Finite Group Databasebeta

← #11989474

Subgroups — #11989474

Order 1280.

652 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611013C211yesmaximal, characteristic
2D5×#423C211yesmaximal, characteristic
3C4×D5×M16C211yesmaximal, characteristic
4C5×#1299C211yesmaximal, characteristic, complemented
5#10598234C211yesmaximal, characteristic, complemented
6#10598201C211yesmaximal, characteristic, complemented
7#10598160C211yesmaximal, characteristic, complemented
8C2×D5×M16—21no—
9C2×D5×M16C412yes—
10C2×C42×D5C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C5×#423C2211yescharacteristic
13C4×C5×M16C2211yescharacteristic
14#65407C412yes—
15M16×Dic5—21no—
16#65214C2211yescharacteristic
17#65213C2211yescharacteristic
18C4×#681C2211yescharacteristic
19#65126—21no—
20#65126—21no—
21#65126C412yes—
22#65124C412yes—
23D5×C4⋊C8—21no—
24D5×C4⋊C8—21no—
25#65015—21no—
26#65008—21no—
27#64996C412yes—
28D5×#97C412yes—
29C4×#676—21no—
30C4×#676—21no—
31#64974—21no—
32C4×C8×D5—21no—
33#8063—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5D411yescharacteristic
36C22×C4×D5Q811yescharacteristic
37C2×C5×M16—21no—
38C2×C5×M16C2×C412yes—
39C2×C42×C5C2311yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5Q811yescharacteristic
43C2×#681—21no—
44C2×#681C2×C412yes—
45D5×M16—28no—
46D5×M16—44no—
47C2×#676—22no—
48C2×#676—22no—
49C2×#676—22no—
50C2×C8×D5—22no—
51C2×C8×D5—22no—
52C42×D5C2×C411yescharacteristic
53C42×D5C2×C411yescharacteristic
54C42×D5C2×C411yescharacteristic
55C42×D5C2×C411yescharacteristic
56C42×D5D411yescharacteristic
57C42×D5D411yescharacteristic
58C42×D5D411yescharacteristic
59C42×D5D411yescharacteristic
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8C2×C412yes—
63C5×C22⋊C8—21no—
64C5×#97C2×C412yes—
65C4×C5×C8—21no—
66C4×C5×C8—21no—
67C22⋊#168—21no—
68#3952—22no—
69#3947—22no—
70#3947—22no—
71#3946—22no—
72#3946—22no—
73#3946—22no—
74C8×Dic5—22no—
75C4⋊#168—21no—
76C4⋊#168—21no—
77C4⋊#168C2×C412yes—
78#3935C2×C412yes—
79C4×#168—21no—
80C4×#168—21no—
81#2920—51no—
82C2×#423—51no—
83C2×C4×M16—51no—
84#1299—51no—
85#1299—51no—
86#1299—51no—
87#1299D511yescharacteristic, complemented
88C23×D5C4⋊C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×Q811yescharacteristic
92C22×Dic5C4⋊C411yescharacteristic
93C22×Dic5C4⋊C411yescharacteristic
94C22×Dic5C4⋊C411yescharacteristic
95C2×C4×D5—22no—
96C2×C4×D5—22no—
97C2×C4×D5—24no—
98C2×C4×D5—42no—
99C2×C4×D5C4211yescharacteristic
100C2×C4×D5C4211yescharacteristic
101C2×C4×D5C22⋊C411yescharacteristic
102C2×C4×D5C22⋊C411yescharacteristic
103C2×C4×D5C22⋊C411yescharacteristic
104C2×C4×D5C22⋊C411yescharacteristic
105C2×C4×D5C22⋊C411yescharacteristic
106C2×C4×D5C22⋊C411yescharacteristic
107C2×C4×D5C4⋊C411yescharacteristic
108C2×C4×D5C4⋊C411yescharacteristic
109C2×C4×D5C4⋊C411yescharacteristic
110C2×C4×D5C4⋊C411yescharacteristic
111C5×M16—24no—
112C5×M16—42no—
113C2×C5×C8—22no—
114C2×C5×C8—22no—
115C2×C5×C8—22no—
116C42×C5C22×C411yescharacteristic
117C42×C5C22×C411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5C2×D411yescharacteristic
