Group #13183064 — subgroups

Subgroups — C₅×#66985 #13183064

Order 1760.

136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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	C₂×C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#4339	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4324	C₂	1	2	yes	maximal, complemented
4	C₅×#4323	C₂	1	2	yes	maximal, complemented
5	C₅×#4318	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₅×C₁₁	—	2	1	no	—
7	C₅×D₄×C₁₁	—	2	1	no	—
8	C₅×D₄×C₁₁	C₂²	1	2	yes	—
9	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
10	C₅×C₂²⋊D₁₁	—	2	1	no	—
11	C₅×D₄₄	C₂²	1	1	yes	characteristic, complemented
12	C₄×C₅×D₁₁	—	2	1	no	—
13	C₅×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
14	C₅×C₁₁⋊C₈	C₂²	1	2	yes	complemented
15	#66985	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₅×C₁₁	—	2	2	no	—
17	C₂²×C₅×C₁₁	—	4	2	no	—
18	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
19	C₂×C₅×D₁₁	—	2	1	no	—
20	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
21	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
22	C₅×Dic₁₁	—	2	1	no	—
23	C₂×D₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
24	#4339	C₂×C₅	1	1	yes	characteristic, complemented
25	#4324	C₂×C₅	1	2	yes	complemented
26	#4323	C₂×C₅	1	2	yes	complemented
27	#4318	C₂×C₅	1	1	yes	characteristic, complemented
28	C₅×AGL(1,ℤ/8)	—	11	1	no	maximal, Hall
29	C₂×C₅×C₁₁	—	2	1	no	—
30	C₂×C₅×C₁₁	—	4	2	no	—
31	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₅×D₁₁	—	4	1	no	—
33	C₂³×C₁₁	—	2	1	no	—
34	D₄×C₁₁	—	2	1	no	—
35	D₄×C₁₁	C₂²×C₅	1	2	yes	—
36	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
37	C₂²⋊D₁₁	—	2	1	no	—
38	D₄₄	C₂²×C₅	1	1	yes	characteristic, complemented
39	C₄×D₁₁	—	2	1	no	—
40	Dic₂₂	C₂²×C₅	1	1	yes	characteristic, complemented
41	C₁₁⋊C₈	C₂²×C₅	1	2	yes	complemented
42	C₅×#41	—	11	1	no	—
43	C₂×C₅×D₄	D₁₁	1	1	yes	characteristic, complemented
44	C₅×SD₁₆	—	11	2	no	—
45	C₅×D₈	—	11	2	no	—
46	C₅×M₁₆	—	11	1	no	—
47	C₅×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₁₁	—	2	2	no	—
49	C₂²×C₁₁	—	4	2	no	—
50	C₂²×C₁₁	C₅×D₄	1	1	yes	characteristic
51	C₂×D₁₁	—	2	1	no	—
52	C₄×C₁₁	C₅×D₄	1	1	yes	characteristic
53	C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
54	Dic₁₁	—	2	1	no	—
55	C₂³×C₅	—	2	1	no	—
56	C₅×Q₈	—	11	1	no	—
57	C₅×D₄	—	2	1	no	—
58	C₅×D₄	—	11	1	no	—
59	C₅×D₄	—	22	1	no	—
60	C₅×D₄	C₂×D₁₁	1	2	yes	—
61	C₂×C₄×C₅	—	22	1	no	—
62	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
63	C₅×C₈	—	11	2	no	—
64	AGL(1,ℤ/8)	—	11	1	no	Sylow
65	C₂×C₁₁	—	2	1	no	—
66	C₂×C₁₁	—	4	2	no	—
67	C₂×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
68	D₁₁	—	4	1	no	—
69	C₂²×C₅	—	2	2	no	—
70	C₂²×C₅	—	4	2	no	—
71	C₂²×C₅	—	22	1	no	—
72	C₂²×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
73	C₄×C₅	—	22	1	no	—
74	C₄×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
75	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
76	#41	—	11	1	no	—
77	C₂×D₄	C₅×D₁₁	1	1	yes	characteristic, complemented
78	SD₁₆	—	11	2	no	—
79	D₈	—	11	2	no	—
80	M₁₆	—	11	1	no	—
81	C₁₁	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₅	—	2	1	no	—
83	C₂×C₅	—	4	2	no	—
84	C₂×C₅	—	44	1	no	—
85	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
86	C₂³	—	2	1	no	—
87	Q₈	—	11	1	no	—
88	D₄	—	2	1	no	—
89	D₄	—	11	1	no	—
90	D₄	—	22	1	no	—
91	D₄	C₂×C₅×D₁₁	1	2	yes	—
92	C₂×C₄	—	22	1	no	—
93	C₂×C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
94	C₈	—	11	2	no	—
95	C₅	#66985	1	1	yes	characteristic, direct product factor, Sylow
96	C₂²	—	2	2	no	—
97	C₂²	—	4	2	no	—
98	C₂²	—	22	1	no	—
99	C₂²	C₅×C₂²⋊D₁₁	1	1	yes	characteristic
100	C₄	—	22	1	no	—
101	C₄	C₅×C₂²⋊D₁₁	1	1	yes	characteristic
102	C₄	C₂²×C₅×D₁₁	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	4	2	no	—
105	C₂	—	44	1	no	—
106	C₂	C₂×C₅×C₂²⋊D₁₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×D₄×C₁₁

