Group #23764370 — subgroups

Subgroups — #23764370

Order 10112.

260 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14579072	C₂	1	1	yes	maximal, characteristic
2	#19098433	C₂	1	1	yes	maximal, characteristic
3	#19098325	C₂	1	4	yes	maximal
4	C₂×#125×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₇₉	—	2	2	no	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	#14579072	—	2	2	no	—
9	#125×C₇₉	—	2	2	no	—
10	#125×C₇₉	C₄	1	4	yes	complemented
11	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
12	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×Dic₇₉	—	2	2	no	—
15	C₂×C₇₉⋊C₈	—	2	2	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂×C₇₉⋊C₈	Q₈	1	4	yes	—
18	C₄⋊Dic₇₉	—	2	4	no	—
19	C₄⋊Dic₇₉	—	4	4	no	—
20	C₂²×C₄×C₇₉	—	2	2	no	—
21	C₂²×C₄×C₇₉	D₄	1	2	yes	—
22	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₇₉	—	2	8	no	—
24	C₄⋊C₄×C₇₉	—	2	2	no	—
25	C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
26	C₄²×C₇₉	C₂×C₄	1	2	yes	—
27	C₄²×C₇₉	D₄	1	2	yes	—
28	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	2	no	—
30	C₂×C₄×C₇₉	—	2	2	no	—
31	C₂×C₄×C₇₉	—	2	4	no	—
32	C₂×C₄×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	—	4	2	no	—
34	C₂×C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
35	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₇₉	#41	1	2	yes	—
39	C₂×Dic₇₉	—	4	2	no	—
40	C₂×Dic₇₉	—	4	4	no	—
41	C₇₉⋊C₈	—	2	4	no	—
42	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₇₉	#124	1	1	yes	characteristic
44	C₂²×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
45	C₂²×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
46	C₂²×C₇₉	#137	1	2	yes	—
47	C₄×C₇₉	—	2	4	no	—
48	C₄×C₇₉	—	4	4	no	—
49	C₄×C₇₉	C₄×Q₈	1	2	yes	—
50	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
51	Dic₇₉	—	8	2	no	—
52	C₂×C₇₉	#391	1	1	yes	characteristic
53	C₂×C₇₉	#417	1	2	yes	—
54	C₂×C₇₉	#490	1	1	yes	characteristic
55	C₂×C₇₉	#491	1	1	yes	characteristic
56	C₂×C₇₉	#501	1	2	yes	—
57	#1992	—	79	1	no	maximal, Sylow
58	C₇₉	#1992	1	1	yes	characteristic, complemented, Sylow
59	C₂×#125	D₇₉	1	1	yes	characteristic
60	C₂×#97	—	79	1	no	—
61	#384	—	79	1	no	—
62	#340	—	79	4	no	—
63	C₂²×C₈	—	79	2	no	—
64	#125	—	2	2	no	—
65	#125	Dic₇₉	1	4	yes	complemented
66	C₂×C₄⋊C₄	—	2	2	no	—
67	C₂×C₄⋊C₄	—	79	2	no	—
68	C₂×C₄⋊C₄	—	158	2	no	—
69	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
70	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
71	#97	—	158	2	no	—
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	—	158	2	no	—
74	C₂²×C₄	C₂²⋊D₇₉	1	2	yes	—
75	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
76	C₂×C₈	—	79	4	no	—
77	C₂×C₈	—	158	2	no	—
78	C₂×C₈	—	158	2	no	—
79	C₄⋊C₄	—	2	8	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	316	4	no	—
82	C₄⋊C₄	—	158	4	no	—
83	C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
84	C₄²	C₂×Dic₇₉	1	2	yes	—
85	C₄²	C₂²⋊D₇₉	1	2	yes	—
86	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	316	2	no	—
93	C₂×C₄	—	316	4	no	—
94	C₂×C₄	C₂²⋊Dic₇₉	1	4	yes	—
95	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
96	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
97	C₂×C₄	Q₈×D₇₉	1	2	yes	—
98	C₂×C₄	#11929625	1	2	yes	—
99	C₈	—	158	4	no	—
100	C₂²	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
101	C₂²	#14579150	1	1	yes	characteristic
102	C₂²	#14579159	1	1	yes	characteristic
103	C₂²	#14579186	1	2	yes	—
104	C₂²	#14579191	1	2	yes	—
105	C₄	—	2	4	no	—
106	C₄	—	4	4	no	—
107	C₄	—	632	2	no	—
108	C₄	Q₈×Dic₇₉	1	2	yes	—
109	C₄	#14579137	1	2	yes	—
110	C₂	#19098470	1	1	yes	characteristic
111	C₂	#19098564	1	2	yes	—
112	C₂	#19098929	1	1	yes	characteristic
113	C₂	#19098933	1	1	yes	characteristic
114	C₂	#19098973	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579072

C₂

yes

maximal, characteristic

#19098433

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal

C₂×#125×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

#14579072

—

#125×C₇₉

—

#125×C₇₉

C₄

yes

complemented

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

Q₈

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₉

#124

yes

characteristic

C₂²×C₇₉

C₄⋊Q₈

yes

characteristic

C₂²×C₇₉

AGL(1,ℤ/8)

yes

—

C₂²×C₇₉

#137

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×Q₈

yes

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

Dic₇₉

—

C₂×C₇₉

#391

yes

characteristic

C₂×C₇₉

#417

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

#1992

—

maximal, Sylow

C₇₉

#1992

yes

characteristic, complemented, Sylow

C₂×#125

D₇₉

yes

characteristic

C₂×#97

—

#384

—

#340

—

C₂²×C₈

—

#125

—

#125

Dic₇₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#97

—

158

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²⋊D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄⋊C₄

C₂×Dic₇₉

yes

—

C₄²

C₂×Dic₇₉

yes

—

C₄²

C₂²⋊D₇₉

yes

—

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

C₂²⋊Dic₇₉

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

Q₈×D₇₉

yes

—

C₂×C₄

#11929625

yes

—

C₈

—

158

—

100

C₂²

C₂×C₂²⋊Dic₇₉

yes

characteristic

101

C₂²

#14579150

yes

characteristic

102

C₂²

#14579159

yes

characteristic

103

C₂²

#14579186

yes

—

104

C₂²

#14579191

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

632

—

108

C₄

Q₈×Dic₇₉

yes

—

109

C₄

#14579137

yes

—

110

C₂

#19098470

yes

characteristic

111

C₂

#19098564

yes

—

112

C₂

#19098929

yes

characteristic

113

C₂

#19098933

yes

characteristic

114

C₂

#19098973

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#125×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×#125	D₇₉
hypocenter	C₇₉	#1992
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#125×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
10. #125×C₇₉	C₄	semidirect
58. C₇₉	#1992	semidirect
65. #125	Dic₇₉	semidirect

H ≅ G/N

type

10. #125×C₇₉

C₄

semidirect

58. C₇₉

#1992

semidirect

65. #125

Dic₇₉

semidirect

Subgroups — #23764370

Conjugacy classes of subgroups

Complements