Group #11931507 — subgroups

Subgroups — C₅×#8787 #11931507

Order 1280.

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

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 190 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×#1842	C₂	1	2	yes	maximal
2	C₅×#1744	C₂	1	1	yes	maximal, characteristic
3	C₅×#1277	C₂	1	4	yes	maximal
4	C₂×C₅×C₄⋊C₈	—	2	2	no	—
5	C₂×C₅×C₄⋊C₈	—	2	2	no	—
6	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
7	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
8	C₄³×C₅	C₂²	1	1	yes	characteristic
9	C₅×#336	C₄	1	4	yes	—
10	#8787	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₅×C₈	—	2	4	no	—
12	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
13	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
15	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₅	Q₈	1	2	yes	—
17	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
18	C₅×C₄⋊C₈	—	2	8	no	—
19	C₅×C₄⋊C₈	—	4	4	no	—
20	C₅×C₄⋊C₈	—	4	4	no	—
21	C₄×C₅×C₈	—	2	4	no	—
22	#1842	C₂×C₅	1	2	yes	—
23	#1744	C₂×C₅	1	1	yes	characteristic
24	#1277	C₂×C₅	1	4	yes	—
25	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
26	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
27	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₅×C₈	—	2	4	no	—
31	C₂×C₅×C₈	—	2	8	no	—
32	C₂×C₅×C₈	—	4	4	no	—
33	C₂×C₅×C₈	—	4	4	no	—
34	C₂×C₅×C₈	—	4	4	no	—
35	C₄²×C₅	—	2	4	no	—
36	C₄²×C₅	—	4	2	no	—
37	C₄²×C₅	D₈	1	2	yes	—
38	C₄²×C₅	SD₁₆	1	4	yes	—
39	C₄²×C₅	Q₁₆	1	2	yes	—
40	C₄²×C₅	#41	1	4	yes	—
41	C₂×C₄⋊C₈	—	2	2	no	—
42	C₂×C₄⋊C₈	—	2	2	no	—
43	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
44	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
45	C₄³	C₂²×C₅	1	1	yes	characteristic
46	#336	C₄×C₅	1	4	yes	—
47	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₅	—	2	2	no	—
49	C₂×C₄×C₅	—	2	2	no	—
50	C₂×C₄×C₅	—	2	2	no	—
51	C₂×C₄×C₅	—	2	2	no	—
52	C₂×C₄×C₅	—	2	2	no	—
53	C₂×C₄×C₅	#106	1	4	yes	—
54	C₂×C₄×C₅	#107	1	4	yes	—
55	C₂×C₄×C₅	#117	1	2	yes	—
56	C₂×C₄×C₅	#124	1	2	yes	—
57	C₂×C₄×C₅	#125	1	2	yes	—
58	C₂×C₄×C₅	#131	1	4	yes	—
59	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
60	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
61	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
62	C₅×C₈	—	4	4	no	—
63	C₅×C₈	—	8	4	no	—
64	C₂²×C₈	—	2	4	no	—
65	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
66	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
67	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
68	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
69	C₂×C₄²	C₅×Q₈	1	2	yes	—
70	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
71	C₄⋊C₈	—	2	8	no	—
72	C₄⋊C₈	—	4	4	no	—
73	C₄⋊C₈	—	4	4	no	—
74	C₄×C₈	—	2	4	no	—
75	C₂²×C₅	#382	1	1	yes	characteristic
76	C₂²×C₅	#424	1	2	yes	—
77	C₂²×C₅	C₂×#106	1	1	yes	characteristic
78	C₂²×C₅	C₂×#107	1	1	yes	characteristic
79	C₂²×C₅	#430	1	2	yes	—
80	C₄×C₅	—	2	4	no	—
81	C₄×C₅	—	2	4	no	—
82	C₄×C₅	—	2	2	no	—
83	C₄×C₅	#433	1	4	yes	—
84	C₄×C₅	#486	1	2	yes	—
85	C₄×C₅	#487	1	2	yes	—
86	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
87	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
88	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
89	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
90	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	2	8	no	—
93	C₂×C₈	—	4	4	no	—
94	C₂×C₈	—	4	4	no	—
95	C₂×C₈	—	4	4	no	—
96	C₄²	—	2	4	no	—
97	C₄²	—	4	2	no	—
98	C₄²	C₅×D₈	1	2	yes	—
99	C₄²	C₅×SD₁₆	1	4	yes	—
100	C₄²	C₅×Q₁₆	1	2	yes	—
101	C₄²	C₅×#41	1	4	yes	—
102	C₂×C₅	#1570	1	2	yes	—
103	C₂×C₅	#1571	1	2	yes	—
104	C₂×C₅	#1832	1	1	yes	characteristic
105	C₂×C₅	#1834	1	1	yes	characteristic
106	C₂×C₅	#1838	1	1	yes	characteristic
107	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	C₅×#106	1	4	yes	—
114	C₂×C₄	C₅×#107	1	4	yes	—
115	C₂×C₄	C₅×#117	1	2	yes	—
116	C₂×C₄	C₅×#124	1	2	yes	—
117	C₂×C₄	C₅×#125	1	2	yes	—
118	C₂×C₄	C₅×#131	1	4	yes	—
119	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
120	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
121	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
122	C₈	—	4	4	no	—
123	C₈	—	8	4	no	—
124	C₅	#8787	1	1	yes	characteristic, direct product factor, Sylow
125	C₂²	C₅×#382	1	1	yes	characteristic
126	C₂²	C₅×#424	1	2	yes	—
127	C₂²	C₂×C₅×#106	1	1	yes	characteristic
128	C₂²	C₂×C₅×#107	1	1	yes	characteristic
129	C₂²	C₅×#430	1	2	yes	—
130	C₄	—	2	4	no	—
131	C₄	—	2	4	no	—
132	C₄	—	2	2	no	—
133	C₄	C₅×#433	1	4	yes	—
134	C₄	C₅×#486	1	2	yes	—
135	C₄	C₅×#487	1	2	yes	—
136	C₂	C₅×#1570	1	2	yes	—
137	C₂	C₅×#1571	1	2	yes	—
138	C₂	C₅×#1832	1	1	yes	characteristic
139	C₂	C₅×#1834	1	1	yes	characteristic
140	C₂	C₅×#1838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1842

