Finite Group Databasebeta

← C4×#91298 #14416729

Subgroups — C4×#91298 #14416729

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#235C211yesmaximal, characteristic, complemented
2C2×C3×C4×D20C211yesmaximal, characteristic, complemented
3C2×#91298C211yesmaximal, characteristic
4C4×#6710C211yesmaximal, characteristic, complemented
5#11748470C211yesmaximal, characteristic, complemented
6#11748384C211yesmaximal, characteristic, complemented
7#11748366C211yesmaximal, characteristic, complemented
8#11747048C212yesmaximal, complemented
9C4×#6655C212yesmaximal, complemented
10#11747021C212yesmaximal, complemented
11C4×#6652C212yesmaximal, complemented
12C4×#4095—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5—21no—
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C4×C5×#67—21no—
20C4×C5×#67—21no—
21C5×#926C2211yescharacteristic
22C4×C5×D12C2211yescharacteristic, complemented
23C4×C5×D12C2211yescharacteristic, complemented
24C5×#872—21no—
25C42×C5×D3—21no—
26C4×C5×Dic6C2211yescharacteristic, complemented
27C4×C5×Dic6C2211yescharacteristic, complemented
28C2×C3×#685—21no—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C3×C4×D20—21no—
31C3×C4×D20—21no—
32C3×C4×D20C2212yes—
33C3×C4×D20C2212yes—
34C2×#6655C2212yes—
35#91298C418yesdirect product factor
36C2×#6652C2212yes—
37#91087C2212yescomplemented
38C4×C3⋊#168C2212yescomplemented
39#90989C2212yescomplemented
40#90986C2212yescomplemented
41#90972C2212yescomplemented
42#90966C2212yescomplemented
43#90964C2212yes—
44#90964C2212yes—
45C4×#932—51nomaximal, Hall
46C4×C5×#41—31no—
47C2×#4095—31no—
48C2×C4×D20D311yescharacteristic, complemented
49#65521—31no—
50#65315—32no—
51C4×#688—32no—
52#65303—32no—
53C4×#686—32no—
54#65290—31no—
55#65284—31no—
56C4×#681—31no—
57C23×C3×D5—21no—
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C2×C5×#67—21no—
62C5×#235—22no—
63C5×#235C2×C414yescomplemented
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C4×C5×D3—21no—
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C2×C3×D20—21no—
71C2×C3×D20—22no—
72C2×C3×D20C2×C414yescomplemented
73C2×C3×D20C2312yes—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—44no—
77C3×C42×C5D411yescharacteristic
78C3×C42×C5D411yescharacteristic
79C3×C42×C5C2311yescharacteristic
80C3×C42×C5C2311yescharacteristic
81#6710—22no—
82#6710C2×C414yescomplemented
83C2×C3⋊#168C2312yes—
84C2×C3⋊#168C2312yes—
85C5×#217—21no—
86C5×(C2×D3)⋊C4—21no—
87C5×(C2×D3)⋊C4—21no—
88C5×C4⋊Dic3C2311yescharacteristic
89C5×C4⋊Dic3C2311yescharacteristic
90C5×Dic3⋊C4—21no—
91C5×Dic3⋊C4—21no—
92C4×C5×Dic3—21no—
93C4×C5×Dic3—21no—
94C4×C5×Dic3—21no—
95C3×#685—22no—
96C3×#685—22no—
97C3×C4⋊Dic5—21no—
98C3×C4⋊Dic5C2312yes—
99#6655C2×C418yescomplemented
100#6652C2×C418yescomplemented
101C2×C3×C4×D4—51no—
102C2×#932—51no—
103C4×#235D511yescharacteristic, complemented
104#5215—51no—
105#5018—52no—
106C4×#214—52no—
107#5014—52no—
108C4×#213—52no—
