Finite Group Databasebeta

← #12016749

Subgroups — #12016749

Order 1280.

490 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3407C211yesmaximal, characteristic, complemented
2#10615530C211yesmaximal, characteristic
3#10602805C211yesmaximal, characteristic, complemented
4#10602233C212yesmaximal, complemented
5#10598309C212yesmaximal, complemented
6C2×C5×#131C2211yescharacteristic
7#66164—21no—
8C22×D40C2211yescharacteristic
9C5×#504—24no—
10C2×C5×M32—22no—
11C2×C5×M32C2212yes—
12#65529—21no—
13#65424C414yescomplemented
14#65420—21no—
15#65404—22no—
16#65395C2212yes—
17#65395C2211yescharacteristic
18#64777—21no—
19#64729—24no—
20#13074—51nomaximal, Sylow
21C2×C5×#41D411yescharacteristic
22C22×D20—21no—
23C5×#131—22no—
24C5×#131—22no—
25C2×C5×M16C2×C412yes—
26C2×C5×M16D411yescharacteristic
27C22×C5×C8D412yes—
28C22×C5×C8C2311yescharacteristic
29#4093—41no—
30#4086—41no—
31#4083—42no—
32#4076—24no—
33#4072—21no—
34#4072—22no—
35C2×D40—22no—
36C2×D40—22no—
37C2×D40—21no—
38C2×D40C2×C412yes—
39C5×M32—24no—
40C5×M32—22no—
41C5×M32—22no—
42C2×C5×C16—24no—
43C2×C5×C16D414yescomplemented
44#3966—42no—
45#3953—24no—
46#3950—21no—
47#3950—22no—
48#3949—22no—
49#3949C2×C412yes—
50#3407D511yescharacteristic, complemented
51#3058—51no—
52#2140—52no—
53#1812—51no—
54#1384—52no—
55C23×D5—41no—
56C5×#41—22no—
57C5×#41—22no—
58C2×C5×Q8SD1611yescharacteristic
59C2×C5×D4D812yes—
60C2×C5×D4SD1611yescharacteristic
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C2×D411yescharacteristic
63C2×C22⋊D5—44no—
64C2×D20—22no—
65C2×D20—42no—
66C2×D20—42no—
67C2×D20—41no—
68C5×M16—22no—
69C5×M16—24no—
70C2×C5×C8—22no—
71C2×C5×C8—22no—
72C2×C5×C8C22⋊C412yes—
73C2×C5×C8C22×C411yescharacteristic
74C2×C5×C8C2×D412yes—
75C2×C5×C8C2×D411yescharacteristic
76C2×C5×C8#4112yes—
77C22⋊Dic5—41no—
78C22⋊Dic5—42no—
79#685—44no—
80C4⋊Dic5—22no—
81C4⋊Dic5—42no—
82C4×Dic5—41no—
83C4×Dic5—42no—
84D40—24no—
85D40—41no—
86D40—41no—
87C5×C16—24no—
88C22×D8—51no—
89C2×#131C2×D511yescharacteristic
90#535—101no—
91#504—24no—
92C2×M32—22no—
93C2×M32C2×D512yes—
94#469—54no—
95#466—102no—
96#427—51no—
97#427—52no—
98#418—101no—
99#410—101no—
100#357—104no—
101H(3,ℤ/4)—101no—
102C23×C5#10212yes—
103C23×C5C2×D811yescharacteristic
104C22×D5—42no—
105C22×D5—82no—
106C22×D5—162no—
107C5×Q8—22no—
108C5×D4—24no—
109C5×D4—22no—
110C2×C4×C5—22no—
111C2×C4×C5—22no—
112C2×C4×C5#10212yes—
113C2×C4×C5C2×C22⋊C411yescharacteristic
114C2×C4×C5#12112yes—
115C2×C4×C5C2×SD1611yescharacteristic
116C2×C4×C5#13512yes—
117C22⋊D5—164no—
118C2×Dic5—42no—
119C2×Dic5—82no—
120D20—42no—
121D20—42no—
122D20—82no—
123C5×C8—22no—
124C5×C8C4×D412yes—
125C5×C8#12011yescharacteristic
126C5×C8#12311yescharacteristic
127C2×#41D2011yescharacteristic
128C22×D4—101no—
129C2×D8—52no—
130C2×D8—102no—
131C2×D8—102no—
132C2×D8—101no—
133#131—22no—
134#131—22no—
135C2×M16C4×D512yes—
