Finite Group Databasebeta

← C2×#10612843 #12971348

Subgroups — C2×#10612843 #12971348

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×#65912C211yesmaximal, characteristic
3C2×C5×#477C211yesmaximal, characteristic, complemented
4C2×#65380C211yesmaximal, characteristic, complemented
5C2×#65310C211yesmaximal, characteristic, complemented
6#10612843C2116yesmaximal, direct product factor
7C2×#65173C212yesmaximal
8C2×#65163C212yesmaximal, complemented
9C2×#65139C211yesmaximal, characteristic, complemented
10C2×#65122C211yesmaximal, characteristic
11C2×#65098C212yesmaximal
12C2×#65081C212yesmaximal, complemented
13C22×Q8×D5—21no—
14C2×C5×C4⋊Q8C2211yescharacteristic
15C2×C4×C5×Q8C2211yescharacteristic
16C2×#4092C2211yescharacteristic
17C2×#4090—21no—
18C2×#4090C2211yescharacteristic
19D5×C4⋊Q8—24no—
20D5×C4⋊Q8C2218yes—
21#65912—24no—
22#65912C2218yes—
23C2×#4043C2211yescharacteristic
24C2×#4042—21no—
25C2×D5×C4⋊C4—21no—
26C2×D5×C4⋊C4C2212yes—
27C2×#4035—21no—
28C2×#4034—21no—
29C2×#4034C2212yes—
30C2×#4034C2211yescharacteristic
31C2×#4018—21no—
32C2×C42×D5C2211yescharacteristic
33C2×#4015C2211yescharacteristic
34C2×C4×Dic10—21no—
35C2×C4×Dic10C2211yescharacteristic
36C5×#477C2218yescomplemented
37C2×C5×#107C2212yes—
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#103C2212yes—
40C2×#3967C2212yes—
41C2×#3952C2212yes—
42C2×#3950C2212yes—
43C2×#3948C2212yes—
44C2×C8×Dic5C2212yes—
45#65380C2218yescomplemented
46#65310C2218yescomplemented
47C2×#3942C2212yes—
48C2×#3939C2212yes—
49C2×#3939C2212yes—
50C2×C4⋊#168C2211yescharacteristic
51#65173C22116yes—
52#65163C22116yescomplemented
53#65139C2218yescomplemented
54#65122C2218yes—
55#65098C22116yes—
56#65081C22116yescomplemented
57C2×#3230—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C22×C5×Q8C2311yescharacteristic
60C2×Q8×D5—28no—
61C2×Q8×D5—48no—
62C22×C4×D5—22no—
63C22×C4×D5D411yescharacteristic
64C22×C4×D5D411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×Dic10—21no—
67C22×Dic10—21no—
68C22×Dic10—22no—
69C22×Dic10C2311yescharacteristic
70C22×C5×C8C2312yes—
71C5×C4⋊Q8—22no—
72C5×C4⋊Q8C2314yes—
73C4×C5×Q8—22no—
74C4×C5×Q8C2314yes—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4C2312yes—
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C42×C5—21no—
80C2×C42×C5C2311yescharacteristic
81#4092—22no—
82#4092C2314yes—
83#4090—28no—
84#4090—22no—
85#4090C2314yes—
86C2×#685—21no—
87C2×#685—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2312yes—
92C2×#683—21no—
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96C2×#683—21no—
97C2×#683—22no—
98C2×#683—22no—
99C2×C4×Dic5—21no—
100C2×C4×Dic5D411yescharacteristic
101C2×C4×Dic5D411yescharacteristic
102C2×C4×Dic5C2311yescharacteristic
103C22×#168C2312yes—
104#4043—22no—
105#4043C2314yes—
106#4042—28no—
107D5×C4⋊C4—24no—
108D5×C4⋊C4—28no—
109D5×C4⋊C4C2318yes—
110#4035—28no—
111#4034—24no—
112#4034—28no—
113#4034—22no—
114#4034C2318yes—
115#4034C2314yes—
116#4018—28no—
117C42×D5D414yes—
118C42×D5C2314yes—
119#4015—22no—
