Finite Group Databasebeta

← C2×#10599105 #12066541

Subgroups — C2×#10599105 #12066541

Order 1280.

1098 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65958C211yesmaximal, characteristic
2C2×#65008C211yesmaximal, characteristic, complemented
3C2×#64939C211yesmaximal, characteristic, complemented
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×#64758C211yesmaximal, characteristic, complemented
6C2×#64690C211yesmaximal, characteristic
7C2×#64671C211yesmaximal, characteristic
8#10599105C218yesmaximal, direct product factor
9C2×C5×C22⋊Q8C2211yescharacteristic
10C2×#4093C411yescharacteristic, complemented
11C2×Q8×Dic5C411yescharacteristic, complemented
12C2×#4076C2211yescharacteristic
13C22×#683—21no—
14C22×C4×Dic5C2211yescharacteristic
15#65958—22no—
16#65958—22no—
17#65958C414yescomplemented
18#65958C2214yes—
19C2×#4044—21no—
20C2×#4039C411yescharacteristic, complemented
21C2×#4038—21no—
22C2×#4036C411yescharacteristic, complemented
23C2×#4032—21no—
24C2×#4027—21no—
25C2×C5×C22⋊C8C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×#3963—21no—
28C2×#3963C2211yescharacteristic
29C2×C22⋊#168C2211yescharacteristic
30C2×#3947—21no—
31C2×#3946—21no—
32#65008—22no—
33#65008C2214yescomplemented
34#64939—22no—
35#64939C2214yescomplemented
36C5×#328C2214yescomplemented
37#64758C2214yescomplemented
38#64690C2214yes—
39#64671C2214yes—
40C2×#1512—51nomaximal, Sylow
41C22×C5×Q8C2×C411yescharacteristic
42C23×C4×C5—21no—
43C23×C4×C5C2311yescharacteristic
44C22×C22⋊D5—21no—
45C23×Dic5—21no—
46C23×Dic5D411yescharacteristic
47C23×Dic5D411yescharacteristic
48C22×D20C2×C411yescharacteristic
49C22×C4×D5—21no—
50C22×C5×C8—21no—
51C5×C22⋊Q8—21no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8C2×C412yes—
54C5×C22⋊Q8C2312yes—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4C2×C411yescharacteristic
57C2×C5×C22⋊C4—21no—
58#4093—22no—
59#4093C2×C414yescomplemented
60Q8×Dic5—22no—
61Q8×Dic5C2×C414yescomplemented
62#4076—21no—
63#4076—21no—
64#4076C2×C412yes—
65#4076C2312yes—
66C2×#685—21no—
67C2×#685—21no—
68C2×#685—21no—
69C2×#685—21no—
70C2×C4⋊Dic5—21no—
71C2×C4⋊Dic5—21no—
72C2×C4⋊Dic5C2×C411yescharacteristic
73C2×#683—21no—
74C2×#683—24no—
75C2×#683—44no—
76C2×C4×Dic5—21no—
77C2×C4×Dic5C2×C411yescharacteristic
78C2×C4×Dic5C2×C411yescharacteristic
79C2×C4×Dic5C2×C412yes—
80C2×C4×Dic5D412yes—
81C2×C4×Dic5D411yescharacteristic
82C2×C4×Dic5D411yescharacteristic
83C2×C4×Dic5D412yes—
84C2×C4×Dic5C2312yes—
85C22×#168—21no—
86#4044—24no—
87#4044—24no—
88#4039—22no—
89#4039C2×C414yescomplemented
90#4038—24no—
91#4038—24no—
92#4036—22no—
93#4036C2×C414yescomplemented
94#4032—24no—
95#4032—24no—
96#4027—24no—
97#4027—24no—
98C5×C22⋊C8—21no—
99C5×C22⋊C8C2312yes—
100C5×#95—21no—
101C5×#95C2312yes—
102#3963—21no—
103#3963—24no—
104#3963C2312yes—
105C22⋊#168—21no—
106C22⋊#168C2312yes—
107#3947—24no—
108#3946—24no—
109C2×#529—51no—
110C2×#432—51no—
111C2×#382—51no—
112#1512—58no—
113C2×#328—51no—
