Group #15756632 — subgroups

Subgroups — #15756632

Order 3328.

220 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 99 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	#13113599	C₂	1	2	yes	maximal
2	#13112698	C₂	1	4	yes	maximal
3	C₁₃×#1452	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#431	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	#11718587	C₂²	1	4	yes	—
7	C₁₃×#322	C₄	1	4	yes	—
8	#11718050	—	2	2	no	—
9	#11718049	—	2	2	no	—
10	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
11	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
12	C₁₃×C₄⋊C₈	—	2	2	no	—
13	C₁₃×C₂²⋊C₈	—	2	2	no	—
14	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
15	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²⋊#1055	—	2	4	no	—
19	C₄⋊#1055	—	2	4	no	—
20	#88043	—	2	4	no	—
21	#8798	—	13	1	no	maximal, Sylow
22	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	#41	1	2	yes	—
24	C₂×C₈×C₁₃	—	2	4	no	—
25	C₂×C₈×C₁₃	—	4	2	no	—
26	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₄²×C₁₃	#41	1	2	yes	—
31	C₂×#1055	—	4	4	no	—
32	#1568	—	13	2	no	—
33	#1452	D₁₃	1	1	yes	characteristic
34	#1287	—	13	4	no	—
35	C₂³×C₁₃	#125	1	1	yes	characteristic
36	C₂×C₄×C₁₃	—	2	2	no	—
37	C₂×C₄×C₁₃	—	4	2	no	—
38	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₃	#117	1	2	yes	—
40	C₂×C₄×C₁₃	#124	1	2	yes	—
41	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
42	C₈×C₁₃	—	2	2	no	—
43	C₈×C₁₃	—	2	2	no	—
44	C₈×C₁₃	—	4	4	no	—
45	#1055	—	8	4	no	—
46	#432	—	13	4	no	—
47	#431	C₂×D₁₃	1	2	yes	—
48	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
49	#335	—	26	2	no	—
50	#334	—	26	2	no	—
51	#322	Dic₁₃	1	4	yes	—
52	C₂²×C₁₃	—	2	2	no	—
53	C₂²×C₁₃	—	2	1	no	—
54	C₂²×C₁₃	#382	1	1	yes	characteristic
55	C₄×C₁₃	—	2	2	no	—
56	C₄×C₁₃	—	2	2	no	—
57	C₄×C₁₃	—	2	1	no	—
58	C₄×C₁₃	#430	1	2	yes	—
59	C₂²×C₈	Dic₂₆	1	2	yes	—
60	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
61	C₄⋊C₈	—	2	2	no	—
62	C₄⋊C₈	—	26	4	no	—
63	C₂²⋊C₈	—	2	2	no	—
64	C₂²⋊C₈	—	26	4	no	—
65	#97	—	26	4	no	—
66	C₄×C₈	D₅₂	1	1	yes	characteristic
67	C₄×C₈	D₅₂	1	1	yes	characteristic
68	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
69	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
70	C₂×C₁₃	—	4	1	no	—
71	C₂×C₁₃	#1833	1	2	yes	—
72	C₂×C₁₃	#1838	1	1	yes	characteristic
73	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
74	C₂²×C₄	#6127	1	2	yes	—
75	C₂×C₈	—	2	4	no	—
76	C₂×C₈	—	4	2	no	—
77	C₂×C₈	—	52	4	no	—
78	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
79	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
80	C₄²	C₂×D₅₂	1	1	yes	characteristic
81	C₄²	#6127	1	2	yes	—
82	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
83	C₁₃	#8798	1	1	yes	characteristic, complemented, Sylow
84	C₂³	#88124	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	#88124	1	1	yes	characteristic
88	C₂×C₄	#88129	1	2	yes	—
89	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
90	C₂×C₄	#88180	1	2	yes	—
91	C₈	—	2	2	no	—
92	C₈	—	2	2	no	—
93	C₈	—	4	4	no	—
94	C₈	—	104	4	no	—
95	C₂²	—	2	2	no	—
96	C₂²	—	2	1	no	—
97	C₂²	#11718597	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	#11718786	1	2	yes	—
102	C₂	—	4	1	no	—
103	C₂	#13114960	1	2	yes	—
104	C₂	#13114977	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13113599

C₂

yes

maximal

#13112698

C₂

yes

maximal

C₁₃×#1452

C₂

yes

maximal, characteristic

C₁₃×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

#11718587

C₂²

yes

—

C₁₃×#322

C₄

yes

—

#11718050

—

#11718049

—

C₂²×C₈×C₁₃

Q₈

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

D₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

characteristic

C₂²⋊#1055

—

—

—

—

C₂²×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₂×#1055

—

#1568

—

#1452

D₁₃

yes

characteristic

#1287

—

C₂³×C₁₃

#125

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

#125

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#432

—

#431

C₂×D₁₃

yes

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

—

Dic₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#382

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#430

yes

—

C₂²×C₈

Dic₂₆

yes

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

D₅₂

yes

characteristic

C₄×C₈

D₅₂

yes

characteristic

C₄×C₈

C₂×Dic₁₃

yes

—

C₄×C₈

C₂×Dic₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

#1833

yes

—

C₂×C₁₃

#1838

yes

characteristic

C₂²×C₄

C₂×Dic₂₆

yes

characteristic

C₂²×C₄

#6127

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₃

yes

—

C₂×C₈

C₄⋊Dic₁₃

yes

—

C₄²

C₂×D₅₂

yes

characteristic

C₄²

#6127

yes

—

C₄²

C₂²×Dic₁₃

yes

characteristic

C₁₃

#8798

yes

characteristic, complemented, Sylow

C₂³

#88124

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#88124

yes

characteristic

C₂×C₄

#88129

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

C₂×C₄

#88180

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

104

—

C₂²

—

C₂²

—

C₂²

#11718597

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

#11718786

yes

—

102

C₂

—

103

C₂

#13114960

yes

—

104

C₂

#13114977

yes

characteristic

	subgroup	G/H
center	C₂²	#11718597
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1452	C₂
socle	C₂²×C₁₃	#382
prime radical	C₂³×C₁₃	#125
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1452	D₁₃
hypocenter	C₁₃	#8798
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#11718597

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1452

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
83. C₁₃	#8798	semidirect

H ≅ G/N

type

83. C₁₃

#8798

semidirect

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

subgroup	index
#13113599	2
#13112698	2
C₁₃×#1452	2
#8798	13

subgroup

index

#13113599

#13112698

C₁₃×#1452

#8798

Subgroups — #15756632

Conjugacy classes of subgroups

Complements

Maximal subgroups