Subgroups — C₃⋊(C₃⋊(C₁₉⋊#1039)) #30685694

Order 17100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#1039)	—	3	4	no	maximal
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₂₈₅	—	5	6	no	maximal
5	C₂×C₃×C₅²×C₁₉	D₃	1	4	yes	—
6	C₁₉⋊#1039	—	9	1	no	Hall
7	C₂×C₃²×C₅×C₁₉	D₅	1	6	yes	—
8	C₃×C₅²×C₁₉	Dic₃	1	4	yes	complemented
9	Dic₂₈₅	—	15	24	no	—
10	C₂×C₅²×C₁₉	C₃⋊D₃	1	1	yes	characteristic
11	C₃⋊(C₃⋊#1039)	—	19	1	no	maximal, Hall
12	C₃²×C₅×C₁₉	Dic₅	1	6	yes	complemented
13	C₃⋊Dic₅₇	—	25	1	no	Hall
14	C₂×C₃×C₅×C₁₉	D₁₅	1	24	yes	—
15	C₅²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃²×C₅²	D₁₉	1	1	yes	characteristic
17	Dic₉₅	—	45	6	no	—
18	C₂×C₃²×C₁₉	C₅⋊D₅	1	1	yes	characteristic
19	C₃⋊#1039	—	57	4	no	—
20	C₃×C₅×C₁₉	Dic₁₅	1	24	yes	complemented
21	Dic₅₇	—	75	4	no	—
22	C₃²×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₁₉	C₃⋊D₁₅	1	6	yes	—
24	C₃⋊Dic₁₅	—	95	6	no	—
25	C₃²×C₁₉	#1039	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅²	D₅₇	1	4	yes	—
27	C₂×C₃×C₁₉	C₃⋊(C₅⋊D₅)	1	4	yes	—
28	#1039	—	171	1	no	Hall
29	C₅×C₁₉	C₃⋊Dic₁₅	1	6	yes	complemented
30	C₂×C₃²×C₅	D₉₅	1	6	yes	—
31	Dic₁₉	—	225	1	no	Hall
32	C₃×C₅²	Dic₅₇	1	4	yes	complemented
33	Dic₁₅	—	285	24	no	—
34	C₃×C₁₉	C₃⋊#1039	1	4	yes	complemented
35	C₂×C₅²	C₃⋊D₅₇	1	1	yes	characteristic
36	C₃²×C₅	Dic₉₅	1	6	yes	complemented
37	C₂×C₁₉	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic
38	C₃⋊Dic₃	—	475	1	no	Hall
39	C₂×C₃×C₅	D₂₈₅	1	24	yes	—
40	C₅²	C₃⋊Dic₅₇	1	1	yes	characteristic, complemented, Sylow
41	Dic₅	—	855	6	no	—
42	C₁₉	C₃⋊(C₃⋊#1039)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃²	C₅⋊D₉₅	1	1	yes	characteristic
44	C₃×C₅	Dic₂₈₅	1	24	yes	complemented
45	Dic₃	—	1425	4	no	—
46	C₂×C₅	C₃⋊D₂₈₅	1	6	yes	—
47	C₃²	C₁₉⋊#1039	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₃⋊(C₅⋊D₉₅)	1	4	yes	—
49	C₅	C₃⋊Dic₂₈₅	1	6	yes	complemented
50	C₄	—	4275	1	no	Sylow
51	C₃	C₃⋊(C₁₉⋊#1039)	1	4	yes	complemented
52	C₂	C₃⋊(C₃⋊(C₅⋊D₉₅))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₃⋊(C₅⋊D₉₅))
commutator, hypocenter	C₃²×C₅²×C₁₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃²×C₅²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₉	C₄	semidirect
8. C₃×C₅²×C₁₉	Dic₃	semidirect
12. C₃²×C₅×C₁₉	Dic₅	semidirect
15. C₅²×C₁₉	C₃⋊Dic₃	semidirect
20. C₃×C₅×C₁₉	Dic₁₅	semidirect
22. C₃²×C₅²	Dic₁₉	semidirect
25. C₃²×C₁₉	#1039	semidirect
29. C₅×C₁₉	C₃⋊Dic₁₅	semidirect
32. C₃×C₅²	Dic₅₇	semidirect
34. C₃×C₁₉	C₃⋊#1039	semidirect
36. C₃²×C₅	Dic₉₅	semidirect
40. C₅²	C₃⋊Dic₅₇	semidirect
42. C₁₉	C₃⋊(C₃⋊#1039)	semidirect
44. C₃×C₅	Dic₂₈₅	semidirect
47. C₃²	C₁₉⋊#1039	semidirect
49. C₅	C₃⋊Dic₂₈₅	semidirect
51. C₃	C₃⋊(C₁₉⋊#1039)	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×C₁₉	2
C₃⋊(C₁₉⋊#1039)	3
C₃⋊Dic₂₈₅	5
C₃⋊(C₃⋊#1039)	19

Subgroups — C3⋊(C3⋊(C19⋊#1039)) #30685694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(C₁₉⋊#1039)) #30685694