Subgroups — C₃×C₄₉×C₆₁⋊C₃ #41002005

Order 26901.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₆₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₄₉×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₆₁⋊C₃	C₇	1	1	yes	maximal, characteristic
4	C₄₉×C₆₁	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₆₁	C₃×C₇	1	1	yes	characteristic
6	C₇×C₆₁⋊C₃	C₃×C₇	1	3	yes	—
7	C₃×C₆₁⋊C₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₄₉	—	61	1	no	maximal, Hall
9	C₇×C₆₁	C₃²×C₇	1	1	yes	characteristic
10	C₃×C₆₁	C₃×C₄₉	1	1	yes	characteristic, complemented
11	C₆₁⋊C₃	C₃×C₄₉	1	3	yes	direct product factor
12	C₃×C₄₉	—	61	3	no	—
13	C₃×C₄₉	C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
14	C₃²×C₇	—	61	1	no	—
15	C₆₁	C₃²×C₄₉	1	1	yes	characteristic, complemented, Sylow
16	C₄₉	C₃×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₇	—	61	3	no	—
18	C₃×C₇	C₇×C₆₁⋊C₃	1	1	yes	characteristic
19	C₃²	—	61	1	no	Sylow
20	C₇	C₃×C₇×C₆₁⋊C₃	1	1	yes	characteristic
21	C₃	—	61	3	no	—
22	C₃	C₄₉×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor

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.