Subgroups — C₂×C₃²×C₅×C₃₅₃ #44540928

Order 31770.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₅₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅×C₃₅₃	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₃₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₃₅₃	C₂×C₃	1	4	yes	direct product factor
5	C₂×C₅×C₃₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₃₅₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₅₃	C₃×C₅	1	4	yes	direct product factor
8	C₅×C₃₅₃	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₃₅₃	C₂×C₃×C₅	1	4	yes	direct product factor
10	C₂×C₃₅₃	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃₅₃	C₂×C₃²×C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃²×C₅	C₃₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅	C₂×C₃₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅	C₃×C₃₅₃	1	4	yes	direct product factor
15	C₂×C₃²	C₅×C₃₅₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅	C₂×C₃×C₃₅₃	1	4	yes	direct product factor
17	C₂×C₅	C₃²×C₃₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃²	C₂×C₅×C₃₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₃×C₅×C₃₅₃	1	4	yes	direct product factor
20	C₅	C₂×C₃²×C₃₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂×C₃×C₅×C₃₅₃	1	4	yes	direct product factor
22	C₂	C₃²×C₅×C₃₅₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₃₅₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₃₅₃	C₃	direct (N × H)
3. C₂×C₃²×C₃₅₃	C₅	direct (N × H)
4. C₃×C₅×C₃₅₃	C₂×C₃	direct (N × H)
5. C₂×C₅×C₃₅₃	C₃²	direct (N × H)
6. C₃²×C₃₅₃	C₂×C₅	direct (N × H)
7. C₂×C₃×C₃₅₃	C₃×C₅	direct (N × H)
8. C₅×C₃₅₃	C₂×C₃²	direct (N × H)
9. C₃×C₃₅₃	C₂×C₃×C₅	direct (N × H)
10. C₂×C₃₅₃	C₃²×C₅	direct (N × H)
11. C₃₅₃	C₂×C₃²×C₅	direct (N × H)
12. C₂×C₃²×C₅	C₃₅₃	direct (N × H)
13. C₃²×C₅	C₂×C₃₅₃	direct (N × H)
14. C₂×C₃×C₅	C₃×C₃₅₃	direct (N × H)
15. C₂×C₃²	C₅×C₃₅₃	direct (N × H)
16. C₃×C₅	C₂×C₃×C₃₅₃	direct (N × H)
17. C₂×C₅	C₃²×C₃₅₃	direct (N × H)
18. C₃²	C₂×C₅×C₃₅₃	direct (N × H)
19. C₂×C₃	C₃×C₅×C₃₅₃	direct (N × H)
20. C₅	C₂×C₃²×C₃₅₃	direct (N × H)
21. C₃	C₂×C₃×C₅×C₃₅₃	direct (N × H)
22. C₂	C₃²×C₅×C₃₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₃₅₃	2
C₂×C₃×C₅×C₃₅₃	3
C₂×C₃²×C₃₅₃	5
C₂×C₃²×C₅	353

Subgroups — C2×C32×C5×C353 #44540928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₃₅₃ #44540928