Finite Group Databasebeta

← C4×#91299 #14416731

Subgroups — C4×#91299 #14416731

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
1C2×C4×C5×D12C211yesmaximal, characteristic, complemented
2C3×C4×#709C211yesmaximal, characteristic, complemented
3C2×#91299C211yesmaximal, characteristic
4C4×#6710C211yesmaximal, characteristic, complemented
5#11748472C211yesmaximal, characteristic, complemented
6#11748386C211yesmaximal, characteristic, complemented
7#11748368C211yesmaximal, characteristic, complemented
8#11747050C212yesmaximal, complemented
9C4×#6656C212yesmaximal, complemented
10#11747021C212yesmaximal, complemented
11C4×#6652C212yesmaximal, complemented
12C4×#4078—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3—21no—
15C2×C3×#709C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4—21no—
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C4×C5×D12—21no—
22C4×C5×D12—21no—
23C4×C5×D12C2212yes—
24C4×C5×D12C2212yes—
25C3×C4×C22⋊D5—21no—
26C3×C4×C22⋊D5—21no—
27C3×#4072C2211yescharacteristic
28C3×C4×D20C2211yescharacteristic, complemented
29C3×C4×D20C2211yescharacteristic, complemented
30C3×#4018—21no—
31C3×C42×D5—21no—
32C3×C4×Dic10C2211yescharacteristic, complemented
33C3×C4×Dic10C2211yescharacteristic, complemented
34C2×#6656C2212yes—
35#91299C418yesdirect product factor
36C2×#6652C2212yes—
37#91087C2212yescomplemented
38C4×C3⋊#168C2212yescomplemented
39#90989C2212yescomplemented
40#90986C2212yescomplemented
41#90970C2212yescomplemented
42#90966C2212yes—
43#90966C2212yes—
44#90964C2212yescomplemented
45C4×#949—51nomaximal, Hall
46C2×C4×C5×D4—31no—
47C2×#4078—31no—
48C4×#709D311yescharacteristic, complemented
49#65504—31no—
50#65307—32no—
51C4×#687—32no—
52#65303—32no—
53C4×#686—32no—
54#65255—31no—
55#65253—31no—
56C4×#681—31no—
57C23×C5×D3—21no—
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C5×Dic3—21no—
62C2×C5×D12—21no—
63C2×C5×D12—22no—
64C2×C5×D12C2×C414yescomplemented
65C2×C5×D12C2312yes—
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3—22no—
68C2×C4×C5×D3—44no—
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709C2×C414yescomplemented
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—21no—
76C2×C3×Dic10C2311yescharacteristic
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×(C2×D3)⋊C4—22no—
86C5×(C2×D3)⋊C4—22no—
87C5×C4⋊Dic3—21no—
88C5×C4⋊Dic3C2312yes—
89C3×C22⋊Dic5—21no—
90C3×#685—21no—
91C3×#685—21no—
92C3×C4⋊Dic5C2311yescharacteristic
93C3×C4⋊Dic5C2311yescharacteristic
94C3×#683—21no—
95C3×#683—21no—
96C3×C4×Dic5—21no—
97C3×C4×Dic5—21no—
98C3×C4×Dic5—21no—
99#6656C2×C418yescomplemented
100#6652C2×C418yescomplemented
101C3×C4×#41—51no—
102C2×#949—51no—
103C2×C4×D12D511yescharacteristic, complemented
104#5232—51no—
105#5026—52no—
106C4×#215—52no—
107#5014—52no—
108C4×#213—52no—
109#5001—51no—
110#4995—51no—
111C4×#208—51no—
112C22×C5×D4—31no—
113C23×C4×C5—61no—
114C2×#709C2×D311yescharacteristic
115C4×C5×D4—32no—
116C4×C5×D4—32no—
117C4×C5×D4—61no—
118C4×C5×D4—61no—
119C2×C5×C4⋊C4—31no—
120C2×C5×C22⋊C4—61no—
121C2×C42×C5C2×D311yescharacteristic
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C4×C22⋊D5—21no—
126C4×C22⋊D5—21no—
127#4072C2×D311yescharacteristic
128C2×#681—31no—
129C2×#681—31no—
130C4×D20C2×D311yescharacteristic, complemented
131C4×D20C2×D311yescharacteristic, complemented
