Finite Group Databasebeta

← C4×#91831 #14416828

Subgroups — C4×#91831 #14416828

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2C2×#91831C211yesmaximal, characteristic
3C4×#6817C211yesmaximal, characteristic
4#11751326C211yesmaximal, characteristic, complemented
5#11751131C212yesmaximal, complemented
6C4×#6718C212yesmaximal, complemented
7#11751127C212yesmaximal, complemented
8C4×#6717C212yesmaximal, complemented
9#11751067C211yesmaximal, characteristic
10#11751065C211yesmaximal, characteristic, complemented
11C4×#6710C211yesmaximal, characteristic, complemented
12C4×#4088—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C3×C4×C5×Q8—21no—
16C3×C4×C5×Q8—21no—
17C3×C4×C5×Q8C2212yes—
18C3×C4×C5×Q8C2212yes—
19C2×C3×C5×C4⋊C4—21no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C42×C5—21no—
22C2×C3×C42×C5C2211yescharacteristic
23C2×#6718C2212yes—
24#91831C418yesdirect product factor
25C2×#6717C2212yes—
26C4×#1220—21no—
27C4×#1220—21no—
28#91815C2211yescharacteristic
29C2×#6710C2211yescharacteristic
30C2×#6710C2211yescharacteristic
31C4×D60C2211yescharacteristic
32C4×D60C2211yescharacteristic
33#91761—21no—
34C42×D15—21no—
35C4×Dic30C2211yescharacteristic
36C4×Dic30C2211yescharacteristic
37#91119C2212yes—
38#91119C2212yes—
39#91094C2212yes—
40#91093C2212yes—
41#91092C2212yes—
42#91091C2212yes—
43#91087C2212yes—
44C4×C3⋊#168C2212yes—
45C4×#942—51nomaximal, Hall
46C2×C4×C5×Q8D311yescharacteristic, complemented
47C2×#4088—31no—
48C4×#709—31no—
49#65514—31no—
50#65319—32no—
51C4×#689—32no—
52#65315—32no—
53C4×#688—32no—
54#65255—31no—
55#65253—31no—
56C4×#681—31no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2×C414yescomplemented
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5D411yescharacteristic
64C22×C3×C4×C5D411yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C2×#1220—21no—
67#6817—22no—
68#6817C2×C414yes—
69C2×D60C2311yescharacteristic
70C2×C4×D15—21no—
71C2×C4×D15—21no—
72C2×C4×D15—21no—
73C2×Dic30C2311yescharacteristic
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C4⋊C4—21no—
77C3×C5×C4⋊C4C2312yes—
78C3×C42×C5—22no—
79C3×C42×C5—22no—
80C3×C42×C5D411yescharacteristic
81C3×C42×C5D411yescharacteristic
82C3×C42×C5C2311yescharacteristic
83C3×C42×C5C2311yescharacteristic
84#6719—21no—
85#6718C2×C418yescomplemented
86#6717C2×C418yescomplemented
87#6714—21no—
88#6714—21no—
89C4⋊Dic15C2311yescharacteristic
90C4⋊Dic15C2311yescharacteristic
91#6712—21no—
92#6712—21no—
93C4×Dic15—21no—
94C4×Dic15—21no—
95C4×Dic15—21no—
96#6710—22no—
97#6710C2×C414yescomplemented
98C2×C3⋊#168C2312yes—
99C2×C3⋊#168C2312yes—
100C2×C3×C4×Q8D511yescharacteristic, complemented
101C2×#942—51no—
102C4×#235—51no—
103#5225—51no—
104#5030—52no—
105C4×#216—52no—
106#5026—52no—
107C4×#215—52no—
108#4966—51no—
109#4964—51no—
110C4×#208—51no—
111C22×C5×Q8C2×D311yescharacteristic
112C2×#709—31no—
113C4×C5×Q8—21no—
114C4×C5×Q8—21no—
115C4×C5×Q8C2×D312yes—
116C4×C5×Q8C2×D312yes—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4C2×D311yescharacteristic
119C2×C42×C5—21no—
120C2×C42×C5C2×D311yescharacteristic
121C2×#689—32no—
122#4088—38no—
123C2×#688—32no—
124C4×C22⋊D5—61no—
125C4×C22⋊D5—61no—
126#4072—31no—
127C2×#681—31no—
128C2×#681—31no—
129C4×D20—31no—
130C4×D20—31no—
131#4018—61no—
132C42×D5—61no—
133C4×Dic10—31no—
