Group #11985346 — subgroups

Subgroups — C₂³×C₅×SD₃₂ #11985346

Order 1280.

2334 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

normal subgroups only

This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1054 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	C₂³×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×D₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×SD₃₂	C₂	1	28	yes	maximal, direct product factor
4	C₂³×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×Q₈	—	2	1	no	—
6	C₂³×C₅×D₄	—	2	1	no	—
7	C₂²×C₅×Q₁₆	—	2	7	no	—
8	C₂²×C₅×Q₁₆	C₂²	1	14	yes	complemented
9	C₂²×C₅×D₈	—	2	7	no	—
10	C₂²×C₅×D₈	C₂²	1	14	yes	—
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×SD₃₂	C₂²	1	112	yes	direct product factor
13	C₂²×C₅×C₁₆	C₂²	1	14	yes	complemented
14	C₂³×SD₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂⁵×C₅	—	4	1	no	—
16	C₂²×C₅×Q₈	—	2	14	no	—
17	C₂²×C₅×Q₈	—	4	7	no	—
18	C₂²×C₅×D₄	—	2	14	no	—
19	C₂²×C₅×D₄	—	4	7	no	—
20	C₂³×C₄×C₅	—	4	1	no	—
21	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
22	C₂×C₅×Q₁₆	—	2	42	no	—
23	C₂×C₅×Q₁₆	C₂³	1	28	yes	complemented
24	C₂×C₅×D₈	—	2	42	no	—
25	C₂×C₅×D₈	C₂³	1	28	yes	—
26	C₂²×C₅×C₈	D₄	1	7	yes	—
27	C₂²×C₅×C₈	C₂³	1	7	yes	—
28	C₅×SD₃₂	C₂³	1	64	yes	direct product factor
29	C₂×C₅×C₁₆	C₂³	1	28	yes	complemented
30	C₂³×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
31	C₂³×D₈	C₂×C₅	1	1	yes	characteristic
32	C₂²×SD₃₂	C₂×C₅	1	28	yes	direct product factor
33	C₂³×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
34	C₂⁴×C₅	—	4	14	no	—
35	C₂⁴×C₅	—	8	8	no	—
36	C₂⁴×C₅	D₈	1	1	yes	characteristic
37	C₂×C₅×Q₈	—	2	28	no	—
38	C₂×C₅×Q₈	—	4	42	no	—
39	C₂×C₅×D₄	—	2	28	no	—
40	C₂×C₅×D₄	—	4	42	no	—
41	C₂²×C₄×C₅	—	4	14	no	—
42	C₂²×C₄×C₅	D₈	1	7	yes	—
43	C₂²×C₄×C₅	C₂×D₄	1	7	yes	—
44	C₅×Q₁₆	—	2	28	no	—
45	C₅×Q₁₆	C₂⁴	1	8	yes	complemented
46	C₅×D₈	—	2	28	no	—
47	C₅×D₈	C₂⁴	1	8	yes	—
48	C₂×C₅×C₈	C₂×D₄	1	21	yes	—
49	C₂×C₅×C₈	C₂⁴	1	7	yes	—
50	C₅×C₁₆	C₂⁴	1	8	yes	complemented
51	C₂³×Q₈	—	2	1	no	—
52	C₂³×D₄	—	2	1	no	—
53	C₂²×Q₁₆	—	2	7	no	—
54	C₂²×Q₁₆	C₂²×C₅	1	14	yes	complemented
55	C₂²×D₈	—	2	7	no	—
56	C₂²×D₈	C₂²×C₅	1	14	yes	—
57	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
58	C₂×SD₃₂	C₂²×C₅	1	112	yes	direct product factor
59	C₂²×C₁₆	C₂²×C₅	1	14	yes	complemented
60	C₂³×C₅	—	4	28	no	—
