Subgroups — C₄²×D₅₄₇ #31775950

Order 17504.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₄₇	C₂	1	3	yes	maximal
2	C₄×Dic₅₄₇	C₂	1	3	yes	maximal, complemented
3	C₄²×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅₄₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₅₄₇	C₂²	1	3	yes	—
6	C₄×D₅₄₇	C₄	1	12	yes	direct product factor
7	C₂×C₄×C₅₄₇	C₂²	1	3	yes	—
8	C₂²×C₅₄₇	C₂³	1	1	yes	characteristic
9	C₂×D₅₄₇	C₂×C₄	1	6	yes	—
10	C₄×C₅₄₇	C₂×C₄	1	6	yes	complemented
11	Dic₅₄₇	C₂×C₄	1	6	yes	complemented
12	C₂×C₅₄₇	C₂²×C₄	1	3	yes	—
13	D₅₄₇	C₄²	1	4	yes	direct product factor
14	C₅₄₇	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄²	—	547	1	no	maximal, Sylow
16	C₂²×C₄	—	547	3	no	—
17	C₄²	—	547	3	no	—
18	C₄²	D₅₄₇	1	1	yes	characteristic, direct product factor
19	C₂³	—	547	1	no	—
20	C₂×C₄	—	547	3	no	—
21	C₂×C₄	—	547	12	no	—
22	C₂×C₄	C₂×D₅₄₇	1	3	yes	—
23	C₂²	—	547	6	no	—
24	C₂²	C₂²×D₅₄₇	1	1	yes	characteristic
25	C₄	—	547	6	no	—
26	C₄	C₄×D₅₄₇	1	6	yes	direct product factor
27	C₂	—	547	4	no	—
28	C₂	C₂×C₄×D₅₄₇	1	3	yes	—

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.