Subgroups — C₃⋊(C₃⋊(C₅⋊D₂₆₅)) #37558739

Order 23850.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₂₆₅)	—	3	4	no	maximal
3	C₃⋊D₇₉₅	—	5	6	no	maximal
4	C₃×C₅²×C₅₃	D₃	1	4	yes	complemented
5	C₅⋊D₂₆₅	—	9	1	no	Hall
6	C₃²×C₅×C₅₃	D₅	1	6	yes	complemented
7	D₇₉₅	—	15	24	no	—
8	C₅²×C₅₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊D₁₅₉	—	25	1	no	Hall
10	C₃×C₅×C₅₃	D₁₅	1	24	yes	complemented
11	D₂₆₅	—	45	6	no	—
12	C₃²×C₅₃	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₃⋊(C₅⋊D₅))	—	53	1	no	maximal, Hall
14	D₁₅₉	—	75	4	no	—
15	C₅×C₅₃	C₃⋊D₁₅	1	6	yes	complemented
16	C₃²×C₅²	D₅₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅₃	C₃⋊(C₅⋊D₅)	1	4	yes	complemented
18	C₃⋊(C₅⋊D₅)	—	159	4	no	—
19	D₅₃	—	225	1	no	Hall
20	C₃⋊D₁₅	—	265	6	no	—
21	C₃×C₅²	D₁₅₉	1	4	yes	complemented
22	C₅₃	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic, complemented, Sylow
23	C₅⋊D₅	—	477	1	no	Hall
24	C₃²×C₅	D₂₆₅	1	6	yes	complemented
25	D₁₅	—	795	24	no	—
26	C₅²	C₃⋊D₁₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₃⋊D₃	—	1325	1	no	Hall
28	C₃×C₅	D₇₉₅	1	24	yes	complemented
29	D₅	—	2385	6	no	—
30	C₃²	C₅⋊D₂₆₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3975	4	no	—
32	C₅	C₃⋊D₇₉₅	1	6	yes	complemented
33	C₃	C₃⋊(C₅⋊D₂₆₅)	1	4	yes	complemented
34	C₂	—	11925	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅²×C₅₃	C₂
LCS	G ▷ C₃²×C₅²×C₅₃
UCS	C₁

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

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