Finite Group Databasebeta

← C4×#91840 #14416822

Subgroups — C4×#91840 #14416822

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
1C3×C4×C5×#41C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic
3C2×C4×Dic30C211yesmaximal, characteristic, complemented
4#11751333C211yesmaximal, characteristic
5#11751131C212yesmaximal, complemented
6C4×#6718C212yesmaximal, complemented
7#11751119C212yesmaximal, complemented
8C4×#6716C212yesmaximal, complemented
9#11751105C211yesmaximal, characteristic, complemented
10#11751096C211yesmaximal, characteristic, complemented
11C4×#6710C211yesmaximal, characteristic, complemented
12C4×#4097—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C3×C4×C5×Q8C2211yescharacteristic
16C3×C4×C5×Q8C2211yescharacteristic
17C3×C4×C5×D4—21no—
18C3×C4×C5×D4—21no—
19C3×C4×C5×D4C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×C5×#117—21no—
22C3×C5×#117C2211yescharacteristic
23C2×C3×C42×C5—21no—
24C2×C3×C42×C5C2211yescharacteristic
25#91840C418yesdirect product factor
26C2×#6718C2212yes—
27C2×#6716C2212yes—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712—21no—
30C2×C4×Dic15—21no—
31C2×#6710C2211yescharacteristic
32C2×#6710C2211yescharacteristic
33C4×Dic30—21no—
34C4×Dic30—21no—
35C4×Dic30C2212yes—
36C4×Dic30C2212yes—
37#91119C2212yes—
38#91116C2212yes—
39#91094C2212yes—
40#91094C2212yes—
41#91092C2212yes—
42#91091C2212yes—
43#91087C2212yes—
44C4×C3⋊#168C2212yes—
45C4×#951—51nomaximal, Hall
46C4×C5×#41D311yescharacteristic
47C2×#4097—31no—
48C2×C4×Dic10—31no—
49#65521—31no—
50#65319—32no—
51C4×#689—32no—
52#65307—32no—
53C4×#687—32no—
54#65293—31no—
55#65284—31no—
56C4×#681—31no—
57C3×C5×#41—22no—
58C3×C5×#41C2×C414yes—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—21no—
65C22×C3×C4×C5D411yescharacteristic
66C22×C3×C4×C5D411yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15—21no—
69C22×Dic15—21no—
70C2×Dic30—21no—
71C2×Dic30—22no—
72C2×Dic30C2×C414yescomplemented
73C2×Dic30C2312yes—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C22⋊C4—21no—
79C3×C5×C22⋊C4—21no—
80C3×C5×C22⋊C4—21no—
81C3×C42×C5—21no—
82C3×C42×C5—21no—
83C3×C42×C5—21no—
84C3×C42×C5D411yescharacteristic
85C3×C42×C5D411yescharacteristic
86C3×C42×C5C2311yescharacteristic
87C3×C42×C5C2311yescharacteristic
88#6718C2×C418yescomplemented
89#6716C2×C418yescomplemented
90C4⋊Dic15—21no—
91C4⋊Dic15C2312yes—
92#6712—22no—
93#6712—22no—
94C4×Dic15—22no—
95C4×Dic15—22no—
96#6710—22no—
97#6710C2×C414yescomplemented
98C2×C3⋊#168C2312yes—
99C2×C3⋊#168C2312yes—
100C3×C4×#41D511yescharacteristic
101C2×#951—51no—
102C2×C4×Dic6—51no—
103#5232—51no—
104#5030—52no—
105C4×#216—52no—
106#5018—52no—
107C4×#214—52no—
108#5004—51no—
109#4995—51no—
110C4×#208—51no—
111C2×C5×#41C2×D311yescharacteristic
112C22×Dic10—31no—
113C4×C5×Q8C2×D311yescharacteristic
114C4×C5×Q8C2×D311yescharacteristic
115C4×C5×D4—21no—
116C4×C5×D4—21no—
117C4×C5×D4C2×D311yescharacteristic
118C4×C5×D4C2×D311yescharacteristic
119C5×#117—21no—
120C5×#117C2×D311yescharacteristic
121C2×C42×C5—21no—
122C2×C42×C5C2×D311yescharacteristic
123#4097—38no—
124C2×#689—32no—
125C2×#687—32no—
126C2×C4⋊Dic5—31no—
