Subgroups — C₅²×C₃⋊#92150 #49137741

Order 36300.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×#92150	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊#92150	C₅	1	6	yes	maximal, direct product factor
5	C₅²×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic
6	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	1	6	yes	—
7	C₅²×C₁₁²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×#92150	—	3	6	no	—
9	C₃×C₅×C₁₁²	C₄×C₅	1	6	yes	complemented
10	C₃×C₅²×D₁₁	—	22	6	no	—
11	C₃⋊#92150	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₁₁⋊D₁₁	C₅×D₃	1	6	yes	—
13	C₃×C₅²×C₁₁	—	2	6	no	—
14	C₃×C₁₁⋊D₁₁	C₂×C₅²	1	1	yes	characteristic
15	C₅×C₁₁²	C₅×Dic₃	1	6	yes	complemented
16	C₅²×D₁₁	—	22	6	no	—
17	#92150	—	3	1	no	Hall
18	C₃×C₁₁²	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×D₁₁	—	22	36	no	—
20	C₅²×Dic₃	—	121	1	no	maximal, Hall
21	C₅²×C₁₁	—	2	6	no	—
22	C₁₁⋊D₁₁	C₅²×D₃	1	1	yes	characteristic
23	C₃×C₅×C₁₁	—	2	36	no	—
24	C₂×C₃×C₅²	—	121	1	no	—
25	C₁₁²	C₅²×Dic₃	1	1	yes	characteristic, complemented, Sylow
26	C₅×D₁₁	—	22	36	no	—
27	C₄×C₅²	—	363	1	no	Hall
28	C₃×C₅²	#92150	1	1	yes	characteristic, complemented, Hall
29	C₃×D₁₁	—	22	6	no	—
30	C₅×Dic₃	—	121	6	no	—
31	C₅×C₁₁	—	2	36	no	—
32	C₂×C₅²	—	121	1	no	—
33	C₃×C₁₁	—	2	6	no	—
34	C₂×C₃×C₅	—	121	6	no	—
35	C₅²	C₃⋊#92150	1	1	yes	characteristic, direct product factor, Sylow
36	D₁₁	—	22	6	no	—
37	C₄×C₅	—	363	6	no	—
38	C₃×C₅	C₅×#92150	1	6	yes	complemented
39	Dic₃	—	121	1	no	Hall
40	C₁₁	—	2	6	no	—
41	C₂×C₅	—	121	6	no	—
42	C₂×C₃	—	121	1	no	—
43	C₅	C₅×C₃⋊#92150	1	6	yes	direct product factor
44	C₄	—	363	1	no	Sylow
45	C₃	C₅²×#92150	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	C₃⋊#92150
commutator, hypocenter	C₃×C₁₁²	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₅²×C₁₁⋊D₁₁	C₂
cosocle	C₃×C₁₁⋊D₁₁	C₂×C₅²
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₁²	C₄	semidirect
4. C₅×C₃⋊#92150	C₅	direct (N × H)
7. C₅²×C₁₁²	Dic₃	semidirect
9. C₃×C₅×C₁₁²	C₄×C₅	semidirect
11. C₃⋊#92150	C₅²	direct (N × H)
15. C₅×C₁₁²	C₅×Dic₃	semidirect
18. C₃×C₁₁²	C₄×C₅²	semidirect
25. C₁₁²	C₅²×Dic₃	semidirect
28. C₃×C₅²	#92150	semidirect
35. C₅²	C₃⋊#92150	direct (N × H)
38. C₃×C₅	C₅×#92150	semidirect
43. C₅	C₅×C₃⋊#92150	direct (N × H)
45. C₃	C₅²×#92150	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁⋊D₁₁	2
C₅²×#92150	3
C₅×C₃⋊#92150	5
C₅²×Dic₃	121

Subgroups — C52×C3⋊#92150 #49137741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊#92150 #49137741