Subgroups — C₂×C₅₉⋊#401 #21427392

Order 7552.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉⋊#401	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₅₉⋊#95	C₂	1	3	yes	maximal
3	C₂×C₅₉⋊#95	C₂	1	3	yes	maximal
4	C₂×#95×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₅₉	C₂²	1	1	yes	characteristic
6	C₂³×Dic₅₉	C₂²	1	3	yes	—
7	C₅₉⋊#95	C₂²	1	12	yes	—
8	C₅₉⋊#95	C₂²	1	12	yes	—
9	C₂³×C₄×C₅₉	C₂²	1	3	yes	—
10	#95×C₅₉	C₂²	1	4	yes	—
11	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₅₉	—	2	6	no	—
13	C₂²×C₄×C₅₉	—	2	12	no	—
14	C₂²×C₄×C₅₉	C₂³	1	6	yes	—
15	C₂²×Dic₅₉	—	2	6	no	—
16	C₂²×Dic₅₉	—	2	6	no	—
17	C₂²×Dic₅₉	—	2	6	no	—
18	C₂²×Dic₅₉	—	2	6	no	—
19	C₂²×Dic₅₉	C₂³	1	6	yes	—
20	C₂²×Dic₅₉	C₂³	1	2	yes	—
21	C₂³×C₅₉	#41	1	6	yes	—
22	C₂³×C₅₉	#41	1	6	yes	—
23	C₂³×C₅₉	#41	1	2	yes	—
24	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₅₉	—	2	12	no	—
26	C₂×C₄×C₅₉	—	2	6	no	—
27	C₂×C₄×C₅₉	—	4	12	no	—
28	C₂×Dic₅₉	—	2	6	no	—
29	C₂×Dic₅₉	—	2	6	no	—
30	C₂×Dic₅₉	—	2	6	no	—
31	C₂×Dic₅₉	—	2	6	no	—
32	C₂×Dic₅₉	—	4	4	no	—
33	C₂×Dic₅₉	—	4	12	no	—
34	C₂²×C₅₉	#126	1	12	yes	—
35	C₂²×C₅₉	#126	1	4	yes	—
36	C₂²×C₅₉	#126	1	12	yes	—
37	C₂²×C₅₉	C₂×#41	1	3	yes	—
38	C₂²×C₅₉	C₂×#41	1	3	yes	—
39	C₂²×C₅₉	C₂×#41	1	1	yes	characteristic
40	C₄×C₅₉	—	4	6	no	—
41	Dic₅₉	—	4	2	no	—
42	Dic₅₉	—	4	6	no	—
43	C₂×#401	—	59	1	no	maximal, Sylow
44	C₂×C₅₉	#401	1	8	yes	complemented
45	C₂×C₅₉	C₂×#126	1	3	yes	—
46	C₂×C₅₉	C₂×#126	1	1	yes	characteristic
47	C₂×C₅₉	C₂×#126	1	3	yes	—
48	#401	—	59	8	no	—
49	C₂×#95	—	59	3	no	—
50	C₂×#95	—	59	3	no	—
51	C₂×#95	D₅₉	1	1	yes	characteristic
52	C₅₉	C₂×#401	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₄	—	59	1	no	—
54	C₂³×C₄	—	59	3	no	—
55	C₂³×C₄	C₂×D₅₉	1	3	yes	—
56	#95	—	59	12	no	—
57	#95	—	59	12	no	—
58	#95	C₂×D₅₉	1	4	yes	—
59	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
60	C₂²×C₄	—	2	6	no	—
61	C₂²×C₄	—	2	12	no	—
62	C₂²×C₄	—	59	6	no	—
63	C₂²×C₄	—	59	2	no	—
64	C₂²×C₄	—	118	6	no	—
65	C₂²×C₄	—	118	6	no	—
66	C₂²×C₄	—	118	6	no	—
67	C₂²×C₄	—	118	6	no	—
68	C₂²×C₄	C₂²×D₅₉	1	6	yes	—
69	C₂³	#11745685	1	6	yes	—
70	C₂³	#11745687	1	6	yes	—
71	C₂³	#11745689	1	2	yes	—
72	C₂³	C₂³×D₅₉	1	1	yes	characteristic
73	C₂×C₄	—	2	12	no	—
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	4	12	no	—
76	C₂×C₄	—	118	6	no	—
77	C₂×C₄	—	118	6	no	—
78	C₂×C₄	—	118	6	no	—
79	C₂×C₄	—	118	6	no	—
80	C₂×C₄	—	236	4	no	—
81	C₂×C₄	—	236	12	no	—
82	C₂²	#14273720	1	12	yes	—
83	C₂²	#14273721	1	4	yes	—
84	C₂²	#14273722	1	12	yes	—
85	C₂²	C₂×#11745687	1	3	yes	—
86	C₂²	C₂×#11745685	1	3	yes	—
87	C₂²	C₂×#11745689	1	1	yes	characteristic
88	C₄	—	4	6	no	—
89	C₄	—	236	2	no	—
90	C₄	—	236	6	no	—
91	C₂	C₅₉⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#14273720	1	3	yes	—
93	C₂	C₂×#14273721	1	1	yes	characteristic
94	C₂	C₂×#14273722	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₅₉
commutator	C₂³×C₅₉	C₂⁴
Frattini	C₂³	C₂³×D₅₉
Fitting	C₂×#95×C₅₉	C₂
socle	C₂⁴×C₅₉	C₂³
hypercenter	C₂×#95	D₅₉
hypocenter	C₅₉	C₂×#401
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₅₉⋊#401	C₂	direct (N × H)
44. C₂×C₅₉	#401	semidirect
52. C₅₉	C₂×#401	semidirect
91. C₂	C₅₉⋊#401	direct (N × H)

Subgroups — C2×C59⋊#401 #21427392

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅₉⋊#401 #21427392