127C2×#683—61no—
128C2×C4×Dic5—61no—
129C2×#681—31no—
130C2×#681—31no—
131C4×Dic10—32no—
132C4×Dic10—32no—
133C4×Dic10—61no—
134C4×Dic10—61no—
135#3967—32no—
136#3964—32no—
137#3942—32no—
138#3942—32no—
139#3940—32no—
140#3939—32no—
141#3935—32no—
142C4×#168—32no—
143C4×#137—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C3×C5×Q8—21no—
147C3×C5×Q8C22×C412yes—
148C3×C5×D4—24no—
149C3×C5×D4—21no—
150C3×C5×D4C22×C412yes—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—24no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—41no—
157C2×C3×C4×C5—42no—
158C2×C3×C4×C5—42no—
159C2×C3×C4×C5C22×C412yes—
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D411yescharacteristic
163C2×C3×C4×C5C2×D411yescharacteristic
164C2×C3×C4×C5C2×D411yescharacteristic
165C2×C3×C4×C5#4112yes—
166C2×C3×C4×C5C2411yescharacteristic
167C2×Dic15—24no—
168C2×Dic15—22no—
169C2×Dic15—22no—
170C2×Dic15—42no—
171Dic30—24no—
172Dic30—22no—
173Dic30C22×C414yes—
174C3⋊#168—22no—
175C3⋊#168C22×C414yes—
176C2×C3×#41C2×D511yescharacteristic
177C22×Dic6—51no—
178C3×C4×Q8C2×D511yescharacteristic
179C3×C4×Q8C2×D511yescharacteristic
180C3×C4×D4—21no—
181C3×C4×D4—21no—
182C3×C4×D4C2×D511yescharacteristic
183C3×C4×D4C2×D511yescharacteristic
184C3×#117—21no—
185C3×#117C2×D511yescharacteristic
186C2×C3×C42—21no—
187C2×C3×C42C2×D511yescharacteristic
188#951—58no—
189C2×#216—52no—
190C2×#214—52no—
191C2×C4⋊Dic3—51no—
192C2×Dic3⋊C4—101no—
193C2×C4×Dic3—101no—
194C2×#208—51no—
195C2×#208—51no—
196C4×Dic6—52no—
197C4×Dic6—52no—
198C4×Dic6—101no—
199C4×Dic6—101no—
200#835—52no—
201#832—52no—
202#810—52no—
203#810—52no—
204#808—52no—
205#807—52no—
206#803—52no—
207C4×C3⋊C8—52no—
208C5×#41—22no—
209C5×#41C4×D314yes—
210C2×C5×Q8C22×D311yescharacteristic
211C2×C5×D4—21no—
212C2×C5×D4C22×D311yescharacteristic
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5#6711yescharacteristic
217C22×C4×C5#6711yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×Dic5—61no—
220C22×Dic5—61no—
221C2×Dic10—34no—
222C2×Dic10—32no—
223C2×Dic10—62no—
224C2×Dic10—61no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4C22×D311yescharacteristic
228C5×C4⋊C4C22×D311yescharacteristic
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—21no—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5#6711yescharacteristic
236C42×C5#6711yescharacteristic
237C42×C5C22×D311yescharacteristic
238C42×C5C22×D311yescharacteristic
239#689—38no—
240#687—38no—
241C4⋊Dic5—32no—
242C4⋊Dic5—61no—
243#683—62no—
244#683—62no—
245C4×Dic5—62no—
246C4×Dic5—62no—
247#681—34no—
248#681—62no—
249C2×#168—32no—
250C2×#168—32no—
251C2×#137—151no—
252C4×#41D1511yescharacteristic
253C2×C4×Q8—151no—
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×C5—22no—
265C22×C3×C5—41no—
266C22×C3×C5—41no—
267C22×C3×C5C4×D412yes—
268C22×C3×C5C22×D411yescharacteristic
269C3×C4×C5—22no—
270C3×C4×C5—21no—
271C3×C4×C5—21no—
272C3×C4×C5—21no—
273C3×C4×C5—41no—
274C3×C4×C5—41no—
275C3×C4×C5C4×D412yes—
276C3×C4×C5#13712yescomplemented
277C3×C4×C5C23×C411yescharacteristic
278C3×C4×C5C2×#4111yescharacteristic
279Dic15—24no—
280Dic15—42no—
281C3×#41—22no—
282C3×#41C4×D514yes—
