Subgroups — #10598317

Order 640.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	#64724	C₂	1	1	yes	maximal, characteristic
3	C₂×#3926	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₁₆	—	2	1	no	—
5	C₅×Q₃₂	—	2	1	no	—
6	C₅×Q₃₂	C₄	1	2	yes	complemented
7	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	#3950	—	2	1	no	—
9	#3926	—	2	1	no	—
10	#1416	—	5	1	no	maximal, Sylow
11	C₂×C₅×Q₈	—	4	1	no	—
12	C₅×Q₁₆	—	2	2	no	—
13	C₅×Q₁₆	—	4	1	no	—
14	C₂×C₅×C₈	D₄	1	1	yes	characteristic
15	C₄⋊Dic₅	—	4	1	no	—
16	C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₅×C₁₆	D₄	1	1	yes	characteristic
18	C₂×Q₃₂	D₅	1	1	yes	characteristic
19	C₂×C₃₂	—	5	1	no	—
20	#366	—	5	1	no	—
21	C₅×Q₈	—	4	2	no	—
22	C₅×Q₈	—	8	1	no	—
23	C₂×C₄×C₅	—	8	1	no	—
24	C₂×C₄×C₅	D₈	1	1	yes	characteristic
25	C₂×Dic₅	—	8	1	no	—
26	C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₅×C₈	SD₁₆	1	1	yes	characteristic
28	C₂×Q₁₆	—	2	1	no	—
29	Q₃₂	—	2	1	no	—
30	Q₃₂	Dic₅	1	2	yes	complemented
31	C₂×C₁₆	C₂×D₅	1	1	yes	characteristic
32	#107	—	10	1	no	—
33	C₃₂	—	10	1	no	—
34	C₂²×C₅	D₁₆	1	1	yes	characteristic
35	C₄×C₅	—	8	2	no	—
36	C₄×C₅	#102	1	1	yes	characteristic
37	C₄×C₅	SD₃₂	1	1	yes	characteristic
38	Dic₅	—	16	1	no	—
39	C₂×Q₈	—	4	1	no	—
40	Q₁₆	—	2	2	no	—
41	Q₁₆	—	4	1	no	—
42	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
43	C₄⋊C₄	—	20	1	no	—
44	C₁₆	C₂×Dic₅	1	1	yes	characteristic
45	C₁₆	C₂²⋊D₅	1	1	yes	characteristic
46	C₂×C₅	#357	1	1	yes	characteristic
47	C₂×C₅	SD₆₄	1	1	yes	characteristic
48	C₂×C₅	Q₆₄	1	1	yes	characteristic
49	Q₈	—	4	2	no	—
50	Q₈	—	8	1	no	—
51	C₂×C₄	—	8	1	no	—
52	C₂×C₄	—	40	1	no	—
53	C₂×C₄	#686	1	1	yes	characteristic
54	C₈	#687	1	1	yes	characteristic
55	C₈	C₂²⋊Dic₅	1	1	yes	characteristic
56	C₅	#1416	1	1	yes	characteristic, complemented, Sylow
57	C₂²	#3958	1	1	yes	characteristic
58	C₄	—	8	2	no	—
59	C₄	—	80	1	no	—
60	C₄	#3959	1	1	yes	characteristic
61	C₄	#3964	1	1	yes	characteristic
62	C₂	#64741	1	1	yes	characteristic
63	C₂	#64742	1	1	yes	characteristic
64	C₂	#64782	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#3958
commutator	C₅×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₅
Fitting	C₂×C₅×Q₃₂	C₂
socle, prime radical	C₂²×C₅	D₁₆
cosocle	C₂×C₅×C₁₆	C₂²
hypercenter	C₂×Q₃₂	D₅
hypocenter	C₅	#1416
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
6. C₅×Q₃₂	C₄	semidirect
30. Q₃₂	Dic₅	semidirect
56. C₅	#1416	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₃₂	2
#64724	2
C₂×#3926	2
#1416	5