Finite Group Databasebeta

← #11995063

Subgroups — #11995063

Order 1280.

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

normal subgroups only

This group has 586 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#10613806C211yesmaximal, characteristic
2C2×#65226C211yesmaximal, characteristic
3C5×#1817C211yesmaximal, characteristic
4C2×#64687C212yesmaximal
5#10598166C212yesmaximal
6C22×C42×C5C2211yescharacteristic
7C2×#4070C2211yescharacteristic
8C2×C5×C22⋊C8C2212yes—
9#65501C2211yescharacteristic
10#65500—21no—
11#65499—21no—
12C2×#3963—21no—
13C2×#3963—21no—
14C2×#3963C2212yes—
15#65226—24no—
16#65222—22no—
17#65218C412yescomplemented
18#65217C412yescomplemented
19C5×#336—22no—
20#64687—24no—
21#9153—51nomaximal, Sylow
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C23×Dic5—22no—
26C22×Dic10C2×C411yescharacteristic
27C22×C5×C8—22no—
28C2×C42×C5—22no—
29C2×C42×C5—22no—
30C2×C42×C5C2×C412yes—
31C2×C42×C5D412yes—
32C2×C22⋊Dic5—21no—
33C2×C22⋊Dic5—21no—
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C412yes—
36#4070—22no—
37#4070—22no—
38C2×#683—22no—
39C2×#683—21no—
40C5×C22⋊C8—22no—
41C5×C22⋊C8—22no—
42#3963—24no—
43#3963—24no—
44#3963—22no—
45#3963—22no—
46#3963—22no—
47#3963—21no—
48#3963—22no—
49#3963D414yes—
50#2855—51no—
51C2×#383—51no—
52#1817D511yescharacteristic
53C2×#328—52no—
54#1294—52no—
55C24×C5C2×D411yescharacteristic
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5C22⋊C412yes—
65C22×C4×C5C22⋊C412yes—
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D412yes—
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5#4112yes—
70C22×Dic5—21no—
71C22×Dic5—22no—
72C22×Dic5—21no—
73C22×Dic5—24no—
74C22×Dic5—44no—
75C22×Dic5—44no—
76C22×Dic5—42no—
77C22×Dic5—42no—
78C2×Dic10—22no—
79C2×Dic10—42no—
80C2×C5×C8—44no—
81C2×C5×C8—42no—
82C42×C5—24no—
83C42×C5—24no—
84C22⋊Dic5—41no—
85C22⋊Dic5—41no—
86C22⋊Dic5—42no—
87C4⋊Dic5—22no—
88C4⋊Dic5—42no—
89#683—44no—
90#683—42no—
91C2×C22⋊Q8—51no—
92C22×C42C2×D511yescharacteristic
93C2×C22⋊C8C2×D512yes—
94#391—52no—
95#389—52no—
96#387—102no—
97#385—101no—
98#383—104no—
99#381—101no—
100#380—51no—
101C2×#95—52no—
102C2×#95—101no—
103C2×#95—101no—
104#336—22no—
105#328—104no—
106C23×C5—22no—
107C23×C5—22no—
108C23×C5C2×C22⋊C411yescharacteristic
109C23×C5#12011yescharacteristic
110C23×C5#12311yescharacteristic
111C23×C5#13512yes—
112C23×C5#13712yes—
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—22no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5C4×D412yes—
128C2×C4×C5#12112yes—
129C2×Dic5—44no—
130C2×Dic5—44no—
131C2×Dic5—41no—
132C2×Dic5—41no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—44no—
139C2×Dic5—84no—
140C2×Dic5—84no—
141Dic10—82no—
142C5×C8—82no—
143C22×Q8—51no—
144C23×C4—102no—
145C23×C4D2011yescharacteristic
146C23×C4D2011yescharacteristic
147C23×C4C22×D511yescharacteristic
148C22×C8—22no—
149C22⋊Q8—102no—
150C22⋊Q8—102no—
151C2×C4⋊C4—51no—
152C2×C4⋊C4—52no—
153C2×C4⋊C4—102no—
154C2×C4⋊C4—101no—
155C2×C22⋊C4—101no—
156C2×C22⋊C4—101no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42C4×D512yes—
160C2×C42C22⋊D512yes—
161C22⋊C8—22no—
162C22⋊C8—22no—
163#95—54no—
164#95—104no—
165#95—104no—
166#95—102no—
167#95—102no—
168#95—102no—
169#95—102no—
170#95—101no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—24no—
176C22×C5—24no—
177C22×C5#38611yescharacteristic
178C22×C5#41012yes—
179C22×C5#41611yescharacteristic
180C22×C5#41911yescharacteristic
181C22×C5#42112yes—
182C22×C5#45212yes—
183C22×C5#48512yes—
184C4×C5—22no—
185C4×C5—22no—
186C4×C5—42no—
187C4×C5—42no—
188Dic5—84no—
189Dic5—81no—
190Dic5—81no—
191Dic5—82no—
192C24C2×D2011yescharacteristic
193C2×Q8—102no—
194C2×Q8—202no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—104no—
204C22×C4—102no—
205C22×C4—101no—
206C22×C4—101no—
207C22×C4—204no—
208C22×C4—204no—
209C22×C4—202no—
210C22×C4—202no—
211C22×C4#68512yes—
212C22×C4#68512yes—
213C22×C4C2×C4×D511yescharacteristic
214C22×C4D4×D512yes—
215C22×C4#71112yes—
216C22×C4C2×C22⋊D511yescharacteristic
217C2×C8—44no—
218C2×C8—42no—
219C4⋊C4—102no—
220C4⋊C4—202no—
221C4⋊C4—204no—
222C4⋊C4—202no—
223C22⋊C4—201no—
224C22⋊C4—201no—
225C22⋊C4—202no—
226C42—24no—
227C42—24no—
228C2×C5—22no—
229C2×C5—22no—
230C2×C5#151512yes—
231C2×C5#152112yes—
232C2×C5#187311yescharacteristic
233C2×C5#189711yescharacteristic
234C2×C5#189911yescharacteristic
235C23—22no—
236C23—22no—
237C23#402811yescharacteristic
238C23#403211yescharacteristic
239C23#405012yes—
240C23#405512yes—
241C23C2×#68511yescharacteristic
242Q8—402no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—204no—
258C2×C4—204no—
259C2×C4—202no—
260C2×C4—202no—
261C2×C4—202no—
262C2×C4—202no—
263C2×C4—202no—
264C2×C4—201no—
265C2×C4—201no—
266C2×C4—204no—
267C2×C4—404no—
268C2×C4—404no—
269C2×C4#402712yes—
270C2×C4#408512yes—
271C8—82no—
272C5#915311yescharacteristic, complemented, Sylow
273C22—21no—
274C22—21no—
275C22—24no—
276C22—21no—
277C22—21no—
278C22—24no—
279C22#6501212yes—
280C22#6502212yes—
281C22#6524711yescharacteristic
282C22#6529512yes—
283C22#6540211yescharacteristic
284C22#6540911yescharacteristic
285C22#6542812yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—404no—
291C4—401no—
292C4—402no—
293C4—401no—
294C2—22no—
295C2—22no—
296C2#1060032811yescharacteristic
297C2#1060072411yescharacteristic
298C2#1060075911yescharacteristic
299C2#1060158412yes—
300C2#1060163012yes—
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#1817C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#1817D5
hypocenterC5#9153
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
17. #65218C4semidirect
18. #65217C4semidirect
272. C5#9153semidirect

Maximal subgroups

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

subgroupindex
#106138062
C2×#652262
C5×#18172
C2×#646872
#105981662
#91535