Group #23777548 — subgroups

Subgroups — #23777548

Order 10112.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	#19099317	C₂	1	10	yes	maximal, complemented
2	#19099311	C₂	1	5	yes	maximal, complemented
3	#19099119	C₂	1	5	yes	maximal, complemented
4	#19099098	C₂	1	10	yes	maximal, complemented
5	#564×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579160	C₂²	1	10	yes	—
7	#14579156	C₂²	1	20	yes	—
8	#14579153	C₂²	1	5	yes	—
9	#14579149	C₂²	1	10	yes	—
10	#14579146	C₂²	1	20	yes	—
11	#14579141	C₂²	1	10	yes	—
12	#14579139	C₂²	1	20	yes	—
13	#14579136	C₂²	1	10	yes	—
14	#14579126	C₂²	1	10	yes	—
15	#14579123	C₂²	1	10	yes	—
16	#14579119	C₂²	1	10	yes	—
17	C₄²×D₇₉	C₂²	1	5	yes	—
18	#125×C₇₉	C₂²	1	5	yes	—
19	#125×C₇₉	C₂²	1	10	yes	—
20	C₂×Dic₁₅₈	C₂³	1	10	yes	—
21	C₂×D₃₁₆	C₂³	1	10	yes	—
22	C₂×C₄×D₇₉	C₂³	1	5	yes	—
23	C₂×C₄×D₇₉	C₂³	1	10	yes	—
24	C₄⋊Dic₇₉	C₂³	1	10	yes	—
25	Dic₇₉⋊C₄	C₂³	1	20	yes	—
26	(C₂×D₇₉)⋊C₄	C₂³	1	20	yes	—
27	(C₂×D₇₉)⋊C₄	C₂³	1	20	yes	—
28	C₄×Dic₇₉	C₂³	1	10	yes	—
29	C₄×Dic₇₉	C₂³	1	5	yes	—
30	C₄⋊C₄×C₇₉	C₂³	1	10	yes	—
31	C₄⋊C₄×C₇₉	C₂³	1	10	yes	—
32	C₄⋊C₄×C₇₉	C₂³	1	10	yes	—
33	C₄²×C₇₉	C₂³	1	5	yes	—
34	C₂²×D₇₉	C₂⁴	1	5	yes	—
35	C₂×C₄×C₇₉	C₂⁴	1	5	yes	—
36	C₂×C₄×C₇₉	C₂⁴	1	10	yes	—
37	C₂×Dic₇₉	C₂⁴	1	10	yes	—
38	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
39	D₃₁₆	—	4	10	no	—
40	C₄×D₇₉	—	2	10	no	—
41	C₄×D₇₉	—	4	10	no	—
42	Dic₁₅₈	—	4	10	no	—
43	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
44	C₂×D₇₉	—	2	5	no	—
45	C₂×D₇₉	—	2	10	no	—
46	C₄×C₇₉	—	2	5	no	—
47	C₄×C₇₉	—	2	10	no	—
48	Dic₇₉	—	2	10	no	—
49	Dic₇₉	2₋¹⁺⁴	1	2	yes	—
50	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
51	C₂×C₇₉	#585	1	2	yes	—
52	D₇₉	—	4	5	no	—
53	#3531	—	79	1	no	maximal, Sylow
54	C₇₉	#3531	1	1	yes	characteristic, complemented, Sylow
55	#564	D₇₉	1	1	yes	characteristic, complemented
56	#563	—	79	10	no	—
57	#562	—	79	5	no	—
58	#533	—	79	5	no	—
59	#529	—	79	10	no	—
60	C₄⋊Q₈	—	79	10	no	—
61	#126	—	79	20	no	—
62	#125	—	79	5	no	—
63	#125	C₂×D₇₉	1	10	yes	—
64	#125	C₂×D₇₉	1	5	yes	—
65	#124	—	79	10	no	—
66	#123	—	79	20	no	—
67	C₂²⋊Q₈	—	79	10	no	—
68	C₂²⋊Q₈	—	79	20	no	—
69	#121	—	79	10	no	—
70	C₄×Q₈	—	79	10	no	—
71	C₄×D₄	—	79	10	no	—
72	#117	—	79	10	no	—
73	C₂×C₄²	—	79	5	no	—
74	C₂×Q₈	—	79	10	no	—
75	C₂×D₄	—	79	10	no	—
76	C₂²×C₄	—	79	10	no	—
77	C₂²×C₄	—	79	5	no	—
78	C₄⋊C₄	—	79	20	no	—
79	C₄⋊C₄	—	79	10	no	—
80	C₄⋊C₄	C₂²×D₇₉	1	10	yes	—
81	C₄⋊C₄	C₂²×D₇₉	1	10	yes	—
82	C₄⋊C₄	C₂²×D₇₉	1	10	yes	—
83	C₂²⋊C₄	—	79	20	no	—
84	C₂²⋊C₄	—	79	20	no	—
85	C₄²	—	79	10	no	—
86	C₄²	—	79	5	no	—
87	C₄²	C₂²×D₇₉	1	5	yes	—
88	C₂³	—	79	5	no	—
89	Q₈	—	316	10	no	—
90	D₄	—	316	10	no	—
91	C₂×C₄	—	316	10	no	—
92	C₂×C₄	—	79	1	no	—
93	C₂×C₄	—	79	10	no	—
94	C₂×C₄	—	158	10	no	—
95	C₂×C₄	C₂³×D₇₉	1	5	yes	—
96	C₂×C₄	C₂³×D₇₉	1	10	yes	—
97	C₂²	—	158	5	no	—
98	C₂²	—	158	10	no	—
99	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
100	C₄	—	2	5	no	—
101	C₄	—	2	10	no	—
102	C₄	—	79	2	no	—
103	C₄	—	158	10	no	—
104	C₂	—	316	5	no	—
105	C₂	2₋¹⁺⁴×D₇₉	1	1	yes	characteristic
106	C₂	#19099400	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099317

