Subgroups — C₂×C₃×C₅×C₁₁²⋊C₃ #24926196

Order 10890.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₁²⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₅×C₁₁²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₁₁²⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₁₁²⋊C₃	C₂×C₃	1	3	yes	direct product factor
7	C₂×C₅×C₁₁²	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁²⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₁₁²	C₃×C₅	1	1	yes	characteristic, complemented
10	C₂×C₁₁²⋊C₃	C₃×C₅	1	3	yes	direct product factor
11	C₅×C₁₁²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
13	C₁₁²⋊C₃	C₂×C₃×C₅	1	3	yes	direct product factor
14	C₂×C₃×C₅×C₁₁	—	3	4	no	—
15	C₂×C₁₁²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×C₁₁	—	3	4	no	—
17	C₁₁²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×C₁₁	—	3	4	no	—
19	C₂×C₃²×C₅	—	121	1	no	maximal, Hall
20	C₂×C₃×C₁₁	—	3	4	no	—
21	C₅×C₁₁	—	3	4	no	—
22	C₃²×C₅	—	121	1	no	Hall
23	C₃×C₁₁	—	3	4	no	—
24	C₂×C₃×C₅	—	121	3	no	—
25	C₂×C₃×C₅	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor
26	C₂×C₁₁	—	3	4	no	—
27	C₂×C₃²	—	121	1	no	Hall
28	C₃×C₅	—	121	3	no	—
29	C₃×C₅	C₂×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor
30	C₁₁	—	3	4	no	—
31	C₂×C₅	C₃×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃²	—	121	1	no	Sylow
33	C₂×C₃	—	121	3	no	—
34	C₂×C₃	C₅×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor
35	C₅	C₂×C₃×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₃	—	121	3	no	—
37	C₃	C₂×C₅×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂	C₃×C₅×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	C₁₁²⋊C₃
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁²	C₃
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. C₃×C₅×C₁₁²⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₁₁²⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₅×C₁₁²	C₃	semidirect
4. C₂×C₃×C₁₁²⋊C₃	C₅	direct (N × H)
5. C₃×C₅×C₁₁²	C₂×C₃	semidirect
6. C₅×C₁₁²⋊C₃	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₁²	C₃²	semidirect
8. C₃×C₁₁²⋊C₃	C₂×C₅	direct (N × H)
9. C₂×C₃×C₁₁²	C₃×C₅	semidirect
10. C₂×C₁₁²⋊C₃	C₃×C₅	direct (N × H)
11. C₅×C₁₁²	C₂×C₃²	semidirect
12. C₃×C₁₁²	C₂×C₃×C₅	semidirect
13. C₁₁²⋊C₃	C₂×C₃×C₅	direct (N × H)
15. C₂×C₁₁²	C₃²×C₅	semidirect
17. C₁₁²	C₂×C₃²×C₅	semidirect
25. C₂×C₃×C₅	C₁₁²⋊C₃	direct (N × H)
29. C₃×C₅	C₂×C₁₁²⋊C₃	direct (N × H)
31. C₂×C₅	C₃×C₁₁²⋊C₃	direct (N × H)
34. C₂×C₃	C₅×C₁₁²⋊C₃	direct (N × H)
35. C₅	C₂×C₃×C₁₁²⋊C₃	direct (N × H)
37. C₃	C₂×C₅×C₁₁²⋊C₃	direct (N × H)
38. C₂	C₃×C₅×C₁₁²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁²⋊C₃	2
C₂×C₅×C₁₁²⋊C₃	3
C₂×C₃×C₅×C₁₁²	3
C₂×C₃×C₁₁²⋊C₃	5
C₂×C₃²×C₅	121

Subgroups — C2×C3×C5×C112⋊C3 #24926196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₁²⋊C₃ #24926196