Group #11933078 — subgroups

Subgroups — C₅×#10358 #11933078

Order 1280.

484 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2844	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#1961	C₂	1	3	yes	maximal
3	C₅×#1295	C₂	1	3	yes	maximal, complemented
4	C₂×C₅×#127	C₂²	1	1	yes	characteristic
5	C₂×C₅×#102	—	2	3	no	—
6	C₂×C₅×#102	—	2	3	no	—
7	C₂×C₅×#97	C₂²	1	3	yes	—
8	C₅×#400	—	2	3	no	—
9	C₅×#395	—	2	3	no	—
10	C₅×#382	C₂²	1	3	yes	—
11	#10358	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₅×Q₈	—	2	1	no	—
13	C₂²×C₅×D₄	—	2	3	no	—
14	C₂²×C₅×C₈	—	2	3	no	—
15	C₅×#127	—	2	3	no	—
16	C₅×#127	Q₈	1	2	yes	complemented
17	C₂×C₅×C₄⋊C₄	—	2	3	no	—
18	C₂×C₅×C₄⋊C₄	D₄	1	3	yes	—
19	C₂×C₅×C₄⋊C₄	D₄	1	3	yes	—
20	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
21	C₅×#102	—	4	6	no	—
22	C₅×#102	—	4	6	no	—
23	C₅×#97	—	2	6	no	—
24	C₅×#95	—	2	3	no	—
25	C₅×#95	—	2	1	no	—
26	C₅×#95	—	2	6	no	—
27	#2844	C₂×C₅	1	1	yes	characteristic, complemented
28	#1961	C₂×C₅	1	3	yes	—
29	#1295	C₂×C₅	1	3	yes	complemented
30	C₂⁴×C₅	—	4	1	no	—
31	C₂×C₅×Q₈	—	8	3	no	—
32	C₂×C₅×D₄	—	2	6	no	—
33	C₂×C₅×D₄	—	4	3	no	—
34	C₂×C₅×D₄	—	4	3	no	—
35	C₂×C₅×D₄	—	4	3	no	—
36	C₂×C₅×D₄	—	4	3	no	—
37	C₂×C₅×D₄	—	4	3	no	—
38	C₂²×C₄×C₅	—	2	3	no	—
39	C₂²×C₄×C₅	—	2	3	no	—
40	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
41	C₂×C₅×C₈	—	2	6	no	—
42	C₂×C₅×C₈	—	4	3	no	—
43	C₂×C₅×C₈	—	4	3	no	—
44	C₅×C₄⋊C₄	—	4	3	no	—
45	C₅×C₄⋊C₄	—	4	3	no	—
46	C₅×C₄⋊C₄	—	8	3	no	—
47	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₅	#41	1	3	yes	—
49	C₂×#127	C₂²×C₅	1	1	yes	characteristic
50	C₂×#102	—	2	3	no	—
51	C₂×#102	—	2	3	no	—
52	C₂×#97	C₂²×C₅	1	3	yes	—
53	#400	—	2	3	no	—
54	#395	—	2	3	no	—
55	#382	C₂²×C₅	1	3	yes	—
56	C₂³×C₅	—	4	2	no	—
57	C₂³×C₅	—	8	3	no	—
58	C₂³×C₅	—	8	3	no	—
59	C₂³×C₅	#120	1	1	yes	characteristic
60	C₅×Q₈	—	8	4	no	—
61	C₅×D₄	—	4	6	no	—
62	C₅×D₄	—	4	6	no	—
63	C₅×D₄	—	8	3	no	—
64	C₅×D₄	—	8	3	no	—
65	C₂×C₄×C₅	—	2	3	no	—
66	C₂×C₄×C₅	—	2	3	no	—
67	C₂×C₄×C₅	—	4	3	no	—
68	C₂×C₄×C₅	—	4	3	no	—
69	C₂×C₄×C₅	—	4	6	no	—
70	C₂×C₄×C₅	—	4	6	no	—
71	C₂×C₄×C₅	C₂²⋊Q₈	1	3	yes	—
72	C₂×C₄×C₅	#124	1	3	yes	—
