Subgroups — C₃×C₅×C₁₇×C₄₉ #27159727

Order 12495.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₇×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇×C₁₇	C₇	1	1	yes	maximal, characteristic
4	C₁₇×C₄₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₄₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×C₁₇	C₃×C₇	1	1	yes	characteristic
7	C₃×C₇×C₁₇	C₅×C₇	1	1	yes	characteristic
8	C₃×C₅×C₁₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₄₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₄₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₁₇	C₃×C₅×C₇	1	1	yes	characteristic
12	C₃×C₅×C₇	C₇×C₁₇	1	1	yes	characteristic
13	C₅×C₁₇	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₇	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
15	C₄₉	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₇	C₃×C₇×C₁₇	1	1	yes	characteristic
17	C₃×C₇	C₅×C₇×C₁₇	1	1	yes	characteristic
18	C₁₇	C₃×C₅×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
20	C₇	C₃×C₅×C₇×C₁₇	1	1	yes	characteristic
21	C₅	C₃×C₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₅×C₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₃×C₅×C₇×C₁₇
socle, prime radical	C₃×C₅×C₇×C₁₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₄₉	C₃	direct (N × H)
2. C₃×C₁₇×C₄₉	C₅	direct (N × H)
4. C₁₇×C₄₉	C₃×C₅	direct (N × H)
5. C₃×C₅×C₄₉	C₁₇	direct (N × H)
8. C₃×C₅×C₁₇	C₄₉	direct (N × H)
9. C₅×C₄₉	C₃×C₁₇	direct (N × H)
10. C₃×C₄₉	C₅×C₁₇	direct (N × H)
13. C₅×C₁₇	C₃×C₄₉	direct (N × H)
14. C₃×C₁₇	C₅×C₄₉	direct (N × H)
15. C₄₉	C₃×C₅×C₁₇	direct (N × H)
18. C₁₇	C₃×C₅×C₄₉	direct (N × H)
19. C₃×C₅	C₁₇×C₄₉	direct (N × H)
21. C₅	C₃×C₁₇×C₄₉	direct (N × H)
22. C₃	C₅×C₁₇×C₄₉	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×C₁₇×C₄₉	3
C₃×C₁₇×C₄₉	5
C₃×C₅×C₇×C₁₇	7
C₃×C₅×C₄₉	17

Subgroups — C3×C5×C17×C49 #27159727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₇×C₄₉ #27159727