Subgroups — C₂×C₄×C₅×C₁₃×C₂₃ #72190366

Order 11960.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₅×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₁₃×C₂₃	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₅×C₁₃×C₂₃	C₄	1	2	yes	direct product factor
5	C₂×C₅×C₁₃×C₂₃	C₂²	1	1	yes	characteristic
6	C₅×C₁₃×C₂₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₁₃×C₂₃	C₂×C₅	1	1	yes	characteristic
8	C₄×C₁₃×C₂₃	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₄×C₅×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₂₃	C₄×C₅	1	2	yes	direct product factor
11	C₂×C₁₃×C₂₃	C₂²×C₅	1	1	yes	characteristic
12	C₂×C₄×C₅×C₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₂₃	C₂×C₁₃	1	1	yes	characteristic
14	C₄×C₅×C₂₃	C₂×C₁₃	1	2	yes	direct product factor
15	C₁₃×C₂₃	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₅×C₁₃	C₂×C₂₃	1	1	yes	characteristic
17	C₄×C₅×C₁₃	C₂×C₂₃	1	2	yes	direct product factor
18	C₂×C₅×C₂₃	C₄×C₁₃	1	2	yes	direct product factor
19	C₂×C₅×C₂₃	C₂²×C₁₃	1	1	yes	characteristic
20	C₂×C₄×C₂₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₁₃	C₄×C₂₃	1	2	yes	direct product factor
22	C₂×C₅×C₁₃	C₂²×C₂₃	1	1	yes	characteristic
23	C₅×C₂₃	C₂×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₄×C₁₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₂₃	C₂×C₅×C₁₃	1	1	yes	characteristic
26	C₄×C₂₃	C₂×C₅×C₁₃	1	2	yes	direct product factor
27	C₅×C₁₃	C₂×C₄×C₂₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₁₃	C₂×C₅×C₂₃	1	1	yes	characteristic
29	C₄×C₁₃	C₂×C₅×C₂₃	1	2	yes	direct product factor
30	C₂×C₂₃	C₄×C₅×C₁₃	1	2	yes	direct product factor
31	C₂×C₂₃	C₂²×C₅×C₁₃	1	1	yes	characteristic
32	C₂×C₄×C₅	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₃	C₄×C₅×C₂₃	1	2	yes	direct product factor
34	C₂×C₁₃	C₂²×C₅×C₂₃	1	1	yes	characteristic
35	C₂₃	C₂×C₄×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	C₂×C₁₃×C₂₃	1	1	yes	characteristic
37	C₄×C₅	C₂×C₁₃×C₂₃	1	2	yes	direct product factor
38	C₁₃	C₂×C₄×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₅	C₄×C₁₃×C₂₃	1	2	yes	direct product factor
40	C₂×C₅	C₂²×C₁₃×C₂₃	1	1	yes	characteristic
41	C₂×C₄	C₅×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₅	C₂×C₄×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	C₂×C₅×C₁₃×C₂₃	1	1	yes	characteristic
44	C₄	C₂×C₅×C₁₃×C₂₃	1	2	yes	direct product factor
45	C₂	C₄×C₅×C₁₃×C₂₃	1	2	yes	direct product factor
46	C₂	C₂²×C₅×C₁₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅×C₁₃×C₂₃
socle, prime radical	C₂²×C₅×C₁₃×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×C₂₃	C₅	direct (N × H)
3. C₄×C₅×C₁₃×C₂₃	C₂	direct (N × H)
4. C₂×C₅×C₁₃×C₂₃	C₄	direct (N × H)
6. C₅×C₁₃×C₂₃	C₂×C₄	direct (N × H)
8. C₄×C₁₃×C₂₃	C₂×C₅	direct (N × H)
9. C₂×C₄×C₅×C₂₃	C₁₃	direct (N × H)
10. C₂×C₁₃×C₂₃	C₄×C₅	direct (N × H)
12. C₂×C₄×C₅×C₁₃	C₂₃	direct (N × H)
14. C₄×C₅×C₂₃	C₂×C₁₃	direct (N × H)
15. C₁₃×C₂₃	C₂×C₄×C₅	direct (N × H)
17. C₄×C₅×C₁₃	C₂×C₂₃	direct (N × H)
18. C₂×C₅×C₂₃	C₄×C₁₃	direct (N × H)
20. C₂×C₄×C₂₃	C₅×C₁₃	direct (N × H)
21. C₂×C₅×C₁₃	C₄×C₂₃	direct (N × H)
23. C₅×C₂₃	C₂×C₄×C₁₃	direct (N × H)
24. C₂×C₄×C₁₃	C₅×C₂₃	direct (N × H)
26. C₄×C₂₃	C₂×C₅×C₁₃	direct (N × H)
27. C₅×C₁₃	C₂×C₄×C₂₃	direct (N × H)
29. C₄×C₁₃	C₂×C₅×C₂₃	direct (N × H)
30. C₂×C₂₃	C₄×C₅×C₁₃	direct (N × H)
32. C₂×C₄×C₅	C₁₃×C₂₃	direct (N × H)
33. C₂×C₁₃	C₄×C₅×C₂₃	direct (N × H)
35. C₂₃	C₂×C₄×C₅×C₁₃	direct (N × H)
37. C₄×C₅	C₂×C₁₃×C₂₃	direct (N × H)
38. C₁₃	C₂×C₄×C₅×C₂₃	direct (N × H)
39. C₂×C₅	C₄×C₁₃×C₂₃	direct (N × H)
41. C₂×C₄	C₅×C₁₃×C₂₃	direct (N × H)
42. C₅	C₂×C₄×C₁₃×C₂₃	direct (N × H)
44. C₄	C₂×C₅×C₁₃×C₂₃	direct (N × H)
45. C₂	C₄×C₅×C₁₃×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×C₂₃	5
C₂²×C₅×C₁₃×C₂₃	2
C₄×C₅×C₁₃×C₂₃	2
C₂×C₄×C₅×C₂₃	13
C₂×C₄×C₅×C₁₃	23

Subgroups — C2×C4×C5×C13×C23 #72190366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₁₃×C₂₃ #72190366