Subgroups — C₁₇×C₁₉×Dic₁₉ #37589477

Order 24548.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₉²	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₉²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×Dic₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₁₇×C₁₉	—	19	1	no	maximal
5	C₁₇×Dic₁₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₁₉²	C₂×C₁₇	1	1	yes	characteristic
7	C₂×C₁₇×C₁₉	—	2	9	no	—
8	C₂×C₁₇×C₁₉	D₁₉	1	1	yes	characteristic
9	C₂×C₁₇×C₁₉	C₂×C₁₉	1	1	yes	characteristic
10	C₁₉²	C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
11	C₁₇×C₁₉	—	2	9	no	—
12	C₁₇×C₁₉	Dic₁₉	1	1	yes	characteristic, direct product factor
13	C₁₇×C₁₉	C₄×C₁₉	1	1	yes	characteristic, complemented
14	C₄×C₁₉	—	19	1	no	—
15	Dic₁₉	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor
16	C₄×C₁₇	—	19	1	no	Hall
17	C₂×C₁₉	—	2	9	no	—
18	C₂×C₁₉	C₁₇×D₁₉	1	1	yes	characteristic
19	C₂×C₁₉	C₂×C₁₇×C₁₉	1	1	yes	characteristic
20	C₂×C₁₇	C₁₉×D₁₉	1	1	yes	characteristic
21	C₁₉	—	2	9	no	—
22	C₁₉	C₁₇×Dic₁₉	1	1	yes	characteristic, direct product factor
23	C₁₉	C₄×C₁₇×C₁₉	1	1	yes	characteristic, complemented
24	C₁₇	C₁₉×Dic₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₄	—	19	1	no	Sylow
26	C₂	C₁₇×C₁₉×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.