Group #23777894 — subgroups

Subgroups — #23777894

Order 10112.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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⋊#564	C₂	1	3	yes	maximal, complemented
2	#19099290	C₂	1	12	yes	maximal, complemented
3	#19099172	C₂	1	12	yes	maximal
4	#19099119	C₂	1	3	yes	maximal
5	#564×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579160	C₂²	1	12	yes	—
7	#14579160	C₂²	1	6	yes	—
8	#14579156	C₂²	1	12	yes	—
9	#14579155	C₂²	1	4	yes	—
10	#14579153	C₂²	1	3	yes	—
11	#14579152	C₂²	1	12	yes	—
12	#14579151	C₂²	1	12	yes	—
13	#14579151	C₂²	1	12	yes	—
14	#14579151	C₂²	1	12	yes	—
15	#14579139	C₂²	1	12	yes	—
16	C₄×Dic₁₅₈	C₂²	1	12	yes	—
17	#14579126	C₂²	1	12	yes	—
18	#14579126	C₂²	1	12	yes	—
19	#14579119	C₂²	1	6	yes	—
20	C₄²×D₇₉	C₂²	1	1	yes	characteristic
21	#125×C₇₉	C₂²	1	12	yes	—
22	#125×C₇₉	C₂²	1	3	yes	—
23	C₂×Dic₁₅₈	C₂³	1	12	yes	—
24	C₂×C₄×D₇₉	C₂³	1	3	yes	—
25	C₄⋊Dic₇₉	C₂³	1	6	yes	—
26	C₄⋊Dic₇₉	C₂³	1	12	yes	—
27	Dic₇₉⋊C₄	C₂³	1	12	yes	—
28	Dic₇₉⋊C₄	C₂³	1	12	yes	—
29	Dic₇₉⋊C₄	C₂³	1	12	yes	—
30	Dic₇₉⋊C₄	C₂³	1	12	yes	—
31	(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	—
32	C₄×Dic₇₉	C₂³	1	3	yes	—
33	C₄×Dic₇₉	C₂³	1	12	yes	—
34	C₄×Dic₇₉	C₂³	1	12	yes	—
35	C₄⋊C₄×C₇₉	C₂³	1	6	yes	—
36	C₄⋊C₄×C₇₉	C₂³	1	12	yes	—
37	C₄⋊C₄×C₇₉	C₂³	1	12	yes	—
38	C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	C₄²×C₇₉	C₂³	1	4	yes	—
40	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂⁴	1	12	yes	—
42	C₂×C₄×C₇₉	C₂⁴	1	3	yes	—
43	C₂×Dic₇₉	C₂⁴	1	12	yes	—
44	C₂×Dic₇₉	C₂⁴	1	3	yes	—
45	C₄×D₇₉	—	2	6	no	—
46	Dic₁₅₈	—	2	24	no	—
47	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
48	C₂×D₇₉	—	2	3	no	—
49	C₄×C₇₉	—	2	12	no	—
50	C₄×C₇₉	—	2	3	no	—
51	Dic₇₉	—	2	12	no	—
52	Dic₇₉	2₋¹⁺⁴	1	6	yes	—
53	C₂×C₇₉	C₂×2₋¹⁺⁴	1	3	yes	—
54	D₇₉	—	4	1	no	—
55	#3556	—	79	1	no	maximal, Sylow
56	C₇₉	#3556	1	1	yes	characteristic, complemented, Sylow
57	#564	—	79	3	no	—
58	#564	D₇₉	1	1	yes	characteristic, complemented
59	#557	—	79	12	no	—
60	#541	—	79	12	no	—
61	#533	—	79	3	no	—
62	C₄⋊Q₈	—	79	6	no	—
63	C₄⋊Q₈	—	79	12	no	—
64	#126	—	79	12	no	—
65	#126	—	79	4	no	—
66	#125	—	79	12	no	—
67	#125	—	79	12	no	—
68	#125	—	79	12	no	—
69	#125	—	79	12	no	—
70	#125	—	79	3	no	—
71	#125	C₂×D₇₉	1	3	yes	—
72	#125	C₂×D₇₉	1	12	yes	—
73	C₂²⋊Q₈	—	79	12	no	—
74	C₄×Q₈	—	79	12	no	—
75	C₄×Q₈	—	79	12	no	—
76	C₄×Q₈	—	79	12	no	—
77	#117	—	79	6	no	—
78	C₂×C₄²	—	79	1	no	—
79	C₂×Q₈	—	79	12	no	—
80	C₂²×C₄	—	79	3	no	—
81	C₄⋊C₄	—	79	12	no	—
82	C₄⋊C₄	—	79	12	no	—
83	C₄⋊C₄	—	79	12	no	—
84	C₄⋊C₄	—	79	12	no	—
85	C₄⋊C₄	—	79	6	no	—
86	C₄⋊C₄	—	79	12	no	—
87	C₄⋊C₄	C₂²×D₇₉	1	6	yes	—
88	C₄⋊C₄	C₂²×D₇₉	1	12	yes	—
89	C₄⋊C₄	C₂²×D₇₉	1	12	yes	—
90	C₂²⋊C₄	—	79	12	no	—
91	C₄²	—	79	3	no	—
92	C₄²	—	79	12	no	—
93	C₄²	—	79	12	no	—
94	C₄²	C₂²×D₇₉	1	1	yes	characteristic
95	C₄²	C₂²×D₇₉	1	4	yes	—
96	C₂³	—	79	1	no	—
97	Q₈	—	158	24	no	—
98	C₂×C₄	—	79	3	no	—
99	C₂×C₄	—	79	12	no	—
100	C₂×C₄	—	158	6	no	—
101	C₂×C₄	C₂³×D₇₉	1	12	yes	—
102	C₂×C₄	C₂³×D₇₉	1	3	yes	—
103	C₂²	—	158	3	no	—
104	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
105	C₄	—	2	3	no	—
106	C₄	—	2	12	no	—
107	C₄	—	79	6	no	—
108	C₄	—	158	12	no	—
109	C₂	—	316	1	no	—
110	C₂	2₋¹⁺⁴×D₇₉	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₉⋊#564

