Finite Group Databasebeta

← C2×#11756454 #14483624

Subgroups — C2×#11756454 #14483624

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756454C2116yesmaximal, direct product factor
3C2×#91787C212yesmaximal, complemented
4C2×#91784C212yesmaximal, complemented
5C2×#91784C211yesmaximal, characteristic, complemented
6C2×#91784C211yesmaximal, characteristic, complemented
7C2×#91783C212yesmaximal, complemented
8C2×#91782C212yesmaximal, complemented
9C2×#91781C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
11C2×C4×D60C211yesmaximal, characteristic, complemented
12C2×C4×D60C211yesmaximal, characteristic, complemented
13C2×#66029—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×D60C2211yescharacteristic
16C22×D60C2212yes—
17C22×D60C2212yes—
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×D15C2212yes—
21C22×C4×D15C2212yes—
22C3×C5×#125C2218yescomplemented
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2212yes—
26C2×C3×C5×C4⋊C4C2212yes—
27C2×C3×C42×C5C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2212yes—
31C2×#6714C2212yes—
32C2×#6714C2212yes—
33C2×#6714C2212yes—
34C2×C4⋊Dic15C2211yescharacteristic
35C2×C4⋊Dic15C2211yescharacteristic
36C2×#6712C2212yes—
37C2×C4×Dic15C2212yes—
38#91787C22116yescomplemented
39#91784C22116yescomplemented
40#91784C2218yescomplemented
41#91784C2218yescomplemented
42#91783C22116yescomplemented
43#91782C22116yescomplemented
44#91781C2218yescomplemented
45C4⋊C4×D15C2218yescomplemented
46C4×D60C2218yescomplemented
47C4×D60C2218yescomplemented
48C2×#5695—51nomaximal, Hall
49C2×C5×#125D311yescharacteristic, complemented
50#66029—316no—
51C2×#4044—32no—
52C2×#4041—31no—
53C2×#4041—31no—
54C2×#4041—32no—
55C2×#4040—32no—
56C2×#4039—32no—
57C2×#4038—31no—
58C2×D5×C4⋊C4—31no—
59C2×C4×D20—31no—
60C2×C4×D20—31no—
61C23×D15C2311yescharacteristic
62C23×D15C2312yes—
63C23×D15C2311yescharacteristic
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C22×Dic15C2311yescharacteristic
72C2×D60—24no—
73C2×D60—28no—
74C2×D60—24no—
75C2×D60—44no—
76C2×D60C2314yes—
77C2×D60C2314yes—
78C2×D60C2318yes—
79C2×D60C2318yes—
80C2×C4×D15—24no—
81C2×C4×D15—24no—
82C2×C4×D15—44no—
83C2×C4×D15—44no—
84C2×C4×D15C2314yes—
85C2×C4×D15C2314yes—
86C2×C4×D15C2318yes—
87C2×C4×D15C2318yes—
88C3×C5×C4⋊C4C2314yes—
89C3×C5×C4⋊C4C2314yes—
90C3×C5×C4⋊C4C2318yes—
91C3×C5×C4⋊C4C2318yes—
92C3×C42×C5C2314yes—
93#6714C2314yes—
94#6714C2314yes—
95#6714C2318yes—
96#6714C2318yes—
97#6714C2318yes—
98#6714C2318yes—
99C4⋊Dic15C2314yes—
100C4⋊Dic15C2314yes—
101#6712C2318yes—
102C4×Dic15C2318yes—
103C2×C3×#125D511yescharacteristic, complemented
104#5695—516no—
105C2×#898—52no—
106C2×#895—52no—
107C2×#895—51no—
108C2×#895—51no—
109C2×#894—52no—
110C2×#893—52no—
111C2×#892—51no—
112C2×D3×C4⋊C4—51no—
113C2×C4×D12—51no—
