Subgroups — C₃²×C₄×C₅²×C₁₉ #30685629

Order 17100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅²×C₁₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₃²×C₄×C₅×C₁₉	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	4	yes	—
6	C₄×C₅²×C₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₅×C₁₉	C₂×C₅	1	6	yes	—
8	C₃×C₅²×C₁₉	C₃×C₄	1	4	yes	direct product factor
9	C₃×C₄×C₅×C₁₉	C₃×C₅	1	24	yes	direct product factor
10	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₄×C₅²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₅×C₁₉	C₄×C₅	1	6	yes	direct product factor
13	C₃²×C₄×C₁₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	24	yes	—
15	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃²×C₅²	C₂×C₁₉	1	1	yes	characteristic
17	C₄×C₅×C₁₉	C₃²×C₅	1	6	yes	direct product factor
18	C₂×C₃²×C₁₉	C₂×C₅²	1	1	yes	characteristic
19	C₃×C₄×C₅²	C₃×C₁₉	1	4	yes	direct product factor
20	C₃×C₅×C₁₉	C₃×C₄×C₅	1	24	yes	direct product factor
21	C₃×C₄×C₁₉	C₃×C₅²	1	4	yes	direct product factor
22	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₁₉	C₂×C₃²×C₅	1	6	yes	—
24	C₃²×C₄×C₅	C₅×C₁₉	1	6	yes	direct product factor
25	C₃²×C₁₉	C₄×C₅²	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃×C₅²	C₂×C₃×C₁₉	1	4	yes	—
27	C₂×C₃×C₁₉	C₂×C₃×C₅²	1	4	yes	—
28	C₄×C₅²	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₉	C₃²×C₄×C₅	1	6	yes	direct product factor
30	C₂×C₃²×C₅	C₂×C₅×C₁₉	1	6	yes	—
31	C₄×C₁₉	C₃²×C₅²	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₅²	C₃×C₄×C₁₉	1	4	yes	direct product factor
33	C₃×C₄×C₅	C₃×C₅×C₁₉	1	24	yes	direct product factor
34	C₃×C₁₉	C₃×C₄×C₅²	1	4	yes	direct product factor
35	C₂×C₅²	C₂×C₃²×C₁₉	1	1	yes	characteristic
36	C₃²×C₅	C₄×C₅×C₁₉	1	6	yes	direct product factor
37	C₂×C₁₉	C₂×C₃²×C₅²	1	1	yes	characteristic
38	C₃²×C₄	C₅²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	1	24	yes	—
40	C₅²	C₃²×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₄×C₅	C₃²×C₅×C₁₉	1	6	yes	direct product factor
42	C₁₉	C₃²×C₄×C₅²	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃²	C₂×C₅²×C₁₉	1	1	yes	characteristic
44	C₃×C₅	C₃×C₄×C₅×C₁₉	1	24	yes	direct product factor
45	C₃×C₄	C₃×C₅²×C₁₉	1	4	yes	direct product factor
46	C₂×C₅	C₂×C₃²×C₅×C₁₉	1	6	yes	—
47	C₃²	C₄×C₅²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	C₂×C₃×C₅²×C₁₉	1	4	yes	—
49	C₅	C₃²×C₄×C₅×C₁₉	1	6	yes	direct product factor
50	C₄	C₃²×C₅²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₃×C₄×C₅²×C₁₉	1	4	yes	direct product factor
52	C₂	C₂×C₃²×C₅²×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₅²×C₁₉
socle, prime radical	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅²×C₁₉	C₃	direct (N × H)
3. C₃²×C₅²×C₁₉	C₄	direct (N × H)
4. C₃²×C₄×C₅×C₁₉	C₅	direct (N × H)
6. C₄×C₅²×C₁₉	C₃²	direct (N × H)
8. C₃×C₅²×C₁₉	C₃×C₄	direct (N × H)
9. C₃×C₄×C₅×C₁₉	C₃×C₅	direct (N × H)
11. C₃²×C₄×C₅²	C₁₉	direct (N × H)
12. C₃²×C₅×C₁₉	C₄×C₅	direct (N × H)
13. C₃²×C₄×C₁₉	C₅²	direct (N × H)
15. C₅²×C₁₉	C₃²×C₄	direct (N × H)
17. C₄×C₅×C₁₉	C₃²×C₅	direct (N × H)
19. C₃×C₄×C₅²	C₃×C₁₉	direct (N × H)
20. C₃×C₅×C₁₉	C₃×C₄×C₅	direct (N × H)
21. C₃×C₄×C₁₉	C₃×C₅²	direct (N × H)
22. C₃²×C₅²	C₄×C₁₉	direct (N × H)
24. C₃²×C₄×C₅	C₅×C₁₉	direct (N × H)
25. C₃²×C₁₉	C₄×C₅²	direct (N × H)
28. C₄×C₅²	C₃²×C₁₉	direct (N × H)
29. C₅×C₁₉	C₃²×C₄×C₅	direct (N × H)
31. C₄×C₁₉	C₃²×C₅²	direct (N × H)
32. C₃×C₅²	C₃×C₄×C₁₉	direct (N × H)
33. C₃×C₄×C₅	C₃×C₅×C₁₉	direct (N × H)
34. C₃×C₁₉	C₃×C₄×C₅²	direct (N × H)
36. C₃²×C₅	C₄×C₅×C₁₉	direct (N × H)
38. C₃²×C₄	C₅²×C₁₉	direct (N × H)
40. C₅²	C₃²×C₄×C₁₉	direct (N × H)
41. C₄×C₅	C₃²×C₅×C₁₉	direct (N × H)
42. C₁₉	C₃²×C₄×C₅²	direct (N × H)
44. C₃×C₅	C₃×C₄×C₅×C₁₉	direct (N × H)
45. C₃×C₄	C₃×C₅²×C₁₉	direct (N × H)
47. C₃²	C₄×C₅²×C₁₉	direct (N × H)
49. C₅	C₃²×C₄×C₅×C₁₉	direct (N × H)
50. C₄	C₃²×C₅²×C₁₉	direct (N × H)
51. C₃	C₃×C₄×C₅²×C₁₉	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×C₃²×C₅²×C₁₉	2
C₃×C₄×C₅²×C₁₉	3
C₃²×C₄×C₅×C₁₉	5
C₃²×C₄×C₅²	19

Subgroups — C32×C4×C52×C19 #30685629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×C₅²×C₁₉ #30685629