Subgroups — C₅×#380 #65543

Order 320.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
4	C₅×#95	C₂	1	2	yes	maximal, complemented
5	C₂⁴×C₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₅	—	2	4	no	—
7	C₂²×C₄×C₅	C₄	1	4	yes	complemented
8	C₂²×C₄×C₅	C₂²	1	4	yes	—
9	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₅×C₄⋊C₄	—	2	4	no	—
12	C₅×C₂²⋊C₄	—	2	4	no	—
13	#380	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₅	—	2	2	no	—
15	C₂³×C₅	—	2	2	no	—
16	C₂³×C₅	C₂×C₄	1	2	yes	—
17	C₂³×C₅	D₄	1	2	yes	—
18	C₂³×C₅	Q₈	1	2	yes	—
19	C₂³×C₅	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₅	—	2	2	no	—
21	C₂×C₄×C₅	—	2	8	no	—
22	C₂×C₄×C₅	—	2	4	no	—
23	C₂×C₄×C₅	—	2	4	no	—
24	C₂×C₄×C₅	—	2	4	no	—
25	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₅	D₄	1	4	yes	—
28	C₂³×C₄	C₂×C₅	1	1	yes	characteristic
29	C₂×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
30	C₂×C₂²⋊C₄	C₂×C₅	1	2	yes	—
31	#95	C₂×C₅	1	2	yes	complemented
32	C₂²×C₅	—	2	2	no	—
33	C₂²×C₅	—	2	2	no	—
34	C₂²×C₅	—	2	4	no	—
35	C₂²×C₅	—	2	4	no	—
36	C₂²×C₅	C₄⋊C₄	1	4	yes	complemented
37	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₅	C₂×D₄	1	2	yes	—
39	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₅	C₂×Q₈	1	1	yes	characteristic
41	C₂²×C₅	#41	1	2	yes	—
42	C₄×C₅	—	2	2	no	—
43	C₄×C₅	—	4	4	no	—
44	C₄×C₅	C₂²⋊C₄	1	4	yes	complemented
45	C₂⁴	C₂²×C₅	1	1	yes	characteristic
46	C₂²×C₄	—	2	4	no	—
47	C₂²×C₄	C₄×C₅	1	4	yes	complemented
48	C₂²×C₄	C₂²×C₅	1	4	yes	—
49	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
50	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
51	C₄⋊C₄	—	2	4	no	—
52	C₂²⋊C₄	—	2	4	no	—
53	C₂×C₅	—	2	4	no	—
54	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₅	#117	1	1	yes	characteristic
57	C₂×C₅	#121	1	2	yes	—
58	C₂×C₅	C₂²⋊Q₈	1	2	yes	—
59	C₂³	—	2	2	no	—
60	C₂³	—	2	2	no	—
61	C₂³	C₂×C₄×C₅	1	2	yes	—
62	C₂³	C₅×D₄	1	2	yes	—
63	C₂³	C₅×Q₈	1	2	yes	—
64	C₂³	C₂³×C₅	1	1	yes	characteristic
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	8	no	—
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
71	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
72	C₂×C₄	C₅×D₄	1	4	yes	—
73	C₅	#380	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	2	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	2	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	C₅×C₄⋊C₄	1	4	yes	complemented
79	C₂²	C₂²×C₄×C₅	1	1	yes	characteristic
80	C₂²	C₂×C₅×D₄	1	2	yes	—
81	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
82	C₂²	C₂×C₅×Q₈	1	1	yes	characteristic
83	C₂²	C₅×#41	1	2	yes	—
84	C₄	—	2	2	no	—
85	C₄	—	4	4	no	—
86	C₄	C₅×C₂²⋊C₄	1	4	yes	complemented
87	C₂	—	2	4	no	—
88	C₂	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
89	C₂	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
90	C₂	C₅×#117	1	1	yes	characteristic
91	C₂	C₅×#121	1	2	yes	—
92	C₂	C₅×C₂²⋊Q₈	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂³
commutator	C₂²	C₂²×C₄×C₅
Frattini, cosocle	C₂³	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₄⋊C₄	C₂	semidirect
4. C₅×#95	C₂	semidirect
7. C₂²×C₄×C₅	C₄	semidirect
13. #380	C₅	direct (N × H)
29. C₂×C₄⋊C₄	C₂×C₅	semidirect
31. #95	C₂×C₅	semidirect
36. C₂²×C₅	C₄⋊C₄	semidirect
44. C₄×C₅	C₂²⋊C₄	semidirect
47. C₂²×C₄	C₄×C₅	semidirect
73. C₅	#380	direct (N × H)
78. C₂²	C₅×C₄⋊C₄	semidirect
86. C₄	C₅×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅	2
C₂×C₅×C₄⋊C₄	2
C₂×C₅×C₂²⋊C₄	2
C₅×#95	2
#380	5

Subgroups — C5×#380 #65543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#380 #65543