Subgroups — D₁₅×C₁₁²⋊C₃ #24926191

Order 10890.

68 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, complemented, Hall
2	C₁₁²×D₁₅	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×C₁₁²⋊C₃	—	3	1	no	maximal
4	D₃×C₁₁²⋊C₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₁₁²⋊C₃	—	2	1	no	—
7	C₅×C₁₁²⋊C₃	D₃	1	1	yes	characteristic, complemented
8	D₅×C₁₁²	—	3	1	no	Hall
9	C₃×C₁₁²⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₁²	—	5	1	no	—
11	C₂×C₁₁²⋊C₃	—	15	1	no	—
12	C₅×C₁₁²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁²	C₃×D₅	1	1	yes	characteristic, complemented
14	C₁₁²⋊C₃	—	2	1	no	—
15	C₁₁²⋊C₃	D₁₅	1	1	yes	characteristic, direct product factor
16	C₁₁×D₁₅	—	3	4	no	—
17	C₂×C₁₁²	—	15	1	no	Hall
18	C₃×C₅×C₁₁	—	3	4	no	—
19	C₁₁²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
20	D₅×C₁₁	—	9	4	no	—
21	C₃×D₁₅	—	121	1	no	maximal, Hall
22	D₃×C₁₁	—	15	4	no	—
23	C₅×C₁₁	—	3	4	no	—
24	C₃²×C₅	—	121	1	no	Hall
25	C₃×C₁₁	—	3	4	no	—
26	D₁₅	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃×D₅	—	363	1	no	—
28	C₂×C₁₁	—	45	4	no	—
29	C₃×D₃	—	605	1	no	Hall
30	C₃×C₅	—	121	1	no	—
31	C₃×C₅	—	242	1	no	—
32	C₃×C₅	C₂×C₁₁²⋊C₃	1	1	yes	characteristic, complemented
33	C₁₁	—	3	4	no	—
34	D₅	—	3	1	no	Hall
35	C₃²	—	121	1	no	Sylow
36	C₂×C₃	—	1815	1	no	—
37	D₃	—	5	1	no	—
38	C₅	D₃×C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
39	C₃	—	121	1	no	—
40	C₃	—	242	1	no	—
41	C₃	D₅×C₁₁²⋊C₃	1	1	yes	characteristic, complemented
42	C₂	—	15	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁²⋊C₃	C₂	semidirect
2. C₁₁²×D₁₅	C₃	semidirect
5. C₃×C₅×C₁₁²	C₂×C₃	semidirect
7. C₅×C₁₁²⋊C₃	D₃	semidirect
9. C₃×C₁₁²⋊C₃	D₅	semidirect
12. C₅×C₁₁²	C₃×D₃	semidirect
13. C₃×C₁₁²	C₃×D₅	semidirect
15. C₁₁²⋊C₃	D₁₅	direct (N × H)
19. C₁₁²	C₃×D₁₅	semidirect
26. D₁₅	C₁₁²⋊C₃	direct (N × H)
32. C₃×C₅	C₂×C₁₁²⋊C₃	semidirect
38. C₅	D₃×C₁₁²⋊C₃	semidirect
41. C₃	D₅×C₁₁²⋊C₃	semidirect

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
C₁₁²×D₁₅	3
D₅×C₁₁²⋊C₃	3
D₃×C₁₁²⋊C₃	5
C₃×D₁₅	121

Subgroups — D15×C112⋊C3 #24926191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×C₁₁²⋊C₃ #24926191