109#4966—51no—
110#4964—51no—
111C4×#208—51no—
112C2×C5×#41—31no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—21no—
115C4×C5×Q8—31no—
116C4×C5×Q8—31no—
117C4×C5×D4—31no—
118C4×C5×D4—31no—
119C4×C5×D4—61no—
120C4×C5×D4—61no—
121C5×#117—31no—
122C5×#117—61no—
123C2×C42×C5—61no—
124C2×C42×C5C2×D311yescharacteristic
125#4095—38no—
126C2×#688—32no—
127C2×#686—32no—
128C2×#685—21no—
129C2×C4⋊Dic5C2×D311yescharacteristic
130C2×#681—31no—
131C2×#681—31no—
132C4×D20—21no—
133C4×D20—21no—
134C4×D20C2×D312yes—
135C4×D20C2×D312yes—
136#3967—32no—
137#3964—32no—
138#3941—32no—
139#3941—32no—
140#3940—32no—
141#3939—32no—
142#3935—32no—
143C4×#168—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—21no—
147C22×C3×D5—24no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—41no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5#4112yes—
160C2×C3×C4×C5C2411yescharacteristic
161C5×#67—24no—
162C2×C5×Dic3—21no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C5×D12—21no—
166C5×D12C22×C412yescomplemented
167C4×C5×D3—24no—
168C4×C5×D3—42no—
169C4×C5×D3—42no—
170C5×Dic6—21no—
171C5×Dic6C22×C412yescomplemented
172C2×C3×Dic5—22no—
173C2×C3×Dic5—42no—
174C3×D20—24no—
175C3×D20—22no—
176C3×D20C22×C414yes—
177C3×C4×D5—44no—
178C3×C4×D5—44no—
179C3⋊#168—22no—
180C3⋊#168C22×C414yescomplemented
181C22×C3×D4—51no—
182C23×C3×C4—101no—
183C2×#235C2×D511yescharacteristic
184C3×C4×D4—52no—
185C3×C4×D4—52no—
186C3×C4×D4—101no—
187C3×C4×D4—101no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—101no—
190C2×C3×C42C2×D511yescharacteristic
191C2×#214—52no—
192#932—58no—
193C2×#213—52no—
194C4×#67—21no—
195C4×#67—21no—
196#926C2×D511yescharacteristic
197C2×#208—51no—
198C2×#208—51no—
199C4×D12C2×D511yescharacteristic, complemented
200C4×D12C2×D511yescharacteristic, complemented
201#872—21no—
202C42×D3—21no—
203C4×Dic6C2×D511yescharacteristic, complemented
204C4×Dic6C2×D511yescharacteristic, complemented
205#832—52no—
206#832—52no—
207#810—52no—
208#809—52no—
209#808—52no—
210#807—52no—
211#803—52no—
212C4×C3⋊C8—52no—
213C23×D5—21no—
214C5×#41—34no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×D4—31no—
218C2×C5×D4—61no—
219C22×C4×C5—61no—
220C22×C4×C5—61no—
221C22×C4×C5—61no—
222C22×C4×C5#6711yescharacteristic
223C22×C4×C5#6711yescharacteristic
224C22×C4×C5C22×D311yescharacteristic
225C22×Dic5—21no—
226C2×D20—22no—
227C2×D20—21no—
228C2×D20C4×D314yescomplemented
229C2×D20C22×D312yes—
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5—44no—
233C5×C4⋊C4—31no—
234C5×C4⋊C4—31no—
235C5×C4⋊C4—61no—
236C5×C4⋊C4—61no—
237C5×C22⋊C4—61no—
238C5×C22⋊C4—61no—
239C5×C22⋊C4—61no—
240C42×C5—61no—
241C42×C5—61no—
242C42×C5—61no—
243C42×C5#6711yescharacteristic
244C42×C5#6711yescharacteristic
245C42×C5C22×D311yescharacteristic
246C42×C5C22×D311yescharacteristic
247#688—38no—
248#686—38no—
249#685—22no—
250#685—22no—
251C4⋊Dic5—21no—
252C4⋊Dic5C22×D312yes—
