Finite Group Databasebeta

← #12065607

Subgroups — #12065607

Order 1280.

996 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65913C211yesmaximal, characteristic
2#10611067C212yesmaximal
3C5×#1467C211yesmaximal, characteristic, complemented
4#10602417C211yesmaximal, characteristic, complemented
5#10601624C212yesmaximal, complemented
6#10598940C214yesmaximal, complemented
7#10598937C212yesmaximal, complemented
8D5×#324C212yesmaximal, complemented
9C2×C4×C5×Q8C2211yescharacteristic
10C2×#4092C412yes—
11#65913—22no—
12#65913—22no—
13#65913—24no—
14C2×#4042C412yes—
15C2×#4042C2212yes—
16C2×D5×C4⋊C4C2212yes—
17C2×C4×D20C411yescharacteristic
18C2×C4×D20C411yescharacteristic
19C2×C4×D20C2211yescharacteristic
20C2×#4016C411yescharacteristic
21C2×#4016C2211yescharacteristic
22C2×#4015C411yescharacteristic
23C5×#432C2212yes—
24#65214C2212yes—
25#65127—22no—
26#65123—22no—
27#65015C2214yes—
28D5×C22⋊C8C2214yes—
29#64995—24no—
30C5×#324C2212yes—
31C5×#324C2212yes—
32#64748C2211yescharacteristic
33#64748C2211yescharacteristic
34#64748C2212yes—
35#64689C2214yes—
36#64689C2214yes—
37#17426—51nomaximal, Sylow
38C22×C5×Q8C2×C411yescharacteristic
39C22×D20C2×C411yescharacteristic
40C22×C4×D5C2×C412yes—
41C22×C4×D5C2×C412yes—
42C22×C4×D5C2312yes—
43C22×Dic10C2×C412yes—
44C4×C5×Q8—22no—
45C4×C5×Q8—22no—
46C2×C5×C4⋊C4C2×C411yescharacteristic
47C2×C5×C4⋊C4C2311yescharacteristic
48C2×C5×C4⋊C4C2311yescharacteristic
49C2×C42×C5C2×C411yescharacteristic
50C2×C42×C5C2×C411yescharacteristic
51C2×C42×C5C2311yescharacteristic
52#4092—24no—
53#4092—24no—
54C2×#685C2×C412yes—
55C2×#685C2×C412yes—
56C2×#685C2×C412yes—
57C2×C4⋊Dic5C2×C411yescharacteristic
58C2×C4⋊Dic5C2×C412yes—
59C2×C4⋊Dic5C2×C411yescharacteristic
60C2×C4⋊Dic5C2×C411yescharacteristic
61C2×#683C2×C412yes—
62C2×#683C2×C412yes—
63C2×#683C2×C412yes—
64C2×#683C2312yes—
65C2×#676—24no—
66C2×C8×D5—24no—
67#4042—24no—
68#4042—24no—
69#4042—24no—
70#4042—24no—
71D5×C4⋊C4—24no—
72D5×C4⋊C4—24no—
73C4×D20—22no—
74C4×D20—21no—
75C4×D20—21no—
76C4×D20—22no—
77C4×D20—21no—
78C4×D20—21no—
79C4×D20D412yes—
80C4×D20D412yes—
81C4×D20D414yes—
82#4016—22no—
83#4016—22no—
84#4016—22no—
85#4016—22no—
86#4015—22no—
87#4015—22no—
88C5×C4⋊C8—22no—
89C5×C22⋊C8C2314yes—
90C5×#97—22no—
91C22⋊#168C2312yes—
92C22⋊#168C2312yes—
93#3952—24no—
94#3952—24no—
95C4⋊#168—22no—
96C4×#168—22no—
97C2×#554—51no—
98#2974—52no—
99#1472—54no—
100#1470—52no—
101#1467D511yescharacteristic, complemented
102#1463—52no—
103#1461—51no—
104C2×#324—52no—
105C23×D5C22×C412yes—
106C2×C5×Q8—22no—
107C2×C5×Q8—22no—
108C2×C5×Q8—41no—
109C22×C4×C5C22×C411yescharacteristic
110C22×C4×C5C22×C411yescharacteristic
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C22×C411yescharacteristic
113C22×C4×C5C22×C411yescharacteristic
114C22×C4×C5C22×C411yescharacteristic
115C22×C4×C5C2411yescharacteristic
116C22×Dic5C22×C412yes—
117C22×Dic5C22×C412yes—
118C22×Dic5C22×C412yes—
119C2×D20—24no—
120C2×D20C22⋊C412yes—
121C2×D20C22⋊C411yescharacteristic
122C2×D20C22⋊C411yescharacteristic
123C2×C4×D5—22no—
124C2×C4×D5—22no—
125C2×C4×D5—24no—
126C2×C4×D5—22no—
127C2×C4×D5—22no—
128C2×C4×D5—42no—
129C2×C4×D5—82no—
130C2×C4×D5—82no—
131C2×C4×D5C2×D414yes—
132C2×C4×D5C2×D414yes—
