Finite Group Databasebeta

← #12065190

Subgroups — #12065190

Order 1280.

1214 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D5C211yesmaximal, characteristic
2#10611013C212yesmaximal
3C5×#1461C211yesmaximal, characteristic, complemented
4#10602417C211yesmaximal, characteristic, complemented
5#10601579C212yesmaximal, complemented
6#10598937C214yesmaximal
7#10598920C214yesmaximal, complemented
8C22×Q8×D5C411yescharacteristic
9C2×C4×C5×Q8C2211yescharacteristic
10C2×Q8×Dic5C411yescharacteristic
11C4×Q8×D5—22no—
12C4×Q8×D5—22no—
13C4×Q8×D5—22no—
14C4×Q8×D5—22no—
15C2×D5×C4⋊C4C411yescharacteristic
16C2×D5×C4⋊C4C2212yes—
17C2×#4033C411yescharacteristic
18C2×#4033C2212yes—
19C2×C42×D5C412yes—
20C2×C42×D5C2211yescharacteristic
21C2×C4×Dic10C412yes—
22C2×C4×Dic10C2211yescharacteristic
23C5×#431C2212yes—
24#65214C2212yes—
25#65126—22no—
26#65124—22no—
27#65015C2214yes—
28#65008C2214yes—
29C4×#676—22no—
30#64974—22no—
31C5×#324C2214yes—
32#64748C2214yes—
33#64689C2218yes—
34#17365—51nomaximal, Sylow
35C22×C5×Q8C2×C411yescharacteristic
36C2×Q8×D5—24no—
37C2×Q8×D5—22no—
38C2×Q8×D5—22no—
39C2×Q8×D5—24no—
40C22×C4×D5C2×C412yes—
41C22×C4×D5C2×C411yescharacteristic
42C22×C4×D5C2×C411yescharacteristic
43C22×C4×D5C2×C412yes—
44C22×C4×D5C2311yescharacteristic
45C22×Dic10C2×C412yes—
46C22×Dic10C2×C411yescharacteristic
47C4×C5×Q8—22no—
48C4×C5×Q8—22no—
49C2×C5×C4⋊C4C2×C411yescharacteristic
50C2×C5×C4⋊C4C2312yes—
51C2×C42×C5C2×C412yes—
52C2×C42×C5C2311yescharacteristic
53Q8×Dic5—22no—
54Q8×Dic5—22no—
55C2×C4⋊Dic5C2×C412yes—
56C2×C4⋊Dic5C2×C411yescharacteristic
57C2×#683C2×C412yes—
58C2×#683C2×C412yes—
59C2×#683C2312yes—
60C2×C4×Dic5C2×C412yes—
61C2×C4×Dic5C2×C412yes—
62C2×C4×Dic5C2×C412yes—
63C2×C4×Dic5C2×C411yescharacteristic
64C2×C4×Dic5C2×C411yescharacteristic
65C2×C4×Dic5C2311yescharacteristic
66C2×#676—24no—
67D5×C4⋊C4—22no—
68D5×C4⋊C4—22no—
69D5×C4⋊C4—24no—
70D5×C4⋊C4—24no—
71#4033—22no—
72#4033—22no—
73#4033—24no—
74#4033—24no—
75C42×D5—22no—
76C42×D5—22no—
77C42×D5—22no—
78C42×D5—22no—
79C42×D5D412yes—
80C42×D5D412yes—
81C42×D5D412yes—
82C42×D5D412yes—
83C4×Dic10—22no—
84C4×Dic10—22no—
85C4×Dic10—24no—
86C4×Dic10—24no—
87C5×C4⋊C8—22no—
88C5×C22⋊C8C2314yes—
89C4×C5×C8—22no—
90C22⋊#168C2314yes—
91#3952—24no—
92#3947—24no—
93#3946—24no—
94C4⋊#168—22no—
95C4×#168—22no—
96C22×C4×Q8—51no—
97#2920—52no—
98#1467—54no—
99#1463—54no—
100#1461—52no—
101#1461—51no—
102#1461D511yescharacteristic, complemented
103C23×D5C22×C411yescharacteristic
104C2×C5×Q8—22no—
105C2×C5×Q8—22no—
106C2×C5×Q8M1614yescomplemented
107C22×C4×C5C22×C411yescharacteristic
