Subgroups — C₂×C₁₉×C₃⋊D₇₅ #30685523

Order 17100.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊D₇₅
commutator, cosocle, hypocenter	C₃²×C₂₅	C₂²×C₁₉
Frattini	C₅	C₂×C₁₉×C₃⋊D₁₅
Fitting	C₂×C₃²×C₁₉×C₂₅	C₂
socle	C₂×C₃²×C₅×C₁₉	D₅
LCS	G ▷ C₃²×C₂₅
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₃⋊D₇₅	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₂₅	C₂	semidirect
4. C₃²×C₁₉×C₂₅	C₂²	semidirect
7. C₂×C₃×C₁₉×C₂₅	D₃	semidirect
11. C₃×C₁₉×C₂₅	C₂×D₃	semidirect
13. C₂×C₁₉×C₂₅	C₃⋊D₃	semidirect
15. C₂×C₃⋊D₇₅	C₁₉	direct (N × H)
20. C₁₉×C₂₅	C₂×C₃⋊D₃	semidirect
21. C₂×C₃²×C₂₅	C₂×C₁₉	semidirect
22. C₃⋊D₇₅	C₂×C₁₉	direct (N × H)
24. C₂×C₃²×C₁₉	D₂₅	semidirect
29. C₃²×C₂₅	C₂²×C₁₉	semidirect
33. C₃²×C₁₉	C₂×D₂₅	semidirect
34. C₂×C₃×C₂₅	D₃×C₁₉	semidirect
36. C₂×C₃×C₁₉	D₇₅	semidirect
43. C₃×C₂₅	C₂×D₃×C₁₉	semidirect
45. C₃×C₁₉	C₂×D₇₅	semidirect
46. C₂×C₂₅	C₃⋊D₃×C₁₉	semidirect
50. C₂×C₁₉	C₃⋊D₇₅	direct (N × H)
54. C₂₅	C₂×C₃⋊D₃×C₁₉	semidirect
56. C₁₉	C₂×C₃⋊D₇₅	direct (N × H)
57. C₂×C₃²	C₁₉×D₂₅	semidirect
63. C₃²	C₂×C₁₉×D₂₅	semidirect
64. C₂×C₃	C₁₉×D₇₅	semidirect
68. C₃	C₂×C₁₉×D₇₅	semidirect
70. C₂	C₁₉×C₃⋊D₇₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×C₃⋊D₇₅	2
C₂×C₃²×C₁₉×C₂₅	2
C₂×C₁₉×D₇₅	3
C₂×C₁₉×C₃⋊D₁₅	5
C₂×C₃⋊D₇₅	19

Subgroups — C2×C19×C3⋊D75 #30685523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×C₃⋊D₇₅ #30685523