Subgroups — #65002

Order 320.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4020	C₂	1	1	yes	maximal, characteristic
2	#4016	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	#3953	C₂	1	4	yes	maximal, complemented
5	C₂×D₂₀	—	2	2	no	—
6	C₂×D₂₀	C₂²	1	2	yes	—
7	C₂×C₅×C₈	C₂²	1	2	yes	—
8	C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₅	C₂²	1	2	yes	—
10	#683	—	2	2	no	—
11	#490	—	5	1	no	maximal, Sylow
12	C₂²×D₅	—	2	2	no	—
13	C₂×C₄×C₅	D₄	1	2	yes	—
14	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₂×Dic₅	—	2	2	no	—
16	D₂₀	—	2	4	no	—
17	D₂₀	—	4	4	no	—
18	C₅×C₈	—	2	2	no	—
19	#127	—	5	1	no	—
20	#125	—	5	1	no	—
21	#102	—	5	4	no	—
22	#97	D₅	1	1	yes	characteristic, complemented
23	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
24	C₂×D₅	—	4	2	no	—
25	C₂×D₅	—	4	4	no	—
26	C₄×C₅	—	2	2	no	—
27	C₄×C₅	#41	1	2	yes	—
28	Dic₅	—	4	2	no	—
29	C₂×D₄	—	5	2	no	—
30	C₂×D₄	—	10	2	no	—
31	C₂×C₈	C₂×D₅	1	2	yes	—
32	C₄⋊C₄	—	5	2	no	—
33	C₄⋊C₄	—	10	2	no	—
34	C₄²	C₂×D₅	1	1	yes	characteristic
35	C₂×C₅	#124	1	1	yes	characteristic
36	C₂×C₅	AGL(1,ℤ/8)	1	2	yes	—
37	D₅	—	8	2	no	—
38	C₂³	—	10	2	no	—
39	D₄	—	10	4	no	—
40	D₄	—	20	4	no	—
41	C₂×C₄	—	10	2	no	—
42	C₂×C₄	D₂₀	1	2	yes	—
43	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₅	#490	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	20	2	no	—
47	C₂²	—	20	4	no	—
48	C₂²	C₂×D₂₀	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	20	2	no	—
51	C₄	#709	1	2	yes	—
52	C₂	—	40	2	no	—
53	C₂	#4021	1	1	yes	characteristic
54	C₂	#4054	1	2	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.