132#4018—21no—
133C42×D5—21no—
134C4×Dic10C2×D311yescharacteristic, complemented
135C4×Dic10C2×D311yescharacteristic, complemented
136#3964—32no—
137#3964—32no—
138#3942—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—24no—
147C22×C5×D3—22no—
148C22×C5×D3—42no—
149C22×C5×D3—42no—
150C22×C3×D5—21no—
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
161C2×C5×Dic3—22no—
162C2×C5×Dic3—42no—
163C5×D12—24no—
164C5×D12—22no—
165C5×D12C22×C414yes—
166C4×C5×D3—44no—
167C4×C5×D3—44no—
168C3×C22⋊D5—24no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C3×D20—21no—
173C3×D20C22×C412yescomplemented
174C3×C4×D5—24no—
175C3×C4×D5—42no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10C22×C412yescomplemented
179C3⋊#168—22no—
180C3⋊#168C22×C414yescomplemented
181C2×C3×#41—51no—
182C22×D12C2×D511yescharacteristic
183C22×C4×D3—21no—
184C3×C4×Q8—51no—
185C3×C4×Q8—51no—
186C3×C4×D4—51no—
187C3×C4×D4—51no—
188C3×C4×D4—101no—
189C3×C4×D4—101no—
190C3×#117—51no—
191C3×#117—101no—
192C2×C3×C42—101no—
193C2×C3×C42C2×D511yescharacteristic
194#949—58no—
195C2×#215—52no—
196C2×#213—52no—
197C2×(C2×D3)⋊C4—21no—
198C2×C4⋊Dic3C2×D511yescharacteristic
199C2×#208—51no—
200C2×#208—51no—
201C4×D12—21no—
202C4×D12—21no—
203C4×D12C2×D512yes—
204C4×D12C2×D512yes—
205#835—52no—
206#832—52no—
207#809—52no—
208#809—52no—
209#808—52no—
210#807—52no—
211#803—52no—
212C4×C3⋊C8—52no—
213C24×C5—61no—
214C2×C5×D4—34no—
215C2×C5×D4—32no—
216C2×C5×D4—62no—
217C2×C5×D4—61no—
218C22×C4×C5—61no—
219C22×C4×C5—62no—
220C22×C4×C5—62no—
221C22×C4×C5—124no—
222C22×C4×C5#6711yescharacteristic
223C22×C4×C5#6711yescharacteristic
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226#709—22no—
227#709C4×D314yescomplemented
228C2×D20C22×D311yescharacteristic
229C2×C4×D5—21no—
230C2×C4×D5—21no—
231C2×C4×D5—21no—
232C2×Dic10C22×D311yescharacteristic
233C5×C4⋊C4—32no—
234C5×C4⋊C4—61no—
235C5×C22⋊C4—62no—
236C5×C22⋊C4—62no—
237C42×C5#6711yescharacteristic
238C42×C5#6711yescharacteristic
239C42×C5C22×D311yescharacteristic
240C42×C5C22×D311yescharacteristic
241C22⋊Dic5—21no—
242#687—38no—
243#686—38no—
244#685—21no—
245#685—21no—
246C4⋊Dic5C22×D311yescharacteristic
247C4⋊Dic5C22×D311yescharacteristic
248#683—21no—
249#683—21no—
250C4×Dic5—21no—
251C4×Dic5—21no—
252C4×Dic5—21no—
253#681—34no—
254#681—62no—
255C2×#168—32no—
256C2×#168—32no—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—51no—
259C2×C4×D4—31no—
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—24no—
273C2×C5×D3—48no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C3×D5—22no—
277C2×C3×D5—41no—
278C2×C3×D5—41no—
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—22no—
287C3×Dic5—41no—
288C3×Dic5—41no—
289C5×Dic3—42no—
290C23×D3—21no—
291C3×#41—54no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—51no—
295C2×C3×D4—101no—
296C22×C3×C4—101no—
297C22×C3×C4—101no—
298C22×C3×C4—101no—
299C22×C3×C4C22⋊D511yescharacteristic
300C22×C3×C4C22⋊D511yescharacteristic
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—21no—
303C2×D12—22no—
304C2×D12—21no—
305C2×D12C4×D514yescomplemented
306C2×D12C22×D512yes—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—44no—
310C3×C4⋊C4—51no—
311C3×C4⋊C4—51no—
312C3×C4⋊C4—101no—
313C3×C4⋊C4—101no—
314C3×C22⋊C4—101no—
315C3×C22⋊C4—101no—
316C3×C22⋊C4—101no—
317C3×C42—101no—
