Subgroups — C₄²×C₂₃×C₂₅ #72187939

Order 9200.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₃×C₂₅	C₂	1	3	yes	maximal
2	C₂²×C₂₃×C₂₅	C₂²	1	1	yes	characteristic
3	C₄×C₂₃×C₂₅	C₄	1	6	yes	direct product factor
4	C₄²×C₅×C₂₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₃×C₂₅	C₂×C₄	1	3	yes	—
6	C₂×C₄×C₅×C₂₃	C₂×C₅	1	3	yes	—
7	C₂₃×C₂₅	C₄²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₅×C₂₃	C₂²×C₅	1	1	yes	characteristic
9	C₄×C₅×C₂₃	C₄×C₅	1	6	yes	—
10	C₄²×C₂₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₄²×C₂₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₂₃	C₂×C₄×C₅	1	3	yes	—
13	C₂×C₄×C₂₅	C₂×C₂₃	1	3	yes	—
14	C₂×C₄×C₂₃	C₂×C₂₅	1	3	yes	—
15	C₅×C₂₃	C₄²×C₅	1	1	yes	characteristic
16	C₂²×C₂₅	C₂²×C₂₃	1	1	yes	characteristic
17	C₄×C₂₅	C₄×C₂₃	1	6	yes	direct product factor
18	C₂²×C₂₃	C₂²×C₂₅	1	1	yes	characteristic
19	C₄×C₂₃	C₄×C₂₅	1	6	yes	direct product factor
20	C₄²×C₅	C₅×C₂₃	1	1	yes	characteristic
21	C₂×C₂₅	C₂×C₄×C₂₃	1	3	yes	—
22	C₂×C₂₃	C₂×C₄×C₂₅	1	3	yes	—
23	C₂×C₄×C₅	C₂×C₅×C₂₃	1	3	yes	—
24	C₂₅	C₄²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂₃	C₄²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₂²×C₅×C₂₃	1	1	yes	characteristic
27	C₄×C₅	C₄×C₅×C₂₃	1	6	yes	—
28	C₄²	C₂₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅	C₂×C₄×C₅×C₂₃	1	3	yes	—
30	C₂×C₄	C₂×C₂₃×C₂₅	1	3	yes	—
31	C₅	C₄²×C₅×C₂₃	1	1	yes	characteristic
32	C₂²	C₂²×C₂₃×C₂₅	1	1	yes	characteristic
33	C₄	C₄×C₂₃×C₂₅	1	6	yes	direct product factor
34	C₂	C₂×C₄×C₂₃×C₂₅	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₅	C₂²×C₅×C₂₃
socle, prime radical	C₂²×C₅×C₂₃	C₂²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₂₃×C₂₅	C₄	direct (N × H)
7. C₂₃×C₂₅	C₄²	direct (N × H)
10. C₄²×C₂₅	C₂₃	direct (N × H)
11. C₄²×C₂₃	C₂₅	direct (N × H)
17. C₄×C₂₅	C₄×C₂₃	direct (N × H)
19. C₄×C₂₃	C₄×C₂₅	direct (N × H)
24. C₂₅	C₄²×C₂₃	direct (N × H)
25. C₂₃	C₄²×C₂₅	direct (N × H)
28. C₄²	C₂₃×C₂₅	direct (N × H)
33. C₄	C₄×C₂₃×C₂₅	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×C₄×C₂₃×C₂₅	2
C₄²×C₅×C₂₃	5
C₄²×C₂₅	23

Subgroups — C42×C23×C25 #72187939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₂₃×C₂₅ #72187939