Subgroups — C₂×C₃×C₂₅×D₁₉⋊C₃ #30685477

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	1	yes	maximal, characteristic, complemented
2	C₃×C₂₅×D₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₂₅×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₅×D₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₂₅×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic
7	C₃×C₂₅×D₁₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₂₅×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₂₅×D₁₉⋊C₃	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₁₉×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₂₅×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic
13	C₃×C₅×D₁₉⋊C₃	C₂×C₅	1	2	yes	—
14	C₃×C₁₉×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂₅×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
16	C₂×C₃×C₅×D₁₉	C₃×C₅	1	1	yes	characteristic
17	C₂×C₅×D₁₉⋊C₃	C₃×C₅	1	3	yes	—
18	C₂×C₁₉×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₂₅×D₁₉	C₂×C₃²	1	2	yes	complemented
20	C₂²×C₃²×C₂₅	—	19	1	no	maximal, Hall
21	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic
22	C₂×C₃×D₁₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
24	C₃×C₅×D₁₉	C₂×C₃×C₅	1	2	yes	—
25	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	1	3	yes	—
26	C₅×D₁₉⋊C₃	C₂×C₃×C₅	1	6	yes	—
27	C₁₉×C₂₅	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃²×C₂₅	—	19	2	no	—
29	C₂×C₃²×C₂₅	—	19	1	no	—
30	C₂×C₅×D₁₉	C₃²×C₅	1	1	yes	characteristic
31	C₂×C₃×C₁₉⋊C₃	C₂×C₂₅	1	1	yes	characteristic, complemented
32	C₃×D₁₉⋊C₃	C₂×C₂₅	1	2	yes	direct product factor
33	C₂²×C₃×C₂₅	—	19	3	no	—
34	C₂²×C₃×C₂₅	—	19	1	no	—
35	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
36	C₅×C₁₉⋊C₃	C₂²×C₃×C₅	1	3	yes	—
37	C₂×C₃×D₁₉	C₃×C₂₅	1	1	yes	characteristic, complemented
38	C₂×D₁₉⋊C₃	C₃×C₂₅	1	3	yes	direct product factor
39	C₃²×C₂₅	—	19	1	no	Hall
40	C₂×C₅×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic
41	C₅×D₁₉	C₂×C₃²×C₅	1	2	yes	—
42	C₂²×C₃²×C₅	—	19	1	no	—
43	C₃×C₁₉⋊C₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₂₅	—	19	6	no	—
45	C₂×C₃×C₂₅	—	19	3	no	—
46	C₂×C₃×C₂₅	—	19	2	no	—
47	C₂×C₃×C₂₅	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₁₉	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
49	C₃×D₁₉	C₂×C₃×C₂₅	1	2	yes	complemented
50	C₂×C₁₉⋊C₃	C₂×C₃×C₂₅	1	3	yes	complemented
51	D₁₉⋊C₃	C₂×C₃×C₂₅	1	6	yes	direct product factor
52	C₂²×C₂₅	—	19	1	no	Hall
53	C₅×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic
54	C₂×C₃²×C₅	—	19	2	no	—
55	C₂×C₃²×C₅	—	19	1	no	—
56	C₂×D₁₉	C₃²×C₂₅	1	1	yes	characteristic, complemented, Hall
57	C₃×C₂₅	—	19	3	no	—
58	C₃×C₂₅	C₂×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
59	C₂²×C₃×C₅	—	19	3	no	—
60	C₂²×C₃×C₅	—	19	1	no	—
61	C₃×C₁₉	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented
62	C₁₉⋊C₃	C₂²×C₃×C₂₅	1	3	yes	complemented
63	C₂×C₂₅	—	19	2	no	—
64	C₂×C₂₅	C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
65	C₃²×C₅	—	19	1	no	—