134C4×Dic10—31no—
135#3967—32no—
136#3967—32no—
137#3942—32no—
138#3941—32no—
139#3940—32no—
140#3939—32no—
141#3935—32no—
142C4×#168—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C3×C5×Q8—24no—
147C3×C5×Q8—22no—
148C3×C5×Q8C22×C414yes—
149C2×C3×C4×C5—24no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—41no—
154C2×C3×C4×C5—42no—
155C2×C3×C4×C5C22×C412yes—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5#4112yes—
162C2×C3×C4×C5C2411yescharacteristic
163#1220—24no—
164C2×Dic15—21no—
165C2×Dic15—21no—
166C2×Dic15—21no—
167D60—21no—
168D60C22×C412yes—
169C4×D15—24no—
170C4×D15—42no—
171C4×D15—42no—
172Dic30—21no—
173Dic30C22×C412yes—
174C3⋊#168—22no—
175C3⋊#168C22×C414yes—
176C22×C3×Q8C2×D511yescharacteristic
177C2×#235—51no—
178C3×C4×Q8—21no—
179C3×C4×Q8—21no—
180C3×C4×Q8C2×D512yes—
181C3×C4×Q8C2×D512yes—
182C2×C3×C4⋊C4—21no—
183C2×C3×C4⋊C4C2×D511yescharacteristic
184C2×C3×C42—21no—
185C2×C3×C42C2×D511yescharacteristic
186C2×#216—52no—
187#942—58no—
188C2×#215—52no—
189C4×#67—101no—
190C4×#67—101no—
191#926—51no—
192C2×#208—51no—
193C2×#208—51no—
194C4×D12—51no—
195C4×D12—51no—
196#872—101no—
197C42×D3—101no—
198C4×Dic6—51no—
199C4×Dic6—51no—
200#835—52no—
201#835—52no—
202#810—52no—
203#809—52no—
204#808—52no—
205#807—52no—
206#803—52no—
207C4×C3⋊C8—52no—
208C2×C5×Q8—22no—
209C2×C5×Q8—21no—
210C2×C5×Q8C4×D314yescomplemented
211C2×C5×Q8C22×D312yes—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5#6711yescharacteristic
215C22×C4×C5#6711yescharacteristic
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—61no—
218#709—34no—
219#709—62no—
220C2×D20—31no—
221C2×C4×D5—61no—
222C2×C4×D5—61no—
223C2×C4×D5—61no—
224C2×Dic10—31no—
225C5×C4⋊C4—22no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4C22×D312yes—
229C42×C5—22no—
230C42×C5—22no—
231C42×C5#6711yescharacteristic
232C42×C5#6711yescharacteristic
233C42×C5C22×D311yescharacteristic
234C42×C5C22×D311yescharacteristic
235C22⋊Dic5—61no—
236#689—38no—
237#688—38no—
238#685—61no—
239#685—61no—
240C4⋊Dic5—31no—
241C4⋊Dic5—31no—
242#683—61no—
243#683—61no—
244C4×Dic5—61no—
245C4×Dic5—61no—
246C4×Dic5—61no—
247#681—34no—
248#681—62no—
249C2×#168—32no—
250C2×#168—32no—
251C2×#137—151no—
252C4×#41—151no—
253C2×C4×Q8D1511yescharacteristic, complemented
254#441—152no—
255#440—152no—
256C4×Q16—152no—
257C4×SD16—152no—
258#428—151no—
259#419—151no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×D15—22no—
267C2×D15—41no—
268C2×D15—41no—
269C3×C4×C5—24no—
270C3×C4×C5—21no—
271C3×C4×C5—21no—
272C3×C4×C5—21no—
273C3×C4×C5—42no—
274C3×C4×C5C4×D412yes—
275C3×C4×C5#13712yescomplemented
276C3×C4×C5C23×C411yescharacteristic
277C3×C4×C5C2×#4111yescharacteristic
278Dic15—22no—
279Dic15—41no—
280Dic15—41no—
281C2×C3×Q8—22no—
282C2×C3×Q8—21no—
283C2×C3×Q8C4×D514yescomplemented
284C2×C3×Q8C22×D512yes—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4C22⋊D511yescharacteristic
288C22×C3×C4C22⋊D511yescharacteristic
289C22×C3×C4C22×D511yescharacteristic
290C2×#67—101no—
291#235—54no—
292#235—102no—
293C2×D12—51no—
294C2×C4×D3—101no—
295C2×C4×D3—101no—
296C2×C4×D3—101no—
297C2×Dic6—51no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—22no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4C22×D512yes—
302C3×C42—22no—
303C3×C42—22no—
304C3×C42C22⋊D511yescharacteristic
