Group #15750567 — subgroups

Subgroups — #15750567

Order 3328.

126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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	#13113034	C₂	1	1	yes	maximal, characteristic
2	#13112912	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2247	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₃₂	—	2	1	no	—
5	C₂×C₁₃×Q₃₂	C₄	1	2	yes	—
6	C₁₃×#494	—	2	1	no	—
7	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	#11718091	—	2	1	no	—
9	#11718055	—	2	1	no	—
10	C₂×C₁₃×Q₁₆	—	2	2	no	—
11	C₂×C₁₃×Q₁₆	—	4	1	no	—
12	C₁₃×C₄⋊Q₈	—	4	1	no	—
13	C₁₃×Q₃₂	—	4	2	no	—
14	C₁₃×Q₃₂	—	4	1	no	—
15	C₁₃×Q₃₂	—	4	1	no	—
16	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
19	#88052	—	4	1	no	—
20	#88034	—	4	1	no	—
21	#7449	—	13	1	no	maximal, Sylow
22	C₂×Q₈×C₁₃	—	4	2	no	—
23	C₁₃×Q₁₆	—	4	2	no	—
24	C₁₃×Q₁₆	—	4	2	no	—
25	C₁₃×Q₁₆	—	8	1	no	—
26	C₁₃×Q₁₆	—	8	1	no	—
27	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
29	C₁₃×C₄⋊C₄	—	8	2	no	—
30	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
31	C₁₃×C₁₆	—	2	1	no	—
32	C₁₃×C₁₆	D₈	1	1	yes	characteristic
33	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
34	#6090	—	8	1	no	—
35	#2247	D₁₃	1	1	yes	characteristic
36	#1422	—	13	1	no	—
37	#1373	—	13	1	no	—
38	Q₈×C₁₃	—	8	2	no	—
39	Q₈×C₁₃	—	8	2	no	—
40	C₂×C₄×C₁₃	—	2	1	no	—
41	C₂×C₄×C₁₃	—	8	2	no	—
42	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
43	C₈×C₁₃	#100	1	1	yes	characteristic
44	C₈×C₁₃	#102	1	1	yes	characteristic
45	C₈×C₁₃	D₁₆	1	1	yes	characteristic
46	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
47	C₂×Q₃₂	—	2	1	no	—
48	C₂×Q₃₂	Dic₁₃	1	2	yes	—
49	#494	—	2	1	no	—
50	M₆₄	—	26	1	no	—
51	#364	—	26	1	no	—
52	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
53	C₂²×C₁₃	#361	1	1	yes	characteristic
54	C₄×C₁₃	—	2	2	no	—
55	C₄×C₁₃	—	16	2	no	—
56	C₄×C₁₃	#331	1	1	yes	characteristic
57	C₄×C₁₃	#357	1	1	yes	characteristic
58	C₂×Q₁₆	—	2	2	no	—
59	C₂×Q₁₆	—	4	1	no	—
60	C₄⋊Q₈	—	4	1	no	—
61	Q₃₂	—	4	2	no	—
62	Q₃₂	—	4	1	no	—
63	Q₃₂	—	4	1	no	—
64	M₃₂	—	52	1	no	—
65	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
66	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
67	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
68	C₃₂	—	52	1	no	—
69	C₂×C₁₃	—	2	1	no	—
70	C₂×C₁₃	#1361	1	1	yes	characteristic
71	C₂×Q₈	—	4	2	no	—
72	Q₁₆	—	4	2	no	—
73	Q₁₆	—	4	2	no	—
74	Q₁₆	—	8	1	no	—
75	Q₁₆	—	8	1	no	—
76	C₂×C₈	#6104	1	1	yes	characteristic
77	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
78	C₄⋊C₄	—	8	2	no	—
79	C₄²	#6105	1	1	yes	characteristic
80	C₁₆	—	2	1	no	—
81	C₁₆	—	104	1	no	—
82	C₁₆	#6104	1	1	yes	characteristic
83	C₁₆	#6105	1	1	yes	characteristic
84	C₁₃	#7449	1	1	yes	characteristic, complemented, Sylow
85	Q₈	—	8	2	no	—
86	Q₈	—	8	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	8	2	no	—
89	C₂×C₄	#88072	1	1	yes	characteristic
90	C₈	#88066	1	1	yes	characteristic
91	C₈	#88067	1	1	yes	characteristic
92	C₈	#88072	1	1	yes	characteristic
93	C₈	#88073	1	1	yes	characteristic
94	C₂²	#11718155	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	16	2	no	—
97	C₄	#11718136	1	1	yes	characteristic
98	C₄	#11718154	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	#13112882	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13113034

C₂

yes

maximal, characteristic

#13112912

C₂

yes

maximal, characteristic

C₁₃×#2247

C₂

yes

maximal, characteristic

C₂×C₁₃×Q₃₂

—

C₂×C₁₃×Q₃₂

C₄

yes

—

C₁₃×#494

—

C₄×C₁₃×C₁₆

C₂²

yes

characteristic

#11718091

—

#11718055

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₁₃×C₄⋊Q₈

—

C₁₃×Q₃₂

—

C₁₃×Q₃₂

—

C₁₃×Q₃₂

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

D₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

—

—

—

C₂×Q₈×C₁₃

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

D₈

yes

characteristic

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

SD₁₆

yes

characteristic

C₁₃×C₁₆

—

C₁₃×C₁₆

D₈

yes

characteristic

C₁₃×C₁₆

SD₁₆

yes

characteristic

#6090

—

#2247

D₁₃

yes

characteristic

#1422

—

#1373

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

yes

C₈×C₁₃

yes

C₈×C₁₃

yes

C₈×C₁₃

D₁₆

yes

characteristic

C₈×C₁₃

SD₃₂

yes

characteristic

C₂×Q₃₂

—

C₂×Q₃₂

Dic₁₃

yes

—

#494

—

M₆₄

—

#364

—

C₄×C₁₆

C₂×D₁₃

yes

characteristic

C₂²×C₁₃

#361

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₂×Dic₁₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₃

yes

characteristic

C₄×C₈

C₂²⋊D₁₃

yes

characteristic

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

#1361

yes

characteristic

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

#6104

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₃

yes

characteristic

C₄⋊C₄

—

C₄²

#6105

yes

characteristic

C₁₆

—

C₁₆

—

104

—

C₁₆

yes

C₁₆

yes

C₁₃

yes

characteristic, complemented, Sylow

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₈

yes

C₈

yes

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

#13112882

yes

characteristic

	subgroup	G/H
center	C₂	#13112882
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#2247	C₂
socle	C₂×C₁₃	#1361
prime radical	C₂²×C₁₃	#361
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#2247	D₁₃
hypocenter	C₁₃	#7449
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

subgroup

G/H

center

C₂

#13112882

commutator

C₂×C₁₃×C₁₆

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₃

Fitting

C₁₃×#2247

C₂

C₂×C₁₃

C₂²×C₁₃

C₄×C₁₃×C₁₆

C₂²

D₁₃

C₁₃

G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

N	H ≅ G/N	type
84. C₁₃	#7449	semidirect

H ≅ G/N

type

84. C₁₃

#7449

semidirect

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

subgroup	index
#13113034	2
#13112912	2
C₁₃×#2247	2
#7449	13

subgroup

index

#13113034

#13112912

C₁₃×#2247

#7449

Subgroups — #15750567

Conjugacy classes of subgroups

Complements

Maximal subgroups