Finite Group Databasebeta

← #12065191

Subgroups — #12065191

Order 1280.

1214 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×C4×Q8×D5C211yesmaximal, characteristic
2#10611062C212yesmaximal
3C5×#1467C211yesmaximal, characteristic, complemented
4#10602418C211yesmaximal, characteristic, complemented
5#10601623C212yesmaximal, complemented
6#10598937C214yesmaximal
7#10598918C214yesmaximal, 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×#432C2212yes—
24#65215C2212yes—
25#65126—22no—
26#65122—22no—
27#65015C2214yes—
28#65007C2214yes—
29#64996—22no—
30#64994—22no—
31C5×#324C2214yes—
32#64748C2214yes—
33#64689C2218yes—
34#17365—51nomaximal, Sylow
35C22×C5×Q8C2×C411yescharacteristic
36C2×Q8×D5—22no—
37C2×Q8×D5—22no—
38C2×Q8×D5—28no—
39C22×C4×D5C2×C412yes—
40C22×C4×D5C2×C411yescharacteristic
41C22×C4×D5C2×C411yescharacteristic
42C22×C4×D5C2×C412yes—
43C22×C4×D5C2311yescharacteristic
44C22×Dic10C2×C411yescharacteristic
45C22×Dic10C2×C412yes—
46C4×C5×Q8—22no—
47C4×C5×Q8—22no—
48C2×C5×C4⋊C4C2×C411yescharacteristic
49C2×C5×C4⋊C4C2312yes—
50C2×C42×C5C2×C412yes—
51C2×C42×C5C2311yescharacteristic
52Q8×Dic5—22no—
53Q8×Dic5—22no—
54C2×C4⋊Dic5C2×C412yes—
55C2×C4⋊Dic5C2×C411yescharacteristic
56C2×#683C2×C412yes—
57C2×#683C2×C412yes—
58C2×#683C2312yes—
59C2×C4×Dic5C2×C412yes—
60C2×C4×Dic5C2×C412yes—
61C2×C4×Dic5C2×C412yes—
62C2×C4×Dic5C2×C411yescharacteristic
63C2×C4×Dic5C2×C411yescharacteristic
64C2×C4×Dic5C2311yescharacteristic
65C2×#676—24no—
66D5×C4⋊C4—22no—
67D5×C4⋊C4—22no—
68D5×C4⋊C4—24no—
69D5×C4⋊C4—24no—
70#4033—22no—
71#4033—22no—
72#4033—24no—
73#4033—24no—
74C42×D5—22no—
75C42×D5—22no—
76C42×D5—22no—
77C42×D5—22no—
78C42×D5D412yes—
79C42×D5D412yes—
80C42×D5D412yes—
81C42×D5D412yes—
82C4×Dic10—22no—
83C4×Dic10—22no—
84C4×Dic10—24no—
85C4×Dic10—24no—
86C5×C4⋊C8—22no—
87C5×C22⋊C8C2314yes—
88C5×#97—22no—
89C22⋊#168C2314yes—
90#3952—24no—
91#3946—24no—
92C8×Dic5—24no—
93C4⋊#168—22no—
94#3935—22no—
95C22×C4×Q8—51no—
96#2920—52no—
97#1467—52no—
98#1467—51no—
99#1467D511yescharacteristic, complemented
100#1463—54no—
101#1461—54no—
102C23×D5C22×C411yescharacteristic
103C2×C5×Q8—22no—
104C2×C5×Q8—24no—
105C22×C4×C5C22×C411yescharacteristic
106C22×C4×C5C22×C411yescharacteristic
107C22×C4×C5C22×C412yes—
108C22×C4×C5C22×C412yes—
109C22×C4×C5C2411yescharacteristic
110C22×Dic5C22×C411yescharacteristic
111C22×Dic5C22×C412yes—
112C22×Dic5C22×C412yes—
113C22×Dic5C22×C411yescharacteristic
114C22×Dic5C22×C411yescharacteristic
115Q8×D5—216no—
116Q8×D5—216no—
117C2×C4×D5—22no—
118C2×C4×D5—22no—
119C2×C4×D5—24no—
120C2×C4×D5—24no—
121C2×C4×D5—24no—
122C2×C4×D5—24no—
123C2×C4×D5—22no—
124C2×C4×D5—22no—
125C2×C4×D5—42no—
126C2×C4×D5—44no—
127C2×C4×D5C22⋊C412yes—
128C2×C4×D5C22⋊C412yes—
129C2×C4×D5C22⋊C411yescharacteristic
130C2×C4×D5C22⋊C411yescharacteristic
131C2×C4×D5C22⋊C411yescharacteristic
132C2×C4×D5C22⋊C411yescharacteristic
133C2×C4×D5C2×D412yes—
134C2×C4×D5C2×D412yes—
135C2×Dic10—22no—
136C2×Dic10—24no—
137C2×Dic10—24no—
138C2×Dic10—24no—
139C2×Dic10M1618yescomplemented
140C2×C5×C8—24no—
141C5×C4⋊C4—22no—
142C5×C4⋊C4—24no—
143C42×C5—22no—
144C42×C5—22no—
