Subgroups — C₅×#12541 #11935261

Order 1280.

402 conjugacy classes of subgroups.

The subgroup lattice has 134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#347	C₂	1	4	yes	maximal
2	C₄×C₅×M₃₂	C₂	1	2	yes	maximal
3	C₅×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×M₃₂	C₂²	1	4	yes	—
5	C₂×C₅×#97	C₄	1	1	yes	characteristic
6	C₂×C₅×#97	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₅×#376	C₄	1	1	yes	characteristic
10	C₅×#347	C₄	1	16	yes	complemented
11	C₅×#346	C₄	1	4	yes	complemented
12	C₄×C₅×C₁₆	C₄	1	4	yes	complemented
13	#12541	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
15	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
19	C₅×M₃₂	C₂×C₄	1	16	yes	—
20	C₂×C₅×C₁₆	C₂×C₄	1	8	yes	—
21	C₅×#97	—	2	2	no	—
22	C₅×#97	C₂×C₄	1	8	yes	—
23	C₄×C₅×C₈	—	2	4	no	—
24	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
25	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
26	C₅×#95	—	2	2	no	—
27	C₂×#347	C₂×C₅	1	4	yes	—
28	C₄×M₃₂	C₂×C₅	1	2	yes	—
29	#1726	C₂×C₅	1	1	yes	characteristic
30	C₂²×C₄×C₅	—	2	2	no	—
31	C₂²×C₄×C₅	M₁₆	1	2	yes	—
32	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	—	2	2	no	—
35	C₂×C₅×C₈	C₄²	1	4	yes	—
36	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
37	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
38	C₂×C₅×C₈	M₁₆	1	4	yes	—
39	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
40	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
41	C₄²×C₅	—	2	2	no	—
42	C₄²×C₅	C₄²	1	4	yes	—
43	C₄²×C₅	C₄²	1	2	yes	—
44	C₄²×C₅	M₁₆	1	2	yes	—
45	C₅×C₁₆	C₄²	1	16	yes	—
46	C₂×M₃₂	C₂²×C₅	1	4	yes	—
47	C₂×#97	C₄×C₅	1	1	yes	characteristic
48	C₂×#97	C₂²×C₅	1	2	yes	—
49	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
50	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
51	#376	C₄×C₅	1	1	yes	characteristic
52	#347	C₄×C₅	1	16	yes	complemented
53	#346	C₄×C₅	1	4	yes	complemented
54	C₄×C₁₆	C₄×C₅	1	4	yes	complemented
55	C₂³×C₅	C₂×M₁₆	1	1	yes	characteristic
56	C₂×C₄×C₅	—	2	4	no	—
57	C₂×C₄×C₅	—	4	2	no	—
58	C₂×C₄×C₅	—	4	4	no	—
59	C₂×C₄×C₅	#97	1	4	yes	—
60	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
62	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
63	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
64	C₅×C₈	—	2	4	no	—
65	C₅×C₈	#97	1	2	yes	—
66	C₅×C₈	#97	1	2	yes	—
67	C₅×C₈	C₂×C₄²	1	4	yes	—
68	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
69	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
70	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
71	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
72	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
73	M₃₂	C₂×C₄×C₅	1	16	yes	—
74	C₂×C₁₆	C₂×C₄×C₅	1	8	yes	—
75	#97	—	2	2	no	—
76	#97	C₂×C₄×C₅	1	8	yes	—
77	C₄×C₈	—	2	4	no	—
78	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
79	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
80	#95	—	2	2	no	—
81	C₂²×C₅	—	2	2	no	—
82	C₂²×C₅	C₂×#97	1	1	yes	characteristic
83	C₂²×C₅	C₄×M₁₆	1	2	yes	—
84	C₄×C₅	—	2	4	no	—
85	C₄×C₅	—	4	4	no	—
86	C₄×C₅	C₄³	1	1	yes	characteristic
87	C₄×C₅	C₂×#97	1	1	yes	characteristic
88	C₄×C₅	C₄×M₁₆	1	2	yes	—
89	C₂²×C₄	—	2	2	no	—
90	C₂²×C₄	C₅×M₁₆	1	2	yes	—
91	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	C₄²×C₅	1	4	yes	—
95	C₂×C₈	C₄²×C₅	1	1	yes	characteristic
96	C₂×C₈	C₄²×C₅	1	1	yes	characteristic
97	C₂×C₈	C₅×M₁₆	1	4	yes	—
98	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
99	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
100	C₄²	—	2	2	no	—
101	C₄²	C₄²×C₅	1	4	yes	—
102	C₄²	C₄²×C₅	1	2	yes	—
103	C₄²	C₅×M₁₆	1	2	yes	—
104	C₁₆	C₄²×C₅	1	16	yes	—
105	C₂×C₅	—	2	2	no	—
106	C₂×C₅	C₄×#97	1	1	yes	characteristic
107	C₂×C₅	#2110	1	2	yes	—
108	C₂³	C₂×C₅×M₁₆	1	1	yes	characteristic
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	4	4	no	—
112	C₂×C₄	C₅×#97	1	4	yes	—
113	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
114	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
115	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
116	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
117	C₈	—	2	4	no	—
118	C₈	C₅×#97	1	2	yes	—
119	C₈	C₅×#97	1	2	yes	—
120	C₈	C₂×C₄²×C₅	1	4	yes	—
121	C₅	#12541	1	1	yes	characteristic, direct product factor, Sylow
122	C₂²	—	2	2	no	—
123	C₂²	C₂×C₅×#97	1	1	yes	characteristic
124	C₂²	C₄×C₅×M₁₆	1	2	yes	—
125	C₄	—	2	4	no	—
126	C₄	—	4	4	no	—
127	C₄	C₄³×C₅	1	1	yes	characteristic
128	C₄	C₂×C₅×#97	1	1	yes	characteristic
129	C₄	C₄×C₅×M₁₆	1	2	yes	—
130	C₂	—	2	2	no	—
131	C₂	C₄×C₅×#97	1	1	yes	characteristic
132	C₂	C₅×#2110	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₄²
commutator	C₄	C₄³×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×#97
prime radical	C₂³×C₅	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₅×#347	C₄	semidirect
11. C₅×#346	C₄	semidirect
12. C₄×C₅×C₁₆	C₄	semidirect
13. #12541	C₅	direct (N × H)
52. #347	C₄×C₅	semidirect
53. #346	C₄×C₅	semidirect
54. C₄×C₁₆	C₄×C₅	semidirect
121. C₅	#12541	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×#347	2
C₄×C₅×M₃₂	2
C₅×#1726	2
#12541	5

Subgroups — C5×#12541 #11935261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12541 #11935261