Subgroups — #21425856

Order 7552.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#16837357	C₂	1	1	yes	maximal, characteristic
3	Dic₅₉⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#11745664	C₄	1	1	yes	characteristic
6	#14273686	C₄	1	1	yes	characteristic
7	C₂×C₅₉⋊C₁₆	—	2	2	no	—
8	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
9	#14273637	C₄	1	2	yes	—
10	C₈×Dic₅₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	M₃₂×C₅₉	—	2	2	no	—
13	C₂×C₁₆×C₅₉	C₂²	1	2	yes	—
14	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₅₉	D₄	1	2	yes	—
17	C₂×C₈×C₅₉	Q₈	1	2	yes	—
18	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₅₉	C₈	1	2	yes	—
20	C₄⋊Dic₅₉	C₈	1	2	yes	—
21	C₄×Dic₅₉	C₂×C₄	1	2	yes	—
22	#11745664	—	2	2	no	—
23	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
24	C₁₆×C₅₉	—	2	2	no	—
25	C₅₉⋊C₁₆	—	2	2	no	—
26	C₂³×C₅₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₅₉	M₁₆	1	2	yes	—
30	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₅₉	C₂×C₈	1	4	yes	—
32	C₈×C₅₉	C₄⋊C₄	1	2	yes	—
33	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
34	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
35	C₅₉⋊C₈	—	2	2	no	—
36	C₂²×C₅₉	—	2	2	no	—
37	C₂²×C₅₉	C₄⋊C₈	1	2	yes	—
38	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₅₉	C₄⋊C₈	1	2	yes	—
40	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
42	Dic₅₉	—	2	4	no	—
43	#2151	—	59	1	no	maximal, Sylow
44	C₂×C₅₉	—	2	2	no	—
45	C₂×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₅₉	#504	1	2	yes	—
47	C₂×M₃₂	D₅₉	1	1	yes	characteristic
48	C₂²×C₁₆	—	59	1	no	—
49	#405	—	59	1	no	—
50	C₄⋊C₁₆	—	59	4	no	—
51	C₅₉	#2151	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	59	1	no	—
53	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
54	#117	—	59	1	no	—
55	M₃₂	—	2	2	no	—
56	C₂×C₁₆	—	59	2	no	—
57	C₂×C₁₆	—	118	2	no	—
58	C₂×C₁₆	C₂×D₅₉	1	2	yes	—
59	#97	—	59	2	no	—
60	C₄×C₈	—	59	2	no	—
61	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
62	M₁₆	—	118	2	no	—
63	C₂×C₈	—	59	2	no	—
64	C₂×C₈	Dic₁₁₈	1	2	yes	—
65	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
67	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
68	C₄⋊C₄	—	59	2	no	—
69	C₂²⋊C₄	—	59	2	no	—
70	C₄²	—	59	2	no	—
71	C₁₆	—	2	2	no	—
72	C₁₆	—	118	2	no	—
73	C₂³	C₈×D₅₉	1	1	yes	characteristic
74	C₂×C₄	—	59	4	no	—
75	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
76	C₂×C₄	#11745659	1	2	yes	—
77	C₂×C₄	Dic₅₉⋊C₄	1	2	yes	—
78	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
79	C₈	—	118	2	no	—
80	C₈	Dic₅₉⋊C₄	1	2	yes	—
81	C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
82	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	Dic₅₉⋊C₈	1	2	yes	—
85	C₂²	C₂×C₈×D₅₉	1	1	yes	characteristic
86	C₄	—	118	4	no	—
87	C₄	Dic₅₉⋊C₈	1	2	yes	—
88	C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
89	C₄	C₂×#11745659	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×Dic₅₉⋊C₈	1	1	yes	characteristic
92	C₂	#16837820	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₅₉
commutator, socle	C₂²×C₅₉	C₂²×C₈
Fitting	C₂×M₃₂×C₅₉	C₂
hypercenter	C₂×M₃₂	D₅₉
hypocenter	C₅₉	#2151
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. Dic₅₉⋊C₁₆	C₂	semidirect
51. C₅₉	#2151	semidirect