Group #23771664 — subgroups

Subgroups — #23771664

Order 10112.

548 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19098499	C₂	1	4	yes	maximal, complemented
2	#19098486	C₂	1	8	yes	maximal, complemented
3	#19098419	C₂	1	2	yes	maximal
4	#379×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	complemented
6	C₂×Dic₇₉⋊C₄	C₂²	1	8	yes	complemented
7	C₂×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
8	C₂×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
9	C₂×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
10	C₇₉⋊#95	C₂²	1	4	yes	complemented
11	C₂⁵×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	—
13	C₂×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
14	C₂²×Dic₇₉	C₂³	1	8	yes	—
15	C₄⋊Dic₇₉	—	4	4	no	—
16	Dic₇₉⋊C₄	—	4	8	no	—
17	C₂²⋊Dic₇₉	—	4	4	no	—
18	C₂²⋊Dic₇₉	—	4	4	no	—
19	C₂²⋊Dic₇₉	—	4	4	no	—
20	C₂⁴×C₇₉	—	4	4	no	—
21	C₂⁴×C₇₉	—	4	2	no	—
22	C₂⁴×C₇₉	Q₈	1	4	yes	—
23	C₂⁴×C₇₉	C₂³	1	2	yes	—
24	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
26	C₂²⋊C₄×C₇₉	—	4	4	no	—
27	C₂²⋊C₄×C₇₉	—	4	2	no	—
28	C₂³×C₇₉	—	2	4	no	—
29	C₂³×C₇₉	—	2	4	no	—
30	C₂³×C₇₉	—	2	4	no	—
31	C₂³×C₇₉	—	2	4	no	—
32	C₂³×C₇₉	—	2	2	no	—
33	C₂³×C₇₉	—	4	8	no	—
34	C₂³×C₇₉	—	4	4	no	—
35	C₂³×C₇₉	—	4	16	no	—
36	C₂³×C₇₉	C₂×Q₈	1	4	yes	—
37	C₂³×C₇₉	C₂×Q₈	1	2	yes	—
38	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₇₉	—	2	8	no	—
40	C₂×C₄×C₇₉	—	2	4	no	—
41	C₂×Dic₇₉	—	2	8	no	—
42	C₂×Dic₇₉	—	2	8	no	—
43	C₂×Dic₇₉	—	2	8	no	—
44	C₂²×C₇₉	—	2	4	no	—
45	C₂²×C₇₉	—	2	4	no	—
46	C₂²×C₇₉	—	2	4	no	—
47	C₂²×C₇₉	—	2	4	no	—
48	C₂²×C₇₉	—	2	2	no	—
49	C₂²×C₇₉	—	4	16	no	—
50	C₂²×C₇₉	—	4	8	no	—
51	C₂²×C₇₉	—	4	4	no	—
52	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₇₉	H(5,𝔽₂)	1	4	yes	—
54	C₂²×C₇₉	H(5,𝔽₂)	1	2	yes	—
55	C₄×C₇₉	—	4	4	no	—
56	Dic₇₉	—	4	8	no	—
57	C₂×C₇₉	—	4	4	no	—
58	C₂×C₇₉	—	4	2	no	—
59	C₂×C₇₉	#543	1	2	yes	—
60	C₂×C₇₉	#543	1	1	yes	characteristic
61	C₂×C₇₉	#560	1	4	yes	—
62	#2842	—	79	1	no	maximal, Sylow
63	C₇₉	#2842	1	1	yes	characteristic, complemented, Sylow
64	#399	—	79	4	no	—
65	#396	—	79	8	no	—
66	#379	—	79	2	no	—
67	#379	D₇₉	1	1	yes	characteristic
68	C₂⁵	C₂×D₇₉	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	79	8	no	—
70	C₂×C₄⋊C₄	—	79	4	no	—
71	C₂×C₂²⋊C₄	—	79	4	no	—
72	C₂×C₂²⋊C₄	—	79	4	no	—
73	C₂×C₂²⋊C₄	—	79	4	no	—
74	C₂×C₂²⋊C₄	C₂×D₇₉	1	4	yes	—
75	C₂×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
76	#95	—	79	4	no	—
77	C₂⁴	—	4	4	no	—
78	C₂⁴	—	4	2	no	—
79	C₂⁴	Dic₁₅₈	1	4	yes	—
80	C₂⁴	C₂²×D₇₉	1	2	yes	—
81	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
82	C₂²×C₄	—	79	8	no	—
83	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
84	C₄⋊C₄	—	316	8	no	—
85	C₄⋊C₄	—	316	4	no	—
86	C₂²⋊C₄	—	4	4	no	—
87	C₂²⋊C₄	—	4	2	no	—
88	C₂²⋊C₄	—	316	4	no	—
89	C₂²⋊C₄	—	316	4	no	—
90	C₂²⋊C₄	—	316	4	no	—
91	C₂³	—	2	4	no	—
92	C₂³	—	2	2	no	—
93	C₂³	—	2	4	no	—
94	C₂³	—	2	4	no	—
95	C₂³	—	2	4	no	—
96	C₂³	—	4	8	no	—
97	C₂³	—	4	4	no	—
98	C₂³	—	4	16	no	—
99	C₂³	C₂×Dic₁₅₈	1	4	yes	—
100	C₂³	C₂×Dic₁₅₈	1	2	yes	—
101	C₂³	C₂³×D₇₉	1	1	yes	characteristic
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	158	8	no	—
105	C₂×C₄	—	158	8	no	—
106	C₂×C₄	—	158	8	no	—
107	C₂²	—	2	4	no	—
108	C₂²	—	2	2	no	—
109	C₂²	—	2	4	no	—
110	C₂²	—	2	4	no	—
111	C₂²	—	2	4	no	—
112	C₂²	—	4	16	no	—
113	C₂²	—	4	8	no	—
114	C₂²	—	4	4	no	—
115	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
116	C₂²	#14579206	1	4	yes	—
117	C₂²	#14579206	1	2	yes	—
118	C₄	—	4	4	no	—
119	C₄	—	316	8	no	—
120	C₂	—	4	4	no	—
121	C₂	—	4	2	no	—
122	C₂	#19099189	1	2	yes	—
123	C₂	#19099189	1	1	yes	characteristic
124	C₂	#19099302	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098499