253#681—34no—
254#681—62no—
255C2×#168—32no—
256C2×#168—32no—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—31no—
259C2×C4×D4—51no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—151no—
266#417—151no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×C5×D3—22no—
273C2×C5×D3—41no—
274C2×C5×D3—41no—
275C2×C3×D5—24no—
276C2×C3×D5—48no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C3×C4×C5—21no—
280C3×C4×C5—21no—
281C3×C4×C5—21no—
282C3×C4×C5C4×D412yes—
283C3×C4×C5AGL(1,ℤ/8)12yescomplemented
284C3×C4×C5C23×C411yescharacteristic
285C3×C4×C5C2×#4111yescharacteristic
286C3×Dic5—42no—
287C5×Dic3—22no—
288C5×Dic3—41no—
289C5×Dic3—41no—
290C24×C3—101no—
291C2×C3×D4—54no—
292C2×C3×D4—52no—
293C2×C3×D4—102no—
294C2×C3×D4—101no—
295C22×C3×C4—101no—
296C22×C3×C4—102no—
297C22×C3×C4—102no—
298C22×C3×C4—204no—
299C22×C3×C4C22⋊D511yescharacteristic
300C22×C3×C4C22⋊D511yescharacteristic
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—21no—
303#235—22no—
304#235C4×D514yescomplemented
305C2×D12C22×D511yescharacteristic
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×Dic6C22×D511yescharacteristic
310C3×C4⋊C4—52no—
311C3×C4⋊C4—101no—
312C3×C22⋊C4—102no—
313C3×C22⋊C4—102no—
314C3×C42C22⋊D511yescharacteristic
315C3×C42C22⋊D511yescharacteristic
316C3×C42C22×D511yescharacteristic
317C3×C42C22×D511yescharacteristic
318#217—21no—
319#214—58no—
320#213—58no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—21no—
323C4⋊Dic3C22×D511yescharacteristic
324C4⋊Dic3C22×D511yescharacteristic
325Dic3⋊C4—21no—
326Dic3⋊C4—21no—
327C4×Dic3—21no—
328C4×Dic3—21no—
329C4×Dic3—21no—
330#208—54no—
331#208—102no—
332C2×C3⋊C8—52no—
333C2×C3⋊C8—52no—
334C23×C5—61no—
335C23×C5C2×#6711yescharacteristic
336C22×D5—24no—
337C22×D5—22no—
338C22×D5—42no—
339C22×D5—42no—
340C5×Q8—32no—
341C5×Q8—61no—
342C5×D4—32no—
343C5×D4—64no—
344C5×D4—61no—
345C2×C4×C5—22no—
346C2×C4×C5—41no—
347C2×C4×C5—61no—
348C2×C4×C5—64no—
349C2×C4×C5—61no—
350C2×C4×C5—61no—
351C2×C4×C5—122no—
352C2×C4×C5—122no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5#23512yes—
355C2×C4×C5C2×#6711yescharacteristic
356C2×C4×C5C2×#6711yescharacteristic
357C2×C4×C5C2×#6711yescharacteristic
358C2×C4×C5C2×#6711yescharacteristic
359C2×C4×C5C2×#6711yescharacteristic
360C2×C4×C5C23×D311yescharacteristic
361C2×Dic5—22no—
362C2×Dic5—42no—
363D20—24no—
364D20—22no—
365D20C2×C4×D314yes—
366C4×D5—44no—
367C4×D5—44no—
368#168—34no—
369#168—62no—
370C2×#41—31no—
371C22×D4—51no—
372C23×C4—101no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—151no—
377C2×M16—151no—
378C4×Q8—31no—
379C4×Q8—31no—
380C4×D4—31no—
381C4×D4—31no—
382C4×D4—52no—
383C4×D4—52no—
384C4×D4—61no—
385C4×D4—61no—
386C4×D4—101no—
387C4×D4—101no—
388#117—31no—
389#117—61no—
390C2×C4⋊C4—51no—
391C2×C22⋊C4—101no—
392C2×C42—61no—
393C2×C42D3×D511yescharacteristic
394#107—152no—
395#106—152no—
396#103—152no—
397#102—152no—
398#102—152no—
