Subgroups — C₃×#27130990 #49137728

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	#27130990	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14559102	—	5	6	no	maximal
5	C₅²×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×C₁₁⋊D₁₁	D₅	1	6	yes	—
7	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14559102	—	5	6	no	—
9	C₃×C₅×C₁₁²	Dic₅	1	6	yes	complemented
10	C₃×C₅²×D₁₁	—	22	6	no	—
11	C₃×#92150	—	25	1	no	Hall
12	C₅×C₁₁⋊D₁₁	C₃×D₅	1	6	yes	—
13	C₃×C₅²×C₁₁	—	2	6	no	—
14	C₃×C₁₁⋊D₁₁	C₅⋊D₅	1	1	yes	characteristic
15	C₅×C₁₁²	C₃×Dic₅	1	6	yes	complemented
16	C₅²×D₁₁	—	22	6	no	—
17	#92150	—	25	1	no	Hall
18	C₃×C₁₁²	#1039	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×D₁₁	—	22	36	no	—
20	C₃×#1039	—	121	1	no	maximal, Hall
21	C₅²×C₁₁	—	2	6	no	—
22	C₁₁⋊D₁₁	C₃×C₅⋊D₅	1	1	yes	characteristic
23	C₃×C₅×C₁₁	—	2	36	no	—
24	C₂×C₃×C₅²	—	121	1	no	—
25	C₁₁²	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
26	C₅×D₁₁	—	22	36	no	—
27	#1039	—	121	1	no	Hall
28	C₃×C₅²	#92150	1	1	yes	characteristic, complemented, Hall
29	C₃×D₁₁	—	22	6	no	—
30	C₃×Dic₅	—	605	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, complemented, Sylow
36	D₁₁	—	22	6	no	—
37	Dic₅	—	605	6	no	—
38	C₃×C₅	#14559102	1	6	yes	complemented
39	C₃×C₄	—	3025	1	no	Hall
40	C₁₁	—	2	6	no	—
41	C₂×C₅	—	121	6	no	—
42	C₂×C₃	—	121	1	no	—
43	C₅	C₃×#14559102	1	6	yes	complemented
44	C₄	—	3025	1	no	Sylow
45	C₃	#27130990	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#27130990
commutator, hypocenter	C₅²×C₁₁²	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₅²×C₁₁⋊D₁₁	C₂
cosocle	C₅²×C₁₁⋊D₁₁	C₂×C₃
LCS	G ▷ C₅²×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. #27130990	C₃	direct (N × H)
3. C₃×C₅²×C₁₁²	C₄	semidirect
7. C₅²×C₁₁²	C₃×C₄	semidirect
9. C₃×C₅×C₁₁²	Dic₅	semidirect
15. C₅×C₁₁²	C₃×Dic₅	semidirect
18. C₃×C₁₁²	#1039	semidirect
25. C₁₁²	C₃×#1039	semidirect
28. C₃×C₅²	#92150	semidirect
35. C₅²	C₃×#92150	semidirect
38. C₃×C₅	#14559102	semidirect
43. C₅	C₃×#14559102	semidirect
45. C₃	#27130990	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×C₅²×C₁₁⋊D₁₁	2
#27130990	3
C₃×#14559102	5
C₃×#1039	121

Subgroups — C3×#27130990 #49137728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#27130990 #49137728