Group #11933111 — subgroups

Subgroups — C₅×#10391 #11933111

Order 1280.

542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2840	C₂	1	1	yes	maximal, characteristic
2	C₅×#1819	C₂	1	3	yes	maximal
3	C₅×#1304	C₂	1	3	yes	maximal
4	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
5	C₅×#393	—	2	6	no	—
6	C₅×#379	C₂²	1	3	yes	—
7	C₅×#379	C₂²	1	3	yes	—
8	C₅×#342	—	2	6	no	—
9	#10391	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂⁵×C₅	C₂³	1	1	yes	characteristic
11	C₂²×C₅×Q₈	—	2	2	no	—
12	C₂³×C₄×C₅	Q₈	1	2	yes	complemented
13	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
14	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
15	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
16	C₂×C₅×C₂²⋊C₄	—	2	6	no	—
17	C₂×C₅×C₂²⋊C₄	—	2	6	no	—
18	C₂×C₅×C₂²⋊C₄	D₄	1	6	yes	—
19	C₅×#95	—	2	6	no	—
20	#2840	C₂×C₅	1	1	yes	characteristic
21	#1819	C₂×C₅	1	3	yes	—
22	#1304	C₂×C₅	1	3	yes	—
23	C₂⁴×C₅	—	4	2	no	—
24	C₂⁴×C₅	—	8	2	no	—
25	C₂⁴×C₅	C₂×D₄	1	3	yes	—
26	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
27	C₂⁴×C₅	#41	1	3	yes	—
28	C₂×C₅×Q₈	—	8	4	no	—
29	C₂×C₅×Q₈	—	8	2	no	—
30	C₂²×C₄×C₅	—	2	6	no	—
31	C₂²×C₄×C₅	—	2	6	no	—
32	C₂²×C₄×C₅	—	4	3	no	—
33	C₂²×C₄×C₅	—	8	2	no	—
34	C₅×C₂²⋊C₄	—	4	1	no	—
35	C₅×C₂²⋊C₄	—	4	3	no	—
36	C₅×C₂²⋊C₄	—	4	6	no	—
37	C₅×C₂²⋊C₄	—	4	6	no	—
38	C₅×C₂²⋊C₄	—	8	6	no	—
39	C₅×C₂²⋊C₄	—	8	6	no	—
40	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
41	#393	—	2	6	no	—
42	#379	C₂²×C₅	1	3	yes	—
43	#379	C₂²×C₅	1	3	yes	—
44	#342	—	2	6	no	—
45	C₂³×C₅	—	2	6	no	—
46	C₂³×C₅	—	4	2	no	—
47	C₂³×C₅	—	4	1	no	—
48	C₂³×C₅	—	4	6	no	—
49	C₂³×C₅	—	4	6	no	—
50	C₂³×C₅	—	4	3	no	—
51	C₂³×C₅	—	8	8	no	—
52	C₂³×C₅	#120	1	1	yes	characteristic
53	C₂³×C₅	C₂²⋊Q₈	1	3	yes	—
54	C₂³×C₅	#124	1	3	yes	—
55	C₅×Q₈	—	8	8	no	—
56	C₂×C₄×C₅	—	4	12	no	—
57	C₂×C₄×C₅	—	4	2	no	—
58	C₂×C₄×C₅	—	4	6	no	—
59	C₂×C₄×C₅	—	8	6	no	—
60	C₂×C₄×C₅	—	8	3	no	—
61	C₂×C₄×C₅	—	8	6	no	—
62	C₂⁵	C₂³×C₅	1	1	yes	characteristic
63	C₂²×Q₈	—	2	2	no	—
64	C₂³×C₄	C₅×Q₈	1	2	yes	complemented
65	C₂×C₂²⋊C₄	—	2	3	no	—
66	C₂×C₂²⋊C₄	—	2	3	no	—
67	C₂×C₂²⋊C₄	—	2	3	no	—
68	C₂×C₂²⋊C₄	—	2	6	no	—
69	C₂×C₂²⋊C₄	—	2	6	no	—
70	C₂×C₂²⋊C₄	C₅×D₄	1	6	yes	—
71	#95	—	2	6	no	—
72	C₂²×C₅	—	2	2	no	—
73	C₂²×C₅	—	2	3	no	—
74	C₂²×C₅	—	2	3	no	—
75	C₂²×C₅	—	2	6	no	—
76	C₂²×C₅	—	2	6	no	—
77	C₂²×C₅	—	4	4	no	—
78	C₂²×C₅	—	8	6	no	—
79	C₂²×C₅	—	8	6	no	—
80	C₂²×C₅	#393	1	1	yes	characteristic
81	C₂²×C₅	#458	1	2	yes	—
82	C₄×C₅	—	8	6	no	—
83	C₄×C₅	—	8	2	no	—
84	C₄×C₅	—	16	3	no	—
85	C₂⁴	—	4	2	no	—
86	C₂⁴	—	8	2	no	—
87	C₂⁴	C₂×C₅×D₄	1	3	yes	—
88	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
89	C₂⁴	C₅×#41	1	3	yes	—
90	C₂×Q₈	—	8	4	no	—
91	C₂×Q₈	—	8	2	no	—
92	C₂²×C₄	—	2	6	no	—
93	C₂²×C₄	—	2	6	no	—
94	C₂²×C₄	—	4	3	no	—
95	C₂²×C₄	—	8	2	no	—
96	C₂²⋊C₄	—	4	1	no	—
97	C₂²⋊C₄	—	4	3	no	—
98	C₂²⋊C₄	—	4	6	no	—
99	C₂²⋊C₄	—	4	6	no	—
100	C₂²⋊C₄	—	8	6	no	—
101	C₂²⋊C₄	—	8	6	no	—
102	C₂×C₅	—	2	2	no	—
103	C₂×C₅	—	4	3	no	—
104	C₂×C₅	—	4	3	no	—
105	C₂×C₅	#2030	1	1	yes	characteristic
106	C₂×C₅	#2032	1	2	yes	—
107	C₂³	—	2	6	no	—
108	C₂³	—	4	2	no	—
109	C₂³	—	4	1	no	—
110	C₂³	—	4	6	no	—
111	C₂³	—	4	6	no	—
112	C₂³	—	4	3	no	—
113	C₂³	—	8	8	no	—
114	C₂³	C₅×#120	1	1	yes	characteristic
115	C₂³	C₅×C₂²⋊Q₈	1	3	yes	—
116	C₂³	C₅×#124	1	3	yes	—
117	Q₈	—	8	8	no	—
118	C₂×C₄	—	4	12	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	6	no	—
121	C₂×C₄	—	8	6	no	—
122	C₂×C₄	—	8	3	no	—
123	C₂×C₄	—	8	6	no	—
124	C₅	#10391	1	1	yes	characteristic, direct product factor, Sylow
125	C₂²	—	2	2	no	—
126	C₂²	—	2	3	no	—
127	C₂²	—	2	3	no	—
128	C₂²	—	2	6	no	—
129	C₂²	—	2	6	no	—
130	C₂²	—	4	4	no	—
131	C₂²	—	8	6	no	—
132	C₂²	—	8	6	no	—
133	C₂²	C₅×#393	1	1	yes	characteristic
134	C₂²	C₅×#458	1	2	yes	—
135	C₄	—	8	6	no	—
136	C₄	—	8	2	no	—
137	C₄	—	16	3	no	—
138	C₂	—	2	2	no	—
139	C₂	—	4	3	no	—
140	C₂	—	4	3	no	—
141	C₂	C₅×#2030	1	1	yes	characteristic
142	C₂	C₅×#2032	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2840