399#102—152no—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5C2×C4×D411yescharacteristic
404C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C3×C5#57511yescharacteristic
406C3×D5—44no—
407C5×D3—42no—
408C23×C3—102no—
409C23×C3—104no—
410C23×C3—202no—
411C23×C3—202no—
412C23×C3C2×C22⋊D511yescharacteristic
413C22×D3—21no—
414C3×D4—54no—
415C3×D4—102no—
416C3×D4—104no—
417C2×C3×C4—22no—
418C2×C3×C4—41no—
419C2×C3×C4—102no—
420C2×C3×C4—204no—
421C2×C3×C4—202no—
422C2×C3×C4—204no—
423C2×C3×C4C2×C4×D512yes—
424C2×C3×C4#70912yes—
425C2×C3×C4C2×C22⋊D511yescharacteristic
426C2×C3×C4C2×C22⋊D511yescharacteristic
427C2×C3×C4C2×C22⋊D511yescharacteristic
428C2×C3×C4C2×C22⋊D511yescharacteristic
429C2×C3×C4C2×C22⋊D511yescharacteristic
430C2×C3×C4C23×D511yescharacteristic
431#67—24no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435D12—21no—
436D12C2×C4×D512yescomplemented
437C4×D3—24no—
438C4×D3—42no—
439C4×D3—42no—
440Dic6—21no—
441Dic6C2×C4×D512yescomplemented
442C3⋊C8—54no—
443C3⋊C8—102no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—62no—
447C22×C5—121no—
448C22×C5—121no—
449C22×C5C4×#6712yes—
450C22×C5C22×#6711yescharacteristic
451C2×D5—24no—
452C2×D5—48no—
453C2×D5—42no—
454C2×D5—42no—
455C4×C5—21no—
456C4×C5—21no—
457C4×C5—21no—
458C4×C5—62no—
459C4×C5—121no—
460C4×C5—121no—
461C4×C5C4×#6712yes—
462C4×C5#93212yescomplemented
463C4×C5C22×C4×D311yescharacteristic
464C4×C5C2×#23511yescharacteristic
465Dic5—42no—
466C24—101no—
467#41—34no—
468#41—62no—
469C2×Q8—31no—
470C2×D4—31no—
471C2×D4—54no—
472C2×D4—52no—
473C2×D4—61no—
474C2×D4—102no—
475C2×D4—101no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—101no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—204no—
483C22×C4#120111yescharacteristic
484C22×C4#120111yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—154no—
489M16—302no—
490C2×C8—152no—
491C2×C8—152no—
492C4⋊C4—31no—
493C4⋊C4—31no—
494C4⋊C4—52no—
495C4⋊C4—61no—
496C4⋊C4—61no—
497C4⋊C4—101no—
498C22⋊C4—61no—
499C22⋊C4—61no—
500C22⋊C4—61no—
501C22⋊C4—102no—
502C22⋊C4—102no—
503C42—61no—
504C42—61no—
505C42—61no—
506C42#120111yescharacteristic
507C42#120111yescharacteristic
508C42C2×D3×D511yescharacteristic
509C42C2×D3×D511yescharacteristic
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—104no—
514C22×C3—208no—
515C22×C3—202no—
516C22×C3—202no—
517C22×C3C4×C22⋊D512yes—
518C22×C3C22×C22⋊D511yescharacteristic
519C2×D3—22no—
520C2×D3—41no—
521C2×D3—41no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—202no—
526C3×C4C4×C22⋊D512yes—
527C3×C4#409512yescomplemented
528C3×C4C22×C4×D511yescharacteristic
529C3×C4C2×#70911yescharacteristic
530Dic3—22no—
531Dic3—41no—
532Dic3—41no—
533C2×C5—22no—
534C2×C5—122no—
535C2×C5C2×C4×#6711yescharacteristic
536C2×C5C2×#93211yescharacteristic
537C2×C5#582211yescharacteristic
538D5—44no—
539C23—61no—
540C23—104no—
541C23—102no—
542C23—202no—
543C23—202no—
544C23C2×#120111yescharacteristic