108C22×C4×C5C22×C412yes—
109C22×C4×C5C22×C412yes—
110C22×C4×C5C22×C411yescharacteristic
111C22×C4×C5C2411yescharacteristic
112C22×Dic5C22×C411yescharacteristic
113C22×Dic5C22×C411yescharacteristic
114C22×Dic5C22×C412yes—
115C22×Dic5C22×C412yes—
116C22×Dic5C22×C411yescharacteristic
117Q8×D5—216no—
118Q8×D5—216no—
119C2×C4×D5—22no—
120C2×C4×D5—22no—
121C2×C4×D5—24no—
122C2×C4×D5—22no—
123C2×C4×D5—22no—
124C2×C4×D5—24no—
125C2×C4×D5—24no—
126C2×C4×D5—22no—
127C2×C4×D5—22no—
128C2×C4×D5—42no—
129C2×C4×D5—44no—
130C2×C4×D5C22⋊C412yes—
131C2×C4×D5C22⋊C412yes—
132C2×C4×D5C22⋊C411yescharacteristic
133C2×C4×D5C22⋊C411yescharacteristic
134C2×C4×D5C22⋊C411yescharacteristic
135C2×C4×D5C22⋊C411yescharacteristic
136C2×C4×D5C2×D412yes—
137C2×C4×D5C2×D412yes—
138C2×Dic10—22no—
139C2×Dic10—24no—
140C2×Dic10—22no—
141C2×Dic10—24no—
142C2×Dic10—24no—
143C2×Dic10M1614yescomplemented
144C2×C5×C8—24no—
145C5×C4⋊C4—22no—
146C5×C4⋊C4—24no—
147C42×C5—22no—
148C42×C5—22no—
149C42×C5C2×D412yes—
150C42×C5C2×D412yes—
151C4⋊Dic5—22no—
152C4⋊Dic5—24no—
153#683—24no—
154#683—24no—
155#683—24no—
156C4×Dic5—22no—
157C4×Dic5—22no—
158C4×Dic5—22no—
159C4×Dic5—22no—
160C4×Dic5—22no—
161C4×Dic5—22no—
162C4×Dic5C22⋊C412yes—
163C4×Dic5C22⋊C412yes—
164C4×Dic5C22⋊C412yes—
165C4×Dic5C22⋊C412yes—
166C4×Dic5C2×D412yes—
167C4×Dic5C2×D412yes—
168C2×#168—24no—
169#676—48no—
170C23×Q8—51no—
171C2×C4×Q8—51no—
172C2×C4×Q8—51no—
173C2×C4×Q8—52no—
174C2×C4×Q8—52no—
175C2×C4×Q8—51no—
176C2×C4×Q8—102no—
177C2×C4×Q8—102no—
178C2×C4×Q8—102no—
179C2×C4×Q8—102no—
180C2×C4×Q8C2×D511yescharacteristic
181C22×C4⋊C4—51no—
182C22×C4⋊C4—52no—
183C22×C42—51no—
184C22×C42—52no—
185#432—54no—
186#432—102no—
187#431—52no—
188#431—102no—
189#431C2×D512yes—
190#423—102no—
191#407—54no—
192C4×M16—102no—
193#324—54no—
194#324—58no—
195#324C2×D514yes—
196C23×C5C23×C411yescharacteristic
197C22×D5—21no—
198C22×D5—21no—
199C22×D5—22no—
200C22×D5—22no—
201C22×D5C2×C22⋊C411yescharacteristic
202C22×D5C2×C22⋊C411yescharacteristic
203C5×Q8—28no—
204C2×C4×C5—22no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—22no—
208C2×C4×C5—41no—
209C2×C4×C5—42no—
210C2×C4×C5C2×C22⋊C411yescharacteristic
211C2×C4×C5C2×C22⋊C412yes—
212C2×C4×C5C2×C22⋊C411yescharacteristic
213C2×C4×C5C2×M1614yes—
214C2×C4×C5C2×M1612yes—
215C2×C4×C5C2×M1612yes—
216C2×C4×C5C22×D412yes—
217C2×Dic5—22no—
218C2×Dic5—21no—
219C2×Dic5—22no—
220C2×Dic5—21no—
221C2×Dic5—22no—
222C2×Dic5—22no—
223C2×Dic5—41no—
224C2×Dic5—42no—
225C2×Dic5C2×C22⋊C411yescharacteristic
226C2×Dic5C2×C22⋊C412yes—
227C2×Dic5C2×C22⋊C412yes—
