Subgroups — C₃⋊(C₃⋊#16861522) #49147199

Order 36900.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅⋊D₂₀₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16861522	—	3	4	no	maximal
3	C₃²×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#11717962)	—	5	1	no	maximal
5	C₃⋊(C₃⋊#11717961)	—	5	1	no	maximal
6	C₃×C₅⋊D₂₀₅	D₃	1	4	yes	—
7	#16861522	—	9	1	no	Hall
8	C₃²×D₂₀₅	—	5	1	no	—
9	C₃²×D₂₀₅	—	5	1	no	—
10	C₃²×D₂₀₅	—	10	2	no	—
11	C₃×C₅²×C₄₁	Dic₃	1	4	yes	complemented
12	C₃⋊#11717962	—	15	4	no	—
13	C₃⋊#11717961	—	15	4	no	—
14	C₅⋊D₂₀₅	C₃⋊D₃	1	1	yes	characteristic
15	C₃²×C₅×C₄₁	—	2	2	no	—
16	C₃²×C₅×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₃⋊(C₃⋊#4223)	—	25	1	no	Hall
19	C₃×D₂₀₅	—	5	4	no	—
20	C₃×D₂₀₅	—	5	4	no	—
21	C₃×D₂₀₅	—	10	8	no	—
22	C₅²×C₄₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₃⋊(C₃⋊#1044)	—	41	1	no	maximal, Hall
24	#11717962	—	45	1	no	—
25	#11717961	—	45	1	no	—
26	C₃²×D₄₁	—	25	1	no	—
27	C₃×C₅×C₄₁	—	2	8	no	—
28	C₃×C₅×C₄₁	ΓL(1,𝔽₁₆)	1	4	yes	complemented
29	C₃×C₅×C₄₁	ΓL(1,𝔽₁₆)	1	4	yes	complemented
30	C₃⋊#4223	—	75	4	no	—
31	C₃²×C₅⋊D₅	—	41	1	no	—
32	D₂₀₅	—	5	1	no	—
33	D₂₀₅	—	5	1	no	—
34	D₂₀₅	—	10	2	no	—
35	C₃²×C₄₁	#1044	1	1	yes	characteristic, complemented, Hall
36	C₃⋊#1044	—	123	4	no	—
37	C₃×D₄₁	—	25	4	no	—
38	C₃²×C₅²	#4223	1	1	yes	characteristic, complemented, Hall
39	C₅×C₄₁	—	2	2	no	—
40	C₅×C₄₁	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
41	C₅×C₄₁	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
42	C₃⋊ΓL(1,𝔽₁₆)	—	205	1	no	—
43	C₃⋊ΓL(1,𝔽₁₆)	—	205	1	no	—
44	#4223	—	225	1	no	Hall
45	C₃×C₅⋊D₅	—	41	4	no	—
46	C₃×C₄₁	C₃⋊#1044	1	4	yes	complemented
47	#1044	—	369	1	no	Hall
48	C₃²×D₅	—	410	2	no	—
49	C₃²×D₅	—	205	1	no	—
50	C₃²×D₅	—	205	1	no	—
51	D₄₁	—	25	1	no	—
52	C₃×C₅²	C₃⋊#4223	1	4	yes	complemented
53	ΓL(1,𝔽₁₆)	—	615	4	no	—
54	ΓL(1,𝔽₁₆)	—	615	4	no	—
55	C₅⋊D₅	—	41	1	no	—
56	C₃²×C₅	—	2	2	no	—
57	C₃²×C₅	#11717961	1	1	yes	characteristic, complemented
58	C₃²×C₅	#11717962	1	1	yes	characteristic, complemented
59	C₄₁	C₃⋊(C₃⋊#1044)	1	1	yes	characteristic, complemented, Sylow
60	C₃⋊Dic₃	—	1025	1	no	Hall
61	C₃×D₅	—	410	8	no	—
62	C₃×D₅	—	205	4	no	—
63	C₃×D₅	—	205	4	no	—
64	C₅²	C₃⋊(C₃⋊#4223)	1	1	yes	characteristic, complemented, Sylow
65	AGL(1,𝔽₅)	—	1845	1	no	—
66	AGL(1,𝔽₅)	—	1845	1	no	—
67	C₂×C₃²	—	1025	1	no	—
68	C₃×C₅	—	2	8	no	—
69	C₃×C₅	C₃⋊#11717961	1	4	yes	complemented
70	C₃×C₅	C₃⋊#11717962	1	4	yes	complemented
71	Dic₃	—	3075	4	no	—
72	D₅	—	410	2	no	—
73	D₅	—	205	1	no	—
74	D₅	—	205	1	no	—
75	C₃²	#16861522	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	1025	4	no	—
77	C₅	—	2	2	no	—
78	C₅	C₃⋊(C₃⋊#11717961)	1	1	yes	characteristic, complemented
79	C₅	C₃⋊(C₃⋊#11717962)	1	1	yes	characteristic, complemented
80	C₄	—	9225	1	no	Sylow
81	C₃	C₃⋊#16861522	1	4	yes	complemented
82	C₂	—	1025	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₄₁	C₄
prime radical, cosocle	C₃²×C₅⋊D₂₀₅	C₂
LCS	G ▷ C₃²×C₅²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₄₁	C₄	semidirect
11. C₃×C₅²×C₄₁	Dic₃	semidirect
16. C₃²×C₅×C₄₁	AGL(1,𝔽₅)	semidirect
17. C₃²×C₅×C₄₁	AGL(1,𝔽₅)	semidirect
22. C₅²×C₄₁	C₃⋊Dic₃	semidirect
28. C₃×C₅×C₄₁	ΓL(1,𝔽₁₆)	semidirect
29. C₃×C₅×C₄₁	ΓL(1,𝔽₁₆)	semidirect
35. C₃²×C₄₁	#1044	semidirect
38. C₃²×C₅²	#4223	semidirect
40. C₅×C₄₁	C₃⋊ΓL(1,𝔽₁₆)	semidirect
41. C₅×C₄₁	C₃⋊ΓL(1,𝔽₁₆)	semidirect
46. C₃×C₄₁	C₃⋊#1044	semidirect
52. C₃×C₅²	C₃⋊#4223	semidirect
57. C₃²×C₅	#11717961	semidirect
58. C₃²×C₅	#11717962	semidirect
59. C₄₁	C₃⋊(C₃⋊#1044)	semidirect
64. C₅²	C₃⋊(C₃⋊#4223)	semidirect
69. C₃×C₅	C₃⋊#11717961	semidirect
70. C₃×C₅	C₃⋊#11717962	semidirect
75. C₃²	#16861522	semidirect
78. C₅	C₃⋊(C₃⋊#11717961)	semidirect
79. C₅	C₃⋊(C₃⋊#11717962)	semidirect
81. C₃	C₃⋊#16861522	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅⋊D₂₀₅	2
C₃⋊#16861522	3
C₃⋊(C₃⋊#11717962)	5
C₃⋊(C₃⋊#11717961)	5
C₃⋊(C₃⋊#1044)	41

Subgroups — C3⋊(C3⋊#16861522) #49147199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#16861522) #49147199