Subgroups — C₂²×C₅×C₂₅×C₅₉ #72206402

Order 29500.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₅×C₅₉	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₂₅×C₅₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅²×C₅₉	C₅	1	1	yes	maximal, characteristic
4	C₂²×C₂₅×C₅₉	C₅	1	5	yes	maximal, direct product factor
5	C₂×C₅²×C₅₉	C₂×C₅	1	3	yes	—
6	C₂×C₂₅×C₅₉	C₂×C₅	1	15	yes	direct product factor
7	C₅²×C₅₉	C₂²×C₅	1	1	yes	characteristic
8	C₂₅×C₅₉	C₂²×C₅	1	5	yes	direct product factor
9	C₂²×C₅×C₅₉	C₂₅	1	5	yes	direct product factor
10	C₂²×C₅×C₅₉	C₅²	1	1	yes	characteristic
11	C₂×C₅×C₅₉	C₂×C₂₅	1	15	yes	direct product factor
12	C₂×C₅×C₅₉	C₂×C₅²	1	3	yes	—
13	C₂²×C₅×C₂₅	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₅₉	C₂²×C₂₅	1	5	yes	direct product factor
15	C₅×C₅₉	C₂²×C₅²	1	1	yes	characteristic
16	C₂×C₅×C₂₅	C₂×C₅₉	1	3	yes	direct product factor
17	C₂²×C₅₉	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₂₅	C₂²×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅₉	C₂×C₅×C₂₅	1	3	yes	direct product factor
20	C₂²×C₅²	C₅×C₅₉	1	1	yes	characteristic
21	C₂²×C₂₅	C₅×C₅₉	1	5	yes	direct product factor
22	C₅₉	C₂²×C₅×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₅²	C₂×C₅×C₅₉	1	3	yes	—
24	C₂×C₂₅	C₂×C₅×C₅₉	1	15	yes	direct product factor
25	C₅²	C₂²×C₅×C₅₉	1	1	yes	characteristic
26	C₂₅	C₂²×C₅×C₅₉	1	5	yes	direct product factor
27	C₂²×C₅	C₂₅×C₅₉	1	5	yes	direct product factor
28	C₂²×C₅	C₅²×C₅₉	1	1	yes	characteristic
29	C₂×C₅	C₂×C₂₅×C₅₉	1	15	yes	direct product factor
30	C₂×C₅	C₂×C₅²×C₅₉	1	3	yes	—
31	C₅	C₂²×C₂₅×C₅₉	1	5	yes	direct product factor
32	C₅	C₂²×C₅²×C₅₉	1	1	yes	characteristic
33	C₂²	C₅×C₂₅×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅×C₂₅×C₅₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅²×C₅₉
socle, prime radical	C₂²×C₅²×C₅₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₂₅×C₅₉	C₂	direct (N × H)
2. C₅×C₂₅×C₅₉	C₂²	direct (N × H)
4. C₂²×C₂₅×C₅₉	C₅	direct (N × H)
6. C₂×C₂₅×C₅₉	C₂×C₅	direct (N × H)
8. C₂₅×C₅₉	C₂²×C₅	direct (N × H)
9. C₂²×C₅×C₅₉	C₂₅	direct (N × H)
11. C₂×C₅×C₅₉	C₂×C₂₅	direct (N × H)
13. C₂²×C₅×C₂₅	C₅₉	direct (N × H)
14. C₅×C₅₉	C₂²×C₂₅	direct (N × H)
16. C₂×C₅×C₂₅	C₂×C₅₉	direct (N × H)
17. C₂²×C₅₉	C₅×C₂₅	direct (N × H)
18. C₅×C₂₅	C₂²×C₅₉	direct (N × H)
19. C₂×C₅₉	C₂×C₅×C₂₅	direct (N × H)
21. C₂²×C₂₅	C₅×C₅₉	direct (N × H)
22. C₅₉	C₂²×C₅×C₂₅	direct (N × H)
24. C₂×C₂₅	C₂×C₅×C₅₉	direct (N × H)
26. C₂₅	C₂²×C₅×C₅₉	direct (N × H)
27. C₂²×C₅	C₂₅×C₅₉	direct (N × H)
29. C₂×C₅	C₂×C₂₅×C₅₉	direct (N × H)
31. C₅	C₂²×C₂₅×C₅₉	direct (N × H)
33. C₂²	C₅×C₂₅×C₅₉	direct (N × H)
34. C₂	C₂×C₅×C₂₅×C₅₉	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×C₅×C₂₅×C₅₉	2
C₂²×C₅²×C₅₉	5
C₂²×C₂₅×C₅₉	5
C₂²×C₅×C₂₅	59

Subgroups — C22×C5×C25×C59 #72206402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₂₅×C₅₉ #72206402