Subgroups — C₉×D₁₉×C₉₇ #45684283

Order 33174.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₉×C₉₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₉₇	C₂×C₃	1	1	yes	characteristic
4	D₁₉×C₉₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₁₉×C₉₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₉×C₉₇	—	19	1	no	maximal, Hall
7	C₉×C₉₇	D₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₉₇	—	19	1	no	—
9	C₉×D₁₉	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₉₇	C₃×D₁₉	1	1	yes	characteristic
11	C₂×C₉₇	—	19	1	no	Hall
12	C₉×C₁₉	C₂×C₉₇	1	1	yes	characteristic, complemented, Hall
13	C₃×D₁₉	C₃×C₉₇	1	1	yes	characteristic
14	C₉₇	C₉×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₉	C₂×C₃×C₉₇	1	1	yes	characteristic
16	D₁₉	C₉×C₉₇	1	1	yes	characteristic, direct product factor, Hall
17	C₁₉	C₂×C₉×C₉₇	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	19	1	no	Hall
19	C₉	D₁₉×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	19	1	no	—
21	C₃	C₃×D₁₉×C₉₇	1	1	yes	characteristic
22	C₂	—	19	1	no	Sylow

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.