Subgroups — D₈₈₃₅ #31798968

Order 17670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₉₄₅	—	3	1	no	maximal, Hall
3	D₁₇₆₇	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₃₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
6	D₅₈₉	—	15	1	no	Hall
7	D₄₆₅	—	19	1	no	maximal, Hall
8	C₁₉×C₃₁	D₁₅	1	1	yes	characteristic, complemented, Hall
9	D₂₈₅	—	31	1	no	maximal, Hall
10	C₃×C₅×C₃₁	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₁₅₅	—	57	1	no	Hall
12	C₃×C₅×C₁₉	D₃₁	1	1	yes	characteristic, complemented, Hall
13	D₉₅	—	93	1	no	Hall
14	D₉₃	—	95	1	no	Hall
15	C₅×C₃₁	D₅₇	1	1	yes	characteristic, complemented, Hall
16	D₅₇	—	155	1	no	Hall
17	C₅×C₁₉	D₉₃	1	1	yes	characteristic, complemented, Hall
18	C₃×C₃₁	D₉₅	1	1	yes	characteristic, complemented, Hall
19	D₃₁	—	285	1	no	Hall
20	C₃×C₁₉	D₁₅₅	1	1	yes	characteristic, complemented, Hall
21	D₁₉	—	465	1	no	Hall
22	C₃₁	D₂₈₅	1	1	yes	characteristic, complemented, Sylow
23	D₁₅	—	589	1	no	Hall
24	C₁₉	D₄₆₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₅₈₉	1	1	yes	characteristic, complemented, Hall
26	D₅	—	1767	1	no	Hall
27	D₃	—	2945	1	no	Hall
28	C₅	D₁₇₆₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₂₉₄₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	8835	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₉×C₃₁	C₂
LCS	G ▷ C₃×C₅×C₁₉×C₃₁
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.