Subgroups — Dic₆₇₁₅ #41001698

Order 26860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃₄₃	—	5	1	no	maximal, Hall
4	C₂×C₁₇×C₇₉	D₅	1	1	yes	characteristic
5	Dic₃₉₅	—	17	1	no	maximal, Hall
6	C₁₇×C₇₉	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₇₉	D₁₇	1	1	yes	characteristic
8	C₅×C₇₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
9	Dic₈₅	—	79	1	no	maximal, Hall
10	Dic₇₉	—	85	1	no	Hall
11	C₂×C₅×C₁₇	D₇₉	1	1	yes	characteristic
12	C₂×C₇₉	D₈₅	1	1	yes	characteristic
13	C₅×C₁₇	Dic₇₉	1	1	yes	characteristic, complemented, Hall
14	C₇₉	Dic₈₅	1	1	yes	characteristic, complemented, Sylow
15	Dic₁₇	—	395	1	no	Hall
16	C₂×C₁₇	D₃₉₅	1	1	yes	characteristic
17	Dic₅	—	1343	1	no	Hall
18	C₁₇	Dic₃₉₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	D₁₃₄₃	1	1	yes	characteristic
20	C₅	Dic₁₃₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6715	1	no	Sylow
22	C₂	D₆₇₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₇₁₅
commutator, hypocenter	C₅×C₁₇×C₇₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₇×C₇₉	C₂
LCS	G ▷ C₅×C₁₇×C₇₉
UCS	C₁ ◁ C₂

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

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