Subgroups — C₂²×C₃×C₂₅×C₁₉⋊C₃ #30685521

Order 17100.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅×C₁₉⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₂₅×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂²×C₃×C₁₉×C₂₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₅×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₃×C₅×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic
6	C₂×C₂₅×C₁₉⋊C₃	C₂×C₃	1	9	yes	direct product factor
7	C₂×C₃×C₁₉×C₂₅	C₂×C₃	1	3	yes	complemented
8	C₂²×C₁₉×C₂₅	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	3	yes	—
10	C₃×C₁₉×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented
11	C₂₅×C₁₉⋊C₃	C₂²×C₃	1	3	yes	direct product factor
12	C₂²×C₃×C₅×C₁₉	C₃×C₅	1	1	yes	characteristic
13	C₂²×C₅×C₁₉⋊C₃	C₃×C₅	1	3	yes	—
14	C₂×C₁₉×C₂₅	C₂×C₃²	1	3	yes	complemented
15	C₂²×C₃²×C₂₅	—	19	1	no	maximal, Hall
16	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic
17	C₂²×C₃×C₁₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	3	yes	—
19	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	1	9	yes	—
20	C₁₉×C₂₅	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃²×C₂₅	—	19	3	no	—
22	C₂²×C₅×C₁₉	C₃²×C₅	1	1	yes	characteristic
23	C₂×C₃×C₁₉⋊C₃	C₂×C₂₅	1	3	yes	direct product factor
24	C₂²×C₃×C₂₅	—	19	3	no	—
25	C₂²×C₃×C₂₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
27	C₅×C₁₉⋊C₃	C₂²×C₃×C₅	1	3	yes	—
28	C₂²×C₃×C₁₉	C₃×C₂₅	1	1	yes	characteristic, complemented
29	C₂²×C₁₉⋊C₃	C₃×C₂₅	1	3	yes	direct product factor
30	C₃²×C₂₅	—	19	1	no	Hall
31	C₂×C₅×C₁₉	C₂×C₃²×C₅	1	3	yes	—
32	C₂²×C₃²×C₅	—	19	1	no	—
33	C₃×C₁₉⋊C₃	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₂₅	—	19	9	no	—
35	C₂×C₃×C₂₅	C₂×C₁₉⋊C₃	1	3	yes	direct product factor
36	C₂×C₃×C₁₉	C₂×C₃×C₂₅	1	3	yes	complemented
37	C₂×C₁₉⋊C₃	C₂×C₃×C₂₅	1	9	yes	direct product factor
38	C₂²×C₂₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
39	C₅×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic
40	C₂×C₃²×C₅	—	19	3	no	—
41	C₂²×C₁₉	C₃²×C₂₅	1	1	yes	characteristic, complemented, Hall
42	C₃×C₂₅	—	19	3	no	—
43	C₃×C₂₅	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
44	C₂²×C₃×C₅	—	19	3	no	—
45	C₂²×C₃×C₅	C₅×C₁₉⋊C₃	1	1	yes	characteristic
46	C₃×C₁₉	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	C₂²×C₃×C₂₅	1	3	yes	direct product factor
48	C₂×C₂₅	C₂×C₃×C₁₉⋊C₃	1	3	yes	direct product factor
49	C₃²×C₅	—	19	1	no	—
50	C₂×C₁₉	C₂×C₃²×C₂₅	1	3	yes	complemented
51	C₂²×C₃²	—	19	1	no	Hall
52	C₂×C₃×C₅	—	19	9	no	—
53	C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	1	3	yes	—