C₂

yes

maximal, characteristic, complemented

C₅×#4339

C₂

yes

maximal, characteristic, complemented

C₅×#4324

C₂

yes

maximal, complemented

C₅×#4323

C₂

yes

maximal, complemented

C₅×#4318

C₂

yes

maximal, characteristic, complemented

C₂³×C₅×C₁₁

—

C₅×D₄×C₁₁

—

C₅×D₄×C₁₁

C₂²

yes

—

C₂×C₄×C₅×C₁₁

C₂²

yes

characteristic

C₅×C₂²⋊D₁₁

—

C₅×D₄₄

C₂²

yes

characteristic, complemented

C₄×C₅×D₁₁

—

C₅×Dic₂₂

C₂²

yes

characteristic, complemented

C₅×C₁₁⋊C₈

C₂²

yes

complemented

#66985

C₅

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₅×C₁₁

—

C₂²×C₅×C₁₁

—

C₂²×C₅×C₁₁

D₄

yes

characteristic

C₂×C₅×D₁₁

—

C₄×C₅×C₁₁

D₄

yes

characteristic

C₄×C₅×C₁₁

C₂³

yes

characteristic

C₅×Dic₁₁

—

C₂×D₄×C₁₁

C₂×C₅

yes

characteristic, complemented

#4339

C₂×C₅

yes

characteristic, complemented

#4324

C₂×C₅

yes

complemented

#4323

C₂×C₅

yes

complemented

#4318

C₂×C₅

yes

characteristic, complemented

C₅×AGL(1,ℤ/8)

—

maximal, Hall

C₂×C₅×C₁₁

—

C₂×C₅×C₁₁

—

C₂×C₅×C₁₁

C₂×D₄

yes

characteristic

C₅×D₁₁

—

C₂³×C₁₁

—

D₄×C₁₁

—

D₄×C₁₁

C₂²×C₅

yes

—

C₂×C₄×C₁₁

C₂²×C₅

yes

characteristic

C₂²⋊D₁₁

—

D₄₄

C₂²×C₅

yes

characteristic, complemented

C₄×D₁₁

—

Dic₂₂

C₂²×C₅

yes

characteristic, complemented

C₁₁⋊C₈

C₂²×C₅

yes

complemented

C₅×#41

—

C₂×C₅×D₄

D₁₁

yes

characteristic, complemented

C₅×SD₁₆

—

C₅×D₈

—

C₅×M₁₆

—

C₅×C₁₁

AGL(1,ℤ/8)

yes

characteristic, complemented, Hall

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

C₅×D₄

yes

characteristic

C₂×D₁₁

—

C₄×C₁₁

C₅×D₄

yes

characteristic

C₄×C₁₁

C₂³×C₅

yes

characteristic

Dic₁₁

—

C₂³×C₅

—

C₅×Q₈

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

C₂×D₁₁

yes

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₁₁

yes

characteristic

C₅×C₈

—

AGL(1,ℤ/8)