305C3×C42C22⋊D511yescharacteristic
306C3×C42C22×D511yescharacteristic
307C3×C42C22×D511yescharacteristic
308#217—101no—
309#216—58no—
310#215—58no—
311(C2×D3)⋊C4—101no—
312(C2×D3)⋊C4—101no—
313C4⋊Dic3—51no—
314C4⋊Dic3—51no—
315Dic3⋊C4—101no—
316Dic3⋊C4—101no—
317C4×Dic3—101no—
318C4×Dic3—101no—
319C4×Dic3—101no—
320#208—54no—
321#208—102no—
322C2×C3⋊C8—52no—
323C2×C3⋊C8—52no—
324C23×C5C2×#6711yescharacteristic
325C22×D5—61no—
326C5×Q8—24no—
327C5×Q8—22no—
328C5×Q8C2×C4×D314yes—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—41no—
334C2×C4×C5—42no—
335C2×C4×C5C2×C4×D312yes—
336C2×C4×C5#23512yes—
337C2×C4×C5C2×#6711yescharacteristic
338C2×C4×C5C2×#6711yescharacteristic
339C2×C4×C5C2×#6711yescharacteristic
340C2×C4×C5C2×#6711yescharacteristic
341C2×C4×C5C2×#6711yescharacteristic
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—64no—
344C2×Dic5—61no—
345C2×Dic5—61no—
346C2×Dic5—61no—
347D20—32no—
348D20—61no—
349C4×D5—64no—
350C4×D5—122no—
351C4×D5—122no—
352Dic10—32no—
353Dic10—61no—
354#168—34no—
355#168—62no—
356C2×#41—151no—
357C22×Q8C2×D1511yescharacteristic
358#137—158no—
359C2×Q16—152no—
360C2×SD16—152no—
361C2×M16—151no—
362C2×M16—151no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—151no—
366C4×Q8—151no—
367C4×Q8C2×D1512yes—
368C4×Q8C2×D1512yes—
369C4×D4—151no—
370C4×D4—151no—
371C4×D4—301no—
372C4×D4—301no—
373#117—151no—
374#117—301no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C2×D1511yescharacteristic
377C2×C42—21no—
378C2×C42—301no—
379C2×C42C2×D1511yescharacteristic
380#107—152no—
381#106—152no—
382#103—152no—
383#103—152no—
384#103—152no—
385#102—152no—
386#97—152no—
387C4×C8—152no—
388C2×C3×C5—22no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C2×#13711yescharacteristic
391C2×C3×C5#57511yescharacteristic
392D15—42no—
393C23×C3C2×C22⋊D511yescharacteristic
394C22×D3—101no—
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8C2×C4×D514yes—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4C2×C4×D512yes—
405C2×C3×C4#70912yes—
406C2×C3×C4C2×C22⋊D511yescharacteristic
407C2×C3×C4C2×C22⋊D511yescharacteristic
408C2×C3×C4C2×C22⋊D511yescharacteristic
409C2×C3×C4C2×C22⋊D511yescharacteristic
410C2×C3×C4C2×C22⋊D511yescharacteristic
411C2×C3×C4C23×D511yescharacteristic
412#67—104no—
413C2×Dic3—101no—
414C2×Dic3—101no—
415C2×Dic3—101no—
416D12—52no—
417D12—101no—
418C4×D3—104no—
419C4×D3—202no—
420C4×D3—202no—
421Dic6—52no—
422Dic6—101no—
423C3⋊C8—54no—
424C3⋊C8—102no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5C4×#6712yes—
428C22×C5C22×#6711yescharacteristic
429C2×D5—62no—
430C2×D5—121no—
431C2×D5—121no—
432C4×C5—24no—
433C4×C5—21no—
434C4×C5—21no—
435C4×C5—21no—
436C4×C5—42no—
437C4×C5C4×#6712yes—
438C4×C5#94212yescomplemented
439C4×C5C22×C4×D311yescharacteristic
440C4×C5C2×#23511yescharacteristic
441Dic5—62no—
442Dic5—121no—
443Dic5—121no—
444#41—154no—
445#41—302no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—151no—
449C2×Q8C4×D1514yescomplemented
450C2×Q8C22×D1512yes—
451C2×D4—151no—
452C2×D4—301no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—301no—
456C22×C4—301no—
457C22×C4—301no—
458C22×C4#122011yescharacteristic
459C22×C4#122011yescharacteristic
460C22×C4C22×D1511yescharacteristic
461Q16—158no—
462SD16—158no—
463M16—154no—
464M16—302no—
