Group #11932928 — subgroups

Subgroups — C₅×#10208 #11932928

Order 1280.

508 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3214	C₂	1	3	yes	maximal, complemented
2	C₅×#1514	C₂	1	3	yes	maximal, complemented
3	C₅×#1308	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#532	C₂²	1	3	yes	—
5	C₅×#496	—	2	3	no	—
6	C₅×#489	—	2	3	no	—
7	C₅×#461	—	2	3	no	—
8	C₅×#459	—	2	3	no	—
9	C₅×#449	—	2	6	no	—
10	C₅×#432	C₂²	1	3	yes	—
11	C₅×#383	C₂²	1	1	yes	characteristic
12	C₅×#327	—	2	6	no	—
13	#10208	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₅×#41	—	2	3	no	—
15	C₂×C₅×SD₁₆	—	2	6	no	—
16	C₂×C₅×D₈	—	2	6	no	—
17	C₅×C₄⋊Q₈	D₄	1	3	yes	—
18	C₅×#127	D₄	1	3	yes	—
19	C₅×#124	—	2	3	no	—
20	C₅×#121	—	2	3	no	—
21	C₅×#121	—	2	3	no	—
22	C₄×C₅×D₄	—	2	3	no	—
23	C₄×C₅×D₄	—	2	3	no	—
24	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
25	C₅×C₄⋊C₈	—	2	3	no	—
26	C₅×#103	—	2	6	no	—
27	C₅×#102	—	2	6	no	—
28	C₅×C₂²⋊C₈	D₄	1	6	yes	—
29	C₅×#97	—	2	3	no	—
30	C₅×#95	—	2	3	no	—
31	#3214	C₂×C₅	1	3	yes	complemented
32	#1514	C₂×C₅	1	3	yes	complemented
33	#1308	C₂×C₅	1	1	yes	characteristic, complemented
34	C₅×#41	—	8	6	no	—
35	C₂×C₅×Q₈	—	2	3	no	—
36	C₂×C₅×D₄	—	2	3	no	—
37	C₂×C₅×D₄	—	2	3	no	—
38	C₂×C₅×D₄	—	2	3	no	—
39	C₂×C₅×D₄	—	4	3	no	—
40	C₂²×C₄×C₅	—	4	3	no	—
41	C₂²×C₄×C₅	—	4	1	no	—
42	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
43	C₅×SD₁₆	—	8	6	no	—
44	C₅×D₈	—	8	6	no	—
45	C₂×C₅×C₈	—	2	6	no	—
46	C₅×C₄⋊C₄	—	2	3	no	—
47	C₅×C₄⋊C₄	—	2	3	no	—
48	C₅×C₂²⋊C₄	—	4	3	no	—
49	C₅×C₂²⋊C₄	—	4	3	no	—
50	C₄²×C₅	C₂×D₄	1	3	yes	—
51	C₄²×C₅	#41	1	1	yes	characteristic
52	#532	C₂²×C₅	1	3	yes	—
53	#496	—	2	3	no	—
54	#489	—	2	3	no	—
55	#461	—	2	3	no	—
56	#459	—	2	3	no	—
57	#449	—	2	6	no	—
58	#432	C₂²×C₅	1	3	yes	—
59	#383	C₂²×C₅	1	1	yes	characteristic
60	#327	—	2	6	no	—
61	C₂³×C₅	—	4	3	no	—
62	C₂³×C₅	#127	1	1	yes	characteristic
63	C₅×Q₈	—	4	6	no	—
64	C₅×D₄	—	4	3	no	—
65	C₅×D₄	—	4	6	no	—
66	C₅×D₄	—	4	3	no	—
67	C₅×D₄	—	8	3	no	—
68	C₅×D₄	—	8	6	no	—
69	C₂×C₄×C₅	—	4	3	no	—
70	C₂×C₄×C₅	—	4	3	no	—
71	C₂×C₄×C₅	—	8	6	no	—
72	C₂×C₄×C₅	—	8	3	no	—
73	C₂×C₄×C₅	#120	1	3	yes	—
74	C₂×C₄×C₅	#121	1	3	yes	—
75	C₅×C₈	—	4	6	no	—
76	C₂×#41	—	2	3	no	—
77	C₂×SD₁₆	—	2	6	no	—
78	C₂×D₈	—	2	6	no	—
79	C₄⋊Q₈	C₅×D₄	1	3	yes	—
80	#127	C₅×D₄	1	3	yes	—
81	#124	—	2	3	no	—
82	#121	—	2	3	no	—
83	#121	—	2	3	no	—
84	C₄×D₄	—	2	3	no	—
85	C₄×D₄	—	2	3	no	—
86	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
87	C₄⋊C₈	—	2	3	no	—
88	#103	—	2	6	no	—
89	#102	—	2	6	no	—
90	C₂²⋊C₈	C₅×D₄	1	6	yes	—
91	#97	—	2	3	no	—
92	#95	—	2	3	no	—
93	C₂²×C₅	—	2	3	no	—
94	C₂²×C₅	—	8	3	no	—
95	C₂²×C₅	—	8	3	no	—
96	C₂²×C₅	—	8	3	no	—
97	C₂²×C₅	#392	1	1	yes	characteristic
98	C₄×C₅	—	2	3	no	—
99	C₄×C₅	—	2	3	no	—
100	C₄×C₅	—	8	3	no	—
101	C₄×C₅	—	16	1	no	—
102	#41	—	8	6	no	—
103	C₂×Q₈	—	2	3	no	—
104	C₂×D₄	—	2	3	no	—
105	C₂×D₄	—	2	3	no	—
106	C₂×D₄	—	2	3	no	—
107	C₂×D₄	—	4	3	no	—
108	C₂²×C₄	—	4	3	no	—
109	C₂²×C₄	—	4	1	no	—
110	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
111	SD₁₆	—	8	6	no	—
112	D₈	—	8	6	no	—
113	C₂×C₈	—	2	6	no	—
114	C₄⋊C₄	—	2	3	no	—
115	C₄⋊C₄	—	2	3	no	—
116	C₂²⋊C₄	—	4	3	no	—
117	C₂²⋊C₄	—	4	3	no	—
118	C₄²	C₂×C₅×D₄	1	3	yes	—
119	C₄²	C₅×#41	1	1	yes	characteristic
120	C₂×C₅	—	4	1	no	—
121	C₂×C₅	—	16	3	no	—
122	C₂×C₅	#2008	1	3	yes	—
123	C₂³	—	4	3	no	—
124	C₂³	C₅×#127	1	1	yes	characteristic
125	Q₈	—	4	6	no	—
126	D₄	—	4	3	no	—
127	D₄	—	4	6	no	—
128	D₄	—	4	3	no	—
129	D₄	—	8	3	no	—
130	D₄	—	8	6	no	—
131	C₂×C₄	—	4	3	no	—
132	C₂×C₄	—	4	3	no	—
133	C₂×C₄	—	8	6	no	—
134	C₂×C₄	—	8	3	no	—
135	C₂×C₄	C₅×#120	1	3	yes	—
136	C₂×C₄	C₅×#121	1	3	yes	—
137	C₈	—	4	6	no	—
138	C₅	#10208	1	1	yes	characteristic, direct product factor, Sylow
139	C₂²	—	2	3	no	—
140	C₂²	—	8	3	no	—
141	C₂²	—	8	3	no	—
142	C₂²	—	8	3	no	—
143	C₂²	C₅×#392	1	1	yes	characteristic
144	C₄	—	2	3	no	—
145	C₄	—	2	3	no	—
146	C₄	—	8	3	no	—
147	C₄	—	16	1	no	—
148	C₂	—	4	1	no	—
149	C₂	—	16	3	no	—
150	C₂	C₅×#2008	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#3214

