Subgroups — #18069867

Order 4864.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉⋊C₃₂	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉⋊C₃₂	C₄	1	4	yes	—
4	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₈²×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₈	1	2	yes	—
8	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₁₉	C₈	1	2	yes	—
10	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₁₉⋊C₃₂	C₈	1	8	yes	complemented
12	C₂×C₈×C₁₉	C₁₆	1	4	yes	—
13	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₁₆×C₁₉	C₁₆	1	4	yes	—
17	C₁₆×C₁₉	C₂×C₈	1	4	yes	—
18	#7329	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₂×C₁₆	1	2	yes	—
21	C₈×C₁₉	—	2	4	no	—
22	C₈×C₁₉	C₄×C₈	1	2	yes	—
23	C₈×C₁₉	C₂×C₁₆	1	2	yes	—
24	C₄×C₃₂	—	19	2	no	—
25	C₈×C₁₆	D₁₉	1	1	yes	characteristic
26	C₂²×C₁₉	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₁₉	C₈²	1	1	yes	characteristic
28	C₄×C₁₉	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₉	M₆₄	1	4	yes	—
30	C₂×C₃₂	—	19	4	no	—
31	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
32	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
33	C₈²	Dic₁₉	1	1	yes	characteristic
34	C₂×C₁₉	C₈×C₁₆	1	1	yes	characteristic
35	C₂×C₁₉	#1397	1	2	yes	—
36	C₂×C₁₆	C₁₉⋊C₈	1	2	yes	—
37	C₂×C₁₆	C₄×D₁₉	1	2	yes	—
38	C₄×C₈	C₁₉⋊C₈	1	2	yes	—
39	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
40	C₃₂	—	19	8	no	—
41	C₁₉	#7329	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	C₁₉⋊C₁₆	1	4	yes	—
43	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
44	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
45	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
46	C₁₆	C₁₉⋊C₁₆	1	4	yes	—
47	C₁₆	C₈×D₁₉	1	4	yes	—
48	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
49	C₂×C₄	C₂×C₁₉⋊C₁₆	1	2	yes	—
50	C₈	—	2	4	no	—
51	C₈	C₂×C₁₉⋊C₁₆	1	2	yes	—
52	C₈	C₈×Dic₁₉	1	2	yes	—
53	C₂²	C₄×C₁₉⋊C₁₆	1	1	yes	characteristic
54	C₄	C₈×C₁₉⋊C₈	1	1	yes	characteristic
55	C₄	C₄×C₁₉⋊C₁₆	1	1	yes	characteristic
56	C₄	#11926378	1	4	yes	—
57	C₂	C₈×C₁₉⋊C₁₆	1	1	yes	characteristic
58	C₂	#14561769	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₁₆	C₂×D₁₉
commutator	C₂×C₁₉	C₈×C₁₆
Fitting	C₈×C₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₄×C₁₆
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	C₈×C₁₆	D₁₉
hypocenter	C₁₉	#7329
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄×C₁₆ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
11. C₁₉⋊C₃₂	C₈	semidirect
41. C₁₉	#7329	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉⋊C₃₂	2
C₈×C₁₆×C₁₉	2
#7329	19