Subgroups — #10605048

Order 640.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	#65229	C₂	1	7	yes	maximal
3	#65222	C₂	1	7	yes	maximal, complemented
4	C₂×C₄²×C₅	C₂²	1	7	yes	—
5	C₂×#685	C₂²	1	7	yes	—
6	C₂×#683	C₂²	1	7	yes	—
7	#3963	C₂²	1	14	yes	—
8	#2866	—	5	1	no	maximal, Sylow
9	C₂³×D₅	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₅	C₂³	1	7	yes	—
11	C₂²×Dic₅	C₂³	1	7	yes	—
12	C₄²×C₅	—	2	14	no	—
13	#685	—	2	14	no	—
14	#683	—	2	14	no	—
15	#388	—	5	7	no	—
16	#387	—	5	7	no	—
17	C₄³	D₅	1	1	yes	characteristic, complemented
18	C₂³×C₅	C₂⁴	1	1	yes	characteristic
19	C₂²×D₅	—	2	7	no	—
20	C₂×C₄×C₅	—	2	14	no	—
21	C₂×C₄×C₅	#41	1	14	yes	—
22	C₂×Dic₅	—	2	14	no	—
23	C₂×Dic₅	—	2	7	no	—
24	C₂×C₄⋊C₄	—	5	7	no	—
25	C₂×C₂²⋊C₄	—	5	7	no	—
26	C₂×C₄²	C₂×D₅	1	7	yes	—
27	#95	—	5	14	no	—
28	C₂²×C₅	C₂×#41	1	7	yes	—
29	C₂×D₅	—	4	7	no	—
30	C₄×C₅	—	2	14	no	—
31	Dic₅	—	4	7	no	—
32	C₂⁴	—	5	1	no	—
33	C₂²×C₄	—	5	7	no	—
34	C₂²×C₄	C₂²×D₅	1	7	yes	—
35	C₄⋊C₄	—	10	14	no	—
36	C₂²⋊C₄	—	10	14	no	—
37	C₄²	—	2	14	no	—
38	C₂×C₅	#529	1	7	yes	—
39	D₅	—	8	1	no	—
40	C₂³	—	10	7	no	—
41	C₂³	C₂³×D₅	1	1	yes	characteristic
42	C₂×C₄	—	2	14	no	—
43	C₂×C₄	—	10	7	no	—
44	C₂×C₄	—	10	14	no	—
45	C₂×C₄	#709	1	14	yes	—
46	C₅	#2866	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	20	7	no	—
48	C₂²	C₂×#709	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	20	7	no	—
51	C₂	—	40	1	no	—
52	C₂	#65813	1	7	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.