Subgroups — C₃⋊(C₃⋊#13049932) #26043794

Order 11700.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13049932	—	3	4	no	maximal
3	C₃²×C₅²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#63120)	—	5	2	no	maximal
5	C₃×C₁₃×C₅⋊D₅	D₃	1	4	yes	—
6	#13049932	—	9	1	no	Hall
7	C₃²×D₅×C₁₃	—	5	2	no	—
8	C₃²×D₅×C₁₃	—	10	2	no	—
9	C₃×C₅²×C₁₃	Dic₃	1	4	yes	complemented
10	C₃⋊(C₃⋊#1044)	—	13	1	no	maximal, Hall
11	C₃⋊#63120	—	15	8	no	—
12	C₁₃×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
13	C₃²×C₅×C₁₃	—	2	2	no	—
14	C₃²×C₅×C₁₃	AGL(1,𝔽₅)	1	2	yes	complemented
15	C₃⋊Dic₃₉	—	25	1	no	Hall
16	C₃²×C₅⋊D₅	D₁₃	1	1	yes	characteristic
17	C₃×D₅×C₁₃	—	5	8	no	—
18	C₃×D₅×C₁₃	—	10	8	no	—
19	C₅²×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₃⋊#1044	—	39	4	no	—
21	#63120	—	45	2	no	—
22	C₂×C₃²×C₁₃	—	25	1	no	—
23	C₃²×C₅²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₃	—	2	8	no	—
25	C₃×C₅×C₁₃	ΓL(1,𝔽₁₆)	1	8	yes	complemented
26	C₃⋊ΓL(1,𝔽₁₆)	—	65	2	no	—
27	Dic₃₉	—	75	4	no	—
28	C₃×C₅⋊D₅	D₃₉	1	4	yes	—
29	D₅×C₁₃	—	5	2	no	—
30	D₅×C₁₃	—	10	2	no	—
31	C₃²×C₁₃	#1044	1	1	yes	characteristic, complemented, Hall
32	#1044	—	117	1	no	Hall
33	C₃²×D₅	—	5	2	no	—
34	C₃²×D₅	—	10	2	no	—
35	C₂×C₃×C₁₃	—	25	4	no	—
36	C₃×C₅²	Dic₃₉	1	4	yes	complemented
37	C₅×C₁₃	—	2	2	no	—
38	C₅×C₁₃	C₃⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
39	ΓL(1,𝔽₁₆)	—	195	8	no	—
40	Dic₁₃	—	225	1	no	Hall
41	C₅⋊D₅	C₃⋊D₃₉	1	1	yes	characteristic
42	C₃²×C₅	—	2	2	no	—
43	C₃²×C₅	#63120	1	2	yes	complemented
44	C₃×C₁₃	C₃⋊#1044	1	4	yes	complemented
45	C₃⋊Dic₃	—	325	1	no	Hall
46	C₃×D₅	—	5	8	no	—
47	C₃×D₅	—	10	8	no	—
48	C₂×C₁₃	—	25	1	no	—
49	C₅²	C₃⋊Dic₃₉	1	1	yes	characteristic, complemented, Sylow
50	AGL(1,𝔽₅)	—	585	2	no	—
51	C₂×C₃²	—	25	1	no	—
52	C₃×C₅	—	2	8	no	—
53	C₃×C₅	C₃⋊#63120	1	8	yes	complemented
54	C₁₃	C₃⋊(C₃⋊#1044)	1	1	yes	characteristic, complemented, Sylow
55	Dic₃	—	975	4	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₃²	#13049932	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	25	4	no	—
60	C₅	—	2	2	no	—
61	C₅	C₃⋊(C₃⋊#63120)	1	2	yes	complemented
62	C₄	—	2925	1	no	Sylow
63	C₃	C₃⋊#13049932	1	4	yes	complemented
64	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₃	C₄
prime radical, cosocle	C₃²×C₁₃×C₅⋊D₅	C₂
LCS	G ▷ C₃²×C₅²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₃	C₄	semidirect
9. C₃×C₅²×C₁₃	Dic₃	semidirect
14. C₃²×C₅×C₁₃	AGL(1,𝔽₅)	semidirect
19. C₅²×C₁₃	C₃⋊Dic₃	semidirect
23. C₃²×C₅²	Dic₁₃	semidirect
25. C₃×C₅×C₁₃	ΓL(1,𝔽₁₆)	semidirect
31. C₃²×C₁₃	#1044	semidirect
36. C₃×C₅²	Dic₃₉	semidirect
38. C₅×C₁₃	C₃⋊ΓL(1,𝔽₁₆)	semidirect
43. C₃²×C₅	#63120	semidirect
44. C₃×C₁₃	C₃⋊#1044	semidirect
49. C₅²	C₃⋊Dic₃₉	semidirect
53. C₃×C₅	C₃⋊#63120	semidirect
54. C₁₃	C₃⋊(C₃⋊#1044)	semidirect
58. C₃²	#13049932	semidirect
61. C₅	C₃⋊(C₃⋊#63120)	semidirect
63. C₃	C₃⋊#13049932	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₅⋊D₅	2
C₃⋊#13049932	3
C₃⋊(C₃⋊#63120)	5
C₃⋊(C₃⋊#1044)	13

Subgroups — C3⋊(C3⋊#13049932) #26043794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#13049932) #26043794