Subgroups — C₂₃×C₂₅×C₃₂ #72196121

Order 18400.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₂₃×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₃×C₂₅	C₄	1	1	yes	characteristic
3	C₅×C₂₃×C₃₂	C₅	1	1	yes	maximal, characteristic
4	C₄×C₂₃×C₂₅	C₈	1	1	yes	characteristic
5	C₅×C₁₆×C₂₃	C₂×C₅	1	1	yes	characteristic
6	C₂×C₂₃×C₂₅	C₁₆	1	1	yes	characteristic
7	C₅×C₈×C₂₃	C₄×C₅	1	1	yes	characteristic
8	C₂₅×C₃₂	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₃×C₃₂	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂₃×C₂₅	C₃₂	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₅×C₂₃	C₅×C₈	1	1	yes	characteristic
12	C₁₆×C₂₅	C₂×C₂₃	1	1	yes	characteristic
13	C₁₆×C₂₃	C₂×C₂₅	1	1	yes	characteristic
14	C₂×C₅×C₂₃	C₅×C₁₆	1	1	yes	characteristic
15	C₈×C₂₅	C₄×C₂₃	1	1	yes	characteristic
16	C₈×C₂₃	C₄×C₂₅	1	1	yes	characteristic
17	C₅×C₃₂	C₅×C₂₃	1	1	yes	characteristic
18	C₅×C₂₃	C₅×C₃₂	1	1	yes	characteristic
19	C₄×C₂₅	C₈×C₂₃	1	1	yes	characteristic
20	C₄×C₂₃	C₈×C₂₅	1	1	yes	characteristic
21	C₅×C₁₆	C₂×C₅×C₂₃	1	1	yes	characteristic
22	C₂×C₂₅	C₁₆×C₂₃	1	1	yes	characteristic
23	C₂×C₂₃	C₁₆×C₂₅	1	1	yes	characteristic
24	C₅×C₈	C₄×C₅×C₂₃	1	1	yes	characteristic
25	C₃₂	C₂₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂₅	C₂₃×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
27	C₂₃	C₂₅×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
28	C₄×C₅	C₅×C₈×C₂₃	1	1	yes	characteristic
29	C₁₆	C₂×C₂₃×C₂₅	1	1	yes	characteristic
30	C₂×C₅	C₅×C₁₆×C₂₃	1	1	yes	characteristic
31	C₈	C₄×C₂₃×C₂₅	1	1	yes	characteristic
32	C₅	C₅×C₂₃×C₃₂	1	1	yes	characteristic
33	C₄	C₈×C₂₃×C₂₅	1	1	yes	characteristic
34	C₂	C₁₆×C₂₃×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅×C₁₆	C₂×C₅×C₂₃
socle, prime radical	C₂×C₅×C₂₃	C₅×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂₅×C₃₂	C₂₃	direct (N × H)
9. C₂₃×C₃₂	C₂₅	direct (N × H)
10. C₂₃×C₂₅	C₃₂	direct (N × H)
25. C₃₂	C₂₃×C₂₅	direct (N × H)
26. C₂₅	C₂₃×C₃₂	direct (N × H)
27. C₂₃	C₂₅×C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₆×C₂₃×C₂₅	2
C₅×C₂₃×C₃₂	5
C₂₅×C₃₂	23

Subgroups — C23×C25×C32 #72196121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×C₂₅×C₃₂ #72196121