61	C₂³×C₅	—	8	56	no	—
62	C₂³×C₅	SD₃₂	1	8	yes	direct product factor
63	C₂³×C₅	C₂×D₈	1	7	yes	—
64	C₅×Q₈	—	2	8	no	—
65	C₅×Q₈	—	4	28	no	—
66	C₅×D₄	—	2	8	no	—
67	C₅×D₄	—	4	28	no	—
68	C₂×C₄×C₅	—	4	28	no	—
69	C₂×C₄×C₅	C₂×D₈	1	21	yes	—
70	C₂×C₄×C₅	C₂²×D₄	1	7	yes	—
71	C₅×C₈	C₂²×D₄	1	7	yes	—
72	C₅×C₈	C₂⁵	1	1	yes	characteristic
73	C₂⁵	—	4	1	no	—
74	C₂²×Q₈	—	2	14	no	—
75	C₂²×Q₈	—	4	7	no	—
76	C₂²×D₄	—	2	14	no	—
77	C₂²×D₄	—	4	7	no	—
78	C₂³×C₄	—	4	1	no	—
79	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
80	C₂×Q₁₆	—	2	42	no	—
81	C₂×Q₁₆	C₂³×C₅	1	28	yes	complemented
82	C₂×D₈	—	2	42	no	—
83	C₂×D₈	C₂³×C₅	1	28	yes	—
84	C₂²×C₈	C₅×D₄	1	7	yes	—
85	C₂²×C₈	C₂³×C₅	1	7	yes	—
86	SD₃₂	C₂³×C₅	1	64	yes	direct product factor
87	C₂×C₁₆	C₂³×C₅	1	28	yes	complemented
88	C₂²×C₅	—	4	8	no	—
89	C₂²×C₅	—	8	56	no	—
90	C₂²×C₅	C₂×SD₃₂	1	28	yes	direct product factor
91	C₂²×C₅	C₂²×D₈	1	7	yes	—
92	C₄×C₅	—	4	8	no	—
93	C₄×C₅	C₂²×D₈	1	7	yes	—
94	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
95	C₂⁴	—	4	14	no	—
96	C₂⁴	—	8	8	no	—
97	C₂⁴	C₅×D₈	1	1	yes	characteristic
98	C₂×Q₈	—	2	28	no	—
99	C₂×Q₈	—	4	42	no	—
100	C₂×D₄	—	2	28	no	—
101	C₂×D₄	—	4	42	no	—
102	C₂²×C₄	—	4	14	no	—
103	C₂²×C₄	C₅×D₈	1	7	yes	—
104	C₂²×C₄	C₂×C₅×D₄	1	7	yes	—
105	Q₁₆	—	2	28	no	—
106	Q₁₆	C₂⁴×C₅	1	8	yes	complemented
107	D₈	—	2	28	no	—
108	D₈	C₂⁴×C₅	1	8	yes	—
109	C₂×C₈	C₂×C₅×D₄	1	21	yes	—
110	C₂×C₈	C₂⁴×C₅	1	7	yes	—
111	C₁₆	C₂⁴×C₅	1	8	yes	complemented
112	C₂×C₅	—	8	8	no	—
113	C₂×C₅	C₂²×SD₃₂	1	14	yes	direct product factor
114	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
115	C₂³	—	4	28	no	—
116	C₂³	—	8	56	no	—
117	C₂³	C₅×SD₃₂	1	8	yes	direct product factor
118	C₂³	C₂×C₅×D₈	1	7	yes	—
119	Q₈	—	2	8	no	—
120	Q₈	—	4	28	no	—
121	D₄	—	2	8	no	—
122	D₄	—	4	28	no	—
123	C₂×C₄	—	4	28	no	—
124	C₂×C₄	C₂×C₅×D₈	1	21	yes	—
125	C₂×C₄	C₂²×C₅×D₄	1	7	yes	—
126	C₈	C₂²×C₅×D₄	1	7	yes	—
127	C₈	C₂⁵×C₅	1	1	yes	characteristic
128	C₅	C₂³×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
129	C₂²	—	4	8	no	—
130	C₂²	—	8	56	no	—
131	C₂²	C₂×C₅×SD₃₂	1	28	yes	direct product factor
132	C₂²	C₂²×C₅×D₈	1	7	yes	—
133	C₄	—	4	8	no	—
134	C₄	C₂²×C₅×D₈	1	7	yes	—
135	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
136	C₂	—	8	8	no	—
137	C₂	C₂²×C₅×SD₃₂	1	14	yes	direct product factor
138	C₂	C₂³×C₅×D₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₅×Q₁₆

