Subgroups — C₃²×C₄×C₁₃×C₂₃ #24924505

Order 10764.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₃×C₂₃	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₃×C₂₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	4	yes	—
5	C₄×C₁₃×C₂₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₃	C₃×C₄	1	4	yes	direct product factor
7	C₃²×C₄×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₂₃	C₂×C₃²	1	1	yes	characteristic
9	C₃²×C₄×C₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²×C₂₃	C₂×C₁₃	1	1	yes	characteristic
11	C₁₃×C₂₃	C₃²×C₄	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₄×C₂₃	C₃×C₁₃	1	4	yes	direct product factor
13	C₂×C₃²×C₁₃	C₂×C₂₃	1	1	yes	characteristic
14	C₃²×C₂₃	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₄×C₁₃	C₃×C₂₃	1	4	yes	direct product factor
16	C₂×C₃×C₂₃	C₂×C₃×C₁₃	1	4	yes	—
17	C₃²×C₁₃	C₄×C₂₃	1	1	yes	characteristic, direct product factor, Hall
18	C₄×C₂₃	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	4	yes	—
20	C₃×C₂₃	C₃×C₄×C₁₃	1	4	yes	direct product factor
21	C₄×C₁₃	C₃²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₂₃	C₂×C₃²×C₁₃	1	1	yes	characteristic
23	C₃×C₁₃	C₃×C₄×C₂₃	1	4	yes	direct product factor
24	C₃²×C₄	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₃	C₂×C₃²×C₂₃	1	1	yes	characteristic
26	C₂₃	C₃²×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃²	C₂×C₁₃×C₂₃	1	1	yes	characteristic
28	C₁₃	C₃²×C₄×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₄	C₃×C₁₃×C₂₃	1	4	yes	direct product factor
30	C₃²	C₄×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₃×C₂₃	1	4	yes	—
32	C₄	C₃²×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₃×C₂₃	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₁₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₁₃×C₂₃
socle, prime radical	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₁₃×C₂₃	C₃	direct (N × H)
3. C₃²×C₁₃×C₂₃	C₄	direct (N × H)
5. C₄×C₁₃×C₂₃	C₃²	direct (N × H)
6. C₃×C₁₃×C₂₃	C₃×C₄	direct (N × H)
7. C₃²×C₄×C₂₃	C₁₃	direct (N × H)
9. C₃²×C₄×C₁₃	C₂₃	direct (N × H)
11. C₁₃×C₂₃	C₃²×C₄	direct (N × H)
12. C₃×C₄×C₂₃	C₃×C₁₃	direct (N × H)
14. C₃²×C₂₃	C₄×C₁₃	direct (N × H)
15. C₃×C₄×C₁₃	C₃×C₂₃	direct (N × H)
17. C₃²×C₁₃	C₄×C₂₃	direct (N × H)
18. C₄×C₂₃	C₃²×C₁₃	direct (N × H)
20. C₃×C₂₃	C₃×C₄×C₁₃	direct (N × H)
21. C₄×C₁₃	C₃²×C₂₃	direct (N × H)
23. C₃×C₁₃	C₃×C₄×C₂₃	direct (N × H)
24. C₃²×C₄	C₁₃×C₂₃	direct (N × H)
26. C₂₃	C₃²×C₄×C₁₃	direct (N × H)
28. C₁₃	C₃²×C₄×C₂₃	direct (N × H)
29. C₃×C₄	C₃×C₁₃×C₂₃	direct (N × H)
30. C₃²	C₄×C₁₃×C₂₃	direct (N × H)
32. C₄	C₃²×C₁₃×C₂₃	direct (N × H)
33. C₃	C₃×C₄×C₁₃×C₂₃	direct (N × H)

Subgroups — C32×C4×C13×C23 #24924505

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₄×C₁₃×C₂₃ #24924505