Subgroups — #18069277

Order 4864.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561699	C₂	1	2	yes	maximal
2	C₁₉×#1311	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
6	C₈²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	—	2	1	no	—
8	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	—	4	2	no	—
14	C₂×C₈×C₁₉	—	2	1	no	—
15	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
18	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₁₉	—	2	2	no	—
20	C₁₆×C₁₉	—	2	1	no	—
21	C₁₆×C₁₉	C₁₆	1	2	yes	complemented
22	C₁₉⋊C₁₆	—	8	2	no	—
23	#7099	—	19	1	no	maximal, Sylow
24	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
26	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
27	C₈×C₁₉	—	2	1	no	—
28	C₈×C₁₉	—	2	2	no	—
29	C₈×C₁₉	—	4	1	no	—
30	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₁₉	M₃₂	1	1	yes	characteristic
32	#1367	—	19	2	no	—
33	#1311	D₁₉	1	1	yes	characteristic
34	C₂²×C₁₉	#334	1	1	yes	characteristic
35	C₄×C₁₉	—	2	1	no	—
36	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
37	C₄×C₁₉	#364	1	1	yes	characteristic
38	C₄×C₁₉	#365	1	2	yes	—
39	C₄⋊C₁₆	—	38	2	no	—
40	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
41	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
42	C₈²	C₂×D₁₉	1	1	yes	characteristic
43	C₂×C₁₉	#1367	1	1	yes	characteristic
44	C₂×C₁₉	#1368	1	1	yes	characteristic
45	C₂×C₁₉	#1369	1	1	yes	characteristic
46	C₂×C₁₆	—	2	1	no	—
47	C₂×C₁₆	—	76	2	no	—
48	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
49	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
50	C₄×C₈	Dic₃₈	1	1	yes	characteristic
51	C₄×C₈	D₇₆	1	1	yes	characteristic
52	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
53	C₁₉	#7099	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	#64516	1	2	yes	—
56	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
57	C₂×C₈	#64520	1	1	yes	characteristic
58	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
59	C₁₆	—	2	2	no	—
60	C₁₆	—	2	1	no	—
61	C₁₆	—	152	2	no	—
62	C₁₆	C₁₉⋊C₁₆	1	2	yes	complemented
63	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
64	C₂×C₄	#10597274	1	1	yes	characteristic
65	C₂×C₄	#10597276	1	1	yes	characteristic
66	C₈	—	2	1	no	—
67	C₈	—	2	2	no	—
68	C₈	—	4	1	no	—
69	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
70	C₈	#10597269	1	1	yes	characteristic
71	C₂²	#11926295	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
74	C₄	#11926365	1	1	yes	characteristic
75	C₄	#11926367	1	2	yes	—
76	C₂	#14561699	1	1	yes	characteristic
77	C₂	#14561701	1	1	yes	characteristic
78	C₂	#14561703	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597274
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1311	C₂
socle, prime radical	C₂²×C₁₉	#334
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1311	D₁₉
hypocenter	C₁₉	#7099
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1311

Complements

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

N	H ≅ G/N	type
21. C₁₆×C₁₉	C₁₆	semidirect
53. C₁₉	#7099	semidirect
62. C₁₆	C₁₉⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
#14561699	2
C₁₉×#1311	2
#7099	19