Subgroups — C₅×Q₈×D₇ #10587970

Order 560.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×D₇	C₂	1	3	yes	maximal
3	C₅×Dic₁₄	C₂	1	3	yes	maximal, complemented
4	C₂×C₅×D₇	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₇	C₂²	1	3	yes	—
6	C₅×Dic₇	C₂²	1	3	yes	—
7	Q₈×D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×Q₈	—	7	1	no	maximal, Hall
9	C₂×C₅×C₇	C₂³	1	1	yes	characteristic
10	C₅×D₇	Q₈	1	2	yes	direct product factor
11	C₇×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
12	C₄×D₇	C₂×C₅	1	3	yes	—
13	Dic₁₄	C₂×C₅	1	3	yes	complemented
14	C₅×Q₈	—	7	3	no	—
15	C₅×Q₈	D₇	1	1	yes	characteristic, direct product factor
16	C₂×C₄×C₅	—	7	3	no	—
17	C₅×C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
18	C₂×D₇	C₂²×C₅	1	1	yes	characteristic
19	C₄×C₇	C₂²×C₅	1	3	yes	—
20	Dic₇	C₂²×C₅	1	3	yes	—
21	C₂²×C₅	—	7	1	no	—
22	C₄×C₅	—	7	3	no	—
23	C₄×C₅	C₂×D₇	1	3	yes	—
24	C₂×Q₈	—	7	1	no	Sylow
25	C₂×C₇	C₂³×C₅	1	1	yes	characteristic
26	D₇	C₅×Q₈	1	2	yes	direct product factor
27	C₂×C₅	—	7	2	no	—
28	C₂×C₅	C₂²×D₇	1	1	yes	characteristic
29	Q₈	—	7	3	no	—
30	Q₈	C₅×D₇	1	1	yes	characteristic, direct product factor
31	C₂×C₄	—	7	3	no	—
32	C₇	C₂×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
33	C₅	Q₈×D₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	7	1	no	—
35	C₄	—	7	3	no	—
36	C₄	C₂×C₅×D₇	1	3	yes	—
37	C₂	—	7	2	no	—
38	C₂	C₂²×C₅×D₇	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.