120#4015C2314yes—
121C4×Dic10—22no—
122C4×Dic10—28no—
123C4×Dic10C2314yes—
124C5×#107C2318yes—
125C5×C4⋊C8C2314yes—
126C5×#103C2318yes—
127#3967C2318yes—
128#3952C2318yes—
129#3950C2318yes—
130#3948C2318yes—
131C8×Dic5C2318yes—
132#3942C2318yes—
133#3939C2318yes—
134#3939C2318yes—
135C4⋊#168C2314yes—
136C2×#533—51no—
137C22×C4⋊Q8—51no—
138#3230—516no—
139C2×#500—52no—
140C2×#487—52no—
141C2×#484—52no—
142C2×#484—52no—
143C2×#477—51no—
144C2×#477—51no—
145C2×#477—51no—
146C2×#477D511yescharacteristic, complemented
147C2×#431—51no—
148C23×D5C2×D411yescharacteristic
149C2×C5×Q8—21no—
150C2×C5×Q8—24no—
151C2×C5×Q8—22no—
152C2×C5×Q8—22no—
153C2×C5×Q8—44no—
154C2×C5×Q8C2412yes—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—22no—
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2411yescharacteristic
161C22×Dic5—22no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5C2×D411yescharacteristic
165C22×Dic5C2×D411yescharacteristic
166C22×Dic5C2×D411yescharacteristic
167Q8×D5—432no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—24no—
171C2×C4×D5—28no—
172C2×C4×D5—48no—
173C2×C4×D5Q1618yes—
174C2×C4×D5C2×D414yes—
175C2×C4×D5C2×D412yes—
176C2×C4×D5C2×D414yes—
177C2×C4×D5C2412yes—
178C2×Dic10—22no—
179C2×Dic10—22no—
180C2×Dic10—24no—
181C2×Dic10—21no—
182C2×Dic10—28no—
183C2×Dic10—24no—
184C2×Dic10—44no—
185C2×Dic10—44no—
186C2×Dic10—48no—
187C2×Dic10C2412yes—
188C2×C5×C8—24no—
189C2×C5×C8C2414yes—
190C5×C4⋊C4—24no—
191C5×C4⋊C4—24no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4C2412yes—
195C5×C4⋊C4C2414yes—
196C42×C5—24no—
197C42×C5C2×D412yes—
198C42×C5C2412yes—
199#685—24no—
200#685—24no—
201C4⋊Dic5—21no—
202C4⋊Dic5—22no—
203C4⋊Dic5—24no—
204C4⋊Dic5—24no—
205C4⋊Dic5C2412yes—
206C4⋊Dic5C2414yes—
207#683—24no—
208#683—24no—
209#683—24no—
210#683—24no—
211#683—24no—
212#683—28no—
213#683—28no—
214C4×Dic5—24no—
215C4×Dic5C2×D414yes—
216C4×Dic5C2×D412yes—
217C4×Dic5C2×D414yes—
218C4×Dic5C2412yes—
219C2×#168—24no—
220C2×#168C2414yes—
221C23×Q8—101no—
222#533—58no—
223#533—104no—
224C2×C4⋊Q8—58no—
225C2×C4⋊Q8—52no—
226C2×C4⋊Q8—51no—
227C2×C4⋊Q8—51no—
228C2×C4⋊Q8—51no—
229C2×C4⋊Q8—101no—
230C2×C4⋊Q8—104no—
231C2×C4⋊Q8—101no—
232C2×C4⋊Q8C2×D511yescharacteristic
233C2×#125—101no—
234C2×C22⋊Q8—51no—
235C2×C22⋊Q8—51no—
236C2×C22⋊Q8—101no—
237C2×C4×Q8—51no—
238C2×C4×Q8—101no—
239C2×C4×Q8C2×D511yescharacteristic
240C2×#117—101no—
241C22×C4⋊C4—52no—
242C22×C4⋊C4—101no—
243C22×C42—51no—
244#500—516no—
245#487—516no—
246#484—516no—
247#484—516no—
248#477—58no—
249#477—58no—
250#477—58no—
251#477C2×D518yescomplemented
252#431—58no—
253C2×#107—52no—
254C2×#107—52no—
255C2×#107—52no—
256C2×#107C2×D512yes—
257C2×C4⋊C8—51no—
258C2×C4⋊C8C2×D511yescharacteristic
259C2×#103—52no—
260C2×#103—52no—
261C2×#103—52no—
262C2×#103C2×D512yes—
263C2×C22⋊C8—52no—
264C2×C4×C8—52no—
265C23×C5C22×D411yescharacteristic
266C22×D5—22no—
267C22×D5—22no—
268C22×D5C2×Q1614yes—
269C22×D5C22×D412yes—
270C5×Q8—22no—
271C5×Q8—22no—
272C5×Q8—48no—
273C5×Q8—42no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—24no—