C₂

yes

maximal

C₅×#1744

C₂

yes

maximal, characteristic

C₅×#1277

C₂

yes

maximal

C₂×C₅×C₄⋊C₈

—

C₂×C₅×C₄⋊C₈

—

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

—

C₄³×C₅

C₂²

yes

characteristic

C₅×#336

C₄

yes

—

#8787

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

—

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

D₄

yes

characteristic

C₂×C₄²×C₅

D₄

yes

characteristic

C₂×C₄²×C₅

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₄×C₅×C₈

—

#1842

C₂×C₅

yes

—

#1744

C₂×C₅

yes

characteristic

#1277

C₂×C₅

yes

—

C₂²×C₄×C₅

C₄⋊C₄

yes

—

C₂²×C₄×C₅

C₄⋊C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

D₈

yes

—

C₄²×C₅

SD₁₆

yes

—

C₄²×C₅

Q₁₆

yes

—

C₄²×C₅

#41

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

C₄³

C₂²×C₅

yes

characteristic

#336

C₄×C₅

yes

—

C₂³×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#106

yes

—

C₂×C₄×C₅

#107

yes

—

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#124

yes

—

C₂×C₄×C₅

#125

yes

—

C₂×C₄×C₅

#131

yes

—

C₂×C₄×C₅

C₂×D₈

yes

characteristic

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

C₂×Q₁₆

yes

characteristic

C₅×C₈

—

C₅×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₅×D₄

yes

characteristic

C₂×C₄²

C₅×D₄

yes

characteristic

C₂×C₄²

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₂²×C₅

#382

yes

characteristic

C₂²×C₅

#424

yes

—

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#433

yes

—

C₄×C₅

#486

yes

—

C₄×C₅

#487

yes

—

C₂²×C₄

C₅×C₄⋊C₄

yes

—

C₂²×C₄

C₅×C₄⋊C₄

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

C₂²×C₄

C₂×C₅×Q₈

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

C₅×D₈

yes

—

C₄²

C₅×SD₁₆

yes

—

100

C₄²

C₅×Q₁₆

yes

—

101

C₄²

C₅×#41

yes

—

102

C₂×C₅

#1570

yes

—

103

C₂×C₅

#1571

yes

—

104

C₂×C₅

#1832

yes

characteristic

105

C₂×C₅

#1834

yes

characteristic

106

C₂×C₅

#1838

yes

characteristic

107

C₂³

C₂×C₅×C₄⋊C₄

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₅×#106

yes

—

114

C₂×C₄

C₅×#107

yes

—

115

C₂×C₄

C₅×#117

yes

—

116

C₂×C₄

C₅×#124

yes

—

117

C₂×C₄

C₅×#125

yes

—

118

C₂×C₄

C₅×#131

yes

—

119

C₂×C₄

C₂×C₅×D₈

yes

characteristic

120

C₂×C₄

C₂×C₅×SD₁₆

yes

—

121

C₂×C₄

C₂×C₅×Q₁₆

yes

characteristic

122

C₈

—

123

C₈

—

124

C₅

#8787

yes

characteristic, direct product factor, Sylow

125

C₂²

C₅×#382

yes

characteristic

126

C₂²

C₅×#424

yes

—

127

C₂²

C₂×C₅×#106

yes

characteristic

128

C₂²

C₂×C₅×#107

yes

characteristic

129

C₂²

C₅×#430

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

C₅×#433

yes

—

134

C₄

C₅×#486

yes

—

135

C₄

C₅×#487

yes

—

136

C₂

C₅×#1570

yes

—

137

C₂

C₅×#1571

yes

—

138

C₂

C₅×#1832

yes

characteristic

139

C₂

C₅×#1834

yes

characteristic

140

C₂

C₅×#1838

yes

characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

subgroup

G/H

center

C₂²×C₄×C₅

C₂×D₄

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

socle, prime radical

C₂³×C₅

C₂×C₄⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

N	H ≅ G/N	type
10. #8787	C₅	direct (N × H)
124. C₅	#8787	direct (N × H)

H ≅ G/N

type

10. #8787

C₅

direct (N × H)

124. C₅

#8787

direct (N × H)

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

subgroup	index
C₅×#1842	2
C₅×#1744	2
C₅×#1277	2
#8787	5

subgroup

index

Subgroups — C₅×#8787 #11931507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8787 #11931507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8787 #11931507