Subgroups — C₇×Dic₁₁₂₁ #44535995

Order 31388.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₉×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₉×C₅₉	C₂×C₇	1	1	yes	characteristic
5	C₇×Dic₅₉	—	19	1	no	maximal, Hall
6	C₁₉×C₅₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₅₉	D₁₉	1	1	yes	characteristic
8	C₇×Dic₁₉	—	59	1	no	maximal, Hall
9	C₇×C₅₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₁₉	D₅₉	1	1	yes	characteristic
11	Dic₅₉	—	19	1	no	Hall
12	C₇×C₁₉	Dic₅₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₉	C₇×D₁₉	1	1	yes	characteristic
14	Dic₁₉	—	59	1	no	Hall
15	C₅₉	C₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	C₇×D₅₉	1	1	yes	characteristic
17	C₄×C₇	—	1121	1	no	Hall
18	C₁₉	C₇×Dic₅₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇	D₁₁₂₁	1	1	yes	characteristic
20	C₇	Dic₁₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1121	1	no	Sylow
22	C₂	C₇×D₁₁₂₁	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.