Group #23771760 — subgroups

Subgroups — #23771760

Order 10112.

472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14579153	C₂	1	1	yes	maximal, characteristic
2	#19098458	C₂	1	8	yes	maximal
3	#19098432	C₂	1	2	yes	maximal
4	#19098428	C₂	1	2	yes	maximal
5	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#125×C₇₉	C₂	1	1	yes	maximal, characteristic
7	#14579153	—	2	4	no	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×Dic₇₉⋊C₄	C₂²	1	8	yes	—
10	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
14	C₇₉⋊#95	C₂²	1	8	yes	—
15	#125×C₇₉	—	2	4	no	—
16	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₇₉	C₂²	1	4	yes	—
18	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₇₉	C₂³	1	4	yes	—
20	C₂²×Dic₇₉	C₂³	1	2	yes	—
21	C₂²×Dic₇₉	C₂³	1	2	yes	—
22	C₄⋊Dic₇₉	—	2	4	no	—
23	Dic₇₉⋊C₄	—	2	16	no	—
24	Dic₇₉⋊C₄	—	2	8	no	—
25	C₄×Dic₇₉	—	2	8	no	—
26	C₄×Dic₇₉	Q₈	1	4	yes	—
27	C₄×Dic₇₉	Q₈	1	4	yes	—
28	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₇₉	—	2	8	no	—
32	C₄⋊C₄×C₇₉	—	2	4	no	—
33	C₄²×C₇₉	D₄	1	4	yes	—
34	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₇₉	—	2	4	no	—
36	C₂×C₄×C₇₉	—	2	4	no	—
37	C₂×C₄×C₇₉	—	2	8	no	—
38	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
42	C₂×Dic₇₉	—	2	4	no	—
43	C₂×Dic₇₉	—	2	4	no	—
44	C₂×Dic₇₉	—	2	8	no	—
45	C₂×Dic₇₉	C₂×Q₈	1	4	yes	—
46	C₂×Dic₇₉	C₂×Q₈	1	4	yes	—
47	C₂×Dic₇₉	#41	1	8	yes	—
48	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
49	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
50	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₇₉	C₂×#41	1	4	yes	—
52	C₄×C₇₉	—	2	4	no	—
53	C₄×C₇₉	—	4	4	no	—
54	C₄×C₇₉	C₄⋊Q₈	1	4	yes	—
55	Dic₇₉	—	2	4	no	—
56	Dic₇₉	—	4	4	no	—
57	Dic₇₉	#125	1	8	yes	complemented
58	C₂×C₇₉	C₂×#125	1	2	yes	—
59	C₂×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
60	C₂×C₇₉	#532	1	2	yes	—
61	C₂×C₇₉	#533	1	2	yes	—
62	#2859	—	79	1	no	maximal, Sylow
63	C₇₉	#2859	1	1	yes	characteristic, complemented, Sylow
64	C₂×#125	—	79	1	no	—
65	C₂×#125	D₇₉	1	1	yes	characteristic
66	#389	—	79	8	no	—
67	#384	—	79	2	no	—
68	#382	—	79	2	no	—
69	C₄³	—	79	1	no	—
70	#125	—	2	4	no	—
71	#125	—	158	4	no	—
72	C₂×C₄⋊C₄	—	79	2	no	—
73	C₂×C₄⋊C₄	—	79	4	no	—
74	C₂×C₄⋊C₄	—	79	8	no	—
75	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
76	C₂×C₄⋊C₄	C₂×D₇₉	1	4	yes	—
77	C₂×C₄²	—	79	1	no	—
78	C₂×C₄²	—	79	1	no	—
79	C₂×C₄²	—	79	4	no	—
80	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
81	#95	—	79	8	no	—
82	C₂²×C₄	—	79	2	no	—
83	C₂²×C₄	—	79	2	no	—
84	C₂²×C₄	—	79	4	no	—
85	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
86	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
87	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
88	C₄⋊C₄	—	2	8	no	—
89	C₄⋊C₄	—	2	4	no	—
90	C₄⋊C₄	—	158	16	no	—
91	C₄⋊C₄	—	158	8	no	—
92	C₄⋊C₄	—	158	4	no	—
93	C₄²	—	79	4	no	—
94	C₄²	—	79	4	no	—
95	C₄²	—	158	8	no	—
96	C₄²	C₂²⋊D₇₉	1	4	yes	—
97	C₂³	C₂³×D₇₉	1	1	yes	characteristic
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	—	2	8	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	79	4	no	—
102	C₂×C₄	—	79	8	no	—
103	C₂×C₄	—	79	4	no	—
104	C₂×C₄	—	158	8	no	—
105	C₂×C₄	—	158	4	no	—
106	C₂×C₄	—	158	4	no	—
107	C₂×C₄	C₂×C₂²⋊D₇₉	1	4	yes	—
108	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
109	C₂×C₄	Q₈×D₇₉	1	2	yes	—
110	C₂×C₄	Q₈×D₇₉	1	2	yes	—
111	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
112	C₂²	C₂×Q₈×D₇₉	1	1	yes	characteristic
113	C₂²	C₂×Q₈×D₇₉	1	1	yes	characteristic
114	C₂²	#41×D₇₉	1	4	yes	—
115	C₄	—	2	4	no	—
116	C₄	—	4	4	no	—
117	C₄	—	316	4	no	—
118	C₄	—	79	8	no	—
119	C₄	—	158	4	no	—
120	C₄	#14579159	1	4	yes	—
121	C₂	#125×D₇₉	1	2	yes	—
122	C₂	C₂×#14579159	1	1	yes	characteristic
123	C₂	#19099109	1	2	yes	—
124	C₂	#19099119	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579153

