Finite Group Databasebeta

← #11990296

Subgroups — #11990296

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2929C211yesmaximal, characteristic
2#10602760C211yesmaximal, characteristic, complemented
3C8×C22⋊Dic5C211yesmaximal, characteristic, complemented
4#10602500C211yesmaximal, characteristic
5#10602500C211yesmaximal, characteristic
6#10598179C211yesmaximal, characteristic, complemented
7#10598174C211yesmaximal, characteristic, complemented
8C2×C5×#131C411yescharacteristic, complemented
9C23×C5×C8C2211yescharacteristic
10C5×#525C2211yescharacteristic
11C5×#435—21no—
12C5×#435—21no—
13C5×C8×D4—21no—
14C5×C8×D4—21no—
15C5×#424C411yescharacteristic, complemented
16C5×#408C411yescharacteristic, complemented
17C5×#407C2211yescharacteristic
18C5×#405C411yescharacteristic, complemented
19C4×C22⋊Dic5C2211yescharacteristic
20C4×C22⋊Dic5C2211yescharacteristic
21C2×C22⋊#168C2211yescharacteristic
22C2×C22⋊#168C2211yescharacteristic
23C2×#3947—21no—
24C2×C8×Dic5—21no—
25#64770—21no—
26#64770—21no—
27#64758C412yescomplemented
28#64758C412yescomplemented
29#64757C412yescomplemented
30#64757C412yescomplemented
31#8240—51nomaximal, Sylow
32C2×C5×#41C2×C411yescharacteristic
33C23×C4×C5C2311yescharacteristic
34C5×#131—42no—
35C2×C5×M16—21no—
36C2×C5×M16C2×C411yescharacteristic
37C2×C5×M16C2×C411yescharacteristic
38C22×C5×C8—21no—
39C22×C5×C8—42no—
40C22×C5×C8C2×C411yescharacteristic
41C22×C5×C8C2×C411yescharacteristic
42C22×C5×C8D411yescharacteristic
43C22×C5×C8D411yescharacteristic
44C22×C5×C8D411yescharacteristic
45C22×C5×C8D411yescharacteristic
46C5×#123—21no—
47C5×C22⋊Q8C2×C411yescharacteristic
48C5×C22⋊Q8C2×C411yescharacteristic
49C5×#121C2×C411yescharacteristic
50C5×#121C2×C411yescharacteristic
51C5×#120—21no—
52C4×C5×D4—21no—
53C4×C5×D4—21no—
54C5×#117C2×C411yescharacteristic
55C2×C22⋊Dic5—21no—
56C2×C22⋊Dic5—21no—
57C2×C4×Dic5—21no—
58C2×C4×Dic5—21no—
59C22×#168—21no—
60C22×#168—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C22⋊C8—21no—
64C5×C22⋊C8—21no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8—21no—
67C5×#97—21no—
68C4×C5×C8—21no—
69#3963C2×C412yes—
70#3963C2×C412yes—
71C22⋊#168—21no—
72C22⋊#168—21no—
73C22⋊#168C2×C412yes—
74C22⋊#168C2×C412yes—
75#3947—42no—
76C8×Dic5—42no—
77#2929D511yescharacteristic
78#1752—51no—
79C8×C22⋊C4—51no—
80#1501—51no—
81#1501—51no—
82#1298—51no—
83#1297—51no—
84C24×C5#4111yescharacteristic
85C5×#41—41no—
86C5×#41—41no—
87C2×C5×Q8C4211yescharacteristic
88C2×C5×D4—21no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4C4211yescharacteristic
92C22×C4×C5—21no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5C22×C411yescharacteristic
96C22×C4×C5C22×C411yescharacteristic
97C22×C4×C5C22×C411yescharacteristic
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5#4111yescharacteristic
101C22×Dic5—22no—
102C22×Dic5—22no—
103C5×M16—42no—
104C5×M16—41no—
105C5×M16—41no—
106C2×C5×C8—22no—
107C2×C5×C8—22no—
108C2×C5×C8—22no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C2×C5×C8—41no—
114C2×C5×C8—42no—
115C2×C5×C8C22⋊C411yescharacteristic