465C2×C8—152no—
466C2×C8—152no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—151no—
471C4⋊C4—151no—
472C4⋊C4—301no—
473C4⋊C4—301no—
474C4⋊C4C22×D1512yes—
475C22⋊C4—301no—
476C22⋊C4—301no—
477C22⋊C4—301no—
478C42—22no—
479C42—22no—
480C42—301no—
481C42—301no—
482C42—301no—
483C42#122011yescharacteristic
484C42#122011yescharacteristic
485C42C22×D1511yescharacteristic
486C42C22×D1511yescharacteristic
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3C4×C22⋊D512yes—
491C22×C3C22×C22⋊D511yescharacteristic
492C2×D3—102no—
493C2×D3—201no—
494C2×D3—201no—
495C3×C4—24no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—42no—
500C3×C4C4×C22⋊D512yes—
501C3×C4#408812yescomplemented
502C3×C4C22×C4×D511yescharacteristic
503C3×C4C2×#70911yescharacteristic
504Dic3—102no—
505Dic3—201no—
506Dic3—201no—
507C2×C5—22no—
508C2×C5C2×C4×#6711yescharacteristic
509C2×C5C2×#94211yescharacteristic
510C2×C5#582211yescharacteristic
511D5—122no—
512C23—301no—
513C23C2×#122011yescharacteristic
514Q8—24no—
515Q8—22no—
516Q8—152no—
517Q8—301no—
518Q8C2×C4×D1514yes—
519D4—152no—
520D4—304no—
521D4—301no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—301no—
529C2×C4—304no—
530C2×C4—301no—
531C2×C4—301no—
532C2×C4—602no—
533C2×C4—602no—
534C2×C4C2×C4×D1512yes—
535C2×C4#681712yes—
536C2×C4C2×#122011yescharacteristic
537C2×C4C2×#122011yescharacteristic
538C2×C4C2×#122011yescharacteristic
539C2×C4C2×#122011yescharacteristic
540C2×C4C2×#122011yescharacteristic
541C2×C4C23×D1511yescharacteristic
542C8—154no—
543C8—302no—
544C2×C3—22no—
545C2×C3C2×C4×C22⋊D511yescharacteristic
546C2×C3C2×#408811yescharacteristic
547C2×C3#6615611yescharacteristic
548D3—202no—
549C5C4×#94211yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—302no—
553C22—601no—
554C22—601no—
555C22C4×#122012yes—
556C22C22×#122011yescharacteristic
557C4—24no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—302no—
563C4—601no—
564C4—601no—
565C4C4×#122012yes—
566C4#9183112yesdirect product factor
567C4C22×C4×D1511yescharacteristic
568C4C2×#681711yescharacteristic
569C3C4×#408811yescharacteristic, complemented, Sylow
570C2—22no—
571C2—602no—
572C2C2×C4×#122011yescharacteristic
573C2C2×#9183111yescharacteristic
574C2#1175658111yescharacteristic
subgroupG/H
centerC2×C4C2×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C4×C5×Q8C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC2×C4×Q8D15
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
4. #11751326C2semidirect
5. #11751131C2semidirect
6. C4×#6718C2semidirect
7. #11751127C2semidirect
8. C4×#6717C2semidirect
10. #11751065C2semidirect
11. C4×#6710C2semidirect
24. #91831C4direct (N × H)
46. C2×C4×C5×Q8D3semidirect
59. C2×C3×C5×Q8C2×C4semidirect
85. #6718C2×C4semidirect
86. #6717C2×C4semidirect
97. #6710C2×C4semidirect
100. C2×C3×C4×Q8D5semidirect
210. C2×C5×Q8C4×D3semidirect
253. C2×C4×Q8D15semidirect
275. C3×C4×C5#137semidirect
283. C2×C3×Q8C4×D5semidirect
438. C4×C5#942semidirect
449. C2×Q8C4×D15semidirect
487. C3×C5C4×#137semidirect
501. C3×C4#4088semidirect
549. C5C4×#942semidirect
566. C4#91831direct (N × H)
569. C3C4×#4088semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
C2×#918312
C4×#68172
#117513262
#117511312
C4×#67182
#117511272
C4×#67172
#117510672
#117510652
C4×#67102
C4×#40883
C4×#9425