145C42×C5C2×D412yes—
146C42×C5C2×D412yes—
147C4⋊Dic5—22no—
148C4⋊Dic5—24no—
149#683—24no—
150#683—24no—
151#683—24no—
152C4×Dic5—22no—
153C4×Dic5—22no—
154C4×Dic5—22no—
155C4×Dic5—22no—
156C4×Dic5—22no—
157C4×Dic5—22no—
158C4×Dic5C22⋊C412yes—
159C4×Dic5C22⋊C412yes—
160C4×Dic5C22⋊C412yes—
161C4×Dic5C22⋊C412yes—
162C4×Dic5C2×D412yes—
163C4×Dic5C2×D412yes—
164C2×#168—24no—
165#676—48no—
166C23×Q8—51no—
167C2×C4×Q8—51no—
168C2×C4×Q8—51no—
169C2×C4×Q8—52no—
170C2×C4×Q8—52no—
171C2×C4×Q8—51no—
172C2×C4×Q8—102no—
173C2×C4×Q8—102no—
174C2×C4×Q8—102no—
175C2×C4×Q8—102no—
176C2×C4×Q8C2×D511yescharacteristic
177C22×C4⋊C4—51no—
178C22×C4⋊C4—52no—
179C22×C42—51no—
180C22×C42—52no—
181#432—52no—
182#432—102no—
183#432C2×D512yes—
184#431—54no—
185#431—102no—
186#423—102no—
187#407—54no—
188C4×M16—102no—
189#324—54no—
190#324—58no—
191#324C2×D514yes—
192C23×C5C23×C411yescharacteristic
193C22×D5—22no—
194C22×D5—22no—
195C22×D5—22no—
196C22×D5C2×C22⋊C411yescharacteristic
197C22×D5C2×C22⋊C411yescharacteristic
198C5×Q8—28no—
199C2×C4×C5—22no—
200C2×C4×C5—22no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—41no—
205C2×C4×C5—42no—
206C2×C4×C5C2×C22⋊C411yescharacteristic
207C2×C4×C5C2×C22⋊C412yes—
208C2×C4×C5C2×C22⋊C411yescharacteristic
209C2×C4×C5C2×M1614yes—
210C2×C4×C5C22×D412yes—
211C2×Dic5—22no—
212C2×Dic5—22no—
213C2×Dic5—22no—
214C2×Dic5—22no—
215C2×Dic5—41no—
216C2×Dic5—42no—
217C2×Dic5C2×C22⋊C411yescharacteristic
218C2×Dic5C2×C22⋊C412yes—
219C2×Dic5C2×C22⋊C412yes—
220C2×Dic5C2×C22⋊C411yescharacteristic
221C2×Dic5C2×M1614yes—
222C2×Dic5C2×M1614yes—
223C4×D5—28no—
224C4×D5—28no—
225C4×D5—24no—
226C4×D5—22no—
227C4×D5—22no—
228C4×D5—24no—
229C4×D5—24no—
230C4×D5—22no—
231C4×D5—42no—
232C4×D5—44no—
233C4×D5—44no—
234C4×D5#10114yes—
235Dic10—28no—
236Dic10—216no—
237C5×C8—44no—
238#168—44no—
239C22×Q8—52no—
240C22×Q8—51no—
241C22×Q8—102no—
242C22×Q8—102no—
243C22×Q8—108no—
244C22×Q8C4×D511yescharacteristic
245C23×C4—51no—
246C23×C4—51no—
247C23×C4—51no—
248C23×C4—52no—
249C23×C4—52no—
250C2×M16—104no—
251C4×Q8—22no—
252C4×Q8—22no—
253C4×Q8—104no—
254C4×Q8—104no—
255C4×Q8—104no—
256C4×Q8—104no—
257C4×Q8—102no—
258C4×Q8—102no—
259C4×Q8—102no—
260C4×Q8—102no—
261C4×Q8—102no—
262C4×Q8—102no—
263C2×C4⋊C4—52no—
264C2×C4⋊C4—52no—
265C2×C4⋊C4—52no—
266C2×C4⋊C4—51no—
267C2×C4⋊C4—52no—
268C2×C4⋊C4—104no—
269C2×C4⋊C4—104no—
270C2×C4⋊C4—102no—
271C2×C4⋊C4—102no—
272C2×C4⋊C4C4×D511yescharacteristic
273C2×C4⋊C4C22×D512yes—
274C2×C42—51no—
275C2×C42—51no—
276C2×C42—51no—
277C2×C42—52no—
278C2×C42—52no—
279C2×C42—52no—
280C2×C42—52no—
281C2×C42—52no—
282C2×C42—52no—
283C2×C42—52no—
284C2×C42—102no—
285C2×C42—102no—
286C2×C42—102no—
287C2×C42—102no—
288C2×C42C4×D512yes—
289C2×C42C22×D511yescharacteristic
290C4⋊C8—22no—
291C4⋊C8—104no—
292C4⋊C8—102no—
293C22⋊C8—54no—
294C22⋊C8—104no—
295C22⋊C8C22×D514yes—
296#97—22no—
297#97—102no—
298C4×C8—104no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5C22×C22⋊C411yescharacteristic
302C22×C5C22×M1612yes—
303C2×D5—28no—
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—21no—
308C2×D5#41012yes—
309C2×D5C2×#10112yes—
