Group #11930850 — subgroups

Subgroups — C₅×#8130 #11930850

Order 1280.

520 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 230 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×#2920	C₂	1	3	yes	maximal
2	C₅×#1309	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
4	C₅×#432	—	2	6	no	—
5	C₅×#431	—	2	6	no	—
6	C₅×#423	C₂²	1	6	yes	—
7	C₅×#407	C₄	1	6	yes	—
8	C₄×C₅×M₁₆	C₄	1	6	yes	—
9	#8130	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₄×C₅	C₂×C₄	1	3	yes	—
11	C₂×C₅×M₁₆	C₂×C₄	1	12	yes	—
12	C₂×C₄²×C₅	C₂×C₄	1	3	yes	—
13	C₂×C₄²×C₅	D₄	1	6	yes	—
14	C₂×C₄²×C₅	Q₈	1	2	yes	—
15	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
16	C₅×C₄⋊C₈	—	2	12	no	—
17	C₅×C₂²⋊C₈	—	2	12	no	—
18	C₅×#97	—	2	6	no	—
19	C₄×C₅×C₈	—	2	6	no	—
20	#2920	C₂×C₅	1	3	yes	—
21	#1309	C₂×C₅	1	4	yes	complemented
22	C₂⁴×C₅	C₄²	1	1	yes	characteristic
23	C₂²×C₄×C₅	—	4	6	no	—
24	C₂²×C₄×C₅	C₄²	1	3	yes	—
25	C₂²×C₄×C₅	C₂²⋊C₄	1	6	yes	—
26	C₂²×C₄×C₅	C₄⋊C₄	1	6	yes	—
27	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
28	C₅×M₁₆	—	4	12	no	—
29	C₂×C₅×C₈	—	2	12	no	—
30	C₄²×C₅	C₂²⋊C₄	1	3	yes	—
31	C₄²×C₅	C₂²⋊C₄	1	3	yes	—
32	C₄²×C₅	C₄⋊C₄	1	6	yes	—
33	C₄²×C₅	C₂×D₄	1	3	yes	—
34	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
35	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
36	#432	—	2	6	no	—
37	#431	—	2	6	no	—
38	#423	C₂²×C₅	1	6	yes	—
39	#407	C₄×C₅	1	6	yes	—
40	C₄×M₁₆	C₄×C₅	1	6	yes	—
41	C₂³×C₅	—	4	3	no	—
42	C₂³×C₅	#95	1	2	yes	—
43	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
44	C₂×C₄×C₅	—	2	6	no	—
45	C₂×C₄×C₅	—	2	12	no	—
46	C₂×C₄×C₅	—	4	3	no	—
47	C₂×C₄×C₅	—	4	6	no	—
48	C₂×C₄×C₅	#95	1	6	yes	—
49	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
50	C₂×C₄×C₅	C₂×C₄⋊C₄	1	3	yes	—
51	C₅×C₈	—	4	12	no	—
52	C₂³×C₄	C₂×C₄×C₅	1	3	yes	—
53	C₂×M₁₆	C₂×C₄×C₅	1	12	yes	—
54	C₂×C₄²	C₂×C₄×C₅	1	3	yes	—
55	C₂×C₄²	C₅×D₄	1	6	yes	—
56	C₂×C₄²	C₅×Q₈	1	2	yes	—
57	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
58	C₄⋊C₈	—	2	12	no	—
59	C₂²⋊C₈	—	2	12	no	—
60	#97	—	2	6	no	—
61	C₄×C₈	—	2	6	no	—
62	C₂²×C₅	—	2	6	no	—
63	C₂²×C₅	—	2	3	no	—
64	C₂²×C₅	—	4	4	no	—
65	C₂²×C₅	C₂×#95	1	1	yes	characteristic
66	C₄×C₅	—	2	6	no	—
67	C₄×C₅	—	2	3	no	—
68	C₄×C₅	#413	1	6	yes	—
69	C₂⁴	C₄²×C₅	1	1	yes	characteristic
70	C₂²×C₄	—	4	6	no	—
71	C₂²×C₄	C₄²×C₅	1	3	yes	—
72	C₂²×C₄	C₅×C₂²⋊C₄	1	6	yes	—
73	C₂²×C₄	C₅×C₄⋊C₄	1	6	yes	—
74	C₂²×C₄	C₂²×C₄×C₅	1	3	yes	—
75	M₁₆	—	4	12	no	—
76	C₂×C₈	—	2	12	no	—
77	C₄²	C₅×C₂²⋊C₄	1	3	yes	—
78	C₄²	C₅×C₂²⋊C₄	1	3	yes	—
79	C₄²	C₅×C₄⋊C₄	1	6	yes	—
80	C₄²	C₂×C₅×D₄	1	3	yes	—
81	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
82	C₂×C₅	—	4	2	no	—
83	C₂×C₅	—	4	1	no	—
84	C₂×C₅	#1742	1	3	yes	—
85	C₂³	—	4	3	no	—
86	C₂³	C₅×#95	1	2	yes	—
87	C₂³	C₂×C₄²×C₅	1	1	yes	characteristic
88	C₂×C₄	—	2	6	no	—
89	C₂×C₄	—	2	12	no	—
90	C₂×C₄	—	4	3	no	—
91	C₂×C₄	—	4	6	no	—
92	C₂×C₄	C₅×#95	1	6	yes	—
93	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	3	yes	—
94	C₂×C₄	C₂×C₅×C₄⋊C₄	1	3	yes	—
95	C₈	—	4	12	no	—
96	C₅	#8130	1	1	yes	characteristic, direct product factor, Sylow
97	C₂²	—	2	3	no	—
98	C₂²	—	2	6	no	—
99	C₂²	—	4	4	no	—
100	C₂²	C₂×C₅×#95	1	1	yes	characteristic
101	C₄	—	2	3	no	—
102	C₄	—	2	6	no	—
103	C₄	C₅×#413	1	6	yes	—
104	C₂	—	4	1	no	—
105	C₂	—	4	2	no	—
106	C₂	C₅×#1742	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2920

