Finite Group Databasebeta

← C2×#11756896 #14514592

Subgroups — C2×#11756896 #14514592

Order 1920.

1790 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1790 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×A4C211yesmaximal, characteristic, complemented
2C2×#91958C212yesmaximal, complemented
3#11756896C218yesmaximal, direct product factor
4C2×C4⋊(C5⋊S4)C211yesmaximal, characteristic, complemented
5C2×C4×C5⋊S4C212yesmaximal, complemented
6C2×#91948C211yesmaximal, characteristic, complemented
7C2×#66125—31nomaximal, Hall
8C23×C5×A4C2211yescharacteristic
9C22×C5⋊S4C2212yes—
10C2×#6817—41nomaximal
11C2×C4×C5×A4C2211yescharacteristic
12C2×C4×C5×A4C2211yescharacteristic
13C2×C4×C5×A4C2214yescomplemented
14#91958C2218yescomplemented
15C2×A4⋊Dic5C2212yes—
16C4⋊(C5⋊S4)C2214yescomplemented
17C4×C5⋊S4C2218yescomplemented
18#91948C2214yescomplemented
19C2×#5912—51nomaximal, Hall
20C24×C4×C5D311yescharacteristic, complemented
21C22×#709—31no—
22C2×#4099—32no—
23#66125—38no—
24#66125—38no—
25C2×#4076—31no—
26C2×#4076—31no—
27C2×#4075—32no—
28C2×C4×C22⋊D5—32no—
29C2×C4×C22⋊D5—32no—
30C2×#4072—31no—
31C2×#4070—31no—
32C2×#4070—31no—
33C22×C5×A4—22no—
34C22×C5×A4C2312yes—
35C22×C5×A4C2311yescharacteristic
36C2×C5⋊S4—24no—
37C2×C5⋊S4C2314yes—
38C22×C3×C4×C5—41no—
39C2×#1220—42no—
40#6817—48no—
41C2×D60—41no—
42C2×C4×D15—42no—
43C2×Dic30—41no—
44C4×C5×A4C2312yes—
45C4×C5×A4C2312yes—
46A4⋊Dic5C2314yes—
47C22×C4×A4D511yescharacteristic, complemented
48C2×GL(2,ℤ/4)—52no—
49#5912—58no—
50C2×C4⋊S4—51no—
51C2×C4×S4—52no—
52C2×A4⋊Q8—51no—
53C25×C5C2×D311yescharacteristic
54C23×C4×C5—31no—
55C23×C4×C5—31no—
56C23×C4×C5—31no—
57C23×C4×C5—31no—
58C23×C4×C5—34no—
59C23×C4×C5C2×D311yescharacteristic
60C23×C4×C5C2×D311yescharacteristic
61C23×C4×C5C2×D314yescomplemented
62C22×C22⋊D5—32no—
63C22×C22⋊D5—32no—
64C22×C22⋊D5—32no—
65C2×#709—38no—
66C2×#709—61no—
67C2×#709—64no—
68C2×#709—61no—
69C2×#709—61no—
70C2×#709—61no—
71C22×D20—31no—
72C22×C4×D5—32no—
73C22×Dic10—31no—
74#4099—38no—
75#4099—38no—
76C2×C22⋊Dic5—32no—
77C2×C22⋊Dic5—32no—
78C2×C22⋊Dic5—32no—
79#4076—34no—
80#4076—38no—
81#4076—34no—
82#4075—316no—
83C4×C22⋊D5—38no—
84C4×C22⋊D5—316no—
85C4×C22⋊D5—38no—
86C2×#685—32no—
87C2×#685—32no—
88#4072—38no—
89C2×C4⋊Dic5—31no—
90C2×C4⋊Dic5—31no—
91#4070—34no—
92#4070—38no—
93#4070—34no—
94C2×#683—32no—
95C2×#683—32no—
96C2×C4×Dic5—32no—
97C2×#525—151noSylow
98C23×C3×C5—41no—
99C22×D15—42no—
