Subgroups — D₁₇₇₆₅ #48001052

Order 35530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₅₅₃	—	5	1	no	maximal, Hall
3	C₁₁×C₁₇×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
4	D₁₆₁₅	—	11	1	no	maximal, Hall
5	D₁₀₄₅	—	17	1	no	maximal, Hall
6	D₉₃₅	—	19	1	no	maximal, Hall
7	C₅×C₁₇×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×C₁₉	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×C₁₇	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₃₂₃	—	55	1	no	Hall
11	D₂₀₉	—	85	1	no	Hall
12	D₁₈₇	—	95	1	no	Hall
13	C₁₇×C₁₉	D₅₅	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	D₈₅	1	1	yes	characteristic, complemented, Hall
15	D₉₅	—	187	1	no	Hall
16	C₁₁×C₁₇	D₉₅	1	1	yes	characteristic, complemented, Hall
17	D₈₅	—	209	1	no	Hall
18	D₅₅	—	323	1	no	Hall
19	C₅×C₁₉	D₁₈₇	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₇	D₂₀₉	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₁	D₃₂₃	1	1	yes	characteristic, complemented, Hall
22	D₁₉	—	935	1	no	Hall
23	D₁₇	—	1045	1	no	Hall
24	D₁₁	—	1615	1	no	Hall
25	C₁₉	D₉₃₅	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	D₁₀₄₅	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	D₁₆₁₅	1	1	yes	characteristic, complemented, Sylow
28	D₅	—	3553	1	no	Hall
29	C₅	D₃₅₅₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	17765	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₁₇×C₁₉	C₂
LCS	G ▷ C₅×C₁₁×C₁₇×C₁₉
UCS	C₁

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.