Subgroups — C₃₂×C₅₉⋊C₈ #28476014

Order 15104.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉⋊C₃₂	C₄	1	2	yes	—
5	C₄×C₅₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₈×C₅₉⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₃₂×C₅₉	C₄	1	2	yes	—
8	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
9	C₂×C₅₉⋊C₁₆	C₈	1	2	yes	—
10	C₄×C₅₉⋊C₈	C₈	1	2	yes	—
11	C₅₉⋊C₃₂	C₈	1	4	yes	complemented
12	C₂×C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₃₂×C₅₉	C₈	1	4	yes	complemented
16	C₂×C₈×C₅₉	C₄²	1	1	yes	characteristic
17	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
18	C₄²×C₅₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₅₉⋊C₈	C₁₆	1	4	yes	—
20	C₁₆×C₅₉	C₂×C₈	1	2	yes	—
21	C₁₆×C₅₉	C₂×C₈	1	2	yes	—
22	C₅₉⋊C₁₆	C₁₆	1	4	yes	—
23	C₂×C₄×C₅₉	C₄×C₈	1	1	yes	characteristic
24	C₂×C₄×C₅₉	C₂×C₁₆	1	2	yes	—
25	C₈×C₅₉	C₄×C₈	1	1	yes	characteristic
26	C₈×C₅₉	C₄×C₈	1	1	yes	characteristic
27	C₈×C₅₉	C₂×C₁₆	1	2	yes	—
28	C₅₉⋊C₈	C₃₂	1	8	yes	direct product factor
29	C₈×C₃₂	—	59	1	no	maximal, Sylow
30	C₂²×C₅₉	C₄×C₁₆	1	1	yes	characteristic
31	C₄×C₅₉	C₈²	1	1	yes	characteristic
32	C₄×C₅₉	C₄×C₁₆	1	1	yes	characteristic
33	C₄×C₅₉	C₂×C₃₂	1	4	yes	—
34	C₄×C₃₂	—	59	1	no	—
35	C₄×C₃₂	D₅₉	1	1	yes	characteristic
36	C₈×C₁₆	—	59	1	no	—
37	C₂×C₅₉	C₈×C₁₆	1	1	yes	characteristic
38	C₂×C₅₉	C₄×C₃₂	1	2	yes	—
39	C₂×C₃₂	—	59	2	no	—
40	C₂×C₃₂	Dic₅₉	1	2	yes	—
41	C₄×C₁₆	—	59	1	no	—
42	C₄×C₁₆	C₂×D₅₉	1	1	yes	characteristic
43	C₈²	—	59	1	no	—
44	C₅₉	C₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₆	—	59	2	no	—
46	C₂×C₁₆	C₄×D₅₉	1	1	yes	characteristic
47	C₂×C₁₆	C₂×Dic₅₉	1	1	yes	characteristic
48	C₄×C₈	—	59	2	no	—
49	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
50	C₃₂	—	59	4	no	—
51	C₃₂	C₅₉⋊C₈	1	4	yes	direct product factor
52	C₂×C₈	—	59	4	no	—
53	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
54	C₂×C₈	C₄×Dic₅₉	1	1	yes	characteristic
55	C₄²	C₈×D₅₉	1	1	yes	characteristic
56	C₁₆	—	59	4	no	—
57	C₁₆	C₈×D₅₉	1	2	yes	—
58	C₁₆	C₂×C₅₉⋊C₈	1	2	yes	—
59	C₂×C₄	C₈×Dic₅₉	1	1	yes	characteristic
60	C₂×C₄	C₁₆×D₅₉	1	2	yes	—
61	C₈	—	59	8	no	—
62	C₈	C₈×Dic₅₉	1	1	yes	characteristic
63	C₈	C₄×C₅₉⋊C₈	1	1	yes	characteristic
64	C₈	C₁₆×D₅₉	1	2	yes	—
65	C₂²	C₁₆×Dic₅₉	1	1	yes	characteristic
66	C₄	C₈×C₅₉⋊C₈	1	1	yes	characteristic
67	C₄	C₁₆×Dic₅₉	1	1	yes	characteristic
68	C₄	C₃₂×D₅₉	1	4	yes	—
69	C₂	C₁₆×C₅₉⋊C₈	1	1	yes	characteristic
70	C₂	C₃₂×Dic₅₉	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₃₂	D₅₉
commutator, hypocenter	C₅₉	C₈×C₃₂
Frattini	C₄×C₁₆	C₂×D₅₉
Fitting	C₄×C₃₂×C₅₉	C₂
socle, prime radical	C₂²×C₅₉	C₄×C₁₆
cosocle	C₄×C₁₆×C₅₉	C₂²
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
11. C₅₉⋊C₃₂	C₈	semidirect
15. C₃₂×C₅₉	C₈	semidirect
28. C₅₉⋊C₈	C₃₂	direct (N × H)
44. C₅₉	C₈×C₃₂	semidirect
51. C₃₂	C₅₉⋊C₈	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×C₅₉⋊C₃₂	2
C₁₆×C₅₉⋊C₈	2
C₄×C₃₂×C₅₉	2
C₈×C₃₂	59

Subgroups — C32×C59⋊C8 #28476014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₂×C₅₉⋊C₈ #28476014