100C2×C5×A4—22no—
101C2×C5×A4#4112yescomplemented
102C2×C5×A4C2411yescharacteristic
103C5⋊S4—24no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—44no—
107#1220—48no—
108C2×Dic15—42no—
109D60—44no—
110C4×D15—48no—
111Dic30—44no—
112C23×A4C2×D511yescharacteristic
113C22×S4—52no—
114C2×#235—201no—
115C2×C4×A4C2×D511yescharacteristic
116C2×C4×A4C2×D511yescharacteristic
117C2×C4×A4C2×D514yescomplemented
118GL(2,ℤ/4)—58no—
119C2×SL(2,ℤ/4)—52no—
120C4⋊S4—54no—
121C4×S4—58no—
122A4⋊Q8—54no—
123C24×C5—22no—
124C24×C5—31no—
125C24×C5—31no—
126C24×C5—32no—
127C24×C5—62no—
128C24×C5C22×D312yes—
129C24×C5C22×D311yescharacteristic
130C23×D5—32no—
131C22×C4×C5—31no—
132C22×C4×C5—31no—
133C22×C4×C5—31no—
134C22×C4×C5—31no—
135C22×C4×C5—31no—
136C22×C4×C5—34no—
137C22×C4×C5—34no—
138C22×C4×C5—31no—
139C22×C4×C5—31no—
140C22×C4×C5—32no—
141C22×C4×C5—32no—
142C22×C4×C5—34no—
143C22×C4×C5—34no—
144C22×C4×C5—34no—
145C22×C4×C5—62no—
146C22×C4×C5—62no—
147C22×C4×C5—61no—
148C22×C4×C5—62no—
149C22×C4×C5S411yescharacteristic, complemented
150C22×C4×C5C22×D312yes—
151C22×C4×C5C22×D312yes—
152C2×C22⋊D5—38no—
153C2×C22⋊D5—34no—
154C2×C22⋊D5—38no—
155C2×C22⋊D5—34no—
156C2×C22⋊D5—64no—
157C2×C22⋊D5—62no—
158C2×C22⋊D5—64no—
159C2×C22⋊D5—68no—
160C2×C22⋊D5—64no—
161C2×C22⋊D5—62no—
162C22×Dic5—32no—
163C22×Dic5—32no—
164C22×Dic5—32no—
165#709—68no—
166#709—68no—
167#709—68no—
168#709—68no—
169C2×D20—34no—
170C2×D20—61no—
171C2×D20—62no—
172C2×D20—61no—
173C2×C4×D5—38no—
174C2×C4×D5—62no—
175C2×C4×D5—64no—
176C2×C4×D5—62no—
177C2×Dic10—34no—
178C2×Dic10—61no—
179C2×Dic10—62no—
180C2×Dic10—61no—
181C22⋊Dic5—38no—
182C22⋊Dic5—34no—
183C22⋊Dic5—38no—
184C22⋊Dic5—34no—
185#685—38no—
186#685—38no—
187C4⋊Dic5—34no—
188C4⋊Dic5—34no—
189#683—38no—
190#683—38no—
191C4×Dic5—38no—
192C22×#41—151no—
193C24×C4D1511yescharacteristic, complemented
194#525—158no—
195#525—158no—
196C2×#123—152no—
197C2×C22⋊Q8—151no—
198C2×C22⋊Q8—151no—
199C2×#121—151no—
200C2×#121—151no—
201C2×#120—152no—
202C2×C4×D4—152no—
203C2×C4×D4—152no—
204C2×#117—151no—
205C22×C3×C5—41no—
206C22×C3×C5—42no—
207C22×C3×C5—82no—
208C2×D15—44no—
209C2×D15—84no—
210C5×A4C2×#4111yescharacteristic, complemented
211C3×C4×C5—42no—
212C3×C4×C5—42no—
213Dic15—44no—
214C22×A4—22no—
215C22×A4C22×D512yes—
216C22×A4C22×D511yescharacteristic
217C2×S4—54no—
218C2×S4—104no—
219C22×C3×C4—41no—
220C2×#67—202no—
221#235—208no—
222C2×D12—201no—
223C2×C4×D3—202no—
224C2×Dic6—201no—
