Finite Group Databasebeta

← C2×#10599073 #12066539

Subgroups — C2×#10599073 #12066539

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×#65934C211yesmaximal, characteristic
2C2×#65008C211yesmaximal, characteristic, complemented
3C2×#64939C211yesmaximal, characteristic, complemented
4C2×C5×#327C211yesmaximal, characteristic
5C2×#64757C211yesmaximal, characteristic
6C2×#64687C211yesmaximal, characteristic, complemented
7C2×#64672C211yesmaximal, characteristic, complemented
8#10599073C218yesmaximal, direct product factor
9C2×C5×#121C2211yescharacteristic
10C2×#4082C411yescharacteristic, complemented
11C2×#4081—21no—
12C2×D4×Dic5—21no—
13C2×D4×Dic5C411yescharacteristic, complemented
14C2×#4070C2211yescharacteristic
15C22×#683—21no—
16C22×C4×Dic5C2211yescharacteristic
17#65934—22no—
18#65934—22no—
19#65934C414yescomplemented
20#65934C2214yes—
21C2×#4036C411yescharacteristic, complemented
22C2×#4033C411yescharacteristic, complemented
23C2×#4025—21no—
24C2×#4023—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×#327C2214yes—
37#64757C2214yes—
38#64687C2214yescomplemented
39#64672C2214yescomplemented
40C2×#1512—51nomaximal, Sylow
41C22×C5×D4—21no—
42C22×C5×D4C2×C411yescharacteristic
43C23×C4×C5—21no—
44C23×C4×C5C2311yescharacteristic
45C23×Dic5—21no—
46C23×Dic5—21no—
47C23×Dic5D411yescharacteristic
48C23×Dic5D411yescharacteristic
49C22×Dic10C2×C411yescharacteristic
50C22×C5×C8—21no—
51C5×#121—21no—
52C5×#121—21no—
53C5×#121C2×C412yes—
54C5×#121C2312yes—
55C2×C5×C4⋊C4C2×C411yescharacteristic
56C2×C5×C22⋊C4—21no—
57C2×C22⋊Dic5—21no—
58C2×C22⋊Dic5—21no—
59C2×C22⋊Dic5—21no—
60C2×C22⋊Dic5—21no—
61#4082—22no—
62#4082C2×C414yescomplemented
63#4081—24no—
64#4081—24no—
65D4×Dic5—24no—
66D4×Dic5—24no—
67D4×Dic5—22no—
68D4×Dic5C2×C414yescomplemented
69C2×C4⋊Dic5—21no—
70C2×C4⋊Dic5C2×C411yescharacteristic
71#4070—21no—
72#4070—21no—
73#4070C2×C412yes—
74#4070C2312yes—
75C2×#683—21no—
76C2×#683—21no—
77C2×#683—21no—
78C2×#683—24no—
79C2×#683—44no—
80C2×C4×Dic5—21no—
81C2×C4×Dic5C2×C411yescharacteristic
82C2×C4×Dic5C2×C411yescharacteristic
83C2×C4×Dic5C2×C412yes—
84C2×C4×Dic5D412yes—
85C2×C4×Dic5D411yescharacteristic
86C2×C4×Dic5D411yescharacteristic
87C2×C4×Dic5D412yes—
88C2×C4×Dic5C2312yes—
89C22×#168—21no—
90#4036—22no—
91#4036C2×C414yescomplemented
92#4033—22no—
93#4033C2×C414yescomplemented
94#4025—24no—
95#4025—24no—
96#4023—24no—
97#4023—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×#328—51no—
115C2×#327—51no—
116C2×#327D511yescharacteristic
117C24×C5—21no—
118C24×C5C2×D411yescharacteristic
119C2×C5×D4—22no—
120C2×C5×D4—22no—
121C2×C5×D4—21no—
122C2×C5×D4—42no—
123C2×C5×D4—42no—
124C2×C5×D4—42no—
125C2×C5×D4C22×C412yes—
126C22×C4×C5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—42no—
129C22×C4×C5—42no—
130C22×C4×C5—42no—
131C22×C4×C5—42no—
132C22×C4×C5C22×C411yescharacteristic
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C2×D411yescharacteristic