66	C₂×C₁₉	C₂×C₃²×C₂₅	1	1	yes	characteristic, complemented
67	D₁₉	C₂×C₃²×C₂₅	1	2	yes	complemented
68	C₂²×C₃²	—	19	1	no	Hall
69	C₂×C₃×C₅	—	19	6	no	—
70	C₂×C₃×C₅	—	19	2	no	—
71	C₂×C₃×C₅	—	19	3	no	—
72	C₂×C₃×C₅	C₅×D₁₉⋊C₃	1	1	yes	characteristic
73	C₂₅	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₅	—	19	1	no	—
75	C₁₉	C₂²×C₃²×C₂₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃²	—	19	2	no	—
77	C₂×C₃²	—	19	1	no	—
78	C₃×C₅	—	19	3	no	—
79	C₃×C₅	C₂×C₅×D₁₉⋊C₃	1	1	yes	characteristic
80	C₂²×C₃	—	19	3	no	—
81	C₂²×C₃	—	19	1	no	—
82	C₂×C₅	—	19	2	no	—
83	C₂×C₅	C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic
84	C₃²	—	19	1	no	Sylow
85	C₂×C₃	—	19	6	no	—
86	C₂×C₃	—	19	2	no	—
87	C₂×C₃	—	19	3	no	—
88	C₂×C₃	C₂₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
89	C₅	C₂×C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic
90	C₂²	—	19	1	no	Sylow
91	C₃	—	19	3	no	—
92	C₃	C₂×C₂₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
93	C₂	—	19	2	no	—
94	C₂	C₃×C₂₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₅	D₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₃²×C₂₅
Frattini	C₅	C₂×C₃×C₅×D₁₉⋊C₃
Fitting	C₂×C₃×C₁₉×C₂₅	C₂×C₃
socle	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅
prime radical	C₂×C₃×C₅×D₁₉⋊C₃	C₅
cosocle	C₅×C₁₉	C₂²×C₃²×C₅
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×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	semidirect
2. C₃×C₂₅×D₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₂₅×D₁₉	C₃	semidirect
4. C₂×C₂₅×D₁₉⋊C₃	C₃	direct (N × H)
5. C₃×C₂₅×C₁₉⋊C₃	C₂²	semidirect
7. C₃×C₂₅×D₁₉	C₂×C₃	semidirect
8. C₂×C₂₅×C₁₉⋊C₃	C₂×C₃	semidirect
9. C₂₅×D₁₉⋊C₃	C₂×C₃	direct (N × H)
10. C₂×C₃×C₁₉×C₂₅	C₂×C₃	semidirect
11. C₂×C₂₅×D₁₉	C₃²	semidirect
14. C₃×C₁₉×C₂₅	C₂²×C₃	semidirect
15. C₂₅×C₁₉⋊C₃	C₂²×C₃	semidirect
18. C₂×C₁₉×C₂₅	C₂×C₃²	semidirect
19. C₂₅×D₁₉	C₂×C₃²	semidirect
22. C₂×C₃×D₁₉⋊C₃	C₂₅	direct (N × H)
27. C₁₉×C₂₅	C₂²×C₃²	semidirect
31. C₂×C₃×C₁₉⋊C₃	C₂×C₂₅	semidirect
32. C₃×D₁₉⋊C₃	C₂×C₂₅	direct (N × H)
37. C₂×C₃×D₁₉	C₃×C₂₅	semidirect
38. C₂×D₁₉⋊C₃	C₃×C₂₅	direct (N × H)
43. C₃×C₁₉⋊C₃	C₂²×C₂₅	semidirect
47. C₂×C₃×C₂₅	D₁₉⋊C₃	direct (N × H)
48. C₂×C₃×C₁₉	C₂×C₃×C₂₅	semidirect
49. C₃×D₁₉	C₂×C₃×C₂₅	semidirect
50. C₂×C₁₉⋊C₃	C₂×C₃×C₂₅	semidirect
51. D₁₉⋊C₃	C₂×C₃×C₂₅	direct (N × H)
56. C₂×D₁₉	C₃²×C₂₅	semidirect
58. C₃×C₂₅	C₂×D₁₉⋊C₃	direct (N × H)
61. C₃×C₁₉	C₂²×C₃×C₂₅	semidirect
62. C₁₉⋊C₃	C₂²×C₃×C₂₅	semidirect
64. C₂×C₂₅	C₃×D₁₉⋊C₃	direct (N × H)
66. C₂×C₁₉	C₂×C₃²×C₂₅	semidirect
67. D₁₉	C₂×C₃²×C₂₅	semidirect
73. C₂₅	C₂×C₃×D₁₉⋊C₃	direct (N × H)
75. C₁₉	C₂²×C₃²×C₂₅	semidirect
88. C₂×C₃	C₂₅×D₁₉⋊C₃	direct (N × H)
92. C₃	C₂×C₂₅×D₁₉⋊C₃	direct (N × H)
94. C₂	C₃×C₂₅×D₁₉⋊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
C₃×C₂₅×D₁₉⋊C₃	2
C₂×C₃×C₂₅×D₁₉	3
C₂×C₂₅×D₁₉⋊C₃	3
C₂×C₃×C₅×D₁₉⋊C₃	5
C₂²×C₃²×C₂₅	19

Subgroups — C2×C3×C25×D19⋊C3 #30685477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂₅×D₁₉⋊C₃ #30685477