Subgroups — C₂⁵×C₃×C₁₃² #72194202

Order 16224.

11968 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₃²	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₁₃²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂³×C₃×C₁₃²	C₂²	1	155	yes	direct product factor
4	C₂⁴×C₁₃²	C₂×C₃	1	31	yes	direct product factor
5	C₂²×C₃×C₁₃²	C₂³	1	155	yes	direct product factor
6	C₂³×C₁₃²	C₂²×C₃	1	155	yes	direct product factor
7	C₂⁵×C₃×C₁₃	C₁₃	1	14	yes	maximal, direct product factor
8	C₂×C₃×C₁₃²	C₂⁴	1	31	yes	direct product factor
9	C₂²×C₁₃²	C₂³×C₃	1	155	yes	direct product factor
10	C₂⁴×C₃×C₁₃	C₂×C₁₃	1	434	yes	direct product factor
11	C₃×C₁₃²	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
12	C₂⁵×C₁₃	C₃×C₁₃	1	14	yes	direct product factor
13	C₂×C₁₃²	C₂⁴×C₃	1	31	yes	direct product factor
14	C₂³×C₃×C₁₃	C₂²×C₁₃	1	2170	yes	direct product factor
15	C₂⁴×C₁₃	C₂×C₃×C₁₃	1	434	yes	direct product factor
16	C₁₃²	C₂⁵×C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₃×C₁₃	C₂³×C₁₃	1	2170	yes	direct product factor
18	C₂³×C₁₃	C₂²×C₃×C₁₃	1	2170	yes	direct product factor
19	C₂⁵×C₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₁₃	C₂⁴×C₁₃	1	434	yes	direct product factor
21	C₂²×C₁₃	C₂³×C₃×C₁₃	1	2170	yes	direct product factor
22	C₂⁴×C₃	C₂×C₁₃²	1	31	yes	direct product factor
23	C₃×C₁₃	C₂⁵×C₁₃	1	14	yes	direct product factor
24	C₂⁵	C₃×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₃	C₂⁴×C₃×C₁₃	1	434	yes	direct product factor
26	C₂³×C₃	C₂²×C₁₃²	1	155	yes	direct product factor
27	C₂⁴	C₂×C₃×C₁₃²	1	31	yes	direct product factor
28	C₁₃	C₂⁵×C₃×C₁₃	1	14	yes	direct product factor
29	C₂²×C₃	C₂³×C₁₃²	1	155	yes	direct product factor
30	C₂³	C₂²×C₃×C₁₃²	1	155	yes	direct product factor
31	C₂×C₃	C₂⁴×C₁₃²	1	31	yes	direct product factor
32	C₂²	C₂³×C₃×C₁₃²	1	155	yes	direct product factor
33	C₃	C₂⁵×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂⁴×C₃×C₁₃²	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×C₃×C₁₃²	C₂	direct (N × H)
2. C₂⁵×C₁₃²	C₃	direct (N × H)
3. C₂³×C₃×C₁₃²	C₂²	direct (N × H)
4. C₂⁴×C₁₃²	C₂×C₃	direct (N × H)
5. C₂²×C₃×C₁₃²	C₂³	direct (N × H)
6. C₂³×C₁₃²	C₂²×C₃	direct (N × H)
7. C₂⁵×C₃×C₁₃	C₁₃	direct (N × H)
8. C₂×C₃×C₁₃²	C₂⁴	direct (N × H)
9. C₂²×C₁₃²	C₂³×C₃	direct (N × H)
10. C₂⁴×C₃×C₁₃	C₂×C₁₃	direct (N × H)
11. C₃×C₁₃²	C₂⁵	direct (N × H)
12. C₂⁵×C₁₃	C₃×C₁₃	direct (N × H)
13. C₂×C₁₃²	C₂⁴×C₃	direct (N × H)
14. C₂³×C₃×C₁₃	C₂²×C₁₃	direct (N × H)
15. C₂⁴×C₁₃	C₂×C₃×C₁₃	direct (N × H)
16. C₁₃²	C₂⁵×C₃	direct (N × H)
17. C₂²×C₃×C₁₃	C₂³×C₁₃	direct (N × H)
18. C₂³×C₁₃	C₂²×C₃×C₁₃	direct (N × H)
19. C₂⁵×C₃	C₁₃²	direct (N × H)
20. C₂×C₃×C₁₃	C₂⁴×C₁₃	direct (N × H)
21. C₂²×C₁₃	C₂³×C₃×C₁₃	direct (N × H)
22. C₂⁴×C₃	C₂×C₁₃²	direct (N × H)
23. C₃×C₁₃	C₂⁵×C₁₃	direct (N × H)
24. C₂⁵	C₃×C₁₃²	direct (N × H)
25. C₂×C₁₃	C₂⁴×C₃×C₁₃	direct (N × H)
26. C₂³×C₃	C₂²×C₁₃²	direct (N × H)
27. C₂⁴	C₂×C₃×C₁₃²	direct (N × H)
28. C₁₃	C₂⁵×C₃×C₁₃	direct (N × H)
29. C₂²×C₃	C₂³×C₁₃²	direct (N × H)
30. C₂³	C₂²×C₃×C₁₃²	direct (N × H)
31. C₂×C₃	C₂⁴×C₁₃²	direct (N × H)
32. C₂²	C₂³×C₃×C₁₃²	direct (N × H)
33. C₃	C₂⁵×C₁₃²	direct (N × H)
34. C₂	C₂⁴×C₃×C₁₃²	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×C₃×C₁₃²	2
C₂⁵×C₁₃²	3
C₂⁵×C₃×C₁₃	13

Subgroups — C25×C3×C132 #72194202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₃×C₁₃² #72194202