Subgroups — C₂³×C₉×C₁₃×C₂₃ #72199049

Order 21528.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₂₃	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₉×C₁₃×C₂₃	C₂	1	7	yes	maximal, direct product factor
4	C₂×C₉×C₁₃×C₂₃	C₂²	1	7	yes	direct product factor
5	C₂²×C₃×C₁₃×C₂₃	C₂×C₃	1	7	yes	—
6	C₉×C₁₃×C₂₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₁₃×C₂₃	C₂²×C₃	1	7	yes	—
8	C₂³×C₉×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₁₃×C₂₃	C₂×C₉	1	7	yes	direct product factor
10	C₂³×C₉×C₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₃×C₂₃	C₂³×C₃	1	1	yes	characteristic
12	C₂²×C₉×C₂₃	C₂×C₁₃	1	7	yes	direct product factor
13	C₂×C₁₃×C₂₃	C₂²×C₉	1	7	yes	direct product factor
14	C₂³×C₃×C₂₃	C₃×C₁₃	1	1	yes	characteristic
15	C₂²×C₉×C₁₃	C₂×C₂₃	1	7	yes	direct product factor
16	C₂×C₉×C₂₃	C₂²×C₁₃	1	7	yes	direct product factor
17	C₂³×C₃×C₁₃	C₃×C₂₃	1	1	yes	characteristic
18	C₁₃×C₂₃	C₂³×C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₃×C₂₃	C₂×C₃×C₁₃	1	7	yes	—
20	C₂×C₉×C₁₃	C₂²×C₂₃	1	7	yes	direct product factor
21	C₉×C₂₃	C₂³×C₁₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂³×C₂₃	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₃×C₁₃	C₂×C₃×C₂₃	1	7	yes	—
24	C₂×C₃×C₂₃	C₂²×C₃×C₁₃	1	7	yes	—
25	C₉×C₁₃	C₂³×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂³×C₁₃	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂²×C₂₃	C₂×C₉×C₁₃	1	7	yes	direct product factor
28	C₂×C₃×C₁₃	C₂²×C₃×C₂₃	1	7	yes	—
29	C₂³×C₉	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₂₃	C₂³×C₃×C₁₃	1	1	yes	characteristic
31	C₂²×C₁₃	C₂×C₉×C₂₃	1	7	yes	direct product factor
32	C₂×C₂₃	C₂²×C₉×C₁₃	1	7	yes	direct product factor
33	C₃×C₁₃	C₂³×C₃×C₂₃	1	1	yes	characteristic
34	C₂²×C₉	C₂×C₁₃×C₂₃	1	7	yes	direct product factor
35	C₂×C₁₃	C₂²×C₉×C₂₃	1	7	yes	direct product factor
36	C₂³×C₃	C₃×C₁₃×C₂₃	1	1	yes	characteristic
37	C₂₃	C₂³×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₉	C₂²×C₁₃×C₂₃	1	7	yes	direct product factor
39	C₁₃	C₂³×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²×C₃	C₂×C₃×C₁₃×C₂₃	1	7	yes	—
41	C₉	C₂³×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³	C₉×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₂²×C₃×C₁₃×C₂₃	1	7	yes	—
44	C₂²	C₂×C₉×C₁₃×C₂₃	1	7	yes	direct product factor
45	C₃	C₂³×C₃×C₁₃×C₂₃	1	1	yes	characteristic
46	C₂	C₂²×C₉×C₁₃×C₂₃	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₁₃×C₂₃
socle, prime radical	C₂³×C₃×C₁₃×C₂₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₁₃×C₂₃	C₉	direct (N × H)
3. C₂²×C₉×C₁₃×C₂₃	C₂	direct (N × H)
4. C₂×C₉×C₁₃×C₂₃	C₂²	direct (N × H)
6. C₉×C₁₃×C₂₃	C₂³	direct (N × H)
8. C₂³×C₉×C₂₃	C₁₃	direct (N × H)
9. C₂²×C₁₃×C₂₃	C₂×C₉	direct (N × H)
10. C₂³×C₉×C₁₃	C₂₃	direct (N × H)
12. C₂²×C₉×C₂₃	C₂×C₁₃	direct (N × H)
13. C₂×C₁₃×C₂₃	C₂²×C₉	direct (N × H)
15. C₂²×C₉×C₁₃	C₂×C₂₃	direct (N × H)
16. C₂×C₉×C₂₃	C₂²×C₁₃	direct (N × H)
18. C₁₃×C₂₃	C₂³×C₉	direct (N × H)
20. C₂×C₉×C₁₃	C₂²×C₂₃	direct (N × H)
21. C₉×C₂₃	C₂³×C₁₃	direct (N × H)
22. C₂³×C₂₃	C₉×C₁₃	direct (N × H)
25. C₉×C₁₃	C₂³×C₂₃	direct (N × H)
26. C₂³×C₁₃	C₉×C₂₃	direct (N × H)
27. C₂²×C₂₃	C₂×C₉×C₁₃	direct (N × H)
29. C₂³×C₉	C₁₃×C₂₃	direct (N × H)
31. C₂²×C₁₃	C₂×C₉×C₂₃	direct (N × H)
32. C₂×C₂₃	C₂²×C₉×C₁₃	direct (N × H)
34. C₂²×C₉	C₂×C₁₃×C₂₃	direct (N × H)
35. C₂×C₁₃	C₂²×C₉×C₂₃	direct (N × H)
37. C₂₃	C₂³×C₉×C₁₃	direct (N × H)
38. C₂×C₉	C₂²×C₁₃×C₂₃	direct (N × H)
39. C₁₃	C₂³×C₉×C₂₃	direct (N × H)
41. C₉	C₂³×C₁₃×C₂₃	direct (N × H)
42. C₂³	C₉×C₁₃×C₂₃	direct (N × H)
44. C₂²	C₂×C₉×C₁₃×C₂₃	direct (N × H)
46. C₂	C₂²×C₉×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
C₂³×C₃×C₁₃×C₂₃	3
C₂²×C₉×C₁₃×C₂₃	2
C₂³×C₉×C₂₃	13
C₂³×C₉×C₁₃	23

Subgroups — C23×C9×C13×C23 #72199049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₉×C₁₃×C₂₃ #72199049