C₂

yes

maximal, complemented

#19099290

C₂

yes

maximal, complemented

#19099172

C₂

yes

maximal

#19099119

C₂

yes

maximal

#564×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579160

C₂²

yes

—

#14579160

C₂²

yes

—

#14579156

C₂²

yes

—

#14579155

C₂²

yes

—

#14579153

C₂²

yes

—

#14579152

C₂²

yes

—

#14579151

C₂²

yes

—

#14579151

C₂²

yes

—

#14579151

C₂²

yes

—

#14579139

C₂²

yes

—

C₄×Dic₁₅₈

C₂²

yes

—

#14579126

C₂²

yes

—

#14579126

C₂²

yes

—

#14579119

C₂²

yes

—

C₄²×D₇₉

C₂²

yes

characteristic

#125×C₇₉

C₂²

yes

—

#125×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

C₂³

yes

—

C₂×C₄×D₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

C₂³

yes

—

Dic₇₉⋊C₄

C₂³

yes

—

Dic₇₉⋊C₄

C₂³

yes

—

Dic₇₉⋊C₄

C₂³

yes

—

(C₂×D₇₉)⋊C₄

C₂³

yes

—

C₄×Dic₇₉

C₂³

yes

—

C₄×Dic₇₉

C₂³

yes

—

C₄×Dic₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂³

yes

—

C₂²×D₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

—

C₂×Dic₇₉

C₂⁴

yes

—

C₂×Dic₇₉

C₂⁴

yes

—

C₄×D₇₉

—

Dic₁₅₈

—

C₂²×C₇₉

C₂⁵

yes

characteristic

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

2₋¹⁺⁴

yes

—

C₂×C₇₉

C₂×2₋¹⁺⁴

yes

—

D₇₉

—

#3556

—

maximal, Sylow

C₇₉

#3556

yes

characteristic, complemented, Sylow

#564

—

#564

D₇₉

yes

characteristic, complemented

#557

—

#541

—

#533

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

—

C₂×D₇₉

yes

—

#125

C₂×D₇₉

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₉

yes

characteristic

C₄²

C₂²×D₇₉

yes

—

C₂³

—

Q₈

—

158

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

158

—

101

C₂×C₄

C₂³×D₇₉

yes

—

102

C₂×C₄

C₂³×D₇₉

yes

—

103

C₂²

—

158

—

104

C₂²

C₂⁴×D₇₉

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

158

—

109

C₂

—

316

—

110

C₂

2₋¹⁺⁴×D₇₉

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#564×C₇₉	C₂
prime radical	C₂²×D₇₉	C₂⁴
hypercenter	#564	D₇₉
hypocenter	C₇₉	#3556
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₇₉

commutator, socle, cosocle

C₂²×C₇₉

C₂⁵

Fitting

#564×C₇₉

C₂

prime radical

C₂²×D₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. C₇₉⋊#564	C₂	semidirect
2. #19099290	C₂	semidirect
5. #564×C₇₉	C₂	semidirect
56. C₇₉	#3556	semidirect
58. #564	D₇₉	semidirect

H ≅ G/N

type

1. C₇₉⋊#564

C₂

semidirect

2. #19099290

C₂

semidirect

5. #564×C₇₉

C₂

semidirect

56. C₇₉

#3556

semidirect

58. #564

D₇₉

semidirect

Subgroups — #23777894

Conjugacy classes of subgroups

Complements