Group #10616430 — subgroups

Subgroups — C₅×#2835 #10616430

Order 640.

380 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 168 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×#400	C₂	1	6	yes	maximal, complemented
2	C₅×#397	C₂	1	3	yes	maximal
3	C₅×#395	C₂	1	2	yes	maximal, complemented
4	C₅×#393	C₂	1	1	yes	maximal, characteristic
5	C₅×#385	C₂	1	3	yes	maximal
6	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₅×C₄⋊C₄	C₂²	1	6	yes	—
9	C₂×C₅×C₄⋊C₄	C₂²	1	3	yes	—
10	C₂×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
11	C₂×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
12	C₅×#95	C₂²	1	6	yes	—
13	C₅×#95	C₂²	1	3	yes	—
14	C₅×#95	C₂²	1	6	yes	—
15	C₅×#95	C₂²	1	3	yes	—
16	#2835	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂⁴×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₅×Q₈	—	4	3	no	—
19	C₂²×C₄×C₅	—	4	3	no	—
20	C₂²×C₄×C₅	C₂³	1	3	yes	—
21	C₂²×C₄×C₅	C₂³	1	6	yes	—
22	C₂²×C₄×C₅	C₂³	1	3	yes	—
23	C₂²×C₄×C₅	C₂³	1	2	yes	—
24	C₅×C₄⋊C₄	—	4	3	no	—
25	C₅×C₄⋊C₄	—	4	6	no	—
26	C₅×C₂²⋊C₄	—	2	6	no	—
27	C₅×C₂²⋊C₄	—	4	3	no	—
28	#400	C₂×C₅	1	6	yes	complemented
29	#397	C₂×C₅	1	3	yes	—
30	#395	C₂×C₅	1	2	yes	complemented
31	#393	C₂×C₅	1	1	yes	characteristic
32	#385	C₂×C₅	1	3	yes	—
33	C₂³×C₅	—	2	3	no	—
34	C₂³×C₅	—	2	3	no	—
35	C₂³×C₅	#41	1	2	yes	—
36	C₂³×C₅	C₂⁴	1	1	yes	characteristic
37	C₅×Q₈	—	4	4	no	—
38	C₂×C₄×C₅	—	2	6	no	—
39	C₂×C₄×C₅	—	2	3	no	—
40	C₂×C₄×C₅	—	2	3	no	—
41	C₂×C₄×C₅	—	2	6	no	—
42	C₂×C₄×C₅	—	2	6	no	—
43	C₂×C₄×C₅	—	2	6	no	—
44	C₂×C₄×C₅	—	2	6	no	—
45	C₂×C₄×C₅	—	2	6	no	—
46	C₂×C₄×C₅	—	4	4	no	—
47	C₂²×Q₈	C₂²×C₅	1	1	yes	characteristic
48	C₂³×C₄	C₂²×C₅	1	1	yes	characteristic
49	C₂×C₄⋊C₄	C₂²×C₅	1	6	yes	—
50	C₂×C₄⋊C₄	C₂²×C₅	1	3	yes	—
51	C₂×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
52	C₂×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
53	#95	C₂²×C₅	1	6	yes	—
54	#95	C₂²×C₅	1	3	yes	—
55	#95	C₂²×C₅	1	6	yes	—
56	#95	C₂²×C₅	1	3	yes	—
57	C₂²×C₅	—	2	6	no	—
58	C₂²×C₅	—	4	1	no	—
59	C₂²×C₅	—	4	3	no	—
60	C₂²×C₅	C₂×#41	1	1	yes	characteristic
61	C₂²×C₅	H(5,𝔽₂)	1	3	yes	—
62	C₂²×C₅	2₋¹⁺⁴	1	3	yes	—
63	C₄×C₅	—	4	6	no	—
64	C₄×C₅	—	4	2	no	—
65	C₄×C₅	—	4	3	no	—
66	C₄×C₅	—	4	3	no	—
67	C₂⁴	C₂³×C₅	1	1	yes	characteristic
68	C₂×Q₈	—	4	3	no	—
69	C₂²×C₄	—	4	3	no	—
70	C₂²×C₄	C₂³×C₅	1	3	yes	—
71	C₂²×C₄	C₂³×C₅	1	6	yes	—
72	C₂²×C₄	C₂³×C₅	1	3	yes	—
73	C₂²×C₄	C₂³×C₅	1	2	yes	—
74	C₄⋊C₄	—	4	3	no	—
75	C₄⋊C₄	—	4	6	no	—
76	C₂²⋊C₄	—	2	6	no	—
77	C₂²⋊C₄	—	4	3	no	—
78	C₂×C₅	—	4	2	no	—
79	C₂×C₅	#539	1	3	yes	—
80	C₂×C₅	H(3,𝔽₄)	1	1	yes	characteristic
81	C₂×C₅	#563	1	3	yes	—
82	C₂³	—	2	3	no	—
83	C₂³	—	2	3	no	—
84	C₂³	C₅×#41	1	2	yes	—
85	C₂³	C₂⁴×C₅	1	1	yes	characteristic
86	Q₈	—	4	4	no	—
87	C₂×C₄	—	2	6	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	6	no	—
91	C₂×C₄	—	2	6	no	—
92	C₂×C₄	—	2	6	no	—
93	C₂×C₄	—	2	6	no	—
94	C₂×C₄	—	2	6	no	—
95	C₂×C₄	—	4	4	no	—
96	C₅	#2835	1	1	yes	characteristic, direct product factor, Sylow
97	C₂²	—	2	6	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	4	3	no	—
100	C₂²	C₂×C₅×#41	1	1	yes	characteristic
101	C₂²	C₅×H(5,𝔽₂)	1	3	yes	—
102	C₂²	C₅×2₋¹⁺⁴	1	3	yes	—
103	C₄	—	4	6	no	—
104	C₄	—	4	2	no	—
105	C₄	—	4	3	no	—
106	C₄	—	4	3	no	—
107	C₂	—	4	2	no	—
108	C₂	C₅×#539	1	3	yes	—
109	C₂	C₅×H(3,𝔽₄)	1	1	yes	characteristic
110	C₂	C₅×#563	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#400

