Finite Group Databasebeta

← C2×#11756450 #14479792

Subgroups — C2×#11756450 #14479792

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756450C2116yesmaximal, direct product factor
3C2×#91787C212yesmaximal, complemented
4C2×#91786C211yesmaximal, characteristic, complemented
5C2×#91784C211yesmaximal, characteristic
6C2×#91783C212yesmaximal, complemented
7C2×#91782C211yesmaximal, characteristic, complemented
8C2×#91782C212yesmaximal, complemented
9C2×#91781C212yesmaximal, complemented
10C2×#91776C211yesmaximal, characteristic, complemented
11C2×#91764C211yesmaximal, characteristic, complemented
12C2×C42×D15C211yesmaximal, characteristic, complemented
13C2×#66025—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×D60C2212yes—
16C22×C4×D15C2211yescharacteristic
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2212yes—
20C22×Dic30C2211yescharacteristic
21C3×C5×#125C2218yescomplemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2212yes—
26C2×C3×C42×C5C2211yescharacteristic
27C2×#6714C2212yes—
28C2×#6714C2212yes—
29C2×#6714C2212yes—
30C2×#6714C2212yes—
31C2×#6714C2212yes—
32C2×C4⋊Dic15C2212yes—
33C2×#6712C2212yes—
34C2×C4×Dic15C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2212yes—
38#91787C22116yescomplemented
39#91786C2218yescomplemented
40#91784C2218yes—
41#91783C22116yescomplemented
42#91782C2218yescomplemented
43#91782C22116yescomplemented
44#91781C22116yescomplemented
45#91776C2218yescomplemented
46#91764C2218yescomplemented
47C42×D15C2218yescomplemented
48C2×#5691—51nomaximal, Hall
49C2×C5×#125D311yescharacteristic, complemented
50#66025—316no—
51C2×#4044—32no—
52C2×#4043—31no—
53C2×#4041—31no—
54C2×#4040—32no—
55C2×#4039—31no—
56C2×#4039—32no—
57C2×#4038—32no—
58C2×#4033—31no—
59C2×#4021—31no—
60C2×C42×D5—31no—
61C23×D15C2312yes—
62C23×D15C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C22×Dic15C2311yescharacteristic
72C2×D60—28no—
73C2×D60—24no—
74C2×D60C2314yes—
75C2×D60C2318yes—
76C2×C4×D15—24no—
77C2×C4×D15—24no—
78C2×C4×D15—24no—
79C2×C4×D15—28no—
80C2×C4×D15C2314yes—
81C2×C4×D15C2314yes—
82C2×C4×D15C2314yes—
83C2×C4×D15C2318yes—
84C2×Dic30—24no—
85C2×Dic30C2314yes—
86C3×C5×C4⋊C4C2314yes—
87C3×C5×C4⋊C4C2318yes—
88C3×C5×C4⋊C4C2314yes—
89C3×C5×C4⋊C4C2318yes—
90C3×C42×C5C2314yes—
91#6714C2318yes—
92#6714C2318yes—
93#6714C2318yes—
94#6714C2318yes—
95#6714C2318yes—
96C4⋊Dic15C2318yes—
97#6712C2318yes—
98C4×Dic15C2314yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C4×Dic15C2318yes—
102C2×C3×#125D511yescharacteristic, complemented
103#5691—516no—
104C2×#898—52no—
105C2×#897—51no—
106C2×#895—51no—
107C2×#894—52no—
108C2×#893—51no—
109C2×#893—52no—
110C2×#892—52no—
111C2×#887—51no—
112C2×#875—51no—
113C2×C42×D3—51no—
114C22×D20—31no—
115C22×D20—32no—
116C22×C4×D5—31no—
117C22×C4×D5—31no—
118C22×C4×D5—31no—
119C22×C4×D5—32no—
120C22×Dic10—31no—
121C5×#125C2×D318yescomplemented
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C5×C4⋊C4C2×D312yes—
124C2×C5×C4⋊C4C2×D311yescharacteristic
125C2×C5×C4⋊C4C2×D312yes—
126C2×C42×C5C2×D311yescharacteristic
127C2×#685—32no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×C4⋊Dic5—32no—
133C2×#683—32no—
134C2×C4×Dic5—31no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—32no—
138#4044—316no—
139#4043—38no—
