Group #13128984 — subgroups

Subgroups — #13128984

Order 1664.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	C₁₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719405	C₂	1	5	yes	maximal, complemented
3	#11719404	C₂	1	10	yes	maximal, complemented
4	#11719396	C₂	1	10	yes	maximal, complemented
5	#11719393	C₂	1	5	yes	maximal, complemented
6	C₁₃×#125	C₂²	1	5	yes	—
7	C₁₃×#125	C₂²	1	10	yes	—
8	#88152	C₂²	1	20	yes	—
9	#88151	C₂²	1	10	yes	—
10	#88150	C₂²	1	20	yes	—
11	#88149	C₂²	1	10	yes	—
12	#88148	C₂²	1	20	yes	—
13	#88147	C₂²	1	10	yes	—
14	#88146	C₂²	1	10	yes	—
15	#88142	C₂²	1	10	yes	—
16	#88141	C₂²	1	10	yes	—
17	#88129	C₂²	1	10	yes	—
18	C₄²×D₁₃	C₂²	1	5	yes	—
19	#88124	C₂²	1	5	yes	—
20	C₂×D₅₂	C₂³	1	10	yes	—
21	C₂×C₄×D₁₃	C₂³	1	5	yes	—
22	C₂×C₄×D₁₃	C₂³	1	10	yes	—
23	C₂×Dic₂₆	C₂³	1	10	yes	—
24	C₁₃×C₄⋊C₄	C₂³	1	10	yes	—
25	C₁₃×C₄⋊C₄	C₂³	1	10	yes	—
26	C₁₃×C₄⋊C₄	C₂³	1	10	yes	—
27	C₄²×C₁₃	C₂³	1	5	yes	—
28	#6103	C₂³	1	20	yes	—
29	#6103	C₂³	1	20	yes	—
30	C₄⋊Dic₁₃	C₂³	1	10	yes	—
31	#6101	C₂³	1	20	yes	—
32	C₄×Dic₁₃	C₂³	1	10	yes	—
33	C₄×Dic₁₃	C₂³	1	5	yes	—
34	#3531	—	13	1	no	maximal, Sylow
35	C₂²×D₁₃	C₂⁴	1	5	yes	—
36	C₂×C₄×C₁₃	C₂⁴	1	10	yes	—
37	C₂×C₄×C₁₃	C₂⁴	1	5	yes	—
38	C₂×Dic₁₃	C₂⁴	1	10	yes	—
39	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
40	D₅₂	—	4	10	no	—
41	C₄×D₁₃	—	2	10	no	—
42	C₄×D₁₃	—	4	10	no	—
43	Dic₂₆	—	4	10	no	—
44	#564	D₁₃	1	1	yes	characteristic, complemented
45	#563	—	13	10	no	—
46	#562	—	13	5	no	—
47	#533	—	13	5	no	—
48	#529	—	13	10	no	—
49	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
50	C₂×D₁₃	—	2	5	no	—
51	C₂×D₁₃	—	2	10	no	—
52	C₄×C₁₃	—	2	5	no	—
53	C₄×C₁₃	—	2	10	no	—
54	Dic₁₃	—	2	10	no	—
55	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
56	C₄⋊Q₈	—	13	10	no	—
57	#126	—	13	20	no	—
58	#125	—	13	5	no	—
59	#125	C₂×D₁₃	1	10	yes	—
60	#125	C₂×D₁₃	1	5	yes	—
61	#124	—	13	10	no	—
62	#123	—	13	20	no	—
63	C₂²⋊Q₈	—	13	10	no	—
64	C₂²⋊Q₈	—	13	20	no	—
65	#121	—	13	10	no	—
66	C₄×Q₈	—	13	10	no	—
67	C₄×D₄	—	13	10	no	—
68	#117	—	13	10	no	—
69	C₂×C₄²	—	13	5	no	—
70	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
71	C₂×C₁₃	#585	1	2	yes	—
72	D₁₃	—	4	5	no	—
73	C₂×Q₈	—	13	10	no	—
74	C₂×D₄	—	13	10	no	—
75	C₂²×C₄	—	13	5	no	—
76	C₂²×C₄	—	13	10	no	—
77	C₄⋊C₄	—	13	10	no	—
78	C₄⋊C₄	—	13	20	no	—
79	C₄⋊C₄	C₂²×D₁₃	1	10	yes	—
80	C₄⋊C₄	C₂²×D₁₃	1	10	yes	—
81	C₄⋊C₄	C₂²×D₁₃	1	10	yes	—
82	C₂²⋊C₄	—	13	20	no	—
83	C₂²⋊C₄	—	13	20	no	—
84	C₄²	—	13	10	no	—
85	C₄²	—	13	5	no	—
86	C₄²	C₂²×D₁₃	1	5	yes	—
87	C₁₃	#3531	1	1	yes	characteristic, complemented, Sylow
88	C₂³	—	13	5	no	—
89	Q₈	—	52	10	no	—
90	D₄	—	52	10	no	—
91	C₂×C₄	—	13	1	no	—
92	C₂×C₄	—	13	10	no	—
93	C₂×C₄	—	26	10	no	—
94	C₂×C₄	—	52	10	no	—
95	C₂×C₄	C₂³×D₁₃	1	5	yes	—
96	C₂×C₄	C₂³×D₁₃	1	10	yes	—
97	C₂²	—	26	5	no	—
98	C₂²	—	26	10	no	—
99	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
100	C₄	—	2	5	no	—
101	C₄	—	2	10	no	—
102	C₄	—	13	2	no	—
103	C₄	—	26	10	no	—
104	C₂	—	52	5	no	—
105	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic
106	C₂	#11719652	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#564

