Subgroups — #28478064

Order 15104.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14273637	C₂	1	3	yes	maximal
2	C₂×#16837123	C₂	1	3	yes	maximal
3	C₂×C₈²×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#14273637	C₄	1	12	yes	—
5	C₂×C₄×C₅₉⋊C₈	C₂²	1	3	yes	—
6	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
7	#16837123	C₄	1	12	yes	complemented
8	C₂×C₄×C₈×C₅₉	C₂²	1	3	yes	—
9	C₈²×C₅₉	C₄	1	4	yes	complemented
10	C₂²×C₅₉⋊C₈	C₂×C₄	1	6	yes	—
11	C₂×C₄×Dic₅₉	C₂×C₄	1	6	yes	—
12	#14273637	—	2	24	no	—
13	C₄×C₅₉⋊C₈	C₂×C₄	1	12	yes	—
14	C₂²×C₈×C₅₉	C₂×C₄	1	6	yes	—
15	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₅₉	C₂×C₄	1	6	yes	—
17	C₄×C₈×C₅₉	C₂×C₄	1	6	yes	—
18	C₂²×C₄×C₅₉	C₂²×C₄	1	3	yes	—
19	C₂²×Dic₅₉	C₄²	1	4	yes	—
20	C₂×C₈×C₅₉	C₄²	1	12	yes	—
21	C₂×C₈×C₅₉	M₁₆	1	24	yes	—
22	C₄²×C₅₉	C₂²×C₄	1	3	yes	—
23	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×Dic₅₉	—	2	12	no	—
25	C₂×C₅₉⋊C₈	—	2	12	no	—
26	C₂×C₅₉⋊C₈	C₄²	1	12	yes	—
27	C₂³×C₅₉	C₂×C₄²	1	1	yes	characteristic
28	C₂×C₄×C₅₉	C₂×C₄²	1	3	yes	—
29	C₂×C₄×C₅₉	C₂×C₄²	1	3	yes	—
30	C₂×C₄×C₅₉	C₂×M₁₆	1	12	yes	—
31	C₂×Dic₅₉	—	2	12	no	—
32	C₈×C₅₉	#97	1	24	yes	complemented
33	C₅₉⋊C₈	—	2	12	no	—
34	#7846	—	59	1	no	maximal, Sylow
35	C₂²×C₅₉	C₄³	1	1	yes	characteristic
36	C₂²×C₅₉	C₄×M₁₆	1	6	yes	—
37	C₄×C₅₉	C₂×#97	1	6	yes	—
38	C₄×C₅₉	C₄×M₁₆	1	6	yes	—
39	Dic₅₉	—	4	4	no	—
40	C₄×#97	—	59	3	no	—
41	C₂×#322	—	59	3	no	—
42	C₂×C₈²	D₅₉	1	1	yes	characteristic
43	C₂×C₅₉	#1455	1	4	yes	—
44	C₂×C₅₉	C₄×#97	1	3	yes	—
45	C₂×#97	—	59	12	no	—
46	C₂×C₄×C₈	—	59	3	no	—
47	C₂×C₄×C₈	C₂×D₅₉	1	3	yes	—
48	C₄³	—	59	1	no	—
49	#322	—	59	12	no	—
50	C₈²	Dic₅₉	1	4	yes	complemented
51	C₅₉	#7846	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₈	—	59	6	no	—
53	C₂²×C₈	C₄×D₅₉	1	6	yes	—
54	C₂×C₄²	—	59	6	no	—
55	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
56	#97	—	118	24	no	—
57	C₄×C₈	—	59	12	no	—
58	C₄×C₈	C₄×D₅₉	1	6	yes	—
59	C₄×C₈	C₂×Dic₅₉	1	6	yes	—
60	C₂²×C₄	—	59	4	no	—
61	C₂²×C₄	C₂×C₄×D₅₉	1	3	yes	—
62	C₂×C₈	—	59	12	no	—
63	C₂×C₈	—	118	12	no	—
64	C₂×C₈	#11745659	1	24	yes	—
65	C₂×C₈	C₄×Dic₅₉	1	12	yes	—
66	C₄²	—	118	12	no	—
67	C₄²	C₂×C₄×D₅₉	1	3	yes	—
68	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
69	C₂³	C₄²×D₅₉	1	1	yes	characteristic
70	C₂×C₄	—	118	12	no	—
71	C₂×C₄	C₄²×D₅₉	1	3	yes	—
72	C₂×C₄	C₂×C₄×Dic₅₉	1	3	yes	—
73	C₂×C₄	C₂×#11745659	1	12	yes	—
74	C₈	—	118	12	no	—
75	C₈	#14273637	1	24	yes	complemented
76	C₂²	C₄²×Dic₅₉	1	1	yes	characteristic
77	C₂²	C₄×#11745659	1	6	yes	—
78	C₄	—	236	4	no	—
79	C₄	C₂×#14273637	1	6	yes	—
80	C₄	C₄×#11745659	1	6	yes	—
81	C₂	#21422398	1	4	yes	—
82	C₂	C₄×#14273637	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₅₉
commutator	C₂²×C₅₉	C₄³
Fitting	C₂×C₈²×C₅₉	C₂
socle, prime radical	C₂³×C₅₉	C₂×C₄²
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₂×C₈²	D₅₉
hypocenter	C₅₉	#7846
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
7. #16837123	C₄	semidirect
9. C₈²×C₅₉	C₄	semidirect
32. C₈×C₅₉	#97	semidirect
50. C₈²	Dic₅₉	semidirect
51. C₅₉	#7846	semidirect
75. C₈	#14273637	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14273637	2
C₂×#16837123	2
C₂×C₈²×C₅₉	2
#7846	59