277C2×C4×C5—22no—
278C2×C4×C5—42no—
279C2×C4×C5—44no—
280C2×C4×C5—42no—
281C2×C4×C5C2×Q1614yes—
282C2×C4×C5C22×D412yes—
283C2×C4×C5C22×D411yescharacteristic
284C2×C4×C5C22×D412yes—
285C2×C4×C52−1+412yes—
286C2×C4×C52−1+412yes—
287C2×C4×C5C2511yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—24no—
292C2×Dic5—42no—
293C2×Dic5—44no—
294C2×Dic5—42no—
295C2×Dic5C2×Q1614yes—
296C2×Dic5AGL(1,ℤ/8)14yes—
297C2×Dic5C22×D412yes—
298C2×Dic5C22×D412yes—
299C2×Dic5C22×D412yes—
300C4×D5—24no—
301C4×D5—22no—
302C4×D5—22no—
303C4×D5—28no—
304C4×D5—416no—
305C4×D5C2×Q16116yes—
306Dic10—22no—
307Dic10—22no—
308Dic10—48no—
309Dic10—42no—
310Dic10—48no—
311Dic10—416no—
312C5×C8—24no—
313#168—24no—
314C22×Q8—21no—
315C22×Q8—51no—
316C22×Q8—101no—
317C22×Q8—102no—
318C22×Q8—108no—
319C22×Q8—101no—
320C22×Q8—208no—
321C22×Q8C22×D511yescharacteristic
322C23×C4—51no—
323C23×C4—51no—
324C23×C4—51no—
325C23×C4—102no—
326C22×C8—52no—
327C22×C8C22×D512yes—
328C4⋊Q8—22no—
329C4⋊Q8—58no—
330C4⋊Q8—54no—
331C4⋊Q8—54no—
332C4⋊Q8—54no—
333C4⋊Q8—108no—
334C4⋊Q8—104no—
335C4⋊Q8—102no—
336C4⋊Q8—108no—
337C4⋊Q8—102no—
338C4⋊Q8—102no—
339C4⋊Q8C22×D514yes—
340#125—108no—
341C22⋊Q8—54no—
342C22⋊Q8—54no—
343C22⋊Q8—102no—
344C22⋊Q8—108no—
345C22⋊Q8—102no—
346C4×Q8—22no—
347C4×Q8—54no—
348C4×Q8—108no—
349C4×Q8—102no—
350C4×Q8C22×D514yes—
351#117—108no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—52no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—58no—
357C2×C4⋊C4—104no—
358C2×C4⋊C4—108no—
359C2×C4⋊C4—102no—
360C2×C4⋊C4—102no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4—101no—
365C2×C4⋊C4—101no—
366C2×C4⋊C4—101no—
367C2×C4⋊C4—101no—
368C2×C4⋊C4C22×D512yes—
369C2×C4⋊C4C22×D511yescharacteristic
370C2×C22⋊C4—101no—
371C2×C22⋊C4—101no—
372C2×C42—21no—
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—51no—
376C2×C42—54no—
377C2×C42—54no—
378C2×C42—101no—
379C2×C42C22×D511yescharacteristic
380#107—58no—
381#107—58no—
382#107—58no—
383#107C22×D518yes—
384C4⋊C8—54no—
385C4⋊C8C22×D514yes—
386#103—58no—
387#103—58no—
388#103—58no—
389#103C22×D518yes—
390C22⋊C8—58no—
391C4×C8—58no—
392C22×C5#53612yes—
393C22×C5C22×Q1612yes—
394C22×C5C2×AGL(1,ℤ/8)12yes—
395C22×C5C23×D411yescharacteristic
396C2×D5—22no—
397C2×D5—28no—
398C2×D5—22no—
399C2×D5C22×Q1614yes—
400C4×C5—22no—
401C4×C5—42no—
402C4×C5—44no—
403C4×C5—42no—
404C4×C5#53612yes—
405C4×C5C22×Q1614yes—
406C4×C5C2×2−1+411yescharacteristic
407C4×C5C2×2−1+411yescharacteristic
408Dic5—22no—
409Dic5—42no—
410Dic5—44no—
411Dic5—42no—
412Dic5C22×Q1614yes—
413Dic5C2×AGL(1,ℤ/8)14yes—
414C24—51no—
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—44no—
420C2×Q8—52no—
421C2×Q8—104no—
422C2×Q8—108no—
423C2×Q8—101no—
424C2×Q8—104no—
425C2×Q8—102no—
426C2×Q8—102no—
427C2×Q8—204no—
428C2×Q8—208no—
429C2×Q8—204no—
430C2×Q8—2032no—
431C2×Q8C23×D512yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—54no—
438C22×C4—58no—
439C22×C4—51no—
440C22×C4—52no—
441C22×C4—54no—
442C22×C4—52no—
443C22×C4—104no—
