Group #23771780 — subgroups

Subgroups — #23771780

Order 10112.

408 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 149 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	#19098467	C₂	1	3	yes	maximal
2	#19098460	C₂	1	3	yes	maximal
3	#19098450	C₂	1	3	yes	maximal
4	#19098446	C₂	1	3	yes	maximal
5	#19098431	C₂	1	1	yes	maximal, characteristic
6	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic
7	#383×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
10	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
13	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
14	C₇₉⋊#95	C₂²	1	3	yes	—
15	C₇₉⋊#95	C₂²	1	3	yes	—
16	C₇₉⋊#95	C₂²	1	3	yes	—
17	C₇₉⋊#95	C₂²	1	3	yes	—
18	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
19	#95×C₇₉	C₂²	1	3	yes	—
20	#95×C₇₉	C₂²	1	3	yes	—
21	C₂×Dic₁₅₈	—	2	6	no	—
22	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₇₉	C₂³	1	3	yes	—
24	C₂²×Dic₇₉	C₂³	1	3	yes	—
25	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₇₉	—	2	6	no	—
27	Dic₇₉⋊C₄	—	2	6	no	—
28	Dic₇₉⋊C₄	—	2	6	no	—
29	C₄×Dic₇₉	—	2	6	no	—
30	C₄×Dic₇₉	—	2	6	no	—
31	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
33	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
34	C₄²×C₇₉	Q₈	1	4	yes	complemented
35	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₇₉	—	2	3	no	—
37	C₂×C₄×C₇₉	—	2	3	no	—
38	C₂×C₄×C₇₉	—	2	3	no	—
39	C₂×C₄×C₇₉	—	2	3	no	—
40	C₂×C₄×C₇₉	—	2	3	no	—
41	C₂×C₄×C₇₉	—	2	3	no	—
42	C₂×C₄×C₇₉	C₂×Q₈	1	6	yes	—
43	C₂×Dic₇₉	—	2	3	no	—
44	C₂×Dic₇₉	—	2	3	no	—
45	C₂×Dic₇₉	—	2	3	no	—
46	C₂×Dic₇₉	—	2	3	no	—
47	C₂×Dic₇₉	—	2	3	no	—
48	C₂×Dic₇₉	—	2	3	no	—
49	C₂×Dic₇₉	#41	1	6	yes	—
50	C₂×Dic₇₉	#41	1	6	yes	—
51	Dic₁₅₈	—	4	4	no	—
52	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₇₉	C₂×#41	1	3	yes	—
54	C₂²×C₇₉	C₂×#41	1	3	yes	—
55	C₄×C₇₉	—	2	6	no	—
56	C₄×C₇₉	—	4	1	no	—
57	C₄×C₇₉	—	4	3	no	—
58	Dic₇₉	—	2	6	no	—
59	Dic₇₉	—	4	1	no	—
60	Dic₇₉	—	4	3	no	—
61	Dic₇₉	#126	1	4	yes	—
62	C₂×C₇₉	C₂×#126	1	1	yes	characteristic
63	C₂×C₇₉	#529	1	3	yes	—
64	C₂×C₇₉	#533	1	3	yes	—
65	#2863	—	79	1	no	maximal, Sylow
66	C₇₉	#2863	1	1	yes	characteristic, complemented, Sylow
67	#391	—	79	3	no	—
68	#389	—	79	3	no	—
69	#387	—	79	3	no	—
70	#387	—	79	3	no	—
71	#383	—	79	1	no	—
72	#383	D₇₉	1	1	yes	characteristic
73	C₄³	—	79	1	no	—
74	C₂²×Q₈	—	79	1	no	—
75	C₂×C₄⋊C₄	—	79	3	no	—
76	C₂×C₄⋊C₄	—	79	3	no	—
77	C₂×C₄⋊C₄	—	79	3	no	—
78	C₂×C₄²	—	79	3	no	—
79	C₂×C₄²	—	79	3	no	—
80	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
81	#95	—	79	3	no	—
82	#95	—	79	3	no	—
83	#95	—	79	3	no	—
84	#95	—	79	3	no	—
85	#95	C₂×D₇₉	1	3	yes	—
86	#95	C₂×D₇₉	1	3	yes	—
87	C₂×Q₈	—	158	6	no	—
88	C₂²×C₄	—	79	1	no	—
89	C₂²×C₄	—	79	3	no	—
90	C₂²×C₄	—	79	1	no	—
91	C₂²×C₄	—	79	3	no	—
92	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
93	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
94	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
95	C₄⋊C₄	—	158	6	no	—
96	C₄⋊C₄	—	158	6	no	—
97	C₄⋊C₄	—	158	6	no	—
98	C₄²	—	158	6	no	—
99	C₄²	—	158	6	no	—
100	C₄²	Dic₁₅₈	1	4	yes	complemented
101	C₂³	C₂³×D₇₉	1	1	yes	characteristic
102	Q₈	—	316	4	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	3	no	—
105	C₂×C₄	—	2	3	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	79	6	no	—
110	C₂×C₄	—	79	6	no	—
111	C₂×C₄	—	158	3	no	—
112	C₂×C₄	—	158	3	no	—
113	C₂×C₄	—	158	3	no	—
114	C₂×C₄	—	158	3	no	—
115	C₂×C₄	—	158	3	no	—
116	C₂×C₄	—	158	3	no	—
117	C₂×C₄	C₂×Dic₁₅₈	1	6	yes	—
118	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
119	C₂²	#41×D₇₉	1	3	yes	—
120	C₂²	#41×D₇₉	1	3	yes	—
121	C₄	—	2	6	no	—
122	C₄	—	4	1	no	—
123	C₄	—	4	3	no	—
124	C₄	—	316	1	no	—
125	C₄	—	316	3	no	—
126	C₄	—	79	4	no	—
127	C₄	—	158	6	no	—
128	C₂	#126×D₇₉	1	1	yes	characteristic
129	C₂	#19099096	1	3	yes	—
130	C₂	#19099116	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098467

