Subgroups — C₄×C₇₉×C₃₇⋊C₃ #47975122

Order 35076.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃₇×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₉×C₃₇⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃₇×C₇₉	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₇₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₇₉	—	37	1	no	maximal, Hall
7	C₂×C₃×C₇₉	—	37	1	no	—
8	C₄×C₃₇⋊C₃	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇₉	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₇₉	—	37	1	no	Hall
11	C₂×C₃₇⋊C₃	C₂×C₇₉	1	1	yes	characteristic
12	C₂×C₇₉	C₂×C₃₇⋊C₃	1	1	yes	characteristic
13	C₄×C₃₇	C₃×C₇₉	1	1	yes	characteristic, complemented, Hall
14	C₃₇⋊C₃	C₄×C₇₉	1	1	yes	characteristic, direct product factor, Hall
15	C₇₉	C₄×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃₇	C₂×C₃×C₇₉	1	1	yes	characteristic
17	C₃₇	C₃×C₄×C₇₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	37	1	no	Hall
19	C₂×C₃	—	37	1	no	—
20	C₄	C₇₉×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	C₂×C₇₉×C₃₇⋊C₃	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.