Subgroups — C₅×#13282 #11936002

Order 1280.

414 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#500	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#1845	C₂	1	1	yes	maximal, characteristic
4	C₅×#1380	C₂	1	4	yes	maximal
5	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
6	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
7	C₅×#500	—	2	2	no	—
8	C₅×#500	C₄	1	4	yes	complemented
9	C₂×C₅×#107	—	2	1	no	—
10	C₂×C₅×#107	—	2	1	no	—
11	C₂×C₅×#107	C₂²	1	2	yes	—
12	C₂×C₅×#107	C₂²	1	2	yes	—
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#384	—	2	1	no	—
15	C₄×C₅×C₁₆	—	2	2	no	—
16	#13282	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₅×Q₈	—	4	1	no	—
18	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
20	C₅×C₄⋊Q₈	—	2	4	no	—
21	C₅×C₄⋊Q₈	—	4	2	no	—
22	C₂×C₅×C₄⋊C₄	—	2	2	no	—
23	C₂×C₅×C₄⋊C₄	—	2	2	no	—
24	C₂×C₅×C₄⋊C₄	—	4	1	no	—
25	C₂×C₅×C₄⋊C₄	—	4	1	no	—
26	C₂×C₅×C₄⋊C₄	—	4	1	no	—
27	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
28	C₂×C₅×C₁₆	—	2	2	no	—
29	C₂×C₅×C₁₆	—	2	2	no	—
30	C₂×C₅×C₁₆	Q₈	1	4	yes	complemented
31	C₅×#107	—	2	4	no	—
32	C₅×#107	—	2	2	no	—
33	C₅×#107	—	2	4	no	—
34	C₅×#107	—	4	2	no	—
35	C₅×#107	C₂×C₄	1	4	yes	—
36	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
37	C₄×C₅×C₈	D₄	1	2	yes	—
38	C₂×#500	C₂×C₅	1	1	yes	characteristic
39	C₂×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic
40	#1845	C₂×C₅	1	1	yes	characteristic
41	#1380	C₂×C₅	1	4	yes	—
42	C₂×C₅×Q₈	—	4	4	no	—
43	C₂×C₅×Q₈	—	8	2	no	—
44	C₂×C₅×Q₈	—	8	2	no	—
45	C₂²×C₄×C₅	—	4	2	no	—
46	C₂²×C₄×C₅	—	4	2	no	—
47	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
50	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
51	C₂×C₅×C₈	SD₁₆	1	2	yes	—
52	C₂×C₅×C₈	Q₁₆	1	2	yes	—
53	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
55	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
56	C₂×C₅×C₈	#41	1	2	yes	—
57	C₅×C₄⋊C₄	—	2	4	no	—
58	C₅×C₄⋊C₄	—	4	4	no	—
59	C₅×C₄⋊C₄	—	4	2	no	—
60	C₅×C₄⋊C₄	—	4	2	no	—
61	C₅×C₄⋊C₄	—	4	2	no	—
62	C₅×C₄⋊C₄	—	8	2	no	—
63	C₅×C₄⋊C₄	—	8	2	no	—
64	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₅	SD₁₆	1	2	yes	—
66	C₅×C₁₆	—	2	4	no	—
67	C₂×C₄⋊Q₈	—	2	1	no	—
68	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
69	#500	—	2	2	no	—
70	#500	C₄×C₅	1	4	yes	complemented
71	C₂×#107	—	2	1	no	—
72	C₂×#107	—	2	1	no	—
73	C₂×#107	C₂²×C₅	1	2	yes	—
74	C₂×#107	C₂²×C₅	1	2	yes	—
75	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
76	#384	—	2	1	no	—
77	C₄×C₁₆	—	2	2	no	—
78	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
79	C₅×Q₈	—	8	8	no	—
80	C₂×C₄×C₅	—	4	4	no	—
81	C₂×C₄×C₅	—	8	2	no	—
82	C₂×C₄×C₅	—	8	2	no	—
83	C₂×C₄×C₅	—	8	2	no	—
84	C₂×C₄×C₅	—	8	2	no	—
85	C₂×C₄×C₅	—	8	2	no	—
86	C₂×C₄×C₅	#102	1	2	yes	—
87	C₂×C₄×C₅	#102	1	2	yes	—
88	C₂×C₄×C₅	D₁₆	1	2	yes	—
89	C₂×C₄×C₅	SD₃₂	1	2	yes	—
90	C₂×C₄×C₅	SD₃₂	1	2	yes	—
91	C₂×C₄×C₅	Q₃₂	1	2	yes	—
92	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₅	#124	1	1	yes	characteristic
94	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
97	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
98	C₅×C₈	#103	1	4	yes	—
99	C₅×C₈	C₄×Q₈	1	2	yes	—
100	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
101	C₂²×Q₈	—	4	1	no	—
102	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
103	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
104	C₄⋊Q₈	—	2	4	no	—
105	C₄⋊Q₈	—	4	2	no	—
106	C₂×C₄⋊C₄	—	2	2	no	—
107	C₂×C₄⋊C₄	—	2	2	no	—
108	C₂×C₄⋊C₄	—	4	1	no	—
109	C₂×C₄⋊C₄	—	4	1	no	—
110	C₂×C₄⋊C₄	—	4	1	no	—
111	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
112	C₂×C₁₆	—	2	2	no	—
113	C₂×C₁₆	—	2	2	no	—
114	C₂×C₁₆	C₅×Q₈	1	4	yes	complemented
115	#107	—	2	4	no	—
116	#107	—	2	2	no	—
117	#107	—	2	4	no	—
118	#107	—	4	2	no	—
119	#107	C₂×C₄×C₅	1	4	yes	—
120	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
121	C₄×C₈	C₅×D₄	1	2	yes	—