C₂

yes

maximal, complemented

C₅×#1514

C₂

yes

maximal, complemented

C₅×#1308

C₂

yes

maximal, characteristic, complemented

C₅×#532

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

C₅×#383

C₂²

yes

characteristic

C₅×#327

—

#10208

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×#41

—

C₂×C₅×SD₁₆

—

C₂×C₅×D₈

—

C₅×C₄⋊Q₈

D₄

yes

—

C₅×#127

D₄

yes

—

C₅×#124

—

C₅×#121

—

C₅×#121

—

C₄×C₅×D₄

—

C₄×C₅×D₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×#103

—

C₅×#102

—

C₅×C₂²⋊C₈

D₄

yes

—

C₅×#97

—

C₅×#95

—

#3214

C₂×C₅

yes

complemented

#1514

C₂×C₅

yes

complemented

#1308

C₂×C₅

yes

characteristic, complemented

C₅×#41

—

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₅×SD₁₆

—

C₅×D₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

#41

yes

characteristic

#532

C₂²×C₅

yes

—

—

—

—

—

—

C₂²×C₅

yes

—

#383

C₂²×C₅

yes

characteristic

#327

—

C₂³×C₅

—

C₂³×C₅

#127

yes

characteristic

C₅×Q₈

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#120

yes

—

C₂×C₄×C₅

#121

yes

—

C₅×C₈

—

C₂×#41

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

C₅×D₄

yes

—

#127

C₅×D₄

yes

—

#124

—

#121

—

#121

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

#103

—

#102

—

C₂²⋊C₈

C₅×D₄

yes

—

#97

—

#95

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#392

yes

characteristic

C₄×C₅

—

C₄×C₅

—

100

C₄×C₅

—

101

C₄×C₅

—

102

#41

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂×C₅×D₄

yes

—

111

SD₁₆

—

112

D₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

C₂×C₅×D₄

yes

—

119

C₄²

C₅×#41

yes

characteristic

120

C₂×C₅

—

121

C₂×C₅

—

122

C₂×C₅

#2008

yes

—

123

C₂³

—

124

C₂³

C₅×#127

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

C₅×#120

yes

—

136

C₂×C₄

C₅×#121

yes

—

137

C₈

—

138

C₅

#10208

yes

characteristic, direct product factor, Sylow

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₅×#392

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₂

—

149

C₂

—

150

C₂

C₅×#2008

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
1. C₅×#3214	C₂	semidirect
2. C₅×#1514	C₂	semidirect
3. C₅×#1308	C₂	semidirect
13. #10208	C₅	direct (N × H)
31. #3214	C₂×C₅	semidirect
32. #1514	C₂×C₅	semidirect
33. #1308	C₂×C₅	semidirect
138. C₅	#10208	direct (N × H)

H ≅ G/N

type

1. C₅×#3214

C₂

semidirect

2. C₅×#1514

C₂

semidirect

3. C₅×#1308

C₂

semidirect

13. #10208

C₅

direct (N × H)

31. #3214

C₂×C₅

semidirect

32. #1514

C₂×C₅

semidirect

33. #1308

C₂×C₅

semidirect

138. C₅

#10208

direct (N × H)

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

subgroup	index
C₅×#3214	2
C₅×#1514	2
C₅×#1308	2
#10208	5

subgroup

index

Subgroups — C₅×#10208 #11932928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10208 #11932928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10208 #11932928