Group #23763544 — subgroups

Subgroups — #23763544

Order 10112.

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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	#19098409	C₂	1	1	yes	maximal, characteristic
2	#19098318	C₂	1	1	yes	maximal, characteristic
3	#19098317	C₂	1	2	yes	maximal
4	#19098317	C₂	1	2	yes	maximal
5	#336×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
9	C₇₉⋊#95	C₄	1	2	yes	—
10	C₇₉⋊#95	C₄	1	2	yes	—
11	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₇₉	C₂×C₄	1	2	yes	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₄×Dic₇₉	—	2	1	no	—
20	C₄×Dic₇₉	—	2	2	no	—
21	C₄×Dic₇₉	—	2	1	no	—
22	C₂²×C₄×C₇₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₇₉	—	2	2	no	—
25	C₂×C₈×C₇₉	—	2	2	no	—
26	C₂×C₈×C₇₉	—	2	2	no	—
27	C₄²×C₇₉	—	2	2	no	—
28	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	2	no	—
30	C₂×C₄×C₇₉	—	2	2	no	—
31	C₂×C₄×C₇₉	—	2	2	no	—
32	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
33	C₂×C₄×C₇₉	#41	1	2	yes	—
34	C₂×C₄×C₇₉	#41	1	2	yes	—
35	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
36	C₂×Dic₇₉	—	2	1	no	—
37	C₂×Dic₇₉	—	2	1	no	—
38	C₂×Dic₇₉	—	2	2	no	—
39	C₂×Dic₇₉	—	2	2	no	—
40	C₂×Dic₇₉	—	2	2	no	—
41	C₂×Dic₇₉	—	2	2	no	—
42	C₂×Dic₇₉	—	2	2	no	—
43	C₈×C₇₉	—	4	2	no	—
44	C₇₉⋊C₈	—	4	2	no	—
45	C₂²×C₇₉	#117	1	1	yes	characteristic
46	C₂²×C₇₉	#117	1	1	yes	characteristic
47	C₂²×C₇₉	#117	1	1	yes	characteristic
48	C₂²×C₇₉	#131	1	2	yes	—
49	C₂²×C₇₉	#131	1	2	yes	—
50	C₄×C₇₉	—	4	2	no	—
51	C₄×C₇₉	#126	1	2	yes	—
52	C₄×C₇₉	#126	1	2	yes	—
53	Dic₇₉	—	4	1	no	—
54	Dic₇₉	—	4	1	no	—
55	Dic₇₉	—	4	2	no	—
56	C₂×C₇₉	#383	1	1	yes	characteristic
57	C₂×C₇₉	#433	1	1	yes	characteristic
58	C₂×C₇₉	#433	1	2	yes	—
59	C₂×C₇₉	#433	1	1	yes	characteristic
60	C₂×C₇₉	#433	1	2	yes	—
61	#1840	—	79	1	no	maximal, Sylow
62	C₇₉	#1840	1	1	yes	characteristic, complemented, Sylow
63	#376	—	79	1	no	—
64	#336	—	79	2	no	—
65	#336	—	79	2	no	—
66	#336	—	79	1	no	—
67	#336	D₇₉	1	1	yes	characteristic
68	C₂²×C₈	—	79	2	no	—
69	C₂²×C₈	C₂×D₇₉	1	2	yes	—
70	C₂×C₄²	—	79	1	no	—
71	C₂×C₄²	—	79	1	no	—
72	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
73	#95	—	79	2	no	—
74	#95	—	79	2	no	—
75	C₂²×C₄	—	79	1	no	—
76	C₂²×C₄	—	79	1	no	—
77	C₂²×C₄	—	79	2	no	—
78	C₂²×C₄	C₄×D₇₉	1	2	yes	—
79	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	158	2	no	—
84	C₂×C₈	—	158	2	no	—
85	C₂×C₈	—	158	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	—	158	1	no	—
88	C₄²	—	158	2	no	—
89	C₄²	—	158	1	no	—
90	C₂³	C₂×C₄×D₇₉	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	158	1	no	—
95	C₂×C₄	—	158	1	no	—
96	C₂×C₄	—	158	2	no	—
97	C₂×C₄	—	158	2	no	—
98	C₂×C₄	—	158	2	no	—
99	C₂×C₄	—	158	2	no	—
100	C₂×C₄	—	158	2	no	—
101	C₂×C₄	#11929623	1	1	yes	characteristic
102	C₂×C₄	#11929623	1	2	yes	—
103	C₂×C₄	#11929624	1	2	yes	—
104	C₂×C₄	#11929625	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	316	2	no	—
107	C₂²	#14579117	1	1	yes	characteristic
108	C₂²	#14579118	1	1	yes	characteristic
109	C₂²	#14579119	1	1	yes	characteristic
110	C₂²	#14579167	1	2	yes	—
111	C₂²	#14579169	1	2	yes	—
112	C₄	—	4	2	no	—
113	C₄	—	316	1	no	—
114	C₄	—	316	1	no	—
115	C₄	—	316	2	no	—
116	C₄	#14579154	1	2	yes	—
117	C₄	#14579156	1	2	yes	—
118	C₂	#19098430	1	1	yes	characteristic
119	C₂	#19098621	1	2	yes	—
120	C₂	#19098622	1	1	yes	characteristic
121	C₂	#19098623	1	2	yes	—
122	C₂	#19098625	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098409

C₂

yes

maximal, characteristic

#19098318

C₂

yes

maximal, characteristic

#19098317

C₂

yes

maximal

#19098317

C₂

yes

maximal

#336×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₇₉⋊#95

C₄

yes

—

C₇₉⋊#95

C₄

yes

—

C₂²×C₈×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂²×C₇₉

#131

yes

—

C₄×C₇₉

—

C₄×C₇₉

#126

yes

—

C₄×C₇₉

#126

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#433

yes

characteristic

C₂×C₇₉

#433

yes

—

#1840

—

maximal, Sylow

C₇₉

#1840

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄²

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

—

158

—

C₂³

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

100

C₂×C₄

—

158

—

101

C₂×C₄

#11929623

yes

characteristic

102

C₂×C₄

#11929623

yes

—

103

C₂×C₄

#11929624

yes

—

104

C₂×C₄

#11929625

yes

characteristic

105

C₈

—

106

C₈

—

316

—

107

C₂²

#14579117

yes

characteristic

108

C₂²

#14579118

yes

characteristic

109

C₂²

#14579119

yes

characteristic

110

C₂²

#14579167

yes

—

111

C₂²

#14579169

yes

—

112

C₄

—

113

C₄

—

316

—

114

C₄

—

316

—

115

C₄

—

316

—

116

C₄

#14579154

yes

—

117

C₄

#14579156

yes

—

118

C₂

#19098430

yes

characteristic

119

C₂

#19098621

yes

—

120

C₂

#19098622

yes

characteristic

121

C₂

#19098623

yes

—

122

C₂

#19098625

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂²×C₄
Fitting	#336×C₇₉	C₂
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#336	D₇₉
hypocenter	C₇₉	#1840
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₇₉

commutator, socle, prime radical

C₂³×C₇₉

C₂²×C₄

Fitting

#336×C₇₉

C₂

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
62. C₇₉	#1840	semidirect

H ≅ G/N

type

62. C₇₉

#1840

semidirect

Subgroups — #23763544

Conjugacy classes of subgroups

Complements