Subgroups — C₂×D₇₁⋊C₄₉ #28358148

Order 13916.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₁⋊C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇₁⋊C₄₉	C₂	1	2	yes	maximal, direct product factor
3	C₇₁⋊C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₇₁	C₇	1	1	yes	maximal, characteristic
5	C₂×C₇×C₇₁	C₂×C₇	1	1	yes	characteristic
6	C₇×D₇₁	C₂×C₇	1	2	yes	—
7	C₇×C₇₁	C₂²×C₇	1	1	yes	characteristic
8	C₂×D₇₁	C₄₉	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₄₉	—	71	1	no	maximal, Hall
10	C₂×C₇₁	C₂×C₄₉	1	1	yes	characteristic, complemented
11	D₇₁	C₂×C₄₉	1	2	yes	complemented
12	C₂×C₄₉	—	71	2	no	—
13	C₂×C₄₉	—	71	1	no	—
14	C₇₁	C₂²×C₄₉	1	1	yes	characteristic, complemented, Sylow
15	C₄₉	—	71	1	no	Sylow
16	C₂²×C₇	—	497	1	no	—
17	C₂×C₇	—	497	2	no	—
18	C₂×C₇	D₇₁⋊C₇	1	1	yes	characteristic
19	C₇	C₂×D₇₁⋊C₇	1	1	yes	characteristic
20	C₂²	—	497	1	no	Sylow
21	C₂	—	497	2	no	—
22	C₂	D₇₁⋊C₄₉	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.