Subgroups — D₁₂₂₅₅ #37587773

Order 24510.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₀₈₅	—	3	1	no	maximal, Hall
3	D₂₄₅₁	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₄₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₈₁₇	—	15	1	no	Hall
7	D₆₄₅	—	19	1	no	maximal, Hall
8	C₁₉×C₄₃	D₁₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₃	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₂₈₅	—	43	1	no	maximal, Hall
11	D₂₁₅	—	57	1	no	Hall
12	C₃×C₅×C₁₉	D₄₃	1	1	yes	characteristic, complemented, Hall
13	D₁₂₉	—	95	1	no	Hall
14	C₅×C₄₃	D₅₇	1	1	yes	characteristic, complemented, Hall
15	D₉₅	—	129	1	no	Hall
16	C₃×C₄₃	D₉₅	1	1	yes	characteristic, complemented, Hall
17	D₅₇	—	215	1	no	Hall
18	C₅×C₁₉	D₁₂₉	1	1	yes	characteristic, complemented, Hall
19	D₄₃	—	285	1	no	Hall
20	C₃×C₁₉	D₂₁₅	1	1	yes	characteristic, complemented, Hall
21	C₄₃	D₂₈₅	1	1	yes	characteristic, complemented, Sylow
22	D₁₉	—	645	1	no	Hall
23	D₁₅	—	817	1	no	Hall
24	C₁₉	D₆₄₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₈₁₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	2451	1	no	Hall
27	D₃	—	4085	1	no	Hall
28	C₅	D₂₄₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₄₀₈₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	12255	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₉×C₄₃	C₂
LCS	G ▷ C₃×C₅×C₁₉×C₄₃
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.