Subgroups — C₂×D₅×#401 #12265593

Order 1280.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#401	C₂	1	16	yes	maximal, direct product factor
3	C₂×D₅×#95	C₂	1	7	yes	maximal
4	C₂×C₅⋊#401	C₂	1	7	yes	maximal, complemented
5	C₂³×C₄×D₅	C₂²	1	7	yes	—
6	C₅×#401	C₂²	1	8	yes	complemented
7	C₂×C₅×#95	C₂²	1	7	yes	—
8	C₂×#3963	C₂²	1	21	yes	—
9	D₅×#95	C₂²	1	56	yes	—
10	C₅⋊#401	C₂²	1	56	yes	complemented
11	C₂²×#401	—	5	1	no	maximal, Sylow
12	C₂⁴×D₅	C₂³	1	1	yes	characteristic
13	C₂³×C₄×C₅	C₂³	1	7	yes	—
14	C₂³×Dic₅	C₂³	1	7	yes	—
15	C₂²×C₄×D₅	—	2	84	no	—
16	C₂²×C₄×D₅	C₂³	1	28	yes	—
17	C₅×#95	C₂³	1	28	yes	—
18	#3963	C₂³	1	84	yes	—
19	C₂×#401	—	5	16	no	—
20	C₂×#401	—	5	7	no	—
21	C₂×#401	D₅	1	1	yes	characteristic, direct product factor
22	C₂²×#95	—	5	7	no	—
23	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
24	C₂³×D₅	#41	1	28	yes	—
25	C₂³×D₅	C₂⁴	1	2	yes	—
26	C₂²×C₄×C₅	—	2	42	no	—
27	C₂²×C₄×C₅	C₂⁴	1	14	yes	—
28	C₂²×Dic₅	—	2	42	no	—
29	C₂²×Dic₅	C₂⁴	1	14	yes	—
30	C₂×C₄×D₅	—	2	168	no	—
31	C₂×C₄×D₅	—	4	112	no	—
32	C₂⁴×C₄	—	5	7	no	—
33	#401	—	5	56	no	—
34	#401	C₂×D₅	1	8	yes	direct product factor
35	C₂×#95	—	5	21	no	—
36	C₂×#95	—	5	56	no	—
37	C₂×#95	C₂×D₅	1	7	yes	—
38	C₂³×C₅	C₂×#41	1	14	yes	—
39	C₂³×C₅	C₂⁵	1	1	yes	characteristic
40	C₂²×D₅	#126	1	112	yes	—
41	C₂²×D₅	C₂×#41	1	28	yes	—
42	C₂×C₄×C₅	—	2	42	no	—
43	C₂×C₄×C₅	—	4	28	no	—
44	C₂×Dic₅	—	2	42	no	—
45	C₂×Dic₅	—	4	28	no	—
46	C₄×D₅	—	4	112	no	—
47	C₂⁵	—	5	1	no	—
48	C₂³×C₄	—	5	7	no	—
49	C₂³×C₄	—	5	28	no	—
50	C₂³×C₄	—	10	84	no	—
51	C₂³×C₄	C₂²×D₅	1	7	yes	—
52	#95	—	5	84	no	—
53	#95	C₂²×D₅	1	28	yes	—
54	C₂²×C₅	C₂×#126	1	28	yes	—
55	C₂²×C₅	C₂²×#41	1	7	yes	—
56	C₂×D₅	#401	1	64	yes	direct product factor
57	C₂×D₅	C₂×#126	1	56	yes	—
58	C₄×C₅	—	4	14	no	—
59	Dic₅	—	4	14	no	—
60	C₂⁴	—	5	28	no	—
61	C₂⁴	—	5	2	no	—
62	C₂⁴	C₂³×D₅	1	1	yes	characteristic
63	C₂²×C₄	—	2	42	no	—
64	C₂²×C₄	—	5	14	no	—
65	C₂²×C₄	—	10	168	no	—
66	C₂²×C₄	—	10	42	no	—
67	C₂²×C₄	—	20	112	no	—
68	C₂²×C₄	C₂³×D₅	1	14	yes	—
69	C₂×C₅	C₂×#401	1	8	yes	complemented
70	C₂×C₅	C₂²×#126	1	7	yes	—
71	D₅	C₂×#401	1	16	yes	direct product factor
72	C₂³	—	5	28	no	—
73	C₂³	—	5	112	no	—
74	C₂³	D₅×#41	1	14	yes	—
75	C₂³	C₂⁴×D₅	1	1	yes	characteristic
76	C₂×C₄	—	2	42	no	—
77	C₂×C₄	—	4	28	no	—
78	C₂×C₄	—	10	42	no	—
79	C₂×C₄	—	20	112	no	—
80	C₂×C₄	—	20	28	no	—
81	C₅	C₂²×#401	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	5	56	no	—
83	C₂²	—	5	64	no	—
84	C₂²	D₅×#126	1	28	yes	—
85	C₂²	C₂×D₅×#41	1	7	yes	—
86	C₄	—	4	14	no	—
87	C₄	—	20	14	no	—
88	C₂	—	5	16	no	—
89	C₂	D₅×#401	1	8	yes	direct product factor
90	C₂	C₂×D₅×#126	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₅
commutator, cosocle	C₂³×C₅	C₂⁵
Frattini	C₂³	C₂⁴×D₅
Fitting	C₂×C₅×#401	C₂
socle	C₂⁴×C₅	C₂⁴
prime radical	C₂⁴×D₅	C₂³
hypercenter	C₂×#401	D₅
hypocenter	C₅	C₂²×#401
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#401	C₂	semidirect
2. D₅×#401	C₂	direct (N × H)
4. C₂×C₅⋊#401	C₂	semidirect
6. C₅×#401	C₂²	semidirect
10. C₅⋊#401	C₂²	semidirect
21. C₂×#401	D₅	direct (N × H)
34. #401	C₂×D₅	direct (N × H)
56. C₂×D₅	#401	direct (N × H)
69. C₂×C₅	C₂×#401	semidirect
71. D₅	C₂×#401	direct (N × H)
81. C₅	C₂²×#401	semidirect
89. C₂	D₅×#401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#401	2
D₅×#401	2
C₂×D₅×#95	2
C₂×C₅⋊#401	2
C₂²×#401	5

Subgroups — C2×D5×#401 #12265593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#401 #12265593