133C2×Dic10—24no—
134C2×Dic10—82no—
135C2×C5×C8—24no—
136C5×C4⋊C4—22no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—22no—
139C42×C5—21no—
140C42×C5—21no—
141C42×C5—21no—
142C42×C5—21no—
143C42×C5C2×D412yes—
144C42×C5C2×D412yes—
145#685—22no—
146#685—22no—
147#685—22no—
148#685—22no—
149#685C22⋊C414yes—
150#685C22⋊C414yes—
151C4⋊Dic5—21no—
152C4⋊Dic5—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5—24no—
156C4⋊Dic5C22⋊C412yes—
157C4⋊Dic5C22⋊C412yes—
158#683—24no—
159#683—24no—
160#683—24no—
161#683—24no—
162C2×#168—22no—
163C2×#168—22no—
164#676—84no—
165C8×D5—84no—
166#554—102no—
167#554—104no—
168#554—102no—
169C2×C4⋊Q8—51no—
170C2×#125—51no—
171C2×#125—51no—
172C2×C22⋊Q8—52no—
173C2×C22⋊Q8—52no—
174C2×C22⋊Q8—52no—
175C2×C4×Q8C2×D511yescharacteristic
176C2×C4×D4—51no—
177C2×C4×D4—51no—
178C2×C4×D4—51no—
179C22×C4⋊C4—52no—
180#436—102no—
181#435—104no—
182C8×D4—102no—
183#432C2×D512yes—
184#431—52no—
185#407—54no—
186C2×C22⋊C8—54no—
187#324—51no—
188#324—51no—
189#324—52no—
190#324—54no—
191#324—54no—
192#324C2×D512yes—
193#324C2×D512yes—
194C23×C5C23×C411yescharacteristic
195C22×D5—22no—
196C22×D5—22no—
197C22×D5—24no—
198C22×D5—42no—
199C22×D5C2×C22⋊C412yes—
200C22×D5C2×C22⋊C412yes—
201C5×Q8—44no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—22no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5C2×C22⋊C412yes—
216C2×C4×C5C2×C22⋊C411yescharacteristic
217C2×C4×C5C2×C22⋊C411yescharacteristic
218C2×C4×C5#13112yes—
219C2×C4×C5C22×D412yes—
220C2×Dic5—22no—
221C2×Dic5—22no—
222C2×Dic5—22no—
223C2×Dic5—22no—
224C2×Dic5—42no—
225C2×Dic5—42no—
226C2×Dic5C2×C22⋊C414yes—
227D20—24no—
228D20—22no—
229D20#10114yes—
230C4×D5—44no—
231C4×D5—44no—
232C4×D5—44no—
233C4×D5—44no—
234C4×D5—82no—
235C4×D5—82no—
236Dic10—84no—
237C5×C8—44no—
238#168—42no—
239#168—42no—
240C22×Q8—52no—
241C22×Q8C4×D511yescharacteristic
242C22×D4—51no—
243C23×C4—52no—
244C23×C4—52no—
245C23×C4—52no—
246C2×M16—104no—
247C22×C8—104no—
248C4⋊Q8—102no—
249C4⋊Q8—102no—
250#125—102no—
251#125—102no—
252#125—102no—
253#125—102no—
254C22⋊Q8—104no—
255C22⋊Q8—104no—
256C22⋊Q8—104no—
257C22⋊Q8—104no—
258C22⋊Q8—104no—
259C22⋊Q8—104no—
260C4×Q8—22no—
261C4×Q8—22no—
262C4×D4—52no—
263C4×D4—54no—
264C4×D4—52no—
265C4×D4—101no—
266C4×D4—102no—
267C4×D4—101no—
268C4×D4—101no—
269C4×D4—102no—
270C4×D4—101no—
271C2×C4⋊C4—51no—
272C2×C4⋊C4—52no—
273C2×C4⋊C4—52no—
274C2×C4⋊C4—51no—
275C2×C4⋊C4—51no—
276C2×C4⋊C4—52no—
277C2×C4⋊C4—52no—
278C2×C4⋊C4—52no—
279C2×C4⋊C4—104no—
280C2×C4⋊C4—104no—
281C2×C4⋊C4C4×D511yescharacteristic
282C2×C4⋊C4C22×D511yescharacteristic
283C2×C4⋊C4C22×D511yescharacteristic
284C2×C22⋊C4—52no—
285C2×C22⋊C4—52no—
286C2×C22⋊C4—52no—
287C2×C42C4×D511yescharacteristic
288C2×C42C4×D511yescharacteristic
289C2×C42C22×D511yescharacteristic
290C4⋊C8—22no—
291C4⋊C8—102no—
292C22⋊C8—52no—
293C22⋊C8—52no—
294C22⋊C8—104no—
295C22⋊C8—104no—
296C22⋊C8C22×D514yes—
297#97—22no—
298C4×C8—102no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5C22×C22⋊C411yescharacteristic
302C22×C5C2×#13111yescharacteristic
303C22×C5#56811yescharacteristic
304C2×D5—22no—
305C2×D5—22no—
306C2×D5—22no—
307C2×D5—22no—
308C2×D5—22no—
309C2×D5—44no—
310C2×D5—44no—
311C2×D5C2×#10114yes—
