Group #13123400 — subgroups

Subgroups — #13123400

Order 1664.

484 conjugacy classes of subgroups; only the 293 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 293 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×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6099	C₂	1	2	yes	maximal
3	#11718660	C₂	1	8	yes	maximal, complemented
4	#11718585	C₂	1	4	yes	maximal, complemented
5	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#117	C₄	1	4	yes	—
7	C₁₃×#117	C₂²	1	4	yes	—
8	C₂×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
9	C₂×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
10	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
11	C₂×#6099	—	2	8	no	—
12	C₂×#6099	C₂²	1	4	yes	—
13	C₂×#6099	C₂²	1	4	yes	—
14	C₂²×#1055	C₂²	1	4	yes	—
15	C₄⋊#1055	C₂²	1	16	yes	complemented
16	C₂⁴×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₁₃	D₄	1	4	yes	—
21	C₂²×C₄×C₁₃	Q₈	1	4	yes	—
22	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
25	C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
26	C₄²×C₁₃	C₂×C₄	1	4	yes	—
27	C₄²×C₁₃	C₂³	1	4	yes	—
28	#6099	—	2	8	no	—
29	#6099	—	2	8	no	—
30	C₂×#1055	—	2	8	no	—
31	C₂×#1055	C₂³	1	8	yes	—
32	#2905	—	13	1	no	maximal, Sylow
33	C₂³×C₁₃	—	4	2	no	—
34	C₂³×C₁₃	C₄⋊C₄	1	4	yes	—
35	C₂³×C₁₃	C₂²×C₄	1	2	yes	—
36	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	—	4	4	no	—
38	C₂×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
39	C₂×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
40	C₂×C₄×C₁₃	C₂²×C₄	1	8	yes	—
41	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
46	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
48	#1055	—	2	8	no	—
49	C₂²×M₁₆	—	13	2	no	—
50	C₂×#117	D₁₃	1	1	yes	characteristic
51	#424	—	13	8	no	—
52	#423	—	13	4	no	—
53	C₂²×C₁₃	—	2	2	no	—
54	C₂²×C₁₃	—	2	4	no	—
55	C₂²×C₁₃	—	4	4	no	—
56	C₂²×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
57	C₂²×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
58	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
59	C₄×C₁₃	—	2	8	no	—
60	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
61	C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
62	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
63	C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
64	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
65	C₂×M₁₆	—	13	4	no	—
66	C₂×M₁₆	—	13	4	no	—
67	C₂×M₁₆	—	26	8	no	—
68	C₂²×C₈	—	13	4	no	—
69	#117	Dic₁₃	1	4	yes	—
70	#117	C₂×D₁₃	1	4	yes	—
71	C₂×C₄⋊C₄	Dic₁₃	1	2	yes	—
72	C₂×C₂²⋊C₄	Dic₁₃	1	2	yes	—
73	C₂×C₄²	C₂×D₁₃	1	2	yes	—
74	C₄⋊C₈	—	13	16	no	—
75	C₂×C₁₃	—	2	2	no	—
76	C₂×C₁₃	—	2	4	no	—
77	C₂×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₁₃	#568	1	2	yes	—
79	C₂⁴	C₂×Dic₁₃	1	1	yes	characteristic
80	C₂²×C₄	Dic₂₆	1	4	yes	—
81	C₂²×C₄	D₅₂	1	4	yes	—
82	C₂²×C₄	C₂×Dic₁₃	1	4	yes	—
83	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
84	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
85	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
86	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
87	M₁₆	—	26	8	no	—
88	M₁₆	—	26	8	no	—
89	C₂×C₈	—	13	8	no	—
90	C₂×C₈	—	26	8	no	—
91	C₄⋊C₄	C₂×Dic₁₃	1	8	yes	—
92	C₂²⋊C₄	C₂×Dic₁₃	1	8	yes	—
93	C₄²	C₂×Dic₁₃	1	4	yes	—
94	C₄²	C₂²×D₁₃	1	4	yes	—
95	C₁₃	#2905	1	1	yes	characteristic, complemented, Sylow
96	C₂³	—	4	2	no	—
97	C₂³	C₄⋊Dic₁₃	1	4	yes	—
98	C₂³	C₂²×Dic₁₃	1	2	yes	—
99	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
100	C₂×C₄	—	4	4	no	—
101	C₂×C₄	C₄⋊Dic₁₃	1	4	yes	—
102	C₂×C₄	C₄⋊Dic₁₃	1	8	yes	—
103	C₂×C₄	C₂×Dic₂₆	1	2	yes	—
104	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
105	C₂×C₄	C₂×D₅₂	1	4	yes	—
106	C₂×C₄	C₂×D₅₂	1	2	yes	—
107	C₂×C₄	C₂²×Dic₁₃	1	8	yes	—
108	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
109	C₂×C₄	C₂²×Dic₁₃	1	2	yes	—
110	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
111	C₈	—	26	8	no	—
112	C₂²	—	2	2	no	—
113	C₂²	—	2	4	no	—
114	C₂²	—	4	4	no	—
115	C₂²	C₂×C₄⋊Dic₁₃	1	4	yes	—
116	C₂²	C₂×C₄⋊Dic₁₃	1	2	yes	—
117	C₂²	C₂³×Dic₁₃	1	1	yes	characteristic
118	C₄	—	2	8	no	—
119	C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
120	C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
121	C₄	C₂²×Dic₂₆	1	1	yes	characteristic
122	C₄	C₂²×D₅₂	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	2	4	no	—
125	C₂	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
126	C₂	#11719524	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#117