140#4041—38no—
141#4040—316no—
142#4039—38no—
143#4039—316no—
144#4038—316no—
145#4033—38no—
146#4021—38no—
147C42×D5—38no—
148C2×#529—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×D15—22no—
151C22×D15—22no—
152C22×D15—24no—
153C22×D15—24no—
154C22×D15—24no—
155C22×D15#4114yes—
156C22×D15C2414yes—
157C22×D15C2412yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—24no—
161C2×C3×C4×C5—24no—
162C2×C3×C4×C5#4114yes—
163C2×C3×C4×C5C2414yes—
164C2×C3×C4×C5C2412yes—
165C2×C3×C4×C5C2412yes—
166C2×C3×C4×C5C2414yes—
167C2×C3×C4×C5C2412yes—
168C2×Dic15—24no—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15#4114yes—
172C2×Dic15C2412yes—
173C2×Dic15C2412yes—
174C2×Dic15C2414yes—
175C2×Dic15C2412yes—
176D60—216no—
177D60—28no—
178C4×D15—28no—
179C4×D15—28no—
180C4×D15—28no—
181C4×D15—216no—
182Dic30—28no—
183C22×D12—51no—
184C22×D12—52no—
185C22×C4×D3—51no—
186C22×C4×D3—51no—
187C22×C4×D3—51no—
188C22×C4×D3—52no—
189C22×Dic6—51no—
190C3×#125C2×D518yescomplemented
191C2×C3×C4⋊C4C2×D511yescharacteristic
192C2×C3×C4⋊C4C2×D512yes—
193C2×C3×C4⋊C4C2×D511yescharacteristic
194C2×C3×C4⋊C4C2×D512yes—
195C2×C3×C42C2×D511yescharacteristic
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4—52no—
201C2×C4⋊Dic3—52no—
202C2×Dic3⋊C4—52no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—51no—
205C2×C4×Dic3—51no—
206C2×C4×Dic3—52no—
207#898—516no—
208#897—58no—
209#895—58no—
210#894—516no—
211#893—58no—
212#893—516no—
213#892—516no—
214#887—58no—
215#875—58no—
216C42×D3—58no—
217C23×D5—31no—
218C23×D5—32no—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D312yes—
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—31no—
225C22×Dic5—32no—
226C22×Dic5—31no—
227C22×Dic5—31no—
228C2×D20—34no—
229C2×D20—38no—
230C2×D20—68no—
231C2×D20—64no—
232C2×C4×D5—34no—
233C2×C4×D5—34no—
234C2×C4×D5—34no—
235C2×C4×D5—38no—
236C2×C4×D5—64no—
237C2×C4×D5—68no—
238C2×C4×D5—64no—
239C2×C4×D5—64no—
240C2×Dic10—34no—
241C2×Dic10—64no—
242C5×C4⋊C4C22×D314yes—
243C5×C4⋊C4C22×D318yes—
244C5×C4⋊C4C22×D314yes—
245C5×C4⋊C4C22×D318yes—
246C42×C5C22×D314yes—
247#685—38no—
248#685—38no—
249#685—38no—
250#685—38no—
251#685—38no—
252C4⋊Dic5—38no—
253#683—38no—
254C4×Dic5—34no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5—38no—
258#529—1516no—
259C2×#126—152no—
260C2×#125D1511yescharacteristic, complemented
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—151no—
265C2×C4×Q8—151no—
266C2×C4×D4—152no—
267C2×C4×D4—151no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2511yescharacteristic
274C2×D15—28no—
275C2×D15—22no—
276C2×D15—22no—
277C2×D15—24no—
278C2×D15—24no—
279C2×D15—24no—
280C2×D15—48no—
281C2×D15C2×#4114yes—
282C3×C4×C5—22no—
283C3×C4×C5—22no—
284C3×C4×C5—24no—
285C3×C4×C5—24no—
286C3×C4×C5C2×#4114yes—
287Dic15—24no—
288Dic15—22no—
289Dic15—22no—
290Dic15C2×#4114yes—
291C23×D3—51no—
292C23×D3—52no—
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D511yescharacteristic
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D512yes—
297C22×C3×C4C22×D511yescharacteristic
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3—52no—
302C2×D12—54no—
303C2×D12—58no—
304C2×D12—108no—
305C2×D12—104no—
306C2×C4×D3—54no—
307C2×C4×D3—54no—
308C2×C4×D3—54no—
309C2×C4×D3—58no—
310C2×C4×D3—104no—
311C2×C4×D3—108no—
