Subgroups — C₅₉×#7548 #28419657

Order 15104.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#1425	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#1424	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₂×C₅₉	C₂²	1	1	yes	characteristic
5	C₅₉×#368	—	2	1	no	—
6	C₅₉×#366	—	2	1	no	—
7	C₅₉×C₆₄	C₄	1	2	yes	complemented
8	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
9	#108×C₅₉	—	4	1	no	—
10	#107×C₅₉	—	4	1	no	—
11	C₃₂×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₅₉	Q₈	1	1	yes	characteristic
13	M₁₆×C₅₉	—	8	1	no	—
14	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
15	C₄⋊C₄×C₅₉	—	8	1	no	—
16	C₁₆×C₅₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₅₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₅₉	—	16	1	no	—
19	C₂×C₄×C₅₉	D₁₆	1	1	yes	characteristic
20	C₈×C₅₉	—	16	1	no	—
21	C₈×C₅₉	#107	1	1	yes	characteristic
22	C₈×C₅₉	Q₃₂	1	1	yes	characteristic
23	#7548	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₅₉	SD₆₄	1	1	yes	characteristic
25	C₄×C₅₉	—	32	1	no	—
26	C₄×C₅₉	#366	1	1	yes	characteristic
27	C₄×C₅₉	SD₆₄	1	1	yes	characteristic
28	M₁₂₈	C₂×C₅₉	1	1	yes	characteristic
29	#1425	C₂×C₅₉	1	1	yes	characteristic
30	#1424	C₂×C₅₉	1	1	yes	characteristic
31	C₂×C₅₉	—	2	1	no	—
32	C₂×C₅₉	#1424	1	1	yes	characteristic
33	C₂×C₃₂	C₂²×C₅₉	1	1	yes	characteristic
34	#368	—	2	1	no	—
35	#366	—	2	1	no	—
36	C₆₄	C₄×C₅₉	1	2	yes	complemented
37	C₅₉	#7548	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₆	D₄×C₅₉	1	1	yes	characteristic
39	#108	—	4	1	no	—
40	#107	—	4	1	no	—
41	C₃₂	C₂×C₄×C₅₉	1	1	yes	characteristic
42	C₃₂	Q₈×C₅₉	1	1	yes	characteristic
43	M₁₆	—	8	1	no	—
44	C₂×C₈	D₈×C₅₉	1	1	yes	characteristic
45	C₄⋊C₄	—	8	1	no	—
46	C₁₆	C₄⋊C₄×C₅₉	1	1	yes	characteristic
47	C₁₆	Q₁₆×C₅₉	1	1	yes	characteristic
48	C₂×C₄	—	16	1	no	—
49	C₂×C₄	D₁₆×C₅₉	1	1	yes	characteristic
50	C₈	—	16	1	no	—
51	C₈	#107×C₅₉	1	1	yes	characteristic
52	C₈	Q₃₂×C₅₉	1	1	yes	characteristic
53	C₂²	C₅₉×SD₆₄	1	1	yes	characteristic
54	C₄	—	32	1	no	—
55	C₄	C₅₉×#366	1	1	yes	characteristic
56	C₄	C₅₉×SD₆₄	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	C₅₉×#1424	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₉	#1424
commutator	C₃₂	C₂×C₄×C₅₉
Frattini, cosocle	C₂×C₃₂	C₂²×C₅₉
prime radical	C₂²×C₅₉	SD₆₄
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂×C₈×C₅₉ ◁ C₂×C₁₆×C₅₉ ◁ C₂×C₃₂×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₅₉×C₆₄	C₄	semidirect
23. #7548	C₅₉	direct (N × H)
36. C₆₄	C₄×C₅₉	semidirect
37. C₅₉	#7548	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×M₁₂₈	2
C₅₉×#1425	2
C₅₉×#1424	2
#7548	59

Subgroups — C59×#7548 #28419657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#7548 #28419657