225C4×A4C22×D512yes—
226C4×A4C22×D512yes—
227SL(2,ℤ/4)—54no—
228C23×C5—22no—
229C23×C5—31no—
230C23×C5—31no—
231C23×C5—32no—
232C23×C5—32no—
233C23×C5—34no—
234C23×C5—32no—
235C23×C5—32no—
236C23×C5—31no—
237C23×C5—62no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—61no—
241C23×C5—64no—
242C23×C5—62no—
243C23×C5—64no—
244C23×C5#23512yescomplemented
245C23×C5C2×S411yescharacteristic
246C23×C5C23×D311yescharacteristic
247C22×D5—34no—
248C22×D5—62no—
249C22×D5—64no—
250C22×D5—64no—
251C22×D5—62no—
252C2×C4×C5—31no—
253C2×C4×C5—31no—
254C2×C4×C5—34no—
255C2×C4×C5—32no—
256C2×C4×C5—32no—
257C2×C4×C5—32no—
258C2×C4×C5—32no—
259C2×C4×C5—34no—
260C2×C4×C5—34no—
261C2×C4×C5—32no—
262C2×C4×C5—32no—
263C2×C4×C5—61no—
264C2×C4×C5—64no—
265C2×C4×C5—61no—
266C2×C4×C5C2×S411yescharacteristic
267C2×C4×C5C2×S411yescharacteristic
268C2×C4×C5C2×S414yescomplemented
269C22⋊D5—68no—
270C22⋊D5—68no—
271C22⋊D5—64no—
272C22⋊D5—616no—
273C22⋊D5—64no—
274C22⋊D5—68no—
275C2×Dic5—34no—
276C2×Dic5—34no—
277C2×Dic5—34no—
278C2×Dic5—62no—
279C2×Dic5—64no—
280C2×Dic5—64no—
281C2×Dic5—62no—
282D20—64no—
283D20—64no—
284C4×D5—68no—
285C4×D5—68no—
286Dic10—64no—
287Dic10—64no—
288C25C2×D1511yescharacteristic
289C2×#41—158no—
290C2×#41—301no—
291C2×#41—301no—
292C2×#41—301no—
293C2×#41—304no—
294C2×#41—301no—
295C22×Q8—151no—
296C22×D4—151no—
297C22×D4—152no—
298C22×D4—152no—
299C22×D4—152no—
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—34no—
305C23×C4—152no—
306C23×C4C2×D1511yescharacteristic
307C23×C4C2×D1511yescharacteristic
308C23×C4C2×D1514yescomplemented
309#123—1516no—
310C22⋊Q8—154no—
311C22⋊Q8—158no—
312C22⋊Q8—154no—
313#121—154no—
314#121—158no—
315#121—154no—
316#120—158no—
317#120—158no—
318C4×D4—158no—
319C4×D4—1516no—
320C4×D4—158no—
321#117—158no—
322C2×C4⋊C4—151no—
323C2×C4⋊C4—151no—
324C2×C4⋊C4—152no—
325C2×C4⋊C4—152no—
326C2×C22⋊C4—152no—
327C2×C22⋊C4—152no—
328C2×C22⋊C4—152no—
329C2×C22⋊C4—152no—
330C2×C22⋊C4—152no—
331C2×C42—152no—
332C2×C3×C5—42no—
333C2×C3×C5—41no—
334C2×C3×C5—82no—
335D15—84no—
336C23×C3—41no—
337C22×D3—202no—
338C2×A4—22no—
339C2×A4#70912yescomplemented
340C2×A4C23×D511yescharacteristic
341S4—104no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—44no—
345#67—208no—
346C2×Dic3—202no—
347D12—204no—
348C4×D3—208no—
349Dic6—204no—
350C22×C5—22no—
351C22×C5—32no—
352C22×C5—31no—
353C22×C5—32no—
354C22×C5—32no—
355C22×C5—31no—
356C22×C5—31no—
357C22×C5—34no—
