Subgroups — C₃⋊(C₃⋊(C₅⋊D₃₅₅)) #44544095

Order 31950.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₃₅₅)	—	3	4	no	maximal
3	C₃⋊D₁₀₆₅	—	5	6	no	maximal
4	C₃×C₅²×C₇₁	D₃	1	4	yes	complemented
5	C₅⋊D₃₅₅	—	9	1	no	Hall
6	C₃²×C₅×C₇₁	D₅	1	6	yes	complemented
7	D₁₀₆₅	—	15	24	no	—
8	C₅²×C₇₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊D₂₁₃	—	25	1	no	Hall
10	C₃×C₅×C₇₁	D₁₅	1	24	yes	complemented
11	D₃₅₅	—	45	6	no	—
12	C₃²×C₇₁	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₃⋊(C₅⋊D₅))	—	71	1	no	maximal, Hall
14	D₂₁₃	—	75	4	no	—
15	C₅×C₇₁	C₃⋊D₁₅	1	6	yes	complemented
16	C₃²×C₅²	D₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₃⋊(C₅⋊D₅)	1	4	yes	complemented
18	C₃⋊(C₅⋊D₅)	—	213	4	no	—
19	D₇₁	—	225	1	no	Hall
20	C₃⋊D₁₅	—	355	6	no	—
21	C₃×C₅²	D₂₁₃	1	4	yes	complemented
22	C₇₁	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic, complemented, Sylow
23	C₅⋊D₅	—	639	1	no	Hall
24	C₃²×C₅	D₃₅₅	1	6	yes	complemented
25	D₁₅	—	1065	24	no	—
26	C₅²	C₃⋊D₂₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₃⋊D₃	—	1775	1	no	Hall
28	C₃×C₅	D₁₀₆₅	1	24	yes	complemented
29	D₅	—	3195	6	no	—
30	C₃²	C₅⋊D₃₅₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	5325	4	no	—
32	C₅	C₃⋊D₁₀₆₅	1	6	yes	complemented
33	C₃	C₃⋊(C₅⋊D₃₅₅)	1	4	yes	complemented
34	C₂	—	15975	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅²×C₇₁	C₂
LCS	G ▷ C₃²×C₅²×C₇₁
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.