Group #34125387 — subgroups

Subgroups — C₇₉×#13698 #34125387

Order 20224.

190 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 74 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×Q₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2216	C₂	1	2	yes	maximal
4	C₇₉×#1424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1416	C₂	1	2	yes	maximal, complemented
6	C₂×Q₃₂×C₇₉	C₂²	1	2	yes	—
7	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
8	#467×C₇₉	—	2	2	no	—
9	Q₆₄×C₇₉	—	2	2	no	—
10	M₆₄×C₇₉	—	2	2	no	—
11	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
13	#366×C₇₉	C₂²	1	2	yes	—
14	#358×C₇₉	—	2	2	no	—
15	C₂×Q₁₆×C₇₉	—	2	2	no	—
16	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
17	C₂²⋊Q₈×C₇₉	—	4	2	no	—
18	Q₃₂×C₇₉	—	2	2	no	—
19	Q₃₂×C₇₉	—	2	2	no	—
20	C₂×C₁₆×C₇₉	—	2	1	no	—
21	C₂×C₁₆×C₇₉	—	2	1	no	—
22	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
23	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
24	#107×C₇₉	—	2	2	no	—
25	#103×C₇₉	—	4	2	no	—
26	C₃₂×C₇₉	—	2	1	no	—
27	C₃₂×C₇₉	D₄	1	2	yes	—
28	C₂×Q₈×C₇₉	—	4	2	no	—
29	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
30	Q₁₆×C₇₉	—	4	2	no	—
31	Q₁₆×C₇₉	—	4	2	no	—
32	C₂×C₈×C₇₉	—	2	1	no	—
33	C₂×C₈×C₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
35	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₄⋊C₄×C₇₉	—	4	2	no	—
37	C₄⋊C₄×C₇₉	—	8	2	no	—
38	C₂²⋊C₄×C₇₉	—	8	2	no	—
39	C₁₆×C₇₉	—	2	1	no	—
40	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₁₆×C₇₉	#41	1	1	yes	characteristic
42	C₂³×C₇₉	D₁₆	1	1	yes	characteristic
43	Q₈×C₇₉	—	8	2	no	—
44	Q₈×C₇₉	—	8	2	no	—
45	C₂×C₄×C₇₉	—	2	1	no	—
46	C₂×C₄×C₇₉	—	2	1	no	—
47	C₂×C₄×C₇₉	—	8	2	no	—
48	C₂×C₄×C₇₉	—	8	2	no	—
49	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
50	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
51	C₈×C₇₉	—	2	1	no	—
52	C₈×C₇₉	#121	1	1	yes	characteristic
53	C₈×C₇₉	#135	1	1	yes	characteristic
54	C₂²×C₇₉	—	2	1	no	—
55	C₂²×C₇₉	—	2	2	no	—
56	C₂²×C₇₉	C₂×D₁₆	1	1	yes	characteristic
57	C₄×C₇₉	—	2	1	no	—
58	C₄×C₇₉	—	16	2	no	—
59	C₄×C₇₉	—	16	2	no	—
60	C₄×C₇₉	#466	1	1	yes	characteristic
61	C₄×C₇₉	#508	1	1	yes	characteristic
