Subgroups — #13095652

Order 1560.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₉₅	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₁₃×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#10587073	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₃	C₂²	1	1	yes	characteristic
6	Dic₇₈	—	5	1	no	maximal, Hall
7	Dic₆₅	—	3	1	no	—
8	C₅×Dic₁₃	—	3	1	no	—
9	C₁₃×Dic₅	D₃	1	1	yes	characteristic
10	C₃×C₅×C₁₃	Q₈	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₁₃	—	5	1	no	—
12	Dic₃₉	—	5	1	no	—
13	Dic₃₉	D₅	1	1	yes	characteristic
14	C₂×C₅×C₁₃	C₂×D₃	1	1	yes	characteristic
15	#1204	—	13	1	no	maximal, Hall
16	Dic₂₆	—	15	1	no	Hall
17	C₂×C₃×C₁₃	C₂×D₅	1	1	yes	characteristic
18	C₅×C₁₃	Dic₆	1	1	yes	characteristic, complemented, Hall
19	Dic₁₅	—	13	1	no	—
20	C₃×Dic₅	D₁₃	1	1	yes	characteristic
21	C₅×Dic₃	—	13	1	no	—
22	C₄×C₁₃	—	5	1	no	—
23	Dic₁₃	—	3	1	no	—
24	Dic₁₃	—	15	1	no	—
25	Dic₁₀	—	39	1	no	Hall
26	C₃×C₁₃	Dic₁₀	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₅	C₂×D₁₃	1	1	yes	characteristic
28	C₂×C₁₃	D₃×D₅	1	1	yes	characteristic
29	Dic₆	—	65	1	no	Hall
30	C₄×C₅	—	39	1	no	—
31	Dic₅	—	39	1	no	—
32	Dic₅	D₃₉	1	1	yes	characteristic
33	C₃×C₅	Dic₂₆	1	1	yes	characteristic, complemented, Hall
34	C₁₃	#1204	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₄	—	5	1	no	—
36	Dic₃	—	13	1	no	—
37	Dic₃	—	65	1	no	—
38	C₂×C₅	C₂×D₃₉	1	1	yes	characteristic
39	Q₈	—	195	1	no	Sylow
40	C₂×C₃	D₅×D₁₃	1	1	yes	characteristic
41	C₅	Dic₇₈	1	1	yes	characteristic, complemented, Sylow
42	C₄	—	5	1	no	—
43	C₄	—	39	1	no	—
44	C₄	—	195	1	no	—
45	C₃	#10587073	1	1	yes	characteristic, complemented, Sylow
46	C₂	D₅×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₃₉
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₁₃	C₂²
hypocenter	C₃×C₅×C₁₃	Q₈
LCS	G ▷ C₂×C₃×C₅×C₁₃ ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
10. C₃×C₅×C₁₃	Q₈	semidirect
18. C₅×C₁₃	Dic₆	semidirect
26. C₃×C₁₃	Dic₁₀	semidirect
33. C₃×C₅	Dic₂₆	semidirect
34. C₁₃	#1204	semidirect
41. C₅	Dic₇₈	semidirect
45. C₃	#10587073	semidirect

Maximal subgroups

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

subgroup	index
Dic₁₉₅	2
C₅×Dic₃₉	2
C₃×C₁₃×Dic₅	2
#10587073	3
Dic₇₈	5
#1204	13