Subgroups — C₃⋊(C₃⋊(C₅⋊D₆₅)) #19154400

Order 5850.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₆₅)	—	3	4	no	maximal
3	C₃⋊D₁₉₅	—	5	6	no	maximal
4	C₃×C₅²×C₁₃	D₃	1	4	yes	complemented
5	C₅⋊D₆₅	—	9	1	no	Hall
6	C₃²×C₅×C₁₃	D₅	1	6	yes	complemented
7	C₃⋊(C₃⋊(C₅⋊D₅))	—	13	1	no	maximal, Hall
8	D₁₉₅	—	15	24	no	—
9	C₅²×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₃₉	—	25	1	no	Hall
11	C₃²×C₅²	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₁₃	D₁₅	1	24	yes	complemented
13	C₃⋊(C₅⋊D₅)	—	39	4	no	—
14	D₆₅	—	45	6	no	—
15	C₃²×C₁₃	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
16	C₃⋊D₁₅	—	65	6	no	—
17	D₃₉	—	75	4	no	—
18	C₃×C₅²	D₃₉	1	4	yes	complemented
19	C₅×C₁₃	C₃⋊D₁₅	1	6	yes	complemented
20	C₅⋊D₅	—	117	1	no	Hall
21	C₃²×C₅	D₆₅	1	6	yes	complemented
22	C₃×C₁₃	C₃⋊(C₅⋊D₅)	1	4	yes	complemented
23	D₁₅	—	195	24	no	—
24	D₁₃	—	225	1	no	Hall
25	C₅²	C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
26	C₃⋊D₃	—	325	1	no	Hall
27	C₃×C₅	D₁₉₅	1	24	yes	complemented
28	C₁₃	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic, complemented, Sylow
29	D₅	—	585	6	no	—
30	C₃²	C₅⋊D₆₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	975	4	no	—
32	C₅	C₃⋊D₁₉₅	1	6	yes	complemented
33	C₃	C₃⋊(C₅⋊D₆₅)	1	4	yes	complemented
34	C₂	—	2925	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₃	C₂
LCS	G ▷ C₃²×C₅²×C₁₃
UCS	C₁

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