C₂

yes

maximal, characteristic, complemented

C₂³×C₅×D₈

C₂

yes

maximal, characteristic

C₂²×C₅×SD₃₂

C₂

yes

maximal, direct product factor

C₂³×C₅×C₁₆

C₂

yes

maximal, characteristic, complemented

C₂³×C₅×Q₈

—

C₂³×C₅×D₄

—

C₂²×C₅×Q₁₆

—

C₂²×C₅×Q₁₆

C₂²

yes

complemented

C₂²×C₅×D₈

—

C₂²×C₅×D₈

C₂²

yes

—

C₂³×C₅×C₈

C₂²

yes

characteristic

C₂×C₅×SD₃₂

C₂²

112

yes

direct product factor

C₂²×C₅×C₁₆

C₂²

yes

complemented

C₂³×SD₃₂

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂⁵×C₅

—

C₂²×C₅×Q₈

—

C₂²×C₅×Q₈

—

C₂²×C₅×D₄

—

C₂²×C₅×D₄

—

C₂³×C₄×C₅

—

C₂³×C₄×C₅

D₄

yes

characteristic

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

C₂³

yes

complemented

C₂×C₅×D₈

—

C₂×C₅×D₈

C₂³

yes

—

C₂²×C₅×C₈

D₄

yes

—

C₂²×C₅×C₈

C₂³

yes

—

C₅×SD₃₂

C₂³

yes

direct product factor

C₂×C₅×C₁₆

C₂³

yes

complemented

C₂³×Q₁₆

C₂×C₅

yes

characteristic, complemented

C₂³×D₈

C₂×C₅

yes

characteristic

C₂²×SD₃₂

C₂×C₅

yes

direct product factor

C₂³×C₁₆

C₂×C₅

yes

characteristic, complemented

C₂⁴×C₅

—

C₂⁴×C₅

—

C₂⁴×C₅

D₈

yes

characteristic

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

D₈

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₅×Q₁₆

—

C₅×Q₁₆

C₂⁴

yes

complemented

C₅×D₈

—

C₅×D₈

C₂⁴

yes

—

C₂×C₅×C₈

C₂×D₄

yes

—

C₂×C₅×C₈

C₂⁴

yes

—

C₅×C₁₆

C₂⁴

yes

complemented

C₂³×Q₈

—

C₂³×D₄

—

C₂²×Q₁₆

—

C₂²×Q₁₆

C₂²×C₅

yes

complemented

C₂²×D₈

—

C₂²×D₈

C₂²×C₅

yes

—

C₂³×C₈

C₂²×C₅

yes

characteristic

C₂×SD₃₂

C₂²×C₅

112

yes

direct product factor

C₂²×C₁₆

C₂²×C₅

yes

complemented

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

SD₃₂

yes

direct product factor

C₂³×C₅

C₂×D₈

yes

—

C₅×Q₈

—

C₅×Q₈

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₈

yes

—

C₂×C₄×C₅

C₂²×D₄

yes

—

C₅×C₈

C₂²×D₄

yes

—

C₅×C₈

C₂⁵

yes

characteristic

C₂⁵

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

—

C₂³×C₄

C₅×D₄

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

C₂³×C₅

yes

complemented

C₂×D₈

—

C₂×D₈

C₂³×C₅

yes

—

C₂²×C₈

C₅×D₄

yes

—

C₂²×C₈

C₂³×C₅

yes

—

SD₃₂

C₂³×C₅

yes

direct product factor

C₂×C₁₆

C₂³×C₅

yes

complemented

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

C₂×SD₃₂

yes

direct product factor

C₂²×C₅

C₂²×D₈

yes

—

C₄×C₅

—

C₄×C₅

C₂²×D₈

yes

—

C₄×C₅

C₂³×D₄

yes

characteristic

C₂⁴

—

C₂⁴

—

C₂⁴

C₅×D₈

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₅×D₈

yes

—

104

C₂²×C₄

C₂×C₅×D₄

yes

—

105

Q₁₆

—

106

Q₁₆

C₂⁴×C₅

yes

complemented

107

D₈

—

108

D₈

C₂⁴×C₅

yes

—

109

C₂×C₈

C₂×C₅×D₄

yes

—

110

C₂×C₈

C₂⁴×C₅

yes

—

111

C₁₆

C₂⁴×C₅

yes

complemented

112

C₂×C₅

—

113

C₂×C₅

C₂²×SD₃₂

yes

direct product factor

114

C₂×C₅

C₂³×D₈

yes

characteristic

115

C₂³

—

116

C₂³

—

117

C₂³

C₅×SD₃₂

yes

direct product factor

118

C₂³

C₂×C₅×D₈

yes

—

119

Q₈

—

120

Q₈

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂×C₅×D₈

yes

—

125

C₂×C₄

C₂²×C₅×D₄

yes

—

126

C₈

C₂²×C₅×D₄

yes

—

127

C₈

C₂⁵×C₅

yes

characteristic

128

C₅

C₂³×SD₃₂

yes

characteristic, direct product factor, Sylow

129

C₂²

—

130

C₂²

—

131

C₂²

C₂×C₅×SD₃₂

yes

direct product factor

132

C₂²

C₂²×C₅×D₈

yes

—

133

C₄

—

134

C₄

C₂²×C₅×D₈

yes

—

135

C₄

C₂³×C₅×D₄

yes

characteristic

136

C₂

—

137

C₂

C₂²×C₅×SD₃₂

yes

direct product factor

138

C₂

C₂³×C₅×D₈

yes

characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₅
prime radical	C₂³×C₅×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

subgroup

G/H

center, socle

C₂⁴×C₅

D₈

commutator, Frattini, cosocle

C₈

C₂⁵×C₅

prime radical

C₂³×C₅×D₈

C₂

LCS

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂⁴×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

