Group #23762036 — subgroups

Subgroups — #23762036

Order 10112.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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	#19099119	C₂	1	1	yes	maximal, characteristic
2	#19098618	C₂	1	2	yes	maximal
3	#19098305	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098304	C₂	1	2	yes	maximal, complemented
5	#330×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579160	C₄	1	2	yes	—
7	#14579153	C₂²	1	1	yes	characteristic
8	#14579139	—	2	2	no	—
9	#14579126	—	2	2	no	—
10	#14579119	C₄	1	2	yes	—
11	C₄²×D₇₉	C₂²	1	1	yes	characteristic
12	Dic₇₉⋊C₈	—	2	2	no	—
13	(C₂×D₇₉)⋊C₈	—	2	2	no	—
14	#14579072	C₂²	1	2	yes	—
15	#125×C₇₉	C₂²	1	1	yes	characteristic
16	#97×C₇₉	C₂²	1	2	yes	—
17	C₂×Dic₁₅₈	—	2	2	no	—
18	C₂×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₇₉	D₄	1	2	yes	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
22	Dic₇₉⋊C₄	—	2	2	no	—
23	Dic₇₉⋊C₄	—	2	2	no	—
24	(C₂×D₇₉)⋊C₄	—	2	2	no	—
25	C₄×Dic₇₉	—	2	2	no	—
26	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₉	D₄	1	2	yes	—
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₄⋊C₄×C₇₉	—	2	2	no	—
30	C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₂²×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	—	2	2	no	—
34	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
36	C₂×Dic₇₉	—	2	2	no	—
37	C₂×Dic₇₉	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₇₉	—	2	2	no	—
40	C₄×D₇₉	—	4	2	no	—
41	Dic₁₅₈	—	4	4	no	—
42	C₈×C₇₉	—	4	2	no	—
43	C₇₉⋊C₈	—	4	2	no	—
44	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₇₉	—	2	1	no	—
46	C₂×D₇₉	—	2	2	no	—
47	C₄×C₇₉	—	2	1	no	—
48	C₄×C₇₉	—	2	2	no	—
49	C₄×C₇₉	—	4	2	no	—
50	Dic₇₉	—	2	2	no	—
51	Dic₇₉	—	4	2	no	—
52	Dic₇₉	#101	1	2	yes	—
53	C₂×C₇₉	C₂×#101	1	1	yes	characteristic
54	C₂×C₇₉	#421	1	2	yes	—
55	D₇₉	—	4	1	no	—
56	#1537	—	79	1	no	maximal, Sylow
57	C₇₉	#1537	1	1	yes	characteristic, complemented, Sylow
58	#533	—	79	1	no	—
59	#432	—	79	2	no	—
60	#330	—	79	1	no	—
61	#330	—	79	2	no	—
62	#330	D₇₉	1	1	yes	characteristic, complemented
63	C₄⋊Q₈	—	79	2	no	—
64	#125	—	79	1	no	—
65	#125	C₂×D₇₉	1	1	yes	characteristic
66	C₂²⋊Q₈	—	158	2	no	—
67	C₄×Q₈	—	158	2	no	—
68	#117	—	79	2	no	—
69	C₂×C₄²	—	79	1	no	—
70	C₄⋊C₈	—	158	2	no	—
71	C₂²⋊C₈	—	158	2	no	—
72	#97	—	79	2	no	—
73	#97	C₂×D₇₉	1	2	yes	—
74	C₂×Q₈	—	158	2	no	—
75	C₂²×C₄	—	79	2	no	—
76	C₂²×C₄	—	79	1	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	158	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	79	2	no	—
81	C₄⋊C₄	—	158	2	no	—
82	C₄⋊C₄	—	158	2	no	—
83	C₄⋊C₄	C₄×D₇₉	1	2	yes	—
84	C₂²⋊C₄	—	158	2	no	—
85	C₄²	—	79	1	no	—
86	C₄²	—	79	2	no	—
87	C₄²	—	158	2	no	—
88	C₄²	C₂²×D₇₉	1	1	yes	characteristic
89	C₂³	—	79	1	no	—
90	Q₈	—	316	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	316	2	no	—
93	C₂×C₄	—	79	1	no	—
94	C₂×C₄	—	79	2	no	—
95	C₂×C₄	—	158	2	no	—
96	C₂×C₄	—	158	2	no	—
97	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
98	C₂×C₄	D₄×D₇₉	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	316	2	no	—
101	C₂²	—	158	1	no	—
102	C₂²	—	158	2	no	—
103	C₂²	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	316	2	no	—
108	C₄	—	79	2	no	—
109	C₄	—	158	2	no	—
110	C₂	—	316	1	no	—
111	C₂	#101×D₇₉	1	1	yes	characteristic
112	C₂	#19098578	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099119

C₂

yes

maximal, characteristic

#19098618

C₂

yes

maximal

#19098305

C₂

yes

maximal, characteristic, complemented

#19098304

C₂

yes

maximal, complemented

#330×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579160

C₄

yes

—

#14579153

C₂²

yes

—

—

C₄

yes

—

C₄²×D₇₉

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

(C₂×D₇₉)⋊C₈

—

#14579072

C₂²

yes

—

#125×C₇₉

C₂²

yes

characteristic

#97×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×C₄×D₇₉

C₂×C₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²⋊C₄

yes

—

C₂×Dic₇₉

C₂²⋊C₄

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

#101

yes

—

C₂×C₇₉

C₂×#101

yes

characteristic

C₂×C₇₉

#421

yes

—

D₇₉

—

#1537

—

maximal, Sylow

C₇₉

#1537

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic, complemented

C₄⋊Q₈

—

#125

—

#125

C₂×D₇₉

yes

characteristic

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

158

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

158

—

C₂²⋊C₈

—

158

—

#97

—

#97

C₂×D₇₉

yes

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

C₄×D₇₉

yes

—

C₂²⋊C₄

—

158

—

C₄²

—

C₄²

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

Q₈

—

316

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

D₄×D₇₉

yes

—

C₈

—

100

C₈

—

316

—

101

C₂²

—

158

—

102

C₂²

—

158

—

103

C₂²

C₂²⋊C₄×D₇₉

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

316

—

108

C₄

—

109

C₄

—

158

—

110

C₂

—

316

—

111

C₂

#101×D₇₉

yes

characteristic

112

C₂

#19098578

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	#330×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₇₉	C₂²⋊C₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	#330	D₇₉
hypocenter	C₇₉	#1537
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

#330×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₇₉

C₂²⋊C₄

cosocle

C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #19098305	C₂	semidirect
4. #19098304	C₂	semidirect
5. #330×C₇₉	C₂	semidirect
57. C₇₉	#1537	semidirect
62. #330	D₇₉	semidirect

H ≅ G/N

type

3. #19098305

C₂

semidirect

4. #19098304

C₂

semidirect

5. #330×C₇₉

C₂

semidirect

57. C₇₉

#1537

semidirect

62. #330

D₇₉

semidirect

Subgroups — #23762036

Conjugacy classes of subgroups

Complements