Group #11933403 — subgroups

Subgroups — C₅×#10683 #11933403

Order 1280.

526 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 178 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×#1957	C₂	1	3	yes	maximal
2	C₅×#1844	C₂	1	3	yes	maximal, complemented
3	C₅×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#127	C₂²	1	1	yes	characteristic
5	C₂×C₅×#106	—	2	6	no	—
6	C₂×C₅×#102	—	2	6	no	—
7	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
8	C₅×#384	C₂²	1	3	yes	—
9	#10683	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅×D₄	—	2	3	no	—
11	C₂²×C₅×C₈	D₄	1	6	yes	—
12	C₅×#127	—	2	3	no	—
13	C₅×#127	Q₈	1	2	yes	—
14	C₂×C₅×C₄⋊C₄	—	2	3	no	—
15	C₂×C₅×C₄⋊C₄	—	2	6	no	—
16	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
17	C₅×#106	—	4	12	no	—
18	C₅×#102	—	4	12	no	—
19	C₄×C₅×C₈	—	2	6	no	—
20	#1957	C₂×C₅	1	3	yes	—
21	#1844	C₂×C₅	1	3	yes	complemented
22	#1273	C₂×C₅	1	1	yes	characteristic, complemented
23	C₂⁴×C₅	—	4	1	no	—
24	C₂×C₅×D₄	—	2	6	no	—
25	C₂×C₅×D₄	—	4	3	no	—
26	C₂×C₅×D₄	—	4	6	no	—
27	C₂×C₅×D₄	—	4	6	no	—
28	C₂²×C₄×C₅	—	4	3	no	—
29	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
30	C₂×C₅×C₈	—	2	6	no	—
31	C₂×C₅×C₈	—	2	6	no	—
32	C₂×C₅×C₈	SD₁₆	1	12	yes	—
33	C₅×C₄⋊C₄	—	4	6	no	—
34	C₅×C₄⋊C₄	—	4	12	no	—
35	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
36	C₄²×C₅	#41	1	3	yes	—
37	C₂×#127	C₂²×C₅	1	1	yes	characteristic
38	C₂×#106	—	2	6	no	—
39	C₂×#102	—	2	6	no	—
40	C₂×C₄×C₈	C₂²×C₅	1	3	yes	—
41	#384	C₂²×C₅	1	3	yes	—
42	C₂³×C₅	—	4	2	no	—
43	C₂³×C₅	—	8	3	no	—
44	C₂³×C₅	—	8	3	no	—
45	C₂³×C₅	#127	1	1	yes	characteristic
46	C₅×D₄	—	4	12	no	—
47	C₅×D₄	—	8	6	no	—
48	C₂×C₄×C₅	—	8	3	no	—
49	C₂×C₄×C₅	—	8	6	no	—
50	C₂×C₄×C₅	C₂²⋊Q₈	1	3	yes	—
51	C₂×C₄×C₅	#123	1	3	yes	—
52	C₂×C₄×C₅	C₂×SD₁₆	1	6	yes	—
53	C₂×C₄×C₅	AGL(1,ℤ/8)	1	6	yes	—
54	C₅×C₈	—	2	12	no	—
55	C₂²×D₄	—	2	3	no	—
56	C₂²×C₈	C₅×D₄	1	6	yes	—
57	#127	—	2	3	no	—
58	#127	C₅×Q₈	1	2	yes	—
59	C₂×C₄⋊C₄	—	2	3	no	—
60	C₂×C₄⋊C₄	—	2	6	no	—
61	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
62	#106	—	4	12	no	—
63	#102	—	4	12	no	—
64	C₄×C₈	—	2	6	no	—
65	C₂²×C₅	—	8	6	no	—
66	C₂²×C₅	—	16	1	no	—
67	C₂²×C₅	—	16	3	no	—
68	C₂²×C₅	#399	1	1	yes	characteristic
69	C₂²×C₅	#492	1	3	yes	—
70	C₂²×C₅	#496	1	3	yes	—
71	C₄×C₅	—	16	3	no	—
72	C₄×C₅	#476	1	6	yes	—
73	C₄×C₅	#481	1	6	yes	—
74	C₂⁴	—	4	1	no	—
75	C₂×D₄	—	2	6	no	—
76	C₂×D₄	—	4	3	no	—
77	C₂×D₄	—	4	6	no	—
78	C₂×D₄	—	4	6	no	—
79	C₂²×C₄	—	4	3	no	—
80	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
81	C₂×C₈	—	2	6	no	—
82	C₂×C₈	—	2	6	no	—
83	C₂×C₈	C₅×SD₁₆	1	12	yes	—
84	C₄⋊C₄	—	4	6	no	—
85	C₄⋊C₄	—	4	12	no	—
86	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
87	C₄²	C₅×#41	1	3	yes	—
88	C₂×C₅	—	16	2	no	—
89	C₂×C₅	#1705	1	1	yes	characteristic
90	C₂×C₅	#1715	1	3	yes	—
91	C₂×C₅	#2094	1	3	yes	—
92	C₂³	—	4	2	no	—
93	C₂³	—	8	3	no	—
94	C₂³	—	8	3	no	—
95	C₂³	C₅×#127	1	1	yes	characteristic
96	D₄	—	4	12	no	—
97	D₄	—	8	6	no	—
98	C₂×C₄	—	8	3	no	—
99	C₂×C₄	—	8	6	no	—
100	C₂×C₄	C₅×C₂²⋊Q₈	1	3	yes	—
101	C₂×C₄	C₅×#123	1	3	yes	—
102	C₂×C₄	C₂×C₅×SD₁₆	1	6	yes	—
103	C₂×C₄	C₅×AGL(1,ℤ/8)	1	6	yes	—
104	C₈	—	2	12	no	—
105	C₅	#10683	1	1	yes	characteristic, direct product factor, Sylow
106	C₂²	—	8	6	no	—
107	C₂²	—	16	1	no	—
108	C₂²	—	16	3	no	—
109	C₂²	C₅×#399	1	1	yes	characteristic
110	C₂²	C₅×#492	1	3	yes	—
111	C₂²	C₅×#496	1	3	yes	—
112	C₄	—	16	3	no	—
113	C₄	C₅×#476	1	6	yes	—
114	C₄	C₅×#481	1	6	yes	—
115	C₂	—	16	2	no	—
116	C₂	C₅×#1705	1	1	yes	characteristic
117	C₂	C₅×#1715	1	3	yes	—
118	C₂	C₅×#2094	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1957

