Subgroups — C₂×C₅×(C₁₁⋊D₁₁)⋊C₉ #36344906

Order 21780.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×(C₁₁⋊D₁₁)⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅×C₁₁⋊D₁₁	C₃	1	1	yes	maximal, characteristic
4	C₅×C₁₁²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×(C₁₁⋊D₁₁)⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁⋊D₁₁	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×C₁₁⋊D₁₁	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁²⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented
10	(C₁₁⋊D₁₁)⋊C₉	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅×C₁₁²	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×C₁₁⋊D₁₁	C₃×C₅	1	1	yes	characteristic
13	C₂×C₅×C₁₁²	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅×C₁₁⋊D₁₁	C₂×C₉	1	2	yes	complemented
15	C₁₁²⋊C₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic
17	C₃×C₁₁⋊D₁₁	C₂×C₃×C₅	1	2	yes	—
18	C₂×C₃×C₅×D₁₁	—	33	4	no	—
19	C₅×C₁₁²	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁⋊D₁₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁²	C₂²×C₃×C₅	1	1	yes	characteristic
22	C₂×C₃×C₅×C₁₁	—	3	4	no	—
23	C₃×C₅×D₁₁	—	33	8	no	—
24	C₂×C₁₁²	C₂×C₅×C₉	1	1	yes	characteristic, complemented
25	C₁₁⋊D₁₁	C₂×C₅×C₉	1	2	yes	complemented
26	C₂×C₅×D₁₁	—	33	4	no	—
27	C₂²×C₅×C₉	—	121	1	no	maximal, Hall
28	C₃×C₅×C₁₁	—	3	4	no	—
29	C₂×C₃×D₁₁	—	33	4	no	—
30	C₁₁²	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅×C₁₁	—	3	4	no	—
32	C₅×D₁₁	—	33	8	no	—
33	C₂×C₅×C₉	—	121	2	no	—
34	C₂×C₅×C₉	—	121	1	no	—
35	C₂×C₃×C₁₁	—	3	4	no	—
36	C₃×D₁₁	—	33	8	no	—
37	C₂²×C₃×C₅	—	121	1	no	—
38	C₅×C₁₁	—	3	4	no	—
39	C₅×C₉	—	121	1	no	Hall
40	C₂×D₁₁	—	33	4	no	—
41	C₂²×C₉	—	121	1	no	Hall
42	C₃×C₁₁	—	3	4	no	—
43	C₂×C₃×C₅	—	121	2	no	—
44	C₂×C₃×C₅	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
45	C₂×C₁₁	—	3	4	no	—
46	D₁₁	—	33	8	no	—
47	C₂²×C₅	—	121	1	no	Hall
48	C₂×C₉	—	121	2	no	—
49	C₂×C₉	—	121	1	no	—
50	C₃×C₅	C₂×(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
51	C₂²×C₃	—	121	1	no	—
52	C₁₁	—	3	4	no	—
53	C₂×C₅	—	121	2	no	—
54	C₂×C₅	(C₁₁⋊D₁₁)⋊C₉	1	1	yes	characteristic, direct product factor
55	C₉	—	121	1	no	Sylow
56	C₂×C₃	—	121	2	no	—
57	C₂×C₃	C₅×(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
58	C₅	C₂×(C₁₁⋊D₁₁)⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	121	1	no	Sylow
60	C₃	C₂×C₅×(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
61	C₂	—	121	2	no	—
62	C₂	C₅×(C₁₁⋊D₁₁)⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	(C₁₁⋊D₁₁)⋊C₃
commutator, hypocenter	C₁₁²	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×(C₁₁⋊D₁₁)⋊C₃
Fitting, socle	C₂×C₃×C₅×C₁₁²	C₂×C₃
prime radical	C₂×C₃×C₅×C₁₁⋊D₁₁	C₃
cosocle	C₃×C₁₁²	C₂²×C₃×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₃×C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×C₁₁²⋊C₉	C₂	semidirect
2. C₅×(C₁₁⋊D₁₁)⋊C₉	C₂	direct (N × H)
4. C₅×C₁₁²⋊C₉	C₂²	semidirect
5. C₂×(C₁₁⋊D₁₁)⋊C₉	C₅	direct (N × H)
8. C₂×C₅×C₁₁⋊D₁₁	C₉	semidirect
9. C₂×C₁₁²⋊C₉	C₂×C₅	semidirect
10. (C₁₁⋊D₁₁)⋊C₉	C₂×C₅	direct (N × H)
13. C₂×C₅×C₁₁²	C₂×C₉	semidirect
14. C₅×C₁₁⋊D₁₁	C₂×C₉	semidirect
15. C₁₁²⋊C₉	C₂²×C₅	semidirect
19. C₅×C₁₁²	C₂²×C₉	semidirect
20. C₂×C₁₁⋊D₁₁	C₅×C₉	semidirect
24. C₂×C₁₁²	C₂×C₅×C₉	semidirect
25. C₁₁⋊D₁₁	C₂×C₅×C₉	semidirect
30. C₁₁²	C₂²×C₅×C₉	semidirect
54. C₂×C₅	(C₁₁⋊D₁₁)⋊C₉	direct (N × H)
58. C₅	C₂×(C₁₁⋊D₁₁)⋊C₉	direct (N × H)
62. C₂	C₅×(C₁₁⋊D₁₁)⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₁²⋊C₉	2
C₅×(C₁₁⋊D₁₁)⋊C₉	2
C₂×C₃×C₅×C₁₁⋊D₁₁	3
C₂×(C₁₁⋊D₁₁)⋊C₉	5
C₂²×C₅×C₉	121

Subgroups — C2×C5×(C11⋊D11)⋊C9 #36344906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×(C₁₁⋊D₁₁)⋊C₉ #36344906