114C2×#328D511yescharacteristic, complemented
115C2×#327—51no—
116C2×#327—51no—
117C24×C5C2×D411yescharacteristic
118C23×D5—21no—
119C2×C5×Q8—21no—
120C2×C5×Q8—42no—
121C2×C5×Q8C22×C412yes—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—42no—
126C22×C4×C5—42no—
127C22×C4×C5—42no—
128C22×C4×C5—42no—
129C22×C4×C5C22×C411yescharacteristic
130C22×C4×C5C22×C411yescharacteristic
131C22×C4×C5C2×D411yescharacteristic
132C22×C4×C5C2×D411yescharacteristic
133C22×C4×C5C2×D411yescharacteristic
134C22×C4×C5C2411yescharacteristic
135C2×C22⋊D5—22no—
136C2×C22⋊D5—22no—
137C2×C22⋊D5—42no—
138C2×C22⋊D5—42no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—21no—
142C22×Dic5—22no—
143C22×Dic5—42no—
144C22×Dic5—42no—
145C22×Dic5—42no—
146C22×Dic5—42no—
147C22×Dic5C22⋊C411yescharacteristic
148C22×Dic5C22⋊C412yes—
149C22×Dic5C22⋊C411yescharacteristic
150C22×Dic5C22⋊C411yescharacteristic
151C22×Dic5C22⋊C411yescharacteristic
152C22×Dic5C22⋊C412yes—
153C22×Dic5C2×D412yes—
154C22×Dic5C2×D412yes—
155C2×D20—21no—
156C2×D20—42no—
157C2×D20C22×C412yes—
158C2×C4×D5—24no—
159C2×C4×D5—44no—
160C2×C5×C8—22no—
161C2×C5×C8—42no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4C22×C412yes—
166C5×C22⋊C4—22no—
167C5×C22⋊C4—22no—
168#685—22no—
169#685—22no—
170#685—24no—
171#685—24no—
172#685—24no—
173C4⋊Dic5—21no—
174C4⋊Dic5—24no—
175C4⋊Dic5—24no—
176C4⋊Dic5C22×C412yes—
177#683—24no—
178#683—48no—
179C4×Dic5—24no—
180C4×Dic5C22⋊C412yes—
181C4×Dic5C22⋊C412yes—
182C4×Dic5C22⋊C412yes—
183C4×Dic5C22⋊C412yes—
184C4×Dic5C22×C412yes—
185C4×Dic5C22×C412yes—
186C4×Dic5C2×D412yes—
187C4×Dic5C2×D412yes—
188C2×#168—22no—
189C2×#168—42no—
190#529—54no—
191#529—54no—
192#529—102no—
193#529—102no—
194C2×#126—101no—
195C2×#125—51no—
196C2×#124—51no—
197C2×#123—101no—
198C2×C22⋊Q8C2×D511yescharacteristic
199C2×#121—51no—
200C2×C4×Q8—51no—
201C2×C4×D4—51no—
202C2×C4×D4—101no—
203C2×#117—101no—
204C22×C4⋊C4—101no—
205C22×C42—51no—
206#432—54no—
207#432—102no—
208C2×C4⋊C8—101no—
209C2×C22⋊C8—51no—
210C2×C22⋊C8C2×D511yescharacteristic
211C2×#97—101no—
212#382—54no—
213#382—102no—
214C2×#95—51no—
215C2×#95—101no—
216C2×#95C2×D511yescharacteristic
217#328—54no—
218#328C2×D514yescomplemented
219#327—54no—
220#327—54no—
221C23×C5—22no—
222C23×C5—22no—
223C23×C5C2×C22⋊C411yescharacteristic
224C23×C5C2×C22⋊C411yescharacteristic
225C23×C5AGL(1,ℤ/8)12yes—
226C23×C5#13712yes—
227C23×C5C22×D411yescharacteristic
228C22×D5—22no—
229C22×D5—42no—
230C22×D5—42no—
231C22×D5—42no—
232C5×Q8—42no—
233C5×Q8—42no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—84no—
248C2×C4×C5C2×C22⋊C411yescharacteristic
249C2×C4×C5C2×C22⋊C411yescharacteristic
250C2×C4×C5C23×C411yescharacteristic
251C2×C4×C5C22×D411yescharacteristic
252C22⋊D5—42no—
253C22⋊D5—42no—
254C22⋊D5—44no—
255C2×Dic5—22no—
256C2×Dic5—22no—
257C2×Dic5—24no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—22no—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—42no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—84no—
