Subgroups — C₂⁵×C₃²×C₈₃ #72201190

Order 23904.

4488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²×C₈₃	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₃×C₈₃	C₃	1	4	yes	maximal, direct product factor
3	C₂³×C₃²×C₈₃	C₂²	1	155	yes	direct product factor
4	C₂⁴×C₃×C₈₃	C₂×C₃	1	124	yes	direct product factor
5	C₂²×C₃²×C₈₃	C₂³	1	155	yes	direct product factor
6	C₂⁵×C₈₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂³×C₃×C₈₃	C₂²×C₃	1	620	yes	direct product factor
8	C₂×C₃²×C₈₃	C₂⁴	1	31	yes	direct product factor
9	C₂⁴×C₈₃	C₂×C₃²	1	31	yes	direct product factor
10	C₂²×C₃×C₈₃	C₂³×C₃	1	620	yes	direct product factor
11	C₃²×C₈₃	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
12	C₂³×C₈₃	C₂²×C₃²	1	155	yes	direct product factor
13	C₂×C₃×C₈₃	C₂⁴×C₃	1	124	yes	direct product factor
14	C₂²×C₈₃	C₂³×C₃²	1	155	yes	direct product factor
15	C₂⁵×C₃²	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₈₃	C₂⁵×C₃	1	4	yes	direct product factor
17	C₂×C₈₃	C₂⁴×C₃²	1	31	yes	direct product factor
18	C₂⁴×C₃²	C₂×C₈₃	1	31	yes	direct product factor
19	C₂⁵×C₃	C₃×C₈₃	1	4	yes	direct product factor
20	C₈₃	C₂⁵×C₃²	1	1	yes	characteristic, direct product factor, Sylow
21	C₂³×C₃²	C₂²×C₈₃	1	155	yes	direct product factor
22	C₂⁴×C₃	C₂×C₃×C₈₃	1	124	yes	direct product factor
23	C₂²×C₃²	C₂³×C₈₃	1	155	yes	direct product factor
24	C₂⁵	C₃²×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂³×C₃	C₂²×C₃×C₈₃	1	620	yes	direct product factor
26	C₂×C₃²	C₂⁴×C₈₃	1	31	yes	direct product factor
27	C₂⁴	C₂×C₃²×C₈₃	1	31	yes	direct product factor
28	C₂²×C₃	C₂³×C₃×C₈₃	1	620	yes	direct product factor
29	C₃²	C₂⁵×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂³	C₂²×C₃²×C₈₃	1	155	yes	direct product factor
31	C₂×C₃	C₂⁴×C₃×C₈₃	1	124	yes	direct product factor
32	C₂²	C₂³×C₃²×C₈₃	1	155	yes	direct product factor
33	C₃	C₂⁵×C₃×C₈₃	1	4	yes	direct product factor
34	C₂	C₂⁴×C₃²×C₈₃	1	31	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. C₂⁴×C₃²×C₈₃	C₂	direct (N × H)
2. C₂⁵×C₃×C₈₃	C₃	direct (N × H)
3. C₂³×C₃²×C₈₃	C₂²	direct (N × H)
4. C₂⁴×C₃×C₈₃	C₂×C₃	direct (N × H)
5. C₂²×C₃²×C₈₃	C₂³	direct (N × H)
6. C₂⁵×C₈₃	C₃²	direct (N × H)
7. C₂³×C₃×C₈₃	C₂²×C₃	direct (N × H)
8. C₂×C₃²×C₈₃	C₂⁴	direct (N × H)
9. C₂⁴×C₈₃	C₂×C₃²	direct (N × H)
10. C₂²×C₃×C₈₃	C₂³×C₃	direct (N × H)
11. C₃²×C₈₃	C₂⁵	direct (N × H)
12. C₂³×C₈₃	C₂²×C₃²	direct (N × H)
13. C₂×C₃×C₈₃	C₂⁴×C₃	direct (N × H)
14. C₂²×C₈₃	C₂³×C₃²	direct (N × H)
15. C₂⁵×C₃²	C₈₃	direct (N × H)
16. C₃×C₈₃	C₂⁵×C₃	direct (N × H)
17. C₂×C₈₃	C₂⁴×C₃²	direct (N × H)
18. C₂⁴×C₃²	C₂×C₈₃	direct (N × H)
19. C₂⁵×C₃	C₃×C₈₃	direct (N × H)
20. C₈₃	C₂⁵×C₃²	direct (N × H)
21. C₂³×C₃²	C₂²×C₈₃	direct (N × H)
22. C₂⁴×C₃	C₂×C₃×C₈₃	direct (N × H)
23. C₂²×C₃²	C₂³×C₈₃	direct (N × H)
24. C₂⁵	C₃²×C₈₃	direct (N × H)
25. C₂³×C₃	C₂²×C₃×C₈₃	direct (N × H)
26. C₂×C₃²	C₂⁴×C₈₃	direct (N × H)
27. C₂⁴	C₂×C₃²×C₈₃	direct (N × H)
28. C₂²×C₃	C₂³×C₃×C₈₃	direct (N × H)
29. C₃²	C₂⁵×C₈₃	direct (N × H)
30. C₂³	C₂²×C₃²×C₈₃	direct (N × H)
31. C₂×C₃	C₂⁴×C₃×C₈₃	direct (N × H)
32. C₂²	C₂³×C₃²×C₈₃	direct (N × H)
33. C₃	C₂⁵×C₃×C₈₃	direct (N × H)
34. C₂	C₂⁴×C₃²×C₈₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²×C₈₃	2
C₂⁵×C₃×C₈₃	3
C₂⁵×C₃²	83

Subgroups — C25×C32×C83 #72201190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₃²×C₈₃ #72201190