358C22×C5—32no—
359C22×C5—62no—
360C22×C5—62no—
361C22×C5—64no—
362C22×C5—61no—
363C22×C5—62no—
364C22×C5—64no—
365C22×C5—62no—
366C22×C5C2×#23511yescharacteristic, complemented
367C22×C5C22×S412yes—
368C22×C5C22×S411yescharacteristic
369C2×D5—64no—
370C2×D5—64no—
371C2×D5—64no—
372C2×D5—124no—
373C2×D5—124no—
374C4×C5—32no—
375C4×C5—32no—
376C4×C5C22×S412yes—
377C4×C5C22×S412yes—
378Dic5—64no—
379Dic5—64no—
380Dic5—64no—
381C24—22no—
382C24—31no—
383C24—31no—
384C24—32no—
385C24—62no—
386C24—152no—
387C24C22×D1512yes—
388C24C22×D1511yescharacteristic
389#41—308no—
390#41—308no—
391#41—308no—
392#41—308no—
393C2×Q8—154no—
394C2×Q8—301no—
395C2×Q8—302no—
396C2×Q8—301no—
397C2×D4—154no—
398C2×D4—154no—
399C2×D4—158no—
400C2×D4—158no—
401C2×D4—154no—
402C2×D4—301no—
403C2×D4—302no—
404C2×D4—304no—
405C2×D4—302no—
406C2×D4—304no—
407C2×D4—308no—
408C2×D4—304no—
409C2×D4—302no—
410C2×D4—301no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—34no—
417C22×C4—34no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—32no—
421C22×C4—34no—
422C22×C4—32no—
423C22×C4—34no—
424C22×C4—34no—
425C22×C4—62no—
426C22×C4—62no—
427C22×C4—61no—
428C22×C4—62no—
429C22×C4—158no—
430C22×C4—152no—
431C22×C4—152no—
432C22×C4—152no—
433C22×C4—302no—
434C22×C4—304no—
435C22×C4—302no—
436C22×C4C5⋊S411yescharacteristic, complemented
437C22×C4C22×D1512yes—
438C22×C4C22×D1512yes—
439C4⋊C4—154no—
440C4⋊C4—154no—
441C4⋊C4—158no—
442C4⋊C4—158no—
443C22⋊C4—158no—
444C22⋊C4—158no—
445C22⋊C4—158no—
446C22⋊C4—158no—
447C22⋊C4—154no—
448C22⋊C4—154no—
449C42—158no—
450C3×C5—41noHall
451C22×C3—41no—
452C22×C3—42no—
453C22×C3—82no—
454C2×D3—204no—
455C2×D3—404no—
456A4C2×#70911yescharacteristic, complemented
457C3×C4—42no—
458C3×C4—42no—
459Dic3—204no—
460C2×C5—22no—
461C2×C5—31no—
462C2×C5—31no—
463C2×C5—32no—
464C2×C5—62no—
465C2×C5#591212yescomplemented
466C2×C5C23×S411yescharacteristic
467D5—124no—
468C23—22no—
469C23—31no—
470C23—31no—
471C23—32no—
472C23—32no—
473C23—34no—
474C23—32no—
475C23—32no—
476C23—31no—
477C23—62no—
478C23—62no—
479C23—62no—
480C23—61no—
481C23—64no—
482C23—62no—
483C23—64no—
484C23—154no—
485C23—302no—
486C23—304no—
487C23—304no—
488C23—302no—
489C23#681712yescomplemented
490C23C2×C5⋊S411yescharacteristic
491C23C23×D1511yescharacteristic
492Q8—304no—
493Q8—304no—
494D4—304no—
495D4—308no—
496D4—308no—
497D4—304no—
498D4—3016no—
499D4—304no—
500D4—308no—
501D4—304no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—34no—
