Subgroups — C₃×D₃₃₉₅ #35205014

Order 20370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₃₉₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₆₇₉	—	5	1	no	maximal, Hall
4	C₅×C₇×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₄₈₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₉₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₉₇	D₇	1	1	yes	characteristic, complemented, Hall
8	D₆₇₉	—	5	1	no	Hall
9	D₄₈₅	—	7	1	no	Hall
10	C₇×C₉₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₉₇	—	35	1	no	Hall
12	C₅×C₉₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₉₇	D₃₅	1	1	yes	characteristic, complemented, Hall
14	C₃×D₃₅	—	97	1	no	maximal, Hall
15	D₉₇	—	35	1	no	Hall
16	C₃×C₅×C₇	D₉₇	1	1	yes	characteristic, complemented, Hall
17	C₉₇	C₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
18	D₃₅	—	97	1	no	Hall
19	C₃×D₇	—	485	1	no	Hall
20	C₅×C₇	C₃×D₉₇	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	679	1	no	Hall
22	C₃×C₇	D₄₈₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₆₇₉	1	1	yes	characteristic, complemented, Hall
24	D₇	—	485	1	no	Hall
25	D₅	—	679	1	no	Hall
26	C₇	C₃×D₄₈₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3395	1	no	Hall
28	C₅	C₃×D₆₇₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₃₃₉₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3395	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₃₉₅
commutator, cosocle, hypocenter	C₅×C₇×C₉₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₉₇	C₂
LCS	G ▷ C₅×C₇×C₉₇
UCS	C₁ ◁ C₃

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.