Group #34120198 — subgroups

Subgroups — C₇₉×#8509 #34120198

Order 20224.

656 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 158 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	C₂×#564×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#1992	C₂	1	3	yes	maximal
3	C₂×#330×C₇₉	C₂	1	3	yes	maximal
4	#564×C₇₉	—	2	6	no	—
5	#564×C₇₉	C₄	1	4	yes	complemented
6	C₂×#125×C₇₉	—	2	6	no	—
7	C₂×#125×C₇₉	C₂²	1	3	yes	—
8	C₂×#97×C₇₉	C₂²	1	3	yes	—
9	#384×C₇₉	C₂²	1	1	yes	characteristic
10	#340×C₇₉	—	2	6	no	—
11	#330×C₇₉	—	2	6	no	—
12	C₂²×C₈×C₇₉	—	2	3	no	—
13	#125×C₇₉	—	2	24	no	—
14	#125×C₇₉	—	2	24	no	—
15	#125×C₇₉	—	2	6	no	—
16	#125×C₇₉	C₂×C₄	1	6	yes	—
17	#125×C₇₉	D₄	1	6	yes	—
18	C₂×C₄⋊C₄×C₇₉	—	2	6	no	—
19	C₂×C₄⋊C₄×C₇₉	—	2	6	no	—
20	C₂×C₄⋊C₄×C₇₉	—	2	3	no	—
21	C₂×C₄⋊C₄×C₇₉	D₄	1	6	yes	—
22	C₂×C₄²×C₇₉	—	2	2	no	—
23	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
24	#97×C₇₉	—	2	6	no	—
25	C₂²×C₄×C₇₉	—	2	6	no	—
26	C₂²×C₄×C₇₉	—	4	1	no	—
27	C₂²×C₄×C₇₉	C₂×D₄	1	3	yes	—
28	C₂×C₈×C₇₉	—	2	6	no	—
29	C₂×C₈×C₇₉	—	4	3	no	—
30	C₂×C₈×C₇₉	—	4	3	no	—
31	C₄⋊C₄×C₇₉	—	2	24	no	—
32	C₄⋊C₄×C₇₉	—	2	12	no	—
33	C₄⋊C₄×C₇₉	—	2	12	no	—
34	C₄⋊C₄×C₇₉	—	2	6	no	—
35	C₄⋊C₄×C₇₉	—	4	6	no	—
36	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	12	yes	—
37	C₄²×C₇₉	—	2	8	no	—
38	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
39	C₄²×C₇₉	C₂×D₄	1	3	yes	—
40	C₂³×C₇₉	#120	1	1	yes	characteristic
41	C₂×C₄×C₇₉	—	2	3	no	—
42	C₂×C₄×C₇₉	—	2	3	no	—
43	C₂×C₄×C₇₉	—	2	12	no	—
44	C₂×C₄×C₇₉	—	4	6	no	—
45	C₂×C₄×C₇₉	—	4	6	no	—
46	C₂×C₄×C₇₉	—	8	3	no	—
47	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	3	yes	—
48	C₂×C₄×C₇₉	#120	1	3	yes	—
49	C₈×C₇₉	—	4	6	no	—
50	C₂²×C₇₉	#379	1	1	yes	characteristic
51	C₂²×C₇₉	#454	1	3	yes	—
52	C₂²×C₇₉	#456	1	3	yes	—
53	C₄×C₇₉	—	2	3	no	—
54	C₄×C₇₉	—	2	3	no	—
55	C₄×C₇₉	—	4	12	no	—
56	C₄×C₇₉	—	16	1	no	—
57	#8509	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂×C₇₉	#1658	1	1	yes	characteristic
59	C₂×C₇₉	#1663	1	3	yes	—
60	C₂×C₇₉	#1793	1	3	yes	—
61	C₂×#564	C₂×C₇₉	1	1	yes	characteristic
62	#1992	C₂×C₇₉	1	3	yes	—
63	C₂×#330	C₂×C₇₉	1	3	yes	—
64	C₇₉	#8509	1	1	yes	characteristic, direct product factor, Sylow
65	#564	—	2	6	no	—
66	#564	C₄×C₇₉	1	4	yes	complemented
67	C₂×#125	—	2	6	no	—
68	C₂×#125	C₂²×C₇₉	1	3	yes	—
69	C₂×#97	C₂²×C₇₉	1	3	yes	—
70	#384	C₂²×C₇₉	1	1	yes	characteristic
71	#340	—	2	6	no	—
72	#330	—	2	6	no	—
73	C₂²×C₈	—	2	3	no	—
74	#125	—	2	24	no	—
75	#125	—	2	24	no	—
76	#125	—	2	6	no	—
77	#125	C₂×C₄×C₇₉	1	6	yes	—
78	#125	D₄×C₇₉	1	6	yes	—
79	C₂×C₄⋊C₄	—	2	6	no	—
80	C₂×C₄⋊C₄	—	2	6	no	—
81	C₂×C₄⋊C₄	—	2	3	no	—
82	C₂×C₄⋊C₄	D₄×C₇₉	1	6	yes	—
83	C₂×C₄²	—	2	2	no	—
84	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
85	#97	—	2	6	no	—
86	C₂²×C₄	—	2	6	no	—
87	C₂²×C₄	—	4	1	no	—
88	C₂²×C₄	C₂×D₄×C₇₉	1	3	yes	—
89	C₂×C₈	—	2	6	no	—
90	C₂×C₈	—	4	3	no	—
91	C₂×C₈	—	4	3	no	—
92	C₄⋊C₄	—	2	24	no	—
93	C₄⋊C₄	—	2	12	no	—
94	C₄⋊C₄	—	2	12	no	—
95	C₄⋊C₄	—	2	6	no	—
96	C₄⋊C₄	—	4	6	no	—
97	C₄⋊C₄	C₂²⋊C₄×C₇₉	1	12	yes	—
98	C₄²	—	2	8	no	—
99	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
100	C₄²	C₂×D₄×C₇₉	1	3	yes	—
101	C₂³	#120×C₇₉	1	1	yes	characteristic
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	12	no	—
105	C₂×C₄	—	4	6	no	—
106	C₂×C₄	—	4	6	no	—
107	C₂×C₄	—	8	3	no	—
108	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	3	yes	—
109	C₂×C₄	#120×C₇₉	1	3	yes	—
110	C₈	—	4	6	no	—
111	C₂²	#379×C₇₉	1	1	yes	characteristic
112	C₂²	#454×C₇₉	1	3	yes	—
113	C₂²	#456×C₇₉	1	3	yes	—
114	C₄	—	2	3	no	—
115	C₄	—	2	3	no	—
116	C₄	—	4	12	no	—
117	C₄	—	16	1	no	—
118	C₂	C₇₉×#1658	1	1	yes	characteristic
119	C₂	C₇₉×#1663	1	3	yes	—
120	C₂	C₇₉×#1793	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#564×C₇₉

