Finite Group Databasebeta

← #12002850

Subgroups — #12002850

Order 1280.

478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#10606074C211yesmaximal, characteristic
2#10601278C212yesmaximal
3C2×#64704C212yesmaximal
4#10600369C211yesmaximal, characteristic
5C5×#1296C211yesmaximal, characteristic
6C2×C4×Dic10C2212yes—
7C2×C5×C4⋊C8C2212yes—
8C5×#384C2211yescharacteristic
9C2×#3948—22no—
10#65274—22no—
11#65272—22no—
12#65263—22no—
13C2×#3940—22no—
14#65224C2211yescharacteristic
15C2×C4×#168C2211yescharacteristic
16#64771—22no—
17#64704—24no—
18#10437—51nomaximal, Sylow
19C22×Dic10D412yes—
20C22×C5×C8—22no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4D412yes—
23C2×C42×C5C2311yescharacteristic
24C2×C4⋊Dic5—22no—
25C2×C4⋊Dic5—21no—
26C2×C4⋊Dic5—22no—
27C2×C4⋊Dic5D412yes—
28C2×#683—22no—
29C2×C4×Dic5—22no—
30C22×#168—21no—
31C4×Dic10—22no—
32C4×Dic10—22no—
33C4×Dic10—22no—
34C4×Dic10—22no—
35C5×C4⋊C8—22no—
36C5×C4⋊C8—22no—
37#3963—22no—
38#3963—24no—
39#3948—44no—
40#3940—44no—
41C4×#168—21no—
42C4×#168D412yes—
43#2582—51no—
44#1844—51no—
45#1803—52no—
46C2×Q8⋊C8—52no—
47#1296D511yescharacteristic
48C22×C4×C5—22no—
49C22×C4×C5C2×D411yescharacteristic
50C22×C4×C5C2×D412yes—
51C22×Dic5—22no—
52C22×Dic5—22no—
53C22×Dic5—41no—
54C2×Dic10—22no—
55C2×Dic10—22no—
56C2×Dic10—22no—
57C2×Dic10—22no—
58C2×Dic10—22no—
59C2×Dic10SD1614yes—
60C2×C5×C8—42no—
61C2×C5×C8—42no—
62C2×C5×C8—42no—
63C5×C4⋊C4—42no—
64C5×C4⋊C4—42no—
65C5×C4⋊C4—42no—
66C42×C5C2×D411yescharacteristic
67C42×C5#4112yes—
68C42×C5#4111yescharacteristic
69C4⋊Dic5—22no—
70C4⋊Dic5—22no—
71C4⋊Dic5—42no—
72C4⋊Dic5—42no—
73C4⋊Dic5—42no—
74C4⋊Dic5—82no—
75#683—42no—
76#683—42no—
77C4×Dic5—42no—
78C4×Dic5—42no—
79C2×#168—22no—
80C2×#168—22no—
81C2×#168—22no—
82C2×C4×Q8—52no—
83C2×#106—102no—
84C2×C4⋊C8C2×D512yes—
85C2×#103—102no—
86C2×C4×C8—51no—
87#398—102no—
88#391—102no—
89#389—102no—
90#384—51no—
91#384C2×D511yescharacteristic
92#340—102no—
93Q8⋊C8—104no—
94C23×C5#12011yescharacteristic
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—44no—
98C2×C4×C5—42no—
99C2×C4×C5#12112yes—
100C2×C4×C5#12111yescharacteristic
101C2×C4×C5#12312yes—
102C2×C4×C5#12411yescharacteristic
103C2×C4×C5C2×SD1612yes—
104C2×C4×C5#13512yes—
105C2×C4×C5#13712yes—
106C2×C4×C5#13712yes—
107C2×Dic5—24no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C2×Dic5—42no—
113C2×Dic5—82no—
114C2×Dic5—81no—
115Dic10—24no—
116Dic10—24no—
117Dic10—42no—
118Dic10—42no—
119C5×C8—82no—
120#168—24no—
121C22×Q8—52no—
122C22×C8—22no—
123C22×C8—101no—
124C4×Q8—102no—
125C4×Q8—102no—
126C4×Q8—102no—
127C4×Q8—102no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—52no—
130C2×C4⋊C4—102no—
131C2×C4⋊C4—101no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4D2012yes—
135C2×C42—102no—
136C2×C42C22×D511yescharacteristic
137#106—204no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140#103—204no—
141C4×C8—52no—
142C4×C8—101no—
143#95—104no—
144#95—102no—
145C22×C5#39411yescharacteristic
146C22×C5#44812yes—
147C22×C5#45212yes—
148C22×C5#45311yescharacteristic
149C22×C5#45611yescharacteristic
150C4×C5—21no—
151C4×C5—21no—
152C4×C5—82no—
153C4×C5#46512yes—
154C4×C5#47012yes—
155C4×C5#48312yes—
156C4×C5#48512yes—
157Dic5—44no—
158Dic5—82no—
159Dic5—161no—
160C2×Q8—54no—
161C2×Q8—102no—
162C2×Q8—102no—
163C2×Q8—102no—
164C2×Q8—102no—
165C2×Q8—102no—
166C22×C4—22no—
167C22×C4—102no—
168C22×C4—102no—
169C22×C4—201no—
170C22×C4C2×D2011yescharacteristic
171C22×C4D4×D512yes—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—102no—
176C2×C8—102no—
177C2×C8—102no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—102no—
182C4⋊C4—102no—
183C4⋊C4—202no—
184C4⋊C4—202no—
185C4⋊C4—202no—
186C4⋊C4—202no—
187C4⋊C4—202no—
188C4⋊C4—402no—
189C42—202no—
190C42—202no—
191C42#70912yes—
192C42D4×D511yescharacteristic
193C42#71311yescharacteristic
194C2×C5#162311yescharacteristic
195C2×C5#163011yescharacteristic
196C2×C5#165312yes—
197C2×C5#203512yes—
198C2×C5#203911yescharacteristic
199C23#402811yescharacteristic
200Q8—104no—
201Q8—104no—
202Q8—202no—
203Q8—202no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—44no—
208C2×C4—104no—
209C2×C4—202no—
210C2×C4—202no—
211C2×C4—202no—
212C2×C4—202no—
213C2×C4—202no—
214C2×C4—401no—
215C2×C4—402no—
216C2×C4#402111yescharacteristic
217C2×C4#403012yes—
218C2×C4#404012yes—
219C2×C4#404111yescharacteristic
220C2×C4#405812yes—
221C2×C4D5×SD1612yes—
222C2×C4#406112yes—
223C2×C4#406412yes—
224C8—82no—
225C8—104no—
226C5#1043711yescharacteristic, complemented, Sylow
227C22#6496111yescharacteristic
228C22#6503611yescharacteristic
229C22#6504111yescharacteristic
230C22#6507212yes—
231C22#6509512yes—
232C4—21no—
233C4—21no—
234C4—82no—
235C4—204no—
236C4—402no—
237C4—801no—
238C4#6506712yes—
239C4#6510512yes—
240C4#6515112yes—
241C4#6517712yes—
242C2#1059919711yescharacteristic
243C2#1059925612yes—
244C2#1059929711yescharacteristic
245C2#1059961712yes—
246C2#1059976911yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1296C2
socle, prime radicalC23×C5#120
hypercenter#1296D5
hypocenterC5#10437
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
226. C5#10437semidirect

Maximal subgroups

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

subgroupindex
#106060742
#106012782
C2×#647042
#106003692
C5×#12962
#104375