Subgroups — C₅×#63540 #13084629

Order 1440.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
3	#63540	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₃⋊C₁₆	—	6	2	no	—
5	C₃²×C₄×C₅	C₈	1	1	yes	characteristic
6	C₅×C₃₂	—	9	1	no	maximal, Hall
7	C₃⋊(C₃⋊C₁₆)	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₈	—	2	2	no	—
9	C₂×C₃²×C₅	C₁₆	1	1	yes	characteristic
10	C₅×C₁₆	—	9	1	no	—
11	C₃²×C₈	C₄×C₅	1	1	yes	characteristic
12	C₃×C₄×C₅	—	2	2	no	—
13	C₃⋊C₁₆	—	6	2	no	—
14	C₃²×C₅	C₃₂	1	1	yes	characteristic, complemented, Hall
15	C₅×C₈	#157	1	1	yes	characteristic
16	C₃²×C₄	C₅×C₈	1	1	yes	characteristic
17	C₃₂	—	9	1	no	Sylow
18	C₂×C₃×C₅	—	2	2	no	—
19	C₃×C₈	—	2	2	no	—
20	C₄×C₅	#622	1	1	yes	characteristic
21	C₂×C₃²	C₅×C₁₆	1	1	yes	characteristic
22	C₁₆	—	9	1	no	—
23	C₃×C₅	—	2	2	no	—
24	C₃×C₄	—	2	2	no	—
25	C₂×C₅	#3708	1	1	yes	characteristic
26	C₃²	C₅×C₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₈	C₅×#157	1	1	yes	characteristic
28	C₂×C₃	—	2	2	no	—
29	C₅	#63540	1	1	yes	characteristic, direct product factor, Sylow
30	C₄	C₅×#622	1	1	yes	characteristic
31	C₃	—	2	2	no	—
32	C₂	C₅×#3708	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.