Group #34288520 — subgroups

Subgroups — #34288520

Order 20224.

830 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 243 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	#376×D₇₉	C₂	1	1	yes	maximal, characteristic
2	#23763545	C₂	1	1	yes	maximal, characteristic, complemented
3	#23763544	C₂	1	6	yes	maximal, complemented
4	#23763092	C₂	1	6	yes	maximal
5	C₇₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#11929607	C₂²	1	4	yes	—
7	C₂×C₄²×D₇₉	C₂²	1	3	yes	—
8	#19098409	C₂²	1	3	yes	—
9	#19098408	C₄	1	4	yes	—
10	#95×D₇₉	C₄	1	4	yes	—
11	#19098318	C₂²	1	6	yes	—
12	#19098317	C₂²	1	12	yes	—
13	#376×C₇₉	C₂²	1	1	yes	characteristic
14	#336×C₇₉	C₂²	1	6	yes	—
15	C₂²×C₄×D₇₉	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
17	C₂×#11929607	—	2	24	no	—
18	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
19	C₂×C₄×Dic₇₉	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₇₉	C₂³	1	3	yes	—
21	C₄²×D₇₉	—	2	12	no	—
22	C₇₉⋊#95	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
24	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
25	#95×C₇₉	C₂×C₄	1	4	yes	—
26	C₂³×D₇₉	C₂²×C₄	1	1	yes	characteristic
27	C₂²×Dic₇₉	C₂²×C₄	1	6	yes	—
28	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×D₇₉	—	2	12	no	—
30	C₂×C₄×D₇₉	—	4	12	no	—
31	C₂×C₄×D₇₉	#41	1	12	yes	—
32	#11929607	—	4	16	no	—
33	C₂×C₇₉⋊C₈	—	2	12	no	—
34	C₄×Dic₇₉	—	2	12	no	—
35	C₄×Dic₇₉	—	2	6	no	—
36	C₂²×C₄×C₇₉	C₂²×C₄	1	6	yes	—
37	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
38	C₂×C₈×C₇₉	—	2	12	no	—
39	C₄²×C₇₉	—	2	6	no	—
40	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
41	C₂²×D₇₉	—	2	4	no	—
42	C₂²×D₇₉	#117	1	6	yes	—
43	C₂×C₄×C₇₉	—	2	6	no	—
44	C₂×C₄×C₇₉	—	2	12	no	—
45	C₂×C₄×C₇₉	C₂×#41	1	6	yes	—
46	C₂×Dic₇₉	—	2	6	no	—
47	C₂×Dic₇₉	—	2	12	no	—
48	C₂×Dic₇₉	#117	1	6	yes	—
49	C₄×D₇₉	—	4	24	no	—
50	C₄×D₇₉	#126	1	16	yes	—
51	C₈×C₇₉	—	4	4	no	—
52	C₇₉⋊C₈	—	4	4	no	—
53	C₂²×C₇₉	C₂×#117	1	3	yes	—
54	C₂²×C₇₉	#568	1	4	yes	—
55	C₂×D₇₉	—	2	12	no	—
56	C₂×D₇₉	#383	1	4	yes	—
57	C₄×C₇₉	—	4	6	no	—
58	C₄×C₇₉	C₂×#126	1	4	yes	—
59	Dic₇₉	—	4	6	no	—
60	Dic₇₉	#383	1	4	yes	—
61	#20773	—	79	1	no	maximal, Sylow
62	C₂×C₇₉	C₂×#383	1	1	yes	characteristic
63	C₂×C₇₉	#2921	1	6	yes	—
64	D₇₉	—	2	4	no	—
65	C₂×#376	—	79	1	no	—
66	#1840	—	79	1	no	—
67	#1840	—	79	6	no	—
68	#1840	D₇₉	1	1	yes	characteristic, complemented
69	#1728	—	79	6	no	—
70	C₇₉	#20773	1	1	yes	characteristic, complemented, Sylow
71	C₂²×M₁₆	—	79	4	no	—
72	C₂²×C₄²	—	79	3	no	—
73	#376	—	79	3	no	—
74	#376	—	79	4	no	—
75	#376	C₂×D₇₉	1	1	yes	characteristic
76	C₂×#95	—	79	4	no	—
77	#336	—	79	12	no	—
78	#336	—	79	6	no	—
79	#336	C₂×D₇₉	1	6	yes	—
80	C₂³×C₄	—	79	6	no	—
81	C₂³×C₄	—	79	1	no	—
82	C₂×M₁₆	—	158	24	no	—
83	C₂²×C₈	—	79	4	no	—
84	C₂²×C₈	C₂²×D₇₉	1	4	yes	—
85	C₂×C₄²	—	79	6	no	—
86	C₂×C₄²	—	79	3	no	—
87	C₂×C₄²	—	158	12	no	—
88	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
89	#95	—	79	12	no	—
90	#95	C₄×D₇₉	1	4	yes	—
91	C₂⁴	—	79	1	no	—
92	C₂²×C₄	—	316	12	no	—
93	C₂²×C₄	—	79	1	no	—
94	C₂²×C₄	—	79	12	no	—
95	C₂²×C₄	—	79	6	no	—
96	C₂²×C₄	—	158	12	no	—
97	C₂²×C₄	C₂×C₄×D₇₉	1	6	yes	—
98	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
99	M₁₆	—	316	16	no	—
100	C₂×C₈	—	2	12	no	—
101	C₂×C₈	—	158	12	no	—
102	C₄²	—	2	6	no	—
103	C₄²	—	158	12	no	—
104	C₄²	—	158	6	no	—
105	C₂³	—	79	6	no	—
106	C₂³	—	158	4	no	—
107	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
108	C₂×C₄	—	2	6	no	—
109	C₂×C₄	—	2	12	no	—
110	C₂×C₄	—	316	24	no	—
111	C₂×C₄	—	79	6	no	—
112	C₂×C₄	—	79	16	no	—
113	C₂×C₄	—	158	6	no	—
114	C₂×C₄	—	158	12	no	—
115	C₂×C₄	#41×D₇₉	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	316	4	no	—
118	C₂²	—	79	4	no	—
119	C₂²	—	158	12	no	—
120	C₂²	#117×D₇₉	1	3	yes	—
121	C₂²	#19099328	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	316	6	no	—
124	C₄	—	79	4	no	—
125	C₄	#126×D₇₉	1	4	yes	—
126	C₂	—	158	4	no	—
127	C₂	#383×D₇₉	1	1	yes	characteristic
128	C₂	#23772034	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#376×D₇₉

