Group #23765583 — subgroups

Subgroups — #23765583

Order 10112.

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14579095	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098390	C₂	1	2	yes	maximal, complemented
3	#19098364	C₂	1	2	yes	maximal, complemented
4	C₂²⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	#466×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₉	—	2	1	no	—
7	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
8	#14579095	—	2	1	no	—
9	#14579095	C₂²	1	2	yes	—
10	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	#121×C₇₉	—	2	1	no	—
13	#107×C₇₉	C₂²	1	1	yes	characteristic
14	#102×C₇₉	—	2	1	no	—
15	C₂²×Dic₇₉	—	4	1	no	—
16	C₄⋊Dic₇₉	—	2	2	no	—
17	C₄⋊Dic₇₉	—	4	1	no	—
18	C₇₉⋊C₁₆	—	2	2	no	—
19	C₂×D₄×C₇₉	—	2	1	no	—
20	C₂×D₄×C₇₉	—	4	1	no	—
21	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
22	D₈×C₇₉	—	2	2	no	—
23	C₂×C₈×C₇₉	—	2	2	no	—
24	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₇₉	—	2	1	no	—
27	C₂²⋊C₄×C₇₉	—	4	1	no	—
28	C₂³×C₇₉	—	4	1	no	—
29	C₂³×C₇₉	D₈	1	1	yes	characteristic
30	D₄×C₇₉	—	4	1	no	—
31	D₄×C₇₉	—	4	1	no	—
32	D₄×C₇₉	—	8	2	no	—
33	C₂×C₄×C₇₉	—	2	1	no	—
34	C₂×C₄×C₇₉	—	2	1	no	—
35	C₂×C₄×C₇₉	—	4	1	no	—
36	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₉	—	4	2	no	—
39	C₂×Dic₇₉	—	8	2	no	—
40	C₈×C₇₉	—	2	1	no	—
41	C₈×C₇₉	#41	1	2	yes	—
42	C₂²×C₇₉	—	2	1	no	—
43	C₂²×C₇₉	—	2	1	no	—
44	C₂²×C₇₉	—	8	1	no	—
45	C₂²×C₇₉	—	8	1	no	—
46	C₂²×C₇₉	—	8	1	no	—
47	C₂²×C₇₉	SD₃₂	1	2	yes	—
48	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
49	C₄×C₇₉	—	2	1	no	—
50	C₄×C₇₉	—	8	1	no	—
51	C₄×C₇₉	#123	1	1	yes	characteristic
52	C₄×C₇₉	#137	1	1	yes	characteristic
53	Dic₇₉	—	8	2	no	—
54	C₂×C₇₉	—	2	2	no	—
55	C₂×C₇₉	—	16	1	no	—
56	C₂×C₇₉	#480	1	1	yes	characteristic
57	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
58	C₂×C₇₉	#509	1	1	yes	characteristic
59	#2233	—	79	1	no	maximal, Sylow
60	C₇₉	#2233	1	1	yes	characteristic, complemented, Sylow
61	#466	D₇₉	1	1	yes	characteristic
62	C₂×#107	—	79	1	no	—
63	#367	—	79	2	no	—
64	#357	—	79	2	no	—
65	C₂²⋊C₁₆	—	79	1	no	—
66	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
67	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
68	#121	—	2	1	no	—
69	C₂×C₄⋊C₄	—	158	1	no	—
70	C₂×C₁₆	—	79	2	no	—
71	#107	—	79	2	no	—
72	#107	—	158	1	no	—
73	#107	C₂×D₇₉	1	1	yes	characteristic
74	#102	—	2	1	no	—
75	C₂×D₄	—	2	1	no	—
76	C₂×D₄	—	4	1	no	—
77	C₂²×C₄	—	316	1	no	—
78	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
79	D₈	—	2	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	316	1	no	—
85	C₄⋊C₄	—	158	2	no	—
86	C₂²⋊C₄	—	4	1	no	—
87	C₁₆	—	158	2	no	—
88	C₂³	—	4	1	no	—
89	C₂³	#11929609	1	1	yes	characteristic
90	D₄	—	4	1	no	—
91	D₄	—	4	1	no	—
92	D₄	—	8	2	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	316	2	no	—
97	C₂×C₄	—	632	2	no	—
98	C₂×C₄	#11929609	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
100	C₈	—	2	1	no	—
101	C₈	#11929623	1	2	yes	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	—	8	1	no	—
105	C₂²	—	8	1	no	—
106	C₂²	—	8	1	no	—
107	C₂²	#14579105	1	2	yes	—
108	C₂²	C₂×#11929609	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	8	1	no	—
111	C₄	—	632	2	no	—
112	C₄	#14579142	1	1	yes	characteristic
113	C₄	#14579191	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	—	16	1	no	—
116	C₂	#19098874	1	1	yes	characteristic
117	C₂	C₂×#14579105	1	1	yes	characteristic
118	C₂	#19098998	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579095

C₂

yes

maximal, characteristic, complemented

#19098390

C₂

yes

maximal, complemented

#19098364

C₂

yes

maximal, complemented

C₂²⋊(C₇₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#466×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

—

C₂×C₇₉⋊C₁₆

C₂²

yes

—

#14579095

—

#14579095

C₂²

yes

—

C₂×D₈×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#121×C₇₉

—

#107×C₇₉

C₂²

yes

characteristic

#102×C₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

D₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

D₈

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#41

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

SD₃₂

yes

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#480

yes

characteristic

C₂×C₇₉

C₂×SD₃₂

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#466

D₇₉

yes

—

—

—

C₂²⋊C₁₆

—

C₂×D₈

C₂×D₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

#121

—

C₂×C₄⋊C₄

—

158

—

C₂×C₁₆

—

#107

—

#107

—

158

—

#107

C₂×D₇₉

yes

characteristic

#102

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

316

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

C₁₆

—

158

—

C₂³

—

C₂³

#11929609

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

#11929609

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

100

C₈

—

101

C₈

#11929623

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

#14579105

yes

—

108

C₂²

C₂×#11929609

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

632

—

112

C₄

#14579142

yes

characteristic

113

C₄

#14579191

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

#19098874

yes

characteristic

117

C₂

C₂×#14579105

yes

characteristic

118

C₂

#19098998

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting, prime radical	#466×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
hypercenter	#466	D₇₉
hypocenter	C₇₉	#2233
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #466

subgroup

G/H

center

C₂²

C₂×#11929609

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting, prime radical

#466×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #466

N	H ≅ G/N	type
1. C₂×#14579095	C₂	semidirect
2. #19098390	C₂	semidirect
3. #19098364	C₂	semidirect
4. C₂²⋊(C₇₉⋊C₁₆)	C₂	semidirect
60. C₇₉	#2233	semidirect

H ≅ G/N

type

1. C₂×#14579095

C₂

semidirect

2. #19098390

C₂

semidirect

3. #19098364

C₂

semidirect

4. C₂²⋊(C₇₉⋊C₁₆)

C₂

semidirect

60. C₇₉

#2233

semidirect

Subgroups — #23765583

Conjugacy classes of subgroups

Complements