C₂

yes

maximal, complemented

C₅×#397

C₂

yes

maximal

C₅×#395

C₂

yes

maximal, complemented

C₅×#393

C₂

yes

maximal, characteristic

C₅×#385

C₂

yes

maximal

C₂²×C₅×Q₈

C₂²

yes

characteristic

C₂³×C₄×C₅

C₂²

yes

characteristic

C₂×C₅×C₄⋊C₄

C₂²

yes

—

C₂×C₅×C₄⋊C₄

C₂²

yes

—

C₂×C₅×C₂²⋊C₄

C₂²

yes

—

C₂×C₅×C₂²⋊C₄

C₂²

yes

—

C₅×#95

C₂²

yes

—

C₅×#95

C₂²

yes

—

C₅×#95

C₂²

yes

—

C₅×#95

C₂²

yes

—

#2835

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₅

C₂³

yes

characteristic

C₂×C₅×Q₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

#400

C₂×C₅

yes

complemented

#397

C₂×C₅

yes

—

#395

C₂×C₅

yes

complemented

#393

C₂×C₅

yes

characteristic

#385

C₂×C₅

yes

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#41

yes

—

C₂³×C₅

C₂⁴

yes

characteristic

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂²×Q₈

C₂²×C₅

yes

characteristic

C₂³×C₄

C₂²×C₅

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₅

yes

—

C₂×C₄⋊C₄

C₂²×C₅

yes

—

C₂×C₂²⋊C₄

C₂²×C₅

yes

—

C₂×C₂²⋊C₄

C₂²×C₅

yes

—

#95

C₂²×C₅

yes

—

#95

C₂²×C₅

yes

—

#95

C₂²×C₅

yes

—

#95

C₂²×C₅

yes

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

C₂×#41

yes

characteristic

C₂²×C₅

H(5,𝔽₂)

yes

—

C₂²×C₅

2₋¹⁺⁴

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂⁴

C₂³×C₅

yes

characteristic

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂³×C₅

yes

—

C₂²×C₄

C₂³×C₅

yes

—

C₂²×C₄

C₂³×C₅

yes

—

C₂²×C₄

C₂³×C₅

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂×C₅

—

C₂×C₅

#539

yes

—

C₂×C₅

H(3,𝔽₄)

yes

characteristic

C₂×C₅

#563

yes

—

C₂³

—

C₂³

—

C₂³

C₅×#41

yes

—

C₂³

C₂⁴×C₅

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₅

#2835

yes

characteristic, direct product factor, Sylow

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×C₅×#41

yes

characteristic

101

C₂²

C₅×H(5,𝔽₂)

yes

—

102

C₂²

C₅×2₋¹⁺⁴

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₂

—

108

C₂

C₅×#539

yes

—

109

C₂

C₅×H(3,𝔽₄)

yes

characteristic

110

C₂

C₅×#563

yes

—

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

subgroup

G/H

center, socle

C₂³×C₅

C₂⁴

commutator, Frattini, cosocle

C₂³

C₂⁴×C₅

prime radical

C₂⁴×C₅

C₂³

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ G

N	H ≅ G/N	type
1. C₅×#400	C₂	semidirect
3. C₅×#395	C₂	semidirect
16. #2835	C₅	direct (N × H)
28. #400	C₂×C₅	semidirect
30. #395	C₂×C₅	semidirect
96. C₅	#2835	direct (N × H)

H ≅ G/N

type

1. C₅×#400

C₂

semidirect

3. C₅×#395

C₂

semidirect

16. #2835

C₅

direct (N × H)

28. #400

C₂×C₅

semidirect

30. #395

C₂×C₅

semidirect

96. C₅

#2835

direct (N × H)

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

subgroup	index
C₅×#400	2
C₅×#397	2
C₅×#395	2
C₅×#393	2
C₅×#385	2
#2835	5

subgroup

index

Subgroups — C₅×#2835 #10616430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#2835 #10616430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2835 #10616430