135C22×C4×C5C2×D411yescharacteristic
136C22×C4×C5C2×D411yescharacteristic
137C22×C4×C5C2411yescharacteristic
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—21no—
141C22×Dic5—21no—
142C22×Dic5—24no—
143C22×Dic5—22no—
144C22×Dic5—42no—
145C22×Dic5—44no—
146C22×Dic5—42no—
147C22×Dic5—42no—
148C22×Dic5—42no—
149C22×Dic5C22⋊C411yescharacteristic
150C22×Dic5C22⋊C411yescharacteristic
151C22×Dic5C22⋊C411yescharacteristic
152C22×Dic5C22⋊C411yescharacteristic
153C22×Dic5C22⋊C412yes—
154C22×Dic5C22⋊C412yes—
155C22×Dic5C2×D412yes—
156C22×Dic5C2×D412yes—
157C2×Dic10—21no—
158C2×Dic10—42no—
159C2×Dic10C22×C412yes—
160C2×C5×C8—22no—
161C2×C5×C8—42no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4C22×C412yes—
164C5×C22⋊C4—22no—
165C5×C22⋊C4—22no—
166C22⋊Dic5—22no—
167C22⋊Dic5—22no—
168C22⋊Dic5—24no—
169C22⋊Dic5—24no—
170C22⋊Dic5—24no—
171C4⋊Dic5—21no—
172C4⋊Dic5—24no—
173C4⋊Dic5C22×C412yes—
174#683—22no—
175#683—22no—
176#683—24no—
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⋊Q8—51no—
199C2×#121C2×D511yescharacteristic
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#328—54no—
219#327—54no—
220#327C2×D514yes—
221C23×C5—22no—
222C23×C5—22no—
223C23×C5—22no—
224C23×C5—42no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5C2×C22⋊C411yescharacteristic
228C23×C5C2×C22⋊C411yescharacteristic
229C23×C5AGL(1,ℤ/8)12yes—
230C23×C5#13712yes—
231C23×C5C22×D411yescharacteristic
232C5×D4—42no—
233C5×D4—42no—
234C5×D4—42no—
235C5×D4—42no—
236C5×D4—44no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—84no—
249C2×C4×C5C2×C22⋊C411yescharacteristic
250C2×C4×C5C2×C22⋊C411yescharacteristic
251C2×C4×C5C23×C411yescharacteristic
252C2×C4×C5C22×D411yescharacteristic
253C2×Dic5—22no—
254C2×Dic5—22no—
255C2×Dic5—24no—
256C2×Dic5—22no—
257C2×Dic5—22no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—22no—
261C2×Dic5—22no—
262C2×Dic5—42no—
263C2×Dic5—42no—
264C2×Dic5—48no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—84no—
271C2×Dic5C2×C22⋊C412yes—
272C2×Dic5C2×C22⋊C412yes—
273C2×Dic5C2×C22⋊C412yes—
274C2×Dic5C2×C22⋊C412yes—
275Dic10—42no—
276Dic10—42no—
277C5×C8—42no—
278#168—42no—
279C22×Q8—51no—
280C22×D4—21no—
281C22×D4C4×D511yescharacteristic
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—52no—
299C22⋊Q8—52no—
300C22⋊Q8—101no—
301C22⋊Q8—101no—
302#121—21no—
303#121—21no—
304#121C4×D512yes—
305#121C22×D512yes—
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—51no—
315C2×C4⋊C4—101no—
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—42no—
354C22×C5—42no—
355C22×C5—42no—
356C22×C5—84no—
357C22×C5#41012yes—
358C22×C5#41712yes—
359C22×C5#41712yes—
360C22×C5#42112yes—
361C22×C5C22×C22⋊C411yescharacteristic
362C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C5C2×#13711yescharacteristic
364C4×C5—21no—
365C4×C5—21no—
366C4×C5—21no—
367C4×C5—21no—
368C4×C5—42no—
369C4×C5—82no—
370Dic5—22no—
371Dic5—22no—
372Dic5—22no—