312C4×C5—22no—
313C4×C5—22no—
314C4×C5—22no—
315C4×C5—21no—
316C4×C5—41no—
317C4×C5—41no—
318C4×C5—41no—
319C4×C5C2×#10112yes—
320Dic5—24no—
321Dic5—42no—
322Dic5—42no—
323C24—52no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—104no—
328C2×Q8—402no—
329C2×D4—51no—
330C2×D4—52no—
331C2×D4—51no—
332C2×D4—104no—
333C22×C4—52no—
334C22×C4—54no—
335C22×C4—54no—
336C22×C4—52no—
337C22×C4—52no—
338C22×C4—102no—
339C22×C4—102no—
340C22×C4—102no—
341C22×C4—102no—
342C22×C4—104no—
343C22×C4—202no—
344C22×C4—402no—
345C22×C4—402no—
346C22×C4C2×C4×D511yescharacteristic
347C22×C4C2×C4×D511yescharacteristic
348C22×C4C2×C4×D511yescharacteristic
349C22×C4C2×C4×D511yescharacteristic
350C22×C4C2×C4×D511yescharacteristic
351C22×C4C2×C4×D511yescharacteristic
352C22×C4C23×D511yescharacteristic
353M16—404no—
354C2×C8—24no—
355C2×C8—102no—
356C2×C8—102no—
357C2×C8—404no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—52no—
362C4⋊C4—52no—
363C4⋊C4—104no—
364C4⋊C4—104no—
365C4⋊C4—104no—
366C4⋊C4—104no—
367C4⋊C4—101no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4—101no—
371C4⋊C4—104no—
372C22⋊C4—54no—
373C22⋊C4—54no—
374C22⋊C4—102no—
375C22⋊C4—102no—
376C22⋊C4—102no—
377C22⋊C4—102no—
378C42—21no—
379C42—21no—
380C42—21no—
381C42—21no—
382C42D4×D512yes—
383C42D4×D512yes—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5#288011yescharacteristic
387C2×C5#288311yescharacteristic
388C2×C5C22×#10111yescharacteristic
389D5—24no—
390D5—42no—
391C23—52no—
392C23—52no—
393C23—104no—
394C23—102no—
395C23—102no—
396C23—202no—
397C23C22×C4×D511yescharacteristic
398Q8—44no—
399Q8—404no—
400D4—54no—
401D4—104no—
402D4—102no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—54no—
417C2×C4—102no—
418C2×C4—102no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—204no—
422C2×C4—204no—
423C2×C4—204no—
424C2×C4—204no—
425C2×C4—202no—
426C2×C4—202no—
427C2×C4—402no—
428C2×C4—402no—
429C2×C4D5×C22⋊C411yescharacteristic
430C2×C4D5×C22⋊C412yes—
431C2×C4D5×C22⋊C411yescharacteristic
432C2×C4#405312yes—
433C2×C4C2×D4×D512yes—
434C8—44no—
435C8—202no—
436C8—202no—
437C5#1742611yescharacteristic, complemented, Sylow
438C22—21no—
439C22—21no—
440C22—54no—
441C22—102no—
442C22—102no—
443C22—102no—
444C22—102no—
445C22—102no—
446C22—204no—
447C22—204no—
448C22C2×D5×C22⋊C411yescharacteristic
449C22C2×#405311yescharacteristic
450C22#6607911yescharacteristic
451C4—21no—
452C4—22no—
453C4—22no—
454C4—22no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—104no—
459C4—202no—
460C4—202no—
461C4D5×#10112yes—
462C2—21no—
463C2—21no—
464C2—104no—
465C2—202no—
466C2#1061036211yescharacteristic
467C2#1061042511yescharacteristic
468C2C2×D5×#10111yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1467C2
socleC22×C5C22×C22⋊C4
prime radicalC22×D20C2×C4
cosocleC22×C4×C5C24
hypercenter#1467D5
hypocenterC5#17426
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
3. C5×#1467C2semidirect
4. #10602417C2semidirect
5. #10601624C2semidirect
6. #10598940C2semidirect
7. #10598937C2semidirect
8. D5×#324C2semidirect
101. #1467D5semidirect
437. C5#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#659132
#106110672
C5×#14672
#106024172
#106016242
#105989402
#105989372
D5×#3242
#174265