—

Sylow

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

C₂×C₅×D₄

yes

characteristic

D₁₁

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

C₂²⋊D₁₁

yes

characteristic

C₄×C₅

—

C₄×C₅

C₂²⋊D₁₁

yes

characteristic

C₄×C₅

C₂²×D₁₁

yes

characteristic

#41

—

C₂×D₄

C₅×D₁₁

yes

characteristic, complemented

SD₁₆

—

D₈

—

M₁₆

—

C₁₁

C₅×AGL(1,ℤ/8)

yes

characteristic, complemented, Sylow

C₂×C₅

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

C₂×C₂²⋊D₁₁

yes

characteristic

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

C₂×C₅×D₁₁

yes

—

C₂×C₄

—

C₂×C₄

C₂×C₅×D₁₁

yes

characteristic

C₈

—

C₅

#66985

yes

characteristic, direct product factor, Sylow

C₂²

—

C₂²

—

C₂²

—

C₂²

C₅×C₂²⋊D₁₁

yes

characteristic

100

C₄

—

101

C₄

C₅×C₂²⋊D₁₁

yes

characteristic

102

C₄

C₂²×C₅×D₁₁

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

C₂×C₅×C₂²⋊D₁₁

yes

characteristic

	subgroup	G/H
center	C₂×C₅	C₂×C₂²⋊D₁₁
commutator, cosocle	C₄×C₁₁	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₁₁
Fitting	C₂×C₅×D₄×C₁₁	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₂×C₅×D₄	D₁₁
hypocenter	C₁₁	C₅×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×D₄

subgroup

G/H

center

C₂×C₅

C₂×C₂²⋊D₁₁

commutator, cosocle

C₄×C₁₁

C₂³×C₅

Frattini

C₄

C₂²×C₅×D₁₁

Fitting

C₂×C₅×D₄×C₁₁

C₂

socle

C₂×C₅×C₁₁

C₂×D₄

hypercenter

C₂×C₅×D₄

D₁₁

hypocenter

C₁₁

C₅×AGL(1,ℤ/8)

LCS

G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×D₄

N	H ≅ G/N	type
1. C₂×C₅×D₄×C₁₁	C₂	semidirect
2. C₅×#4339	C₂	semidirect
3. C₅×#4324	C₂	semidirect
4. C₅×#4323	C₂	semidirect
5. C₅×#4318	C₂	semidirect
11. C₅×D₄₄	C₂²	semidirect
13. C₅×Dic₂₂	C₂²	semidirect
14. C₅×C₁₁⋊C₈	C₂²	semidirect
15. #66985	C₅	direct (N × H)
23. C₂×D₄×C₁₁	C₂×C₅	semidirect
24. #4339	C₂×C₅	semidirect
25. #4324	C₂×C₅	semidirect
26. #4323	C₂×C₅	semidirect
27. #4318	C₂×C₅	semidirect
38. D₄₄	C₂²×C₅	semidirect
40. Dic₂₂	C₂²×C₅	semidirect
41. C₁₁⋊C₈	C₂²×C₅	semidirect
43. C₂×C₅×D₄	D₁₁	semidirect
47. C₅×C₁₁	AGL(1,ℤ/8)	semidirect
77. C₂×D₄	C₅×D₁₁	semidirect
81. C₁₁	C₅×AGL(1,ℤ/8)	semidirect
95. C₅	#66985	direct (N × H)

H ≅ G/N

type

1. C₂×C₅×D₄×C₁₁

C₂

semidirect

2. C₅×#4339

C₂

semidirect

3. C₅×#4324

C₂

semidirect

4. C₅×#4323

C₂

semidirect

5. C₅×#4318

C₂

semidirect

11. C₅×D₄₄

C₂²

semidirect

13. C₅×Dic₂₂

C₂²

semidirect

14. C₅×C₁₁⋊C₈

C₂²

semidirect

15. #66985

C₅

direct (N × H)

23. C₂×D₄×C₁₁

C₂×C₅

semidirect

24. #4339

C₂×C₅

semidirect

25. #4324

C₂×C₅

semidirect

26. #4323

C₂×C₅

semidirect

27. #4318

C₂×C₅

semidirect

38. D₄₄

C₂²×C₅

semidirect

40. Dic₂₂

C₂²×C₅

semidirect

41. C₁₁⋊C₈

C₂²×C₅

semidirect

43. C₂×C₅×D₄

D₁₁

semidirect

47. C₅×C₁₁

AGL(1,ℤ/8)

semidirect

77. C₂×D₄

C₅×D₁₁

semidirect

81. C₁₁

C₅×AGL(1,ℤ/8)

semidirect

95. C₅

#66985

direct (N × H)

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

subgroup	index
C₂×C₅×D₄×C₁₁	2
C₅×#4339	2
C₅×#4324	2
C₅×#4323	2
C₅×#4318	2
#66985	5
C₅×AGL(1,ℤ/8)	11

subgroup

index

C₂×C₅×D₄×C₁₁

Subgroups — C₅×#66985 #13183064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#66985 #13183064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66985 #13183064