Subgroups — C₁₉×#7464 #18013423

Order 4864.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1373	C₂	1	2	yes	maximal
3	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₁₉×#364	—	2	2	no	—
6	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×M₃₂	—	4	2	no	—
8	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
11	C₁₉×C₃₂	—	2	1	no	—
12	C₁₉×C₃₂	C₈	1	2	yes	—
13	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
15	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
16	C₁₆×C₁₉	—	2	1	no	—
17	C₁₆×C₁₉	—	8	2	no	—
18	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
20	#7464	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₄×C₁₉	—	2	1	no	—
22	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
23	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₁₉	#108	1	1	yes	characteristic
25	C₈×C₁₉	SD₃₂	1	2	yes	—
26	#1397	C₂×C₁₉	1	1	yes	characteristic
27	#1373	C₂×C₁₉	1	2	yes	—
28	C₂²×C₁₉	#368	1	1	yes	characteristic
29	C₄×C₁₉	—	4	1	no	—
30	C₄×C₁₉	#335	1	1	yes	characteristic
31	C₄×C₁₉	#367	1	1	yes	characteristic
32	C₂×C₃₂	C₄×C₁₉	1	1	yes	characteristic
33	C₂×C₃₂	C₄×C₁₉	1	1	yes	characteristic
34	#364	—	2	2	no	—
35	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
36	C₂×C₁₉	—	2	1	no	—
37	C₂×C₁₉	#1372	1	1	yes	characteristic
38	M₃₂	—	4	2	no	—
39	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
40	C₂×C₁₆	Q₈×C₁₉	1	1	yes	characteristic
41	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
42	C₃₂	—	2	1	no	—
43	C₃₂	C₈×C₁₉	1	2	yes	—
44	C₁₉	#7464	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
46	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
47	C₄²	Q₁₆×C₁₉	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	8	2	no	—
50	C₁₆	C₂×C₈×C₁₉	1	1	yes	characteristic
51	C₁₆	M₁₆×C₁₉	1	1	yes	characteristic
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	C₁₉×#107	1	1	yes	characteristic
54	C₈	C₁₉×C₄⋊C₈	1	1	yes	characteristic
55	C₈	C₁₉×#108	1	1	yes	characteristic
56	C₈	C₁₉×SD₃₂	1	2	yes	—
57	C₂²	C₁₉×#368	1	1	yes	characteristic
58	C₄	—	4	1	no	—
59	C₄	C₁₉×#335	1	1	yes	characteristic
60	C₄	C₁₉×#367	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	C₁₉×#1372	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#367
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	#1372
prime radical	C₂²×C₁₉	#368
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
20. #7464	C₁₉	direct (N × H)
44. C₁₉	#7464	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#1397	2
C₁₉×#1373	2
#7464	19

Subgroups — C19×#7464 #18013423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7464 #18013423