Subgroups — C₃⋊(C₃⋊#13133345) #29505999

Order 15300.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13133345	—	3	4	no	maximal
3	C₃²×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#66774)	—	5	6	no	maximal
5	C₃×C₁₇×C₅⋊D₅	D₃	1	4	yes	—
6	#13133345	—	9	1	no	Hall
7	C₃²×D₅×C₁₇	—	5	6	no	—
8	C₃×C₅²×C₁₇	Dic₃	1	4	yes	complemented
9	C₃⋊#66774	—	15	24	no	—
10	C₃⋊(C₃⋊#1043)	—	17	1	no	maximal, Hall
11	C₁₇×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
12	C₃²×C₅×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
13	C₃⋊Dic₅₁	—	25	1	no	Hall
14	C₃×D₅×C₁₇	—	5	24	no	—
15	C₃²×C₅⋊D₅	D₁₇	1	1	yes	characteristic
16	C₅²×C₁₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
17	#66774	—	45	6	no	—
18	C₂×C₃²×C₁₇	—	25	1	no	—
19	C₃⋊#1043	—	51	4	no	—
20	C₃×C₅×C₁₇	ΓL(1,𝔽₁₆)	1	24	yes	complemented
21	C₃²×C₅²	Dic₁₇	1	1	yes	characteristic, complemented, Hall
22	Dic₅₁	—	75	4	no	—
23	C₃⋊ΓL(1,𝔽₁₆)	—	85	6	no	—
24	D₅×C₁₇	—	5	6	no	—
25	C₃²×C₁₇	#1043	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅⋊D₅	D₅₁	1	4	yes	—
27	C₂×C₃×C₁₇	—	25	4	no	—
28	#1043	—	153	1	no	Hall
29	C₃²×D₅	—	5	6	no	—
30	C₅×C₁₇	C₃⋊ΓL(1,𝔽₁₆)	1	6	yes	complemented
31	C₃×C₅²	Dic₅₁	1	4	yes	complemented
32	Dic₁₇	—	225	1	no	Hall
33	ΓL(1,𝔽₁₆)	—	255	24	no	—
34	C₃×C₁₇	C₃⋊#1043	1	4	yes	complemented
35	C₅⋊D₅	C₃⋊D₅₁	1	1	yes	characteristic
36	C₃²×C₅	#66774	1	6	yes	complemented
37	C₃⋊Dic₃	—	425	1	no	Hall
38	C₂×C₁₇	—	25	1	no	—
39	C₃×D₅	—	5	24	no	—
40	C₅²	C₃⋊Dic₅₁	1	1	yes	characteristic, complemented, Sylow
41	AGL(1,𝔽₅)	—	765	6	no	—
42	C₂×C₃²	—	25	1	no	—
43	C₁₇	C₃⋊(C₃⋊#1043)	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₅	C₃⋊#66774	1	24	yes	complemented
45	Dic₃	—	1275	4	no	—
46	D₅	—	5	6	no	—
47	C₃²	#13133345	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	4	no	—
49	C₅	C₃⋊(C₃⋊#66774)	1	6	yes	complemented
50	C₄	—	3825	1	no	Sylow
51	C₃	C₃⋊#13133345	1	4	yes	complemented
52	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₇	C₄
prime radical, cosocle	C₃²×C₁₇×C₅⋊D₅	C₂
LCS	G ▷ C₃²×C₅²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₇	C₄	semidirect
8. C₃×C₅²×C₁₇	Dic₃	semidirect
12. C₃²×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₇	C₃⋊Dic₃	semidirect
20. C₃×C₅×C₁₇	ΓL(1,𝔽₁₆)	semidirect
21. C₃²×C₅²	Dic₁₇	semidirect
25. C₃²×C₁₇	#1043	semidirect
30. C₅×C₁₇	C₃⋊ΓL(1,𝔽₁₆)	semidirect
31. C₃×C₅²	Dic₅₁	semidirect
34. C₃×C₁₇	C₃⋊#1043	semidirect
36. C₃²×C₅	#66774	semidirect
40. C₅²	C₃⋊Dic₅₁	semidirect
43. C₁₇	C₃⋊(C₃⋊#1043)	semidirect
44. C₃×C₅	C₃⋊#66774	semidirect
47. C₃²	#13133345	semidirect
49. C₅	C₃⋊(C₃⋊#66774)	semidirect
51. C₃	C₃⋊#13133345	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₅⋊D₅	2
C₃⋊#13133345	3
C₃⋊(C₃⋊#66774)	5
C₃⋊(C₃⋊#1043)	17

Subgroups — C3⋊(C3⋊#13133345) #29505999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#13133345) #29505999