Subgroups — C₃×C₅×C₂₇×C₅₉ #72201170

Order 23895.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₉×C₅₉	C₃	1	1	yes	maximal, characteristic
2	C₅×C₂₇×C₅₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂₇×C₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₅×C₅₉	C₉	1	1	yes	characteristic
5	C₅×C₉×C₅₉	C₉	1	2	yes	—
6	C₅×C₉×C₅₉	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₅₉	C₃×C₅	1	1	yes	characteristic
8	C₂₇×C₅₉	C₃×C₅	1	3	yes	direct product factor
9	C₃×C₅×C₅₉	C₂₇	1	3	yes	direct product factor
10	C₃×C₅×C₅₉	C₃×C₉	1	1	yes	characteristic
11	C₃²×C₅₉	C₅×C₉	1	1	yes	characteristic
12	C₉×C₅₉	C₅×C₉	1	2	yes	—
13	C₉×C₅₉	C₃²×C₅	1	1	yes	characteristic
14	C₃×C₅×C₂₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₅₉	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅₉	C₅×C₂₇	1	3	yes	direct product factor
17	C₃×C₅₉	C₃×C₅×C₉	1	1	yes	characteristic
18	C₃×C₅×C₉	C₃×C₅₉	1	1	yes	characteristic
19	C₅×C₂₇	C₃×C₅₉	1	3	yes	direct product factor
20	C₃×C₂₇	C₅×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₅₉	C₃×C₅×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₃²×C₅	C₉×C₅₉	1	1	yes	characteristic
23	C₅×C₉	C₉×C₅₉	1	2	yes	—
24	C₅×C₉	C₃²×C₅₉	1	1	yes	characteristic
25	C₃×C₉	C₃×C₅×C₅₉	1	1	yes	characteristic
26	C₂₇	C₃×C₅×C₅₉	1	3	yes	direct product factor
27	C₃×C₅	C₂₇×C₅₉	1	3	yes	direct product factor
28	C₃×C₅	C₃×C₉×C₅₉	1	1	yes	characteristic
29	C₃²	C₅×C₉×C₅₉	1	1	yes	characteristic
30	C₉	C₅×C₉×C₅₉	1	2	yes	—
31	C₉	C₃²×C₅×C₅₉	1	1	yes	characteristic
32	C₅	C₃×C₂₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×C₂₇×C₅₉	1	3	yes	direct product factor
34	C₃	C₃×C₅×C₉×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃²×C₅×C₅₉
socle, prime radical	C₃²×C₅×C₅₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₂₇×C₅₉	C₃	direct (N × H)
3. C₃×C₂₇×C₅₉	C₅	direct (N × H)
8. C₂₇×C₅₉	C₃×C₅	direct (N × H)
9. C₃×C₅×C₅₉	C₂₇	direct (N × H)
14. C₃×C₅×C₂₇	C₅₉	direct (N × H)
15. C₅×C₅₉	C₃×C₂₇	direct (N × H)
16. C₃×C₅₉	C₅×C₂₇	direct (N × H)
19. C₅×C₂₇	C₃×C₅₉	direct (N × H)
20. C₃×C₂₇	C₅×C₅₉	direct (N × H)
21. C₅₉	C₃×C₅×C₂₇	direct (N × H)
26. C₂₇	C₃×C₅×C₅₉	direct (N × H)
27. C₃×C₅	C₂₇×C₅₉	direct (N × H)
32. C₅	C₃×C₂₇×C₅₉	direct (N × H)
33. C₃	C₅×C₂₇×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₉×C₅₉	3
C₅×C₂₇×C₅₉	3
C₃×C₂₇×C₅₉	5
C₃×C₅×C₂₇	59

Subgroups — C3×C5×C27×C59 #72201170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₂₇×C₅₉ #72201170