Finite Group Databasebeta

← #11994357

Subgroups — #11994357

Order 1280.

660 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 143 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×#65272C211yesmaximal, characteristic
2#10613887C211yesmaximal, characteristic
3C2×C5×#324C211yesmaximal, characteristic
4#10600717C212yesmaximal
5#10598166C212yesmaximal
6C22×C5×C4⋊C4C2211yescharacteristic
7C2×#4072—21no—
8C22×C4⋊Dic5C2211yescharacteristic
9C22×#683—21no—
10C2×C5×C22⋊C8C2212yes—
11#65501—21no—
12#65501C2212yes—
13C2×#3963—21no—
14C2×#3963C2211yescharacteristic
15#65274—24no—
16#65272—22no—
17#65272C414yescomplemented
18C5×#324—22no—
19#64771—24no—
20#9027—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C22×C5×C8—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4C2×C412yes—
30C2×C5×C4⋊C4D412yes—
31C2×C22⋊Dic5—22no—
32#4072—42no—
33#4072—42no—
34C2×C4⋊Dic5—22no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5—22no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—22no—
39C2×C4⋊Dic5C2×C412yes—
40C2×C4⋊Dic5D414yes—
41C2×#683—24no—
42C2×#683—42no—
43C2×#683—42no—
44C2×C4×Dic5—22no—
45C5×C22⋊C8—22no—
46C5×C22⋊C8—22no—
47#3963—22no—
48#3963—24no—
49#3963—21no—
50#3963—22no—
51#3963C2×C412yes—
52C2×#398—51no—
53#2316—51no—
54#1823—52no—
55C2×#324D511yescharacteristic
56#1294—52no—
57C24×C5C2×D411yescharacteristic
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5C22⋊C412yes—
67C22×C4×C5C22⋊C412yes—
68C22×C4×C5D812yes—
69C22×C4×C5SD1612yes—
70C22×C4×C5C22×C411yescharacteristic
71C22×C4×C5C2×D412yes—
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5#4112yes—
74C22×Dic5—24no—
75C22×Dic5—22no—
76C22×Dic5—22no—
77C22×Dic5—24no—
78C22×Dic5—42no—
79C22×Dic5—41no—
80C22×Dic5—41no—
81C22×Dic5—41no—
82C22×Dic5—41no—
83C22×Dic5—41no—
84C22×Dic5—41no—
85C22×Dic5—41no—
86C22×Dic5—41no—
87C2×C5×C8—44no—
88C2×C5×C8—42no—
89C5×C4⋊C4—24no—
90C5×C4⋊C4—24no—
91C22⋊Dic5—42no—
92C22⋊Dic5—42no—
93C4⋊Dic5—24no—
94C4⋊Dic5—44no—
95C4⋊Dic5—42no—
96C4⋊Dic5—44no—
97C4⋊Dic5—82no—
98#683—48no—
99C4×Dic5—44no—
100C2×#117—101no—
101C22×C4⋊C4—51no—
102C22×C4⋊C4—101no—
103C22×C4⋊C4C2×D511yescharacteristic
104C2×C22⋊C8C2×D512yes—
105#398—54no—
106#398—102no—
107#389—104no—
108#380—52no—
109#380—101no—
110C2×#95—51no—
111C2×#95—101no—
112#340—104no—
113#324—22no—
114C23×C5—22no—
115C23×C5—22no—
116C23×C5C2×C22⋊C411yescharacteristic
117C23×C5#12011yescharacteristic
118C23×C5#12311yescharacteristic
119C23×C5C2×D811yescharacteristic
120C23×C5C2×SD1611yescharacteristic
121C23×C5AGL(1,ℤ/8)11yescharacteristic
122C23×C5#13711yescharacteristic
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—24no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—42no—
136C2×C4×C5—81no—
137C2×C4×C5#10214yes—
138C2×C4×C5C4×D412yes—
139C2×C4×C5#12112yes—
140C2×Dic5—24no—
141C2×Dic5—44no—
142C2×Dic5—44no—
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—44no—
149C2×Dic5—44no—
150C2×Dic5—44no—
151C2×Dic5—81no—
152C2×Dic5—81no—
153C2×Dic5—81no—
154C2×Dic5—81no—
155C5×C8—82no—
156C23×C4—101no—
157C23×C4—101no—
158C23×C4D2011yescharacteristic
159C23×C4D2011yescharacteristic
160C23×C4C22×D511yescharacteristic
161C22×C8—22no—
162#117—202no—
163#117—202no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—52no—
167C2×C4⋊C4—54no—
168C2×C4⋊C4—102no—