283C2×C3×Q8C22×D511yescharacteristic
284C2×C3×D4—21no—
285C2×C3×D4C22×D511yescharacteristic
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4C22⋊D511yescharacteristic
290C22×C3×C4C22⋊D511yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—101no—
293C22×Dic3—101no—
294C2×Dic6—54no—
295C2×Dic6—52no—
296C2×Dic6—102no—
297C2×Dic6—101no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C22×D511yescharacteristic
301C3×C4⋊C4C22×D511yescharacteristic
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—21no—
308C3×C42C22⋊D511yescharacteristic
309C3×C42C22⋊D511yescharacteristic
310C3×C42C22×D511yescharacteristic
311C3×C42C22×D511yescharacteristic
312#216—58no—
313#214—58no—
314C4⋊Dic3—52no—
315C4⋊Dic3—101no—
316Dic3⋊C4—102no—
317Dic3⋊C4—102no—
318C4×Dic3—102no—
319C4×Dic3—102no—
320#208—54no—
321#208—102no—
322C2×C3⋊C8—52no—
323C2×C3⋊C8—52no—
324C23×C5—21no—
325C23×C5C2×#6711yescharacteristic
326C5×Q8—21no—
327C5×Q8C2×C4×D312yes—
328C5×D4—24no—
329C5×D4—21no—
330C5×D4C2×C4×D312yes—
331C2×C4×C5—21no—
332C2×C4×C5—24no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—41no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5C2×C4×D312yes—
340C2×C4×C5#23512yes—
341C2×C4×C5C2×#6711yescharacteristic
342C2×C4×C5C2×#6711yescharacteristic
343C2×C4×C5C2×#6711yescharacteristic
344C2×C4×C5C2×#6711yescharacteristic
345C2×C4×C5C2×#6711yescharacteristic
346C2×C4×C5C23×D311yescharacteristic
347C2×Dic5—64no—
348C2×Dic5—62no—
349C2×Dic5—62no—
350C2×Dic5—122no—
351Dic10—34no—
352Dic10—64no—
353Dic10—62no—
354#168—34no—
355#168—62no—
356C2×#41C2×D1511yescharacteristic
357C22×Q8—151no—
358#137—158no—
359C2×Q16—152no—
360C2×SD16—152no—
361C2×M16—151no—
362C2×M16—151no—
363C4×Q8—152no—
364C4×Q8—152no—
365C4×Q8—301no—
366C4×Q8—301no—
367C4×Q8C2×D1511yescharacteristic
368C4×Q8C2×D1511yescharacteristic
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C2×D1511yescharacteristic
372C4×D4C2×D1511yescharacteristic
373#117—21no—
374#117C2×D1511yescharacteristic
375C2×C4⋊C4—151no—
376C2×C4⋊C4—301no—
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×C5—42no—
390C2×C3×C5C2×C4×D411yescharacteristic
391C2×C3×C5C2×#13711yescharacteristic
392C2×C3×C5#57511yescharacteristic
393C23×C3—21no—
394C23×C3C2×C22⋊D511yescharacteristic
395C3×Q8—21no—
396C3×Q8C2×C4×D512yes—
397C3×D4—24no—
398C3×D4—21no—
399C3×D4C2×C4×D512yes—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—24no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—41no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4C2×C4×D512yes—
409C2×C3×C4#70912yes—
410C2×C3×C4C2×C22⋊D511yescharacteristic
411C2×C3×C4C2×C22⋊D511yescharacteristic
412C2×C3×C4C2×C22⋊D511yescharacteristic
413C2×C3×C4C2×C22⋊D511yescharacteristic
414C2×C3×C4C2×C22⋊D511yescharacteristic
415C2×C3×C4C23×D511yescharacteristic
416C2×Dic3—102no—
417C2×Dic3—104no—
418C2×Dic3—102no—
419C2×Dic3—202no—
420Dic6—54no—
421Dic6—102no—
422Dic6—104no—
423C3⋊C8—54no—
424C3⋊C8—102no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5—22no—
428C22×C5—41no—
429C22×C5—41no—
430C22×C5C4×#6712yes—
431C22×C5C22×#6711yescharacteristic
432C4×C5—22no—
433C4×C5—21no—