312C2×C4×D3—104no—
313C2×C4×D3—104no—
314C2×Dic6—54no—
315C2×Dic6—104no—
316C3×C4⋊C4C22×D514yes—
317C3×C4⋊C4C22×D518yes—
318C3×C4⋊C4C22×D514yes—
319C3×C4⋊C4C22×D518yes—
320C3×C42C22×D514yes—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323(C2×D3)⋊C4—58no—
324(C2×D3)⋊C4—58no—
325(C2×D3)⋊C4—58no—
326C4⋊Dic3—58no—
327Dic3⋊C4—58no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3—58no—
332C23×C5C23×D311yescharacteristic
333C22×D5—34no—
334C22×D5—32no—
335C22×D5—34no—
336C22×D5—62no—
337C22×D5—62no—
338C22×D5—64no—
339C22×D5—64no—
340C22×D5—64no—
341C2×C4×C5—22no—
342C2×C4×C5—24no—
343C2×C4×C5—22no—
344C2×C4×C5—24no—
345C2×C4×C5#23914yes—
346C2×C4×C5C23×D314yes—
347C2×C4×C5C23×D312yes—
348C2×C4×C5C23×D312yes—
349C2×C4×C5C23×D314yes—
350C2×C4×C5C23×D312yes—
351C2×Dic5—34no—
352C2×Dic5—32no—
353C2×Dic5—32no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—64no—
357C2×Dic5—62no—
358C2×Dic5—62no—
359D20—616no—
360D20—68no—
361C4×D5—68no—
362C4×D5—616no—
363C4×D5—68no—
364C4×D5—68no—
365Dic10—68no—
366C22×Q8—151no—
367C22×D4—152no—
368C22×D4—151no—
369C23×C4—152no—
370C23×C4—151no—
371C23×C4—151no—
372C23×C4—151no—
373#126—1516no—
374#125C2×D1518yescomplemented
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—158no—
379C4×Q8—158no—
380C4×D4—158no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4C2×D1512yes—
386C2×C4⋊C4C2×D1511yescharacteristic
387C2×C4⋊C4C2×D1512yes—
388C2×C4⋊C4C2×D1511yescharacteristic
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—151no—
395C2×C42—152no—
396C2×C42—151no—
397C2×C42—151no—
398C2×C42—158no—
399C2×C42C2×D1511yescharacteristic
400C2×C3×C5#52914yescomplemented
401C2×C3×C5C22×#4111yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404D15—24no—
405D15—44no—
406C23×C3C23×D511yescharacteristic
407C22×D3—54no—
408C22×D3—52no—
409C22×D3—54no—
410C22×D3—102no—
411C22×D3—102no—
412C22×D3—104no—
413C22×D3—104no—
414C22×D3—104no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4#71314yes—
420C2×C3×C4C23×D514yes—
421C2×C3×C4C23×D512yes—
422C2×C3×C4C23×D512yes—
423C2×C3×C4C23×D514yes—
424C2×C3×C4C23×D512yes—
425C2×Dic3—54no—
426C2×Dic3—52no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—54no—
430C2×Dic3—104no—
431C2×Dic3—102no—
432C2×Dic3—102no—
433D12—1016no—
434D12—108no—
435C4×D3—108no—
436C4×D3—1016no—
437C4×D3—108no—
438C4×D3—108no—
439Dic6—108no—
440C22×C5C2×#23912yes—
441C22×C5D3×#4112yes—
442C22×C5D3×#4112yes—
443C22×C5C24×D311yescharacteristic
444C2×D5—34no—
445C2×D5—68no—
446C2×D5—62no—
447C2×D5—62no—
448C2×D5—64no—
449C2×D5—64no—
450C2×D5—64no—
451C2×D5—128no—
452C4×C5—22no—
453C4×C5—24no—
454C4×C5—22no—
455C4×C5—24no—
456C4×C5C2×#23914yes—
457Dic5—34no—
458Dic5—64no—
459Dic5—62no—
460Dic5—62no—
461C24—151no—
462C24—152no—
463C2×Q8—154no—
464C2×Q8—304no—
465C2×D4—158no—
466C2×D4—154no—
467C2×D4—308no—
468C2×D4—304no—
469C22×C4—151no—
470C22×C4—151no—
471C22×C4—151no—
472C22×C4—152no—
473C22×C4—154no—
474C22×C4—154no—
475C22×C4—154no—
476C22×C4—158no—
477C22×C4—304no—
478C22×C4—308no—
479C22×C4—304no—
480C22×C4—304no—
481C22×C4C22×D1511yescharacteristic
482C22×C4C22×D1511yescharacteristic
483C22×C4C22×D1512yes—
484C22×C4C22×D1512yes—
485C22×C4C22×D1511yescharacteristic
486C4⋊C4—158no—
487C4⋊C4—158no—
488C4⋊C4C22×D1518yes—
489C4⋊C4C22×D1514yes—