116C2×C5×C8C22⋊C411yescharacteristic
117C2×C5×C8C22⋊C411yescharacteristic
118C2×C5×C8C22⋊C411yescharacteristic
119C5×C4⋊C4—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4C4211yescharacteristic
122C5×C4⋊C4C4211yescharacteristic
123C5×C22⋊C4—21no—
124C5×C22⋊C4—21no—
125C5×C22⋊C4—21no—
126C5×C22⋊C4—21no—
127C5×C22⋊C4—21no—
128C42×C5—21no—
129C22⋊Dic5—24no—
130C22⋊Dic5—42no—
131C4×Dic5—41no—
132C4×Dic5—41no—
133C4×Dic5—41no—
134C4×Dic5—41no—
135C2×#168—22no—
136C2×#168—22no—
137C2×#168—41no—
138C2×#168—41no—
139C2×#168—41no—
140C2×#168—41no—
141C2×#131Dic511yescharacteristic, complemented
142C23×C8C2×D511yescharacteristic
143#525C2×D511yescharacteristic
144#435—21no—
145#435—21no—
146C8×D4—21no—
147C8×D4—21no—
148#424Dic511yescharacteristic, complemented
149#408Dic511yescharacteristic, complemented
150#407C2×D511yescharacteristic
151C2×C22⋊C8—51no—
152C2×C22⋊C8—51no—
153#405Dic511yescharacteristic, complemented
154C2×#97—101no—
155C2×C4×C8—101no—
156C4×C22⋊C4—51no—
157C4×C22⋊C4—51no—
158#336—101no—
159#336—101no—
160#328—52no—
161#328—52no—
162#327—52no—
163#327—52no—
164C23×C5—22no—
165C23×C5—22no—
166C23×C5—21no—
167C23×C5—41no—
168C23×C5#11711yescharacteristic
169C23×C5C4×D411yescharacteristic
170C23×C5C4×D411yescharacteristic
171C5×Q8—41no—
172C5×D4—41no—
173C5×D4—42no—
174C5×D4—42no—
175C5×D4—42no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5C2×C4211yescharacteristic
191C2×C4×C5C2×C22⋊C411yescharacteristic
192C2×C4×C5C4×D411yescharacteristic
193C2×C4×C5C4×D411yescharacteristic
194C2×Dic5—24no—
195C2×Dic5—42no—
196C2×Dic5—42no—
197C2×Dic5—42no—
198C2×Dic5—42no—
199C2×Dic5—42no—
200C5×C8—21no—
201C5×C8—21no—
202C5×C8—21no—
203C5×C8—41no—
204C5×C8—41no—
205C5×C8#9912yes—
206#168—42no—
207#168—42no—
208C2×#41C2×Dic511yescharacteristic
209C23×C4C22×D511yescharacteristic
210#131—42no—
211C2×M16—21no—
212C2×M16C2×Dic511yescharacteristic
213C2×M16C2×Dic511yescharacteristic
214C22×C8—21no—
215C22×C8—42no—
216C22×C8—101no—
217C22×C8—101no—
218C22×C8C2×Dic511yescharacteristic
219C22×C8C2×Dic511yescharacteristic
220C22×C8C22⋊D511yescharacteristic
221C22×C8C22⋊D511yescharacteristic
222C22×C8C22⋊D511yescharacteristic
223C22×C8C22⋊D511yescharacteristic
224#123—21no—
225C22⋊Q8C4×D511yescharacteristic
226C22⋊Q8C4×D511yescharacteristic
227#121C4×D511yescharacteristic
228#121C4×D511yescharacteristic
229#120—21no—
230C4×D4—21no—
231C4×D4—21no—
232#117C2×Dic511yescharacteristic
233C2×C22⋊C4—101no—
234C2×C22⋊C4—101no—
235C2×C42—101no—
236C2×C42—101no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—52no—
244C22⋊C8—52no—
245C22⋊C8—101no—
246C22⋊C8—101no—
247#97—21no—
248#97—202no—
249C4×C8—21no—
250C4×C8—202no—
251#95—52no—
252#95—52no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—44no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5C4×C22⋊C411yescharacteristic
265C22×C5#44312yes—
266C22×C5#44412yes—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—41no—
271C4×C5—41no—
272C4×C5—41no—
273C4×C5C2×#9911yescharacteristic
274C4×C5#41011yescharacteristic
275Dic5—44no—
276Dic5—82no—
