Subgroups — C₂²×C₄×C₅×C₂₈₁ #72199895

Order 22480.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₂₈₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₂₈₁	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅×C₂₈₁	C₄	1	4	yes	direct product factor
4	C₂²×C₅×C₂₈₁	C₂²	1	3	yes	—
5	C₄×C₅×C₂₈₁	C₂²	1	4	yes	direct product factor
6	C₂²×C₄×C₂₈₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₂₈₁	C₂×C₄	1	6	yes	direct product factor
8	C₂×C₅×C₂₈₁	C₂³	1	1	yes	characteristic
9	C₂³×C₂₈₁	C₂×C₅	1	1	yes	characteristic
10	C₂×C₄×C₂₈₁	C₂×C₅	1	6	yes	direct product factor
11	C₅×C₂₈₁	C₂²×C₄	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₂₈₁	C₄×C₅	1	4	yes	direct product factor
13	C₂²×C₂₈₁	C₂²×C₅	1	3	yes	—
14	C₄×C₂₈₁	C₂²×C₅	1	4	yes	direct product factor
15	C₂×C₂₈₁	C₂×C₄×C₅	1	6	yes	direct product factor
16	C₂×C₂₈₁	C₂³×C₅	1	1	yes	characteristic
17	C₂₈₁	C₂²×C₄×C₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₄×C₅	C₂₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂³×C₅	C₂×C₂₈₁	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂×C₂₈₁	1	6	yes	direct product factor
21	C₂²×C₅	C₄×C₂₈₁	1	4	yes	direct product factor
22	C₂²×C₅	C₂²×C₂₈₁	1	3	yes	—
23	C₄×C₅	C₂²×C₂₈₁	1	4	yes	direct product factor
24	C₂²×C₄	C₅×C₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₂×C₄×C₂₈₁	1	6	yes	direct product factor
26	C₂×C₅	C₂³×C₂₈₁	1	1	yes	characteristic
27	C₂³	C₂×C₅×C₂₈₁	1	1	yes	characteristic
28	C₂×C₄	C₂×C₅×C₂₈₁	1	6	yes	direct product factor
29	C₅	C₂²×C₄×C₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₄×C₅×C₂₈₁	1	4	yes	direct product factor
31	C₂²	C₂²×C₅×C₂₈₁	1	3	yes	—
32	C₄	C₂²×C₅×C₂₈₁	1	4	yes	direct product factor
33	C₂	C₂×C₄×C₅×C₂₈₁	1	6	yes	direct product factor
34	C₂	C₂³×C₅×C₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₅×C₂₈₁
socle, prime radical	C₂³×C₅×C₂₈₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×C₂₈₁	C₂	direct (N × H)
3. C₂²×C₅×C₂₈₁	C₄	direct (N × H)
5. C₄×C₅×C₂₈₁	C₂²	direct (N × H)
6. C₂²×C₄×C₂₈₁	C₅	direct (N × H)
7. C₂×C₅×C₂₈₁	C₂×C₄	direct (N × H)
10. C₂×C₄×C₂₈₁	C₂×C₅	direct (N × H)
11. C₅×C₂₈₁	C₂²×C₄	direct (N × H)
12. C₂²×C₂₈₁	C₄×C₅	direct (N × H)
14. C₄×C₂₈₁	C₂²×C₅	direct (N × H)
15. C₂×C₂₈₁	C₂×C₄×C₅	direct (N × H)
17. C₂₈₁	C₂²×C₄×C₅	direct (N × H)
18. C₂²×C₄×C₅	C₂₈₁	direct (N × H)
20. C₂×C₄×C₅	C₂×C₂₈₁	direct (N × H)
21. C₂²×C₅	C₄×C₂₈₁	direct (N × H)
23. C₄×C₅	C₂²×C₂₈₁	direct (N × H)
24. C₂²×C₄	C₅×C₂₈₁	direct (N × H)
25. C₂×C₅	C₂×C₄×C₂₈₁	direct (N × H)
28. C₂×C₄	C₂×C₅×C₂₈₁	direct (N × H)
29. C₅	C₂²×C₄×C₂₈₁	direct (N × H)
30. C₂²	C₄×C₅×C₂₈₁	direct (N × H)
32. C₄	C₂²×C₅×C₂₈₁	direct (N × H)
33. C₂	C₂×C₄×C₅×C₂₈₁	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×C₅×C₂₈₁	2
C₂×C₄×C₅×C₂₈₁	2
C₂²×C₄×C₂₈₁	5
C₂²×C₄×C₅	281

Subgroups — C22×C4×C5×C281 #72199895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₅×C₂₈₁ #72199895