Subgroups — C₃⋊(C₃⋊(C₅⋊D₁₁₅)) #23780378

Order 10350.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₁₁₅)	—	3	4	no	maximal
3	C₃⋊D₃₄₅	—	5	6	no	maximal
4	C₃×C₅²×C₂₃	D₃	1	4	yes	complemented
5	C₅⋊D₁₁₅	—	9	1	no	Hall
6	C₃²×C₅×C₂₃	D₅	1	6	yes	complemented
7	D₃₄₅	—	15	24	no	—
8	C₅²×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(C₃⋊(C₅⋊D₅))	—	23	1	no	maximal, Hall
10	C₃⋊D₆₉	—	25	1	no	Hall
11	C₃×C₅×C₂₃	D₁₅	1	24	yes	complemented
12	D₁₁₅	—	45	6	no	—
13	C₃²×C₅²	D₂₃	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₂₃	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₅⋊D₅)	—	69	4	no	—
16	D₆₉	—	75	4	no	—
17	C₅×C₂₃	C₃⋊D₁₅	1	6	yes	complemented
18	C₃⋊D₁₅	—	115	6	no	—
19	C₃×C₅²	D₆₉	1	4	yes	complemented
20	C₃×C₂₃	C₃⋊(C₅⋊D₅)	1	4	yes	complemented
21	C₅⋊D₅	—	207	1	no	Hall
22	D₂₃	—	225	1	no	Hall
23	C₃²×C₅	D₁₁₅	1	6	yes	complemented
24	D₁₅	—	345	24	no	—
25	C₅²	C₃⋊D₆₉	1	1	yes	characteristic, complemented, Sylow
26	C₂₃	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic, complemented, Sylow
27	C₃⋊D₃	—	575	1	no	Hall
28	C₃×C₅	D₃₄₅	1	24	yes	complemented
29	D₅	—	1035	6	no	—
30	C₃²	C₅⋊D₁₁₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	1725	4	no	—
32	C₅	C₃⋊D₃₄₅	1	6	yes	complemented
33	C₃	C₃⋊(C₅⋊D₁₁₅)	1	4	yes	complemented
34	C₂	—	5175	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅²×C₂₃	C₂
LCS	G ▷ C₃²×C₅²×C₂₃
UCS	C₁

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