270C2×Dic5C2×C22⋊C412yes—
271C2×Dic5C2×C22⋊C412yes—
272C2×Dic5C2×C22⋊C412yes—
273C2×Dic5C2×C22⋊C412yes—
274D20—42no—
275D20—42no—
276C4×D5—48no—
277C5×C8—42no—
278#168—42no—
279C22×Q8C4×D511yescharacteristic
280C22×D4—51no—
281C22×D4—101no—
282C23×C4—21no—
283C23×C4—51no—
284C23×C4—51no—
285C23×C4—101no—
286C23×C4—101no—
287C23×C4C22×D511yescharacteristic
288C22×C8—21no—
289C22×C8—101no—
290#126—104no—
291#126—104no—
292#125—54no—
293#125—102no—
294#124—54no—
295#124—102no—
296#123—104no—
297#123—104no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8C4×D512yes—
301C22⋊Q8C22×D512yes—
302#121—52no—
303#121—52no—
304#121—101no—
305#121—101no—
306C4×Q8—54no—
307C4×Q8—102no—
308C4×D4—54no—
309C4×D4—102no—
310C4×D4—104no—
311C4×D4—104no—
312#117—104no—
313#117—104no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—51no—
316C2×C4⋊C4—101no—
317C2×C4⋊C4—101no—
318C2×C4⋊C4—101no—
319C2×C4⋊C4—104no—
320C2×C4⋊C4—204no—
321C2×C4⋊C4C4×D511yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—101no—
324C2×C22⋊C4—101no—
325C2×C22⋊C4—101no—
326C2×C22⋊C4—101no—
327C2×C42—51no—
328C2×C42—51no—
329C2×C42—52no—
330C2×C42—51no—
331C2×C42—51no—
332C2×C42—52no—
333C2×C42—52no—
334C2×C42—52no—
335C2×C42—101no—
336C4⋊C8—104no—
337C22⋊C8—21no—
338C22⋊C8—52no—
339C22⋊C8—101no—
340C22⋊C8C22×D512yes—
341#97—104no—
342#95—21no—
343#95—52no—
344#95—104no—
345#95—101no—
346#95C22×D512yes—
347C22×C5—21no—
348C22×C5—21no—
349C22×C5—21no—
350C22×C5—21no—
351C22×C5—24no—
352C22×C5—24no—
353C22×C5#41012yes—
354C22×C5#41712yes—
355C22×C5#41712yes—
356C22×C5#42112yes—
357C22×C5C22×C22⋊C411yescharacteristic
358C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C5C2×#13711yescharacteristic
360C2×D5—42no—
361C2×D5—42no—
362C2×D5—42no—
363C2×D5—84no—
364C4×C5—21no—
365C4×C5—21no—
366C4×C5—21no—
367C4×C5—21no—
368C4×C5—42no—
369C4×C5—42no—
370C4×C5—82no—
371Dic5—22no—
372Dic5—22no—
373Dic5—22no—
374Dic5—22no—
375Dic5—42no—
376Dic5—82no—
377C24—101no—
378C24D4×D511yescharacteristic
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8C2×C4×D512yes—
382C2×D4—52no—
383C2×D4—102no—
384C2×D4—102no—
385C2×D4—101no—
386C2×D4—202no—
387C2×D4—202no—
388C2×D4—202no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—52no—
397C22×C4—52no—
398C22×C4—51no—
399C22×C4—51no—
400C22×C4—51no—
401C22×C4—51no—
402C22×C4—52no—
403C22×C4—52no—
404C22×C4—104no—
405C22×C4—102no—
406C22×C4—102no—
407C22×C4—101no—
408C22×C4—102no—
409C22×C4—204no—
410C22×C4—202no—
411C22×C4—202no—
412C22×C4—202no—
413C22×C4—202no—
414C22×C4C2×C4×D511yescharacteristic
415C22×C4C2×C4×D511yescharacteristic
416C22×C4D4×D511yescharacteristic
417C22×C4D4×D511yescharacteristic
418C22×C4D4×D511yescharacteristic
419C22×C4C23×D511yescharacteristic
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—102no—
423C2×C8—202no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—52no—
428C4⋊C4—104no—
429C4⋊C4—104no—
430C4⋊C4—104no—
431C4⋊C4—101no—