C₂

yes

maximal

#19098460

C₂

yes

maximal

#19098450

C₂

yes

maximal

#19098446

C₂

yes

maximal

#19098431

C₂

yes

maximal, characteristic

C₄²×Dic₇₉

C₂

yes

maximal, characteristic

#383×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#95×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

Q₈

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#41

yes

—

C₂×Dic₇₉

#41

yes

—

Dic₁₅₈

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

#126

yes

—

C₂×C₇₉

C₂×#126

yes

characteristic

C₂×C₇₉

#529

yes

—

C₂×C₇₉

#533

yes

—

#2863

—

maximal, Sylow

C₇₉

#2863

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic

C₄³

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

C₂×D₇₉

yes

—

#95

C₂×D₇₉

yes

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

—

158

—

100

C₄²

Dic₁₅₈

yes

complemented

101

C₂³

C₂³×D₇₉

yes

characteristic

102

Q₈

—

316

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

158

—

112

C₂×C₄

—

158

—

113

C₂×C₄

—

158

—

114

C₂×C₄

—

158

—

115

C₂×C₄

—

158

—

116

C₂×C₄

—

158

—

117

C₂×C₄

C₂×Dic₁₅₈

yes

—

118

C₂²

C₂²×Dic₁₅₈

yes

characteristic

119

C₂²

#41×D₇₉

yes

—

120

C₂²

#41×D₇₉

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

316

—

125

C₄

—

316

—

126

C₄

—

127

C₄

—

158

—

128

C₂

#126×D₇₉

yes

characteristic

129

C₂

#19099096

yes

—

130

C₂

#19099116

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#383×C₇₉	C₂
hypercenter	#383	D₇₉
hypocenter	C₇₉	#2863
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#383×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
34. C₄²×C₇₉	Q₈	semidirect
66. C₇₉	#2863	semidirect
100. C₄²	Dic₁₅₈	semidirect

H ≅ G/N

type

34. C₄²×C₇₉

Q₈

semidirect

66. C₇₉

#2863

semidirect

100. C₄²

Dic₁₅₈

semidirect

Subgroups — #23771780

Conjugacy classes of subgroups

Complements