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#391 #13098540