Subgroups — C₉×D₅×C₁₁² #24926124

Order 10890.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×C₁₁²	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₁₁²	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic
5	D₅×C₁₁²	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁²	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₉×D₅×C₁₁	C₁₁	1	12	yes	maximal, direct product factor
8	C₂×C₃×C₁₁²	—	5	1	no	—
9	C₅×C₁₁²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₁₁	C₂×C₁₁	1	12	yes	complemented
11	C₃×C₁₁²	C₃×D₅	1	1	yes	characteristic
12	C₃×D₅×C₁₁	C₃×C₁₁	1	12	yes	—
13	C₂×C₁₁²	—	5	1	no	Hall
14	C₂×C₉×C₁₁	—	5	12	no	—
15	C₃×C₅×C₁₁	C₂×C₃×C₁₁	1	12	yes	—
16	C₁₁²	C₉×D₅	1	1	yes	characteristic, direct product factor, Sylow
17	D₅×C₁₁	C₉×C₁₁	1	12	yes	direct product factor
18	C₉×C₁₁	D₅×C₁₁	1	12	yes	direct product factor
19	C₉×D₅	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₁₁	—	5	12	no	—
21	C₅×C₁₁	C₂×C₉×C₁₁	1	12	yes	complemented
22	C₅×C₉	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₁	C₃×D₅×C₁₁	1	12	yes	—
24	C₃×D₅	C₃×C₁₁²	1	1	yes	characteristic
25	C₂×C₁₁	—	5	12	no	—
26	C₂×C₉	—	5	1	no	Hall
27	C₃×C₅	C₂×C₃×C₁₁²	1	1	yes	characteristic
28	C₁₁	C₉×D₅×C₁₁	1	12	yes	direct product factor
29	D₅	C₉×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
30	C₉	D₅×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	5	1	no	—
32	C₅	C₂×C₉×C₁₁²	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃×D₅×C₁₁²	1	1	yes	characteristic
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₁₁²	D₅
commutator, hypocenter	C₅	C₂×C₉×C₁₁²
Frattini	C₃	C₃×D₅×C₁₁²
Fitting	C₅×C₉×C₁₁²	C₂
socle	C₃×C₅×C₁₁²	C₂×C₃
prime radical	C₃×D₅×C₁₁²	C₃
cosocle	C₃×C₅	C₂×C₃×C₁₁²
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁²	C₂	semidirect
5. D₅×C₁₁²	C₉	direct (N × H)
6. C₉×C₁₁²	D₅	direct (N × H)
7. C₉×D₅×C₁₁	C₁₁	direct (N × H)
9. C₅×C₁₁²	C₂×C₉	semidirect
10. C₅×C₉×C₁₁	C₂×C₁₁	semidirect
16. C₁₁²	C₉×D₅	direct (N × H)
17. D₅×C₁₁	C₉×C₁₁	direct (N × H)
18. C₉×C₁₁	D₅×C₁₁	direct (N × H)
19. C₉×D₅	C₁₁²	direct (N × H)
21. C₅×C₁₁	C₂×C₉×C₁₁	semidirect
22. C₅×C₉	C₂×C₁₁²	semidirect
28. C₁₁	C₉×D₅×C₁₁	direct (N × H)
29. D₅	C₉×C₁₁²	direct (N × H)
30. C₉	D₅×C₁₁²	direct (N × H)
32. C₅	C₂×C₉×C₁₁²	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₁²	2
C₃×D₅×C₁₁²	3
C₂×C₉×C₁₁²	5
C₉×D₅×C₁₁	11

Subgroups — C9×D5×C112 #24926124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₅×C₁₁² #24926124