318C3×C42—101no—
319C3×C42—101no—
320C3×C42C22⋊D511yescharacteristic
321C3×C42C22⋊D511yescharacteristic
322C3×C42C22×D511yescharacteristic
323C3×C42C22×D511yescharacteristic
324#215—58no—
325#213—58no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—22no—
328C4⋊Dic3—21no—
329C4⋊Dic3C22×D512yes—
330#208—54no—
331#208—102no—
332C2×C3⋊C8—52no—
333C2×C3⋊C8—52no—
334C23×C5—64no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—122no—
338C23×C5C2×#6711yescharacteristic
339C22×D5—21no—
340C5×D4—34no—
341C5×D4—64no—
342C5×D4—62no—
343C2×C4×C5—22no—
344C2×C4×C5—41no—
345C2×C4×C5—62no—
346C2×C4×C5—124no—
347C2×C4×C5—122no—
348C2×C4×C5—124no—
349C2×C4×C5C2×C4×D312yes—
350C2×C4×C5#23512yes—
351C2×C4×C5C2×#6711yescharacteristic
352C2×C4×C5C2×#6711yescharacteristic
353C2×C4×C5C2×#6711yescharacteristic
354C2×C4×C5C2×#6711yescharacteristic
355C2×C4×C5C2×#6711yescharacteristic
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—24no—
358C2×Dic5—21no—
359C2×Dic5—21no—
360C2×Dic5—21no—
361D20—21no—
362D20C2×C4×D312yescomplemented
363C4×D5—24no—
364C4×D5—42no—
365C4×D5—42no—
366Dic10—21no—
367Dic10C2×C4×D312yescomplemented
368#168—34no—
369#168—62no—
370C2×#41—51no—
371C22×D4—31no—
372C23×C4—61no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—151no—
377C2×M16—151no—
378C4×Q8—51no—
379C4×Q8—51no—
380C4×D4—32no—
381C4×D4—32no—
382C4×D4—51no—
383C4×D4—51no—
384C4×D4—61no—
385C4×D4—61no—
386C4×D4—101no—
387C4×D4—101no—
388#117—51no—
389#117—101no—
390C2×C4⋊C4—31no—
391C2×C22⋊C4—61no—
392C2×C42—101no—
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—42no—
407C5×D3—44no—
408C23×C3—101no—
409C23×C3C2×C22⋊D511yescharacteristic
410C22×D3—22no—
411C22×D3—24no—
412C22×D3—42no—
413C22×D3—42no—
414C3×Q8—52no—
415C3×Q8—101no—
416C3×D4—52no—
417C3×D4—104no—
418C3×D4—101no—
419C2×C3×C4—22no—
420C2×C3×C4—41no—
421C2×C3×C4—101no—
422C2×C3×C4—104no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—202no—
426C2×C3×C4—202no—
427C2×C3×C4C2×C4×D512yes—
428C2×C3×C4#70912yes—
429C2×C3×C4C2×C22⋊D511yescharacteristic
430C2×C3×C4C2×C22⋊D511yescharacteristic
431C2×C3×C4C2×C22⋊D511yescharacteristic
432C2×C3×C4C2×C22⋊D511yescharacteristic
433C2×C3×C4C2×C22⋊D511yescharacteristic
434C2×C3×C4C23×D511yescharacteristic
435C2×Dic3—22no—
436C2×Dic3—42no—
437D12—22no—
438D12—24no—
439D12C2×C4×D514yes—
440C4×D3—44no—
441C4×D3—44no—
442C3⋊C8—54no—
443C3⋊C8—102no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—64no—
447C22×C5—128no—
448C22×C5—122no—
449C22×C5—122no—
450C22×C5C4×#6712yes—
451C22×C5C22×#6711yescharacteristic
452C2×D5—22no—
453C2×D5—41no—
454C2×D5—41no—
455C4×C5—21no—
456C4×C5—21no—
457C4×C5—21no—
458C4×C5—122no—
459C4×C5C4×#6712yes—
460C4×C5#94912yescomplemented
461C4×C5C22×C4×D311yescharacteristic
462C4×C5C2×#23511yescharacteristic
463Dic5—22no—
464Dic5—41no—
465Dic5—41no—
466C24—61no—
467#41—54no—
468#41—102no—
469C2×Q8—51no—
470C2×D4—34no—
471C2×D4—32no—
472C2×D4—51no—
473C2×D4—62no—
474C2×D4—61no—
475C2×D4—101no—
476C22×C4—61no—
477C22×C4—62no—
478C22×C4—62no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—124no—
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—32no—
493C4⋊C4—51no—
494C4⋊C4—51no—
495C4⋊C4—61no—
496C4⋊C4—101no—
497C4⋊C4—101no—
498C22⋊C4—62no—
499C22⋊C4—62no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C42—101no—
