Subgroups — C₃×#27130981 #49137737

Order 36300.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊(C₅⋊(C₁₁⋊D₁₁))	C₂	1	1	yes	maximal, characteristic
2	#27130981	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14559097	—	5	2	no	maximal
5	C₅⋊(C₅⋊(C₁₁⋊D₁₁))	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅⋊(C₁₁⋊D₁₁)	—	5	2	no	—
7	C₃×C₅⋊(C₁₁⋊D₁₁)	—	10	2	no	—
8	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	#14559097	—	5	2	no	—
10	C₃×C₅×C₁₁²	—	2	2	no	—
11	C₃×C₅×C₁₁²	AGL(1,𝔽₅)	1	2	yes	complemented
12	C₃×C₅⋊D₅₅	—	22	6	no	—
13	C₃×#92150	—	25	1	no	Hall
14	C₅⋊(C₁₁⋊D₁₁)	—	5	2	no	—
15	C₅⋊(C₁₁⋊D₁₁)	—	10	2	no	—
16	C₃×C₅²×C₁₁	—	2	6	no	—
17	C₃×C₁₁⋊D₁₁	—	25	1	no	—
18	C₅×C₁₁²	—	2	2	no	—
19	C₅×C₁₁²	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
20	C₅⋊D₅₅	—	22	6	no	—
21	#92150	—	25	1	no	Hall
22	C₃×C₁₁²	#1044	1	1	yes	characteristic, complemented, Hall
23	C₃×D₅₅	—	110	12	no	—
24	C₃×D₅₅	—	110	24	no	—
25	C₃×#1044	—	121	1	no	maximal, Hall
26	C₅²×C₁₁	—	2	6	no	—
27	C₁₁⋊D₁₁	—	25	1	no	—
28	C₃×C₅×C₁₁	—	2	24	no	—
29	C₃×C₅×C₁₁	—	2	12	no	—
30	C₃×C₅⋊D₅	—	121	1	no	—
31	C₁₁²	C₃×#1044	1	1	yes	characteristic, complemented, Sylow
32	D₅₅	—	110	12	no	—
33	D₅₅	—	110	24	no	—
34	#1044	—	121	1	no	Hall
35	C₃×C₅²	#92150	1	1	yes	characteristic, complemented, Hall
36	C₃×D₁₁	—	550	6	no	—
37	C₃×AGL(1,𝔽₅)	—	605	2	no	—
38	C₅×C₁₁	—	2	24	no	—
39	C₅×C₁₁	—	2	12	no	—
40	C₅⋊D₅	—	121	1	no	—
41	C₃×C₁₁	—	2	6	no	—
42	C₃×D₅	—	605	2	no	—
43	C₃×D₅	—	1210	2	no	—
44	C₅²	C₃×#92150	1	1	yes	characteristic, complemented, Sylow
45	D₁₁	—	550	6	no	—
46	AGL(1,𝔽₅)	—	605	2	no	—
47	C₃×C₅	—	2	2	no	—
48	C₃×C₅	#14559097	1	2	yes	complemented
49	C₃×C₄	—	3025	1	no	Hall
50	C₁₁	—	2	6	no	—
51	D₅	—	605	2	no	—
52	D₅	—	1210	2	no	—
53	C₂×C₃	—	3025	1	no	—
54	C₅	—	2	2	no	—
55	C₅	C₃×#14559097	1	2	yes	complemented
56	C₄	—	3025	1	no	Sylow
57	C₃	#27130981	1	1	yes	characteristic, direct product factor, Sylow
58	C₂	—	3025	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#27130981
commutator, hypocenter	C₅²×C₁₁²	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₅⋊(C₅⋊(C₁₁⋊D₁₁))	C₂
cosocle	C₅⋊(C₅⋊(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. #27130981	C₃	direct (N × H)
3. C₃×C₅²×C₁₁²	C₄	semidirect
8. C₅²×C₁₁²	C₃×C₄	semidirect
11. C₃×C₅×C₁₁²	AGL(1,𝔽₅)	semidirect
19. C₅×C₁₁²	C₃×AGL(1,𝔽₅)	semidirect
22. C₃×C₁₁²	#1044	semidirect
31. C₁₁²	C₃×#1044	semidirect
35. C₃×C₅²	#92150	semidirect
44. C₅²	C₃×#92150	semidirect
48. C₃×C₅	#14559097	semidirect
55. C₅	C₃×#14559097	semidirect
57. C₃	#27130981	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⋊(C₅⋊(C₁₁⋊D₁₁))	2
#27130981	3
C₃×#14559097	5
C₃×#1044	121

Subgroups — C3×#27130981 #49137737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#27130981 #49137737