Subgroups — Dic₇₇₇₅ #44527340

Order 31100.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₃₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂₅×C₃₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₅₅₅	—	5	1	no	maximal
4	C₂×C₅×C₃₁₁	D₅	1	1	yes	characteristic
5	C₅×C₃₁₁	Dic₅	1	1	yes	characteristic
6	Dic₃₁₁	—	25	1	no	Hall
7	C₂×C₃₁₁	D₂₅	1	1	yes	characteristic
8	C₃₁₁	Dic₂₅	1	1	yes	characteristic, complemented, Sylow
9	Dic₂₅	—	311	1	no	maximal, Hall
10	C₂×C₂₅	D₃₁₁	1	1	yes	characteristic
11	C₂₅	Dic₃₁₁	1	1	yes	characteristic, complemented, Sylow
12	Dic₅	—	1555	1	no	—
13	C₂×C₅	D₁₅₅₅	1	1	yes	characteristic
14	C₅	Dic₁₅₅₅	1	1	yes	characteristic
15	C₄	—	7775	1	no	Sylow
16	C₂	D₇₇₇₅	1	1	yes	characteristic

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.