504C42—101no—
505C42—101no—
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—102no—
514C22×C3—201no—
515C22×C3—201no—
516C22×C3C4×C22⋊D512yes—
517C22×C3C22×C22⋊D511yescharacteristic
518C2×D3—24no—
519C2×D3—48no—
520C2×D3—42no—
521C2×D3—42no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—102no—
526C3×C4—201no—
527C3×C4—201no—
528C3×C4C4×C22⋊D512yes—
529C3×C4#407812yescomplemented
530C3×C4C22×C4×D511yescharacteristic
531C3×C4C2×#70911yescharacteristic
532Dic3—42no—
533C2×C5—22no—
534C2×C5—124no—
535C2×C5C2×C4×#6711yescharacteristic
536C2×C5C2×#94911yescharacteristic
537C2×C5#582211yescharacteristic
538D5—42no—
539C23—64no—
540C23—62no—
541C23—101no—
542C23—122no—
543C23—122no—
544C23C2×#120111yescharacteristic
545Q8—52no—
546Q8—101no—
547D4—34no—
548D4—52no—
549D4—64no—
550D4—62no—
551D4—104no—
552D4—101no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—62no—
556C2×C4—101no—
557C2×C4—104no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—124no—
561C2×C4—122no—
562C2×C4—124no—
563C2×C4—202no—
564C2×C4—202no—
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—202no—
577C2×C3C2×C4×C22⋊D511yescharacteristic
578C2×C3C2×#407811yescharacteristic
579C2×C3#6615611yescharacteristic
580D3—44no—
581C5C4×#94911yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—64no—
585C22—102no—
586C22—128no—
587C22—122no—
588C22—122no—
589C22—201no—
590C22—201no—
591C22C4×#120112yes—
592C22C22×#120111yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—102no—
597C4—122no—
598C4—201no—
599C4—201no—
600C4#9129912yesdirect product factor
601C4C4×#120112yes—
602C4C2×#677111yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3C4×#407811yescharacteristic, complemented, Sylow
605C2—22no—
606C2—124no—
607C2—202no—
608C2C2×#9129911yescharacteristic
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×#91299C2
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. C2×C4×C5×D12C2semidirect
2. C3×C4×#709C2semidirect
4. C4×#6710C2semidirect
5. #11748472C2semidirect
6. #11748386C2semidirect
7. #11748368C2semidirect
8. #11747050C2semidirect
9. C4×#6656C2semidirect
10. #11747021C2semidirect
11. C4×#6652C2semidirect
28. C3×C4×D20C22semidirect
29. C3×C4×D20C22semidirect
32. C3×C4×Dic10C22semidirect
33. C3×C4×Dic10C22semidirect
35. #91299C4direct (N × H)
37. #91087C22semidirect
38. C4×C3⋊#168C22semidirect
39. #90989C22semidirect
40. #90986C22semidirect
41. #90970C22semidirect
44. #90964C22semidirect
48. C4×#709D3semidirect
64. C2×C5×D12C2×C4semidirect
71. C3×#709C2×C4semidirect
82. #6710C2×C4semidirect
99. #6656C2×C4semidirect
100. #6652C2×C4semidirect
103. C2×C4×D12D5semidirect
130. C4×D20C2×D3semidirect
131. C4×D20C2×D3semidirect
134. C4×Dic10C2×D3semidirect
135. C4×Dic10C2×D3semidirect
173. C3×D20C22×C4semidirect
178. C3×Dic10C22×C4semidirect
180. C3⋊#168C22×C4semidirect
227. #709C4×D3semidirect
283. C3×C4×C5AGL(1,ℤ/8)semidirect
305. C2×D12C4×D5semidirect
362. D20C2×C4×D3semidirect
367. Dic10C2×C4×D3semidirect
460. C4×C5#949semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
529. C3×C4#4078semidirect
581. C5C4×#949semidirect
600. C4#91299direct (N × H)
604. C3C4×#4078semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D122
C3×C4×#7092
C2×#912992
C4×#67102
#117484722
#117483862
#117483682
#117470502
C4×#66562
#117470212
C4×#66522
C4×#40783
C4×#9495