Subgroups — D₃×D₅×C₅₂₃ #44535948

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×D₃×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₅₂₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₅₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₅₂₃	—	5	1	no	maximal, Hall
7	C₂×C₅×C₅₂₃	—	3	1	no	—
8	D₅×C₅₂₃	—	3	1	no	—
9	D₅×C₅₂₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₅₂₃	—	5	1	no	—
11	D₃×C₅₂₃	—	5	1	no	—
12	D₃×C₅₂₃	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₅₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₅₂₃	—	15	1	no	Hall
15	C₃×C₅₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅₂₃	—	3	1	no	—
17	C₂×C₅₂₃	—	5	1	no	—
18	C₂×C₅₂₃	—	15	1	no	—
19	C₅₂₃	D₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
20	D₃×D₅	C₅₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	D₁₅	C₂×C₅₂₃	1	1	yes	characteristic, complemented
22	C₃×D₅	C₂×C₅₂₃	1	1	yes	characteristic, complemented
23	C₅×D₃	C₂×C₅₂₃	1	1	yes	characteristic, complemented
24	C₂×D₅	—	3	1	no	Hall
25	C₃×C₅	C₂²×C₅₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	5	1	no	Hall
27	C₂×C₅	—	3	1	no	—
28	D₅	—	3	1	no	—
29	D₅	D₃×C₅₂₃	1	1	yes	characteristic, direct product factor
30	C₂×C₃	—	5	1	no	—
31	D₃	—	5	1	no	—
32	D₃	D₅×C₅₂₃	1	1	yes	characteristic, direct product factor
33	C₅	C₂×D₃×C₅₂₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	15	1	no	Sylow
35	C₃	C₂×D₅×C₅₂₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	5	1	no	—
38	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₅₂₃	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₅₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₅₂₃	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₅₂₃

Complements

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

N	H ≅ G/N	type
1. D₁₅×C₅₂₃	C₂	semidirect
2. C₅×D₃×C₅₂₃	C₂	semidirect
3. C₃×D₅×C₅₂₃	C₂	semidirect
5. C₃×C₅×C₅₂₃	C₂²	semidirect
9. D₅×C₅₂₃	D₃	direct (N × H)
12. D₃×C₅₂₃	D₅	direct (N × H)
13. C₅×C₅₂₃	C₂×D₃	semidirect
15. C₃×C₅₂₃	C₂×D₅	semidirect
19. C₅₂₃	D₃×D₅	direct (N × H)
20. D₃×D₅	C₅₂₃	direct (N × H)
21. D₁₅	C₂×C₅₂₃	semidirect
22. C₃×D₅	C₂×C₅₂₃	semidirect
23. C₅×D₃	C₂×C₅₂₃	semidirect
25. C₃×C₅	C₂²×C₅₂₃	semidirect
29. D₅	D₃×C₅₂₃	direct (N × H)
32. D₃	D₅×C₅₂₃	direct (N × H)
33. C₅	C₂×D₃×C₅₂₃	semidirect
35. C₃	C₂×D₅×C₅₂₃	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×C₅₂₃	2
C₅×D₃×C₅₂₃	2
C₃×D₅×C₅₂₃	2
C₂×D₅×C₅₂₃	3
C₂×D₃×C₅₂₃	5
D₃×D₅	523

Subgroups — D3×D5×C523 #44535948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₅×C₅₂₃ #44535948