C₂

yes

maximal, characteristic

C₂²×#6099

C₂

yes

maximal

#11718660

C₂

yes

maximal, complemented

#11718585

C₂

yes

maximal, complemented

C₂³×C₄×C₁₃

C₂²

yes

characteristic

C₁₃×#117

C₄

yes

—

C₁₃×#117

C₂²

yes

—

C₂×C₁₃×C₄⋊C₄

C₄

yes

—

C₂×C₁₃×C₂²⋊C₄

C₄

yes

—

C₂×C₄²×C₁₃

C₂²

yes

—

C₂×#6099

—

C₂×#6099

C₂²

yes

—

C₂×#6099

C₂²

yes

—

C₂²×#1055

C₂²

yes

—

C₄⋊#1055

C₂²

yes

complemented

C₂⁴×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

Q₈

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₁₃×C₂²⋊C₄

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

—

C₄²×C₁₃

C₂³

yes

—

—

—

—

C₂³

yes

—

#2905

—

maximal, Sylow

C₂³×C₁₃

—

C₂³×C₁₃

C₄⋊C₄

yes

—

C₂³×C₁₃

C₂²×C₄

yes

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

C₂⁴

yes

characteristic

#1055

—

C₂²×M₁₆

—

C₂×#117

D₁₃

yes

characteristic

#424

—

#423

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

—

C₂²×C₁₃

C₂³×C₄

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₄×C₁₃

C₂²×D₄

yes

characteristic

C₄×C₁₃

C₂²×Q₈

yes

characteristic

C₂³×C₄

C₂×D₁₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

Dic₁₃

yes

—

#117

C₂×D₁₃

yes

—

C₂×C₄⋊C₄

Dic₁₃

yes

—

C₂×C₂²⋊C₄

Dic₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

—

C₄⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₁₃

#568

yes

—

C₂⁴

C₂×Dic₁₃

yes

characteristic

C₂²×C₄

Dic₂₆

yes

—

C₂²×C₄

D₅₂

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

C₂²×C₄

C₂×Dic₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₁₃

yes

—

C₂²⋊C₄

C₂×Dic₁₃

yes

—

C₄²

C₂×Dic₁₃

yes

—

C₄²

C₂²×D₁₃

yes

—

C₁₃

#2905

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

C₄⋊Dic₁₃

yes

—

C₂³

C₂²×Dic₁₃

yes

—

C₂³

C₂²×Dic₁₃

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

C₄⋊Dic₁₃

yes

—

102

C₂×C₄

C₄⋊Dic₁₃

yes

—

103

C₂×C₄

C₂×Dic₂₆

yes

—

104

C₂×C₄

C₂×Dic₂₆

yes

—

105

C₂×C₄

C₂×D₅₂

yes

—

106

C₂×C₄

C₂×D₅₂

yes

—

107

C₂×C₄

C₂²×Dic₁₃

yes

—

108

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

109

C₂×C₄

C₂²×Dic₁₃

yes

—

110

C₂×C₄

C₂³×D₁₃

yes

characteristic

111

C₈

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂×C₄⋊Dic₁₃

yes

—

116

C₂²

C₂×C₄⋊Dic₁₃

yes

—

117

C₂²

C₂³×Dic₁₃

yes

characteristic

118

C₄

—

119

C₄

C₂×C₄⋊Dic₁₃

yes

—

120

C₄

C₂×C₄⋊Dic₁₃

yes

—

121

C₄

C₂²×Dic₂₆

yes

characteristic

122

C₄

C₂²×D₅₂

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

C₂²×C₄⋊Dic₁₃

yes

characteristic

126

C₂

#11719524

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₄
Fitting	C₂×C₁₃×#117	C₂
prime radical	C₂⁴×C₁₃	C₂×C₄
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	C₂×#117	D₁₃
hypocenter	C₁₃	#2905
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₃

commutator, socle

C₂²×C₁₃

C₂³×C₄

Fitting

C₂×C₁₃×#117

C₂

prime radical

C₂⁴×C₁₃

C₂×C₄

cosocle

C₂×C₄×C₁₃

C₂⁴

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ C₂×#117

N	H ≅ G/N	type
3. #11718660	C₂	semidirect
4. #11718585	C₂	semidirect
15. C₄⋊#1055	C₂²	semidirect
95. C₁₃	#2905	semidirect

H ≅ G/N

type

3. #11718660

C₂

semidirect

4. #11718585

C₂

semidirect

15. C₄⋊#1055

C₂²

semidirect

95. C₁₃

#2905

semidirect

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

subgroup	index
C₂×C₁₃×#117	2
C₂²×#6099	2
#11718660	2
#11718585	2
#2905	13

subgroup

index

C₂×C₁₃×#117

C₂²×#6099

#11718660

#11718585

#2905

Subgroups — #13123400

Conjugacy classes of subgroups

Complements

Maximal subgroups