Group #23762703 — subgroups

Subgroups — #23762703

Order 10112.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₇₉⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098929	C₂	1	1	yes	maximal, characteristic
3	#19098928	C₂	1	2	yes	maximal
4	#19098304	C₂	1	2	yes	maximal, complemented
5	#330×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579158	C₂²	1	1	yes	characteristic
7	#14579153	C₂²	1	2	yes	—
8	#14579152	—	2	2	no	—
9	#14579151	—	2	2	no	—
10	#14579151	—	2	2	no	—
11	#14579083	—	2	2	no	—
12	#14579083	—	2	2	no	—
13	#14579081	—	2	2	no	—
14	#14579072	C₂²	1	1	yes	characteristic
15	#125×C₇₉	C₂²	1	1	yes	characteristic
16	#97×C₇₉	C₂²	1	2	yes	—
17	C₂×D₃₁₆	—	2	1	no	—
18	C₂×D₃₁₆	—	2	2	no	—
19	C₂×C₇₉⋊C₈	—	2	1	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₄⋊Dic₇₉	D₄	1	2	yes	—
22	C₄⋊Dic₇₉	D₄	1	2	yes	—
23	Dic₇₉⋊C₄	—	2	2	no	—
24	Dic₇₉⋊C₄	—	2	2	no	—
25	Dic₇₉⋊C₄	—	2	2	no	—
26	Dic₇₉⋊C₄	—	2	2	no	—
27	C₄×Dic₇₉	—	2	2	no	—
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₄⋊C₄×C₇₉	—	2	2	no	—
30	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₂²×D₇₉	—	4	1	no	—
33	C₂×C₄×C₇₉	—	2	2	no	—
34	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₉	—	2	2	no	—
37	C₂×Dic₇₉	—	2	2	no	—
38	D₃₁₆	—	4	2	no	—
39	D₃₁₆	—	4	4	no	—
40	C₈×C₇₉	—	4	2	no	—
41	C₇₉⋊C₈	—	4	1	no	—
42	C₂²×C₇₉	#120	1	1	yes	characteristic
43	C₂×D₇₉	—	8	2	no	—
44	C₂×D₇₉	—	8	1	no	—
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	—	2	2	no	—
47	C₄×C₇₉	—	4	2	no	—
48	Dic₇₉	—	4	2	no	—
49	Dic₇₉	—	4	2	no	—
50	C₂×C₇₉	#454	1	2	yes	—
51	C₂×C₇₉	#454	1	1	yes	characteristic
52	D₇₉	—	16	1	no	—
53	#1658	—	79	1	no	maximal, Sylow
54	C₇₉	#1658	1	1	yes	characteristic, complemented, Sylow
55	#564	—	79	1	no	—
56	#490	—	79	1	no	—
57	#490	—	79	2	no	—
58	#330	—	79	2	no	—
59	#330	D₇₉	1	1	yes	characteristic, complemented
60	#127	—	79	1	no	—
61	#125	—	79	2	no	—
62	#125	—	158	2	no	—
63	#125	—	158	2	no	—
64	#125	—	158	2	no	—
65	#125	C₂×D₇₉	1	1	yes	characteristic
66	#102	—	158	2	no	—
67	#102	—	158	2	no	—
68	#102	—	158	2	no	—
69	#97	—	79	1	no	—
70	#97	C₂×D₇₉	1	2	yes	—
71	C₂×D₄	—	158	2	no	—
72	C₂×D₄	—	158	1	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	158	1	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	79	2	no	—
77	C₄⋊C₄	—	79	2	no	—
78	C₄⋊C₄	—	158	2	no	—
79	C₄⋊C₄	—	158	2	no	—
80	C₄⋊C₄	—	158	2	no	—
81	C₄⋊C₄	—	158	2	no	—
82	C₄⋊C₄	—	158	2	no	—
83	C₄⋊C₄	D₃₁₆	1	2	yes	—
84	C₄²	—	158	2	no	—
85	C₄²	C₂²×D₇₉	1	1	yes	characteristic
86	C₂³	—	316	1	no	—
87	D₄	—	316	4	no	—
88	D₄	—	316	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	158	2	no	—
91	C₂×C₄	—	158	2	no	—
92	C₂×C₄	D₄×D₇₉	1	2	yes	—
93	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
94	C₈	—	4	2	no	—
95	C₈	—	316	1	no	—
96	C₂²	—	632	2	no	—
97	C₂²	—	632	1	no	—
98	C₂²	#14579131	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	316	2	no	—
103	C₄	—	316	2	no	—
104	C₂	—	1264	1	no	—
105	C₂	#19098737	1	2	yes	—
106	C₂	#19098738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₉⋊#564

C₂

yes

maximal, characteristic, complemented

#19098929

C₂

yes

maximal, characteristic

#19098928

C₂

yes

maximal

#19098304

C₂

yes

maximal, complemented

#330×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579158

C₂²

yes

characteristic

#14579153

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₇₉

C₂²

yes

characteristic

#97×C₇₉

C₂²

yes

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#120

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#454

yes

—

C₂×C₇₉

#454

yes

characteristic

D₇₉

—

#1658

—

maximal, Sylow

C₇₉

#1658

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic, complemented

#127

—

#125

—

#125

—

158

—

#125

—

158

—

#125

—

158

—

#125

C₂×D₇₉

yes

characteristic

#102

—

158

—

#102

—

158

—

#102

—

158

—

#97

—

#97

C₂×D₇₉

yes

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

D₃₁₆

yes

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

316

—

D₄

—

316

—

D₄

—

316

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

—

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

—

C₈

—

316

—

C₂²

—

632

—

C₂²

—

632

—

C₂²

#14579131

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

316

—

103

C₄

—

316

—

104

C₂

—

1264

—

105

C₂

#19098737

yes

—

106

C₂

#19098738

yes

characteristic

	subgroup	G/H
center	C₂²	#14579131
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#330×C₇₉	C₂
socle	C₂²×C₇₉	#120
prime radical	#14579158	C₂²
hypercenter	#330	D₇₉
hypocenter	C₇₉	#1658
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#14579131

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#330×C₇₉

C₂

C₂²×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
1. C₇₉⋊#564	C₂	semidirect
4. #19098304	C₂	semidirect
5. #330×C₇₉	C₂	semidirect
54. C₇₉	#1658	semidirect
59. #330	D₇₉	semidirect

H ≅ G/N

type

1. C₇₉⋊#564

C₂

semidirect

4. #19098304

C₂

semidirect

5. #330×C₇₉

C₂

semidirect

54. C₇₉

#1658

semidirect

59. #330

D₇₉

semidirect

Subgroups — #23762703

Conjugacy classes of subgroups

Complements