C₂

yes

maximal, characteristic, complemented

#11719405

C₂

yes

maximal, complemented

#11719404

C₂

yes

maximal, complemented

#11719396

C₂

yes

maximal, complemented

#11719393

C₂

yes

maximal, complemented

C₁₃×#125

C₂²

yes

—

C₁₃×#125

C₂²

yes

—

#88152

C₂²

yes

—

#88151

C₂²

yes

—

#88150

C₂²

yes

—

#88149

C₂²

yes

—

#88148

C₂²

yes

—

#88147

C₂²

yes

—

#88146

C₂²

yes

—

#88142

C₂²

yes

—

#88141

C₂²

yes

—

#88129

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

—

#88124

C₂²

yes

—

C₂×D₅₂

C₂³

yes

—

C₂×C₄×D₁₃

C₂³

yes

—

C₂×C₄×D₁₃

C₂³

yes

—

C₂×Dic₂₆

C₂³

yes

—

C₁₃×C₄⋊C₄

C₂³

yes

—

C₁₃×C₄⋊C₄

C₂³

yes

—

C₁₃×C₄⋊C₄

C₂³

yes

—

C₄²×C₁₃

C₂³

yes

—

#6103

C₂³

yes

—

#6103

C₂³

yes

—

C₄⋊Dic₁₃

C₂³

yes

—

#6101

C₂³

yes

—

C₄×Dic₁₃

C₂³

yes

—

C₄×Dic₁₃

C₂³

yes

—

#3531

—

maximal, Sylow

C₂²×D₁₃

C₂⁴

yes

—

C₂×C₄×C₁₃

C₂⁴

yes

—

C₂×C₄×C₁₃

C₂⁴

yes

—

C₂×Dic₁₃

C₂⁴

yes

—

C₂×Dic₁₃

C₂⁴

yes

characteristic

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

#564

D₁₃

yes

characteristic, complemented

—

—

—

—

C₂²×C₁₃

C₂⁵

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

2₋¹⁺⁴

yes

—

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₁₃

yes

—

#125

C₂×D₁₃

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂×C₁₃

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₁₃

#585

yes

—

D₁₃

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₁₃

yes

—

C₄⋊C₄

C₂²×D₁₃

yes

—

C₄⋊C₄

C₂²×D₁₃

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₁₃

yes

—

C₁₃

#3531

yes

characteristic, complemented, Sylow

C₂³

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂³×D₁₃

yes

—

C₂×C₄

C₂³×D₁₃

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₁₃

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₂

—

105

C₂

D₁₃×2₋¹⁺⁴

yes

characteristic

106

C₂

#11719652

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#564	C₂
hypercenter	#564	D₁₃
hypocenter	C₁₃	#3531
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₁₃

commutator, socle, cosocle

C₂²×C₁₃

C₂⁵

Fitting

C₁₃×#564

C₂

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. C₁₃×#564	C₂	semidirect
2. #11719405	C₂	semidirect
3. #11719404	C₂	semidirect
4. #11719396	C₂	semidirect
5. #11719393	C₂	semidirect
44. #564	D₁₃	semidirect
87. C₁₃	#3531	semidirect

H ≅ G/N

type

1. C₁₃×#564

C₂

semidirect

2. #11719405

C₂

semidirect

3. #11719404

C₂

semidirect

4. #11719396

C₂

semidirect

5. #11719393

C₂

semidirect

44. #564

D₁₃

semidirect

87. C₁₃

#3531

semidirect

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

subgroup	index
C₁₃×#564	2
#11719405	2
#11719404	2
#11719396	2
#11719393	2
#3531	13

subgroup

index

C₁₃×#564

Subgroups — #13128984

Conjugacy classes of subgroups

Complements

Maximal subgroups