Group #23771584 — subgroups

Subgroups — #23771584

Order 10112.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098500	C₂	1	1	yes	maximal, characteristic
3	#19098497	C₂	1	3	yes	maximal, complemented
4	#19098495	C₂	1	3	yes	maximal, complemented
5	#19098492	C₂	1	3	yes	maximal
6	#19098437	C₂	1	3	yes	maximal
7	#401×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
10	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
11	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
12	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	3	yes	—
14	C₂×(C₂×D₇₉)⋊C₄	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	#95×C₇₉	C₂²	1	3	yes	—
19	#95×C₇₉	C₂²	1	3	yes	—
20	#95×C₇₉	C₂²	1	1	yes	characteristic
21	C₂³×D₇₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₇₉	C₂³	1	3	yes	—
23	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₇₉	C₂³	1	3	yes	—
25	C₂×C₄×D₇₉	—	4	3	no	—
26	C₄⋊Dic₇₉	—	4	3	no	—
27	C₄⋊Dic₇₉	—	4	3	no	—
28	Dic₇₉⋊C₄	—	4	3	no	—
29	Dic₇₉⋊C₄	—	4	3	no	—
30	(C₂×D₇₉)⋊C₄	—	2	6	no	—
31	(C₂×D₇₉)⋊C₄	—	4	3	no	—
32	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
33	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
34	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
35	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
36	C₂²×D₇₉	—	2	3	no	—
37	C₂²×D₇₉	—	2	3	no	—
38	C₂²×D₇₉	#41	1	2	yes	—
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	—	2	3	no	—
43	C₂×C₄×C₇₉	—	2	3	no	—
44	C₂×C₄×C₇₉	—	2	6	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	—	2	3	no	—
50	C₂×Dic₇₉	—	2	3	no	—
51	C₂×Dic₇₉	—	2	3	no	—
52	C₄×D₇₉	—	4	4	no	—
53	C₂²×C₇₉	C₂×#41	1	1	yes	characteristic
54	C₂²×C₇₉	H(5,𝔽₂)	1	3	yes	—
55	C₂²×C₇₉	2₋¹⁺⁴	1	3	yes	—
56	C₂×D₇₉	—	2	6	no	—
57	C₂×D₇₉	—	4	1	no	—
58	C₂×D₇₉	—	4	3	no	—
59	C₄×C₇₉	—	4	3	no	—
60	C₄×C₇₉	—	4	1	no	—
61	C₄×C₇₉	—	4	3	no	—
62	Dic₇₉	—	4	3	no	—
63	Dic₇₉	—	4	1	no	—
64	Dic₇₉	—	4	3	no	—
65	C₂×C₇₉	#539	1	3	yes	—
66	C₂×C₇₉	#560	1	1	yes	characteristic
67	C₂×C₇₉	#563	1	3	yes	—
68	D₇₉	—	4	2	no	—
69	#2834	—	79	1	no	maximal, Sylow
70	C₇₉	#2834	1	1	yes	characteristic, complemented, Sylow
71	#401	—	79	1	no	—
72	#401	D₇₉	1	1	yes	characteristic, complemented
73	#399	—	79	1	no	—
74	#398	—	79	3	no	—
75	#398	—	79	3	no	—
76	#397	—	79	3	no	—
77	#385	—	79	3	no	—
78	C₂³×C₄	—	79	1	no	—
79	C₂×C₄⋊C₄	—	79	3	no	—
80	C₂×C₄⋊C₄	—	79	3	no	—
81	C₂×C₄⋊C₄	—	79	3	no	—
82	C₂×C₄⋊C₄	—	79	3	no	—
83	C₂×C₂²⋊C₄	—	79	3	no	—
84	C₂×C₂²⋊C₄	—	79	3	no	—
85	#95	—	79	3	no	—
86	#95	—	79	3	no	—
87	#95	—	79	3	no	—
88	#95	C₂×D₇₉	1	3	yes	—
89	#95	C₂×D₇₉	1	3	yes	—
90	#95	C₂×D₇₉	1	1	yes	characteristic
91	C₂⁴	—	79	1	no	—
92	C₂²×C₄	—	316	3	no	—
93	C₂²×C₄	—	79	3	no	—
94	C₂²×C₄	—	79	1	no	—
95	C₂²×C₄	—	79	3	no	—
96	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
97	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
98	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
99	C₄⋊C₄	—	316	3	no	—
100	C₄⋊C₄	—	316	3	no	—
101	C₄⋊C₄	—	316	3	no	—
102	C₄⋊C₄	—	316	3	no	—
103	C₂²⋊C₄	—	316	3	no	—
104	C₂²⋊C₄	—	158	6	no	—
105	C₂³	—	79	2	no	—
106	C₂³	—	158	3	no	—
107	C₂³	—	158	3	no	—
108	C₂³	C₂³×D₇₉	1	1	yes	characteristic
109	C₂×C₄	—	2	3	no	—
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	6	no	—
115	C₂×C₄	—	316	4	no	—
116	C₂×C₄	—	158	3	no	—
117	C₂×C₄	—	158	3	no	—
118	C₂×C₄	—	158	3	no	—
119	C₂×C₄	—	158	3	no	—
120	C₂×C₄	—	158	3	no	—
121	C₂×C₄	—	158	3	no	—
122	C₂×C₄	—	158	3	no	—
123	C₂²	—	316	1	no	—
124	C₂²	—	316	3	no	—
125	C₂²	—	158	6	no	—
126	C₂²	#41×D₇₉	1	1	yes	characteristic
127	C₂²	#14579207	1	3	yes	—
128	C₂²	#14579208	1	3	yes	—
129	C₄	—	4	3	no	—
130	C₄	—	4	1	no	—
131	C₄	—	4	3	no	—
132	C₄	—	316	3	no	—
133	C₄	—	316	1	no	—
134	C₄	—	316	3	no	—
135	C₂	—	316	2	no	—
136	C₂	#19099154	1	3	yes	—
137	C₂	#19099304	1	1	yes	characteristic
138	C₂	#19099315	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₉⋊#401

