Subgroups — C₅×C₁₆³ #72198073

Order 20480.

8774 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₁₆²	C₂	1	7	yes	maximal
2	C₅×C₈²×C₁₆	C₂²	1	7	yes	—
3	C₄×C₅×C₁₆²	C₄	1	28	yes	—
4	C₁₆³	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₅×C₈³	C₂³	1	1	yes	characteristic
6	C₄×C₅×C₈×C₁₆	C₂×C₄	1	42	yes	—
7	C₂×C₅×C₁₆²	C₈	1	112	yes	—
8	C₈×C₁₆²	C₂×C₅	1	7	yes	—
9	C₈²×C₁₆	C₂²×C₅	1	7	yes	—
10	C₄×C₁₆²	C₄×C₅	1	28	yes	—
11	C₄²×C₅×C₁₆	C₄²	1	28	yes	—
12	C₂×C₅×C₈×C₁₆	C₂×C₈	1	168	yes	—
13	C₄×C₅×C₈²	C₂²×C₄	1	7	yes	—
14	C₅×C₁₆²	C₁₆	1	448	yes	direct product factor
15	C₂×C₄×C₅×C₁₆	C₄×C₈	1	168	yes	—
16	C₄²×C₅×C₈	C₂×C₄²	1	7	yes	—
17	C₂×C₅×C₈²	C₂²×C₈	1	28	yes	—
18	C₅×C₈×C₁₆	C₂×C₁₆	1	672	yes	—
19	C₄×C₈×C₁₆	C₂×C₄×C₅	1	42	yes	—
20	C₂×C₁₆²	C₅×C₈	1	112	yes	—
21	C₈³	C₂³×C₅	1	1	yes	characteristic
22	C₂²×C₅×C₁₆	C₈²	1	112	yes	—
23	C₂×C₄×C₅×C₈	C₂×C₄×C₈	1	42	yes	—
24	C₄³×C₅	C₄³	1	1	yes	characteristic
25	C₄×C₅×C₁₆	C₄×C₁₆	1	672	yes	—
26	C₅×C₈²	C₂²×C₁₆	1	112	yes	—
27	C₄²×C₁₆	C₄²×C₅	1	28	yes	—
28	C₂×C₈×C₁₆	C₂×C₅×C₈	1	168	yes	—
29	C₄×C₈²	C₂²×C₄×C₅	1	7	yes	—
30	C₁₆²	C₅×C₁₆	1	448	yes	direct product factor
31	C₂²×C₅×C₈	C₂×C₈²	1	28	yes	—
32	C₂×C₄²×C₅	C₄²×C₈	1	7	yes	—
33	C₂×C₅×C₁₆	C₈×C₁₆	1	672	yes	—
34	C₄×C₅×C₈	C₂×C₄×C₁₆	1	168	yes	—
35	C₂×C₄×C₁₆	C₄×C₅×C₈	1	168	yes	—
36	C₄²×C₈	C₂×C₄²×C₅	1	7	yes	—
37	C₂×C₈²	C₂²×C₅×C₈	1	28	yes	—
38	C₈×C₁₆	C₂×C₅×C₁₆	1	672	yes	—
39	C₂²×C₄×C₅	C₄×C₈²	1	7	yes	—
40	C₂×C₅×C₈	C₂×C₈×C₁₆	1	168	yes	—
41	C₄²×C₅	C₄²×C₁₆	1	28	yes	—
42	C₅×C₁₆	C₁₆²	1	448	yes	direct product factor
43	C₂²×C₁₆	C₅×C₈²	1	112	yes	—
44	C₂×C₄×C₈	C₂×C₄×C₅×C₈	1	42	yes	—
45	C₄³	C₄³×C₅	1	1	yes	characteristic
46	C₄×C₁₆	C₄×C₅×C₁₆	1	672	yes	—
47	C₈²	C₂²×C₅×C₁₆	1	112	yes	—
48	C₂³×C₅	C₈³	1	1	yes	characteristic
49	C₂×C₄×C₅	C₄×C₈×C₁₆	1	42	yes	—
50	C₅×C₈	C₂×C₁₆²	1	112	yes	—
51	C₂²×C₈	C₂×C₅×C₈²	1	28	yes	—
52	C₂×C₄²	C₄²×C₅×C₈	1	7	yes	—
53	C₂×C₁₆	C₅×C₈×C₁₆	1	672	yes	—
54	C₄×C₈	C₂×C₄×C₅×C₁₆	1	168	yes	—
55	C₂²×C₅	C₈²×C₁₆	1	7	yes	—
56	C₄×C₅	C₄×C₁₆²	1	28	yes	—
57	C₂²×C₄	C₄×C₅×C₈²	1	7	yes	—
58	C₂×C₈	C₂×C₅×C₈×C₁₆	1	168	yes	—
59	C₄²	C₄²×C₅×C₁₆	1	28	yes	—
60	C₁₆	C₅×C₁₆²	1	448	yes	direct product factor
61	C₂×C₅	C₈×C₁₆²	1	7	yes	—
62	C₂³	C₅×C₈³	1	1	yes	characteristic
63	C₂×C₄	C₄×C₅×C₈×C₁₆	1	42	yes	—
64	C₈	C₂×C₅×C₁₆²	1	112	yes	—
65	C₅	C₁₆³	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	C₅×C₈²×C₁₆	1	7	yes	—
67	C₄	C₄×C₅×C₁₆²	1	28	yes	—
68	C₂	C₅×C₈×C₁₆²	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈³	C₂³×C₅
socle, prime radical	C₂³×C₅	C₈³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₆³	C₅	direct (N × H)
14. C₅×C₁₆²	C₁₆	direct (N × H)
30. C₁₆²	C₅×C₁₆	direct (N × H)
42. C₅×C₁₆	C₁₆²	direct (N × H)
60. C₁₆	C₅×C₁₆²	direct (N × H)
65. C₅	C₁₆³	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×C₁₆²	2
C₁₆³	5

Subgroups — C5×C163 #72198073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₆³ #72198073