Subgroups — D₁₉×D₁₉₅ #28414906

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₁₉₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₃×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₆₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉×D₃₉	—	5	1	no	maximal, Hall
7	D₁₂₃₅	—	3	1	no	—
8	C₁₉×D₆₅	—	3	1	no	—
9	C₅×C₁₃×D₁₉	D₃	1	1	yes	characteristic, complemented
10	D₇₄₁	—	5	1	no	—
11	C₁₉×D₃₉	—	5	1	no	—
12	C₃×C₁₃×D₁₉	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅×D₁₉	—	13	1	no	maximal, Hall
15	D₁₃×D₁₉	—	15	1	no	Hall
16	C₂×D₁₉₅	—	19	1	no	maximal, Hall
17	C₃×C₁₃×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	D₂₈₅	—	13	1	no	—
19	C₁₉×D₁₅	—	13	1	no	—
20	C₃×C₅×D₁₉	D₁₃	1	1	yes	characteristic, complemented
21	D₂₄₇	—	15	1	no	—
22	C₁₃×D₁₉	D₁₅	1	1	yes	characteristic, complemented
23	C₁₉×D₁₃	—	15	1	no	—
24	C₂×C₃×C₅×C₁₃	—	19	1	no	—
25	D₁₉₅	—	19	1	no	—
26	D₁₉₅	D₁₉	1	1	yes	characteristic, direct product factor
27	D₅×D₁₉	—	39	1	no	Hall
28	C₃×C₅×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₆₅	—	57	1	no	Hall
30	C₁₃×C₁₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
31	D₃×D₁₉	—	65	1	no	Hall
32	C₃×C₅×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
33	D₉₅	—	39	1	no	—
34	C₅×D₁₉	D₃₉	1	1	yes	characteristic, complemented
35	D₅×C₁₉	—	39	1	no	—
36	C₂×D₃₉	—	95	1	no	Hall
37	C₂×C₅×C₁₃	—	19	1	no	—
38	D₆₅	—	3	1	no	—
39	D₆₅	—	57	1	no	—
40	D₅₇	—	65	1	no	—
41	C₃×D₁₉	D₆₅	1	1	yes	characteristic, complemented
42	D₃×C₁₉	—	65	1	no	—
43	C₅×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₃	—	19	1	no	—
45	D₃₉	—	5	1	no	—
46	D₃₉	—	95	1	no	—
47	C₂×D₁₉	—	195	1	no	Hall
48	C₅×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
49	C₂×D₁₅	—	247	1	no	Hall
50	C₃×C₁₉	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	285	1	no	Hall
52	C₃×C₁₃	D₅×D₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₉	—	195	1	no	—
54	D₁₉	—	195	1	no	—
55	D₁₉	D₁₉₅	1	1	yes	characteristic, direct product factor
56	C₂×C₃×C₅	—	19	1	no	—
57	D₁₅	—	13	1	no	—
58	D₁₅	—	247	1	no	—
59	C₂×C₁₃	—	19	1	no	—
60	D₁₃	—	15	1	no	—
61	D₁₃	—	285	1	no	—
62	C₂×D₅	—	741	1	no	Hall
63	C₁₉	C₂×D₁₉₅	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₅	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
65	C₁₃	D₁₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₃	—	1235	1	no	Hall
67	C₂×C₅	—	19	1	no	—
68	D₅	—	39	1	no	—
69	D₅	—	741	1	no	—
70	C₂×C₃	—	19	1	no	—
71	D₃	—	65	1	no	—
72	D₃	—	1235	1	no	—
73	C₅	D₁₉×D₃₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	3705	1	no	Sylow
75	C₃	D₁₉×D₆₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	19	1	no	—
77	C₂	—	3705	1	no	—
78	C₂	—	195	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₇₀₅	C₂	semidirect
2. C₁₉×D₁₉₅	C₂	semidirect
3. C₃×C₅×C₁₃×D₁₉	C₂	semidirect
5. C₃×C₅×C₁₃×C₁₉	C₂²	semidirect
9. C₅×C₁₃×D₁₉	D₃	semidirect
12. C₃×C₁₃×D₁₉	D₅	semidirect
13. C₅×C₁₃×C₁₉	C₂×D₃	semidirect
17. C₃×C₁₃×C₁₉	C₂×D₅	semidirect
20. C₃×C₅×D₁₉	D₁₃	semidirect
22. C₁₃×D₁₉	D₁₅	semidirect
26. D₁₉₅	D₁₉	direct (N × H)
28. C₃×C₅×C₁₉	C₂×D₁₃	semidirect
30. C₁₃×C₁₉	C₂×D₁₅	semidirect
32. C₃×C₅×C₁₃	C₂×D₁₉	semidirect
34. C₅×D₁₉	D₃₉	semidirect
41. C₃×D₁₉	D₆₅	semidirect
43. C₅×C₁₉	C₂×D₃₉	semidirect
48. C₅×C₁₃	D₃×D₁₉	semidirect
50. C₃×C₁₉	C₂×D₆₅	semidirect
52. C₃×C₁₃	D₅×D₁₉	semidirect
55. D₁₉	D₁₉₅	direct (N × H)
63. C₁₉	C₂×D₁₉₅	semidirect
64. C₃×C₅	D₁₃×D₁₉	semidirect
65. C₁₃	D₁₅×D₁₉	semidirect
73. C₅	D₁₉×D₃₉	semidirect
75. C₃	D₁₉×D₆₅	semidirect

Maximal subgroups

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

subgroup	index
D₃₇₀₅	2
C₁₉×D₁₉₅	2
C₃×C₅×C₁₃×D₁₉	2
D₁₉×D₆₅	3
D₁₉×D₃₉	5
D₁₅×D₁₉	13
C₂×D₁₉₅	19

Subgroups — D19×D195 #28414906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×D₁₉₅ #28414906