Subgroups — C₃⋊(C₃⋊#13049918) #26043538

Order 11700.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13049918	—	3	4	no	maximal
3	C₃²×C₅²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₁₉₅	—	5	6	no	maximal
5	C₂×C₃×C₅²×C₁₃	D₃	1	4	yes	—
6	#13049918	—	9	1	no	Hall
7	C₂×C₃²×C₅×C₁₃	D₅	1	6	yes	—
8	C₃×C₅²×C₁₃	Dic₃	1	4	yes	complemented
9	C₃⋊(C₃⋊#1039)	—	13	1	no	maximal, Hall
10	Dic₁₉₅	—	15	24	no	—
11	C₂×C₅²×C₁₃	C₃⋊D₃	1	1	yes	characteristic
12	C₃²×C₅×C₁₃	Dic₅	1	6	yes	complemented
13	C₃⋊Dic₃₉	—	25	1	no	Hall
14	C₂×C₃²×C₅²	D₁₃	1	1	yes	characteristic
15	C₂×C₃×C₅×C₁₃	D₁₅	1	24	yes	—
16	C₅²×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃⋊#1039	—	39	4	no	—
18	Dic₆₅	—	45	6	no	—
19	C₂×C₃²×C₁₃	C₅⋊D₅	1	1	yes	characteristic
20	C₃²×C₅²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	Dic₁₅	1	24	yes	complemented
22	C₃⋊Dic₁₅	—	65	6	no	—
23	Dic₃₉	—	75	4	no	—
24	C₂×C₃×C₅²	D₃₉	1	4	yes	—
25	C₂×C₅×C₁₃	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	D₆₅	1	6	yes	—
29	C₂×C₃×C₁₃	C₃⋊(C₅⋊D₅)	1	4	yes	—
30	C₃×C₅²	Dic₃₉	1	4	yes	complemented
31	C₅×C₁₃	C₃⋊Dic₁₅	1	6	yes	complemented
32	Dic₁₅	—	195	24	no	—
33	Dic₁₃	—	225	1	no	Hall
34	C₂×C₅²	C₃⋊D₃₉	1	1	yes	characteristic
35	C₃²×C₅	Dic₆₅	1	6	yes	complemented
36	C₃×C₁₃	C₃⋊#1039	1	4	yes	complemented
37	C₃⋊Dic₃	—	325	1	no	Hall
38	C₂×C₃×C₅	D₁₉₅	1	24	yes	—
39	C₂×C₁₃	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic
40	C₅²	C₃⋊Dic₃₉	1	1	yes	characteristic, complemented, Sylow
41	Dic₅	—	585	6	no	—
42	C₂×C₃²	C₅⋊D₆₅	1	1	yes	characteristic
43	C₃×C₅	Dic₁₉₅	1	24	yes	complemented
44	C₁₃	C₃⋊(C₃⋊#1039)	1	1	yes	characteristic, complemented, Sylow
45	Dic₃	—	975	4	no	—
46	C₂×C₅	C₃⋊D₁₉₅	1	6	yes	—
47	C₃²	#13049918	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₃⋊(C₅⋊D₆₅)	1	4	yes	—
49	C₅	C₃⋊Dic₁₉₅	1	6	yes	complemented
50	C₄	—	2925	1	no	Sylow
51	C₃	C₃⋊#13049918	1	4	yes	complemented
52	C₂	C₃⋊(C₃⋊(C₅⋊D₆₅))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₃⋊(C₅⋊D₆₅))
commutator, hypocenter	C₃²×C₅²×C₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₅²×C₁₃	C₂
LCS	G ▷ C₃²×C₅²×C₁₃
UCS	C₁ ◁ C₂

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	Dic₁₃	semidirect
21. C₃×C₅×C₁₃	Dic₁₅	semidirect
26. C₃²×C₁₃	#1039	semidirect
30. C₃×C₅²	Dic₃₉	semidirect
31. C₅×C₁₃	C₃⋊Dic₁₅	semidirect
35. C₃²×C₅	Dic₆₅	semidirect
36. C₃×C₁₃	C₃⋊#1039	semidirect
40. C₅²	C₃⋊Dic₃₉	semidirect
43. C₃×C₅	Dic₁₉₅	semidirect
44. C₁₃	C₃⋊(C₃⋊#1039)	semidirect
47. C₃²	#13049918	semidirect
49. C₅	C₃⋊Dic₁₉₅	semidirect
51. C₃	C₃⋊#13049918	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅²×C₁₃	2
C₃⋊#13049918	3
C₃⋊Dic₁₉₅	5
C₃⋊(C₃⋊#1039)	13

Subgroups — C3⋊(C3⋊#13049918) #26043538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#13049918) #26043538