Subgroups — C₁₉×#473 #11926149

Order 1216.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#137	C₂	1	2	yes	maximal
2	C₂×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#131	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#101	C₂	1	2	yes	maximal, complemented
6	#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₁₉	C₂²	1	2	yes	—
8	Q₁₆×C₁₉	—	2	2	no	—
9	Q₁₆×C₁₉	—	2	1	no	—
10	Q₁₆×C₁₉	—	2	1	no	—
11	SD₁₆×C₁₉	—	2	2	no	—
12	M₁₆×C₁₉	—	2	1	no	—
13	M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂×C₈×C₁₉	—	2	1	no	—
16	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	Q₈×C₁₉	—	2	2	no	—
18	Q₈×C₁₉	—	2	2	no	—
19	Q₈×C₁₉	D₄	1	1	yes	characteristic
20	D₄×C₁₉	—	2	1	no	—
21	D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	—	2	2	no	—
24	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₈×C₁₉	—	2	1	no	—
26	C₈×C₁₉	—	2	2	no	—
27	C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₁₉	—	2	1	no	—
30	C₂²×C₁₉	#41	1	1	yes	characteristic
31	C₄×C₁₉	—	2	1	no	—
32	C₄×C₁₉	—	4	2	no	—
33	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	#473	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₁₉	—	2	1	no	—
37	C₂×C₁₉	—	4	1	no	—
38	C₂×C₁₉	#121	1	1	yes	characteristic
39	#137	C₂×C₁₉	1	2	yes	—
40	C₂×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
41	#131	C₂×C₁₉	1	1	yes	characteristic
42	#108	C₂×C₁₉	1	1	yes	characteristic, complemented
43	#101	C₂×C₁₉	1	2	yes	complemented
44	C₁₉	#473	1	1	yes	characteristic, direct product factor, Sylow
45	#41	C₂²×C₁₉	1	1	yes	characteristic
46	C₂×Q₈	C₂²×C₁₉	1	2	yes	—
47	Q₁₆	—	2	2	no	—
48	Q₁₆	—	2	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	2	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	C₂²×C₁₉	1	1	yes	characteristic
53	M₁₆	C₂²×C₁₉	1	2	yes	—
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂²×C₁₉	1	1	yes	characteristic
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	D₄×C₁₉	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₄×C₁₉	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	C₂³×C₁₉	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	2	2	no	—
66	C₈	D₄×C₁₉	1	1	yes	characteristic
67	C₈	D₄×C₁₉	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#41×C₁₉	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	2	no	—
72	C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
73	C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	C₁₉×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#121
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₉
prime radical	#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×C₁₉	C₂	semidirect
4. C₁₉×#108	C₂	semidirect
5. C₁₉×#101	C₂	semidirect
35. #473	C₁₉	direct (N × H)
40. C₂×Q₁₆	C₂×C₁₉	semidirect
42. #108	C₂×C₁₉	semidirect
43. #101	C₂×C₁₉	semidirect
44. C₁₉	#473	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×#137	2
C₂×Q₁₆×C₁₉	2
C₁₉×#131	2
C₁₉×#108	2
C₁₉×#101	2
#473	19

Subgroups — C19×#473 #11926149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#473 #11926149