373Dic5—22no—
374Dic5—42no—
375Dic5—42no—
376Dic5—82no—
377C24—21no—
378C24D4×D511yescharacteristic
379C2×Q8—52no—
380C2×Q8—101no—
381C2×Q8—202no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4C2×C4×D512yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—52no—
396C22×C4—52no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—51no—
400C22×C4—51no—
401C22×C4—52no—
402C22×C4—52no—
403C22×C4—104no—
404C22×C4—102no—
405C22×C4—102no—
406C22×C4—101no—
407C22×C4—101no—
408C22×C4—102no—
409C22×C4—202no—
410C22×C4—204no—
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—21no—
425C4⋊C4—52no—
426C4⋊C4—104no—
427C4⋊C4—104no—
428C4⋊C4—104no—
429C4⋊C4—102no—
430C4⋊C4—101no—
431C4⋊C4—102no—
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—82no—
454C2×C5#151214yescomplemented
455C2×C5C2×#41011yescharacteristic
456C2×C5C2×#41711yescharacteristic
457C2×C5C2×#42111yescharacteristic
458C23—22no—
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23D5×C22⋊C411yescharacteristic
465C23D5×C22⋊C411yescharacteristic
466C23#405712yes—
467C23#406112yes—
468C23C2×D4×D511yescharacteristic
469Q8—202no—
470Q8—202no—
471D4—42no—
472D4—42no—
473D4—44no—
474D4—42no—
475D4—42no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—52no—
488C2×C4—52no—
489C2×C4—52no—
490C2×C4—52no—
491C2×C4—84no—
492C2×C4—104no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—102no—
501C2×C4—202no—
502C2×C4—202no—
503C2×C4—208no—
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—42no—
524C22—42no—
525C22—42no—
526C22—84no—
527C22#6502912yes—
528C22#6506012yes—
529C22#6506012yes—
530C22#6511012yes—
531C22C2×D5×C22⋊C411yescharacteristic
532C22C2×#405711yescharacteristic
533C22C2×#406111yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—82no—
540C4—102no—
541C4—102no—
542C4—102no—
543C4—102no—
544C4—202no—
545C4—202no—
546C4—402no—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—82no—
551C2#1059907314yesdirect product factor
552C2C2×#6502911yescharacteristic
553C2C2×#6506011yescharacteristic
554C2C2×#6511011yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#327C2
socleC23×C5C2×C22⋊C4
prime radicalC2×C5×#121C22
cosocleC22×C4×C5C24
hypercenterC2×#327D5
hypocenterC5C2×#1512
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#65008C2semidirect
3. C2×#64939C2semidirect
6. C2×#64687C2semidirect
7. C2×#64672C2semidirect
8. #10599073C2direct (N × H)
10. C2×#4082C4semidirect
13. C2×D4×Dic5C4semidirect
19. #65934C4semidirect
21. C2×#4036C4semidirect
22. C2×#4033C4semidirect
33. #65008C22semidirect
35. #64939C22semidirect
38. #64687C22semidirect
39. #64672C22semidirect
62. #4082C2×C4semidirect
68. D4×Dic5C2×C4semidirect
91. #4036C2×C4semidirect
93. #4033C2×C4semidirect
454. C2×C5#1512semidirect
516. C5C2×#1512semidirect
551. C2#10599073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659342
C2×#650082
C2×#649392
C2×C5×#3272
C2×#647572
C2×#646872
C2×#646722
#105990732
C2×#15125