228C2×Dic5C2×C22⋊C411yescharacteristic
229C2×Dic5C2×M1614yes—
230C4×D5—28no—
231C4×D5—28no—
232C4×D5—24no—
233C4×D5—22no—
234C4×D5—24no—
235C4×D5—24no—
236C4×D5—22no—
237C4×D5—22no—
238C4×D5—42no—
239C4×D5—44no—
240C4×D5—44no—
241C4×D5#10114yes—
242Dic10—216no—
243Dic10—28no—
244C5×C8—44no—
245#168—44no—
246C22×Q8—51no—
247C22×Q8—52no—
248C22×Q8—102no—
249C22×Q8—102no—
250C22×Q8—104no—
251C22×Q8—104no—
252C22×Q8C4×D511yescharacteristic
253C23×C4—51no—
254C23×C4—51no—
255C23×C4—51no—
256C23×C4—52no—
257C23×C4—52no—
258C2×M16—104no—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×Q8—104no—
262C4×Q8—104no—
263C4×Q8—104no—
264C4×Q8—104no—
265C4×Q8—102no—
266C4×Q8—102no—
267C4×Q8—102no—
268C4×Q8—102no—
269C4×Q8—102no—
270C4×Q8—102no—
271C2×C4⋊C4—52no—
272C2×C4⋊C4—52no—
273C2×C4⋊C4—52no—
274C2×C4⋊C4—51no—
275C2×C4⋊C4—52no—
276C2×C4⋊C4—104no—
277C2×C4⋊C4—104no—
278C2×C4⋊C4—102no—
279C2×C4⋊C4—102no—
280C2×C4⋊C4C4×D511yescharacteristic
281C2×C4⋊C4C22×D512yes—
282C2×C42—51no—
283C2×C42—51no—
284C2×C42—51no—
285C2×C42—52no—
286C2×C42—52no—
287C2×C42—52no—
288C2×C42—52no—
289C2×C42—52no—
290C2×C42—52no—
291C2×C42—52no—
292C2×C42—102no—
293C2×C42—102no—
294C2×C42—102no—
295C2×C42—102no—
296C2×C42C4×D512yes—
297C2×C42C22×D511yescharacteristic
298C4⋊C8—22no—
299C4⋊C8—104no—
300C4⋊C8—102no—
301C22⋊C8—54no—
302C22⋊C8—104no—
303C22⋊C8C22×D514yes—
304#97—104no—
305C4×C8—22no—
306C4×C8—102no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5C22×C22⋊C411yescharacteristic
310C22×C5C22×M1611yescharacteristic
311C22×C5C22×M1611yescharacteristic
312C2×D5—24no—
313C2×D5—24no—
314C2×D5—21no—
315C2×D5—21no—
316C2×D5—21no—
317C2×D5—21no—
318C2×D5#41012yes—
319C2×D5C2×#10112yes—
320C4×C5—24no—
321C4×C5—22no—
322C4×C5—21no—
323C4×C5—42no—
324C4×C5#40714yes—
325C4×C5C2×#10112yes—
326Dic5—22no—
327Dic5—24no—
328Dic5—22no—
329Dic5—21no—
330Dic5—42no—
331Dic5C2×#10112yes—
332C24—51no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—54no—
336C2×Q8—104no—
337C2×Q8—104no—
338C2×Q8—1016no—
339C2×Q8—1016no—
340C2×Q8—102no—
341C2×Q8—104no—
342C2×Q8—102no—
343C2×Q8#67614yescomplemented
344C22×C4—51no—
345C22×C4—51no—
346C22×C4—51no—
347C22×C4—52no—
348C22×C4—51no—
349C22×C4—52no—
350C22×C4—51no—
351C22×C4—51no—
352C22×C4—52no—
353C22×C4—52no—
354C22×C4—51no—
355C22×C4—52no—
356C22×C4—52no—
357C22×C4—104no—
358C22×C4—104no—
359C22×C4—102no—
360C22×C4—102no—
361C22×C4—102no—
362C22×C4—102no—
363C22×C4—104no—
364C22×C4—102no—
365C22×C4—102no—
366C22×C4—202no—
367C22×C4—204no—
368C22×C4C2×C4×D511yescharacteristic
369C22×C4C2×C4×D512yes—
370C22×C4C2×C4×D512yes—
