Subgroups — C₄×C₁₉×#564 #18040314

Order 4864.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#564	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2382	C₂	1	15	yes	maximal
3	C₄×C₁₉×#125	C₂	1	15	yes	maximal
4	C₁₉×#564	C₄	1	16	yes	direct product factor
5	C₂×C₁₉×#125	C₂²	1	15	yes	—
6	C₁₉×#389	C₂²	1	30	yes	—
7	C₁₉×#387	C₂²	1	60	yes	—
8	C₁₉×#382	C₂²	1	15	yes	—
9	C₄×C₄⋊C₄×C₁₉	C₂²	1	30	yes	—
10	C₄³×C₁₉	C₂²	1	5	yes	—
11	C₁₉×#125	C₂×C₄	1	120	yes	—
12	C₂×C₄⋊C₄×C₁₉	C₂³	1	30	yes	—
13	C₂×C₄⋊C₄×C₁₉	C₂³	1	30	yes	—
14	C₂×C₄²×C₁₉	C₂³	1	15	yes	—
15	C₂×C₄²×C₁₉	C₂³	1	15	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	5	yes	—
17	C₁₉×#95	C₂³	1	60	yes	—
18	C₂²×C₄×C₁₉	C₂⁴	1	15	yes	—
19	C₂²×C₄×C₁₉	C₂⁴	1	15	yes	—
20	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	4	30	no	—
22	C₄⋊C₄×C₁₉	C₂²×C₄	1	120	yes	—
23	C₄²×C₁₉	—	2	30	no	—
24	C₄²×C₁₉	—	4	15	no	—
25	C₄²×C₁₉	C₂²×C₄	1	20	yes	—
26	C₄×#564	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
28	C₂×C₄×C₁₉	—	2	15	no	—
29	C₂×C₄×C₁₉	—	2	15	no	—
30	C₂×C₄×C₁₉	—	2	15	no	—
31	C₂×C₄×C₁₉	—	2	30	no	—
32	C₂×C₄×C₁₉	C₂³×C₄	1	30	yes	—
33	C₂×C₄×C₁₉	2₋¹⁺⁴	1	6	yes	—
34	C₂×#564	C₂×C₁₉	1	1	yes	characteristic
35	#2382	C₂×C₁₉	1	15	yes	—
36	C₄×#125	C₂×C₁₉	1	15	yes	—
37	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
38	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	3	yes	—
39	C₂²×C₁₉	#585	1	3	yes	—
40	C₄×C₁₉	—	2	30	no	—
41	C₄×C₁₉	—	4	15	no	—
42	C₄×C₁₉	#564	1	4	yes	direct product factor
43	#564	C₄×C₁₉	1	16	yes	direct product factor
44	C₂×#125	C₂²×C₁₉	1	15	yes	—
45	#389	C₂²×C₁₉	1	30	yes	—
46	#387	C₂²×C₁₉	1	60	yes	—
47	#382	C₂²×C₁₉	1	15	yes	—
48	C₄×C₄⋊C₄	C₂²×C₁₉	1	30	yes	—
49	C₄³	C₂²×C₁₉	1	5	yes	—
50	C₂×C₁₉	C₄×2₋¹⁺⁴	1	3	yes	—
51	C₂×C₁₉	C₂×#564	1	1	yes	characteristic
52	C₂×C₁₉	#3531	1	3	yes	—
53	#125	C₂×C₄×C₁₉	1	120	yes	—
54	C₂×C₄⋊C₄	C₂³×C₁₉	1	30	yes	—
55	C₂×C₄⋊C₄	C₂³×C₁₉	1	30	yes	—
56	C₂×C₄²	C₂³×C₁₉	1	15	yes	—
57	C₂×C₄²	C₂³×C₁₉	1	15	yes	—
58	C₂×C₄²	C₂³×C₁₉	1	5	yes	—
59	#95	C₂³×C₁₉	1	60	yes	—
60	C₁₉	C₄×#564	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₄	C₂⁴×C₁₉	1	15	yes	—
62	C₂²×C₄	C₂⁴×C₁₉	1	15	yes	—
63	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
64	C₄⋊C₄	—	4	30	no	—
65	C₄⋊C₄	C₂²×C₄×C₁₉	1	120	yes	—
66	C₄²	—	2	30	no	—
67	C₄²	—	4	15	no	—
68	C₄²	C₂²×C₄×C₁₉	1	20	yes	—
69	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	2	15	no	—
73	C₂×C₄	—	2	30	no	—
74	C₂×C₄	C₂³×C₄×C₁₉	1	30	yes	—
75	C₂×C₄	C₁₉×2₋¹⁺⁴	1	6	yes	—
76	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
77	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	3	yes	—
78	C₂²	C₁₉×#585	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	4	15	no	—
81	C₄	C₁₉×#564	1	4	yes	direct product factor
82	C₂	C₄×C₁₉×2₋¹⁺⁴	1	3	yes	—
83	C₂	C₂×C₁₉×#564	1	1	yes	characteristic
84	C₂	C₁₉×#3531	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle, prime radical	C₂³×C₁₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#564	C₄	direct (N × H)
26. C₄×#564	C₁₉	direct (N × H)
42. C₄×C₁₉	#564	direct (N × H)
43. #564	C₄×C₁₉	direct (N × H)
60. C₁₉	C₄×#564	direct (N × H)
81. C₄	C₁₉×#564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#564	2
C₁₉×#2382	2
C₄×C₁₉×#125	2
C₄×#564	19

Subgroups — C4×C19×#564 #18040314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#564 #18040314