Subgroups — C₂⁴×C₂₅×C₇₃ #72206136

Order 29200.

402 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₅×C₇₃	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₅×C₇₃	C₅	1	1	yes	maximal, characteristic
3	C₂³×C₅×C₇₃	C₂×C₅	1	15	yes	—
4	C₂²×C₂₅×C₇₃	C₂²	1	35	yes	direct product factor
5	C₂×C₂₅×C₇₃	C₂³	1	15	yes	direct product factor
6	C₂₅×C₇₃	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₅×C₇₃	C₂²×C₅	1	35	yes	—
8	C₂⁴×C₇₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₇₃	C₂³×C₅	1	15	yes	—
10	C₂³×C₇₃	C₂×C₂₅	1	15	yes	direct product factor
11	C₂⁴×C₂₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₇₃	C₂⁴×C₅	1	1	yes	characteristic
13	C₂²×C₇₃	C₂²×C₂₅	1	35	yes	direct product factor
14	C₂³×C₂₅	C₂×C₇₃	1	15	yes	direct product factor
15	C₂×C₇₃	C₂³×C₂₅	1	15	yes	direct product factor
16	C₂²×C₂₅	C₂²×C₇₃	1	35	yes	direct product factor
17	C₂⁴×C₅	C₅×C₇₃	1	1	yes	characteristic
18	C₇₃	C₂⁴×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₂₅	C₂³×C₇₃	1	15	yes	direct product factor
20	C₂³×C₅	C₂×C₅×C₇₃	1	15	yes	—
21	C₂₅	C₂⁴×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₅	C₂²×C₅×C₇₃	1	35	yes	—
23	C₂⁴	C₂₅×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₅	C₂³×C₅×C₇₃	1	15	yes	—
25	C₂³	C₂×C₂₅×C₇₃	1	15	yes	direct product factor
26	C₅	C₂⁴×C₅×C₇₃	1	1	yes	characteristic
27	C₂²	C₂²×C₂₅×C₇₃	1	35	yes	direct product factor
28	C₂	C₂³×C₂₅×C₇₃	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂⁴×C₅×C₇₃
socle, prime radical	C₂⁴×C₅×C₇₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂₅×C₇₃	C₂	direct (N × H)
4. C₂²×C₂₅×C₇₃	C₂²	direct (N × H)
5. C₂×C₂₅×C₇₃	C₂³	direct (N × H)
6. C₂₅×C₇₃	C₂⁴	direct (N × H)
8. C₂⁴×C₇₃	C₂₅	direct (N × H)
10. C₂³×C₇₃	C₂×C₂₅	direct (N × H)
11. C₂⁴×C₂₅	C₇₃	direct (N × H)
13. C₂²×C₇₃	C₂²×C₂₅	direct (N × H)
14. C₂³×C₂₅	C₂×C₇₃	direct (N × H)
15. C₂×C₇₃	C₂³×C₂₅	direct (N × H)
16. C₂²×C₂₅	C₂²×C₇₃	direct (N × H)
18. C₇₃	C₂⁴×C₂₅	direct (N × H)
19. C₂×C₂₅	C₂³×C₇₃	direct (N × H)
21. C₂₅	C₂⁴×C₇₃	direct (N × H)
23. C₂⁴	C₂₅×C₇₃	direct (N × H)
25. C₂³	C₂×C₂₅×C₇₃	direct (N × H)
27. C₂²	C₂²×C₂₅×C₇₃	direct (N × H)
28. C₂	C₂³×C₂₅×C₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂₅×C₇₃	2
C₂⁴×C₅×C₇₃	5
C₂⁴×C₂₅	73

Subgroups — C24×C25×C73 #72206136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₂₅×C₇₃ #72206136