Subgroups — C₂×C₅×C₇×C₁₃×C₂₇ #72201809

Order 24570.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₂₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₃×C₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₁₃×C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₂₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₅×C₇×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
6	C₅×C₇×C₉×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₇×C₁₃	C₉	1	1	yes	characteristic
8	C₂×C₅×C₇×C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₃×C₂₇	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇×C₉×C₁₃	C₃×C₅	1	1	yes	characteristic
11	C₃×C₅×C₇×C₁₃	C₂×C₉	1	1	yes	characteristic
12	C₂×C₅×C₉×C₁₃	C₃×C₇	1	1	yes	characteristic
13	C₅×C₇×C₂₇	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₇×C₁₃	C₂₇	1	1	yes	characteristic, direct product factor, Hall
15	C₇×C₉×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
16	C₂×C₁₃×C₂₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₇×C₉	C₃×C₁₃	1	1	yes	characteristic
18	C₅×C₉×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic
19	C₂×C₃×C₇×C₁₃	C₅×C₉	1	1	yes	characteristic
20	C₅×C₇×C₁₃	C₂×C₂₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅×C₁₃	C₇×C₉	1	1	yes	characteristic
22	C₂×C₇×C₂₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₁₃×C₂₇	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₇×C₉	C₂×C₃×C₁₃	1	1	yes	characteristic
25	C₃×C₇×C₁₃	C₂×C₅×C₉	1	1	yes	characteristic
26	C₂×C₅×C₂₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₉×C₁₃	C₃×C₅×C₇	1	1	yes	characteristic
28	C₂×C₃×C₅×C₇	C₉×C₁₃	1	1	yes	characteristic
29	C₃×C₅×C₁₃	C₂×C₇×C₉	1	1	yes	characteristic
30	C₇×C₂₇	C₂×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₇×C₁₃	C₅×C₂₇	1	1	yes	characteristic, direct product factor, Hall
32	C₅×C₂₇	C₂×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₅×C₁₃	C₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₇×C₉	C₃×C₅×C₁₃	1	1	yes	characteristic
35	C₉×C₁₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic
36	C₃×C₅×C₇	C₂×C₉×C₁₃	1	1	yes	characteristic
37	C₇×C₁₃	C₂×C₅×C₂₇	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₅×C₉	C₃×C₇×C₁₃	1	1	yes	characteristic
39	C₂×C₃×C₁₃	C₅×C₇×C₉	1	1	yes	characteristic
40	C₂×C₅×C₇	C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
41	C₅×C₁₃	C₂×C₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
42	C₇×C₉	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
43	C₂×C₂₇	C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
44	C₅×C₉	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic
45	C₂×C₃×C₇	C₅×C₉×C₁₃	1	1	yes	characteristic
46	C₃×C₁₃	C₂×C₅×C₇×C₉	1	1	yes	characteristic
47	C₅×C₇	C₂×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₃×C₅	C₇×C₉×C₁₃	1	1	yes	characteristic
49	C₂₇	C₂×C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₁₃	C₅×C₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
51	C₃×C₇	C₂×C₅×C₉×C₁₃	1	1	yes	characteristic
52	C₂×C₉	C₃×C₅×C₇×C₁₃	1	1	yes	characteristic
53	C₃×C₅	C₂×C₇×C₉×C₁₃	1	1	yes	characteristic
54	C₂×C₇	C₅×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
55	C₁₃	C₂×C₅×C₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₅	C₇×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
57	C₉	C₂×C₃×C₅×C₇×C₁₃	1	1	yes	characteristic
58	C₇	C₂×C₅×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₃	C₅×C₇×C₉×C₁₃	1	1	yes	characteristic
60	C₅	C₂×C₇×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
61	C₃	C₂×C₅×C₇×C₉×C₁₃	1	1	yes	characteristic
62	C₂	C₅×C₇×C₁₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₅×C₇×C₁₃
socle, prime radical	C₂×C₃×C₅×C₇×C₁₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₃×C₂₇	C₂	direct (N × H)
2. C₂×C₇×C₁₃×C₂₇	C₅	direct (N × H)
3. C₂×C₅×C₁₃×C₂₇	C₇	direct (N × H)
4. C₇×C₁₃×C₂₇	C₂×C₅	direct (N × H)
8. C₂×C₅×C₇×C₂₇	C₁₃	direct (N × H)
9. C₅×C₁₃×C₂₇	C₂×C₇	direct (N × H)
13. C₅×C₇×C₂₇	C₂×C₁₃	direct (N × H)
14. C₂×C₅×C₇×C₁₃	C₂₇	direct (N × H)
16. C₂×C₁₃×C₂₇	C₅×C₇	direct (N × H)
20. C₅×C₇×C₁₃	C₂×C₂₇	direct (N × H)
22. C₂×C₇×C₂₇	C₅×C₁₃	direct (N × H)
23. C₁₃×C₂₇	C₂×C₅×C₇	direct (N × H)
26. C₂×C₅×C₂₇	C₇×C₁₃	direct (N × H)
30. C₇×C₂₇	C₂×C₅×C₁₃	direct (N × H)
31. C₂×C₇×C₁₃	C₅×C₂₇	direct (N × H)
32. C₅×C₂₇	C₂×C₇×C₁₃	direct (N × H)
33. C₂×C₅×C₁₃	C₇×C₂₇	direct (N × H)
37. C₇×C₁₃	C₂×C₅×C₂₇	direct (N × H)
40. C₂×C₅×C₇	C₁₃×C₂₇	direct (N × H)
41. C₅×C₁₃	C₂×C₇×C₂₇	direct (N × H)
43. C₂×C₂₇	C₅×C₇×C₁₃	direct (N × H)
47. C₅×C₇	C₂×C₁₃×C₂₇	direct (N × H)
49. C₂₇	C₂×C₅×C₇×C₁₃	direct (N × H)
50. C₂×C₁₃	C₅×C₇×C₂₇	direct (N × H)
54. C₂×C₇	C₅×C₁₃×C₂₇	direct (N × H)
55. C₁₃	C₂×C₅×C₇×C₂₇	direct (N × H)
56. C₂×C₅	C₇×C₁₃×C₂₇	direct (N × H)
58. C₇	C₂×C₅×C₁₃×C₂₇	direct (N × H)
60. C₅	C₂×C₇×C₁₃×C₂₇	direct (N × H)
62. C₂	C₅×C₇×C₁₃×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
C₅×C₇×C₁₃×C₂₇	2
C₂×C₇×C₁₃×C₂₇	5
C₂×C₅×C₁₃×C₂₇	7
C₂×C₅×C₇×C₉×C₁₃	3
C₂×C₅×C₇×C₂₇	13

Subgroups — C2×C5×C7×C13×C27 #72201809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₁₃×C₂₇ #72201809