Subgroups — C₅×D₂₆₉₇ #41004196

Order 26970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₈₉₉	—	3	1	no	maximal, Hall
3	D₂₆₉₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₉×C₃₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₈₉₉	—	3	1	no	Hall
7	C₅×D₉₃	—	29	1	no	maximal, Hall
8	C₂₉×C₃₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
9	C₅×D₈₇	—	31	1	no	maximal, Hall
10	C₃×C₅×C₃₁	D₂₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₂₉	D₃₁	1	1	yes	characteristic, complemented, Hall
12	C₅×D₃₁	—	87	1	no	Hall
13	C₅×D₂₉	—	93	1	no	Hall
14	D₉₃	—	29	1	no	Hall
15	D₈₇	—	31	1	no	Hall
16	C₅×C₃₁	D₈₇	1	1	yes	characteristic, complemented, Hall
17	C₅×C₂₉	D₉₃	1	1	yes	characteristic, complemented, Hall
18	C₃×C₃₁	C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₂₉	C₅×D₃₁	1	1	yes	characteristic, complemented, Hall
20	D₃₁	—	87	1	no	Hall
21	D₂₉	—	93	1	no	Hall
22	C₃₁	C₅×D₈₇	1	1	yes	characteristic, complemented, Sylow
23	C₅×D₃	—	899	1	no	Hall
24	C₂₉	C₅×D₉₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₈₉₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	2697	1	no	Hall
27	D₃	—	899	1	no	Hall
28	C₅	D₂₆₉₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₈₉₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	2697	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₆₉₇
commutator, cosocle, hypocenter	C₃×C₂₉×C₃₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₉×C₃₁	C₂
LCS	G ▷ C₃×C₂₉×C₃₁
UCS	C₁ ◁ C₅

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.