Group #13120781 — subgroups

Subgroups — #13120781

Order 1664.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×#88124	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718883	C₂	1	8	yes	maximal, complemented
4	#11718882	C₂	1	4	yes	maximal, complemented
5	#11718593	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
7	C₂²×D₄×C₁₃	C₂²	1	4	yes	—
8	C₁₃×#127	—	2	4	no	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Dic₁₃	C₂²	1	16	yes	—
11	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
12	C₂×#6101	C₂²	1	4	yes	—
13	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
14	#88124	—	2	4	no	—
15	#88071	C₂²	1	4	yes	—
16	C₂⁴×C₁₃	C₂³	1	4	yes	—
17	C₂×D₄×C₁₃	—	2	8	no	—
18	C₂×D₄×C₁₃	—	2	4	no	—
19	C₂×D₄×C₁₃	—	2	8	no	—
20	C₂×D₄×C₁₃	—	4	8	no	—
21	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₃	C₂³	1	4	yes	—
24	C₂²×Dic₁₃	C₂³	1	4	yes	—
25	C₄²×C₁₃	D₄	1	4	yes	—
26	C₂²⋊Dic₁₃	—	4	16	no	—
27	C₄⋊Dic₁₃	—	2	4	no	—
28	#6101	—	2	8	no	—
29	C₄×Dic₁₃	—	2	4	no	—
30	#2641	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	—	2	4	no	—
32	C₂³×C₁₃	—	2	8	no	—
33	C₂³×C₁₃	—	2	16	no	—
34	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
35	D₄×C₁₃	—	4	16	no	—
36	D₄×C₁₃	—	4	8	no	—
37	C₂×C₄×C₁₃	—	2	4	no	—
38	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₁₃	#41	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	C₂×#127	D₁₃	1	1	yes	characteristic
46	C₂×#125	—	13	1	no	—
47	#394	—	13	8	no	—
48	#390	—	13	4	no	—
49	#376	—	13	1	no	—
50	C₂²×C₁₃	—	4	4	no	—
51	C₂²×C₁₃	—	4	8	no	—
52	C₂²×C₁₃	—	4	16	no	—
53	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
54	C₂²×C₁₃	C₂×#41	1	2	yes	—
55	C₂²×C₁₃	H(5,𝔽₂)	1	4	yes	—
56	C₄×C₁₃	—	2	4	no	—
57	C₄×C₁₃	#124	1	4	yes	—
58	Dic₁₃	—	4	4	no	—
59	Dic₁₃	—	4	4	no	—
60	C₂²×D₄	C₂×D₁₃	1	2	yes	—
61	C₂²×D₄	C₂×D₁₃	1	4	yes	—
62	#127	—	2	4	no	—
63	#125	—	26	4	no	—
64	C₂×C₄⋊C₄	—	13	4	no	—
65	C₂×C₄⋊C₄	—	13	2	no	—
66	C₂×C₂²⋊C₄	—	13	16	no	—
67	C₂×C₄²	—	13	2	no	—
68	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
69	#95	—	13	4	no	—
70	C₂×C₁₃	—	8	4	no	—
71	C₂×C₁₃	C₂×#124	1	1	yes	characteristic
72	C₂×C₁₃	#535	1	2	yes	—
73	C₂×C₁₃	#540	1	4	yes	—
74	C₂⁴	C₂²×D₁₃	1	4	yes	—
75	C₂×D₄	—	2	8	no	—
76	C₂×D₄	—	2	8	no	—
77	C₂×D₄	—	2	4	no	—
78	C₂×D₄	—	4	8	no	—
79	C₂²×C₄	—	13	4	no	—
80	C₂²×C₄	—	13	4	no	—
81	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
82	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
83	C₄⋊C₄	—	26	8	no	—
84	C₄⋊C₄	—	26	4	no	—
85	C₂²⋊C₄	—	52	16	no	—
86	C₄²	—	26	4	no	—
87	C₄²	C₂²⋊D₁₃	1	4	yes	—
88	C₁₃	#2641	1	1	yes	characteristic, complemented, Sylow
89	C₂³	—	2	8	no	—
90	C₂³	—	2	16	no	—
91	C₂³	—	2	4	no	—
92	C₂³	C₂³×D₁₃	1	1	yes	characteristic
93	D₄	—	4	16	no	—
94	D₄	—	4	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	26	4	no	—
97	C₂×C₄	—	26	8	no	—
98	C₂×C₄	—	26	8	no	—
99	C₂×C₄	—	26	4	no	—
100	C₂×C₄	#6129	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₁₃	1	4	yes	—
102	C₂×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
103	C₂²	—	4	16	no	—
104	C₂²	—	4	4	no	—
105	C₂²	—	4	8	no	—
106	C₂²	C₂×#6129	1	2	yes	—
107	C₂²	#88251	1	4	yes	—
108	C₂²	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
109	C₄	—	2	4	no	—
110	C₄	—	52	4	no	—
111	C₄	—	52	4	no	—
112	C₄	#88190	1	4	yes	—
113	C₂	—	8	4	no	—
114	C₂	#11719424	1	4	yes	—
115	C₂	C₂×#88190	1	1	yes	characteristic
116	C₂	#11719510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#127

