Finite Group Databasebeta

← C2×#10612187 #12967337

Subgroups — C2×#10612187 #12967337

Order 1280.

2138 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C211yesmaximal, characteristic
2C2×C4×Q8×D5C211yesmaximal, characteristic
3C2×C5×#462C211yesmaximal, characteristic, complemented
4C2×#65475C212yesmaximal
5C2×Q16×Dic5C212yesmaximal, complemented
6C2×#65379C211yesmaximal, characteristic, complemented
7C2×#65310C211yesmaximal, characteristic, complemented
8#10612187C2116yesmaximal, direct product factor
9C2×#65139C211yesmaximal, characteristic, complemented
10C2×#65122C211yesmaximal, characteristic
11C2×#65098C212yesmaximal
12C2×#65079C212yesmaximal, complemented
13C22×Q8×D5C2211yescharacteristic
14C22×C5×Q16C2212yes—
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C4×C5×Q8C2211yescharacteristic
17C2×#4092C2212yes—
18C2×Q8×Dic5C2211yescharacteristic
19C2×Q8×Dic5C2212yes—
20C22×#689C2212yes—
21#66062—24no—
22#66062C2218yes—
23C4×Q8×D5—24no—
24C4×Q8×D5C2218yes—
25C2×#4043—21no—
26C2×#4038—21no—
27C2×D5×C4⋊C4—21no—
28C2×D5×C4⋊C4C2211yescharacteristic
29C2×#4036—21no—
30C2×#4033—21no—
31C2×#4033—21no—
32C2×#4033C2211yescharacteristic
33C2×C42×D5—21no—
34C2×C42×D5C2211yescharacteristic
35C2×#4015C2211yescharacteristic
36C2×C4×Dic10—21no—
37C2×C4×Dic10C2211yescharacteristic
38C5×#462C2218yescomplemented
39C2×C5×C4⋊C8C2211yescharacteristic
40C2×C5×#103C2212yes—
41C2×#3967C2212yes—
42C2×#3967C2212yes—
43#65475C22116yes—
44Q16×Dic5C22116yescomplemented
45C2×#3952C2212yes—
46C2×#3950C2212yes—
47C2×#3948C2212yes—
48C2×C8×Dic5C2212yes—
49#65379C2218yescomplemented
50#65310C2218yescomplemented
51C2×#3939C2212yes—
52C2×C4⋊#168C2211yescharacteristic
53#65139C2218yescomplemented
54#65122C2218yes—
55#65098C22116yes—
56#65079C22116yescomplemented
57C2×#3104—51nomaximal, Sylow
58C22×C5×Q8C2312yes—
59C22×C5×Q8C2311yescharacteristic
60C2×Q8×D5—24no—
61C2×Q8×D5—22no—
62C2×Q8×D5—24no—
63C2×Q8×D5C2314yes—
64C22×C4×D5—21no—
65C22×C4×D5—21no—
66C22×C4×D5D411yescharacteristic
67C22×C4×D5D411yescharacteristic
68C22×C4×D5C2311yescharacteristic
69C22×Dic10—21no—
70C22×Dic10—21no—
71C22×Dic10C2311yescharacteristic
72C2×C5×Q16—28no—
73C2×C5×Q16C2318yes—
74C22×C5×C8C2312yes—
75C5×C4⋊Q8—22no—
76C5×C4⋊Q8C2314yes—
77C4×C5×Q8—22no—
78C4×C5×Q8C2314yes—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C42×C5—21no—
84C2×C42×C5C2311yescharacteristic
85#4092—24no—
86#4092C2318yes—
87Q8×Dic5—24no—
88Q8×Dic5—22no—
89Q8×Dic5C2318yes—
90Q8×Dic5C2314yes—
91C2×#689—28no—
92C2×#689C2318yes—
93C2×#685—22no—
94C2×C4⋊Dic5—21no—
95C2×C4⋊Dic5—21no—
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5C2311yescharacteristic
98C2×C4⋊Dic5C2312yes—
99C2×#683—21no—
100C2×#683—21no—
101C2×#683—21no—
102C2×#683—22no—
103C2×C4×Dic5—21no—
104C2×C4×Dic5—21no—
105C2×C4×Dic5—21no—
106C2×C4×Dic5—22no—
107C2×C4×Dic5D411yescharacteristic
108C2×C4×Dic5D411yescharacteristic
109C2×C4×Dic5C2311yescharacteristic
110C22×#168C2312yes—
111#4043—28no—
112#4038—28no—
113D5×C4⋊C4—28no—
114D5×C4⋊C4—22no—
115D5×C4⋊C4C2314yes—
116#4036—28no—
117#4033—28no—
118#4033—28no—
119#4033—22no—
120#4033C2314yes—
121C42×D5—28no—
122C42×D5D414yes—
123C42×D5C2314yes—
