Group #23766506 — subgroups

Subgroups — #23766506

Order 10112.

448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 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	#19098449	C₂	1	4	yes	maximal
2	#19098449	C₂	1	4	yes	maximal
3	C₄⋊C₄×Dic₇₉	C₂	1	4	yes	maximal
4	#19098409	C₂	1	2	yes	maximal
5	C₂×#125×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
7	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
8	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
9	C₇₉⋊#95	C₂²	1	2	yes	—
10	C₇₉⋊#95	C₂²	1	2	yes	—
11	C₇₉⋊#95	C₂²	1	4	yes	—
12	C₇₉⋊#95	C₂²	1	4	yes	—
13	C₇₉⋊#95	C₂²	1	4	yes	—
14	#125×C₇₉	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₄×C₇₉	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
17	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×Dic₇₉	C₂³	1	4	yes	—
19	C₂²×Dic₇₉	C₂³	1	4	yes	—
20	C₄⋊Dic₇₉	—	2	8	no	—
21	C₄×Dic₇₉	—	2	8	no	—
22	C₄×Dic₇₉	—	2	8	no	—
23	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
26	C₄⋊C₄×C₇₉	C₂×C₄	1	16	yes	—
27	C₄⋊C₄×C₇₉	C₂×C₄	1	8	yes	—
28	C₄²×C₇₉	C₂×C₄	1	4	yes	—
29	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₇₉	—	2	4	no	—
31	C₂×C₄×C₇₉	—	2	4	no	—
32	C₂×C₄×C₇₉	—	2	4	no	—
33	C₂×C₄×C₇₉	—	2	2	no	—
34	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₇₉	C₂²×C₄	1	8	yes	—
37	C₂×Dic₇₉	—	2	4	no	—
38	C₂×Dic₇₉	—	2	4	no	—
39	C₂×Dic₇₉	—	2	4	no	—
40	C₂×Dic₇₉	—	2	4	no	—
41	C₂×Dic₇₉	—	2	4	no	—
42	C₂×Dic₇₉	#41	1	8	yes	—
43	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
44	C₂²×C₇₉	C₂×#41	1	4	yes	—
45	C₂²×C₇₉	2₋¹⁺⁴	1	2	yes	—
46	C₄×C₇₉	—	2	4	no	—
47	C₄×C₇₉	—	2	8	no	—
48	C₄×C₇₉	—	2	2	no	—
49	Dic₇₉	—	2	8	no	—
50	Dic₇₉	—	4	4	no	—
51	C₂×C₇₉	C₄×#41	1	2	yes	—
52	C₂×C₇₉	#519	1	1	yes	characteristic
53	C₂×C₇₉	#552	1	4	yes	—
54	#2371	—	79	1	no	maximal, Sylow
55	C₇₉	#2371	1	1	yes	characteristic, complemented, Sylow
56	C₂×#125	D₇₉	1	1	yes	characteristic
57	#387	—	79	4	no	—
58	#387	—	79	4	no	—
59	C₄×C₄⋊C₄	—	79	4	no	—
60	#376	—	79	2	no	—
61	#125	Dic₇₉	1	8	yes	complemented
62	C₂×C₄⋊C₄	—	79	4	no	—
63	C₂×C₄⋊C₄	C₂×D₇₉	1	4	yes	—
64	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
65	C₂×C₄²	—	79	4	no	—
66	C₂×C₄²	—	79	4	no	—
67	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
68	#95	—	79	2	no	—
69	#95	—	79	4	no	—
70	#95	—	79	2	no	—
71	#95	—	79	4	no	—
72	#95	—	79	4	no	—
73	C₂²×C₄	—	79	4	no	—
74	C₂²×C₄	—	79	4	no	—
75	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
76	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
77	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
78	C₄⋊C₄	—	158	8	no	—
79	C₄⋊C₄	C₂×Dic₇₉	1	16	yes	—
80	C₄⋊C₄	C₂×Dic₇₉	1	8	yes	—
81	C₄²	—	158	8	no	—
82	C₄²	—	158	8	no	—
83	C₄²	C₂×Dic₇₉	1	4	yes	—
84	C₂³	C₂³×D₇₉	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	79	8	no	—
90	C₂×C₄	—	158	4	no	—
91	C₂×C₄	—	158	4	no	—
92	C₂×C₄	—	158	4	no	—
93	C₂×C₄	—	158	4	no	—
94	C₂×C₄	—	158	4	no	—
95	C₂×C₄	C₂²×Dic₇₉	1	4	yes	—
96	C₂×C₄	C₂²×Dic₇₉	1	2	yes	—
97	C₂×C₄	C₂²×Dic₇₉	1	8	yes	—
98	C₂²	C₂³×Dic₇₉	1	1	yes	characteristic
99	C₂²	#41×D₇₉	1	4	yes	—
100	C₂²	#14579209	1	2	yes	—
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	2	2	no	—
104	C₄	—	316	4	no	—
105	C₄	—	158	8	no	—
106	C₂	#41×Dic₇₉	1	2	yes	—
107	C₂	#19099041	1	1	yes	characteristic
108	C₂	#19099245	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098449

C₂

yes

maximal

#19098449

C₂

yes

maximal

C₄⋊C₄×Dic₇₉

C₂

yes

maximal

#19098409

C₂

yes

maximal

C₂×#125×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

#125×C₇₉

C₄

yes

complemented

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

—

C₄⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#41

yes

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₄×#41

yes

—

C₂×C₇₉

#519

yes

characteristic

C₂×C₇₉

#552

yes

—

#2371

—

maximal, Sylow

C₇₉

#2371

yes

characteristic, complemented, Sylow

C₂×#125

D₇₉

yes

characteristic

#387

—

#387

—

C₄×C₄⋊C₄

—

#376

—

#125

Dic₇₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

158

—

C₄⋊C₄

C₂×Dic₇₉

yes

—

C₄⋊C₄

C₂×Dic₇₉

yes

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

C₂×Dic₇₉

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂²×Dic₇₉

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

—

C₂²

C₂³×Dic₇₉

yes

characteristic

C₂²

#41×D₇₉

yes

—

100

C₂²

#14579209

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

316

—

105

C₄

—

158

—

106

C₂

#41×Dic₇₉

yes

—

107

C₂

#19099041

yes

characteristic

108

C₂

#19099245

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Fitting	C₂×#125×C₇₉	C₂
socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
hypercenter	C₂×#125	D₇₉
hypocenter	C₇₉	#2371
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Fitting

C₂×#125×C₇₉

C₂

socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
14. #125×C₇₉	C₄	semidirect
55. C₇₉	#2371	semidirect
61. #125	Dic₇₉	semidirect

H ≅ G/N

type

14. #125×C₇₉

C₄

semidirect

55. C₇₉

#2371

semidirect

61. #125

Dic₇₉

semidirect

Subgroups — #23766506

Conjugacy classes of subgroups

Complements