Subgroups — C₅×Dic₁₆₇₉ #46777149

Order 33580.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₆₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₇₃	C₂×C₅	1	1	yes	characteristic
5	C₂₃×C₇₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₇₃	—	23	1	no	maximal, Hall
7	C₂×C₅×C₇₃	D₂₃	1	1	yes	characteristic
8	C₅×Dic₂₃	—	73	1	no	maximal, Hall
9	C₅×C₇₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
10	Dic₇₃	—	23	1	no	Hall
11	C₂×C₅×C₂₃	D₇₃	1	1	yes	characteristic
12	C₂×C₇₃	C₅×D₂₃	1	1	yes	characteristic
13	C₅×C₂₃	Dic₇₃	1	1	yes	characteristic, complemented, Hall
14	Dic₂₃	—	73	1	no	Hall
15	C₇₃	C₅×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	C₅×D₇₃	1	1	yes	characteristic
17	C₂₃	C₅×Dic₇₃	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	1679	1	no	Hall
19	C₂×C₅	D₁₆₇₉	1	1	yes	characteristic
20	C₅	Dic₁₆₇₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1679	1	no	Sylow
22	C₂	C₅×D₁₆₇₉	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.