Subgroups — C₂×C₇×C₂₇×C₅₃ #72197692

Order 20034.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₇×C₅₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₇×C₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₇×C₉×C₅₃	C₃	1	1	yes	maximal, characteristic
4	C₇×C₉×C₅₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₃×C₇×C₅₃	C₉	1	1	yes	characteristic
6	C₂₇×C₅₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₅₃	C₂×C₉	1	1	yes	characteristic
8	C₂×C₉×C₅₃	C₃×C₇	1	1	yes	characteristic
9	C₂×C₇×C₅₃	C₂₇	1	1	yes	characteristic, direct product factor, Hall
10	C₉×C₅₃	C₂×C₃×C₇	1	1	yes	characteristic
11	C₂×C₇×C₂₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₃	C₂×C₂₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₅₃	C₇×C₉	1	1	yes	characteristic
14	C₇×C₂₇	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅₃	C₂×C₇×C₉	1	1	yes	characteristic
16	C₂×C₇×C₉	C₃×C₅₃	1	1	yes	characteristic
17	C₂×C₅₃	C₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₉	C₂×C₃×C₅₃	1	1	yes	characteristic
19	C₂×C₂₇	C₇×C₅₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅₃	C₂×C₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₃×C₇	C₉×C₅₃	1	1	yes	characteristic
22	C₂₇	C₂×C₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₇	C₂×C₉×C₅₃	1	1	yes	characteristic
24	C₂×C₉	C₃×C₇×C₅₃	1	1	yes	characteristic
25	C₂×C₇	C₂₇×C₅₃	1	1	yes	characteristic, direct product factor, Hall
26	C₉	C₂×C₃×C₇×C₅₃	1	1	yes	characteristic
27	C₇	C₂×C₂₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	C₇×C₉×C₅₃	1	1	yes	characteristic
29	C₃	C₂×C₇×C₉×C₅₃	1	1	yes	characteristic
30	C₂	C₇×C₂₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₇×C₅₃
socle, prime radical	C₂×C₃×C₇×C₅₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₇×C₅₃	C₂	direct (N × H)
2. C₂×C₂₇×C₅₃	C₇	direct (N × H)
6. C₂₇×C₅₃	C₂×C₇	direct (N × H)
9. C₂×C₇×C₅₃	C₂₇	direct (N × H)
11. C₂×C₇×C₂₇	C₅₃	direct (N × H)
12. C₇×C₅₃	C₂×C₂₇	direct (N × H)
14. C₇×C₂₇	C₂×C₅₃	direct (N × H)
17. C₂×C₅₃	C₇×C₂₇	direct (N × H)
19. C₂×C₂₇	C₇×C₅₃	direct (N × H)
20. C₅₃	C₂×C₇×C₂₇	direct (N × H)
22. C₂₇	C₂×C₇×C₅₃	direct (N × H)
25. C₂×C₇	C₂₇×C₅₃	direct (N × H)
27. C₇	C₂×C₂₇×C₅₃	direct (N × H)
30. C₂	C₇×C₂₇×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₇×C₅₃	2
C₂×C₂₇×C₅₃	7
C₂×C₇×C₉×C₅₃	3
C₂×C₇×C₂₇	53

Subgroups — C2×C7×C27×C53 #72197692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₇×C₅₃ #72197692