434C4×C5—21no—
435C4×C5—21no—
436C4×C5—41no—
437C4×C5—41no—
438C4×C5C4×#6712yes—
439C4×C5#95112yescomplemented
440C4×C5C22×C4×D311yescharacteristic
441C4×C5C2×#23511yescharacteristic
442Dic5—64no—
443Dic5—122no—
444#41—22no—
445#41C4×D1514yes—
446C2×Q8—154no—
447C2×Q8—152no—
448C2×Q8—302no—
449C2×Q8—301no—
450C2×Q8C22×D1511yescharacteristic
451C2×D4—21no—
452C2×D4C22×D1511yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
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—21no—
468C4⋊C4—21no—
469C4⋊C4—152no—
470C4⋊C4—301no—
471C4⋊C4—302no—
472C4⋊C4—302no—
473C4⋊C4C22×D1511yescharacteristic
474C4⋊C4C22×D1511yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—302no—
482C42—302no—
483C42#122011yescharacteristic
484C42#122011yescharacteristic
485C42C22×D1511yescharacteristic
486C42C22×D1511yescharacteristic
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3C4×C22⋊D512yes—
494C22×C3C22×C22⋊D511yescharacteristic
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4C4×C22⋊D512yes—
502C3×C4#409712yescomplemented
503C3×C4C22×C4×D511yescharacteristic
504C3×C4C2×#70911yescharacteristic
505Dic3—104no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5C2×C4×#6711yescharacteristic
510C2×C5#582211yescharacteristic
511C2×C5C2×#95111yescharacteristic
512C23—21no—
513C23C2×#122011yescharacteristic
514Q8—21no—
515Q8—154no—
516Q8—304no—
517Q8—302no—
518Q8C2×C4×D1512yes—
519D4—24no—
520D4—21no—
521D4C2×C4×D1512yes—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—304no—
531C2×C4—302no—
532C2×C4—302no—
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×C3—42no—
546C2×C3C2×C4×C22⋊D511yescharacteristic
547C2×C3#6615611yescharacteristic
548C2×C3C2×#409711yescharacteristic
549C5C4×#95111yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22C4×#122012yes—
556C22C22×#122011yescharacteristic
557C4—22no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—304no—
564C4—602no—
565C4C4×#122012yes—
566C4#9184012yesdirect product factor
567C4C22×C4×D1511yescharacteristic
568C4C2×#681711yescharacteristic
569C3C4×#409711yescharacteristic, complemented, Sylow
570C2—22no—
571C2—42no—
572C2C2×C4×#122011yescharacteristic
573C2#1175658111yescharacteristic
574C2C2×#9184011yescharacteristic
subgroupG/H
centerC2×C4C2×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C4×C5×#41C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C4×C5C24
hypercenterC4×#41D15
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic30C2semidirect
5. #11751131C2semidirect
6. C4×#6718C2semidirect
7. #11751119C2semidirect
8. C4×#6716C2semidirect
9. #11751105C2semidirect
10. #11751096C2semidirect
11. C4×#6710C2semidirect
25. #91840C4direct (N × H)
72. C2×Dic30C2×C4semidirect
88. #6718C2×C4semidirect
89. #6716C2×C4semidirect
97. #6710C2×C4semidirect
276. C3×C4×C5#137semidirect
439. C4×C5#951semidirect
487. C3×C5C4×#137semidirect
502. C3×C4#4097semidirect
549. C5C4×#951semidirect
566. C4#91840direct (N × H)
569. C3C4×#4097semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×#412
C2×#918402
C2×C4×Dic302
#117513332
#117511312
C4×#67182
#117511192
C4×#67162
#117511052
#117510962
C4×#67102
C4×#40973
C4×#9515