Finite Group Databasebeta

← #12002849

Subgroups — #12002849

Order 1280.

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

normal subgroups only

This group has 478 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
1#10606074C211yesmaximal, characteristic
2C5×#1844C211yesmaximal, characteristic
3C2×#64676C212yesmaximal
4#10600381C212yesmaximal
5#10598125C211yesmaximal, characteristic
6C2×C4×Dic10C2212yes—
7C2×C5×#106—22no—
8C2×C4×C5×C8C2211yescharacteristic
9C5×#384C2211yescharacteristic
10C5×#384C2211yescharacteristic
11#65274—22no—
12#65272—22no—
13#65263—22no—
14C2×#3942—22no—
15C2×C4⋊#168C2212yes—
16#64749—22no—
17#64676—24no—
18#10437—51nomaximal, Sylow
19C22×Dic10D412yes—
20C22×C5×C8—21no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4D412yes—
25C2×C42×C5C2311yescharacteristic
26C2×C4⋊Dic5—22no—
27C2×C4⋊Dic5D412yes—
28C2×#683—22no—
29C2×C4×Dic5—22no—
30C22×#168—22no—
31C4×Dic10—22no—
32C4×Dic10—22no—
33C4×Dic10—22no—
34C4×Dic10—22no—
35C5×#106—44no—
36C4×C5×C8—21no—
37C4×C5×C8D412yes—
38#3963—22no—
39#3963—24no—
40#3942—44no—
41C4⋊#168—22no—
42C4⋊#168—22no—
43#2582—51no—
44#1844D511yescharacteristic
45#1803—52no—
46C2×Q8⋊C8—52no—
47#1296—51no—
48C22×C4×C5—22no—
49C22×C4×C5—41no—
50C22×C4×C5C2×D412yes—
51C22×C4×C5C2×D411yescharacteristic
52C22×Dic5—22no—
53C22×Dic5—22no—
54C2×Dic10—22no—
55C2×Dic10—22no—
56C2×Dic10—22no—
57C2×Dic10—22no—
58C2×Dic10—22no—
59C2×Dic10SD1614yes—
60C2×C5×C8—22no—
61C2×C5×C8—22no—
62C2×C5×C8—22no—
63C5×C4⋊C4—42no—
64C5×C4⋊C4—42no—
65C5×C4⋊C4—42no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C42×C5C2×D411yescharacteristic
70C42×C5#4111yescharacteristic
71C42×C5#4112yes—
72C4⋊Dic5—22no—
73C4⋊Dic5—22no—
74C4⋊Dic5—82no—
75#683—42no—
76#683—42no—
77C4×Dic5—42no—
78C4×Dic5—42no—
79C2×#168—42no—
80C2×#168—42no—
81C2×#168—42no—
82C2×C4×Q8—52no—
83C2×#106—22no—
84C2×C4⋊C8—52no—
85C2×#103—102no—
86C2×C4×C8C2×D511yescharacteristic
87#398—102no—
88#391—102no—
89#389—102no—
90#384C2×D511yescharacteristic
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—82no—
100C2×C4×C5—81no—
101C2×C4×C5#12112yes—
102C2×C4×C5#12111yescharacteristic
103C2×C4×C5#12312yes—
104C2×C4×C5#12411yescharacteristic
105C2×C4×C5C2×SD1612yes—
106C2×C4×C5#13512yes—
107C2×C4×C5#13712yes—
108C2×C4×C5#13712yes—
109C2×Dic5—24no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C2×Dic5—42no—
113C2×Dic5—42no—
114C2×Dic5—42no—
115Dic10—24no—
116Dic10—24no—
117Dic10—42no—
118Dic10—42no—
119C5×C8—24no—
120#168—82no—
121C22×Q8—52no—
122C22×C8—21no—
123C22×C8—102no—
124C4×Q8—102no—
125C4×Q8—102no—
126C4×Q8—102no—
127C4×Q8—102no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4C22⋊D512yes—
135C2×C42—102no—
136C2×C42C22×D511yescharacteristic
137#106—44no—
138C4⋊C8—102no—
139C4⋊C8—102no—
140#103—204no—
141C4×C8—21no—
142C4×C8D2012yes—
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—161no—
154C4×C5#46512yes—
155C4×C5#47012yes—
156C4×C5#48312yes—
157C4×C5#48512yes—
158Dic5—44no—
159Dic5—82no—
160C2×Q8—54no—
161C2×Q8—102no—
162C2×Q8—102no—
163C2×Q8—102no—
164C2×Q8—102no—
165C2×Q8—102no—
166C22×C4—22no—
167C22×C4—41no—
168C22×C4—102no—
169C22×C4—102no—
170C22×C4D4×D512yes—
171C22×C4C2×C22⋊D511yescharacteristic
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—202no—
176C2×C8—202no—
177C2×C8—202no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—102no—
185C4⋊C4—102no—
186C4⋊C4—202no—
187C4⋊C4—202no—
188C4⋊C4—402no—
189C42—202no—
190C42—202no—
191C42C2×D2011yescharacteristic
192C42#70911yescharacteristic
193C42#71312yes—
194C2×C5#162311yescharacteristic
195C2×C5#163011yescharacteristic
196C2×C5#165312yes—
197C2×C5#203512yes—
198C2×C5#203911yescharacteristic
199C23#408311yescharacteristic
200Q8—104no—
201Q8—104no—
202Q8—202no—
203Q8—202no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—44no—
208C2×C4—81no—
209C2×C4—82no—
210C2×C4—104no—
211C2×C4—202no—
212C2×C4—202no—
213C2×C4—202no—
214C2×C4—202no—
215C2×C4—202no—
216C2×C4#404012yes—
217C2×C4#404112yes—
218C2×C4D5×SD1612yes—
219C2×C4#406112yes—
220C2×C4#406112yes—
221C2×C4#406212yes—
222C2×C4#407611yescharacteristic
223C2×C4#409311yescharacteristic
224C8—24no—
225C8—402no—
226C5#1043711yescharacteristic, complemented, Sylow
227C22#6528011yescharacteristic
228C22#6536611yescharacteristic
229C22#6538411yescharacteristic
230C22#6545912yes—
231C22#6546212yes—
232C4—21no—
233C4—21no—
234C4—82no—
235C4—161no—
236C4—204no—
237C4—402no—
238C4#6515112yes—
239C4#6515312yes—
240C4#6515612yes—
241C4#6515712yes—
242C2#1060038611yescharacteristic
243C2#1060137512yes—
244C2#1060206211yescharacteristic
245C2#1060206311yescharacteristic
246C2#1060214012yes—
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1844C2
socle, prime radicalC23×C5#120
hypercenter#1844D5
hypocenterC5#10437
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

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
C5×#18442
C2×#646762
#106003812
#105981252
#104375