Subgroups — C₂×C₉×#10597245 #24926119

Order 10890.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#10597245	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×#10597245	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#10597245	C₂×C₃	1	1	yes	characteristic
5	C₂×#10597245	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₉×C₁₁⋊C₅	—	11	2	no	maximal
8	C₂×C₃×C₁₁²	C₃×C₅	1	1	yes	characteristic
9	#10597245	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₉×C₁₁⋊C₅	—	11	2	no	—
11	C₃×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₃×C₁₁⋊C₅	—	11	2	no	—
13	C₂×C₁₁²	C₅×C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₁₁	—	5	2	no	—
15	C₂×C₉×C₁₁	C₁₁⋊C₅	1	2	yes	complemented
16	C₃×C₁₁⋊C₅	—	11	2	no	—
17	C₁₁²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁⋊C₅	—	11	2	no	—
19	C₉×C₁₁	—	5	2	no	—
20	C₉×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	complemented
21	C₂×C₅×C₉	—	121	1	no	Hall
22	C₂×C₃×C₁₁	—	5	2	no	—
23	C₂×C₃×C₁₁	C₃×C₁₁⋊C₅	1	2	yes	—
24	C₁₁⋊C₅	—	11	2	no	—
25	C₅×C₉	—	121	1	no	Hall
26	C₃×C₁₁	—	5	2	no	—
27	C₃×C₁₁	C₂×C₃×C₁₁⋊C₅	1	2	yes	—
28	C₂×C₃×C₅	—	121	1	no	—
29	C₂×C₁₁	—	5	2	no	—
30	C₂×C₁₁	C₉×C₁₁⋊C₅	1	2	yes	complemented
31	C₂×C₉	#10597245	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₅	—	121	1	no	—
33	C₁₁	—	5	2	no	—
34	C₁₁	C₂×C₉×C₁₁⋊C₅	1	2	yes	complemented
35	C₂×C₅	—	121	1	no	Hall
36	C₉	C₂×#10597245	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃	C₃×#10597245	1	1	yes	characteristic
38	C₅	—	121	1	no	Sylow
39	C₃	C₂×C₃×#10597245	1	1	yes	characteristic
40	C₂	C₉×#10597245	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₉	#10597245
commutator, hypocenter	C₁₁²	C₂×C₅×C₉
Frattini	C₃	C₂×C₃×#10597245
Fitting	C₂×C₉×C₁₁²	C₅
socle	C₂×C₃×C₁₁²	C₃×C₅
prime radical	C₂×C₃×#10597245	C₃
cosocle	C₃×C₁₁²	C₂×C₃×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×#10597245	C₂	direct (N × H)
3. C₂×C₉×C₁₁²	C₅	semidirect
5. C₂×#10597245	C₉	direct (N × H)
6. C₉×C₁₁²	C₂×C₅	semidirect
9. #10597245	C₂×C₉	direct (N × H)
13. C₂×C₁₁²	C₅×C₉	semidirect
15. C₂×C₉×C₁₁	C₁₁⋊C₅	semidirect
17. C₁₁²	C₂×C₅×C₉	semidirect
20. C₉×C₁₁	C₂×C₁₁⋊C₅	semidirect
30. C₂×C₁₁	C₉×C₁₁⋊C₅	semidirect
31. C₂×C₉	#10597245	direct (N × H)
34. C₁₁	C₂×C₉×C₁₁⋊C₅	semidirect
36. C₉	C₂×#10597245	direct (N × H)
40. C₂	C₉×#10597245	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#10597245	2
C₂×C₃×#10597245	3
C₂×C₉×C₁₁²	5
C₂×C₉×C₁₁⋊C₅	11

Subgroups — C2×C9×#10597245 #24926119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#10597245 #24926119