Group #13122873 — subgroups

Subgroups — #13122873

Order 1664.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88178	C₂	1	2	yes	maximal
2	C₁₃×#381	C₂	1	1	yes	maximal, characteristic
3	#11718614	C₂	1	4	yes	maximal
4	#11718320	C₂	1	4	yes	maximal, complemented
5	#11718317	C₂	1	4	yes	maximal, complemented
6	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₆	C₂²	1	2	yes	—
8	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₁₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
12	#88178	—	2	8	no	—
13	C₂×#6101	C₂²	1	4	yes	—
14	C₁₃×#95	C₂²	1	4	yes	—
15	#88071	C₂²	1	8	yes	—
16	#88071	C₂²	1	4	yes	—
17	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₃	—	4	2	no	—
19	C₂²×C₄×C₁₃	D₄	1	4	yes	—
20	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
21	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
22	C₂²×Dic₁₃	C₂³	1	4	yes	—
23	C₂²×Dic₁₃	C₂³	1	4	yes	—
24	C₂×Dic₂₆	—	2	4	no	—
25	C₂×Dic₂₆	—	4	4	no	—
26	C₁₃×C₂²⋊C₄	—	4	2	no	—
27	C₂²⋊Dic₁₃	—	2	8	no	—
28	C₄⋊Dic₁₃	—	2	4	no	—
29	C₄⋊Dic₁₃	—	4	4	no	—
30	#6101	—	2	8	no	—
31	#2817	—	13	1	no	maximal, Sylow
32	C₂³×C₁₃	—	2	2	no	—
33	C₂³×C₁₃	—	2	4	no	—
34	C₂³×C₁₃	C₂×D₄	1	2	yes	—
35	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₁₃	—	2	4	no	—
37	C₂×C₄×C₁₃	—	2	4	no	—
38	C₂×C₄×C₁₃	—	2	8	no	—
39	C₂×C₄×C₁₃	—	4	4	no	—
40	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
41	C₂×Dic₁₃	—	2	4	no	—
42	C₂×Dic₁₃	—	2	4	no	—
43	C₂×Dic₁₃	—	2	8	no	—
44	C₂×Dic₁₃	—	2	8	no	—
45	Dic₂₆	—	4	8	no	—
46	C₂×C₂²⋊Q₈	—	13	2	no	—
47	#400	—	13	4	no	—
48	#397	—	13	4	no	—
49	#395	—	13	4	no	—
50	#381	D₁₃	1	1	yes	characteristic
51	C₂²×C₁₃	—	2	2	no	—
52	C₂²×C₁₃	—	2	4	no	—
53	C₂²×C₁₃	—	4	4	no	—
54	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
55	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
56	C₂²×C₁₃	2₋¹⁺⁴	1	4	yes	—
57	C₄×C₁₃	—	2	4	no	—
58	C₄×C₁₃	—	4	4	no	—
59	Dic₁₃	—	4	4	no	—
60	Dic₁₃	—	4	4	no	—
61	C₂²×Q₈	—	13	2	no	—
62	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
63	C₂²⋊Q₈	—	26	8	no	—
64	C₂×C₄⋊C₄	—	13	4	no	—
65	C₂×C₄⋊C₄	—	13	2	no	—
66	C₂×C₄⋊C₄	—	13	4	no	—
67	C₂×C₂²⋊C₄	—	13	4	no	—
68	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
69	#95	—	13	8	no	—
70	#95	—	13	4	no	—
71	#95	C₂×D₁₃	1	4	yes	—
72	C₂×C₁₃	—	4	2	no	—
73	C₂×C₁₃	#534	1	1	yes	characteristic
74	C₂×C₁₃	#536	1	2	yes	—
75	C₂×C₁₃	#563	1	4	yes	—
76	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
77	C₂×Q₈	—	26	4	no	—
78	C₂×Q₈	—	52	4	no	—
79	C₂²×C₄	—	4	2	no	—
80	C₂²×C₄	—	13	4	no	—
81	C₂²×C₄	—	13	4	no	—
82	C₂²×C₄	D₅₂	1	4	yes	—
83	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
84	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
85	C₄⋊C₄	—	26	8	no	—
86	C₄⋊C₄	—	26	4	no	—
87	C₄⋊C₄	—	52	4	no	—
88	C₂²⋊C₄	—	4	2	no	—
89	C₂²⋊C₄	—	26	8	no	—
90	C₁₃	#2817	1	1	yes	characteristic, complemented, Sylow
91	C₂³	—	2	2	no	—
92	C₂³	—	2	4	no	—
93	C₂³	C₂×D₅₂	1	2	yes	—
94	C₂³	C₂³×D₁₃	1	1	yes	characteristic
95	Q₈	—	52	8	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	2	8	no	—
99	C₂×C₄	—	4	4	no	—
100	C₂×C₄	—	26	4	no	—
101	C₂×C₄	—	26	4	no	—
102	C₂×C₄	—	26	8	no	—
103	C₂×C₄	—	26	8	no	—
104	C₂×C₄	C₂×D₅₂	1	4	yes	—
105	C₂²	—	2	2	no	—
106	C₂²	—	2	4	no	—
107	C₂²	—	4	4	no	—
108	C₂²	C₂²×D₅₂	1	1	yes	characteristic
109	C₂²	#88251	1	2	yes	—
110	C₂²	#88257	1	4	yes	—
111	C₄	—	2	4	no	—
112	C₄	—	4	4	no	—
113	C₄	—	52	4	no	—
114	C₄	—	52	4	no	—
115	C₂	—	4	2	no	—
116	C₂	#11719198	1	1	yes	characteristic
117	C₂	#11719231	1	2	yes	—
118	C₂	#11719356	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88178