C₂

yes

maximal, complemented

#19099311

C₂

yes

maximal, complemented

#19099119

C₂

yes

maximal, complemented

#19099098

C₂

yes

maximal, complemented

#564×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579160

C₂²

yes

—

#14579156

C₂²

yes

—

#14579153

C₂²

yes

—

#14579149

C₂²

yes

—

#14579146

C₂²

yes

—

#14579141

C₂²

yes

—

#14579139

C₂²

yes

—

#14579136

C₂²

yes

—

#14579126

C₂²

yes

—

#14579123

C₂²

yes

—

#14579119

C₂²

yes

—

C₄²×D₇₉

C₂²

yes

—

#125×C₇₉

C₂²

yes

—

#125×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

C₂³

yes

—

C₂×D₃₁₆

C₂³

yes

—

C₂×C₄×D₇₉

C₂³

yes

—

C₂×C₄×D₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

C₂³

yes

—

(C₂×D₇₉)⋊C₄

C₂³

yes

—

(C₂×D₇₉)⋊C₄

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

—

C₂²×D₇₉

C₂⁴

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

—

C₂×Dic₇₉

C₂⁴

yes

—

C₂×Dic₇₉

C₂⁴

yes

characteristic

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₂²×C₇₉

C₂⁵

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

2₋¹⁺⁴

yes

—

C₂×C₇₉

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₇₉

#585

yes

—

D₇₉

—

#3531

—

maximal, Sylow

C₇₉

#3531

yes

characteristic, complemented, Sylow

#564

D₇₉

yes

characteristic, complemented

—

—

—

—

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₇₉

yes

—

#125

C₂×D₇₉

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₉

yes

—

C₂³

—

Q₈

—

316

—

D₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

C₂³×D₇₉

yes

—

C₂×C₄

C₂³×D₇₉

yes

—

C₂²

—

158

—

C₂²

—

158

—

C₂²

C₂⁴×D₇₉

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

158

—

104

C₂

—

316

—

105

C₂

2₋¹⁺⁴×D₇₉

yes

characteristic

106

C₂

#19099400

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#564×C₇₉	C₂
hypercenter	#564	D₇₉
hypocenter	C₇₉	#3531
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

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. #19099317	C₂	semidirect
2. #19099311	C₂	semidirect
3. #19099119	C₂	semidirect
4. #19099098	C₂	semidirect
5. #564×C₇₉	C₂	semidirect
54. C₇₉	#3531	semidirect
55. #564	D₇₉	semidirect

H ≅ G/N

type

1. #19099317

C₂

semidirect

2. #19099311

C₂

semidirect

3. #19099119

C₂

semidirect

4. #19099098

C₂

semidirect

5. #564×C₇₉

C₂

semidirect

54. C₇₉

#3531

semidirect

55. #564

D₇₉

semidirect

Subgroups — #23777548

Conjugacy classes of subgroups

Complements