Subgroups — Dic₁₉⋊C₆₄ #18070434

Order 4864.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₁₉	C₄	1	1	yes	characteristic
6	C₁₉⋊C₆₄	—	2	1	no	—
7	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₉×C₆₄	—	2	1	no	—
9	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₁₉	C₈	1	1	yes	characteristic
11	C₂×C₁₉⋊C₁₆	C₈	1	1	yes	characteristic
12	C₁₉×C₃₂	D₄	1	1	yes	characteristic
13	C₁₉×C₃₂	Q₈	1	1	yes	characteristic
14	C₁₉⋊C₃₂	—	2	1	no	—
15	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₄×Dic₁₉	C₁₆	1	1	yes	characteristic
17	C₂×C₁₉⋊C₈	C₁₆	1	1	yes	characteristic
18	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
20	C₁₉⋊C₁₆	—	2	1	no	—
21	C₄⋊C₆₄	—	19	1	no	maximal, Sylow
22	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
23	C₂×Dic₁₉	C₃₂	1	1	yes	characteristic
24	C₂×Dic₁₉	C₃₂	1	1	yes	characteristic
25	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₉	M₃₂	1	1	yes	characteristic
27	C₁₉⋊C₈	—	2	1	no	—
28	C₂×C₆₄	—	19	1	no	—
29	C₂×C₆₄	D₁₉	1	1	yes	characteristic
30	C₄×C₃₂	—	19	1	no	—
31	C₂²×C₁₉	C₂×C₃₂	1	1	yes	characteristic
32	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
33	C₄×C₁₉	M₆₄	1	1	yes	characteristic
34	Dic₁₉	—	2	1	no	—
35	Dic₁₉	C₆₄	1	2	yes	complemented
36	C₂×C₃₂	—	19	1	no	—
37	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
38	C₄×C₁₆	—	19	1	no	—
39	C₆₄	—	2	1	no	—
40	C₆₄	—	38	1	no	—
41	C₂×C₁₉	C₄⋊C₃₂	1	1	yes	characteristic
42	C₂×C₁₉	C₂×C₆₄	1	1	yes	characteristic
43	C₂×C₁₉	M₁₂₈	1	1	yes	characteristic
44	C₂×C₁₆	—	19	1	no	—
45	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
46	C₄×C₈	—	19	1	no	—
47	C₃₂	—	38	1	no	—
48	C₃₂	Dic₃₈	1	1	yes	characteristic
49	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
50	C₁₉	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	19	1	no	—
52	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
53	C₄²	—	19	1	no	—
54	C₁₆	—	38	1	no	—
55	C₁₆	#64515	1	1	yes	characteristic
56	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
57	C₂×C₄	—	19	1	no	—
58	C₂×C₄	—	19	1	no	—
59	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
60	C₈	—	38	1	no	—
61	C₈	#10597255	1	1	yes	characteristic
62	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
63	C₂²	C₃₂×D₁₉	1	1	yes	characteristic
64	C₄	—	19	2	no	—
65	C₄	—	38	1	no	—
66	C₄	Dic₁₉⋊C₁₆	1	1	yes	characteristic
67	C₄	#11926377	1	1	yes	characteristic
68	C₂	Dic₁₉⋊C₃₂	1	1	yes	characteristic
69	C₂	D₁₉×C₆₄	1	1	yes	characteristic
70	C₂	#14561845	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₉
commutator	C₂×C₁₉	C₂×C₆₄
Fitting	C₂×C₁₉×C₆₄	C₂
socle, prime radical	C₂²×C₁₉	C₂×C₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₉
hypocenter	C₁₉	C₄⋊C₆₄
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
35. Dic₁₉	C₆₄	semidirect
50. C₁₉	C₄⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉⋊C₆₄	2
C₃₂×Dic₁₉	2
C₂×C₁₉×C₆₄	2
C₄⋊C₆₄	19

Subgroups — Dic19⋊C64 #18070434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₉⋊C₆₄ #18070434