136C2×M16D2011yescharacteristic
137C22×C8C22⋊D512yes—
138C22×C8C22×D511yescharacteristic
139#127—201no—
140#124—201no—
141#121—104no—
142#120—202no—
143#117—101no—
144#117—102no—
145M32—24no—
146M32—22no—
147M32—22no—
148C2×C16—24no—
149C2×C16C22⋊D514yescomplemented
150#107—101no—
151#107—102no—
152#106—52no—
153#106—102no—
154#102—104no—
155#99—202no—
156C22×C5—22no—
157C22×C5—41no—
158C22×C5—42no—
159C22×C5C2×#10211yescharacteristic
160C22×C5#46612yes—
161C2×D5—84no—
162C2×D5—82no—
163C2×D5—164no—
164C4×C5—22no—
165C4×C5#38611yescharacteristic
166C4×C5#41611yescharacteristic
167C4×C5#46512yes—
168Dic5—82no—
169Dic5—162no—
170C24—201no—
171#41—22no—
172#41—22no—
173C2×Q8#67711yescharacteristic
174C2×D4—102no—
175C2×D4—204no—
176C2×D4—201no—
177C2×D4—202no—
178C2×D4—202no—
179C2×D4#67711yescharacteristic
180C2×D4D4012yes—
181C22×C4#68512yes—
182C22×C4C2×D2011yescharacteristic
183D8—104no—
184D8—201no—
185D8—201no—
186M16—22no—
187M16—24no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8#68512yes—
191C2×C8C2×C4×D511yescharacteristic
192C2×C8#70912yes—
193C2×C8C2×C22⋊D512yes—
194C2×C8C2×C22⋊D511yescharacteristic
195C4⋊C4—102no—
196C4⋊C4—202no—
197C22⋊C4—201no—
198C22⋊C4—204no—
199C22⋊C4—202no—
200C42—201no—
201C42—202no—
202C16—24no—
203C2×C5—21no—
204C2×C5—22no—
205C2×C5—42no—
206C2×C5#189311yescharacteristic
207D5—162no—
208C23—202no—
209C23—402no—
210C23—802no—
211C23#395312yes—
212C23C2×D4011yescharacteristic
213Q8—22no—
214D4—24no—
215D4—22no—
216D4—202no—
217D4—202no—
218D4—402no—
219D4—804no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—202no—
223C2×C4—402no—
224C2×C4#395312yes—
225C2×C4C2×#67711yescharacteristic
226C2×C4#405012yes—
227C2×C4C2×#68511yescharacteristic
228C2×C4#407612yes—
229C8—22no—
230C8C4×C22⋊D512yes—
231C8#407511yescharacteristic
232C8#409911yescharacteristic
233C5#1307411yescharacteristic, complemented, Sylow
234C22—22no—
235C22—41no—
236C22—42no—
237C22—404no—
238C22—402no—
239C22—804no—
240C22C2×#395311yescharacteristic
241C22#6540412yes—
242C4—22no—
243C4—402no—
244C4—802no—
245C4#6540211yescharacteristic
246C4#6540312yes—
247C4#6550211yescharacteristic
248C2—21no—
249C2—22no—
250C2—42no—
251C2—802no—
252C2#1060276611yescharacteristic
subgroupG/H
centerC2#10602766
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#3407C2
socleC2×C5#1893
prime radical#10615530C2
cosocleC22×C5×C8C23
hypercenter#3407D5
hypocenterC5#13074
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
1. C5×#3407C2semidirect
3. #10602805C2semidirect
4. #10602233C2semidirect
5. #10598309C2semidirect
13. #65424C4semidirect
43. C2×C5×C16D4semidirect
50. #3407D5semidirect
149. C2×C16C22⋊D5semidirect
233. C5#13074semidirect

Maximal subgroups

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

subgroupindex
C5×#34072
#106155302
#106028052
#106022332
#105983092
#130745