Subgroups — C₅×#376 #65539

Order 320.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅	C₂	1	3	yes	maximal
2	C₅×#95	C₂	1	4	yes	maximal
3	C₂²×C₄×C₅	C₂²	1	6	yes	—
4	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₄²×C₅	C₄	1	12	yes	complemented
6	#376	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₅	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₅	—	2	12	no	—
9	C₂×C₄×C₅	C₂×C₄	1	12	yes	—
10	C₂×C₄×C₅	C₂×C₄	1	6	yes	—
11	C₂×C₄²	C₂×C₅	1	3	yes	—
12	#95	C₂×C₅	1	4	yes	—
13	C₂²×C₅	C₂²×C₄	1	3	yes	—
14	C₂²×C₅	#41	1	4	yes	—
15	C₄×C₅	—	2	12	no	—
16	C₄×C₅	C₄²	1	4	yes	—
17	C₂²×C₄	C₂²×C₅	1	6	yes	—
18	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
19	C₄²	C₄×C₅	1	12	yes	complemented
20	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
21	C₂×C₅	#117	1	6	yes	—
22	C₂³	C₂³×C₅	1	1	yes	characteristic
23	C₂×C₄	—	2	12	no	—
24	C₂×C₄	C₂×C₄×C₅	1	12	yes	—
25	C₂×C₄	C₂×C₄×C₅	1	6	yes	—
26	C₅	#376	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	C₂²×C₄×C₅	1	3	yes	—
28	C₂²	C₅×#41	1	4	yes	—
29	C₄	—	2	12	no	—
30	C₄	C₄²×C₅	1	4	yes	—
31	C₂	C₂×C₄²×C₅	1	1	yes	characteristic
32	C₂	C₅×#117	1	6	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.