C₂

yes

maximal, characteristic, complemented

#19098500

C₂

yes

maximal, characteristic

#19098497

C₂

yes

maximal, complemented

#19098495

C₂

yes

maximal, complemented

#19098492

C₂

yes

maximal

#19098437

C₂

yes

maximal

#401×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

characteristic

C₂³×D₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂×C₄×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

#41

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₄×D₇₉

—

C₂²×C₇₉

C₂×#41

yes

characteristic

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#539

yes

—

C₂×C₇₉

#560

yes

characteristic

C₂×C₇₉

#563

yes

—

D₇₉

—

#2834

—

maximal, Sylow

C₇₉

#2834

yes

characteristic, complemented, Sylow

#401

—

#401

D₇₉

yes

characteristic, complemented

—

—

—

—

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

C₂×D₇₉

yes

—

#95

C₂×D₇₉

yes

—

#95

C₂×D₇₉

yes

characteristic

C₂⁴

—

C₂²×C₄

—

316

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

100

C₄⋊C₄

—

316

—

101

C₄⋊C₄

—

316

—

102

C₄⋊C₄

—

316

—

103

C₂²⋊C₄

—

316

—

104

C₂²⋊C₄

—

158

—

105

C₂³

—

106

C₂³

—

158

—

107

C₂³

—

158

—

108

C₂³

C₂³×D₇₉

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

316

—

116

C₂×C₄

—

158

—

117

C₂×C₄

—

158

—

118

C₂×C₄

—

158

—

119

C₂×C₄

—

158

—

120

C₂×C₄

—

158

—

121

C₂×C₄

—

158

—

122

C₂×C₄

—

158

—

123

C₂²

—

316

—

124

C₂²

—

316

—

125

C₂²

—

158

—

126

C₂²

#41×D₇₉

yes

characteristic

127

C₂²

#14579207

yes

—

128

C₂²

#14579208

yes

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

316

—

133

C₄

—

316

—

134

C₄

—

316

—

135

C₂

—

316

—

136

C₂

#19099154

yes

—

137

C₂

#19099304

yes

characteristic

138

C₂

#19099315

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#401×C₇₉	C₂
prime radical	C₂³×D₇₉	C₂³
hypercenter	#401	D₇₉
hypocenter	C₇₉	#2834
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#401×C₇₉

C₂

prime radical

C₂³×D₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
1. C₇₉⋊#401	C₂	semidirect
3. #19098497	C₂	semidirect
4. #19098495	C₂	semidirect
7. #401×C₇₉	C₂	semidirect
70. C₇₉	#2834	semidirect
72. #401	D₇₉	semidirect

H ≅ G/N

type

1. C₇₉⋊#401

C₂

semidirect

3. #19098497

C₂

semidirect

4. #19098495

C₂

semidirect

7. #401×C₇₉

C₂

semidirect

70. C₇₉

#2834

semidirect

72. #401

D₇₉

semidirect

Subgroups — #23771584

Conjugacy classes of subgroups

Complements