Subgroups — C₄×C₁₉⋊C₆₄ #18070342

Order 4864.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊C₆₄	C₂	1	2	yes	maximal
2	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊C₆₄	C₄	1	4	yes	direct product factor
4	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₉	C₈	1	1	yes	characteristic
10	C₁₉×C₃₂	C₈	1	2	yes	—
11	C₁₉×C₃₂	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₉	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₁₉	C₁₆	1	1	yes	characteristic
15	C₁₆×C₁₉	C₁₆	1	2	yes	—
16	C₁₆×C₁₉	C₄²	1	1	yes	characteristic
17	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
18	C₄×C₆₄	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	C₃₂	1	2	yes	—
20	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
21	C₈×C₁₉	C₃₂	1	2	yes	—
22	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
23	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₆₄	—	19	2	no	—
25	C₄×C₃₂	D₁₉	1	1	yes	characteristic
26	C₂²×C₁₉	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₁₉	C₆₄	1	4	yes	complemented
28	C₄×C₁₉	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₉	C₂×C₃₂	1	1	yes	characteristic
30	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
31	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
32	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
33	C₆₄	—	19	4	no	—
34	C₂×C₁₉	C₄×C₃₂	1	1	yes	characteristic
35	C₂×C₁₉	C₂×C₆₄	1	2	yes	—
36	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
37	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
38	C₄×C₈	C₁₉⋊C₈	1	1	yes	characteristic
39	C₃₂	C₁₉⋊C₈	1	2	yes	—
40	C₃₂	C₄×D₁₉	1	2	yes	—
41	C₁₉	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
44	C₄²	C₁₉⋊C₁₆	1	1	yes	characteristic
45	C₁₆	C₁₉⋊C₁₆	1	2	yes	—
46	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
47	C₁₆	C₄×Dic₁₉	1	1	yes	characteristic
48	C₂×C₄	C₁₉⋊C₃₂	1	2	yes	—
49	C₂×C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
50	C₈	C₁₉⋊C₃₂	1	2	yes	—
51	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
53	C₂²	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic
54	C₄	C₁₉⋊C₆₄	1	4	yes	direct product factor
55	C₄	C₄×C₁₉⋊C₁₆	1	1	yes	characteristic
56	C₄	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic
57	C₂	C₄×C₁₉⋊C₃₂	1	1	yes	characteristic
58	C₂	C₂×C₁₉⋊C₆₄	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉⋊C₆₄	C₄	direct (N × H)
27. C₄×C₁₉	C₆₄	semidirect
41. C₁₉	C₄×C₆₄	semidirect
54. C₄	C₁₉⋊C₆₄	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×C₁₉⋊C₆₄	2
C₄×C₁₉×C₃₂	2
C₄×C₆₄	19

Subgroups — C4×C19⋊C64 #18070342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉⋊C₆₄ #18070342