277C24#70911yescharacteristic
278#41—41no—
279#41—41no—
280C2×Q8C4×Dic511yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4C4×Dic511yescharacteristic
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—102no—
289C22×C4—102no—
290C22×C4C2×C4×D511yescharacteristic
291C22×C4C2×C4×D511yescharacteristic
292C22×C4#70911yescharacteristic
293C22×C4C22×Dic511yescharacteristic
294C22×C4C2×C22⋊D511yescharacteristic
295C22×C4C2×C22⋊D511yescharacteristic
296M16—42no—
297M16—41no—
298M16—41no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—42no—
308C2×C8—102no—
309C2×C8—102no—
310C2×C8—201no—
311C2×C8—201no—
312C2×C8—201no—
313C2×C8—201no—
314C2×C8C22⋊Dic511yescharacteristic
315C2×C8C22⋊Dic511yescharacteristic
316C2×C8C22⋊Dic511yescharacteristic
317C2×C8C22⋊Dic511yescharacteristic
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4C4×Dic511yescharacteristic
321C4⋊C4C4×Dic511yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—104no—
328C22⋊C4—202no—
329C42—21no—
330C42—201no—
331C42—201no—
332C42—201no—
333C42—201no—
334C2×C5—22no—
335C2×C5—22no—
336C2×C5—41no—
337C2×C5—81no—
338C2×C5C4×#9911yescharacteristic
339C2×C5#176411yescharacteristic
340C2×C5#176511yescharacteristic
341C23—22no—
342C23—22no—
343C23—21no—
344C23—41no—
345C23#407211yescharacteristic
346C23C4×C22⋊D511yescharacteristic
347C23C4×C22⋊D511yescharacteristic
348Q8—41no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—42no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—104no—
368C2×C4—202no—
369C2×C4—202no—
370C2×C4—202no—
371C2×C4—202no—
372C2×C4—202no—
373C2×C4C2×C4×Dic511yescharacteristic
374C2×C4C4×C22⋊D511yescharacteristic
375C2×C4C4×C22⋊D511yescharacteristic
376C2×C4C2×C22⋊Dic511yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8—41no—
381C8—41no—
382C8—202no—
383C8—202no—
384C8#396612yes—
385C5#824011yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22#6543312yes—
398C22#6543412yes—
399C22C4×C22⋊Dic511yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—204no—
407C4—402no—
408C4C2×#396611yescharacteristic
409C4#6552911yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—81no—
414C2C4×#396611yescharacteristic
415C2#1060280111yescharacteristic
416C2#1060280211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic5
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC5×#2929C2
socleC22×C5C4×C22⋊C4
prime radicalC5×#525C22
cosocleC23×C4×C5C23
hypercenter#2929D5
hypocenterC5#8240
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #10602760C2semidirect
3. C8×C22⋊Dic5C2semidirect
6. #10598179C2semidirect
7. #10598174C2semidirect
8. C2×C5×#131C4semidirect
15. C5×#424C4semidirect
16. C5×#408C4semidirect
18. C5×#405C4semidirect
27. #64758C4semidirect
28. #64758C4semidirect
29. #64757C4semidirect
30. #64757C4semidirect
141. C2×#131Dic5semidirect
148. #424Dic5semidirect
149. #408Dic5semidirect
153. #405Dic5semidirect
385. C5#8240semidirect

Maximal subgroups

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

subgroupindex
C5×#29292
#106027602
C8×C22⋊Dic52
#106025002
#105981792
#105981742
#82405