Subgroups — #64996

Order 320.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#676	C₂	1	2	yes	maximal
2	C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×Dic₅	C₂	1	2	yes	maximal, complemented
5	#3935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₅	C₄	1	2	yes	—
7	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×C₅×C₈	C₂²	1	2	yes	—
9	C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄×Dic₅	C₄	1	2	yes	—
11	C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×#168	C₂²	1	2	yes	—
13	#676	C₄	1	8	yes	complemented
14	C₄×M₁₆	—	5	1	no	maximal, Sylow
15	C₂²×D₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₅	C₂×C₄	1	2	yes	—
20	C₄×D₅	—	2	4	no	—
21	C₄×D₅	C₂×C₄	1	4	yes	—
22	C₅×C₈	C₂×C₄	1	4	yes	complemented
23	#168	C₂×C₄	1	4	yes	complemented
24	C₂×M₁₆	—	5	2	no	—
25	C₂×C₄²	—	5	1	no	—
26	#97	—	5	1	no	—
27	#97	D₅	1	1	yes	characteristic, complemented
28	C₄×C₈	—	5	2	no	—
29	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
30	C₂×D₅	—	2	2	no	—
31	C₂×D₅	C₄²	1	2	yes	—
32	C₄×C₅	—	2	2	no	—
33	C₄×C₅	C₂²×C₄	1	2	yes	—
34	Dic₅	C₄²	1	2	yes	—
35	Dic₅	M₁₆	1	4	yes	complemented
36	C₂²×C₄	—	5	1	no	—
37	C₂²×C₄	—	5	2	no	—
38	M₁₆	—	5	8	no	—
39	C₂×C₈	—	5	2	no	—
40	C₂×C₈	C₂×D₅	1	2	yes	—
41	C₄²	—	5	2	no	—
42	C₄²	—	5	1	no	—
43	C₄²	C₂×D₅	1	1	yes	characteristic
44	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₅	C₂×M₁₆	1	2	yes	—
46	D₅	—	2	2	no	—
47	C₂³	—	5	1	no	—
48	C₂×C₄	—	5	1	no	—
49	C₂×C₄	—	5	2	no	—
50	C₂×C₄	—	5	4	no	—
51	C₂×C₄	—	10	4	no	—
52	C₂×C₄	C₄×D₅	1	2	yes	—
53	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
54	C₈	—	5	4	no	—
55	C₈	C₄×D₅	1	4	yes	complemented
56	C₅	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	5	2	no	—
58	C₂²	—	10	2	no	—
59	C₂²	C₂×C₄×D₅	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	5	2	no	—
62	C₄	—	5	4	no	—
63	C₄	C₂×C₄×D₅	1	2	yes	—
64	C₂	—	10	2	no	—
65	C₂	C₄²×D₅	1	1	yes	characteristic
66	C₂	D₅×M₁₆	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₅
commutator	C₂×C₅	C₂×C₄²
Fitting	C₅×#97	C₂
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂²×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	#97	D₅
hypocenter	C₅	C₄×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅×#97	C₂	semidirect
4. C₈×Dic₅	C₂	semidirect
5. #3935	C₂	semidirect
13. #676	C₄	semidirect
22. C₅×C₈	C₂×C₄	semidirect
23. #168	C₂×C₄	semidirect
27. #97	D₅	semidirect
35. Dic₅	M₁₆	semidirect
55. C₈	C₄×D₅	semidirect
56. C₅	C₄×M₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#676	2
C₄²×D₅	2
C₅×#97	2
C₈×Dic₅	2
#3935	2
C₄×M₁₆	5