C₂

yes

maximal, characteristic

C₂×#88124

C₂

yes

maximal, characteristic, complemented

#11718883

C₂

yes

maximal, complemented

#11718882

C₂

yes

maximal, complemented

#11718593

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₃

C₂²

yes

—

C₂²×D₄×C₁₃

C₂²

yes

—

C₁₃×#127

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

—

#88124

—

#88071

C₂²

yes

—

C₂⁴×C₁₃

C₂³

yes

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₄²×C₁₃

D₄

yes

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

—

#2641

—

maximal, Sylow

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂⁴

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×#127

D₁₃

yes

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²×D₄

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

H(5,𝔽₂)

yes

—

C₄×C₁₃

—

C₄×C₁₃

#124

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×D₄

C₂×D₁₃

yes

—

C₂²×D₄

C₂×D₁₃

yes

—

#127

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

#95

—

C₂×C₁₃

—

C₂×C₁₃

C₂×#124

yes

characteristic

C₂×C₁₃

#535

yes

—

C₂×C₁₃

#540

yes

—

C₂⁴

C₂²×D₁₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₃

yes

—

C₁₃

#2641

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₃

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

#6129

yes

—

101

C₂×C₄

C₂×C₂²⋊D₁₃

yes

—

102

C₂×C₄

C₂×C₂²⋊D₁₃

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×#6129

yes

—

107

C₂²

#88251

yes

—

108

C₂²

C₂²×C₂²⋊D₁₃

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

#88190

yes

—

113

C₂

—

114

C₂

#11719424

yes

—

115

C₂

C₂×#88190

yes

characteristic

116

C₂

#11719510

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting, prime radical	C₂×C₁₃×#127	C₂
hypercenter	C₂×#127	D₁₃
hypocenter	C₁₃	#2641
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#127

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, cosocle

C₂³×C₁₃

C₂⁴

Fitting, prime radical

C₂×C₁₃×#127

C₂

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ C₂×#127

N	H ≅ G/N	type
2. C₂×#88124	C₂	semidirect
3. #11718883	C₂	semidirect
4. #11718882	C₂	semidirect
5. #11718593	C₂	semidirect
88. C₁₃	#2641	semidirect

H ≅ G/N

type

2. C₂×#88124

C₂

semidirect

3. #11718883

C₂

semidirect

4. #11718882

C₂

semidirect

5. #11718593

C₂

semidirect

88. C₁₃

#2641

semidirect

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

subgroup	index
C₂×C₁₃×#127	2
C₂×#88124	2
#11718883	2
#11718882	2
#11718593	2
#2641	13

subgroup

index

C₂×C₁₃×#127

Subgroups — #13120781

Conjugacy classes of subgroups

Complements

Maximal subgroups