122	C₂²×C₅	C₂×#102	1	1	yes	characteristic
123	C₂²×C₅	#486	1	1	yes	characteristic
124	C₂²×C₅	#500	1	1	yes	characteristic
125	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
126	C₂²×C₅	C₂×SD₃₂	1	1	yes	characteristic
127	C₂²×C₅	C₂×SD₃₂	1	1	yes	characteristic
128	C₂²×C₅	C₂×Q₃₂	1	1	yes	characteristic
129	C₄×C₅	—	8	4	no	—
130	C₄×C₅	—	16	2	no	—
131	C₄×C₅	#357	1	4	yes	—
132	C₄×C₅	#358	1	4	yes	—
133	C₄×C₅	#391	1	1	yes	characteristic
134	C₄×C₅	C₂×#103	1	1	yes	characteristic
135	C₄×C₅	#487	1	1	yes	characteristic
136	C₄×C₅	#498	1	1	yes	characteristic
137	C₂×Q₈	—	4	4	no	—
138	C₂×Q₈	—	8	2	no	—
139	C₂×Q₈	—	8	2	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	—	4	2	no	—
142	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
143	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
144	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
145	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
146	C₂×C₈	C₅×SD₁₆	1	2	yes	—
147	C₂×C₈	C₅×Q₁₆	1	2	yes	—
148	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
149	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
150	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
151	C₂×C₈	C₅×#41	1	2	yes	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	8	2	no	—
158	C₄⋊C₄	—	8	2	no	—
159	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
160	C₄²	C₅×SD₁₆	1	2	yes	—
161	C₁₆	—	2	4	no	—
162	C₂×C₅	#1990	1	1	yes	characteristic
163	C₂×C₅	C₂×#357	1	1	yes	characteristic
164	C₂×C₅	C₂×#358	1	1	yes	characteristic
165	C₂×C₅	#2240	1	1	yes	characteristic
166	C₂×C₅	#2241	1	1	yes	characteristic
167	C₂×C₅	#2252	1	1	yes	characteristic
168	C₂×C₅	#2254	1	1	yes	characteristic
169	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
170	Q₈	—	8	8	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	8	2	no	—
173	C₂×C₄	—	8	2	no	—
174	C₂×C₄	—	8	2	no	—
175	C₂×C₄	—	8	2	no	—
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	C₅×#102	1	2	yes	—
178	C₂×C₄	C₅×#102	1	2	yes	—
179	C₂×C₄	C₅×D₁₆	1	2	yes	—
180	C₂×C₄	C₅×SD₃₂	1	2	yes	—
181	C₂×C₄	C₅×SD₃₂	1	2	yes	—
182	C₂×C₄	C₅×Q₃₂	1	2	yes	—
183	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄	C₅×#124	1	1	yes	characteristic
185	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
186	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
187	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
188	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
189	C₈	C₅×#103	1	4	yes	—
190	C₈	C₄×C₅×Q₈	1	2	yes	—
191	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
192	C₅	#13282	1	1	yes	characteristic, direct product factor, Sylow
193	C₂²	C₂×C₅×#102	1	1	yes	characteristic
194	C₂²	C₅×#486	1	1	yes	characteristic
195	C₂²	C₅×#500	1	1	yes	characteristic
196	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
197	C₂²	C₂×C₅×SD₃₂	1	1	yes	characteristic
198	C₂²	C₂×C₅×SD₃₂	1	1	yes	characteristic
199	C₂²	C₂×C₅×Q₃₂	1	1	yes	characteristic
200	C₄	—	8	4	no	—
201	C₄	—	16	2	no	—
202	C₄	C₅×#357	1	4	yes	—
203	C₄	C₅×#358	1	4	yes	—
204	C₄	C₅×#391	1	1	yes	characteristic
205	C₄	C₂×C₅×#103	1	1	yes	characteristic
206	C₄	C₅×#487	1	1	yes	characteristic
207	C₄	C₅×#498	1	1	yes	characteristic
208	C₂	C₅×#1990	1	1	yes	characteristic
209	C₂	C₂×C₅×#357	1	1	yes	characteristic
210	C₂	C₂×C₅×#358	1	1	yes	characteristic
211	C₂	C₅×#2240	1	1	yes	characteristic
212	C₂	C₅×#2241	1	1	yes	characteristic
213	C₂	C₅×#2252	1	1	yes	characteristic
214	C₂	C₅×#2254	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#500	C₄	semidirect
16. #13282	C₅	direct (N × H)
30. C₂×C₅×C₁₆	Q₈	semidirect
70. #500	C₄×C₅	semidirect
114. C₂×C₁₆	C₅×Q₈	semidirect
192. C₅	#13282	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×#500	2
C₂×C₄×C₅×C₁₆	2
C₅×#1845	2
C₅×#1380	2
#13282	5

Subgroups — C5×#13282 #11936002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13282 #11936002