Subgroups — #401×Dic₅₉ #28510553

Order 15104.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21422358	C₂	1	7	yes	maximal
2	#95×Dic₅₉	C₂	1	7	yes	maximal
3	C₂×C₅₉×#401	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Dic₅₉	C₂²	1	7	yes	—
5	C₂×C₅₉⋊#95	C₂²	1	21	yes	—
6	C₅₉×#401	C₄	1	8	yes	complemented
7	C₂×#95×C₅₉	C₂²	1	7	yes	—
8	C₂³×Dic₅₉	C₂³	1	7	yes	—
9	C₂³×Dic₅₉	C₂³	1	1	yes	characteristic
10	C₂×C₄×Dic₅₉	—	2	42	no	—
11	C₅₉⋊#95	—	2	42	no	—
12	C₂³×C₄×C₅₉	C₂³	1	7	yes	—
13	#95×C₅₉	C₂×C₄	1	28	yes	—
14	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	—	2	21	no	—
16	C₂²×C₄×C₅₉	—	2	21	no	—
17	C₂²×C₄×C₅₉	C₂²×C₄	1	14	yes	—
18	C₂²×Dic₅₉	—	2	21	no	—
19	C₂²×Dic₅₉	—	2	21	no	—
20	C₂²×Dic₅₉	#41	1	14	yes	—
21	C₂²×Dic₅₉	#41	1	14	yes	—
22	C₄×Dic₅₉	—	4	28	no	—
23	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
24	C₂³×C₅₉	C₂×#41	1	7	yes	—
25	C₂³×C₅₉	C₂×#41	1	7	yes	—
26	C₂×C₄×C₅₉	—	2	42	no	—
27	C₂×C₄×C₅₉	—	4	7	no	—
28	C₂×C₄×C₅₉	—	4	21	no	—
29	C₂×Dic₅₉	—	2	42	no	—
30	C₂×Dic₅₉	—	4	7	no	—
31	C₂×Dic₅₉	—	4	21	no	—
32	C₂×Dic₅₉	#126	1	28	yes	—
33	C₄×#401	—	59	1	no	maximal, Sylow
34	C₂²×C₅₉	C₄×#41	1	7	yes	—
35	C₂²×C₅₉	C₂×#126	1	7	yes	—
36	C₂²×C₅₉	#529	1	21	yes	—
37	C₄×C₅₉	—	4	14	no	—
38	Dic₅₉	—	4	14	no	—
39	Dic₅₉	#401	1	8	yes	direct product factor
40	C₂×#401	D₅₉	1	1	yes	characteristic
41	#1443	—	59	7	no	—
42	C₄×#95	—	59	7	no	—
43	C₂×C₅₉	C₄×#126	1	7	yes	—
44	C₂×C₅₉	C₂×#401	1	1	yes	characteristic
45	C₂×C₅₉	#2401	1	7	yes	—
46	C₂²×C₄²	—	59	7	no	—
47	#401	Dic₅₉	1	8	yes	direct product factor
48	C₂×#95	—	59	21	no	—
49	C₂×#95	C₂×D₅₉	1	7	yes	—
50	C₅₉	C₄×#401	1	1	yes	characteristic, complemented, Sylow
51	C₂³×C₄	—	59	1	no	—
52	C₂³×C₄	—	59	7	no	—
53	C₂³×C₄	C₂²×D₅₉	1	7	yes	—
54	C₂×C₄²	—	118	42	no	—
55	#95	—	118	42	no	—
56	#95	C₂×Dic₅₉	1	28	yes	—
57	C₂⁴	C₂³×D₅₉	1	1	yes	characteristic
58	C₂²×C₄	—	2	21	no	—
59	C₂²×C₄	—	2	21	no	—
60	C₂²×C₄	—	59	14	no	—
61	C₂²×C₄	—	59	14	no	—
62	C₂²×C₄	—	118	21	no	—
63	C₂²×C₄	—	118	21	no	—
64	C₂²×C₄	C₂²×Dic₅₉	1	14	yes	—
65	C₄²	—	236	28	no	—
66	C₂³	C₂³×Dic₅₉	1	1	yes	characteristic
67	C₂³	#41×D₅₉	1	7	yes	—
68	C₂³	#41×D₅₉	1	7	yes	—
69	C₂×C₄	—	2	42	no	—
70	C₂×C₄	—	4	7	no	—
71	C₂×C₄	—	4	21	no	—
72	C₂×C₄	—	59	28	no	—
73	C₂×C₄	—	118	42	no	—
74	C₂×C₄	—	236	7	no	—
75	C₂×C₄	—	236	21	no	—
76	C₂²	#41×Dic₅₉	1	7	yes	—
77	C₂²	#126×D₅₉	1	7	yes	—
78	C₂²	#16837935	1	21	yes	—
79	C₄	—	4	14	no	—
80	C₄	—	59	8	no	—
81	C₄	—	236	14	no	—
82	C₂	#126×Dic₅₉	1	7	yes	—
83	C₂	#401×D₅₉	1	1	yes	characteristic
84	C₂	#21427399	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₅₉
commutator	C₂³×C₅₉	C₂³×C₄
Fitting	C₂×C₅₉×#401	C₂
socle, prime radical, cosocle	C₂⁴×C₅₉	C₂⁴
hypercenter	C₂×#401	D₅₉
hypocenter	C₅₉	C₄×#401
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
6. C₅₉×#401	C₄	semidirect
39. Dic₅₉	#401	direct (N × H)
47. #401	Dic₅₉	direct (N × H)
50. C₅₉	C₄×#401	semidirect

Maximal subgroups

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

subgroup	index
#21422358	2
#95×Dic₅₉	2
C₂×C₅₉×#401	2
C₄×#401	59

Subgroups — #401×Dic59 #28510553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #401×Dic₅₉ #28510553