Subgroups — #564×D₅₉ #21438238

Order 7552.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉⋊#564	C₂	1	15	yes	maximal, complemented
2	#125×D₅₉	C₂	1	15	yes	maximal
3	C₅₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273719	C₂²	1	15	yes	—
5	#14273718	C₂²	1	30	yes	—
6	#14273717	C₂²	1	60	yes	—
7	C₄⋊C₄×D₅₉	C₂²	1	30	yes	—
8	C₄²×D₅₉	C₂²	1	5	yes	—
9	#125×C₅₉	C₂²	1	15	yes	—
10	C₂×C₄×D₅₉	C₂³	1	15	yes	—
11	C₄⋊C₄×C₅₉	C₂³	1	30	yes	—
12	C₄²×C₅₉	C₂³	1	5	yes	—
13	C₄⋊Dic₅₉	C₂³	1	30	yes	—
14	Dic₅₉⋊C₄	C₂³	1	60	yes	—
15	C₄×Dic₅₉	C₂³	1	15	yes	—
16	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
17	C₂×C₄×C₅₉	C₂⁴	1	15	yes	—
18	C₂×Dic₅₉	C₂⁴	1	15	yes	—
19	C₄×D₅₉	—	2	30	no	—
20	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
21	C₂×D₅₉	2₋¹⁺⁴	1	6	yes	—
22	C₄×C₅₉	—	2	15	no	—
23	Dic₅₉	—	2	15	no	—
24	C₂×#564	—	59	1	no	maximal, Sylow
25	C₂×C₅₉	C₂×2₋¹⁺⁴	1	3	yes	—
26	D₅₉	#564	1	4	yes	direct product factor
27	#564	—	59	15	no	—
28	#564	D₅₉	1	1	yes	characteristic, direct product factor
29	C₂×#125	—	59	15	no	—
30	C₅₉	C₂×#564	1	1	yes	characteristic, complemented, Sylow
31	#125	—	59	60	no	—
32	#125	—	59	30	no	—
33	#125	—	59	15	no	—
34	#125	C₂×D₅₉	1	15	yes	—
35	C₂×C₄⋊C₄	—	59	30	no	—
36	C₂×C₄²	—	59	5	no	—
37	C₂²×C₄	—	59	15	no	—
38	C₄⋊C₄	—	59	60	no	—
39	C₄⋊C₄	—	59	30	no	—
40	C₄⋊C₄	C₂²×D₅₉	1	30	yes	—
41	C₄²	—	59	15	no	—
42	C₄²	C₂²×D₅₉	1	5	yes	—
43	C₂³	—	59	1	no	—
44	C₂×C₄	—	59	15	no	—
45	C₂×C₄	—	118	30	no	—
46	C₂×C₄	C₂³×D₅₉	1	15	yes	—
47	C₂²	—	59	6	no	—
48	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
49	C₄	—	2	15	no	—
50	C₄	—	118	15	no	—
51	C₂	—	59	4	no	—
52	C₂	2₋¹⁺⁴×D₅₉	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#564	C₂
hypercenter	#564	D₅₉
hypocenter	C₅₉	C₂×#564
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #564

Complements

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

N	H ≅ G/N	type
1. C₅₉⋊#564	C₂	semidirect
3. C₅₉×#564	C₂	semidirect
26. D₅₉	#564	direct (N × H)
28. #564	D₅₉	direct (N × H)
30. C₅₉	C₂×#564	semidirect

Subgroups — #564×D59 #21438238

Conjugacy classes of subgroups

Complements

Subgroups — #564×D₅₉ #21438238