Subgroups — C₅×#416 #65579

Order 320.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#103	C₂	1	2	yes	maximal, complemented
5	C₅×#102	C₂	1	2	yes	maximal, complemented
6	C₅×#41	—	2	2	no	—
7	C₅×#41	C₄	1	4	yes	complemented
8	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×D₄	—	2	1	no	—
10	C₂×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅	—	2	1	no	—
12	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₈	—	2	2	no	—
14	C₂×C₅×C₈	C₂²	1	2	yes	—
15	C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₅×C₂²⋊C₄	—	2	1	no	—
17	C₄²×C₅	—	2	1	no	—
18	#416	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₅	—	2	1	no	—
20	C₂³×C₅	D₄	1	1	yes	characteristic
21	C₅×Q₈	—	2	1	no	—
22	C₅×Q₈	C₂×C₄	1	2	yes	—
23	C₅×D₄	—	2	4	no	—
24	C₅×D₄	—	2	1	no	—
25	C₅×D₄	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₅	—	2	1	no	—
27	C₂×C₄×C₅	—	2	4	no	—
28	C₂×C₄×C₅	—	2	2	no	—
29	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
30	C₂×C₄×C₅	D₄	1	2	yes	—
31	C₂×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₅×C₈	—	2	2	no	—
34	C₂×#41	C₂×C₅	1	1	yes	characteristic
35	C₂²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
36	#117	C₂×C₅	1	1	yes	characteristic, complemented
37	#103	C₂×C₅	1	2	yes	complemented
38	#102	C₂×C₅	1	2	yes	complemented
39	C₂²×C₅	—	2	2	no	—
40	C₂²×C₅	—	2	2	no	—
41	C₂²×C₅	—	4	2	no	—
42	C₂²×C₅	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	—	4	2	no	—
46	C₄×C₅	C₂²⋊C₄	1	2	yes	—
47	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
48	C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	#41	—	2	2	no	—
50	#41	C₄×C₅	1	4	yes	complemented
51	C₂×Q₈	C₂²×C₅	1	1	yes	characteristic
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂²×C₅	1	1	yes	characteristic
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
56	C₂×C₈	—	2	2	no	—
57	C₂×C₈	C₂²×C₅	1	2	yes	—
58	C₄⋊C₄	C₂²×C₅	1	2	yes	—
59	C₂²⋊C₄	—	2	1	no	—
60	C₄²	—	2	1	no	—
61	C₂×C₅	—	2	2	no	—
62	C₂×C₅	—	4	2	no	—
63	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₅	#135	1	2	yes	—
65	C₂³	—	2	1	no	—
66	C₂³	C₅×D₄	1	1	yes	characteristic
67	Q₈	—	2	1	no	—
68	Q₈	C₂×C₄×C₅	1	2	yes	—
69	D₄	—	2	4	no	—
70	D₄	—	2	1	no	—
71	D₄	C₂×C₄×C₅	1	2	yes	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
76	C₂×C₄	C₅×D₄	1	1	yes	characteristic
77	C₂×C₄	C₅×D₄	1	2	yes	—
78	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₅	#416	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²	—	2	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	4	2	no	—
84	C₂²	C₅×C₂²⋊C₄	1	2	yes	—
85	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	4	2	no	—
88	C₄	C₅×C₂²⋊C₄	1	2	yes	—
89	C₄	C₂²×C₄×C₅	1	1	yes	characteristic
90	C₄	C₂×C₅×D₄	1	1	yes	characteristic
91	C₂	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
94	C₂	C₅×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	D₄
commutator	C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂³×C₅
socle	C₂²×C₅	C₂×D₄
prime radical	C₂×C₅×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×C₈	C₂	semidirect
3. C₅×#117	C₂	semidirect
4. C₅×#103	C₂	semidirect
5. C₅×#102	C₂	semidirect
7. C₅×#41	C₄	semidirect
18. #416	C₅	direct (N × H)
35. C₂²×C₈	C₂×C₅	semidirect
36. #117	C₂×C₅	semidirect
37. #103	C₂×C₅	semidirect
38. #102	C₂×C₅	semidirect
50. #41	C₄×C₅	semidirect
80. C₅	#416	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#41	2
C₂²×C₅×C₈	2
C₅×#117	2
C₅×#103	2
C₅×#102	2
#416	5

Subgroups — C5×#416 #65579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#416 #65579