54	C₂₅	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₅	C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic
56	C₁₉	C₂²×C₃²×C₂₅	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃²	—	19	3	no	—
58	C₃×C₅	—	19	3	no	—
59	C₃×C₅	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic
60	C₂²×C₃	—	19	3	no	—
61	C₂²×C₃	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂×C₅	C₂×C₃×C₅×C₁₉⋊C₃	1	3	yes	—
63	C₃²	—	19	1	no	Sylow
64	C₂×C₃	—	19	9	no	—
65	C₂×C₃	C₂×C₂₅×C₁₉⋊C₃	1	3	yes	direct product factor
66	C₅	C₂²×C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic
67	C₂²	C₃×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
68	C₃	—	19	3	no	—
69	C₃	C₂²×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
70	C₂	C₂×C₃×C₂₅×C₁₉⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₂₅	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₃²×C₂₅
Frattini	C₅	C₂²×C₃×C₅×C₁₉⋊C₃
Fitting	C₂²×C₃×C₁₉×C₂₅	C₃
socle	C₂²×C₃×C₅×C₁₉	C₃×C₅
prime radical	C₂²×C₃×C₅×C₁₉⋊C₃	C₅
cosocle	C₅×C₁₉	C₂²×C₃²×C₅
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₅×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂²×C₂₅×C₁₉⋊C₃	C₃	direct (N × H)
3. C₂²×C₃×C₁₉×C₂₅	C₃	semidirect
4. C₃×C₂₅×C₁₉⋊C₃	C₂²	direct (N × H)
6. C₂×C₂₅×C₁₉⋊C₃	C₂×C₃	direct (N × H)
7. C₂×C₃×C₁₉×C₂₅	C₂×C₃	semidirect
8. C₂²×C₁₉×C₂₅	C₃²	semidirect
10. C₃×C₁₉×C₂₅	C₂²×C₃	semidirect
11. C₂₅×C₁₉⋊C₃	C₂²×C₃	direct (N × H)
14. C₂×C₁₉×C₂₅	C₂×C₃²	semidirect
17. C₂²×C₃×C₁₉⋊C₃	C₂₅	direct (N × H)
20. C₁₉×C₂₅	C₂²×C₃²	semidirect
23. C₂×C₃×C₁₉⋊C₃	C₂×C₂₅	direct (N × H)
25. C₂²×C₃×C₂₅	C₁₉⋊C₃	direct (N × H)
28. C₂²×C₃×C₁₉	C₃×C₂₅	semidirect
29. C₂²×C₁₉⋊C₃	C₃×C₂₅	direct (N × H)
33. C₃×C₁₉⋊C₃	C₂²×C₂₅	direct (N × H)
35. C₂×C₃×C₂₅	C₂×C₁₉⋊C₃	direct (N × H)
36. C₂×C₃×C₁₉	C₂×C₃×C₂₅	semidirect
37. C₂×C₁₉⋊C₃	C₂×C₃×C₂₅	direct (N × H)
38. C₂²×C₂₅	C₃×C₁₉⋊C₃	direct (N × H)
41. C₂²×C₁₉	C₃²×C₂₅	semidirect
43. C₃×C₂₅	C₂²×C₁₉⋊C₃	direct (N × H)
46. C₃×C₁₉	C₂²×C₃×C₂₅	semidirect
47. C₁₉⋊C₃	C₂²×C₃×C₂₅	direct (N × H)
48. C₂×C₂₅	C₂×C₃×C₁₉⋊C₃	direct (N × H)
50. C₂×C₁₉	C₂×C₃²×C₂₅	semidirect
54. C₂₅	C₂²×C₃×C₁₉⋊C₃	direct (N × H)
56. C₁₉	C₂²×C₃²×C₂₅	semidirect
61. C₂²×C₃	C₂₅×C₁₉⋊C₃	direct (N × H)
65. C₂×C₃	C₂×C₂₅×C₁₉⋊C₃	direct (N × H)
67. C₂²	C₃×C₂₅×C₁₉⋊C₃	direct (N × H)
69. C₃	C₂²×C₂₅×C₁₉⋊C₃	direct (N × H)
70. C₂	C₂×C₃×C₂₅×C₁₉⋊C₃	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×C₃×C₂₅×C₁₉⋊C₃	2
C₂²×C₂₅×C₁₉⋊C₃	3
C₂²×C₃×C₁₉×C₂₅	3
C₂²×C₃×C₅×C₁₉⋊C₃	5
C₂²×C₃²×C₂₅	19

Subgroups — C22×C3×C25×C19⋊C3 #30685521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₂₅×C₁₉⋊C₃ #30685521