120C4×Dic5C4211yescharacteristic
121C4×Dic5C4211yescharacteristic
122C4×Dic5C22⋊C411yescharacteristic
123C4×Dic5C22⋊C411yescharacteristic
124C4×Dic5C22⋊C411yescharacteristic
125C4×Dic5C22⋊C411yescharacteristic
126C4×Dic5C22⋊C411yescharacteristic
127C4×Dic5C22⋊C411yescharacteristic
128C4×Dic5C4⋊C411yescharacteristic
129C4×Dic5C4⋊C411yescharacteristic
130C4×Dic5C4⋊C411yescharacteristic
131C4×Dic5C4⋊C411yescharacteristic
132#681—24no—
133#681—42no—
134C2×#168—22no—
135C2×#168—22no—
136C2×#168—22no—
137#676—28no—
138#676—44no—
139#676—44no—
140C8×D5—28no—
141C8×D5—44no—
142C22×M16—52no—
143C22×M16—101no—
144C22×C42—51no—
145#432—52no—
146#432—101no—
147#431—51no—
148#431—101no—
149#431C2×D511yescharacteristic
150#423—52no—
151#423—52no—
152#423—51no—
153#423—101no—
154#423—101no—
155#423C2×D511yescharacteristic
156C2×C4⋊C8—101no—
157C2×C4⋊C8—101no—
158#407—101no—
159C4×M16—51no—
160C4×M16—52no—
161C4×M16—101no—
162C4×M16—101no—
163C4×M16—101no—
164C4×M16C2×D511yescharacteristic
165C2×#97—52no—
166C2×C4×C8—101no—
167C23×C5C2×C4⋊C411yescharacteristic
168C22×D5—22no—
169C22×D5—22no—
170C22×D5—41no—
171C22×D5#9511yescharacteristic
172C22×D5#9511yescharacteristic
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5C2×C4211yescharacteristic
178C2×C4×C5C2×C22⋊C411yescharacteristic
179C2×C4×C5C2×C22⋊C411yescharacteristic
180C2×C4×C5C2×C22⋊C411yescharacteristic
181C2×C4×C5C2×C4⋊C411yescharacteristic
182C2×C4×C5C2×C4⋊C411yescharacteristic
183C2×Dic5—22no—
184C2×Dic5—22no—
185C2×Dic5—41no—
186C2×Dic5#9511yescharacteristic
187C2×Dic5#9511yescharacteristic
188C2×Dic5#9511yescharacteristic
189C2×Dic5#9511yescharacteristic
190C2×Dic5#9511yescharacteristic
191C2×Dic5#9511yescharacteristic
192C4×D5—22no—
193C4×D5—22no—
194C4×D5—21no—
195C4×D5—21no—
196C4×D5—22no—
197C4×D5—22no—
198C4×D5—22no—
199C4×D5—22no—
200C4×D5—22no—
201C4×D5—41no—
202C4×D5—41no—
203C4×D5#10012yes—
204C4×D5#10112yes—
205C4×D5#10414yes—
206C5×C8—24no—
207C5×C8—42no—
208C5×C8—42no—
209#168—24no—
210#168—42no—
211#168—42no—
212C23×C4—51no—
213C23×C4—51no—
214C23×C4—51no—
215C2×M16—21no—
216C2×M16—52no—
217C2×M16—102no—
218C2×M16—102no—
219C2×M16—102no—
220C2×M16—108no—
221C2×M16—101no—
222C2×M16—204no—
223C2×M16C4×D512yes—
224C22×C8—102no—
225C22×C8—102no—
226C2×C42—51no—
227C2×C42—51no—
228C2×C42—51no—
229C2×C42—51no—
230C2×C42—51no—
231C2×C42—51no—
232C2×C42—51no—
233C2×C42—51no—
234C2×C42—51no—
235C2×C42—51no—
236C2×C42—51no—
237C2×C42C22×D511yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—52no—
241C4⋊C8—102no—
242C4⋊C8—102no—
243C4⋊C8—102no—
244C4⋊C8—101no—
245C4⋊C8—101no—
246C4⋊C8C4×D512yes—
247C22⋊C8—21no—
248C22⋊C8—102no—
249C22⋊C8—101no—
250#97—52no—
251#97—102no—
252#97—102no—
253#97C4×D512yes—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—102no—
257C4×C8—101no—
258C4×C8—101no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5C2×#9511yescharacteristic
263C2×D5—21no—
264C2×D5—21no—
265C2×D5—21no—
266C2×D5—21no—
267C2×D5—44no—
268C2×D5#33912yes—
269C2×D5#34312yes—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5—21no—