444C22×C4—108no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—102no—
450C22×C4—208no—
451C22×C4D4×D511yescharacteristic
452C22×C4D4×D511yescharacteristic
453C22×C4C23×D511yescharacteristic
454C2×C8—24no—
455C2×C8—54no—
456C2×C8—104no—
457C2×C8C23×D514yes—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—54no—
463C4⋊C4—52no—
464C4⋊C4—108no—
465C4⋊C4—108no—
466C4⋊C4—104no—
467C4⋊C4—104no—
468C4⋊C4—104no—
469C4⋊C4—104no—
470C4⋊C4—104no—
471C4⋊C4—102no—
472C4⋊C4—101no—
473C4⋊C4—104no—
474C4⋊C4—104no—
475C4⋊C4C23×D514yes—
476C4⋊C4C23×D512yes—
477C22⋊C4—104no—
478C22⋊C4—104no—
479C42—24no—
480C42—54no—
481C42—54no—
482C42—52no—
483C42—52no—
484C42—104no—
485C42D4×D512yes—
486C42C23×D512yes—
487C2×C5#323014yescomplemented
488C2×C5C2×#53611yescharacteristic
489C2×C5C23×Q1611yescharacteristic
490C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
491D5—24no—
492C23—54no—
493C23—52no—
494C23—102no—
495C23—102no—
496C23C2×D4×D511yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—48no—
500Q8—42no—
501Q8—102no—
502Q8—102no—
503Q8—208no—
504Q8—2016no—
505Q8—208no—
506Q8—202no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—54no—
515C2×C4—54no—
516C2×C4—52no—
517C2×C4—52no—
518C2×C4—516no—
519C2×C4—52no—
520C2×C4—108no—
521C2×C4—102no—
522C2×C4—104no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—104no—
528C2×C4—2016no—
529C2×C4—204no—
530C2×C4—202no—
531C2×C4—202no—
532C2×C4D5×Q1614yes—
533C2×C4C2×D4×D512yes—
534C2×C4C2×D4×D512yes—
535C2×C4C2×D4×D511yescharacteristic
536C2×C4#414712yes—
537C2×C4#415012yes—
538C2×C4C24×D511yescharacteristic
539C8—24no—
540C8—104no—
541C5C2×#323011yescharacteristic, complemented, Sylow
542C22—54no—
543C22—102no—
544C22—108no—
545C22—102no—
546C22#6596212yes—
547C22C2×D5×Q1612yes—
548C22D5×AGL(1,ℤ/8)12yes—
549C22C22×D4×D511yescharacteristic
550C4—22no—
551C4—42no—
552C4—44no—
553C4—42no—
554C4—54no—
555C4—54no—
556C4—102no—
557C4—202no—
558C4—204no—
559C4—202no—
560C4#6596212yes—
561C4C2×D5×Q1614yes—
562C4C2×#414711yescharacteristic
563C4C2×#415011yescharacteristic
564C2—104no—
565C2#1061284314yesdirect product factor
566C2C2×#6596211yescharacteristic
567C2C22×D5×Q1611yescharacteristic
568C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#477C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#477D5
hypocenterC5C2×#3230
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×C5×#477C2semidirect
4. C2×#65380C2semidirect
5. C2×#65310C2semidirect
6. #10612843C2direct (N × H)
8. C2×#65163C2semidirect
9. C2×#65139C2semidirect
12. C2×#65081C2semidirect
36. C5×#477C22semidirect
45. #65380C22semidirect
46. #65310C22semidirect
52. #65163C22semidirect
53. #65139C22semidirect
56. #65081C22semidirect
146. C2×#477D5semidirect
251. #477C2×D5semidirect
487. C2×C5#3230semidirect
541. C5C2×#3230semidirect
565. C2#10612843direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×#659122
C2×C5×#4772
C2×#653802
C2×#653102
#106128432
C2×#651732
C2×#651632
C2×#651392
C2×#651222
C2×#650982
C2×#650812
C2×#32305