Subgroups — #18070343

Order 4864.

82 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	C₄	1	2	yes	complemented
7	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₉×C₆₄	C₄	1	2	yes	complemented
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	C₂×C₄	1	1	yes	characteristic
13	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
14	C₁₉⋊C₃₂	C₈	1	2	yes	—
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	C₄²	1	1	yes	characteristic
19	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₁₉⋊C₁₆	C₁₆	1	2	yes	—
21	#7510	—	19	1	no	maximal, Sylow
22	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
23	C₂×Dic₁₉	C₃₂	1	2	yes	—
24	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
25	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
26	C₁₉⋊C₈	C₃₂	1	2	yes	—
27	C₂×C₆₄	—	19	1	no	—
28	C₂×C₆₄	D₁₉	1	1	yes	characteristic
29	C₄×C₃₂	—	19	1	no	—
30	C₂²×C₁₉	C₂×C₃₂	1	1	yes	characteristic
31	C₄×C₁₉	C₄×C₁₆	1	1	yes	characteristic
32	C₄×C₁₉	C₂×C₃₂	1	1	yes	characteristic
33	Dic₁₉	—	2	2	no	—
34	C₂×C₃₂	—	19	1	no	—
35	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
36	C₄×C₁₆	—	19	1	no	—
37	C₆₄	—	19	2	no	—
38	C₆₄	Dic₁₉	1	2	yes	complemented
39	C₂×C₁₉	C₄×C₃₂	1	1	yes	characteristic
40	C₂×C₁₉	M₁₂₈	1	2	yes	—
41	C₂×C₁₆	—	19	1	no	—
42	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
43	C₄×C₈	—	19	1	no	—
44	C₃₂	—	19	2	no	—
45	C₃₂	C₄×D₁₉	1	1	yes	characteristic
46	C₃₂	C₂×Dic₁₉	1	1	yes	characteristic
47	C₁₉	#7510	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₈	—	19	1	no	—
49	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
50	C₄²	—	19	1	no	—
51	C₁₆	—	19	2	no	—
52	C₁₆	C₈×D₁₉	1	1	yes	characteristic
53	C₁₆	C₄×Dic₁₉	1	1	yes	characteristic
54	C₂×C₄	—	19	2	no	—
55	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
56	C₈	—	19	2	no	—
57	C₈	C₁₆×D₁₉	1	1	yes	characteristic
58	C₈	C₈×Dic₁₉	1	1	yes	characteristic
59	C₂²	C₃₂×D₁₉	1	1	yes	characteristic
60	C₄	—	38	2	no	—
61	C₄	C₁₆×Dic₁₉	1	1	yes	characteristic
62	C₄	C₃₂×D₁₉	1	1	yes	characteristic
63	C₂	C₃₂×Dic₁₉	1	1	yes	characteristic
64	C₂	#14561845	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₉
commutator	C₂×C₁₉	C₄×C₃₂
Fitting	C₂×C₁₉×C₆₄	C₂
socle, prime radical	C₂²×C₁₉	C₂×C₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₉
hypocenter	C₁₉	#7510
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
6. C₁₉⋊C₆₄	C₄	semidirect
8. C₁₉×C₆₄	C₄	semidirect
38. C₆₄	Dic₁₉	semidirect
47. C₁₉	#7510	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
#7510	19