Subgroups — #18069156

Order 4864.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561553	C₂	1	1	yes	maximal, characteristic
2	#14561552	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1312	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₉⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
7	C₄×C₁₆×C₁₉	C₄	1	2	yes	—
8	C₈²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	—	2	2	no	—
10	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	—	2	2	no	—
14	C₂×C₁₉⋊C₁₆	C₈	1	2	yes	—
15	C₂×C₁₉⋊C₁₆	C₈	1	2	yes	—
16	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
19	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
20	C₄²×C₁₉	C₄²	1	1	yes	characteristic
21	C₁₆×C₁₉	—	4	2	no	—
22	C₁₉⋊C₁₆	—	2	2	no	—
23	C₁₉⋊C₁₆	—	4	2	no	—
24	C₁₉⋊C₁₆	C₁₆	1	4	yes	complemented
25	#7053	—	19	1	no	maximal, Sylow
26	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
28	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
29	C₈×C₁₉	—	2	2	no	—
30	C₈×C₁₉	—	2	2	no	—
31	C₈×C₁₉	C₂×C₁₆	1	2	yes	—
32	C₈×C₁₉	M₃₂	1	2	yes	—
33	#1312	—	19	1	no	—
34	#1312	D₁₉	1	1	yes	characteristic
35	#1311	—	19	1	no	—
36	C₂²×C₁₉	#322	1	1	yes	characteristic
37	C₄×C₁₉	C₄×C₁₆	1	1	yes	characteristic
38	C₄×C₁₉	#346	1	1	yes	characteristic
39	C₄×C₁₉	#347	1	2	yes	—
40	C₄×C₁₉	#347	1	2	yes	—
41	C₄×C₁₆	—	19	1	no	—
42	C₄×C₁₆	—	19	1	no	—
43	C₄×C₁₆	—	19	2	no	—
44	C₄×C₁₆	Dic₁₉	1	2	yes	—
45	C₈²	C₂×D₁₉	1	1	yes	characteristic
46	C₂×C₁₉	#1312	1	1	yes	characteristic
47	C₂×C₁₉	#1313	1	1	yes	characteristic
48	C₂×C₁₉	#1313	1	1	yes	characteristic
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	—	19	2	no	—
51	C₂×C₁₆	—	19	2	no	—
52	C₂×C₁₆	—	38	2	no	—
53	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
54	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
55	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
56	C₁₉	#7053	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
58	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
59	C₂×C₈	#64515	1	2	yes	—
60	C₂×C₈	#64520	1	2	yes	—
61	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
62	C₁₆	—	4	2	no	—
63	C₁₆	—	19	4	no	—
64	C₁₆	—	38	2	no	—
65	C₁₆	—	76	2	no	—
66	C₂×C₄	#10597260	1	1	yes	characteristic
67	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
68	C₂×C₄	#10597272	1	1	yes	characteristic
69	C₈	—	2	2	no	—
70	C₈	—	2	2	no	—
71	C₈	C₁₆×D₁₉	1	2	yes	—
72	C₈	#10597255	1	2	yes	—
73	C₂²	#11926266	1	1	yes	characteristic
74	C₄	C₁₆×Dic₁₉	1	1	yes	characteristic
75	C₄	#11926319	1	1	yes	characteristic
76	C₄	#11926321	1	2	yes	—
77	C₄	#11926322	1	2	yes	—
78	C₂	#14561554	1	1	yes	characteristic
79	C₂	#14561556	1	1	yes	characteristic
80	C₂	#14561557	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄×Dic₁₉
commutator	C₄×C₁₉	C₄×C₁₆
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1312	C₂
socle, prime radical	C₂²×C₁₉	#322
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1312	D₁₉
hypocenter	C₁₉	#7053
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ #1312

Complements

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

N	H ≅ G/N	type
24. C₁₉⋊C₁₆	C₁₆	semidirect
56. C₁₉	#7053	semidirect

Maximal subgroups

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

subgroup	index
#14561553	2
#14561552	2
C₁₉×#1312	2
#7053	19