Group #15767428 — subgroups

Subgroups — #15767428

Order 3328.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#13114969	C₂	1	3	yes	maximal
2	#13112717	C₂	1	3	yes	maximal
3	C₁₃×#2845	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#398	—	2	6	no	—
5	C₁₃×#382	C₂²	1	3	yes	—
6	#11718596	C₂²	1	1	yes	characteristic
7	C₂×#88043	C₂²	1	3	yes	—
8	#11718121	—	2	6	no	—
9	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
10	C₂×C₁₃×C₄⋊C₄	D₄	1	6	yes	—
11	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₃	—	2	3	no	—
13	C₂²×#1055	—	2	3	no	—
14	C₁₃×#95	—	2	2	no	—
15	C₁₃×#95	—	2	6	no	—
16	#88043	—	2	3	no	—
17	#88043	Q₈	1	6	yes	—
18	#10586	—	13	1	no	maximal, Sylow
19	C₂²×C₄×C₁₃	—	2	6	no	—
20	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
21	C₂²×Dic₁₃	—	4	1	no	—
22	C₁₃×C₄⋊C₄	—	4	6	no	—
23	C₁₃×C₄⋊C₄	—	8	6	no	—
24	C₄²×C₁₃	C₂×Q₈	1	3	yes	—
25	C₄²×C₁₃	#41	1	1	yes	characteristic
26	C₄⋊Dic₁₃	—	4	6	no	—
27	C₂×#1055	—	2	6	no	—
28	C₂×#1055	—	4	3	no	—
29	C₂×#1055	—	4	3	no	—
30	#2845	D₁₃	1	1	yes	characteristic
31	#1836	—	13	3	no	—
32	#1295	—	13	3	no	—
33	C₂³×C₁₃	#120	1	1	yes	characteristic
34	C₂×C₄×C₁₃	—	2	3	no	—
35	C₂×C₄×C₁₃	—	2	3	no	—
36	C₂×C₄×C₁₃	—	4	6	no	—
37	C₂×C₄×C₁₃	—	4	6	no	—
38	C₂×C₄×C₁₃	—	4	6	no	—
39	C₂×C₄×C₁₃	C₂²⋊Q₈	1	3	yes	—
40	C₂×C₄×C₁₃	C₄⋊Q₈	1	3	yes	—
41	C₂×Dic₁₃	—	8	3	no	—
42	#1055	—	4	6	no	—
43	C₂×#97	—	13	3	no	—
44	#398	—	2	6	no	—
45	#384	—	13	1	no	—
46	#382	C₂×D₁₃	1	3	yes	—
47	#340	—	26	6	no	—
48	C₂²×C₁₃	#395	1	1	yes	characteristic
49	C₂²×C₁₃	#454	1	3	yes	—
50	C₂²×C₁₃	#455	1	3	yes	—
51	C₄×C₁₃	—	2	3	no	—
52	C₄×C₁₃	—	2	3	no	—
53	C₄×C₁₃	—	8	6	no	—
54	Dic₁₃	—	16	1	no	—
55	C₂²×C₈	—	26	3	no	—
56	C₂×C₄⋊C₄	—	2	6	no	—
57	C₂×C₄⋊C₄	—	26	3	no	—
58	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	6	yes	—
59	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
60	#97	—	13	6	no	—
61	#97	—	26	3	no	—
62	#95	—	2	2	no	—
63	#95	—	2	6	no	—
64	C₂×C₁₃	#1658	1	1	yes	characteristic
65	C₂×C₁₃	#1662	1	3	yes	—
66	C₂×C₁₃	#2061	1	3	yes	—
67	C₂²×C₄	—	2	6	no	—
68	C₂²×C₄	—	52	1	no	—
69	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
70	C₂×C₈	—	26	6	no	—
71	C₂×C₈	—	52	3	no	—
72	C₂×C₈	—	52	3	no	—
73	C₄⋊C₄	—	4	6	no	—
74	C₄⋊C₄	—	8	6	no	—
75	C₄⋊C₄	—	52	6	no	—
76	C₄²	Q₈×D₁₃	1	3	yes	—
77	C₄²	#6131	1	1	yes	characteristic
78	C₁₃	#10586	1	1	yes	characteristic, complemented, Sylow
79	C₂³	#88207	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	104	3	no	—
86	C₂×C₄	#88198	1	3	yes	—
87	C₂×C₄	#88200	1	3	yes	—
88	C₈	—	52	6	no	—
89	C₂²	#11718890	1	1	yes	characteristic
90	C₂²	#11718903	1	3	yes	—
91	C₂²	#11718906	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	208	1	no	—
96	C₂	#13114138	1	1	yes	characteristic
97	C₂	#13114159	1	3	yes	—
98	C₂	#13116183	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13114969

C₂

yes

maximal

#13112717

C₂

yes

maximal

C₁₃×#2845

C₂

yes

maximal, characteristic

C₁₃×#398

—

C₁₃×#382

C₂²

yes

—

#11718596

C₂²

yes

characteristic

C₂×#88043

C₂²

yes

—

#11718121

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

—

C₁₃×#95

—

C₁₃×#95

—

#88043

—

#88043

Q₈

yes

—

#10586

—

maximal, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×Dic₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

—

—

—

D₁₃

yes

characteristic

#1836

—

#1295

—

C₂³×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

—

C₂×Dic₁₃

—

#1055

—

C₂×#97

—

#398

—

#384

—

#382

C₂×D₁₃

yes

—

#340

—

C₂²×C₁₃

#395

yes

characteristic

C₂²×C₁₃

#454

yes

—

C₂²×C₁₃

#455

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₃

yes

—

C₂×C₄²

C₂²×D₁₃

yes

—

—

—

—

C₂×C₁₃

#1658

yes

characteristic

C₂×C₁₃

#1662

yes

—

C₂×C₁₃

#2061

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Q₈×D₁₃

yes

—

C₄²

#6131

yes

characteristic

C₁₃

#10586

yes

characteristic, complemented, Sylow

C₂³

#88207

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

104

—

C₂×C₄

#88198

yes

—

C₂×C₄

#88200

yes

—

C₈

—

C₂²

#11718890

yes

characteristic

C₂²

#11718903

yes

—

C₂²

#11718906

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

208

—

C₂

#13114138

yes

characteristic

C₂

#13114159

yes

—

C₂

#13116183

yes

—

	subgroup	G/H
center	C₂³	#88207
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2845	C₂
socle, prime radical	C₂³×C₁₃	#120
hypercenter	#2845	D₁₃
hypocenter	C₁₃	#10586
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#88207

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#2845

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
78. C₁₃	#10586	semidirect

H ≅ G/N

type

78. C₁₃

#10586

semidirect

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

subgroup	index
#13114969	2
#13112717	2
C₁₃×#2845	2
#10586	13

subgroup

index

#13114969

#13112717

C₁₃×#2845

#10586

Subgroups — #15767428

Conjugacy classes of subgroups

Complements

Maximal subgroups