Subgroups — D₁₅⋊D₅₂₃ #44535951

Order 31380.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₂₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₅₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅₂₃	—	5	1	no	maximal, Hall
7	D₂₆₁₅	D₃	1	1	yes	characteristic, complemented
8	C₅×D₅₂₃	—	3	1	no	—
9	D₅×C₅₂₃	—	3	1	no	—
10	D₁₅₆₉	D₅	1	1	yes	characteristic, complemented
11	C₃×D₅₂₃	—	5	1	no	—
12	D₃×C₅₂₃	—	5	1	no	—
13	C₅×C₅₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₅₂₃	—	15	1	no	Hall
15	C₃×C₅₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅₂₃	—	15	1	no	—
17	D₅₂₃	—	3	1	no	—
18	D₅₂₃	—	5	1	no	—
19	C₅₂₃	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₅	—	523	1	no	maximal, Hall
21	D₁₅	D₅₂₃	1	1	yes	characteristic, complemented
22	C₃×D₅	—	523	1	no	—
23	C₅×D₃	—	523	1	no	—
24	C₂×D₅	—	1569	1	no	Hall
25	C₃×C₅	C₂×D₅₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	2615	1	no	Hall
27	C₂×C₅	—	1569	1	no	—
28	D₅	—	3	1	no	—
29	D₅	—	523	1	no	—
30	C₂×C₃	—	2615	1	no	—
31	D₃	—	5	1	no	—
32	D₃	—	523	1	no	—
33	C₅	D₃×D₅₂₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	7845	1	no	Sylow
35	C₃	D₅×D₅₂₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	15	1	no	—
37	C₂	—	1569	1	no	—
38	C₂	—	2615	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₅₂₃	C₂²
LCS	G ▷ C₃×C₅×C₅₂₃
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.