124#4015—22no—
125#4015C2314yes—
126C4×Dic10—22no—
127C4×Dic10—28no—
128C4×Dic10C2314yes—
129C5×C4⋊C8C2314yes—
130C5×#103C2318yes—
131#3967C2318yes—
132#3967C2318yes—
133#3952C2318yes—
134#3950C2318yes—
135#3948C2318yes—
136C8×Dic5C2318yes—
137#3939C2318yes—
138C4⋊#168C2314yes—
139C2×#533—51no—
140C22×C4×Q8—51no—
141#3104—516no—
142C2×#484—52no—
143C2×#477—51no—
144C2×#477—51no—
145C2×#462—51no—
146C2×#462D511yescharacteristic, complemented
147C2×#451—52no—
148C2×C4×Q16—52no—
149C2×C4×Q16—52no—
150C2×#431—51no—
151C23×D5C2×D411yescharacteristic
152C2×C5×Q8—21no—
153C2×C5×Q8—22no—
154C2×C5×Q8—22no—
155C2×C5×Q8—24no—
156C2×C5×Q8—24no—
157C2×C5×Q8#4114yes—
158C2×C5×Q8C2414yes—
159C2×C5×Q8C2412yes—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—22no—
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2411yescharacteristic
166C22×Dic5—21no—
167C22×Dic5—22no—
168C22×Dic5—21no—
169C22×Dic5C2×D411yescharacteristic
170C22×Dic5C2×D411yescharacteristic
171C22×Dic5C2×D411yescharacteristic
172Q8×D5—216no—
173Q8×D5—28no—
174Q8×D5—28no—
175C2×C4×D5—28no—
176C2×C4×D5—24no—
177C2×C4×D5—22no—
178C2×C4×D5—22no—
179C2×C4×D5—24no—
180C2×C4×D5—42no—
181C2×C4×D5—44no—
182C2×C4×D5Q1618yescomplemented
183C2×C4×D5C2×D412yes—
184C2×C4×D5C2×D414yes—
185C2×C4×D5C2×D414yes—
186C2×C4×D5C2412yes—
187C2×Dic10—28no—
188C2×Dic10—21no—
189C2×Dic10—22no—
190C2×Dic10—24no—
191C2×Dic10—24no—
192C2×Dic10—44no—
193C2×Dic10#4114yes—
194C2×Dic10C2412yes—
195C5×Q16—216no—
196C2×C5×C8—24no—
197C2×C5×C8C2414yes—
198C5×C4⋊C4—24no—
199C5×C4⋊C4—24no—
200C5×C4⋊C4—24no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C2412yes—
203C42×C5—24no—
204C42×C5C2×D412yes—
205C42×C5C2412yes—
206#689—216no—
207#685—28no—
208C4⋊Dic5—21no—
209C4⋊Dic5—22no—
210C4⋊Dic5—24no—
211C4⋊Dic5—24no—
212C4⋊Dic5—28no—
213C4⋊Dic5C2414yes—
214C4⋊Dic5C2412yes—
215#683—24no—
216#683—24no—
217#683—24no—
218#683—28no—
219C4×Dic5—24no—
220C4×Dic5—24no—
221C4×Dic5—24no—
222C4×Dic5—28no—
223C4×Dic5C2×D414yes—
224C4×Dic5C2×D412yes—
225C4×Dic5C2×D414yes—
226C4×Dic5C2412yes—
227C2×#168—24no—
228C2×#168C2414yes—
229C23×Q8—51no—
230C22×Q16—52no—
231C22×Q16C2×D512yes—
232#533—58no—
233#533—104no—
234C2×C4⋊Q8—51no—
235C2×C4⋊Q8C2×D511yescharacteristic
236C2×#125—101no—
237C2×C22⋊Q8—52no—
238C2×C22⋊Q8—101no—
239C2×C4×Q8—51no—
240C2×C4×Q8—52no—
241C2×C4×Q8—58no—
242C2×C4×Q8—51no—
243C2×C4×Q8—51no—
244C2×C4×Q8—101no—
245C2×C4×Q8—101no—
246C2×C4×Q8—101no—
247C2×C4×Q8—104no—
248C2×C4×Q8C2×D511yescharacteristic
249C2×#117—101no—
250C22×C4⋊C4—51no—
251C22×C4⋊C4—101no—
252C22×C42—51no—
253C22×C42—101no—
254#484—516no—
255#477—58no—
256#477—58no—
257#462—58no—
258#462C2×D518yescomplemented
259#451—516no—
260C4×Q16—516no—
261C4×Q16—516no—
262#431—58no—
263C2×#107—52no—
264C2×#107—52no—
265C2×C4⋊C8—51no—
266C2×C4⋊C8C2×D511yescharacteristic
267C2×#103—52no—
268C2×#103—52no—
269C2×#103—52no—
270C2×#103C2×D512yes—
271C2×C22⋊C8—52no—
272C2×C4×C8—52no—
273C23×C5C22×D411yescharacteristic
274C22×D5—22no—
275C22×D5—22no—
276C22×D5C2×Q1614yes—
277C22×D5C22×D412yes—
278C5×Q8—24no—
279C5×Q8—22no—
280C5×Q8—24no—
281C5×Q8—24no—
282C5×Q8—44no—
283C5×Q8C2×#4114yes—
