Group #13120796 — subgroups

Subgroups — #13120796

Order 1664.

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

normal subgroups only

This group has 420 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	C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718600	C₂	1	3	yes	maximal
3	#11718589	C₂	1	3	yes	maximal, complemented
4	#11718337	C₂	1	2	yes	maximal, complemented
5	#11718336	C₂	1	6	yes	maximal, complemented
6	C₂²×D₅₂	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
8	C₂×#6103	C₂²	1	6	yes	—
9	C₂×#6103	C₂²	1	6	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	3	yes	—
11	C₂×#6101	C₂²	1	6	yes	—
12	C₁₃×#95	C₂²	1	3	yes	—
13	C₁₃×#95	C₂²	1	1	yes	characteristic
14	#88071	C₂²	1	6	yes	—
15	C₂³×D₁₃	C₂³	1	2	yes	—
16	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₃	C₂³	1	6	yes	—
20	C₂×D₅₂	—	2	6	no	—
21	C₄²×C₁₃	—	2	6	no	—
22	#6103	—	4	6	no	—
23	#6103	—	4	6	no	—
24	C₄⋊Dic₁₃	—	2	6	no	—
25	#6101	—	4	6	no	—
26	#2644	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
28	C₂²×D₁₃	—	2	6	no	—
29	C₂²×D₁₃	—	2	6	no	—
30	C₂²×D₁₃	—	2	2	no	—
31	C₂×C₄×C₁₃	—	2	3	no	—
32	C₂×C₄×C₁₃	—	2	3	no	—
33	C₂×C₄×C₁₃	—	2	3	no	—
34	C₂×C₄×C₁₃	—	2	3	no	—
35	C₂×C₄×C₁₃	—	2	3	no	—
36	C₂×C₄×C₁₃	—	2	3	no	—
37	C₂×C₄×C₁₃	#41	1	6	yes	—
38	C₂×Dic₁₃	—	2	6	no	—
39	C₂×Dic₁₃	—	2	6	no	—
40	C₂×Dic₁₃	—	2	6	no	—
41	D₅₂	—	4	4	no	—
42	#397	—	13	6	no	—
43	#396	—	13	2	no	—
44	#390	—	13	3	no	—
45	#389	—	13	3	no	—
46	#376	D₁₃	1	1	yes	characteristic, complemented
47	C₂²×C₁₃	C₂×#41	1	3	yes	—
48	C₂²×C₁₃	H(5,𝔽₂)	1	3	yes	—
49	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
50	C₂×D₁₃	—	4	2	no	—
51	C₂×D₁₃	—	4	6	no	—
52	C₂×D₁₃	—	4	6	no	—
53	C₄×C₁₃	—	4	3	no	—
54	C₄×C₁₃	—	4	3	no	—
55	C₄×C₁₃	#126	1	4	yes	—
56	Dic₁₃	—	4	6	no	—
57	C₂²×D₄	—	13	1	no	—
58	C₂×C₄⋊C₄	—	13	3	no	—
59	C₂×C₄⋊C₄	—	13	6	no	—
60	C₂×C₂²⋊C₄	—	13	6	no	—
61	C₂×C₂²⋊C₄	—	13	6	no	—
62	C₂×C₄²	C₂×D₁₃	1	3	yes	—
63	#95	—	13	6	no	—
64	#95	C₂×D₁₃	1	1	yes	characteristic
65	#95	C₂×D₁₃	1	3	yes	—
66	C₂×C₁₃	C₂×#126	1	1	yes	characteristic
67	C₂×C₁₃	#540	1	3	yes	—
68	C₂×C₁₃	#542	1	3	yes	—
69	D₁₃	—	8	2	no	—
70	C₂⁴	—	13	2	no	—
71	C₂×D₄	—	26	6	no	—
72	C₂²×C₄	—	13	6	no	—
73	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
74	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
75	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
76	C₄⋊C₄	—	26	6	no	—
77	C₄⋊C₄	—	52	6	no	—
78	C₂²⋊C₄	—	52	6	no	—
79	C₂²⋊C₄	—	52	6	no	—
80	C₄²	—	2	6	no	—
81	C₁₃	#2644	1	1	yes	characteristic, complemented, Sylow
82	C₂³	—	26	6	no	—
83	C₂³	—	26	6	no	—
84	C₂³	—	26	2	no	—
85	C₂³	C₂³×D₁₃	1	1	yes	characteristic
86	D₄	—	52	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	26	6	no	—
94	C₂×C₄	—	26	6	no	—
95	C₂×C₄	—	26	6	no	—
96	C₂×C₄	#6127	1	6	yes	—
97	C₂²	—	52	2	no	—
98	C₂²	—	52	6	no	—
99	C₂²	—	52	6	no	—
100	C₂²	C₂×#6127	1	3	yes	—
101	C₂²	#88256	1	3	yes	—
102	C₂²	#88257	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	52	6	no	—
106	C₄	#88130	1	4	yes	—
107	C₂	—	104	2	no	—
108	C₂	C₂×#88130	1	1	yes	characteristic
109	C₂	#11719239	1	3	yes	—
110	C₂	#11719240	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#376

C₂

yes

maximal, characteristic, complemented

#11718600

C₂

yes

maximal

#11718589

C₂

yes

maximal, complemented

#11718337

C₂

yes

maximal, complemented

#11718336

C₂

yes

maximal, complemented

C₂²×D₅₂

C₂²

yes

characteristic

C₂×C₄²×C₁₃

C₂²

yes

—

C₂×#6103

C₂²

yes

—

C₂×#6103

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

C₁₃×#95

C₂²

yes

characteristic

#88071

C₂²

yes

—

C₂³×D₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂×D₅₂

—

C₄²×C₁₃

—

#6103

—

#6103

—

C₄⋊Dic₁₃

—

#6101

—

#2644

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

—

—

—

—

D₁₃

yes

characteristic, complemented

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

H(5,𝔽₂)

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#126

yes

—

Dic₁₃

—

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₃

yes

—

#95

—

#95

C₂×D₁₃

yes

characteristic

#95

C₂×D₁₃

yes

—

C₂×C₁₃

C₂×#126

yes

characteristic

C₂×C₁₃

#540

yes

—

C₂×C₁₃

#542

yes

—

D₁₃

—

C₂⁴

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₃

#2644

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₃

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#6127

yes

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#6127

yes

—

101

C₂²

#88256

yes

—

102

C₂²

#88257

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

#88130

yes

—

107

C₂

—

104

—

108

C₂

C₂×#88130

yes

characteristic

109

C₂

#11719239

yes

—

110

C₂

#11719240

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#376	C₂
prime radical	C₂²×D₅₂	C₂²
hypercenter	#376	D₁₃
hypocenter	C₁₃	#2644
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#376

C₂

prime radical

C₂²×D₅₂

C₂²

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. C₁₃×#376	C₂	semidirect
3. #11718589	C₂	semidirect
4. #11718337	C₂	semidirect
5. #11718336	C₂	semidirect
46. #376	D₁₃	semidirect
81. C₁₃	#2644	semidirect

H ≅ G/N

type

1. C₁₃×#376

C₂

semidirect

3. #11718589

C₂

semidirect

4. #11718337

C₂

semidirect

5. #11718336

C₂

semidirect

46. #376

D₁₃

semidirect

81. C₁₃

#2644

semidirect

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

subgroup	index
C₁₃×#376	2
#11718600	2
#11718589	2
#11718337	2
#11718336	2
#2644	13

subgroup

index

C₁₃×#376

Subgroups — #13120796

Conjugacy classes of subgroups

Complements

Maximal subgroups