169C2×C4⋊C4—102no—
170C2×C4⋊C4—102no—
171C2×C4⋊C4—104no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4—102no—
174C2×C4⋊C4—202no—
175C2×C4⋊C4—202no—
176C2×C4⋊C4C4×D512yes—
177C2×C4⋊C4C22⋊D512yes—
178C2×C22⋊C4—102no—
179C2×C42—102no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#95—52no—
183#95—102no—
184#95—104no—
185#95—102no—
186#95—101no—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5#38611yescharacteristic
196C22×C5C2×#10211yescharacteristic
197C22×C5#41711yescharacteristic
198C22×C5#44711yescharacteristic
199C22×C5#44811yescharacteristic
200C22×C5#45612yes—
201C22×C5#45812yes—
202C22×C5#48011yescharacteristic
203C22×C5#48111yescharacteristic
204C4×C5—24no—
205C4×C5—22no—
206C4×C5—22no—
207C4×C5—42no—
208Dic5—44no—
209Dic5—84no—
210Dic5—82no—
211C24C2×D2011yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—104no—
221C22×C4—102no—
222C22×C4—104no—
223C22×C4—102no—
224C22×C4—202no—
225C22×C4—201no—
226C22×C4—201no—
227C22×C4—201no—
228C22×C4—201no—
229C22×C4—201no—
230C22×C4—201no—
231C22×C4—201no—
232C22×C4—201no—
233C22×C4#67712yes—
234C22×C4D4012yes—
235C22×C4#68512yes—
236C22×C4#68512yes—
237C22×C4C2×C4×D511yescharacteristic
238C22×C4D4×D512yes—
239C22×C4#71112yes—
240C22×C4C2×C22⋊D511yescharacteristic
241C2×C8—44no—
242C2×C8—42no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—104no—
246C4⋊C4—204no—
247C4⋊C4—204no—
248C4⋊C4—208no—
249C4⋊C4—202no—
250C4⋊C4—402no—
251C22⋊C4—202no—
252C22⋊C4—202no—
253C42—204no—
254C2×C5—21no—
255C2×C5—21no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#161012yes—
259C2×C5#161112yes—
260C2×C5#187411yescharacteristic
261C2×C5#188611yescharacteristic
262C2×C5#189011yescharacteristic
263C23—22no—
264C23—22no—
265C23#402811yescharacteristic
266C23#403211yescharacteristic
267C23C2×#67711yescharacteristic
268C23C2×D4011yescharacteristic
269C23#405411yescharacteristic
270C23#405511yescharacteristic
271C23C2×#68511yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—104no—
287C2×C4—204no—
288C2×C4—204no—
289C2×C4—202no—
290C2×C4—202no—
291C2×C4—204no—
292C2×C4—204no—
293C2×C4—202no—
294C2×C4—202no—
295C2×C4—202no—
296C2×C4—204no—
297C2×C4—401no—
298C2×C4—401no—
299C2×C4—401no—
300C2×C4—401no—
301C2×C4#395314yes—
302C2×C4#402712yes—
303C2×C4#408512yes—
304C8—82no—
305C5#902711yescharacteristic, complemented, Sylow
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22#6502111yescharacteristic
315C22#6502411yescharacteristic
316C22#6502511yescharacteristic
317C22#6502711yescharacteristic
318C22#6503112yes—
319C22#6504112yes—
320C22#6524711yescharacteristic
321C22C2×#395311yescharacteristic
322C22#6542211yescharacteristic
323C4—24no—
324C4—22no—
325C4—22no—
326C4—42no—
327C4—204no—
328C4—404no—
329C4—402no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1059892812yes—
335C2#1059893312yes—
336C2#1060072511yescharacteristic
337C2#1060081611yescharacteristic
338C2#1060089611yescharacteristic
subgroupG/H
centerC23#4028
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#324C2
socleC23×C5#120
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#324D5
hypocenterC5#9027
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
17. #65272C4semidirect
305. C5#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#652722
#106138872
C2×C5×#3242
#106007172
#105981662
#90275