Subgroups — C₄×C₉×C₁₉×C₂₃ #30628539

Order 15732.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₉×C₂₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉×C₂₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₉×C₂₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₉×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₂₃	C₂×C₉	1	1	yes	characteristic
8	C₄×C₉×C₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₉×C₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×C₂₃	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₂₃	C₂×C₁₉	1	1	yes	characteristic
12	C₂×C₉×C₁₉	C₂×C₂₃	1	1	yes	characteristic
13	C₃×C₄×C₂₃	C₃×C₁₉	1	1	yes	characteristic
14	C₃×C₄×C₁₉	C₃×C₂₃	1	1	yes	characteristic
15	C₉×C₂₃	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₉×C₁₉	C₄×C₂₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₂₃	C₂×C₃×C₁₉	1	1	yes	characteristic
18	C₂×C₃×C₁₉	C₂×C₃×C₂₃	1	1	yes	characteristic
19	C₄×C₂₃	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
20	C₄×C₁₉	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₂₃	C₃×C₄×C₁₉	1	1	yes	characteristic
22	C₃×C₁₉	C₃×C₄×C₂₃	1	1	yes	characteristic
23	C₂×C₂₃	C₂×C₉×C₁₉	1	1	yes	characteristic
24	C₂×C₁₉	C₂×C₉×C₂₃	1	1	yes	characteristic
25	C₄×C₉	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂₃	C₄×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₉	C₄×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	C₂×C₁₉×C₂₃	1	1	yes	characteristic
29	C₃×C₄	C₃×C₁₉×C₂₃	1	1	yes	characteristic
30	C₉	C₄×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₉×C₂₃	1	1	yes	characteristic
32	C₄	C₉×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₉×C₂₃	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₉×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₁₉×C₂₃
socle, prime radical	C₂×C₃×C₁₉×C₂₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₉×C₂₃	C₄	direct (N × H)
5. C₄×C₁₉×C₂₃	C₉	direct (N × H)
8. C₄×C₉×C₂₃	C₁₉	direct (N × H)
9. C₄×C₉×C₁₉	C₂₃	direct (N × H)
10. C₁₉×C₂₃	C₄×C₉	direct (N × H)
15. C₉×C₂₃	C₄×C₁₉	direct (N × H)
16. C₉×C₁₉	C₄×C₂₃	direct (N × H)
19. C₄×C₂₃	C₉×C₁₉	direct (N × H)
20. C₄×C₁₉	C₉×C₂₃	direct (N × H)
25. C₄×C₉	C₁₉×C₂₃	direct (N × H)
26. C₂₃	C₄×C₉×C₁₉	direct (N × H)
27. C₁₉	C₄×C₉×C₂₃	direct (N × H)
30. C₉	C₄×C₁₉×C₂₃	direct (N × H)
32. C₄	C₉×C₁₉×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₉×C₂₃	2
C₃×C₄×C₁₉×C₂₃	3
C₄×C₉×C₂₃	19
C₄×C₉×C₁₉	23

Subgroups — C4×C9×C19×C23 #30628539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₁₉×C₂₃ #30628539