Group #13120786 — subgroups

Subgroups — #13120786

Order 1664.

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

normal subgroups only

This group has 416 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×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#88124	C₂	1	1	yes	maximal, characteristic
3	#11718891	C₂	1	4	yes	maximal
4	#11718643	C₂	1	8	yes	maximal
5	#11718593	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
7	C₁₃×C₄⋊Q₈	—	2	4	no	—
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×#6101	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
13	#88124	—	2	4	no	—
14	#88071	C₂²	1	4	yes	—
15	#88071	C₂²	1	16	yes	—
16	C₂×Q₈×C₁₃	—	2	4	no	—
17	C₂×Q₈×C₁₃	—	2	8	no	—
18	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
19	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₃	C₂³	1	4	yes	—
22	C₂²×Dic₁₃	C₂³	1	4	yes	—
23	C₁₃×C₄⋊C₄	—	2	8	no	—
24	C₄²×C₁₃	D₄	1	4	yes	—
25	C₄⋊Dic₁₃	—	2	4	no	—
26	#6101	—	2	8	no	—
27	C₄×Dic₁₃	—	2	4	no	—
28	#2642	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
30	Q₈×C₁₃	—	4	8	no	—
31	C₂×C₄×C₁₃	—	2	4	no	—
32	C₂×C₄×C₁₃	—	2	4	no	—
33	C₂×C₄×C₁₃	—	2	8	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
35	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₁₃	#41	1	4	yes	—
37	C₂×Dic₁₃	—	2	4	no	—
38	C₂×Dic₁₃	—	2	4	no	—
39	C₂×Dic₁₃	—	2	8	no	—
40	C₂×Dic₁₃	—	2	8	no	—
41	C₂×C₄⋊Q₈	D₁₃	1	1	yes	characteristic
42	C₂×#125	—	13	1	no	—
43	#400	—	13	8	no	—
44	#391	—	13	4	no	—
45	#376	—	13	1	no	—
46	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
47	C₂²×C₁₃	C₂×#41	1	2	yes	—
48	C₂²×C₁₃	2₋¹⁺⁴	1	4	yes	—
49	C₄×C₁₃	—	2	4	no	—
50	C₄×C₁₃	—	4	4	no	—
51	C₄×C₁₃	#124	1	4	yes	—
52	Dic₁₃	—	4	4	no	—
53	Dic₁₃	—	4	4	no	—
54	C₂²×Q₈	C₂×D₁₃	1	2	yes	—
55	C₄⋊Q₈	—	2	4	no	—
56	#125	—	26	4	no	—
57	C₂×C₄⋊C₄	—	13	4	no	—
58	C₂×C₄⋊C₄	—	13	2	no	—
59	C₂×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
60	C₂×C₄²	—	13	2	no	—
61	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
62	#95	—	13	4	no	—
63	#95	—	13	16	no	—
64	C₂×C₁₃	C₂×#124	1	1	yes	characteristic
65	C₂×C₁₃	#536	1	2	yes	—
66	C₂×C₁₃	#541	1	4	yes	—
67	C₂×Q₈	—	2	8	no	—
68	C₂×Q₈	—	2	4	no	—
69	C₂²×C₄	—	13	4	no	—
70	C₂²×C₄	—	13	4	no	—
71	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
72	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
73	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
74	C₄⋊C₄	—	2	8	no	—
75	C₄⋊C₄	—	26	8	no	—
76	C₄⋊C₄	—	26	4	no	—
77	C₄²	—	26	4	no	—
78	C₄²	C₂²⋊D₁₃	1	4	yes	—
79	C₁₃	#2642	1	1	yes	characteristic, complemented, Sylow
80	C₂³	C₂³×D₁₃	1	1	yes	characteristic
81	Q₈	—	4	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	8	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	26	4	no	—
86	C₂×C₄	—	26	8	no	—
87	C₂×C₄	—	26	8	no	—
88	C₂×C₄	—	26	4	no	—
89	C₂×C₄	#6129	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₁₃	1	4	yes	—
91	C₂×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
92	C₂²	C₂×#6129	1	2	yes	—
93	C₂²	#88254	1	4	yes	—
94	C₂²	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	52	4	no	—
98	C₄	—	52	4	no	—
99	C₄	#88190	1	4	yes	—
100	C₂	#11719436	1	4	yes	—
101	C₂	C₂×#88190	1	1	yes	characteristic
102	C₂	#11719521	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×#88124

C₂

yes

maximal, characteristic

#11718891

C₂

yes

maximal

#11718643

C₂

yes

maximal

#11718593

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₃

C₂²

yes

—

C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

—

#88124

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

D₄

yes

—

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

—

#2642

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×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×C₄⋊Q₈

D₁₃

yes

—

—

—

—

C₂²×C₁₃

C₂²×D₄

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#124

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

C₂×D₁₃

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

#95

—

#95

—

C₂×C₁₃

C₂×#124

yes

characteristic

C₂×C₁₃

#536

yes

—

C₂×C₁₃

#541

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₃

yes

—

C₁₃

#2642

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#6129

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

—

C₂²

C₂×#6129

yes

—

C₂²

#88254

yes

—

C₂²

C₂²×C₂²⋊D₁₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#88190

yes

—

100

C₂

#11719436

yes

—

101

C₂

C₂×#88190

yes

characteristic

102

C₂

#11719521

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₂×C₁₃×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₁₃
hypocenter	C₁₃	#2642
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₂×C₁₃×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
79. C₁₃	#2642	semidirect

H ≅ G/N

type

79. C₁₃

#2642

semidirect

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

subgroup	index
C₂×C₁₃×C₄⋊Q₈	2
C₂×#88124	2
#11718891	2
#11718643	2
#11718593	2
#2642	13

subgroup

index

C₂×C₁₃×C₄⋊Q₈

Subgroups — #13120786

Conjugacy classes of subgroups

Complements

Maximal subgroups