Subgroups — C₅×#12594 #11935314

Order 1280.

354 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×M₃₂	C₂	1	2	yes	maximal
2	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₅×#1375	C₂	1	4	yes	maximal
4	C₂×C₅×M₃₂	C₂²	1	4	yes	—
5	C₂×C₅×#97	C₄	1	2	yes	—
6	C₂×C₅×#97	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
8	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₄³×C₅	C₄	1	1	yes	characteristic
10	C₅×#346	C₄	1	4	yes	complemented
11	C₄×C₅×C₁₆	C₄	1	4	yes	complemented
12	#12594	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
14	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₅	—	2	2	no	—
17	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
19	C₅×M₃₂	—	2	8	no	—
20	C₂×C₅×C₁₆	C₂×C₄	1	8	yes	—
21	C₅×#97	—	2	4	no	—
22	C₅×#97	C₈	1	8	yes	—
23	C₄×C₅×C₈	—	2	2	no	—
24	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
25	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
26	C₄×M₃₂	C₂×C₅	1	2	yes	—
27	C₄×#97	C₂×C₅	1	1	yes	characteristic
28	#1375	C₂×C₅	1	4	yes	—
29	C₂²×C₄×C₅	—	2	2	no	—
30	C₂²×C₄×C₅	M₁₆	1	2	yes	—
31	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₅×C₈	—	2	2	no	—
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	C₄²	1	2	yes	—
35	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
36	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
37	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
38	C₂×C₅×C₈	#41	1	4	yes	—
39	C₄²×C₅	—	2	2	no	—
40	C₄²×C₅	—	4	4	no	—
41	C₄²×C₅	C₄²	1	1	yes	characteristic
42	C₄²×C₅	C₄²	1	1	yes	characteristic
43	C₄²×C₅	C₂×C₈	1	4	yes	—
44	C₄²×C₅	M₁₆	1	2	yes	—
45	C₅×C₁₆	—	2	8	no	—
46	C₂×M₃₂	C₂²×C₅	1	4	yes	—
47	C₂×#97	C₄×C₅	1	2	yes	—
48	C₂×#97	C₂²×C₅	1	2	yes	—
49	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
50	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
51	C₄³	C₄×C₅	1	1	yes	characteristic
52	#346	C₄×C₅	1	4	yes	complemented
53	C₄×C₁₆	C₄×C₅	1	4	yes	complemented
54	C₂³×C₅	C₂×M₁₆	1	1	yes	characteristic
55	C₂×C₄×C₅	—	2	4	no	—
56	C₂×C₄×C₅	—	2	4	no	—
57	C₂×C₄×C₅	—	4	4	no	—
58	C₂×C₄×C₅	#97	1	2	yes	—
59	C₂×C₄×C₅	#97	1	2	yes	—
60	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₅	#117	1	2	yes	—
62	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
63	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
64	C₅×C₈	—	2	4	no	—
65	C₅×C₈	C₄×C₈	1	4	yes	—
66	C₅×C₈	#117	1	4	yes	—
67	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
68	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
69	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
70	C₂×C₄²	—	2	2	no	—
71	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
72	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
73	M₃₂	—	2	8	no	—
74	C₂×C₁₆	C₂×C₄×C₅	1	8	yes	—
75	#97	—	2	4	no	—
76	#97	C₅×C₈	1	8	yes	—
77	C₄×C₈	—	2	2	no	—
78	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
79	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
80	C₂²×C₅	—	2	2	no	—
81	C₂²×C₅	C₂×#97	1	1	yes	characteristic
82	C₂²×C₅	#431	1	2	yes	—
83	C₄×C₅	—	2	2	no	—
84	C₄×C₅	—	4	4	no	—
85	C₄×C₅	#347	1	4	yes	—
86	C₄×C₅	#376	1	1	yes	characteristic
87	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
88	C₄×C₅	#431	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	2	yes	—
95	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
96	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
97	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
98	C₂×C₈	C₅×#41	1	4	yes	—
99	C₄²	—	2	2	no	—
100	C₄²	—	4	4	no	—
101	C₄²	C₄²×C₅	1	1	yes	characteristic
102	C₄²	C₄²×C₅	1	1	yes	characteristic
103	C₄²	C₂×C₅×C₈	1	4	yes	—
104	C₄²	C₅×M₁₆	1	2	yes	—
105	C₁₆	—	2	8	no	—
106	C₂×C₅	—	2	2	no	—
107	C₂×C₅	#1744	1	1	yes	characteristic
108	C₂×C₅	C₂×#347	1	2	yes	—
109	C₂³	C₂×C₅×M₁₆	1	1	yes	characteristic
110	C₂×C₄	—	2	4	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	4	4	no	—
113	C₂×C₄	C₅×#97	1	2	yes	—
114	C₂×C₄	C₅×#97	1	2	yes	—
115	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
116	C₂×C₄	C₅×#117	1	2	yes	—
117	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
118	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
119	C₈	—	2	4	no	—
120	C₈	C₄×C₅×C₈	1	4	yes	—
121	C₈	C₅×#117	1	4	yes	—
122	C₅	#12594	1	1	yes	characteristic, direct product factor, Sylow
123	C₂²	—	2	2	no	—
124	C₂²	C₂×C₅×#97	1	1	yes	characteristic
125	C₂²	C₅×#431	1	2	yes	—
126	C₄	—	2	2	no	—
127	C₄	—	4	4	no	—
128	C₄	C₅×#347	1	4	yes	—
129	C₄	C₅×#376	1	1	yes	characteristic
130	C₄	C₂×C₄×C₅×C₈	1	1	yes	characteristic
131	C₄	C₅×#431	1	2	yes	—
132	C₂	—	2	2	no	—
133	C₂	C₅×#1744	1	1	yes	characteristic
134	C₂	C₂×C₅×#347	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
10. C₅×#346	C₄	semidirect
11. C₄×C₅×C₁₆	C₄	semidirect
12. #12594	C₅	direct (N × H)
52. #346	C₄×C₅	semidirect
53. C₄×C₁₆	C₄×C₅	semidirect
122. C₅	#12594	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×M₃₂	2
C₄×C₅×#97	2
C₅×#1375	2
#12594	5

Subgroups — C5×#12594 #11935314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12594 #11935314