Subgroups — C₅²×D₂₁₉ #24926558

Order 10950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₇₃	—	3	1	no	maximal, Hall
3	C₅×D₂₁₉	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₇₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₇₃	C₂×C₅	1	6	yes	complemented
6	C₅×D₇₃	—	3	6	no	—
7	D₂₁₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇₃	C₅×D₃	1	6	yes	complemented
9	C₃×C₇₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	C₅²×D₃	—	73	1	no	maximal, Hall
11	D₇₃	—	3	1	no	Hall
12	C₃×C₅²	D₇₃	1	1	yes	characteristic, complemented, Hall
13	C₇₃	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅²	—	219	1	no	Hall
15	C₅×D₃	—	73	6	no	—
16	C₅²	D₂₁₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₅×D₇₃	1	6	yes	complemented
18	C₂×C₅	—	219	6	no	—
19	D₃	—	73	1	no	Hall
20	C₅	C₅×D₂₁₉	1	6	yes	direct product factor
21	C₃	C₅²×D₇₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	219	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₂₁₉
commutator, cosocle, hypocenter	C₃×C₇₃	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₃	C₂
LCS	G ▷ C₃×C₇₃
UCS	C₁ ◁ C₅²

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.