Finite Group Databasebeta

← #11994362

Subgroups — #11994362

Order 1280.

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

normal subgroups only

This group has 696 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
1C2×#65242C211yesmaximal, characteristic
2#10613824C211yesmaximal, characteristic
3C2×C5×#323C211yesmaximal, characteristic
4#10600717C212yesmaximal, complemented
5#10598166C212yesmaximal, complemented
6C22×C5×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic5—21no—
8C22×C4⋊Dic5C2211yescharacteristic
9C2×C5×C22⋊C8C2212yes—
10#65536—21no—
11#65501C2212yes—
12C4×C22⋊Dic5—21no—
13C2×#3963—21no—
14C2×#3963C2211yescharacteristic
15#65242—22no—
16#65242C414yescomplemented
17#65240—24no—
18C5×#323—22no—
19#64771—24no—
20#9028—51nomaximal, Sylow
21C25×C5D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C22×C5×C8—22no—
27C2×C5×C22⋊C4—22no—
28C2×C5×C22⋊C4—22no—
29C2×C5×C22⋊C4C2×C412yes—
30C2×C5×C22⋊C4D412yes—
31C2×C22⋊Dic5—24no—
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5—22no—
35C2×C22⋊Dic5—44no—
36C2×C4⋊Dic5—22no—
37C2×C4⋊Dic5—22no—
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5C2×C412yes—
40C2×C4⋊Dic5D414yes—
41C2×C4×Dic5—22no—
42C5×C22⋊C8—22no—
43C5×C22⋊C8—22no—
44#3963—22no—
45#3963—24no—
46#3963—22no—
47#3963—21no—
48#3963C2×C412yes—
49C2×#397—51no—
50#2312—51no—
51#1823—52no—
52C2×#323D511yescharacteristic
53#1294—52no—
54C24×C5—21no—
55C24×C5—22no—
56C24×C5—21no—
57C24×C5—22no—
58C24×C5—42no—
59C24×C5—42no—
60C24×C5C22⋊C412yes—
61C24×C5C2×D411yescharacteristic
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5C22⋊C412yes—
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D412yes—
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5#4112yes—
71C22×Dic5—22no—
72C22×Dic5—22no—
73C22×Dic5—24no—
74C22×Dic5—42no—
75C22×Dic5—42no—
76C22×Dic5—41no—
77C22×Dic5—41no—
78C22×Dic5—42no—
79C22×Dic5—42no—
80C22×Dic5—42no—
81C2×C5×C8—44no—
82C2×C5×C8—42no—
83C5×C22⋊C4—24no—
84C5×C22⋊C4—24no—
85C22⋊Dic5—48no—
86C22⋊Dic5—42no—
87C22⋊Dic5—42no—
88C22⋊Dic5—82no—
89C22⋊Dic5—82no—
90C4⋊Dic5—24no—
91C4⋊Dic5—42no—
92C4⋊Dic5—44no—
93C4×Dic5—82no—
94C22×C4⋊C4—51no—
95C22×C22⋊C4—101no—
96C22×C22⋊C4C2×D511yescharacteristic
97C2×C22⋊C8C2×D512yes—
98#397—54no—
99#397—102no—
100#388—104no—
101#380—52no—
102#379—101no—
103C4×C22⋊C4—101no—
104C2×#95—51no—
105C2×#95—101no—
106#340—104no—
107#323—22no—
108C23×C5—22no—
109C23×C5—22no—
110C23×C5—22no—
111C23×C5—22no—
112C23×C5—22no—
113C23×C5—42no—
114C23×C5—42no—
115C23×C5—48no—
116C23×C5—42no—
117C23×C5—42no—
118C23×C5—42no—
119C23×C5—42no—
120C23×C5—81no—
121C23×C5—81no—
122C23×C5—84no—
123C23×C5C2×C22⋊C411yescharacteristic
124C23×C5#12011yescharacteristic
125C23×C5#12311yescharacteristic
126C23×C5#13512yes—
127C23×C5AGL(1,ℤ/8)12yes—
128C2×C4×C5—24no—
129C2×C4×C5—22no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—81no—
136C2×C4×C5C4×D412yes—
137C2×C4×C5#12112yes—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—42no—
143C2×Dic5—42no—
144C2×Dic5—44no—
145C2×Dic5—44no—
146C2×Dic5—44no—
147C2×Dic5—84no—
148C2×Dic5—82no—
149C2×Dic5—82no—
150C5×C8—82no—
151C25D2011yescharacteristic
152C23×C4—101no—
153C23×C4—101no—
154C23×C4D2011yescharacteristic
155C23×C4C22×D511yescharacteristic
156C22×C8—22no—
157C2×C4⋊C4—52no—
158C2×C4⋊C4—54no—
159C2×C4⋊C4—102no—
160C2×C4⋊C4—102no—