C₂

yes

maximal, characteristic

#19098458

C₂

yes

maximal

#19098432

C₂

yes

maximal

#19098428

C₂

yes

maximal

C₄²×Dic₇₉

C₂

yes

maximal, characteristic

C₂×#125×C₇₉

C₂

yes

maximal, characteristic

#14579153

—

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

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₇₉⋊#95

C₂²

yes

—

#125×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

Q₈

yes

—

C₄×Dic₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

#41

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄⋊Q₈

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

#125

yes

complemented

C₂×C₇₉

C₂×#125

yes

—

C₂×C₇₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₉

#532

yes

—

C₂×C₇₉

#533

yes

—

#2859

—

maximal, Sylow

C₇₉

#2859

yes

characteristic, complemented, Sylow

C₂×#125

—

C₂×#125

D₇₉

yes

—

—

—

C₄³

—

#125

—

#125

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₄²

—

C₄²

—

158

—

C₄²

C₂²⋊D₇₉

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

158

—

105

C₂×C₄

—

158

—

106

C₂×C₄

—

158

—

107

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

108

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

109

C₂×C₄

Q₈×D₇₉

yes

—

110

C₂×C₄

Q₈×D₇₉

yes

—

111

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

112

C₂²

C₂×Q₈×D₇₉

yes

characteristic

113

C₂²

C₂×Q₈×D₇₉

yes

characteristic

114

C₂²

#41×D₇₉

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

316

—

118

C₄

—

119

C₄

—

158

—

120

C₄

#14579159

yes

—

121

C₂

#125×D₇₉

yes

—

122

C₂

C₂×#14579159

yes

characteristic

123

C₂

#19099109

yes

—

124

C₂

#19099119

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	C₂×#125×C₇₉	C₂
hypercenter	C₂×#125	D₇₉
hypocenter	C₇₉	#2859
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

C₂×#125×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
57. Dic₇₉	#125	semidirect
63. C₇₉	#2859	semidirect

H ≅ G/N

type

57. Dic₇₉

#125

semidirect

63. C₇₉

#2859

semidirect

Subgroups — #23771760

Conjugacy classes of subgroups

Complements