73	C₅×C₈	—	4	6	no	—
74	C₂²×Q₈	—	2	1	no	—
75	C₂²×D₄	—	2	3	no	—
76	C₂²×C₈	—	2	3	no	—
77	#127	—	2	3	no	—
78	#127	C₅×Q₈	1	2	yes	complemented
79	C₂×C₄⋊C₄	—	2	3	no	—
80	C₂×C₄⋊C₄	C₅×D₄	1	3	yes	—
81	C₂×C₄⋊C₄	C₅×D₄	1	3	yes	—
82	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
83	#102	—	4	6	no	—
84	#102	—	4	6	no	—
85	#97	—	2	6	no	—
86	#95	—	2	3	no	—
87	#95	—	2	1	no	—
88	#95	—	2	6	no	—
89	C₂²×C₅	—	8	6	no	—
90	C₂²×C₅	—	16	1	no	—
91	C₂²×C₅	—	16	3	no	—
92	C₂²×C₅	#393	1	1	yes	characteristic
93	C₂²×C₅	#453	1	3	yes	—
94	C₂²×C₅	#454	1	3	yes	—
95	C₄×C₅	—	2	3	no	—
96	C₄×C₅	—	2	3	no	—
97	C₄×C₅	—	8	3	no	—
98	C₄×C₅	—	8	3	no	—
99	C₂⁴	—	4	1	no	—
100	C₂×Q₈	—	8	3	no	—
101	C₂×D₄	—	2	6	no	—
102	C₂×D₄	—	4	3	no	—
103	C₂×D₄	—	4	3	no	—
104	C₂×D₄	—	4	3	no	—
105	C₂×D₄	—	4	3	no	—
106	C₂×D₄	—	4	3	no	—
107	C₂²×C₄	—	2	3	no	—
108	C₂²×C₄	—	2	3	no	—
109	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
110	C₂×C₈	—	2	6	no	—
111	C₂×C₈	—	4	3	no	—
112	C₂×C₈	—	4	3	no	—
113	C₄⋊C₄	—	4	3	no	—
114	C₄⋊C₄	—	4	3	no	—
115	C₄⋊C₄	—	8	3	no	—
116	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
117	C₄²	C₅×#41	1	3	yes	—
118	C₂×C₅	—	16	2	no	—
119	C₂×C₅	#1655	1	1	yes	characteristic
120	C₂×C₅	#1657	1	3	yes	—
121	C₂×C₅	#2027	1	3	yes	—
122	C₂³	—	4	2	no	—
123	C₂³	—	8	3	no	—
124	C₂³	—	8	3	no	—
125	C₂³	C₅×#120	1	1	yes	characteristic
126	Q₈	—	8	4	no	—
127	D₄	—	4	6	no	—
128	D₄	—	4	6	no	—
129	D₄	—	8	3	no	—
130	D₄	—	8	3	no	—
131	C₂×C₄	—	2	3	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	4	3	no	—
134	C₂×C₄	—	4	3	no	—
135	C₂×C₄	—	4	6	no	—
136	C₂×C₄	—	4	6	no	—
137	C₂×C₄	C₅×C₂²⋊Q₈	1	3	yes	—
138	C₂×C₄	C₅×#124	1	3	yes	—
139	C₈	—	4	6	no	—
140	C₅	#10358	1	1	yes	characteristic, direct product factor, Sylow
141	C₂²	—	8	6	no	—
142	C₂²	—	16	1	no	—
143	C₂²	—	16	3	no	—
144	C₂²	C₅×#393	1	1	yes	characteristic
145	C₂²	C₅×#453	1	3	yes	—
146	C₂²	C₅×#454	1	3	yes	—
147	C₄	—	2	3	no	—
148	C₄	—	2	3	no	—
149	C₄	—	8	3	no	—
150	C₄	—	8	3	no	—
151	C₂	—	16	2	no	—
152	C₂	C₅×#1655	1	1	yes	characteristic
153	C₂	C₅×#1657	1	3	yes	—
154	C₂	C₅×#2027	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2844