310C4×C5—22no—
311C4×C5—24no—
312C4×C5—22no—
313C4×C5—21no—
314C4×C5—42no—
315C4×C5C2×#10112yes—
316Dic5—24no—
317Dic5—22no—
318Dic5—21no—
319Dic5—42no—
320Dic5#40714yes—
321Dic5C2×#10112yes—
322C24—51no—
323C2×Q8—22no—
324C2×Q8—24no—
325C2×Q8—58no—
326C2×Q8—104no—
327C2×Q8—104no—
328C2×Q8—104no—
329C2×Q8—1016no—
330C2×Q8—1016no—
331C2×Q8—102no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—52no—
336C22×C4—51no—
337C22×C4—52no—
338C22×C4—51no—
339C22×C4—51no—
340C22×C4—51no—
341C22×C4—52no—
342C22×C4—52no—
343C22×C4—52no—
344C22×C4—52no—
345C22×C4—104no—
346C22×C4—104no—
347C22×C4—104no—
348C22×C4—102no—
349C22×C4—102no—
350C22×C4—102no—
351C22×C4—102no—
352C22×C4—104no—
353C22×C4—202no—
354C22×C4—204no—
355C22×C4C2×C4×D511yescharacteristic
356C22×C4C2×C4×D511yescharacteristic
357C22×C4C2×C4×D512yes—
358C22×C4C2×C4×D512yes—
359C22×C4C23×D511yescharacteristic
360M16—208no—
361C2×C8—24no—
362C2×C8—104no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—104no—
366C4⋊C4—104no—
367C4⋊C4—104no—
368C4⋊C4—104no—
369C4⋊C4—102no—
370C42—22no—
371C42—22no—
372C42—52no—
373C42—52no—
374C42—52no—
375C42—52no—
376C42—52no—
377C42—52no—
378C42—102no—
379C42—102no—
380C42—102no—
381C42—102no—
382C42—102no—
383C42—102no—
384C42D4×D512yes—
385C42D4×D512yes—
386C2×C5—22no—
387C2×C5C2×#40711yescharacteristic
388C2×C5C2×#41011yescharacteristic
389C2×C5C22×#10111yescharacteristic
390D5—22no—
391D5—22no—
392C23—51no—
393C23—51no—
394C23—102no—
395C23—102no—
396C23—102no—
397C23C22×C4×D511yescharacteristic
398Q8—28no—
399Q8—1016no—
400Q8—108no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—51no—
409C2×C4—52no—
410C2×C4—54no—
411C2×C4—54no—
412C2×C4—51no—
413C2×C4—52no—
414C2×C4—54no—
415C2×C4—104no—
416C2×C4—104no—
417C2×C4—102no—
418C2×C4—104no—
419C2×C4—102no—
420C2×C4—108no—
421C2×C4—108no—
422C2×C4—102no—
423C2×C4—102no—
424C2×C4—102no—
425C2×C4—102no—
426C2×C4—102no—
427C2×C4—202no—
428C2×C4—204no—
429C2×C4—204no—
430C2×C4—201no—
431C2×C4—202no—
432C2×C4D5×C22⋊C411yescharacteristic
433C2×C4D5×C22⋊C412yes—
434C2×C4D5×C22⋊C411yescharacteristic
435C2×C4D5×M1614yes—
436C2×C4C2×D4×D512yes—
437C8—44no—
438C8—204no—
439C5#1736511yescharacteristic, complemented, Sylow
440C22—21no—
441C22—21no—
442C22—52no—
443C22—52no—
444C22—108no—
445C22—101no—
446C22—101no—
447C22—101no—
448C22—101no—
449C22C2×D5×C22⋊C411yescharacteristic
450C22C2×D5×M1612yes—
451C4—21no—
452C4—22no—
453C4—24no—
454C4—22no—
455C4—42no—
456C4—52no—
457C4—54no—
458C4—101no—
459C4—104no—
460C4—102no—
461C4—202no—
462C4D5×#10112yes—
463C2—22no—
464C2—102no—
465C2—102no—
466C2D5×#40711yescharacteristic
467C2D5×#41011yescharacteristic
468C2C2×D5×#10111yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1467C2
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenter#1467D5
hypocenterC5#17365
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. #10602418C2semidirect
5. #10601623C2semidirect
7. #10598918C2semidirect
99. #1467D5semidirect
139. C2×Dic10M16semidirect
439. 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
#106110622
C5×#14672
#106024182
#106016232
#105989372
#105989182
#173655