C₂

yes

maximal, complemented

#19098486

C₂

yes

maximal, complemented

#19098419

C₂

yes

maximal

#379×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

complemented

C₂×Dic₇₉⋊C₄

C₂²

yes

complemented

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

complemented

C₂⁵×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂⁴×C₇₉

—

C₂⁴×C₇₉

—

C₂⁴×C₇₉

Q₈

yes

—

C₂⁴×C₇₉

C₂³

yes

—

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×Q₈

yes

—

C₂³×C₇₉

C₂×Q₈

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₄×C₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#543

yes

—

C₂×C₇₉

#543

yes

characteristic

C₂×C₇₉

#560

yes

—

#2842

—

maximal, Sylow

C₇₉

#2842

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic

C₂⁵

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

#95

—

C₂⁴

—

C₂⁴

—

C₂⁴

Dic₁₅₈

yes

—

C₂⁴

C₂²×D₇₉

yes

—

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

316

—

C₂²⋊C₄

—

316

—

C₂²⋊C₄

—

316

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×Dic₁₅₈

yes

—

100

C₂³

C₂×Dic₁₅₈

yes

—

101

C₂³

C₂³×D₇₉

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

158

—

105

C₂×C₄

—

158

—

106

C₂×C₄

—

158

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂²×Dic₁₅₈

yes

characteristic

116

C₂²

#14579206

yes

—

117

C₂²

#14579206

yes

—

118

C₄

—

119

C₄

—

316

—

120

C₂

—

121

C₂

—

122

C₂

#19099189

yes

—

123

C₂

#19099189

yes

characteristic

124

C₂

#19099302

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#379×C₇₉	C₂
prime radical	C₂⁵×C₇₉	C₂²
hypercenter	#379	D₇₉
hypocenter	C₇₉	#2842
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #379

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#379×C₇₉

C₂

prime radical

C₂⁵×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #379

N	H ≅ G/N	type
1. #19098499	C₂	semidirect
2. #19098486	C₂	semidirect
5. C₂×C₄⋊Dic₇₉	C₂²	semidirect
6. C₂×Dic₇₉⋊C₄	C₂²	semidirect
10. C₇₉⋊#95	C₂²	semidirect
63. C₇₉	#2842	semidirect

H ≅ G/N

type

1. #19098499

C₂

semidirect

2. #19098486

C₂

semidirect

5. C₂×C₄⋊Dic₇₉

C₂²

semidirect

6. C₂×Dic₇₉⋊C₄

C₂²

semidirect

10. C₇₉⋊#95

C₂²

semidirect

63. C₇₉

#2842

semidirect

Subgroups — #23771664

Conjugacy classes of subgroups

Complements