Subgroups — #10615520

Order 640.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	#66153	C₂	1	2	yes	maximal
3	#65414	C₂	1	6	yes	maximal, complemented
4	C₂×#3951	C₂	1	6	yes	maximal, complemented
5	C₂×C₅×#41	C₂²	1	1	yes	characteristic
6	C₅×#131	C₄	1	8	yes	—
7	C₂×C₅×M₁₆	C₂²	1	3	yes	—
8	C₂²×C₅×C₈	C₂²	1	3	yes	—
9	#4094	—	2	8	no	—
10	C₂×#681	C₂²	1	12	yes	—
11	#3951	C₂²	1	4	yes	—
12	#3951	C₂²	1	12	yes	—
13	#2916	—	5	1	no	maximal, Sylow
14	C₅×#41	C₂×C₄	1	4	yes	—
15	C₅×#41	D₄	1	4	yes	—
16	C₂×C₅×Q₈	Q₈	1	1	yes	characteristic
17	C₂×C₅×D₄	Q₈	1	3	yes	—
18	C₂²×C₄×C₅	C₂³	1	3	yes	—
19	C₅×M₁₆	C₂×C₄	1	12	yes	—
20	C₂×C₅×C₈	C₂×C₄	1	12	yes	—
21	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂³	1	3	yes	—
23	#681	—	2	12	no	—
24	#681	C₂³	1	8	yes	—
25	C₂×#168	—	2	12	no	—
26	#568	—	5	2	no	—
27	C₂×#131	D₅	1	1	yes	characteristic
28	#430	—	5	6	no	—
29	C₂×#108	—	5	6	no	—
30	C₂³×C₅	C₂×Q₈	1	3	yes	—
31	C₅×Q₈	C₄⋊C₄	1	4	yes	—
32	C₅×D₄	C₄⋊C₄	1	12	yes	—
33	C₂×C₄×C₅	C₂²×C₄	1	6	yes	—
34	C₂×C₄×C₅	C₂×D₄	1	6	yes	—
35	C₂×C₄×C₅	C₂×Q₈	1	3	yes	—
36	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
37	C₅×C₈	C₂²×C₄	1	2	yes	—
38	C₅×C₈	C₂²×C₄	1	6	yes	—
39	#168	—	2	8	no	—
40	C₂×#41	C₂×D₅	1	1	yes	characteristic
41	#131	—	10	8	no	—
42	#131	Dic₅	1	8	yes	—
43	C₂×M₁₆	—	5	12	no	—
44	C₂×M₁₆	C₂×D₅	1	3	yes	—
45	C₂²×C₈	C₂×D₅	1	3	yes	—
46	#108	—	5	4	no	—
47	#108	—	5	12	no	—
48	C₂²×C₅	—	4	3	no	—
49	C₂²×C₅	C₂×C₄⋊C₄	1	6	yes	—
50	C₂²×C₅	C₂²×Q₈	1	1	yes	characteristic
51	C₄×C₅	C₂×C₄⋊C₄	1	6	yes	—
52	C₄×C₅	C₂³×C₄	1	1	yes	characteristic
53	C₄×C₅	C₂²×D₄	1	1	yes	characteristic
54	#41	D₂₀	1	4	yes	—
55	#41	C₂×Dic₅	1	4	yes	—
56	C₂×Q₈	Dic₁₀	1	1	yes	characteristic
57	C₂×D₄	Dic₁₀	1	3	yes	—
58	C₂²×C₄	C₂²×D₅	1	3	yes	—
59	M₁₆	—	5	8	no	—
60	M₁₆	—	10	12	no	—
61	M₁₆	C₂×Dic₅	1	12	yes	—
62	C₂×C₈	—	10	12	no	—
63	C₂×C₈	C₂×Dic₅	1	12	yes	—
64	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
65	C₂×C₈	C₂²×D₅	1	3	yes	—
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	—	2	6	no	—
68	C₂×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
69	C₂³	C₂×Dic₁₀	1	3	yes	—
70	Q₈	C₄⋊Dic₅	1	4	yes	—
71	D₄	C₄⋊Dic₅	1	12	yes	—
72	C₂×C₄	C₂×Dic₁₀	1	3	yes	—
73	C₂×C₄	C₂×D₂₀	1	6	yes	—
74	C₂×C₄	C₂²×Dic₅	1	6	yes	—
75	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
76	C₈	—	10	8	no	—
77	C₈	C₂²×Dic₅	1	2	yes	—
78	C₈	C₂²×Dic₅	1	6	yes	—
79	C₅	#2916	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	4	3	no	—
81	C₂²	C₂×C₄⋊Dic₅	1	6	yes	—
82	C₂²	C₂²×Dic₁₀	1	1	yes	characteristic
83	C₄	C₂×C₄⋊Dic₅	1	6	yes	—
84	C₄	C₂²×D₂₀	1	1	yes	characteristic
85	C₄	C₂³×Dic₅	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2	6	no	—
88	C₂	C₂²×C₄⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₂₀
commutator	C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₅
Fitting	C₂×C₅×#131	C₂
socle	C₂×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	C₂²
cosocle	C₂×C₄×C₅	C₂⁴
hypercenter	C₂×#131	D₅
hypocenter	C₅	#2916
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
3. #65414	C₂	semidirect
4. C₂×#3951	C₂	semidirect
79. C₅	#2916	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#131	2
#66153	2
#65414	2
C₂×#3951	2
#2916	5