C₂

yes

maximal, characteristic, complemented

C₅×#1961

C₂

yes

maximal

C₅×#1295

C₂

yes

maximal, complemented

C₂×C₅×#127

C₂²

yes

characteristic

C₂×C₅×#102

—

C₂×C₅×#102

—

C₂×C₅×#97

C₂²

yes

—

C₅×#400

—

C₅×#395

—

C₅×#382

C₂²

yes

—

#10358

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

—

C₂²×C₅×D₄

—

C₂²×C₅×C₈

—

C₅×#127

—

C₅×#127

Q₈

yes

complemented

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

D₄

yes

—

C₂×C₅×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#102

—

C₅×#102

—

C₅×#97

—

C₅×#95

—

C₅×#95

—

C₅×#95

—

#2844

C₂×C₅

yes

characteristic, complemented

#1961

C₂×C₅

yes

—

#1295

C₂×C₅

yes

complemented

C₂⁴×C₅

—

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

#41

yes

—

C₂×#127

C₂²×C₅

yes

characteristic

C₂×#102

—

C₂×#102

—

C₂×#97

C₂²×C₅

yes

—

#400

—

#395

—

#382

C₂²×C₅

yes

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#120

yes

characteristic

C₅×Q₈

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₂×C₄×C₅

#124

yes

—

C₅×C₈

—

C₂²×Q₈

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

C₅×Q₈

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₅×D₄

yes

—

C₂×C₄⋊C₄

C₅×D₄

yes

—

C₂×C₄²

C₂³×C₅

yes

—

—

—

—

—

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#393

yes

characteristic

C₂²×C₅

#453

yes

—

C₂²×C₅

#454

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂⁴

—

100

C₂×Q₈

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂×C₅×D₄

yes

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄²

C₂×C₅×Q₈

yes

characteristic

117

C₄²

C₅×#41

yes

—

118

C₂×C₅

—

119

C₂×C₅

#1655

yes

characteristic

120

C₂×C₅

#1657

yes

—

121

C₂×C₅

#2027

yes

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

C₅×#120

yes

characteristic

126

Q₈

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

138

C₂×C₄

C₅×#124

yes

—

139

C₈

—

140

C₅

#10358

yes

characteristic, direct product factor, Sylow

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

C₅×#393

yes

characteristic

145

C₂²

C₅×#453

yes

—

146

C₂²

C₅×#454

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₂

—

152

C₂

C₅×#1655

yes

characteristic

153

C₂

C₅×#1657

yes

—

154

C₂

C₅×#2027

yes

—

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂³×C₅

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂×C₅×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
1. C₅×#2844	C₂	semidirect
3. C₅×#1295	C₂	semidirect
11. #10358	C₅	direct (N × H)
16. C₅×#127	Q₈	semidirect
27. #2844	C₂×C₅	semidirect
29. #1295	C₂×C₅	semidirect
78. #127	C₅×Q₈	semidirect
140. C₅	#10358	direct (N × H)

H ≅ G/N

type

1. C₅×#2844

C₂

semidirect

3. C₅×#1295

C₂

semidirect

11. #10358

C₅

direct (N × H)

16. C₅×#127

Q₈

semidirect

27. #2844

C₂×C₅

semidirect

29. #1295

C₂×C₅

semidirect

78. #127

C₅×Q₈

semidirect

140. C₅

#10358

direct (N × H)

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

subgroup	index
C₅×#2844	2
C₅×#1961	2
C₅×#1295	2
#10358	5

subgroup

index

Subgroups — C₅×#10358 #11933078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10358 #11933078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10358 #11933078