Subgroups — #28476592

Order 15104.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#21422300	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#1425	C₂	1	1	yes	maximal, characteristic
4	#16837232	—	2	1	no	—
5	C₅₉⋊C₆₄	C₄	1	2	yes	—
6	C₂×C₃₂×C₅₉	C₂²	1	1	yes	characteristic
7	C₅₉×#368	—	2	1	no	—
8	#14273663	—	4	1	no	—
9	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
10	#108×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	#11745664	—	8	1	no	—
16	C₁₆×C₅₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₅₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₅₉	D₁₆	1	1	yes	characteristic
19	C₈×C₅₉	—	16	1	no	—
20	C₈×C₅₉	#107	1	1	yes	characteristic
21	C₈×C₅₉	Q₃₂	1	1	yes	characteristic
22	C₅₉⋊C₈	—	16	1	no	—
23	#7547	—	59	1	no	maximal, Sylow
24	C₂²×C₅₉	Q₆₄	1	1	yes	characteristic
25	C₄×C₅₉	#366	1	1	yes	characteristic
26	C₄×C₅₉	D₃₂	1	1	yes	characteristic
27	C₂×C₆₄	—	59	1	no	—
28	#1425	—	59	1	no	—
29	#1425	D₅₉	1	1	yes	characteristic
30	C₂×C₅₉	—	2	1	no	—
31	C₂×C₅₉	#1423	1	1	yes	characteristic
32	C₂×C₃₂	C₂×D₅₉	1	1	yes	characteristic
33	#368	—	2	1	no	—
34	#368	—	118	1	no	—
35	C₆₄	—	59	2	no	—
36	C₅₉	#7547	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	236	1	no	—
40	C₃₂	Dic₁₁₈	1	1	yes	characteristic
41	C₃₂	C₄×D₅₉	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	472	1	no	—
44	C₂×C₈	#11745669	1	1	yes	characteristic
45	C₁₆	Dic₅₉⋊C₄	1	1	yes	characteristic
46	C₁₆	#11745672	1	1	yes	characteristic
47	C₂×C₄	#14273668	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	944	1	no	—
50	C₈	#14273660	1	1	yes	characteristic
51	C₈	#14273673	1	1	yes	characteristic
52	C₂²	#16837242	1	1	yes	characteristic
53	C₄	#16837227	1	1	yes	characteristic
54	C₄	#16837237	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#21422295	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16837237
commutator	C₃₂×C₅₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₅₉
Fitting	C₅₉×#1425	C₂
socle	C₂×C₅₉	#1423
prime radical	C₂²×C₅₉	Q₆₄
cosocle	C₂×C₃₂×C₅₉	C₂²
hypercenter	#1425	D₅₉
hypocenter	C₅₉	#7547
LCS	G ▷ C₃₂×C₅₉ ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
36. C₅₉	#7547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉⋊C₆₄	2
#21422300	2
C₅₉×#1425	2
#7547	59