Subgroups — C₃×C₅×C₈×C₁₉₉ #72201166

Order 23880.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₁₉₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₈×C₁₉₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄×C₅×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×C₁₉₉	C₄	1	1	yes	characteristic
5	C₄×C₅×C₁₉₉	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×C₁₉₉	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₄×C₁₉₉	C₂×C₅	1	1	yes	characteristic
8	C₂×C₅×C₁₉₉	C₃×C₄	1	1	yes	characteristic
9	C₈×C₁₉₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₁₉₉	C₄×C₅	1	1	yes	characteristic
11	C₅×C₁₉₉	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₁₉₉	C₂×C₃×C₅	1	1	yes	characteristic
13	C₃×C₁₉₉	C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₉₉	C₃×C₄×C₅	1	1	yes	characteristic
15	C₁₉₉	C₃×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
16	C₃×C₅×C₈	C₁₉₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₄×C₅	C₂×C₁₉₉	1	1	yes	characteristic
18	C₅×C₈	C₃×C₁₉₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₅	C₄×C₁₉₉	1	1	yes	characteristic
20	C₃×C₈	C₅×C₁₉₉	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₅	C₂×C₃×C₁₉₉	1	1	yes	characteristic
22	C₃×C₅	C₈×C₁₉₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₄	C₂×C₅×C₁₉₉	1	1	yes	characteristic
24	C₂×C₅	C₃×C₄×C₁₉₉	1	1	yes	characteristic
25	C₈	C₃×C₅×C₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃	C₄×C₅×C₁₉₉	1	1	yes	characteristic
27	C₅	C₃×C₈×C₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₄	C₂×C₃×C₅×C₁₉₉	1	1	yes	characteristic
29	C₃	C₅×C₈×C₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₄×C₅×C₁₉₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₅×C₁₉₉
socle, prime radical	C₂×C₃×C₅×C₁₉₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₈×C₁₉₉	C₃	direct (N × H)
2. C₃×C₈×C₁₉₉	C₅	direct (N × H)
6. C₃×C₅×C₁₉₉	C₈	direct (N × H)
9. C₈×C₁₉₉	C₃×C₅	direct (N × H)
11. C₅×C₁₉₉	C₃×C₈	direct (N × H)
13. C₃×C₁₉₉	C₅×C₈	direct (N × H)
15. C₁₉₉	C₃×C₅×C₈	direct (N × H)
16. C₃×C₅×C₈	C₁₉₉	direct (N × H)
18. C₅×C₈	C₃×C₁₉₉	direct (N × H)
20. C₃×C₈	C₅×C₁₉₉	direct (N × H)
22. C₃×C₅	C₈×C₁₉₉	direct (N × H)
25. C₈	C₃×C₅×C₁₉₉	direct (N × H)
27. C₅	C₃×C₈×C₁₉₉	direct (N × H)
29. C₃	C₅×C₈×C₁₉₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×C₁₉₉	3
C₃×C₈×C₁₉₉	5
C₃×C₄×C₅×C₁₉₉	2
C₃×C₅×C₈	199

Subgroups — C3×C5×C8×C199 #72201166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₈×C₁₉₉ #72201166