62	#13698	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂×C₇₉	—	4	1	no	—
64	C₂×C₇₉	#2215	1	1	yes	characteristic
65	C₂×C₇₉	#2264	1	2	yes	—
66	C₂×Q₆₄	C₂×C₇₉	1	1	yes	characteristic, complemented
67	C₂×M₆₄	C₂×C₇₉	1	1	yes	characteristic
68	#2216	C₂×C₇₉	1	2	yes	—
69	#1424	C₂×C₇₉	1	1	yes	characteristic, complemented
70	#1416	C₂×C₇₉	1	2	yes	complemented
71	C₇₉	#13698	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×Q₃₂	C₂²×C₇₉	1	2	yes	—
73	C₂²×C₁₆	C₂²×C₇₉	1	1	yes	characteristic
74	#467	—	2	2	no	—
75	Q₆₄	—	2	2	no	—
76	M₆₄	—	2	2	no	—
77	C₂×C₃₂	C₂²×C₇₉	1	1	yes	characteristic
78	C₂×C₃₂	C₂²×C₇₉	1	1	yes	characteristic
79	#366	C₂²×C₇₉	1	2	yes	—
80	#358	—	2	2	no	—
81	C₂×Q₁₆	—	2	2	no	—
82	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
83	C₂²⋊Q₈	—	4	2	no	—
84	Q₃₂	—	2	2	no	—
85	Q₃₂	—	2	2	no	—
86	C₂×C₁₆	—	2	1	no	—
87	C₂×C₁₆	—	2	1	no	—
88	C₂×C₁₆	D₄×C₇₉	1	1	yes	characteristic
89	C₂×C₁₆	C₂³×C₇₉	1	1	yes	characteristic
90	#107	—	2	2	no	—
91	#103	—	4	2	no	—
92	C₃₂	—	2	1	no	—
93	C₃₂	D₄×C₇₉	1	2	yes	—
94	C₂×Q₈	—	4	2	no	—
95	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
96	Q₁₆	—	4	2	no	—
97	Q₁₆	—	4	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	D₈×C₇₉	1	1	yes	characteristic
101	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	8	2	no	—
104	C₂²⋊C₄	—	8	2	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	C₂×D₄×C₇₉	1	1	yes	characteristic
107	C₁₆	#41×C₇₉	1	1	yes	characteristic
108	C₂³	D₁₆×C₇₉	1	1	yes	characteristic
109	Q₈	—	8	2	no	—
110	Q₈	—	8	2	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	8	2	no	—
114	C₂×C₄	—	8	2	no	—
115	C₂×C₄	D₁₆×C₇₉	1	1	yes	characteristic
116	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	#121×C₇₉	1	1	yes	characteristic
119	C₈	#135×C₇₉	1	1	yes	characteristic
120	C₂²	—	2	2	no	—
121	C₂²	—	2	1	no	—
122	C₂²	C₂×D₁₆×C₇₉	1	1	yes	characteristic
123	C₄	—	2	1	no	—
124	C₄	—	16	2	no	—
125	C₄	—	16	2	no	—
126	C₄	#466×C₇₉	1	1	yes	characteristic
127	C₄	#508×C₇₉	1	1	yes	characteristic
128	C₂	—	4	1	no	—
129	C₂	C₇₉×#2215	1	1	yes	characteristic
130	C₂	C₇₉×#2264	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₆₄×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×M₆₄×C₇₉

