Subgroups — C₃²×C₅×C₁₉×C₃₁ #40997113

Order 26505.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₃₁	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₁₉×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₉×C₃₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₁₉×C₃₁	C₃×C₅	1	4	yes	direct product factor
5	C₃²×C₅×C₃₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₅×C₁₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₉×C₃₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅×C₃₁	C₃×C₁₉	1	4	yes	direct product factor
9	C₃×C₅×C₁₉	C₃×C₃₁	1	4	yes	direct product factor
10	C₃²×C₃₁	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×C₁₉	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₃₁	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₁₉	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₃₁	C₃×C₅×C₁₉	1	4	yes	direct product factor
15	C₃×C₁₉	C₃×C₅×C₃₁	1	4	yes	direct product factor
16	C₃²×C₅	C₁₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃₁	C₃²×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₉	C₃²×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₃×C₁₉×C₃₁	1	4	yes	direct product factor
20	C₃²	C₅×C₁₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃²×C₁₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₅×C₁₉×C₃₁	1	4	yes	direct product factor

	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. C₃×C₅×C₁₉×C₃₁	C₃	direct (N × H)
2. C₃²×C₁₉×C₃₁	C₅	direct (N × H)
3. C₅×C₁₉×C₃₁	C₃²	direct (N × H)
4. C₃×C₁₉×C₃₁	C₃×C₅	direct (N × H)
5. C₃²×C₅×C₃₁	C₁₉	direct (N × H)
6. C₃²×C₅×C₁₉	C₃₁	direct (N × H)
7. C₁₉×C₃₁	C₃²×C₅	direct (N × H)
8. C₃×C₅×C₃₁	C₃×C₁₉	direct (N × H)
9. C₃×C₅×C₁₉	C₃×C₃₁	direct (N × H)
10. C₃²×C₃₁	C₅×C₁₉	direct (N × H)
11. C₃²×C₁₉	C₅×C₃₁	direct (N × H)
12. C₅×C₃₁	C₃²×C₁₉	direct (N × H)
13. C₅×C₁₉	C₃²×C₃₁	direct (N × H)
14. C₃×C₃₁	C₃×C₅×C₁₉	direct (N × H)
15. C₃×C₁₉	C₃×C₅×C₃₁	direct (N × H)
16. C₃²×C₅	C₁₉×C₃₁	direct (N × H)
17. C₃₁	C₃²×C₅×C₁₉	direct (N × H)
18. C₁₉	C₃²×C₅×C₃₁	direct (N × H)
19. C₃×C₅	C₃×C₁₉×C₃₁	direct (N × H)
20. C₃²	C₅×C₁₉×C₃₁	direct (N × H)
21. C₅	C₃²×C₁₉×C₃₁	direct (N × H)
22. C₃	C₃×C₅×C₁₉×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉×C₃₁	3
C₃²×C₁₉×C₃₁	5
C₃²×C₅×C₃₁	19
C₃²×C₅×C₁₉	31

Subgroups — C32×C5×C19×C31 #40997113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₁₉×C₃₁ #40997113