161C2×C4⋊C4—101no—
162C2×C22⋊C4—22no—
163C2×C22⋊C4—22no—
164C2×C22⋊C4—104no—
165C2×C22⋊C4—102no—
166C2×C22⋊C4—102no—
167C2×C22⋊C4—102no—
168C2×C22⋊C4—204no—
169C2×C22⋊C4C4×D512yes—
170C2×C22⋊C4C22⋊D512yes—
171C2×C42—102no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174#95—52no—
175#95—102no—
176#95—104no—
177#95—102no—
178#95—101no—
179C22×C5—24no—
180C22×C5—24no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5—21no—
184C22×C5—21no—
185C22×C5—44no—
186C22×C5—42no—
187C22×C5—42no—
188C22×C5—42no—
189C22×C5—82no—
190C22×C5—84no—
191C22×C5—84no—
192C22×C5#38611yescharacteristic
193C22×C5#41611yescharacteristic
194C22×C5#41811yescharacteristic
195C22×C5#44912yes—
196C22×C5#45512yes—
197C22×C5#45812yes—
198C22×C5#48212yes—
199C4×C5—22no—
200C4×C5—22no—
201C4×C5—42no—
202Dic5—82no—
203Dic5—84no—
204Dic5—82no—
205C24—21no—
206C24—22no—
207C24—21no—
208C24—22no—
209C24—42no—
210C24—42no—
211C24#68512yes—
212C24C2×D2011yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—104no—
218C22×C4—102no—
219C22×C4—102no—
220C22×C4—202no—
221C22×C4—202no—
222C22×C4—201no—
223C22×C4—201no—
224C22×C4—202no—
225C22×C4—202no—
226C22×C4—202no—
227C22×C4#68512yes—
228C22×C4C2×C4×D511yescharacteristic
229C22×C4D4×D512yes—
230C22×C4#71112yes—
231C22×C4C2×C22⋊D511yescharacteristic
232C2×C8—44no—
233C2×C8—42no—
234C4⋊C4—104no—
235C4⋊C4—204no—
236C4⋊C4—202no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—208no—
240C22⋊C4—202no—
241C22⋊C4—202no—
242C22⋊C4—402no—
243C22⋊C4—402no—
244C42—402no—
245C2×C5—21no—
246C2×C5—21no—
247C2×C5—22no—
248C2×C5—82no—
249C2×C5#161214yes—
250C2×C5#187511yescharacteristic
251C2×C5#188511yescharacteristic
252C2×C5#189011yescharacteristic
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23—48no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—81no—
266C23—81no—
267C23—84no—
268C23#402811yescharacteristic
269C23#403211yescharacteristic
270C23#405012yes—
271C23#405412yes—
272C23C2×#68511yescharacteristic
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—204no—
284C2×C4—204no—
285C2×C4—202no—
286C2×C4—202no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—204no—
290C2×C4—404no—
291C2×C4—402no—
292C2×C4—402no—
293C2×C4#402712yes—
294C2×C4#408512yes—
295C8—82no—
296C5#902811yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—24no—
303C22—44no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—82no—
308C22—84no—
309C22—84no—
310C22#6502312yes—
311C22#6502612yes—
312C22#6503112yes—
313C22#6503512yes—
314C22#6524711yescharacteristic
315C22#6540211yescharacteristic
316C22#6542011yescharacteristic
317C4—22no—
318C4—22no—
319C4—42no—
320C4—402no—
321C4—402no—
322C4—404no—
323C2—21no—
324C2—22no—
325C2—21no—
326C2—82no—
327C2#1059890414yes—
328C2#1060072611yescharacteristic
329C2#1060081611yescharacteristic
330C2#1060086211yescharacteristic
subgroupG/H
centerC23#4028
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#323C2
socleC23×C5#120
prime radicalC25×C5D4
cosocleC23×C4×C5C23
hypercenterC2×#323D5
hypocenterC5#9028
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
4. #10600717C2semidirect
5. #10598166C2semidirect
16. #65242C4semidirect
296. C5#9028semidirect

Maximal subgroups

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

subgroupindex
C2×#652422
#106138242
C2×C5×#3232
#106007172
#105981662
#90285