Subgroups — #10602303

Order 640.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#508	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#64742	C₂	1	2	yes	maximal, complemented
4	#64740	C₂	1	2	yes	maximal, complemented
5	#64719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#135	—	2	1	no	—
7	C₂×Dic₂₀	—	2	1	no	—
8	C₅×Q₃₂	C₂²	1	1	yes	characteristic
9	C₅×SD₃₂	—	2	1	no	—
10	C₅×D₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
12	Dic₄₀	—	2	1	no	—
13	Dic₄₀	C₂²	1	2	yes	—
14	#3926	C₂²	1	2	yes	—
15	#2264	—	5	1	no	maximal, Sylow
16	C₅×#41	—	4	1	no	—
17	C₂×Dic₁₀	—	4	1	no	—
18	C₅×Q₁₆	—	2	1	no	—
19	C₅×SD₁₆	—	4	1	no	—
20	C₅×D₈	—	2	1	no	—
21	C₂×C₅×C₈	D₄	1	1	yes	characteristic
22	Dic₂₀	—	2	2	no	—
23	Dic₂₀	—	4	1	no	—
24	C₅×C₁₆	D₄	1	1	yes	characteristic
25	C₅×C₁₆	C₂³	1	1	yes	characteristic
26	#508	D₅	1	1	yes	characteristic
27	C₂×Q₃₂	—	5	1	no	—
28	Q₆₄	—	5	2	no	—
29	SD₆₄	—	5	2	no	—
30	M₆₄	—	5	1	no	—
31	C₅×Q₈	—	4	1	no	—
32	C₅×D₄	—	4	1	no	—
33	C₅×D₄	—	8	1	no	—
34	C₂×C₄×C₅	—	8	1	no	—
35	C₂×C₄×C₅	D₈	1	1	yes	characteristic
36	C₂×Dic₅	—	8	1	no	—
37	Dic₁₀	—	4	2	no	—
38	Dic₁₀	—	8	1	no	—
39	C₅×C₈	D₈	1	1	yes	characteristic
40	C₅×C₈	C₂×D₄	1	1	yes	characteristic
41	#135	—	2	1	no	—
42	C₂×Q₁₆	—	10	1	no	—
43	Q₃₂	—	5	2	no	—
44	Q₃₂	—	10	1	no	—
45	Q₃₂	C₂×D₅	1	1	yes	characteristic
46	SD₃₂	—	2	1	no	—
47	D₁₆	C₂×D₅	1	1	yes	characteristic
48	C₂×C₁₆	C₂×D₅	1	1	yes	characteristic
49	C₃₂	—	5	2	no	—
50	C₂²×C₅	—	8	1	no	—
51	C₂²×C₅	D₁₆	1	1	yes	characteristic
52	C₄×C₅	—	8	1	no	—
53	C₄×C₅	D₁₆	1	1	yes	characteristic
54	C₄×C₅	C₂×D₈	1	1	yes	characteristic
55	Dic₅	—	8	2	no	—
56	#41	—	4	1	no	—
57	C₂×Q₈	—	20	1	no	—
58	Q₁₆	—	2	1	no	—
59	Q₁₆	—	10	2	no	—
60	Q₁₆	—	20	1	no	—
61	SD₁₆	—	4	1	no	—
62	D₈	—	2	1	no	—
63	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
64	C₁₆	C₂²⋊D₅	1	1	yes	characteristic
65	C₁₆	C₂²×D₅	1	1	yes	characteristic
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	—	16	1	no	—
68	C₂×C₅	C₂×D₁₆	1	1	yes	characteristic
69	Q₈	—	4	1	no	—
70	Q₈	—	20	2	no	—
71	Q₈	—	40	1	no	—
72	D₄	—	4	1	no	—
73	D₄	—	8	1	no	—
74	C₂×C₄	—	8	1	no	—
75	C₂×C₄	—	40	1	no	—
76	C₂×C₄	#686	1	1	yes	characteristic
77	C₈	#686	1	1	yes	characteristic
78	C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
79	C₅	#2264	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	8	1	no	—
81	C₂²	#3958	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	40	2	no	—
84	C₄	#3958	1	1	yes	characteristic
85	C₄	C₂×#686	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×#3958	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#3958
commutator, cosocle	C₅×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₅
Fitting, prime radical	C₅×#508	C₂
socle	C₂×C₅	C₂×D₁₆
hypercenter	#508	D₅
hypocenter	C₅	#2264
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₄₀	C₂	semidirect
3. #64742	C₂	semidirect
4. #64740	C₂	semidirect
5. #64719	C₂	semidirect
79. C₅	#2264	semidirect

Maximal subgroups

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

subgroup	index
C₅×#508	2
C₂×Dic₄₀	2
#64742	2
#64740	2
#64719	2
#2264	5