N	H ≅ G/N	type
1. C₂³×C₅×Q₁₆	C₂	semidirect
3. C₂²×C₅×SD₃₂	C₂	direct (N × H)
4. C₂³×C₅×C₁₆	C₂	semidirect
8. C₂²×C₅×Q₁₆	C₂²	semidirect
12. C₂×C₅×SD₃₂	C₂²	direct (N × H)
13. C₂²×C₅×C₁₆	C₂²	semidirect
14. C₂³×SD₃₂	C₅	direct (N × H)
23. C₂×C₅×Q₁₆	C₂³	semidirect
28. C₅×SD₃₂	C₂³	direct (N × H)
29. C₂×C₅×C₁₆	C₂³	semidirect
30. C₂³×Q₁₆	C₂×C₅	semidirect
32. C₂²×SD₃₂	C₂×C₅	direct (N × H)
33. C₂³×C₁₆	C₂×C₅	semidirect
45. C₅×Q₁₆	C₂⁴	semidirect
50. C₅×C₁₆	C₂⁴	semidirect
54. C₂²×Q₁₆	C₂²×C₅	semidirect
58. C₂×SD₃₂	C₂²×C₅	direct (N × H)
59. C₂²×C₁₆	C₂²×C₅	semidirect
62. C₂³×C₅	SD₃₂	direct (N × H)
81. C₂×Q₁₆	C₂³×C₅	semidirect
86. SD₃₂	C₂³×C₅	direct (N × H)
87. C₂×C₁₆	C₂³×C₅	semidirect
90. C₂²×C₅	C₂×SD₃₂	direct (N × H)
106. Q₁₆	C₂⁴×C₅	semidirect
111. C₁₆	C₂⁴×C₅	semidirect
113. C₂×C₅	C₂²×SD₃₂	direct (N × H)
117. C₂³	C₅×SD₃₂	direct (N × H)
128. C₅	C₂³×SD₃₂	direct (N × H)
131. C₂²	C₂×C₅×SD₃₂	direct (N × H)
137. C₂	C₂²×C₅×SD₃₂	direct (N × H)

H ≅ G/N

type

1. C₂³×C₅×Q₁₆

C₂

semidirect

3. C₂²×C₅×SD₃₂

C₂

direct (N × H)

4. C₂³×C₅×C₁₆

C₂

semidirect

8. C₂²×C₅×Q₁₆

C₂²

semidirect

12. C₂×C₅×SD₃₂

C₂²

direct (N × H)

13. C₂²×C₅×C₁₆

C₂²

semidirect

14. C₂³×SD₃₂

C₅

direct (N × H)

23. C₂×C₅×Q₁₆

C₂³

semidirect

28. C₅×SD₃₂

C₂³

direct (N × H)

29. C₂×C₅×C₁₆

C₂³

semidirect

30. C₂³×Q₁₆

C₂×C₅

semidirect

32. C₂²×SD₃₂

C₂×C₅

direct (N × H)

33. C₂³×C₁₆

C₂×C₅

semidirect

45. C₅×Q₁₆

C₂⁴

semidirect

50. C₅×C₁₆

C₂⁴

semidirect

54. C₂²×Q₁₆

C₂²×C₅

semidirect

58. C₂×SD₃₂

C₂²×C₅

direct (N × H)

59. C₂²×C₁₆

C₂²×C₅

semidirect

62. C₂³×C₅

SD₃₂

direct (N × H)

81. C₂×Q₁₆

C₂³×C₅

semidirect

86. SD₃₂

C₂³×C₅

direct (N × H)

87. C₂×C₁₆

C₂³×C₅

semidirect

90. C₂²×C₅

C₂×SD₃₂

direct (N × H)

106. Q₁₆

C₂⁴×C₅

semidirect

111. C₁₆

C₂⁴×C₅

semidirect

113. C₂×C₅

C₂²×SD₃₂

direct (N × H)

117. C₂³

C₅×SD₃₂

direct (N × H)

128. C₅

C₂³×SD₃₂

direct (N × H)

131. C₂²

C₂×C₅×SD₃₂

direct (N × H)

137. C₂

C₂²×C₅×SD₃₂

direct (N × H)

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

subgroup	index
C₂³×C₅×Q₁₆	2
C₂³×C₅×D₈	2
C₂²×C₅×SD₃₂	2
C₂³×C₅×C₁₆	2
C₂³×SD₃₂	5

subgroup

index

C₂³×C₅×Q₁₆

C₂³×C₅×D₈

C₂²×C₅×SD₃₂

C₂³×C₅×C₁₆

C₂³×SD₃₂

Subgroups — C₂³×C₅×SD₃₂ #11985346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×C5×SD32 #11985346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×SD₃₂ #11985346