C₂

yes

maximal

C₁₃×#381

C₂

yes

maximal, characteristic

#11718614

C₂

yes

maximal

#11718320

C₂

yes

maximal, complemented

#11718317

C₂

yes

maximal, complemented

C₂³×C₄×C₁₃

C₂²

yes

characteristic

C₂²×Dic₂₆

C₂²

yes

—

C₂×C₁₃×C₂²⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

#88178

—

C₂×#6101

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂⁴×C₁₃

C₂³

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₁₃×C₂²⋊C₄

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

#2817

—

maximal, Sylow

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×D₄

yes

—

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

C₂×C₂²⋊Q₈

—

—

—

—

D₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²×D₄

yes

characteristic

C₂²×C₁₃

H(5,𝔽₂)

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

—

C₂³×C₄

C₂×D₁₃

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₃

yes

—

#95

—

#95

—

#95

C₂×D₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

#534

yes

characteristic

C₂×C₁₃

#536

yes

—

C₂×C₁₃

#563

yes

—

C₂⁴

C₂²×D₁₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₅₂

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₁₃

#2817

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

C₂×D₅₂

yes

—

C₂³

C₂³×D₁₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×D₅₂

yes

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂²×D₅₂

yes

characteristic

109

C₂²

#88251

yes

—

110

C₂²

#88257

yes

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₂

—

116

C₂

#11719198

yes

characteristic

117

C₂

#11719231

yes

—

118

C₂

#11719356

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#381	C₂
prime radical	C₂⁴×C₁₃	C₂³
hypercenter	#381	D₁₃
hypocenter	C₁₃	#2817
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#381

C₂

prime radical

C₂⁴×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
4. #11718320	C₂	semidirect
5. #11718317	C₂	semidirect
90. C₁₃	#2817	semidirect

H ≅ G/N

type

4. #11718320

C₂

semidirect

5. #11718317

C₂

semidirect

90. C₁₃

#2817

semidirect

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

subgroup	index
C₂×#88178	2
C₁₃×#381	2
#11718614	2
#11718320	2
#11718317	2
#2817	13

subgroup

index

C₁₃×#381

Subgroups — #13122873

Conjugacy classes of subgroups

Complements

Maximal subgroups