284C2×C4×C5—24no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—24no—
289C2×C4×C5—44no—
290C2×C4×C5—42no—
291C2×C4×C5C2×Q1614yes—
292C2×C4×C5C22×D412yes—
293C2×C4×C5C22×D411yescharacteristic
294C2×C4×C5C22×D412yes—
295C2×C4×C5C2×#4112yes—
296C2×C4×C5C2×#4112yes—
297C2×C4×C5C2511yescharacteristic
298C2×Dic5—22no—
299C2×Dic5—24no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—24no—
304C2×Dic5—44no—
305C2×Dic5—42no—
306C2×Dic5C2×Q1614yes—
307C2×Dic5C22×D412yes—
308C2×Dic5C22×D412yes—
309C2×Dic5C22×D412yes—
310C4×D5—216no—
311C4×D5—24no—
312C4×D5—22no—
313C4×D5—22no—
314C4×D5—44no—
315C4×D5—48no—
316C4×D5C2×Q16116yescomplemented
317Dic10—216no—
318Dic10—24no—
319Dic10—22no—
320Dic10—48no—
321Dic10C2×#4114yes—
322C5×C8—24no—
323#168—24no—
324C22×Q8—54no—
325C22×Q8—51no—
326C22×Q8—101no—
327C22×Q8—102no—
328C22×Q8—104no—
329C22×Q8—104no—
330C22×Q8—101no—
331C22×Q8C22×D512yes—
332C22×Q8C22×D511yescharacteristic
333C23×C4—51no—
334C23×C4—51no—
335C23×C4—51no—
336C23×C4—101no—
337C23×C4—101no—
338C2×Q16—28no—
339C2×Q16—58no—
340C2×Q16—108no—
341C2×Q16C22×D518yes—
342C22×C8—52no—
343C22×C8C22×D512yes—
344C4⋊Q8—22no—
345C4⋊Q8—54no—
346C4⋊Q8—102no—
347C4⋊Q8C22×D514yes—
348#125—108no—
349C22⋊Q8—58no—
350C22⋊Q8—108no—
351C22⋊Q8—104no—
352C4×Q8—22no—
353C4×Q8—54no—
354C4×Q8—58no—
355C4×Q8—54no—
356C4×Q8—54no—
357C4×Q8—108no—
358C4×Q8—108no—
359C4×Q8—102no—
360C4×Q8—108no—
361C4×Q8—102no—
362C4×Q8—104no—
363C4×Q8—102no—
364C4×Q8C22×D514yes—
365#117—108no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—52no—
371C2×C4⋊C4—54no—
372C2×C4⋊C4—102no—
373C2×C4⋊C4—108no—
374C2×C4⋊C4—101no—
375C2×C4⋊C4—101no—
376C2×C4⋊C4—101no—
377C2×C4⋊C4—102no—
378C2×C4⋊C4—102no—
379C2×C4⋊C4—101no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4C22×D511yescharacteristic
382C2×C22⋊C4—102no—
383C2×C42—21no—
384C2×C42—51no—
385C2×C42—51no—
386C2×C42—51no—
387C2×C42—54no—
388C2×C42—54no—
389C2×C42—108no—
390C2×C42—102no—
391C2×C42—101no—
392C2×C42—101no—
393C2×C42—101no—
394C2×C42C22×D511yescharacteristic
395#107—58no—
396#107—58no—
397C4⋊C8—54no—
398C4⋊C8C22×D514yes—
399#103—58no—
400#103—58no—
401#103—58no—
402#103C22×D518yes—
403C22⋊C8—58no—
404C4×C8—58no—
405C22×C5#52512yes—
406C22×C5C22×Q1612yes—
407C22×C5#57512yes—
408C22×C5C23×D411yescharacteristic
409C2×D5—28no—
410C2×D5—22no—
411C2×D5—22no—
412C2×D5C22×Q1614yes—
413C4×C5—24no—
414C4×C5—22no—
415C4×C5—44no—
416C4×C5—42no—
417C4×C5#52512yes—
418C4×C5C22×Q1614yes—
419C4×C5C22×#4111yescharacteristic
420C4×C5C22×#4111yescharacteristic
421Dic5—22no—
422Dic5—24no—
423Dic5—22no—
424Dic5—44no—
425Dic5—42no—
426Dic5C22×Q1614yes—
427C24—51no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—24no—
432C2×Q8—24no—
433C2×Q8—54no—
434C2×Q8—52no—
435C2×Q8—104no—
436C2×Q8—108no—
437C2×Q8—108no—
438C2×Q8—1016no—
439C2×Q8—108no—
440C2×Q8—101no—
441C2×Q8—104no—
442C2×Q8—102no—
443C2×Q8—204no—
444C2×Q8#71114yes—
445C2×Q8C23×D514yes—
446C2×Q8C23×D512yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—51no—
451C22×C4—54no—
452C22×C4—58no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—52no—
456C22×C4—52no—
457C22×C4—54no—
458C22×C4—104no—
459C22×C4—108no—
460C22×C4—104no—
