Subgroups — C₁₉×(C₃⋊D₃)⋊D₂₅ #30685510

Order 17100.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₉×D₇₅	C₂	1	2	yes	maximal, complemented
3	D₃×C₁₉×D₂₅	—	3	2	no	maximal
4	C₃²×C₁₉×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₉×(C₃⋊D₃)⋊D₅	—	5	1	no	maximal
6	C₁₉×D₇₅	D₃	1	2	yes	complemented
7	D₃×C₁₉×C₂₅	—	3	2	no	—
8	D₃×C₁₉×C₂₅	—	6	1	no	—
9	C₃×C₁₉×D₂₅	—	3	2	no	—
10	C₂×C₁₉×D₂₅	—	9	1	no	Hall
11	C₅×C₃⋊D₃×C₁₉	D₅	1	1	yes	characteristic
12	C₃×C₁₉×D₁₅	—	5	2	no	—
13	C₃×C₁₉×C₂₅	—	2	1	no	—
14	C₃×C₁₉×C₂₅	C₂×D₃	1	2	yes	complemented
15	D₃×D₅×C₁₉	—	15	2	no	—
16	C₂×C₁₉×C₂₅	—	9	1	no	—
17	C₁₉×D₂₅	—	3	2	no	—
18	(C₃⋊D₃)⋊D₂₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃²×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic
20	D₃²×C₁₉	—	25	1	no	Hall
21	C₁₉×D₁₅	—	5	2	no	—
22	C₅×D₃×C₁₉	—	3	2	no	—
23	C₅×D₃×C₁₉	—	6	1	no	—
24	C₃×D₅×C₁₉	—	15	2	no	—
25	C₁₉×C₂₅	D₃²	1	1	yes	characteristic, complemented, Hall
26	C₃⋊D₃×C₂₅	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₃×D₇₅	C₂×C₁₉	1	2	yes	complemented
28	C₂×D₅×C₁₉	—	45	1	no	—
29	C₃⋊D₃×C₁₉	D₂₅	1	1	yes	characteristic, complemented
30	C₃×D₃×C₁₉	—	25	2	no	—
31	D₃×D₂₅	—	3	2	no	—
32	C₃×C₅×C₁₉	—	2	1	no	—
33	C₃×C₅×C₁₉	D₃×D₅	1	2	yes	—
34	C₂×D₃×C₁₉	—	75	2	no	—
35	C₃²×C₂₅	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₉	—	9	1	no	—
37	D₅×C₁₉	—	15	2	no	—
38	(C₃⋊D₃)⋊D₅	—	5	1	no	—
39	C₃²×C₁₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
40	D₇₅	D₃×C₁₉	1	2	yes	complemented
41	C₃×D₂₅	—	3	2	no	—
42	D₃×C₂₅	—	3	2	no	—
43	D₃×C₂₅	—	6	1	no	—
44	C₂×C₃×C₁₉	—	75	2	no	—
45	D₃×C₁₉	—	3	2	no	—
46	D₃×C₁₉	—	6	1	no	—
47	D₃×C₁₉	—	25	2	no	—
48	C₂×D₂₅	—	9	1	no	Hall
49	C₅×C₁₉	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic
50	C₅×C₃⋊D₃	D₅×C₁₉	1	1	yes	characteristic
51	C₃×D₁₅	—	5	2	no	—
52	C₂²×C₁₉	—	225	1	no	Hall
53	C₃×C₂₅	—	2	1	no	—
54	C₃×C₂₅	C₂×D₃×C₁₉	1	2	yes	complemented
55	D₃×D₅	—	15	2	no	—
56	C₃×C₁₉	—	2	1	no	—
57	C₃×C₁₉	D₃×D₂₅	1	2	yes	complemented
58	C₂×C₂₅	—	9	1	no	—
59	D₂₅	—	3	2	no	—
60	C₃²×C₅	C₂×D₅×C₁₉	1	1	yes	characteristic
61	C₂×C₁₉	—	9	1	no	—
62	C₂×C₁₉	—	75	2	no	—
63	D₃²	—	25	1	no	Hall
64	D₁₅	—	5	2	no	—
65	C₃×D₅	—	15	2	no	—
66	C₅×D₃	—	3	2	no	—
67	C₅×D₃	—	6	1	no	—
68	C₂₅	D₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	45	1	no	—
70	C₁₉	(C₃⋊D₃)⋊D₂₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₃⋊D₃	C₁₉×D₂₅	1	1	yes	characteristic, complemented
72	C₃×D₃	—	25	2	no	—
73	C₃×C₅	—	2	1	no	—
74	C₃×C₅	D₃×D₅×C₁₉	1	2	yes	—
75	C₂×D₃	—	75	2	no	—
76	C₂×C₅	—	9	1	no	—
77	D₅	—	15	2	no	—
78	C₃²	C₂×C₁₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	75	2	no	—
80	D₃	—	3	2	no	—
81	D₃	—	6	1	no	—
82	D₃	—	25	2	no	—
83	C₅	C₁₉×(C₃⋊D₃)⋊D₅	1	1	yes	characteristic
84	C₂²	—	225	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×C₁₉×D₂₅	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	75	2	no	—

	subgroup	G/H
center, hypercenter	C₁₉	(C₃⋊D₃)⋊D₂₅
commutator, cosocle, hypocenter	C₃²×C₂₅	C₂²×C₁₉
Frattini	C₅	C₁₉×(C₃⋊D₃)⋊D₅
Fitting	C₃²×C₁₉×C₂₅	C₂²
socle	C₃²×C₅×C₁₉	C₂×D₅
LCS	G ▷ C₃²×C₂₅
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₁₉×C₂₅	C₂	semidirect
2. C₃×C₁₉×D₇₅	C₂	semidirect
4. C₃²×C₁₉×C₂₅	C₂²	semidirect
6. C₁₉×D₇₅	D₃	semidirect
14. C₃×C₁₉×C₂₅	C₂×D₃	semidirect
18. (C₃⋊D₃)⋊D₂₅	C₁₉	direct (N × H)
25. C₁₉×C₂₅	D₃²	semidirect
26. C₃⋊D₃×C₂₅	C₂×C₁₉	semidirect
27. C₃×D₇₅	C₂×C₁₉	semidirect
29. C₃⋊D₃×C₁₉	D₂₅	semidirect
35. C₃²×C₂₅	C₂²×C₁₉	semidirect
39. C₃²×C₁₉	C₂×D₂₅	semidirect
40. D₇₅	D₃×C₁₉	semidirect
54. C₃×C₂₅	C₂×D₃×C₁₉	semidirect
57. C₃×C₁₉	D₃×D₂₅	semidirect
68. C₂₅	D₃²×C₁₉	semidirect
70. C₁₉	(C₃⋊D₃)⋊D₂₅	direct (N × H)
71. C₃⋊D₃	C₁₉×D₂₅	semidirect
78. C₃²	C₂×C₁₉×D₂₅	semidirect
86. C₃	D₃×C₁₉×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₁₉×C₂₅	2
C₃×C₁₉×D₇₅	2
D₃×C₁₉×D₂₅	3
C₁₉×(C₃⋊D₃)⋊D₅	5
(C₃⋊D₃)⋊D₂₅	19

Subgroups — C19×(C3⋊D3)⋊D25 #30685510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×(C₃⋊D₃)⋊D₂₅ #30685510