371C22×C4C2×C4×D511yescharacteristic
372C22×C4C23×D511yescharacteristic
373M16—208no—
374C2×C8—24no—
375C2×C8—104no—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—104no—
379C4⋊C4—104no—
380C4⋊C4—104no—
381C4⋊C4—104no—
382C4⋊C4—102no—
383C42—22no—
384C42—22no—
385C42—52no—
386C42—52no—
387C42—52no—
388C42—52no—
389C42—52no—
390C42—52no—
391C42—102no—
392C42—102no—
393C42—102no—
394C42—102no—
395C42—102no—
396C42—102no—
397C42D4×D512yes—
398C42D4×D512yes—
399C2×C5—21no—
400C2×C5—21no—
401C2×C5C2×#40711yescharacteristic
402C2×C5C2×#41011yescharacteristic
403C2×C5C22×#10111yescharacteristic
404D5—22no—
405D5—22no—
406C23—51no—
407C23—51no—
408C23—102no—
409C23—102no—
410C23—101no—
411C23—101no—
412C23C22×C4×D511yescharacteristic
413Q8—28no—
414Q8—1016no—
415Q8—108no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—51no—
423C2×C4—54no—
424C2×C4—51no—
425C2×C4—52no—
426C2×C4—52no—
427C2×C4—54no—
428C2×C4—102no—
429C2×C4—104no—
430C2×C4—102no—
431C2×C4—108no—
432C2×C4—108no—
433C2×C4—102no—
434C2×C4—101no—
435C2×C4—102no—
436C2×C4—102no—
437C2×C4—101no—
438C2×C4—102no—
439C2×C4—104no—
440C2×C4—104no—
441C2×C4—102no—
442C2×C4—202no—
443C2×C4—204no—
444C2×C4—204no—
445C2×C4—201no—
446C2×C4—202no—
447C2×C4D5×C22⋊C411yescharacteristic
448C2×C4D5×C22⋊C412yes—
449C2×C4D5×C22⋊C411yescharacteristic
450C2×C4C2×#67614yes—
451C2×C4C2×#67612yes—
452C2×C4D5×M1612yes—
453C2×C4C2×D4×D512yes—
454C8—44no—
455C8—204no—
456C5#1736511yescharacteristic, complemented, Sylow
457C22—21no—
458C22—21no—
459C22—52no—
460C22—52no—
461C22—104no—
462C22—104no—
463C22—101no—
464C22—101no—
465C22—101no—
466C22—101no—
467C22C2×D5×C22⋊C411yescharacteristic
468C22C22×#67611yescharacteristic
469C22C2×D5×M1611yescharacteristic
470C4—21no—
471C4—24no—
472C4—22no—
473C4—42no—
474C4—52no—
475C4—101no—
476C4—102no—
477C4—104no—
478C4—102no—
479C4—202no—
480C4#6501514yes—
481C4D5×#10112yes—
482C2—21no—
483C2—21no—
484C2—102no—
485C2—102no—
486C2C2×#6501511yescharacteristic
487C2D5×#41011yescharacteristic
488C2C2×D5×#10111yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1461C2
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenter#1461D5
hypocenterC5#17365
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
3. C5×#1461C2semidirect
4. #10602417C2semidirect
5. #10601579C2semidirect
7. #10598920C2semidirect
102. #1461D5semidirect
106. C2×C5×Q8M16semidirect
143. C2×Dic10M16semidirect
343. C2×Q8#676semidirect
456. C5#17365semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D52
#106110132
C5×#14612
#106024172
#106015792
#105989372
#105989202
#173655