C₂

yes

maximal

C₅×#1309

C₂

yes

maximal, complemented

C₂²×C₄²×C₅

C₂²

yes

—

—

C₂²

yes

—

C₅×#407

C₄

yes

—

C₄×C₅×M₁₆

C₄

yes

—

#8130

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₄×C₅

C₂×C₄

yes

—

C₂×C₅×M₁₆

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

D₄

yes

—

C₂×C₄²×C₅

Q₈

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₄×C₅×C₈

—

#2920

C₂×C₅

yes

—

#1309

C₂×C₅

yes

complemented

C₂⁴×C₅

C₄²

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₄²

yes

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₄⋊C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₄²×C₅

C₂²⋊C₄

yes

—

C₄²×C₅

C₂²⋊C₄

yes

—

C₄²×C₅

C₄⋊C₄

yes

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₂²×C₄²

C₂²×C₅

yes

—

—

C₂²×C₅

yes

—

#407

C₄×C₅

yes

—

C₄×M₁₆

C₄×C₅

yes

—

C₂³×C₅

—

C₂³×C₅

#95

yes

—

C₂³×C₅

C₂×C₄²

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#95

yes

—

C₂×C₄×C₅

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₅×C₈

—

C₂³×C₄

C₂×C₄×C₅

yes

—

C₂×M₁₆

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₅×D₄

yes

—

C₂×C₄²

C₅×Q₈

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

C₂×#95

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#413

yes

—

C₂⁴

C₄²×C₅

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄²×C₅

yes

—

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

C₂²×C₄

C₅×C₄⋊C₄

yes

—

C₂²×C₄

C₂²×C₄×C₅

yes

—

M₁₆

—

C₂×C₈

—

C₄²

C₅×C₂²⋊C₄

yes

—

C₄²

C₅×C₂²⋊C₄

yes

—

C₄²

C₅×C₄⋊C₄

yes

—

C₄²

C₂×C₅×D₄

yes

—

C₄²

C₂×C₅×Q₈

yes

characteristic

C₂×C₅

—

C₂×C₅

—

C₂×C₅

#1742

yes

—

C₂³

—

C₂³

C₅×#95

yes

—

C₂³

C₂×C₄²×C₅

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₅×#95

yes

—

C₂×C₄

C₂×C₅×C₂²⋊C₄

yes

—

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

—

C₈

—

C₅

#8130

yes

characteristic, direct product factor, Sylow

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×C₅×#95

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

C₅×#413

yes

—

104

C₂

—

105

C₂

—

106

C₂

C₅×#1742

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#95
commutator	C₂³	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂⁴×C₅	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

C₂×#95

commutator

C₂³

C₂×C₄²×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂⁴×C₅

C₄²

LCS

G ▷ C₂³ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

N	H ≅ G/N	type
2. C₅×#1309	C₂	semidirect
9. #8130	C₅	direct (N × H)
21. #1309	C₂×C₅	semidirect
96. C₅	#8130	direct (N × H)

H ≅ G/N

type

2. C₅×#1309

C₂

semidirect

9. #8130

C₅

direct (N × H)

21. #1309

C₂×C₅

semidirect

96. C₅

#8130

direct (N × H)

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

subgroup	index
C₅×#2920	2
C₅×#1309	2
#8130	5

subgroup

index

C₅×#2920

C₅×#1309

#8130

Subgroups — C₅×#8130 #11930850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8130 #11930850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8130 #11930850