C₂

yes

maximal, characteristic

C₇₉×#2216

C₂

yes

maximal

C₇₉×#1424

C₂

yes

maximal, characteristic, complemented

C₇₉×#1416

C₂

yes

maximal, complemented

C₂×Q₃₂×C₇₉

C₂²

yes

—

C₂²×C₁₆×C₇₉

C₂²

yes

characteristic

#467×C₇₉

—

Q₆₄×C₇₉

—

M₆₄×C₇₉

—

C₂×C₃₂×C₇₉

C₂²

yes

characteristic

C₂×C₃₂×C₇₉

C₂²

yes

characteristic

#366×C₇₉

C₂²

yes

—

#358×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²⋊Q₈×C₇₉

—

Q₃₂×C₇₉

—

Q₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

D₄

yes

characteristic

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

#103×C₇₉

—

C₃₂×C₇₉

—

C₃₂×C₇₉

D₄

yes

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

D₈

yes

characteristic

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₈

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₁₆×C₇₉

C₂×D₄

yes

characteristic

C₁₆×C₇₉

#41

yes

characteristic

C₂³×C₇₉

D₁₆

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₇₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₇₉

—

C₂×C₇₉

#2215

yes

characteristic

C₂×C₇₉

#2264

yes

—

C₂×Q₆₄

C₂×C₇₉

yes

characteristic, complemented

C₂×M₆₄

C₂×C₇₉

yes

characteristic

#2216

C₂×C₇₉

yes

—

#1424

C₂×C₇₉

yes

characteristic, complemented

#1416

C₂×C₇₉

yes

complemented

C₇₉

#13698

yes

characteristic, direct product factor, Sylow

C₂×Q₃₂

C₂²×C₇₉

yes

—

C₂²×C₁₆

C₂²×C₇₉

yes

characteristic

#467

—

Q₆₄

—

M₆₄

—

C₂×C₃₂

C₂²×C₇₉

yes

characteristic

C₂×C₃₂

C₂²×C₇₉

yes

characteristic

#366

C₂²×C₇₉

yes

—

#358

—

C₂×Q₁₆

—

C₂²×C₈

D₄×C₇₉

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

D₄×C₇₉

yes

characteristic

C₂×C₁₆

C₂³×C₇₉

yes

characteristic

#107

—

#103

—

C₃₂

—

C₃₂

D₄×C₇₉

yes

—

C₂×Q₈

—

C₂²×C₄

D₈×C₇₉

yes

characteristic

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

D₈×C₇₉

yes

characteristic

101

C₂×C₈

C₂×D₄×C₇₉

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₁₆

—

106

C₁₆

C₂×D₄×C₇₉

yes

characteristic

107

C₁₆

#41×C₇₉

yes

characteristic

108

C₂³

D₁₆×C₇₉

yes

characteristic

109

Q₈

—

110

Q₈

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

D₁₆×C₇₉

yes

characteristic

116

C₂×C₄

C₂×D₈×C₇₉

yes

characteristic

117

C₈

—

118

C₈

#121×C₇₉

yes

characteristic

119

C₈

#135×C₇₉

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

C₂×D₁₆×C₇₉

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

#466×C₇₉

yes

characteristic

127

C₄

#508×C₇₉

yes

characteristic

128

C₂

—

129

C₂

C₇₉×#2215

yes

characteristic

130

C₂

C₇₉×#2264

yes

—

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	C₂³×C₇₉	D₁₆
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₈×C₇₉ ◁ C₂²×C₁₆×C₇₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₇₉

prime radical

C₂³×C₇₉

D₁₆

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₈×C₇₉ ◁ C₂²×C₁₆×C₇₉ ◁ G

N	H ≅ G/N	type
1. C₂×Q₆₄×C₇₉	C₂	semidirect
4. C₇₉×#1424	C₂	semidirect
5. C₇₉×#1416	C₂	semidirect
62. #13698	C₇₉	direct (N × H)
66. C₂×Q₆₄	C₂×C₇₉	semidirect
69. #1424	C₂×C₇₉	semidirect
70. #1416	C₂×C₇₉	semidirect
71. C₇₉	#13698	direct (N × H)

H ≅ G/N

type

1. C₂×Q₆₄×C₇₉

C₂

semidirect

4. C₇₉×#1424

C₂

semidirect

5. C₇₉×#1416

C₂

semidirect

62. #13698

C₇₉

direct (N × H)

66. C₂×Q₆₄

C₂×C₇₉

semidirect

69. #1424

C₂×C₇₉

semidirect

70. #1416

C₂×C₇₉

semidirect

71. C₇₉

#13698

direct (N × H)

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

subgroup	index
C₂×Q₆₄×C₇₉	2
C₂×M₆₄×C₇₉	2
C₇₉×#2216	2
C₇₉×#1424	2
C₇₉×#1416	2
#13698	79

subgroup

index

C₂×Q₆₄×C₇₉

C₂×M₆₄×C₇₉

C₇₉×#2216

C₇₉×#1424

C₇₉×#1416

#13698

Subgroups — C₇₉×#13698 #34125387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C79×#13698 #34125387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#13698 #34125387