Group #11931502 — subgroups

Subgroups — C₅×#8782 #11931502

Order 1280.

262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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	C₅×#1746	C₂	1	1	yes	maximal, characteristic
2	C₅×#1564	C₂	1	2	yes	maximal
3	C₅×#1281	C₂	1	2	yes	maximal
4	C₅×#1274	C₂	1	2	yes	maximal
5	C₅×#431	C₂²	1	4	yes	—
6	C₂×C₅×#97	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₅×#376	C₂²	1	1	yes	characteristic
9	C₅×#336	C₄	1	4	yes	—
10	C₅×#335	—	2	2	no	—
11	C₅×#334	—	2	2	no	—
12	#8782	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
14	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
17	C₅×C₄⋊C₈	—	2	4	no	—
18	C₅×C₂²⋊C₈	—	2	4	no	—
19	C₅×#97	—	2	2	no	—
20	C₄×C₅×C₈	—	2	4	no	—
21	C₄×C₅×C₈	D₄	1	1	yes	characteristic
22	C₄×C₅×C₈	D₄	1	1	yes	characteristic
23	C₄×C₅×C₈	Q₈	1	2	yes	—
24	C₅×#95	—	2	2	no	—
25	#1746	C₂×C₅	1	1	yes	characteristic
26	#1564	C₂×C₅	1	2	yes	—
27	#1281	C₂×C₅	1	2	yes	—
28	#1274	C₂×C₅	1	2	yes	—
29	C₂²×C₄×C₅	—	2	2	no	—
30	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₅	#41	1	2	yes	—
32	C₂×C₅×C₈	—	2	4	no	—
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	—	2	4	no	—
35	C₂×C₅×C₈	—	4	4	no	—
36	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
37	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
38	C₄²×C₅	—	2	4	no	—
39	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
40	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
41	C₄²×C₅	#41	1	2	yes	—
42	#431	C₂²×C₅	1	4	yes	—
43	C₂×#97	C₂²×C₅	1	1	yes	characteristic
44	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
45	#376	C₂²×C₅	1	1	yes	characteristic
46	#336	C₄×C₅	1	4	yes	—
47	#335	—	2	2	no	—
48	#334	—	2	2	no	—
49	C₂³×C₅	#117	1	1	yes	characteristic
50	C₂×C₄×C₅	—	4	2	no	—
51	C₂×C₄×C₅	—	4	4	no	—
52	C₂×C₄×C₅	—	4	2	no	—
53	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₅	#117	1	1	yes	characteristic
55	C₂×C₄×C₅	#124	1	2	yes	—
56	C₂×C₄×C₅	#125	1	2	yes	—
57	C₂×C₄×C₅	#131	1	4	yes	—
58	C₅×C₈	—	2	2	no	—
59	C₅×C₈	—	2	2	no	—
60	C₅×C₈	—	4	2	no	—
61	C₅×C₈	—	8	4	no	—
62	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
63	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
64	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
65	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
66	C₄⋊C₈	—	2	4	no	—
67	C₂²⋊C₈	—	2	4	no	—
68	#97	—	2	2	no	—
69	C₄×C₈	—	2	4	no	—
70	C₄×C₈	C₅×D₄	1	1	yes	characteristic
71	C₄×C₈	C₅×D₄	1	1	yes	characteristic
72	C₄×C₈	C₅×Q₈	1	2	yes	—
73	#95	—	2	2	no	—
74	C₂²×C₅	—	2	2	no	—
75	C₂²×C₅	#382	1	1	yes	characteristic
76	C₂²×C₅	#433	1	2	yes	—
77	C₄×C₅	—	2	2	no	—
78	C₄×C₅	—	2	2	no	—
79	C₄×C₅	—	8	2	no	—
80	C₄×C₅	#424	1	2	yes	—
81	C₄×C₅	#433	1	2	yes	—
82	C₂²×C₄	—	2	2	no	—
83	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
84	C₂²×C₄	C₅×#41	1	2	yes	—
85	C₂×C₈	—	2	4	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	4	no	—
88	C₂×C₈	—	4	4	no	—
89	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
90	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
91	C₄²	—	2	4	no	—
92	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
93	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
94	C₄²	C₅×#41	1	2	yes	—
95	C₂×C₅	—	2	2	no	—
96	C₂×C₅	#1832	1	1	yes	characteristic
97	C₂×C₅	#1833	1	2	yes	—
98	C₂³	C₅×#117	1	1	yes	characteristic
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	4	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄	C₅×#117	1	1	yes	characteristic
104	C₂×C₄	C₅×#124	1	2	yes	—
105	C₂×C₄	C₅×#125	1	2	yes	—
106	C₂×C₄	C₅×#131	1	4	yes	—
107	C₈	—	2	2	no	—
108	C₈	—	2	2	no	—
109	C₈	—	4	2	no	—
110	C₈	—	8	4	no	—
111	C₅	#8782	1	1	yes	characteristic, direct product factor, Sylow
112	C₂²	—	2	2	no	—
113	C₂²	C₅×#382	1	1	yes	characteristic
114	C₂²	C₅×#433	1	2	yes	—
115	C₄	—	2	2	no	—
116	C₄	—	2	2	no	—
117	C₄	—	8	2	no	—
118	C₄	C₅×#424	1	2	yes	—
119	C₄	C₅×#433	1	2	yes	—
120	C₂	—	2	2	no	—
121	C₂	C₅×#1832	1	1	yes	characteristic
122	C₂	C₅×#1833	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1746