C₂

yes

maximal, characteristic

C₅×#1819

C₂

yes

maximal

C₅×#1304

C₂

yes

maximal

C₂²×C₅×C₂²⋊C₄

C₂²

yes

characteristic

C₅×#393

—

C₅×#379

C₂²

yes

—

C₅×#379

C₂²

yes

—

C₅×#342

—

#10391

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂⁵×C₅

C₂³

yes

characteristic

C₂²×C₅×Q₈

—

C₂³×C₄×C₅

Q₈

yes

complemented

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

D₄

yes

—

C₅×#95

—

#2840

C₂×C₅

yes

characteristic

#1819

C₂×C₅

yes

—

#1304

C₂×C₅

yes

—

C₂⁴×C₅

—

C₂⁴×C₅

—

C₂⁴×C₅

C₂×D₄

yes

—

C₂⁴×C₅

C₂×Q₈

yes

characteristic

C₂⁴×C₅

#41

yes

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₂²×C₂²⋊C₄

C₂²×C₅

yes

characteristic

#393

—

#379

C₂²×C₅

yes

—

#379

C₂²×C₅

yes

—

#342

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#120

yes

characteristic

C₂³×C₅

C₂²⋊Q₈

yes

—

C₂³×C₅

#124

yes

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂⁵

C₂³×C₅

yes

characteristic

C₂²×Q₈

—

C₂³×C₄

C₅×Q₈

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₅×D₄

yes

—

#95

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#393

yes

characteristic

C₂²×C₅

#458

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂×C₅×D₄

yes

—

C₂⁴

C₂×C₅×Q₈

yes

characteristic

C₂⁴

C₅×#41

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₂×C₅

—

103

C₂×C₅

—

104

C₂×C₅

—

105

C₂×C₅

#2030

yes

characteristic

106

C₂×C₅

#2032

yes

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

C₅×#120

yes

characteristic

115

C₂³

C₅×C₂²⋊Q₈

yes

—

116

C₂³

C₅×#124

yes

—

117

Q₈

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₅

#10391

yes

characteristic, direct product factor, Sylow

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₅×#393

yes

characteristic

134

C₂²

C₅×#458

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₂

—

139

C₂

—

140

C₂

—

141

C₂

C₅×#2030

yes

characteristic

142

C₂

C₅×#2032

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₅
prime radical	C₂⁵×C₅	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂⁵×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#393

commutator, Frattini, cosocle

C₂⁵

C₂³×C₅

prime radical

C₂⁵×C₅

C₂³

LCS

G ▷ C₂⁵ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂⁵×C₅ ◁ G

N	H ≅ G/N	type
9. #10391	C₅	direct (N × H)
12. C₂³×C₄×C₅	Q₈	semidirect
64. C₂³×C₄	C₅×Q₈	semidirect
124. C₅	#10391	direct (N × H)

H ≅ G/N

type

9. #10391

C₅

direct (N × H)

12. C₂³×C₄×C₅

Q₈

semidirect

64. C₂³×C₄

C₅×Q₈

semidirect

124. C₅

#10391

direct (N × H)

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

subgroup	index
C₅×#2840	2
C₅×#1819	2
C₅×#1304	2
#10391	5

subgroup

index

Subgroups — C₅×#10391 #11933111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10391 #11933111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10391 #11933111