273C4×C5C2×#10011yescharacteristic
274C4×C5C2×#10111yescharacteristic
275C4×C5C2×#10412yes—
276C4×C5#43012yes—
277Dic5—21no—
278Dic5—21no—
279Dic5—21no—
280Dic5—21no—
281Dic5#33912yes—
282Dic5#34312yes—
283C24—51no—
284C22×C4—51no—
285C22×C4—51no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—104no—
300C22×C4—102no—
301C22×C4—102no—
302C22×C4—202no—
303C22×C4C2×C4×D511yescharacteristic
304C22×C4D4×D511yescharacteristic
305C22×C4Q8×D511yescharacteristic
306M16—24no—
307M16—42no—
308M16—108no—
309M16—104no—
310M16—204no—
311M16—204no—
312M16—202no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—108no—
317C2×C8—102no—
318C2×C8—102no—
319C2×C8—102no—
320C2×C8—204no—
321C42—51no—
322C42—51no—
323C42—51no—
324C42—51no—
325C42—51no—
326C42—51no—
327C42—51no—
328C42—51no—
329C42—51no—
330C42—51no—
331C42—51no—
332C42—51no—
333C42C2×C4×D511yescharacteristic
334C42C2×C4×D511yescharacteristic
335C42D4×D511yescharacteristic
336C42D4×D511yescharacteristic
337C2×C5—41no—
338C2×C5C2×#33911yescharacteristic
339C2×C5#173811yescharacteristic
340C2×C5C2×#34311yescharacteristic
341D5—22no—
342D5—22no—
343C23—51no—
344C23—51no—
345C23—102no—
346C23—102no—
347C23—201no—
348C23D5×C4⋊C411yescharacteristic
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—51no—
354C2×C4—51no—
355C2×C4—52no—
356C2×C4—52no—
357C2×C4—54no—
358C2×C4—51no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—51no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4—102no—
365C2×C4—102no—
366C2×C4—102no—
367C2×C4—102no—
368C2×C4—101no—
369C2×C4—101no—
370C2×C4—102no—
371C2×C4—102no—
372C2×C4—102no—
373C2×C4—201no—
374C2×C4—201no—
375C2×C4—201no—
376C2×C4C42×D511yescharacteristic
377C2×C4D5×C22⋊C411yescharacteristic
378C2×C4D5×C22⋊C411yescharacteristic
379C2×C4D5×C22⋊C411yescharacteristic
380C2×C4D5×C4⋊C411yescharacteristic
381C2×C4D5×C4⋊C411yescharacteristic
382C8—24no—
383C8—42no—
384C8—42no—
385C8—104no—
386C8—202no—
387C8—202no—
388C5#806311yescharacteristic, complemented, Sylow
389C22—21no—
390C22—21no—
391C22—21no—
392C22—52no—
393C22—52no—
394C22—101no—
395C22—101no—
396C22—101no—
397C22—101no—
398C22—204no—
399C22D5×#9511yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—52no—
404C4—52no—
405C4—101no—
406C4—101no—
407C4—101no—
408C4—101no—
409C4D5×#10011yescharacteristic
410C4D5×#10111yescharacteristic
411C4D5×#10412yes—
412C4#6518212yes—
413C2—41no—
414C2—102no—
415C2—102no—
416C2D5×#33911yescharacteristic
417C2#1059973111yescharacteristic
418C2D5×#34311yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1299C2
socleC22×C5C2×#95
prime radicalC23×D5C4⋊C4
cosocleC2×C42×C5C23
hypercenter#1299D5
hypocenterC5#8063
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
4. C5×#1299C2semidirect
5. #10598234C2semidirect
6. #10598201C2semidirect
7. #10598160C2semidirect
87. #1299D5semidirect
388. C5#8063semidirect

Maximal subgroups

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

subgroupindex
#106110132
D5×#4232
C4×D5×M162
C5×#12992
#105982342
#105982012
#105981602
#80635