C₂

yes

maximal, characteristic

C₅×#1564

C₂

yes

maximal

C₅×#1281

C₂

yes

maximal

C₅×#1274

C₂

yes

maximal

C₅×#431

C₂²

yes

—

C₂×C₅×#97

C₂²

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#376

C₂²

yes

characteristic

C₅×#336

C₄

yes

—

C₅×#335

—

C₅×#334

—

#8782

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₄×C₅×C₈

—

C₄×C₅×C₈

D₄

yes

characteristic

C₄×C₅×C₈

D₄

yes

characteristic

C₄×C₅×C₈

Q₈

yes

—

C₅×#95

—

#1746

C₂×C₅

yes

characteristic

#1564

C₂×C₅

yes

—

#1281

C₂×C₅

yes

—

#1274

C₂×C₅

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

#41

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₄²×C₅

—

C₄²×C₅

C₂×D₄

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

#41

yes

—

#431

C₂²×C₅

yes

—

C₂×#97

C₂²×C₅

yes

characteristic

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#376

C₂²×C₅

yes

characteristic

#336

C₄×C₅

yes

—

#335

—

#334

—

C₂³×C₅

#117

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

#125

yes

—

C₂×C₄×C₅

#131

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

C₅×D₄

yes

characteristic

C₄×C₈

C₅×D₄

yes

characteristic

C₄×C₈

C₅×Q₈

yes

—

#95

—

C₂²×C₅

—

C₂²×C₅

#382

yes

characteristic

C₂²×C₅

#433

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#424

yes

—

C₄×C₅

#433

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

C₅×#41

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₂×C₈

C₅×C₄⋊C₄

yes

—

C₄²

—

C₄²

C₂×C₅×D₄

yes

characteristic

C₄²

C₂×C₅×Q₈

yes

characteristic

C₄²

C₅×#41

yes

—

C₂×C₅

—

C₂×C₅

#1832

yes

characteristic

C₂×C₅

#1833

yes

—

C₂³

C₅×#117

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

103

C₂×C₄

C₅×#117

yes

characteristic

104

C₂×C₄

C₅×#124

yes

—

105

C₂×C₄

C₅×#125

yes

—

106

C₂×C₄

C₅×#131

yes

—

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₅

#8782

yes

characteristic, direct product factor, Sylow

112

C₂²

—

113

C₂²

C₅×#382

yes

characteristic

114

C₂²

C₅×#433

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

C₅×#424

yes

—

119

C₄

C₅×#433

yes

—

120

C₂

—

121

C₂

C₅×#1832

yes

characteristic

122

C₂

C₅×#1833

yes

—

	subgroup	G/H
center	C₂×C₄×C₅	#117
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	#382
prime radical	C₂³×C₅	#117
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#376 ◁ G

subgroup

G/H

center

C₂×C₄×C₅

#117

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

C₂²×C₅

C₂³×C₅

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂×C₄×C₅ ◁ C₅×#376 ◁ G

N	H ≅ G/N	type
12. #8782	C₅	direct (N × H)
111. C₅	#8782	direct (N × H)

H ≅ G/N

type

12. #8782

C₅

direct (N × H)

111. C₅

#8782

direct (N × H)

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

subgroup	index
C₅×#1746	2
C₅×#1564	2
C₅×#1281	2
C₅×#1274	2
#8782	5

subgroup

index

Subgroups — C₅×#8782 #11931502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8782 #11931502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8782 #11931502