490C4⋊C4C22×D1518yes—
491C4⋊C4C22×D1514yes—
492C22⋊C4—158no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—154no—
498C42—154no—
499C42—154no—
500C42—158no—
501C42C22×D1514yes—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3C2×#71312yes—
504C22×C3D5×#4112yes—
505C22×C3D5×#4112yes—
506C22×C3C24×D511yescharacteristic
507C2×D3—54no—
508C2×D3—102no—
509C2×D3—102no—
510C2×D3—108no—
511C2×D3—104no—
512C2×D3—104no—
513C2×D3—104no—
514C2×D3—208no—
515C3×C4—22no—
516C3×C4—24no—
517C3×C4—22no—
518C3×C4—24no—
519C3×C4C2×#71314yes—
520Dic3—54no—
521Dic3—104no—
522Dic3—102no—
523Dic3—102no—
524C2×C5#569114yescomplemented
525C2×C5C22×#23911yescharacteristic
526C2×C5C2×D3×#4111yescharacteristic
527C2×C5C2×D3×#4111yescharacteristic
528D5—64no—
529D5—124no—
530C23—154no—
531C23—152no—
532C23—154no—
533C23—302no—
534C23—302no—
535C23—304no—
536C23—304no—
537C23—304no—
538C23C23×D1511yescharacteristic
539Q8—308no—
540D4—3016no—
541D4—308no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—154no—
547C2×C4—152no—
548C2×C4—152no—
549C2×C4—152no—
550C2×C4—154no—
551C2×C4—308no—
552C2×C4—3016no—
553C2×C4—308no—
554C2×C4—302no—
555C2×C4—304no—
556C2×C4—302no—
557C2×C4—308no—
558C2×C4#682114yes—
559C2×C4C23×D1512yes—
560C2×C4C23×D1512yes—
561C2×C4C23×D1514yes—
562C2×C4C23×D1514yes—
563C2×C4C23×D1512yes—
564C2×C3#6602514yescomplemented
565C2×C3C22×#71311yescharacteristic
566C2×C3C2×D5×#4111yescharacteristic
567C2×C3C2×D5×#4111yescharacteristic
568D3—104no—
569D3—204no—
570C5C2×#569111yescharacteristic, complemented, Sylow
571C22—154no—
572C22—302no—
573C22—302no—
574C22—308no—
575C22—304no—
576C22—304no—
577C22—304no—
578C22—608no—
579C22C2×#682112yes—
580C22#41×D1512yes—
581C22#41×D1512yes—
582C22C24×D1511yescharacteristic
583C4—22no—
584C4—24no—
585C4—22no—
586C4—24no—
587C4—154no—
588C4—302no—
589C4—304no—
590C4—302no—
591C4C2×#682114yes—
592C3C2×#6602511yescharacteristic, complemented, Sylow
593C2—304no—
594C2—604no—
595C2#1175645014yesdirect product factor
596C2C22×#682111yescharacteristic
597C2C2×#41×D1511yescharacteristic
598C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
prime radicalC2×#91784C2
hypercenterC2×#125D15
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
2. #11756450C2direct (N × H)
3. C2×#91787C2semidirect
4. C2×#91786C2semidirect
6. C2×#91783C2semidirect
7. C2×#91782C2semidirect
8. C2×#91782C2semidirect
9. C2×#91781C2semidirect
10. C2×#91776C2semidirect
11. C2×#91764C2semidirect
12. C2×C42×D15C2semidirect
21. C3×C5×#125C22semidirect
38. #91787C22semidirect
39. #91786C22semidirect
41. #91783C22semidirect
42. #91782C22semidirect
43. #91782C22semidirect
44. #91781C22semidirect
45. #91776C22semidirect
46. #91764C22semidirect
47. C42×D15C22semidirect
49. C2×C5×#125D3semidirect
102. C2×C3×#125D5semidirect
121. C5×#125C2×D3semidirect
190. C3×#125C2×D5semidirect
260. C2×#125D15semidirect
374. #125C2×D15semidirect
400. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
524. C2×C5#5691semidirect
564. C2×C3#66025semidirect
570. C5C2×#5691semidirect
592. C3C2×#66025semidirect
595. C2#11756450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1252
#117564502
C2×#917872
C2×#917862
C2×#917842
C2×#917832
C2×#917822
C2×#917812
C2×#917762
C2×#917642
C2×C42×D152
C2×#660253
C2×#56915