Subgroups — C₅×C₂₃×D₁₄₅ #45688649

Order 33350.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₁₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×C₂₃×D₂₉	—	5	1	no	maximal
4	C₅×C₂₃×C₂₉	—	2	2	no	—
5	C₅×C₂₃×C₂₉	D₅	1	1	yes	characteristic, complemented
6	C₅×C₂₃×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅×D₁₄₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×D₂₉	—	5	1	no	Hall
9	C₅×D₅×C₂₃	—	29	1	no	maximal, Hall
10	C₅²×C₂₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂₃×C₂₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
12	C₅²×C₂₃	D₂₉	1	1	yes	characteristic, complemented, Hall
13	D₁₄₅	C₅×C₂₃	1	1	yes	characteristic, direct product factor
14	C₅×D₂₉	—	5	1	no	—
15	C₂×C₅×C₂₃	—	145	1	no	—
16	D₅×C₂₃	—	29	1	no	—
17	C₅×C₂₉	—	2	2	no	—
18	C₅×C₂₉	D₅×C₂₃	1	1	yes	characteristic, complemented
19	C₅×C₂₉	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
20	C₅×C₂₃	—	2	2	no	—
21	C₅×C₂₃	C₅×D₂₉	1	1	yes	characteristic, complemented
22	C₅×C₂₃	D₁₄₅	1	1	yes	characteristic, direct product factor
23	D₂₉	—	5	1	no	Hall
24	C₅×D₅	—	29	1	no	Hall
25	C₂×C₂₃	—	145	1	no	Hall
26	C₂₉	C₅×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₅²	C₂₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
28	C₂₃	C₅×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅	—	145	1	no	—
30	D₅	—	29	1	no	—
31	C₅	—	2	2	no	—
32	C₅	C₅×C₂₃×D₂₉	1	1	yes	characteristic, complemented
33	C₅	C₂₃×D₁₄₅	1	1	yes	characteristic, direct product factor
34	C₂	—	145	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₁₄₅
commutator, cosocle, hypocenter	C₅×C₂₉	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅²×C₂₃×C₂₉	C₂
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅²×C₂₃×C₂₉	C₂	semidirect
2. C₂₃×D₁₄₅	C₅	direct (N × H)
5. C₅×C₂₃×C₂₉	D₅	semidirect
6. C₅×C₂₃×C₂₉	C₂×C₅	semidirect
7. C₅×D₁₄₅	C₂₃	direct (N × H)
10. C₅²×C₂₉	C₂×C₂₃	semidirect
11. C₂₃×C₂₉	C₅×D₅	semidirect
12. C₅²×C₂₃	D₂₉	semidirect
13. D₁₄₅	C₅×C₂₃	direct (N × H)
18. C₅×C₂₉	D₅×C₂₃	semidirect
19. C₅×C₂₉	C₂×C₅×C₂₃	semidirect
21. C₅×C₂₃	C₅×D₂₉	semidirect
22. C₅×C₂₃	D₁₄₅	direct (N × H)
26. C₂₉	C₅×D₅×C₂₃	semidirect
27. C₅²	C₂₃×D₂₉	semidirect
28. C₂₃	C₅×D₁₄₅	direct (N × H)
32. C₅	C₅×C₂₃×D₂₉	semidirect
33. C₅	C₂₃×D₁₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₂₃×C₂₉	2
C₂₃×D₁₄₅	5
C₅×C₂₃×D₂₉	5
C₅×D₁₄₅	23
C₅×D₅×C₂₃	29

Subgroups — C5×C23×D145 #45688649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₃×D₁₄₅ #45688649