Subgroups — C₂×C₅×C₁₃²×C₁₉ #44545768

Order 32110.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×C₁₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃²×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₁₉	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅×C₁₃×C₁₉	C₁₃	1	14	yes	maximal, direct product factor
5	C₂×C₅×C₁₃²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×C₁₉	C₂×C₁₃	1	14	yes	direct product factor
7	C₅×C₁₃²	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₃×C₁₉	C₅×C₁₃	1	14	yes	direct product factor
9	C₂×C₁₃²	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×C₁₉	C₂×C₅×C₁₃	1	14	yes	direct product factor
11	C₂×C₅×C₁₉	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃²	C₂×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₅×C₁₃	C₁₃×C₁₉	1	14	yes	direct product factor
14	C₅×C₁₉	C₂×C₁₃²	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₁₃	C₂×C₁₃×C₁₉	1	14	yes	direct product factor
16	C₂×C₁₉	C₅×C₁₃²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₃	C₅×C₁₃×C₁₉	1	14	yes	direct product factor
18	C₁₉	C₂×C₅×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	C₂×C₅×C₁₃×C₁₉	1	14	yes	direct product factor
20	C₂×C₅	C₁₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₅	C₂×C₁₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₅×C₁₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃²×C₁₉	C₂	direct (N × H)
2. C₂×C₁₃²×C₁₉	C₅	direct (N × H)
3. C₁₃²×C₁₉	C₂×C₅	direct (N × H)
4. C₂×C₅×C₁₃×C₁₉	C₁₃	direct (N × H)
5. C₂×C₅×C₁₃²	C₁₉	direct (N × H)
6. C₅×C₁₃×C₁₉	C₂×C₁₃	direct (N × H)
7. C₅×C₁₃²	C₂×C₁₉	direct (N × H)
8. C₂×C₁₃×C₁₉	C₅×C₁₃	direct (N × H)
9. C₂×C₁₃²	C₅×C₁₉	direct (N × H)
10. C₁₃×C₁₉	C₂×C₅×C₁₃	direct (N × H)
11. C₂×C₅×C₁₉	C₁₃²	direct (N × H)
12. C₁₃²	C₂×C₅×C₁₉	direct (N × H)
13. C₂×C₅×C₁₃	C₁₃×C₁₉	direct (N × H)
14. C₅×C₁₉	C₂×C₁₃²	direct (N × H)
15. C₅×C₁₃	C₂×C₁₃×C₁₉	direct (N × H)
16. C₂×C₁₉	C₅×C₁₃²	direct (N × H)
17. C₂×C₁₃	C₅×C₁₃×C₁₉	direct (N × H)
18. C₁₉	C₂×C₅×C₁₃²	direct (N × H)
19. C₁₃	C₂×C₅×C₁₃×C₁₉	direct (N × H)
20. C₂×C₅	C₁₃²×C₁₉	direct (N × H)
21. C₅	C₂×C₁₃²×C₁₉	direct (N × H)
22. C₂	C₅×C₁₃²×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃²×C₁₉	2
C₂×C₁₃²×C₁₉	5
C₂×C₅×C₁₃×C₁₉	13
C₂×C₅×C₁₃²	19

Subgroups — C2×C5×C132×C19 #44545768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃²×C₁₉ #44545768