Subgroups — C₅×C₁₁×C₁₇×C₂₇ #72202471

Order 25245.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₁₇×C₂₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₉×C₁₁×C₁₇	C₃	1	1	yes	maximal, characteristic
4	C₃×C₅×C₁₁×C₁₇	C₉	1	1	yes	characteristic
5	C₉×C₁₁×C₁₇	C₃×C₅	1	1	yes	characteristic
6	C₅×C₁₁×C₂₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₇	C₂₇	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₉×C₁₇	C₃×C₁₁	1	1	yes	characteristic
9	C₃×C₁₁×C₁₇	C₅×C₉	1	1	yes	characteristic
10	C₅×C₉×C₁₁	C₃×C₁₇	1	1	yes	characteristic
11	C₁₇×C₂₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×C₂₇	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₁₇	C₉×C₁₁	1	1	yes	characteristic
14	C₁₁×C₁₇	C₅×C₂₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₁₁	C₉×C₁₇	1	1	yes	characteristic
16	C₉×C₁₇	C₃×C₅×C₁₁	1	1	yes	characteristic
17	C₅×C₂₇	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₉×C₁₁	C₃×C₅×C₁₇	1	1	yes	characteristic
19	C₅×C₁₇	C₁₁×C₂₇	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₁	C₁₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₇	C₅×C₉×C₁₁	1	1	yes	characteristic
22	C₅×C₉	C₃×C₁₁×C₁₇	1	1	yes	characteristic
23	C₃×C₁₁	C₅×C₉×C₁₇	1	1	yes	characteristic
24	C₂₇	C₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₁₇	C₅×C₁₁×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₅	C₉×C₁₁×C₁₇	1	1	yes	characteristic
27	C₁₁	C₅×C₁₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₉	C₃×C₅×C₁₁×C₁₇	1	1	yes	characteristic
29	C₅	C₁₁×C₁₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₃	C₅×C₉×C₁₁×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃×C₅×C₁₁×C₁₇
socle, prime radical	C₃×C₅×C₁₁×C₁₇	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₂₇	C₅	direct (N × H)
2. C₅×C₁₇×C₂₇	C₁₁	direct (N × H)
6. C₅×C₁₁×C₂₇	C₁₇	direct (N × H)
7. C₅×C₁₁×C₁₇	C₂₇	direct (N × H)
11. C₁₇×C₂₇	C₅×C₁₁	direct (N × H)
12. C₁₁×C₂₇	C₅×C₁₇	direct (N × H)
14. C₁₁×C₁₇	C₅×C₂₇	direct (N × H)
17. C₅×C₂₇	C₁₁×C₁₇	direct (N × H)
19. C₅×C₁₇	C₁₁×C₂₇	direct (N × H)
20. C₅×C₁₁	C₁₇×C₂₇	direct (N × H)
24. C₂₇	C₅×C₁₁×C₁₇	direct (N × H)
25. C₁₇	C₅×C₁₁×C₂₇	direct (N × H)
27. C₁₁	C₅×C₁₇×C₂₇	direct (N × H)
29. C₅	C₁₁×C₁₇×C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×C₂₇	5
C₅×C₁₇×C₂₇	11
C₅×C₉×C₁₁×C₁₇	3
C₅×C₁₁×C₂₇	17

Subgroups — C5×C11×C17×C27 #72202471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×C₁₇×C₂₇ #72202471