Subgroups — C₃⋊(C₃⋊#13049937) #26043799

Order 11700.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13049937	—	3	4	no	maximal
3	C₃²×C₅²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#63118)	—	5	6	no	maximal
5	C₃×C₅²×D₁₃	D₃	1	4	yes	—
6	#13049937	—	9	1	no	Hall
7	C₃²×C₅×D₁₃	D₅	1	6	yes	—
8	C₃×C₅²×C₁₃	Dic₃	1	4	yes	complemented
9	C₃⋊(C₃⋊#1039)	—	13	1	no	maximal, Hall
10	C₃⋊#63118	—	15	24	no	—
11	C₅²×D₁₃	C₃⋊D₃	1	1	yes	characteristic
12	C₃²×C₅×C₁₃	Dic₅	1	6	yes	complemented
13	C₃⋊(C₃⋊#261)	—	25	1	no	Hall
14	C₂×C₃²×C₅²	—	13	1	no	—
15	C₃×C₅×D₁₃	D₁₅	1	24	yes	—
16	C₅²×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃⋊#1039	—	39	4	no	—
18	#63118	—	45	6	no	—
19	C₃²×D₁₃	C₅⋊D₅	1	1	yes	characteristic
20	C₃²×C₅²	#261	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	Dic₁₅	1	24	yes	complemented
22	C₃⋊Dic₁₅	—	65	6	no	—
23	C₃⋊#261	—	75	4	no	—
24	C₂×C₃×C₅²	—	13	4	no	—
25	C₅×D₁₃	C₃⋊D₁₅	1	6	yes	—
26	C₃²×C₁₃	#1039	1	1	yes	characteristic, complemented, Hall
27	#1039	—	117	1	no	Hall
28	C₂×C₃²×C₅	—	13	6	no	—
29	C₃×D₁₃	C₃⋊(C₅⋊D₅)	1	4	yes	—
30	C₃×C₅²	C₃⋊#261	1	4	yes	complemented
31	C₅×C₁₃	C₃⋊Dic₁₅	1	6	yes	complemented
32	Dic₁₅	—	195	24	no	—
33	#261	—	225	1	no	Hall
34	C₂×C₅²	—	13	1	no	—
35	C₃²×C₅	#63118	1	6	yes	complemented
36	C₃×C₁₃	C₃⋊#1039	1	4	yes	complemented
37	C₃⋊Dic₃	—	325	1	no	Hall
38	C₂×C₃×C₅	—	13	24	no	—
39	D₁₃	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic
40	C₅²	C₃⋊(C₃⋊#261)	1	1	yes	characteristic, complemented, Sylow
41	Dic₅	—	585	6	no	—
42	C₂×C₃²	—	13	1	no	—
43	C₃×C₅	C₃⋊#63118	1	24	yes	complemented
44	C₁₃	C₃⋊(C₃⋊#1039)	1	1	yes	characteristic, complemented, Sylow
45	Dic₃	—	975	4	no	—
46	C₂×C₅	—	13	6	no	—
47	C₃²	#13049937	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	13	4	no	—
49	C₅	C₃⋊(C₃⋊#63118)	1	6	yes	complemented
50	C₄	—	2925	1	no	Sylow
51	C₃	C₃⋊#13049937	1	4	yes	complemented
52	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₃	C₄
prime radical, cosocle	C₃²×C₅²×D₁₃	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
8. C₃×C₅²×C₁₃	Dic₃	semidirect
12. C₃²×C₅×C₁₃	Dic₅	semidirect
16. C₅²×C₁₃	C₃⋊Dic₃	semidirect
20. C₃²×C₅²	#261	semidirect
21. C₃×C₅×C₁₃	Dic₁₅	semidirect
26. C₃²×C₁₃	#1039	semidirect
30. C₃×C₅²	C₃⋊#261	semidirect
31. C₅×C₁₃	C₃⋊Dic₁₅	semidirect
35. C₃²×C₅	#63118	semidirect
36. C₃×C₁₃	C₃⋊#1039	semidirect
40. C₅²	C₃⋊(C₃⋊#261)	semidirect
43. C₃×C₅	C₃⋊#63118	semidirect
44. C₁₃	C₃⋊(C₃⋊#1039)	semidirect
47. C₃²	#13049937	semidirect
49. C₅	C₃⋊(C₃⋊#63118)	semidirect
51. C₃	C₃⋊#13049937	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×D₁₃	2
C₃⋊#13049937	3
C₃⋊(C₃⋊#63118)	5
C₃⋊(C₃⋊#1039)	13

Subgroups — C3⋊(C3⋊#13049937) #26043799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#13049937) #26043799