432C4⋊C4—208no—
433C4⋊C4C2×C4×D512yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—104no—
437C22⋊C4—104no—
438C22⋊C4—104no—
439C22⋊C4—102no—
440C22⋊C4—102no—
441C42—52no—
442C42—52no—
443C42—52no—
444C42—52no—
445C42—52no—
446C42—52no—
447C42—52no—
448C42—52no—
449C42—104no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—22no—
453C2×C5#151214yescomplemented
454C2×C5C2×#41011yescharacteristic
455C2×C5C2×#41711yescharacteristic
456C2×C5C2×#42111yescharacteristic
457D5—82no—
458C23—22no—
459C23—22no—
460C23—102no—
461C23—202no—
462C23—202no—
463C23—202no—
464C23D5×C22⋊C411yescharacteristic
465C23D5×C22⋊C411yescharacteristic
466C23#406012yes—
467C23#406412yes—
468C23C2×D4×D511yescharacteristic
469Q8—42no—
470Q8—42no—
471D4—202no—
472D4—202no—
473D4—202no—
474D4—202no—
475D4—204no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—52no—
490C2×C4—52no—
491C2×C4—52no—
492C2×C4—52no—
493C2×C4—84no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—104no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4—208no—
503C2×C4—202no—
504C2×C4—202no—
505C2×C4—202no—
506C2×C4—202no—
507C2×C4—202no—
508C2×C4—202no—
509C2×C4—404no—
510C2×C4D5×C22⋊C411yescharacteristic
511C2×C4D5×C22⋊C411yescharacteristic
512C2×C4C22×C4×D511yescharacteristic
513C2×C4C2×D4×D511yescharacteristic
514C8—42no—
515C8—202no—
516C5C2×#151211yescharacteristic, complemented, Sylow
517C22—21no—
518C22—21no—
519C22—24no—
520C22—24no—
521C22—21no—
522C22—21no—
523C22—202no—
524C22—202no—
525C22—202no—
526C22—404no—
527C22#6502912yes—
528C22#6509212yes—
529C22#6509212yes—
530C22#6511012yes—
531C22C2×D5×C22⋊C411yescharacteristic
532C22C2×#406011yescharacteristic
533C22C2×#406411yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—42no—
540C4—82no—
541C4—102no—
542C4—102no—
543C4—102no—
544C4—102no—
545C4—202no—
546C4—402no—
547C2—21no—
548C2—21no—
549C2—22no—
550C2—402no—
551C2#1059910514yesdirect product factor
552C2C2×#6502911yescharacteristic
553C2C2×#6509211yescharacteristic
554C2C2×#6511011yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#328C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#4076C22
cosocleC22×C4×C5C24
hypercenterC2×#328D5
hypocenterC5C2×#1512
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#65008C2semidirect
3. C2×#64939C2semidirect
4. C2×C5×#328C2semidirect
5. C2×#64758C2semidirect
8. #10599105C2direct (N × H)
10. C2×#4093C4semidirect
11. C2×Q8×Dic5C4semidirect
17. #65958C4semidirect
20. C2×#4039C4semidirect
22. C2×#4036C4semidirect
33. #65008C22semidirect
35. #64939C22semidirect
36. C5×#328C22semidirect
37. #64758C22semidirect
59. #4093C2×C4semidirect
61. Q8×Dic5C2×C4semidirect
89. #4039C2×C4semidirect
93. #4036C2×C4semidirect
114. C2×#328D5semidirect
218. #328C2×D5semidirect
453. C2×C5#1512semidirect
516. C5C2×#1512semidirect
551. C2#10599105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659582
C2×#650082
C2×#649392
C2×C5×#3282
C2×#647582
C2×#646902
C2×#646712
#105991052
C2×#15125