Subgroups — C₄×C₁₉×C₂₅₆ #72197113

Order 19456.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×C₂₅₆	C₂	1	2	yes	maximal
3	C₄×C₂₅₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₁₉×C₁₂₈	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₁₂₈	C₂²	1	1	yes	characteristic
6	C₄×C₁₉×C₆₄	C₄	1	1	yes	characteristic
7	C₁₉×C₂₅₆	C₄	1	4	yes	direct product factor
8	C₂×C₁₉×C₆₄	C₈	1	1	yes	characteristic
9	C₂×C₁₉×C₆₄	C₂×C₄	1	1	yes	characteristic
10	C₄×C₁₉×C₃₂	C₈	1	1	yes	characteristic
11	C₁₉×C₁₂₈	C₈	1	2	yes	—
12	C₁₉×C₁₂₈	C₂×C₄	1	2	yes	—
13	C₂×C₁₉×C₃₂	C₁₆	1	1	yes	characteristic
14	C₂×C₁₉×C₃₂	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₆×C₁₉	C₁₆	1	1	yes	characteristic
16	C₁₉×C₆₄	C₁₆	1	2	yes	—
17	C₁₉×C₆₄	C₄²	1	1	yes	characteristic
18	C₁₉×C₆₄	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₆×C₁₉	C₃₂	1	1	yes	characteristic
20	C₂×C₁₆×C₁₉	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₈×C₁₉	C₃₂	1	1	yes	characteristic
22	C₁₉×C₃₂	C₃₂	1	2	yes	—
23	C₁₉×C₃₂	C₄×C₈	1	1	yes	characteristic
24	C₁₉×C₃₂	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₂₅₆	C₂×C₁₉	1	2	yes	—
26	C₄×C₁₂₈	C₂×C₁₉	1	1	yes	characteristic
27	C₂×C₈×C₁₉	C₆₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	C₂×C₃₂	1	1	yes	characteristic
29	C₄²×C₁₉	C₆₄	1	1	yes	characteristic
30	C₁₆×C₁₉	C₆₄	1	2	yes	—
31	C₁₆×C₁₉	C₄×C₁₆	1	1	yes	characteristic
32	C₁₆×C₁₉	C₂×C₃₂	1	1	yes	characteristic
33	C₂×C₁₂₈	C₄×C₁₉	1	1	yes	characteristic
34	C₂×C₁₂₈	C₂²×C₁₉	1	1	yes	characteristic
35	C₄×C₆₄	C₄×C₁₉	1	1	yes	characteristic
36	C₂₅₆	C₄×C₁₉	1	4	yes	direct product factor
37	C₂×C₄×C₁₉	C₁₂₈	1	2	yes	—
38	C₂×C₄×C₁₉	C₂×C₆₄	1	1	yes	characteristic
39	C₈×C₁₉	C₁₂₈	1	2	yes	—
40	C₈×C₁₉	C₄×C₃₂	1	1	yes	characteristic
41	C₈×C₁₉	C₂×C₆₄	1	1	yes	characteristic
42	C₂×C₆₄	C₈×C₁₉	1	1	yes	characteristic
43	C₂×C₆₄	C₂×C₄×C₁₉	1	1	yes	characteristic
44	C₄×C₃₂	C₈×C₁₉	1	1	yes	characteristic
45	C₁₂₈	C₈×C₁₉	1	2	yes	—
46	C₁₂₈	C₂×C₄×C₁₉	1	2	yes	—
47	C₂²×C₁₉	C₂×C₁₂₈	1	1	yes	characteristic
48	C₄×C₁₉	C₂₅₆	1	4	yes	direct product factor
49	C₄×C₁₉	C₄×C₆₄	1	1	yes	characteristic
50	C₄×C₁₉	C₂×C₁₂₈	1	1	yes	characteristic
51	C₂×C₃₂	C₁₆×C₁₉	1	1	yes	characteristic
52	C₂×C₃₂	C₂×C₈×C₁₉	1	1	yes	characteristic
53	C₄×C₁₆	C₁₆×C₁₉	1	1	yes	characteristic
54	C₆₄	C₁₆×C₁₉	1	2	yes	—
55	C₆₄	C₄²×C₁₉	1	1	yes	characteristic
56	C₆₄	C₂×C₈×C₁₉	1	1	yes	characteristic
57	C₂×C₁₉	C₄×C₁₂₈	1	1	yes	characteristic
58	C₂×C₁₉	C₂×C₂₅₆	1	2	yes	—
59	C₂×C₁₆	C₁₉×C₃₂	1	1	yes	characteristic
60	C₂×C₁₆	C₂×C₁₆×C₁₉	1	1	yes	characteristic
61	C₄×C₈	C₁₉×C₃₂	1	1	yes	characteristic
62	C₃₂	C₁₉×C₃₂	1	2	yes	—
63	C₃₂	C₄×C₈×C₁₉	1	1	yes	characteristic
64	C₃₂	C₂×C₁₆×C₁₉	1	1	yes	characteristic
65	C₁₉	C₄×C₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₈	C₁₉×C₆₄	1	1	yes	characteristic
67	C₂×C₈	C₂×C₁₉×C₃₂	1	1	yes	characteristic
68	C₄²	C₁₉×C₆₄	1	1	yes	characteristic
69	C₁₆	C₁₉×C₆₄	1	2	yes	—
70	C₁₆	C₄×C₁₆×C₁₉	1	1	yes	characteristic
71	C₁₆	C₂×C₁₉×C₃₂	1	1	yes	characteristic
72	C₂×C₄	C₁₉×C₁₂₈	1	2	yes	—
73	C₂×C₄	C₂×C₁₉×C₆₄	1	1	yes	characteristic
74	C₈	C₁₉×C₁₂₈	1	2	yes	—
75	C₈	C₄×C₁₉×C₃₂	1	1	yes	characteristic
76	C₈	C₂×C₁₉×C₆₄	1	1	yes	characteristic
77	C₂²	C₂×C₁₉×C₁₂₈	1	1	yes	characteristic
78	C₄	C₁₉×C₂₅₆	1	4	yes	direct product factor
79	C₄	C₄×C₁₉×C₆₄	1	1	yes	characteristic
80	C₄	C₂×C₁₉×C₁₂₈	1	1	yes	characteristic
81	C₂	C₂×C₁₉×C₂₅₆	1	2	yes	—
82	C₂	C₄×C₁₉×C₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₂₈	C₂²×C₁₉
socle, prime radical	C₂²×C₁₉	C₂×C₁₂₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₂₅₆	C₁₉	direct (N × H)
7. C₁₉×C₂₅₆	C₄	direct (N × H)
36. C₂₅₆	C₄×C₁₉	direct (N × H)
48. C₄×C₁₉	C₂₅₆	direct (N × H)
65. C₁₉	C₄×C₂₅₆	direct (N × H)
78. C₄	C₁₉×C₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×C₁₂₈	2
C₂×C₁₉×C₂₅₆	2
C₄×C₂₅₆	19

Subgroups — C4×C19×C256 #72197113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×C₂₅₆ #72197113