Subgroups — C₅×#8804 #11931524

Order 1280.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1455	C₂	1	1	yes	maximal, characteristic
2	C₅×#1291	C₂	1	3	yes	maximal
3	C₅×#1288	C₂	1	3	yes	maximal
4	C₅×#432	C₂²	1	3	yes	—
5	C₄×C₅×M₁₆	C₂²	1	3	yes	—
6	C₅×#383	C₂²	1	1	yes	characteristic
7	C₅×#322	C₄	1	3	yes	complemented
8	C₅×C₈²	C₄	1	1	yes	characteristic, complemented
9	#8804	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₅×M₁₆	—	2	3	no	—
11	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
12	C₅×C₄⋊C₈	—	2	3	no	—
13	C₅×C₂²⋊C₈	—	2	3	no	—
14	C₅×#97	—	2	3	no	—
15	C₅×#97	—	2	3	no	—
16	C₄×C₅×C₈	C₂×C₄	1	3	yes	—
17	C₄×C₅×C₈	C₂×C₄	1	3	yes	—
18	C₅×#95	—	2	3	no	—
19	#1455	C₂×C₅	1	1	yes	characteristic
20	#1291	C₂×C₅	1	3	yes	—
21	#1288	C₂×C₅	1	3	yes	—
22	C₂²×C₄×C₅	—	4	1	no	—
23	C₂²×C₄×C₅	#41	1	3	yes	—
24	C₅×M₁₆	—	4	6	no	—
25	C₂×C₅×C₈	—	2	3	no	—
26	C₂×C₅×C₈	—	2	3	no	—
27	C₂×C₅×C₈	—	4	3	no	—
28	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
29	C₄²×C₅	#41	1	3	yes	—
30	#432	C₂²×C₅	1	3	yes	—
31	C₄×M₁₆	C₂²×C₅	1	3	yes	—
32	#383	C₂²×C₅	1	1	yes	characteristic
33	#322	C₄×C₅	1	3	yes	complemented
34	C₈²	C₄×C₅	1	1	yes	characteristic, complemented
35	C₂³×C₅	#126	1	1	yes	characteristic
36	C₂×C₄×C₅	—	4	3	no	—
37	C₂×C₄×C₅	—	8	3	no	—
38	C₂×C₄×C₅	#117	1	3	yes	—
39	C₂×C₄×C₅	#126	1	3	yes	—
40	C₅×C₈	—	2	6	no	—
41	C₅×C₈	—	4	3	no	—
42	C₅×C₈	—	8	3	no	—
43	C₂×M₁₆	—	2	3	no	—
44	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
45	C₄⋊C₈	—	2	3	no	—
46	C₂²⋊C₈	—	2	3	no	—
47	#97	—	2	3	no	—
48	#97	—	2	3	no	—
49	C₄×C₈	C₂×C₄×C₅	1	3	yes	—
50	C₄×C₈	C₂×C₄×C₅	1	3	yes	—
51	#95	—	2	3	no	—
52	C₂²×C₅	—	2	3	no	—
53	C₂²×C₅	#383	1	1	yes	characteristic
54	C₄×C₅	—	2	3	no	—
55	C₄×C₅	—	2	3	no	—
56	C₄×C₅	—	16	1	no	—
57	C₂²×C₄	—	4	1	no	—
58	C₂²×C₄	C₅×#41	1	3	yes	—
59	M₁₆	—	4	6	no	—
60	C₂×C₈	—	2	3	no	—
61	C₂×C₈	—	2	3	no	—
62	C₂×C₈	—	4	3	no	—
63	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
64	C₄²	C₅×#41	1	3	yes	—
65	C₂×C₅	—	4	1	no	—
66	C₂×C₅	#1841	1	3	yes	—
67	C₂³	C₅×#126	1	1	yes	characteristic
68	C₂×C₄	—	4	3	no	—
69	C₂×C₄	—	8	3	no	—
70	C₂×C₄	C₅×#117	1	3	yes	—
71	C₂×C₄	C₅×#126	1	3	yes	—
72	C₈	—	2	6	no	—
73	C₈	—	4	3	no	—
74	C₈	—	8	3	no	—
75	C₅	#8804	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	—	2	3	no	—
77	C₂²	C₅×#383	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	2	3	no	—
80	C₄	—	16	1	no	—
81	C₂	—	4	1	no	—
82	C₂	C₅×#1841	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	#383
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	#126
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₅×#322	C₄	semidirect
8. C₅×C₈²	C₄	semidirect
9. #8804	C₅	direct (N × H)
33. #322	C₄×C₅	semidirect
34. C₈²	C₄×C₅	semidirect
75. C₅	#8804	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1455	2
C₅×#1291	2
C₅×#1288	2
#8804	5

Subgroups — C5×#8804 #11931524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8804 #11931524