Subgroups — C₃⋊(C₅⋊(D₃₆₁⋊C₃)) #44570440

Order 32490.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₄₁₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(D₃₆₁⋊C₃)	—	3	1	no	maximal
4	C₃⋊(D₃₆₁⋊C₃)	—	5	1	no	maximal, Hall
5	C₅×C₃₆₁⋊C₃	—	2	1	no	—
6	C₅×C₃₆₁⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₃₆₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₈₀₅	—	3	1	no	Hall
9	C₃×C₃₆₁⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
10	D₁₀₈₃	—	5	1	no	—
11	D₃₆₁⋊C₃	—	15	1	no	—
12	C₅×C₃₆₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₅⋊(D₁₉⋊C₃))	—	19	1	no	maximal
14	C₃×C₃₆₁	C₃×D₅	1	1	yes	characteristic, complemented
15	C₃₆₁⋊C₃	—	2	1	no	—
16	C₃₆₁⋊C₃	D₁₅	1	1	yes	characteristic, complemented
17	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
18	D₃₆₁	—	15	1	no	Hall
19	D₂₈₅	—	19	1	no	—
20	C₅⋊(D₁₉⋊C₃)	—	57	1	no	—
21	C₃₆₁	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
22	C₃⋊(D₁₉⋊C₃)	—	95	1	no	—
23	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic
24	C₅×C₁₉⋊C₃	—	19	1	no	—
25	C₅×C₁₉⋊C₃	—	38	1	no	—
26	D₉₅	—	57	1	no	—
27	C₃×C₁₉⋊C₃	—	19	1	no	—
28	D₅₇	—	95	1	no	—
29	D₁₉⋊C₃	—	285	1	no	—
30	C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic
31	C₃×D₁₅	—	361	1	no	Hall
32	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic
33	C₁₉⋊C₃	—	19	1	no	—
34	C₁₉⋊C₃	—	38	1	no	—
35	C₃²×C₅	—	361	1	no	Hall
36	D₁₉	—	285	1	no	—
37	D₁₅	—	361	1	no	—
38	C₃×D₅	—	1083	1	no	—
39	C₁₉	C₃⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic
40	C₃×D₃	—	1805	1	no	Hall
41	C₃×C₅	—	361	1	no	—
42	C₃×C₅	—	722	1	no	—
43	C₃×C₅	D₃₆₁⋊C₃	1	1	yes	characteristic, complemented
44	D₅	—	1083	1	no	Hall
45	C₃²	—	361	1	no	Sylow
46	C₂×C₃	—	5415	1	no	—
47	D₃	—	1805	1	no	—
48	C₅	C₃⋊(D₃₆₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	361	1	no	—
50	C₃	—	722	1	no	—
51	C₃	C₅⋊(D₃₆₁⋊C₃)	1	1	yes	characteristic, complemented
52	C₂	—	5415	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₅×C₃₆₁	C₂×C₃
Frattini	C₁₉	C₃⋊(C₅⋊(D₁₉⋊C₃))
socle	C₃×C₅×C₁₉	D₁₉⋊C₃
LCS	G ▷ C₃×C₅×C₃₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₃₆₁⋊C₃	C₂	semidirect
2. D₅₄₁₅	C₃	semidirect
6. C₅×C₃₆₁⋊C₃	D₃	semidirect
7. C₃×C₅×C₃₆₁	C₂×C₃	semidirect
9. C₃×C₃₆₁⋊C₃	D₅	semidirect
12. C₅×C₃₆₁	C₃×D₃	semidirect
14. C₃×C₃₆₁	C₃×D₅	semidirect
16. C₃₆₁⋊C₃	D₁₅	semidirect
21. C₃₆₁	C₃×D₁₅	semidirect
43. C₃×C₅	D₃₆₁⋊C₃	semidirect
48. C₅	C₃⋊(D₃₆₁⋊C₃)	semidirect
51. C₃	C₅⋊(D₃₆₁⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₃₆₁⋊C₃	2
D₅₄₁₅	3
C₅⋊(D₃₆₁⋊C₃)	3
C₃⋊(D₃₆₁⋊C₃)	5
C₃⋊(C₅⋊(D₁₉⋊C₃))	19

Subgroups — C3⋊(C5⋊(D361⋊C3)) #44570440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊(D₃₆₁⋊C₃)) #44570440