Subgroups — #18069871

Order 4864.

118 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	C₁₆×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	C₄	1	2	yes	—
5	C₄×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₃₂	C₄	1	2	yes	—
8	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	C₈	1	2	yes	—
13	C₄×C₁₉⋊C₈	C₈	1	1	yes	characteristic
14	C₄×C₁₉⋊C₈	C₈	1	1	yes	characteristic
15	C₁₉×C₃₂	—	2	2	no	—
16	C₁₉⋊C₃₂	—	2	2	no	—
17	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₂×C₁₉⋊C₈	C₁₆	1	2	yes	—
21	C₂×C₁₉⋊C₈	C₁₆	1	2	yes	—
22	C₁₆×C₁₉	M₁₆	1	2	yes	—
23	C₁₆×C₁₉	M₁₆	1	2	yes	—
24	C₁₉⋊C₁₆	—	2	2	no	—
25	#7331	—	19	1	no	maximal, Sylow
26	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
29	C₈×C₁₉	#97	1	1	yes	characteristic
30	C₈×C₁₉	#97	1	1	yes	characteristic
31	C₈×C₁₉	M₃₂	1	2	yes	—
32	C₁₉⋊C₈	—	2	2	no	—
33	C₁₉⋊C₈	C₃₂	1	4	yes	complemented
34	C₄×C₃₂	—	19	1	no	—
35	C₄×C₃₂	D₁₉	1	1	yes	characteristic
36	C₈×C₁₆	—	19	1	no	—
37	C₂²×C₁₉	C₄×C₁₆	1	1	yes	characteristic
38	C₄×C₁₉	#322	1	1	yes	characteristic
39	C₄×C₁₉	#346	1	1	yes	characteristic
40	C₄×C₁₉	C₂×C₃₂	1	2	yes	—
41	C₄×C₁₉	M₆₄	1	2	yes	—
42	C₂×C₃₂	—	19	2	no	—
43	C₂×C₃₂	Dic₁₉	1	2	yes	—
44	C₄×C₁₆	—	19	1	no	—
45	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
46	C₈²	—	19	1	no	—
47	C₂×C₁₉	#1312	1	1	yes	characteristic
48	C₂×C₁₉	C₄×C₃₂	1	1	yes	characteristic
49	C₂×C₁₉	#1397	1	1	yes	characteristic
50	C₂×C₁₆	—	19	2	no	—
51	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
52	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
53	C₄×C₈	—	19	1	no	—
54	C₄×C₈	—	19	1	no	—
55	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
56	C₃₂	—	2	2	no	—
57	C₃₂	—	38	2	no	—
58	C₁₉	#7331	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₈	—	19	2	no	—
60	C₂×C₈	—	19	2	no	—
61	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
62	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
63	C₄²	C₈×D₁₉	1	1	yes	characteristic
64	C₁₆	—	38	2	no	—
65	C₁₆	#64515	1	2	yes	—
66	C₁₆	#64520	1	2	yes	—
67	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
68	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
69	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
70	C₈	—	19	4	no	—
71	C₈	—	38	2	no	—
72	C₈	#10597255	1	2	yes	—
73	C₈	#10597260	1	1	yes	characteristic
74	C₈	#10597272	1	1	yes	characteristic
75	C₂²	C₁₆×Dic₁₉	1	1	yes	characteristic
76	C₄	#11926266	1	1	yes	characteristic
77	C₄	#11926319	1	1	yes	characteristic
78	C₄	C₃₂×D₁₉	1	2	yes	—
79	C₄	#11926377	1	2	yes	—
80	C₂	#14561554	1	1	yes	characteristic
81	C₂	C₃₂×Dic₁₉	1	1	yes	characteristic
82	C₂	#14561768	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₁₆	C₂×D₁₉
commutator	C₂×C₁₉	C₄×C₃₂
Fitting	C₄×C₁₉×C₃₂	C₂
socle, prime radical	C₂²×C₁₉	C₄×C₁₆
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	C₄×C₃₂	D₁₉
hypocenter	C₁₉	#7331
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
33. C₁₉⋊C₈	C₃₂	semidirect
58. C₁₉	#7331	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
C₁₆×C₁₉⋊C₈	2
C₄×C₁₉×C₃₂	2
#7331	19