C₂

yes

maximal, characteristic

C₇₉×#1992

C₂

yes

maximal

C₂×#330×C₇₉

C₂

yes

maximal

#564×C₇₉

—

#564×C₇₉

C₄

yes

complemented

C₂×#125×C₇₉

—

C₂×#125×C₇₉

C₂²

yes

—

C₂×#97×C₇₉

C₂²

yes

—

#384×C₇₉

C₂²

yes

characteristic

#340×C₇₉

—

#330×C₇₉

—

C₂²×C₈×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

C₂×C₄

yes

—

#125×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#97×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

#120

yes

—

C₈×C₇₉

—

C₂²×C₇₉

#379

yes

characteristic

C₂²×C₇₉

#454

yes

—

C₂²×C₇₉

#456

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

#8509

C₇₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₇₉

#1658

yes

characteristic

C₂×C₇₉

#1663

yes

—

C₂×C₇₉

#1793

yes

—

C₂×#564

C₂×C₇₉

yes

characteristic

#1992

C₂×C₇₉

yes

—

C₂×#330

C₂×C₇₉

yes

—

C₇₉

#8509

yes

characteristic, direct product factor, Sylow

#564

—

#564

C₄×C₇₉

yes

complemented

C₂×#125

—

C₂×#125

C₂²×C₇₉

yes

—

C₂×#97

C₂²×C₇₉

yes

—

#384

C₂²×C₇₉

yes

characteristic

#340

—

#330

—

C₂²×C₈

—

—

—

—

C₂×C₄×C₇₉

yes

—

#125

D₄×C₇₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂³×C₇₉

yes

characteristic

#97

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₇₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊C₄×C₇₉

yes

—

C₄²

—

C₄²

C₂²×C₄×C₇₉

yes

characteristic

100

C₄²

C₂×D₄×C₇₉

yes

—

101

C₂³

#120×C₇₉

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₂×C₂²⋊C₄×C₇₉

yes

—

109

C₂×C₄

#120×C₇₉

yes

—

110

C₈

—

111

C₂²

#379×C₇₉

yes

characteristic

112

C₂²

#454×C₇₉

yes

—

113

C₂²

#456×C₇₉

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₂

C₇₉×#1658

yes

characteristic

119

C₂

C₇₉×#1663

yes

—

120

C₂

C₇₉×#1793

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₉	#120
commutator	C₄²	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₄²	C₂³×C₇₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₇₉

#120

commutator

C₄²

C₂²×C₄×C₇₉

Frattini, cosocle

C₂×C₄²

C₂³×C₇₉

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

N	H ≅ G/N	type
5. #564×C₇₉	C₄	semidirect
57. #8509	C₇₉	direct (N × H)
64. C₇₉	#8509	direct (N × H)
66. #564	C₄×C₇₉	semidirect

H ≅ G/N

type

5. #564×C₇₉

C₄

semidirect

57. #8509

C₇₉

direct (N × H)

64. C₇₉

#8509

direct (N × H)

66. #564

C₄×C₇₉

semidirect

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

subgroup	index
C₂×#564×C₇₉	2
C₇₉×#1992	2
C₂×#330×C₇₉	2
#8509	79

subgroup

index

C₂×#564×C₇₉

C₇₉×#1992

C₂×#330×C₇₉

#8509

Subgroups — C₇₉×#8509 #34120198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C79×#8509 #34120198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#8509 #34120198