Subgroups — #18070219

Order 4864.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#14561711	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1373	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉⋊C₃₂	C₄	1	1	yes	characteristic
6	#11926365	—	2	1	no	—
7	C₁₉×#364	—	2	1	no	—
8	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×M₃₂	—	4	1	no	—
10	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
12	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
13	#10597269	—	4	1	no	—
14	C₁₉⋊C₃₂	—	2	1	no	—
15	C₁₉⋊C₃₂	C₈	1	2	yes	—
16	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
18	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
19	C₁₆×C₁₉	—	2	1	no	—
20	C₁₆×C₁₉	—	8	1	no	—
21	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
22	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
23	C₁₉⋊C₁₆	—	8	1	no	—
24	#7462	—	19	1	no	maximal, Sylow
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
27	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₁₉	#108	1	1	yes	characteristic
29	C₈×C₁₉	D₁₆	1	1	yes	characteristic
30	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
31	C₄×C₃₂	—	19	1	no	—
32	#1373	—	19	1	no	—
33	#1373	D₁₉	1	1	yes	characteristic
34	C₂²×C₁₉	#368	1	1	yes	characteristic
35	C₄×C₁₉	—	2	2	no	—
36	C₄×C₁₉	#335	1	1	yes	characteristic
37	C₄×C₁₉	#366	1	1	yes	characteristic
38	C₂×C₃₂	—	19	1	no	—
39	C₂×C₃₂	—	19	1	no	—
40	#364	—	2	1	no	—
41	#364	—	38	1	no	—
42	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
43	C₂×C₁₉	—	2	1	no	—
44	C₂×C₁₉	#1371	1	1	yes	characteristic
45	M₃₂	—	4	1	no	—
46	M₃₂	—	76	1	no	—
47	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
48	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
49	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
50	C₃₂	—	19	2	no	—
51	C₃₂	—	38	1	no	—
52	C₁₉	#7462	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
54	C₂×C₈	#64525	1	1	yes	characteristic
55	C₄²	#64528	1	1	yes	characteristic
56	C₁₆	—	2	1	no	—
57	C₁₆	—	8	1	no	—
58	C₁₆	—	152	1	no	—
59	C₁₆	C₈×D₁₉	1	1	yes	characteristic
60	C₁₆	#64515	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#10597264	1	1	yes	characteristic
63	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
64	C₈	#10597279	1	1	yes	characteristic
65	C₈	#10597283	1	1	yes	characteristic
66	C₈	#10597286	1	1	yes	characteristic
67	C₂²	#11926373	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	#11926296	1	1	yes	characteristic
70	C₄	#11926369	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#14561706	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10597283
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1373	C₂
socle	C₂×C₁₉	#1371
prime radical	C₂²×C₁₉	#368
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1373	D₁₉
hypocenter	C₁₉	#7462
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
52. C₁₉	#7462	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
#14561711	2
C₁₉×#1373	2
#7462	19