Subgroups — C₇×C₉×C₇₁⋊C₇ #44531149

Order 31311.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₇₁⋊C₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₇₁⋊C₇	C₇	1	7	yes	maximal, direct product factor
3	C₇×C₉×C₇₁	C₇	1	1	yes	maximal, characteristic, complemented
4	C₇×C₇₁⋊C₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₇×C₇₁	C₃×C₇	1	1	yes	characteristic
6	C₃×C₇₁⋊C₇	C₃×C₇	1	7	yes	—
7	C₉×C₇₁	C₇²	1	1	yes	characteristic, complemented, Hall
8	C₇×C₇₁	C₇×C₉	1	1	yes	characteristic, complemented
9	C₇₁⋊C₇	C₇×C₉	1	7	yes	direct product factor
10	C₇²×C₉	—	71	1	no	maximal, Hall
11	C₃×C₇₁	C₃×C₇²	1	1	yes	characteristic
12	C₃×C₇²	—	71	1	no	—
13	C₇₁	C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₉	—	71	7	no	—
15	C₇×C₉	C₇₁⋊C₇	1	1	yes	characteristic, direct product factor
16	C₇²	—	71	1	no	Sylow
17	C₃×C₇	—	71	7	no	—
18	C₃×C₇	C₃×C₇₁⋊C₇	1	1	yes	characteristic
19	C₉	C₇×C₇₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	—	71	7	no	—
21	C₇	C₉×C₇₁⋊C₇	1	1	yes	characteristic, direct product factor
22	C₃	C₃×C₇×C₇₁⋊C₇	1	1	yes	characteristic

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.