C₂

yes

maximal

C₅×#1844

C₂

yes

maximal, complemented

C₅×#1273

C₂

yes

maximal, characteristic, complemented

C₂×C₅×#127

C₂²

yes

characteristic

C₂×C₅×#106

—

C₂×C₅×#102

—

C₂×C₄×C₅×C₈

C₂²

yes

—

C₅×#384

C₂²

yes

—

#10683

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×D₄

—

C₂²×C₅×C₈

D₄

yes

—

C₅×#127

—

C₅×#127

Q₈

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#106

—

C₅×#102

—

C₄×C₅×C₈

—

#1957

C₂×C₅

yes

—

#1844

C₂×C₅

yes

complemented

#1273

C₂×C₅

yes

characteristic, complemented

C₂⁴×C₅

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

SD₁₆

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

#41

yes

—

C₂×#127

C₂²×C₅

yes

characteristic

C₂×#106

—

C₂×#102

—

C₂×C₄×C₈

C₂²×C₅

yes

—

#384

C₂²×C₅

yes

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#127

yes

characteristic

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₂×C₄×C₅

#123

yes

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₅×C₈

—

C₂²×D₄

—

C₂²×C₈

C₅×D₄

yes

—

#127

—

#127

C₅×Q₈

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₅

yes

characteristic

#106

—

#102

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#399

yes

characteristic

C₂²×C₅

#492

yes

—

C₂²×C₅

#496

yes

—

C₄×C₅

—

C₄×C₅

#476

yes

—

C₄×C₅

#481

yes

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₅×D₄

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₅×SD₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×C₅×Q₈

yes

characteristic

C₄²

C₅×#41

yes

—

C₂×C₅

—

C₂×C₅

#1705

yes

characteristic

C₂×C₅

#1715

yes

—

C₂×C₅

#2094

yes

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₅×#127

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

101

C₂×C₄

C₅×#123

yes

—

102

C₂×C₄

C₂×C₅×SD₁₆

yes

—

103

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

104

C₈

—

105

C₅

#10683

yes

characteristic, direct product factor, Sylow

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₅×#399

yes

characteristic

110

C₂²

C₅×#492

yes

—

111

C₂²

C₅×#496

yes

—

112

C₄

—

113

C₄

C₅×#476

yes

—

114

C₄

C₅×#481

yes

—

115

C₂

—

116

C₂

C₅×#1705

yes

characteristic

117

C₂

C₅×#1715

yes

—

118

C₂

C₅×#2094

yes

—

	subgroup	G/H
center, socle	C₂³×C₅	#127
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

#127

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
2. C₅×#1844	C₂	semidirect
3. C₅×#1273	C₂	semidirect
9. #10683	C₅	direct (N × H)
21. #1844	C₂×C₅	semidirect
22. #1273	C₂×C₅	semidirect
105. C₅	#10683	direct (N × H)

H ≅ G/N

type

2. C₅×#1844

C₂

semidirect

3. C₅×#1273

C₂

semidirect

9. #10683

C₅

direct (N × H)

21. #1844

C₂×C₅

semidirect

22. #1273

C₂×C₅

semidirect

105. C₅

#10683

direct (N × H)

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

subgroup	index
C₅×#1957	2
C₅×#1844	2
C₅×#1273	2
#10683	5

subgroup

index

Subgroups — C₅×#10683 #11933403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10683 #11933403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10683 #11933403