505C2×C4—32no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—34no—
510C2×C4—34no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—61no—
514C2×C4—64no—
515C2×C4—61no—
516C2×C4—154no—
517C2×C4—154no—
518C2×C4—154no—
519C2×C4—308no—
520C2×C4—302no—
521C2×C4—304no—
522C2×C4—304no—
523C2×C4—302no—
524C2×C4—308no—
525C2×C4C2×C5⋊S411yescharacteristic
526C2×C4C2×C5⋊S411yescharacteristic
527C2×C4C2×C5⋊S414yescomplemented
528C2×C3—42no—
529C2×C3—41no—
530C2×C3—82no—
531D3—404no—
532C5C2×#591211yescharacteristic, complemented, Sylow
533C22—22no—
534C22—32no—
535C22—31no—
536C22—32no—
537C22—32no—
538C22—31no—
539C22—31no—
540C22—34no—
541C22—32no—
542C22—62no—
543C22—62no—
544C22—64no—
545C22—61no—
546C22—62no—
547C22—64no—
548C22—62no—
549C22—304no—
550C22—304no—
551C22—304no—
552C22—604no—
553C22—604no—
554C22C2×#681711yescharacteristic, complemented
555C22C22×C5⋊S412yes—
556C22C22×C5⋊S411yescharacteristic
557C4—32no—
558C4—32no—
559C4—304no—
560C4—304no—
561C4—304no—
562C4C22×C5⋊S412yes—
563C4C22×C5⋊S412yes—
564C3—41noSylow
565C2—22no—
566C2—31no—
567C2—31no—
568C2—32no—
569C2—62no—
570C2—604no—
571C2#1175689612yesdirect product factor
572C2C23×C5⋊S411yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, cosocleC2×C5×A4C24
FrattiniC2C23×C5⋊S4
FittingC24×C4×C5D3
socleC24×C5C22×D3
hypercenterC22×C4C5⋊S4
hypocenterC5×A4C2×#41
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×A4C2semidirect
2. C2×#91958C2semidirect
3. #11756896C2direct (N × H)
4. C2×C4⋊(C5⋊S4)C2semidirect
5. C2×C4×C5⋊S4C2semidirect
6. C2×#91948C2semidirect
13. C2×C4×C5×A4C22semidirect
14. #91958C22semidirect
16. C4⋊(C5⋊S4)C22semidirect
17. C4×C5⋊S4C22semidirect
18. #91948C22semidirect
20. C24×C4×C5D3semidirect
47. C22×C4×A4D5semidirect
61. C23×C4×C5C2×D3semidirect
101. C2×C5×A4#41semidirect
117. C2×C4×A4C2×D5semidirect
149. C22×C4×C5S4semidirect
193. C24×C4D15semidirect
210. C5×A4C2×#41semidirect
244. C23×C5#235semidirect
268. C2×C4×C5C2×S4semidirect
308. C23×C4C2×D15semidirect
339. C2×A4#709semidirect
366. C22×C5C2×#235semidirect
436. C22×C4C5⋊S4semidirect
456. A4C2×#709semidirect
465. C2×C5#5912semidirect
489. C23#6817semidirect
527. C2×C4C2×C5⋊S4semidirect
532. C5C2×#5912semidirect
554. C22C2×#6817semidirect
571. C2#11756896direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×A42
C2×#919582
#117568962
C2×C4⋊(C5⋊S4)2
C2×C4×C5⋊S42
C2×#919482
C2×#661253
C2×#68174
C2×#59125