461C22×C4—101no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—101no—
465C22×C4—102no—
466C22×C4—202no—
467C22×C4—204no—
468C22×C4D4×D511yescharacteristic
469C22×C4D4×D511yescharacteristic
470C22×C4C23×D511yescharacteristic
471Q16—216no—
472Q16—1016no—
473C2×C8—24no—
474C2×C8—54no—
475C2×C8—104no—
476C2×C8C23×D514yes—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—52no—
482C4⋊C4—54no—
483C4⋊C4—104no—
484C4⋊C4—104no—
485C4⋊C4—104no—
486C4⋊C4—108no—
487C4⋊C4—108no—
488C4⋊C4—101no—
489C4⋊C4—102no—
490C4⋊C4—104no—
491C4⋊C4—104no—
492C4⋊C4C23×D512yes—
493C22⋊C4—108no—
494C42—24no—
495C42—52no—
496C42—54no—
497C42—54no—
498C42—52no—
499C42—104no—
500C42—104no—
501C42—108no—
502C42—104no—
503C42D4×D512yes—
504C42C23×D512yes—
505C2×C5#310414yescomplemented
506C2×C5C2×#52511yescharacteristic
507C2×C5C23×Q1611yescharacteristic
508C2×C5C2×#57511yescharacteristic
509D5—24no—
510C23—54no—
511C23—52no—
512C23—102no—
513C23—102no—
514C23C2×D4×D511yescharacteristic
515Q8—24no—
516Q8—22no—
517Q8—24no—
518Q8—24no—
519Q8—44no—
520Q8—54no—
521Q8—1016no—
522Q8—104no—
523Q8—102no—
524Q8—208no—
525Q8C2×#71114yes—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—54no—
534C2×C4—52no—
535C2×C4—516no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—1016no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—104no—
542C2×C4—102no—
543C2×C4—104no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—104no—
548C2×C4—204no—
549C2×C4—208no—
550C2×C4—202no—
551C2×C4—204no—
552C2×C4D5×Q1614yes—
553C2×C4C2×D4×D512yes—
554C2×C4C2×D4×D512yes—
555C2×C4C2×D4×D511yescharacteristic
556C2×C4C2×#71112yes—
557C2×C4D5×#4112yes—
558C2×C4C24×D511yescharacteristic
559C8—24no—
560C8—104no—
561C5C2×#310411yescharacteristic, complemented, Sylow
562C22—54no—
563C22—102no—
564C22—108no—
565C22—102no—
566C22#6594012yes—
567C22C2×D5×Q1612yes—
568C22#6611112yes—
569C22C22×D4×D511yescharacteristic
570C4—22no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—54no—
575C4—102no—
576C4—102no—
577C4—104no—
578C4—202no—
579C4—204no—
580C4#6594012yes—
581C4C2×D5×Q1614yes—
582C4C22×#71111yescharacteristic
583C4C2×D5×#4111yescharacteristic
584C2—104no—
585C2#1061218714yesdirect product factor
586C2C2×#6594011yescharacteristic
587C2C22×D5×Q1611yescharacteristic
588C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#462C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#462D5
hypocenterC5C2×#3104
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×C5×#462C2semidirect
5. C2×Q16×Dic5C2semidirect
6. C2×#65379C2semidirect
7. C2×#65310C2semidirect
8. #10612187C2direct (N × H)
9. C2×#65139C2semidirect
12. C2×#65079C2semidirect
38. C5×#462C22semidirect
44. Q16×Dic5C22semidirect
49. #65379C22semidirect
50. #65310C22semidirect
53. #65139C22semidirect
56. #65079C22semidirect
146. C2×#462D5semidirect
182. C2×C4×D5Q16semidirect
258. #462C2×D5semidirect
316. C4×D5C2×Q16semidirect
505. C2×C5#3104semidirect
561. C5C2×#3104semidirect
585. C2#10612187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660622
C2×C4×Q8×D52
C2×C5×#4622
C2×#654752
C2×Q16×Dic52
C2×#653792
C2×#653102
#106121872
C2×#651392
C2×#651222
C2×#650982
C2×#650792
C2×#31045