545Q8—32no—
546Q8—61no—
547D4—32no—
548D4—54no—
549D4—64no—
550D4—61no—
551D4—104no—
552D4—102no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—61no—
556C2×C4—64no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—102no—
560C2×C4—122no—
561C2×C4—122no—
562C2×C4—204no—
563C2×C4—202no—
564C2×C4—204no—
565C2×C4#677112yes—
566C2×C4C4×D3×D512yes—
567C2×C4C2×#120111yescharacteristic
568C2×C4C2×#120111yescharacteristic
569C2×C4C2×#120111yescharacteristic
570C2×C4C2×#120111yescharacteristic
571C2×C4C2×#120111yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—154no—
574C8—302no—
575C2×C3—22no—
576C2×C3—204no—
577C2×C3C2×C4×C22⋊D511yescharacteristic
578C2×C3C2×#409511yescharacteristic
579C2×C3#6615611yescharacteristic
580D3—42no—
581C5C4×#93211yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—62no—
585C22—104no—
586C22—121no—
587C22—121no—
588C22—208no—
589C22—202no—
590C22—202no—
591C22C4×#120112yes—
592C22C22×#120111yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—62no—
597C4—121no—
598C4—121no—
599C4—202no—
600C4#9129812yesdirect product factor
601C4C4×#120112yes—
602C4C2×#677111yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3C4×#409511yescharacteristic, complemented, Sylow
605C2—22no—
606C2—122no—
607C2—204no—
608C2C2×#9129811yescharacteristic
609C2#1175413811yescharacteristic
610C2C2×C4×#120111yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
prime radicalC2×#91298C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×C5×#235C2semidirect
2. C2×C3×C4×D20C2semidirect
4. C4×#6710C2semidirect
5. #11748470C2semidirect
6. #11748384C2semidirect
7. #11748366C2semidirect
8. #11747048C2semidirect
9. C4×#6655C2semidirect
10. #11747021C2semidirect
11. C4×#6652C2semidirect
22. C4×C5×D12C22semidirect
23. C4×C5×D12C22semidirect
26. C4×C5×Dic6C22semidirect
27. C4×C5×Dic6C22semidirect
35. #91298C4direct (N × H)
37. #91087C22semidirect
38. C4×C3⋊#168C22semidirect
39. #90989C22semidirect
40. #90986C22semidirect
41. #90972C22semidirect
42. #90966C22semidirect
48. C2×C4×D20D3semidirect
63. C5×#235C2×C4semidirect
72. C2×C3×D20C2×C4semidirect
82. #6710C2×C4semidirect
99. #6655C2×C4semidirect
100. #6652C2×C4semidirect
103. C4×#235D5semidirect
166. C5×D12C22×C4semidirect
171. C5×Dic6C22×C4semidirect
180. C3⋊#168C22×C4semidirect
199. C4×D12C2×D5semidirect
200. C4×D12C2×D5semidirect
203. C4×Dic6C2×D5semidirect
204. C4×Dic6C2×D5semidirect
228. C2×D20C4×D3semidirect
283. C3×C4×C5AGL(1,ℤ/8)semidirect
304. #235C4×D5semidirect
436. D12C2×C4×D5semidirect
441. Dic6C2×C4×D5semidirect
462. C4×C5#932semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
527. C3×C4#4095semidirect
581. C5C4×#932semidirect
600. C4#91298direct (N × H)
604. C3C4×#4095semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#2352
C2×C3×C4×D202
C2×#912982
C4×#67102
#117484702
#117483842
#117483662
#117470482
C4×#66552
#117470212
C4×#66522
C4×#40953
C4×#9325