C₂

yes

maximal, characteristic

#23763545

C₂

yes

maximal, characteristic, complemented

#23763544

C₂

yes

maximal, complemented

#23763092

C₂

yes

maximal

C₇₉×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×#11929607

C₂²

yes

—

C₂×C₄²×D₇₉

C₂²

yes

—

#19098409

C₂²

yes

—

#19098408

C₄

yes

—

#95×D₇₉

C₄

yes

—

#19098318

C₂²

yes

—

#19098317

C₂²

yes

—

#376×C₇₉

C₂²

yes

characteristic

#336×C₇₉

C₂²

yes

—

C₂²×C₄×D₇₉

C₂×C₄

yes

—

C₂²×C₄×D₇₉

C₂³

yes

characteristic

C₂×#11929607

—

C₂²×C₇₉⋊C₈

C₂³

yes

—

C₂×C₄×Dic₇₉

C₂×C₄

yes

—

C₂×C₄×Dic₇₉

C₂³

yes

—

C₄²×D₇₉

—

C₇₉⋊#95

C₂×C₄

yes

—

C₂²×C₈×C₇₉

C₂³

yes

—

C₂×C₄²×C₇₉

C₂³

yes

—

#95×C₇₉

C₂×C₄

yes

—

C₂³×D₇₉

C₂²×C₄

yes

characteristic

C₂²×Dic₇₉

C₂²×C₄

yes

—

C₂²×Dic₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

#41

yes

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

—

C₂²×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×C₈×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂³×C₄

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

#117

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#117

yes

—

C₄×D₇₉

—

C₄×D₇₉

#126

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×#117

yes

—

C₂²×C₇₉

#568

yes

—

C₂×D₇₉

—

C₂×D₇₉

#383

yes

—

C₄×C₇₉

—

C₄×C₇₉

C₂×#126

yes

—

Dic₇₉

—

Dic₇₉

#383

yes

—

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

D₇₉

—

—

—

—

D₇₉

yes

characteristic, complemented

#1728

—

C₇₉

#20773

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₇₉

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₇₉

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂×M₁₆

—

158

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

158

—

C₂×C₄²

C₂²×D₇₉

yes

—

#95

—

#95

C₄×D₇₉

yes

—

C₂⁴

—

C₂²×C₄

—

316

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂×C₄×D₇₉

yes

—

C₂²×C₄

C₂³×D₇₉

yes

characteristic

M₁₆

—

316

—

100

C₂×C₈

—

101

C₂×C₈

—

158

—

102

C₄²

—

103

C₄²

—

158

—

104

C₄²

—

158

—

105

C₂³

—

106

C₂³

—

158

—

107

C₂³

C₂²×C₄×D₇₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

316

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

158

—

114

C₂×C₄

—

158

—

115

C₂×C₄

#41×D₇₉

yes

—

116

C₈

—

117

C₈

—

316

—

118

C₂²

—

119

C₂²

—

158

—

120

C₂²

#117×D₇₉

yes

—

121

C₂²

#19099328

yes

—

122

C₄

—

123

C₄

—

316

—

124

C₄

—

125

C₄

#126×D₇₉

yes

—

126

C₂

—

158

—

127

C₂

#383×D₇₉

yes

characteristic

128

C₂

#23772034

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1840	C₂
prime radical	C₂³×D₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1840	D₇₉
hypocenter	C₇₉	#20773
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₇₉

commutator, socle

C₂³×C₇₉

C₂³×C₄

Fitting

C₇₉×#1840

C₂

prime radical

C₂³×D₇₉

C₂²×C₄

cosocle

C₂²×C₄×C₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #23763545	C₂	semidirect
3. #23763544	C₂	semidirect
5. C₇₉×#1840	C₂	semidirect
68. #1840	D₇₉	semidirect
70. C₇₉	#20773	semidirect

H ≅ G/N

type

2. #23763545

C₂

semidirect

3. #23763544

C₂

semidirect

5. C₇₉×#1840

C₂

semidirect

68. #1840

D₇₉

semidirect

70. C₇₉

#20773

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#376×D₇₉	2
#23763545	2
#23763544	2
#23763092	2
C₇₉×#1840	2
#20773	79

subgroup

index

#376×D₇₉

C₇₉×#1840

Subgroups — #34288520

Conjugacy classes of subgroups

Complements

Maximal subgroups