Subgroups — D₉₇₃₅ #34085696

Order 19470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₄₅	—	3	1	no	maximal, Hall
3	D₁₉₄₇	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₅₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₅₉	D₅	1	1	yes	characteristic, complemented, Hall
6	D₈₈₅	—	11	1	no	maximal, Hall
7	D₆₄₉	—	15	1	no	Hall
8	C₃×C₅×C₅₉	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₉	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₂₉₅	—	33	1	no	Hall
11	D₁₇₇	—	55	1	no	Hall
12	D₁₆₅	—	59	1	no	maximal, Hall
13	C₅×C₅₉	D₃₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅₉	D₅₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	D₅₉	1	1	yes	characteristic, complemented, Hall
16	D₅₉	—	165	1	no	Hall
17	D₅₅	—	177	1	no	Hall
18	D₃₃	—	295	1	no	Hall
19	C₅₉	D₁₆₅	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₁₁	D₁₇₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₂₉₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	649	1	no	Hall
23	D₁₁	—	885	1	no	Hall
24	C₃×C₅	D₆₄₉	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₈₈₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	1947	1	no	Hall
27	D₃	—	3245	1	no	Hall
28	C₅	D₁₉₄₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₃₂₄₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	9735	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₁×C₅₉	C₂
LCS	G ▷ C₃×C₅×C₁₁×C₅₉
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.