Subgroups — C₇×Dic₆₈₉ #34064367

Order 19292.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₆₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×Dic₅₃	—	13	1	no	maximal, Hall
5	C₂×C₁₃×C₅₃	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₅₃	D₁₃	1	1	yes	characteristic
7	C₁₃×C₅₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₅₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
9	C₇×Dic₁₃	—	53	1	no	maximal, Hall
10	Dic₅₃	—	13	1	no	Hall
11	C₂×C₇×C₁₃	D₅₃	1	1	yes	characteristic
12	C₂×C₅₃	C₇×D₁₃	1	1	yes	characteristic
13	C₇×C₁₃	Dic₅₃	1	1	yes	characteristic, complemented, Hall
14	C₅₃	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
15	Dic₁₃	—	53	1	no	Hall
16	C₄×C₇	—	689	1	no	Hall
17	C₂×C₁₃	C₇×D₅₃	1	1	yes	characteristic
18	C₂×C₇	D₆₈₉	1	1	yes	characteristic
19	C₁₃	C₇×Dic₅₃	1	1	yes	characteristic, complemented, Sylow
20	C₇	Dic₆₈₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	689	1	no	Sylow
22	C₂	C₇×D₆₈₉	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.