Subgroups — #18070352

Order 4864.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561846	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2258	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊C₆₄	—	2	1	no	—
5	C₁₉⋊C₆₄	—	2	1	no	—
6	C₁₉×#504	C₄	1	1	yes	characteristic
7	C₁₉×M₆₄	—	2	1	no	—
8	C₁₉×M₆₄	C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₃₂	—	2	1	no	—
10	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₉×#131	C₈	1	1	yes	characteristic
12	C₁₉×M₃₂	—	2	1	no	—
13	C₁₉×M₃₂	C₈	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	—	2	1	no	—
15	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×C₃₂	—	2	1	no	—
17	C₁₉×C₃₂	D₄	1	1	yes	characteristic
18	C₁₉×C₃₂	D₄	1	1	yes	characteristic
19	#41×C₁₉	C₁₆	1	1	yes	characteristic
20	M₁₆×C₁₉	—	2	1	no	—
21	M₁₆×C₁₉	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₁₉	—	2	1	no	—
25	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
27	#7514	—	19	1	no	maximal, Sylow
28	Q₈×C₁₉	C₃₂	1	1	yes	characteristic
29	D₄×C₁₉	—	2	1	no	—
30	D₄×C₁₉	C₃₂	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₁₉	—	2	1	no	—
34	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
35	C₈×C₁₉	M₃₂	1	1	yes	characteristic
36	#2258	D₁₉	1	1	yes	characteristic
37	M₁₂₈	—	19	1	no	—
38	C₂×C₆₄	—	19	1	no	—
39	C₂²×C₁₉	—	2	1	no	—
40	C₂²×C₁₉	M₆₄	1	1	yes	characteristic
41	C₄×C₁₉	—	2	1	no	—
42	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₄×C₁₉	C₂×C₃₂	1	1	yes	characteristic
44	#504	Dic₁₉	1	1	yes	characteristic
45	M₆₄	—	2	1	no	—
46	M₆₄	Dic₁₉	1	1	yes	characteristic
47	C₂×C₃₂	—	2	1	no	—
48	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
49	C₆₄	—	38	1	no	—
50	C₆₄	—	38	1	no	—
51	C₂×C₁₉	—	2	1	no	—
52	C₂×C₁₉	—	4	1	no	—
53	C₂×C₁₉	C₂²⋊C₃₂	1	1	yes	characteristic
54	#131	C₁₉⋊C₈	1	1	yes	characteristic
55	M₃₂	—	2	1	no	—
56	M₃₂	C₁₉⋊C₈	1	1	yes	characteristic
57	C₂×C₁₆	—	2	1	no	—
58	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
59	C₃₂	—	2	1	no	—
60	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
61	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
62	C₁₉	#7514	1	1	yes	characteristic, complemented, Sylow
63	#41	C₁₉⋊C₁₆	1	1	yes	characteristic
64	M₁₆	—	2	1	no	—
65	M₁₆	C₁₉⋊C₁₆	1	1	yes	characteristic
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	#64520	1	1	yes	characteristic
70	C₁₆	C₂²⋊Dic₁₉	1	1	yes	characteristic
71	Q₈	C₁₉⋊C₃₂	1	1	yes	characteristic
72	D₄	—	2	1	no	—
73	D₄	C₁₉⋊C₃₂	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	#10597269	1	1	yes	characteristic
78	C₈	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
79	C₂²	—	2	1	no	—
80	C₂²	#11926378	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	C₂²⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
83	C₄	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	4	1	no	—
86	C₂	C₂²⋊(C₁₉⋊C₃₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#2258	C₂
socle	C₂×C₁₉	C₂²⋊C₃₂
prime radical	#41×C₁₉	C₁₆
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#2258	D₁₉
hypocenter	C₁₉	#7514
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ #2258

Complements

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

N	H ≅ G/N	type
1. #14561846	C₂	semidirect
2. C₂×C₁₉⋊C₆₄	C₂	semidirect
62. C₁₉	#7514	semidirect

Maximal subgroups

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

subgroup	index
#14561846	2
C₂×C₁₉⋊C₆₄	2
C₁₉×#2258	2
#7514	19