Subgroups — C₅×Q₈×C₂₇ #11761686

Order 1080.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₂₇	C₂	1	3	yes	maximal
2	C₅×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₂₇	C₂²	1	1	yes	characteristic
4	Q₈×C₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₅×C₉	C₂×C₃	1	3	yes	—
6	C₅×C₂₇	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×Q₈	C₉	1	1	yes	characteristic
8	C₄×C₂₇	C₂×C₅	1	3	yes	—
9	C₂×C₅×C₉	C₂²×C₃	1	1	yes	characteristic
10	Q₈×C₉	C₃×C₅	1	1	yes	characteristic
11	C₃×C₄×C₅	C₂×C₉	1	3	yes	—
12	C₂×C₂₇	C₂²×C₅	1	1	yes	characteristic
13	C₅×C₉	C₃×Q₈	1	1	yes	characteristic
14	C₅×Q₈	C₂₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₉	C₂×C₃×C₅	1	3	yes	—
16	C₂×C₃×C₅	C₂²×C₉	1	1	yes	characteristic
17	C₂₇	C₅×Q₈	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×Q₈	C₅×C₉	1	1	yes	characteristic
19	C₄×C₅	C₂×C₂₇	1	3	yes	—
20	C₂×C₉	C₂²×C₃×C₅	1	1	yes	characteristic
21	C₃×C₅	Q₈×C₉	1	1	yes	characteristic
22	C₃×C₄	C₂×C₅×C₉	1	3	yes	—
23	C₂×C₅	C₂²×C₂₇	1	1	yes	characteristic
24	C₉	C₃×C₅×Q₈	1	1	yes	characteristic
25	Q₈	C₅×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃	C₂²×C₅×C₉	1	1	yes	characteristic
27	C₅	Q₈×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₄	C₂×C₅×C₂₇	1	3	yes	—
29	C₃	C₅×Q₈×C₉	1	1	yes	characteristic
30	C₂	C₂²×C₅×C₂₇	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.