Subgroups — C₅×C₃⋊(C₃⋊#92150) #36345347

Order 21780.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#92150	—	3	4	no	maximal
3	C₃²×C₅×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#92150)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₁⋊D₁₁	D₃	1	4	yes	—
6	C₅×#92150	—	9	1	no	Hall
7	C₃²×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₁²	Dic₃	1	4	yes	complemented
9	C₃⋊#92150	—	3	4	no	—
10	C₅×C₁₁⋊D₁₁	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₅×D₁₁	—	22	6	no	—
13	C₃×C₁₁⋊D₁₁	C₅×D₃	1	4	yes	—
14	C₅×C₁₁²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₃²×C₅×C₁₁	—	2	6	no	—
16	#92150	—	9	1	no	Hall
17	C₃×C₁₁²	C₅×Dic₃	1	4	yes	complemented
18	C₃×C₅×D₁₁	—	22	24	no	—
19	C₁₁⋊D₁₁	C₅×C₃⋊D₃	1	1	yes	characteristic
20	C₃²×D₁₁	—	22	6	no	—
21	C₅×C₃⋊Dic₃	—	121	1	no	maximal, Hall
22	C₃×C₅×C₁₁	—	2	24	no	—
23	C₁₁²	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
24	C₅×D₁₁	—	22	6	no	—
25	C₃²×C₁₁	—	2	6	no	—
26	C₂×C₃²×C₅	—	121	1	no	—
27	C₃×D₁₁	—	22	24	no	—
28	C₅×Dic₃	—	363	4	no	—
29	C₅×C₁₁	—	2	6	no	—
30	C₃²×C₅	#92150	1	1	yes	characteristic, complemented, Hall
31	C₃⋊Dic₃	—	121	1	no	Hall
32	C₃×C₁₁	—	2	24	no	—
33	C₂×C₃×C₅	—	121	4	no	—
34	D₁₁	—	22	6	no	—
35	C₄×C₅	—	1089	1	no	Hall
36	C₂×C₃²	—	121	1	no	—
37	C₃×C₅	C₃⋊#92150	1	4	yes	complemented
38	Dic₃	—	363	4	no	—
39	C₁₁	—	2	6	no	—
40	C₂×C₅	—	121	1	no	—
41	C₃²	C₅×#92150	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	121	4	no	—
43	C₅	C₃⋊(C₃⋊#92150)	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	1089	1	no	Sylow
45	C₃	C₅×C₃⋊#92150	1	4	yes	complemented
46	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₃⋊#92150)
commutator, hypocenter	C₃²×C₁₁²	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁²	C₄
prime radical	C₃²×C₅×C₁₁⋊D₁₁	C₂
cosocle	C₃²×C₁₁⋊D₁₁	C₂×C₅
LCS	G ▷ C₃²×C₁₁²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅×C₁₁²	C₄	semidirect
4. C₃⋊(C₃⋊#92150)	C₅	direct (N × H)
8. C₃×C₅×C₁₁²	Dic₃	semidirect
11. C₃²×C₁₁²	C₄×C₅	semidirect
14. C₅×C₁₁²	C₃⋊Dic₃	semidirect
17. C₃×C₁₁²	C₅×Dic₃	semidirect
23. C₁₁²	C₅×C₃⋊Dic₃	semidirect
30. C₃²×C₅	#92150	semidirect
37. C₃×C₅	C₃⋊#92150	semidirect
41. C₃²	C₅×#92150	semidirect
43. C₅	C₃⋊(C₃⋊#92150)	direct (N × H)
45. C₃	C₅×C₃⋊#92150	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₁⋊D₁₁	2
C₅×C₃⋊#92150	3
C₃⋊(C₃⋊#92150)	5
C₅×C₃⋊Dic₃	121

Subgroups — C5×C3⋊(C3⋊#92150) #36345347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(C₃⋊#92150) #36345347