Subgroups — C₃×D₇₆ #90706

Order 456.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₁₉	C₂²	1	1	yes	characteristic
5	C₃×D₁₉	—	2	2	no	—
6	C₂×D₁₉	C₂×C₃	1	2	yes	complemented
7	C₄×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₁₉	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	D₁₉	—	2	2	no	—
11	C₃×D₄	—	19	1	no	maximal, Hall
12	C₁₉	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₃	—	19	2	no	—
14	C₃×C₄	D₁₉	1	1	yes	characteristic, complemented
15	D₄	—	19	1	no	Sylow
16	C₂×C₃	—	38	2	no	—
17	C₂×C₃	C₂×D₁₉	1	1	yes	characteristic
18	C₂²	—	19	2	no	—
19	C₄	C₃×D₁₉	1	1	yes	characteristic, complemented
20	C₃	D₇₆	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	38	2	no	—
22	C₂	C₂×C₃×D₁₉	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.