Subgroups — #21422007

Order 7552.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837459	C₂	1	2	yes	maximal
2	C₅₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
4	C₂²⋊(C₅₉⋊C₈)	C₄	1	4	yes	—
5	#14273638	—	2	2	no	—
6	C₂×M₁₆×C₅₉	C₄	1	2	yes	—
7	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₅₉	—	2	2	no	—
9	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
11	M₁₆×C₅₉	—	4	2	no	—
12	C₂×C₈×C₅₉	—	2	2	no	—
13	C₄²×C₅₉	D₄	1	1	yes	characteristic
14	C₄²×C₅₉	D₄	1	2	yes	—
15	C₄²×C₅₉	Q₈	1	1	yes	characteristic
16	C₂×C₅₉⋊C₈	—	2	4	no	—
17	C₂³×C₅₉	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₅₉	—	2	1	no	—
19	C₂×C₄×C₅₉	—	2	1	no	—
20	C₂×C₄×C₅₉	—	4	2	no	—
21	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
25	C₈×C₅₉	—	4	2	no	—
26	C₅₉⋊C₈	—	4	4	no	—
27	C₂²×C₅₉	—	2	1	no	—
28	C₂²×C₅₉	—	2	2	no	—
29	C₂²×C₅₉	#95	1	1	yes	characteristic
30	C₄×C₅₉	—	2	1	no	—
31	C₄×C₅₉	—	2	2	no	—
32	C₄×C₅₉	—	2	2	no	—
33	C₄×C₅₉	#100	1	1	yes	characteristic
34	C₄×C₅₉	#101	1	1	yes	characteristic
35	#1307	—	59	1	no	maximal, Sylow
36	C₂×C₅₉	—	4	1	no	—
37	C₂×C₅₉	#343	1	1	yes	characteristic
38	C₂×C₅₉	#344	1	2	yes	—
39	#432	—	59	2	no	—
40	#423	D₅₉	1	1	yes	characteristic
41	C₅₉	#1307	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	Dic₅₉	1	2	yes	—
43	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
44	C₄⋊C₈	—	2	2	no	—
45	C₄⋊C₈	—	118	2	no	—
46	C₂²⋊C₈	—	59	4	no	—
47	#97	—	118	2	no	—
48	C₂²×C₄	C₄×D₅₉	1	2	yes	—
49	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
50	M₁₆	—	4	2	no	—
51	C₂×C₈	—	2	2	no	—
52	C₂×C₈	—	118	4	no	—
53	C₄²	Dic₁₁₈	1	1	yes	characteristic
54	C₄²	D₂₃₆	1	1	yes	characteristic
55	C₄²	C₂²⋊D₅₉	1	2	yes	—
56	C₂³	C₄×Dic₅₉	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	Dic₅₉⋊C₄	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
62	C₂×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
63	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
64	C₈	—	4	2	no	—
65	C₈	—	236	4	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₅₉⋊#95	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	2	no	—
72	C₄	#14273644	1	1	yes	characteristic
73	C₄	#14273646	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	#16837171	1	1	yes	characteristic
76	C₂	#16837174	1	2	yes	—

	subgroup	G/H
center	C₂²	C₅₉⋊#95
commutator	C₂³×C₅₉	C₄²
Frattini	C₂×C₄²	C₂×D₅₉
Fitting	C₅₉×#423	C₂
socle	C₂²×C₅₉	#95
hypercenter	#423	D₅₉
hypocenter	C₅₉	#1307
LCS	G ▷ C₂³×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
41. C₅₉	#1307	semidirect