114C2×C4×D12—51no—
115C22×D20—31no—
116C22×D20—31no—
117C22×D20—32no—
118C22×D20—32no—
119C22×C4×D5—31no—
120C22×C4×D5—31no—
121C22×C4×D5—32no—
122C22×C4×D5—32no—
123C5×#125C2×D318yescomplemented
124C2×C5×C4⋊C4C2×D311yescharacteristic
125C2×C5×C4⋊C4C2×D311yescharacteristic
126C2×C5×C4⋊C4C2×D312yes—
127C2×C5×C4⋊C4C2×D312yes—
128C2×C42×C5C2×D311yescharacteristic
129C2×#685—31no—
130C2×#685—31no—
131C2×#685—32no—
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135C2×C4⋊Dic5—31no—
136C2×C4⋊Dic5—31no—
137C2×#683—32no—
138C2×C4×Dic5—32no—
139#4044—316no—
140#4041—316no—
141#4041—38no—
142#4041—38no—
143#4040—316no—
144#4039—316no—
145#4038—38no—
146D5×C4⋊C4—38no—
147C4×D20—38no—
148C4×D20—38no—
149C2×#553—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×D15—22no—
152C22×D15—22no—
153C22×D15—22no—
154C22×D15—24no—
155C22×D15—22no—
156C22×D15—24no—
157C22×D15—24no—
158C22×D15—22no—
159C22×D15#4114yes—
160C22×D15C2412yes—
161C22×D15C2414yes—
162C22×D15C2412yes—
163C2×C3×C4×C5—24no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—24no—
167C2×C3×C4×C5#4114yes—
168C2×C3×C4×C5C2414yes—
169C2×C3×C4×C5C2414yes—
170C2×C3×C4×C5C2412yes—
171C2×C3×C4×C5C2412yes—
172C2×C3×C4×C5C2412yes—
173C2×Dic15—22no—
174C2×Dic15—22no—
175C2×Dic15—24no—
176C2×Dic15C2412yes—
177C2×Dic15C2414yes—
178C2×Dic15C2412yes—
179D60—28no—
180D60—216no—
181D60—28no—
182D60—48no—
183C4×D15—28no—
184C4×D15—28no—
185C4×D15—48no—
186C4×D15—48no—
187C22×D12—51no—
188C22×D12—51no—
189C22×D12—52no—
190C22×D12—52no—
191C22×C4×D3—51no—
192C22×C4×D3—51no—
193C22×C4×D3—52no—
194C22×C4×D3—52no—
195C3×#125C2×D518yescomplemented
196C2×C3×C4⋊C4C2×D511yescharacteristic
197C2×C3×C4⋊C4C2×D511yescharacteristic
198C2×C3×C4⋊C4C2×D512yes—
199C2×C3×C4⋊C4C2×D512yes—
200C2×C3×C42C2×D511yescharacteristic
201C2×(C2×D3)⋊C4—51no—
202C2×(C2×D3)⋊C4—51no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—52no—
206C2×(C2×D3)⋊C4—52no—
207C2×C4⋊Dic3—51no—
208C2×C4⋊Dic3—51no—
209C2×Dic3⋊C4—52no—
210C2×C4×Dic3—52no—
211#898—516no—
212#895—516no—
213#895—58no—
214#895—58no—
215#894—516no—
216#893—516no—
217#892—58no—
218D3×C4⋊C4—58no—
219C4×D12—58no—
220C4×D12—58no—
221C23×D5—31no—
222C23×D5—31no—
223C23×D5—32no—
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C22×C4×C5C22×D312yes—
227C22×C4×C5C22×D312yes—
228C22×C4×C5C22×D311yescharacteristic
229C22×Dic5—32no—
230C22×Dic5—31no—
231C22×Dic5—31no—
232C2×D20—34no—
233C2×D20—34no—
234C2×D20—38no—
235C2×D20—38no—
236C2×D20—64no—
237C2×D20—68no—
238C2×D20—64no—
239C2×D20—124no—
240C2×C4×D5—34no—
241C2×C4×D5—34no—
242C2×C4×D5—38no—
243C2×C4×D5—38no—
244C2×C4×D5—64no—
245C2×C4×D5—64no—
246C2×C4×D5—124no—
247C2×C4×D5—124no—
248C5×C4⋊C4C22×D314yes—
249C5×C4⋊C4C22×D314yes—
250C5×C4⋊C4C22×D318yes—
251C5×C4⋊C4C22×D318yes—
252C42×C5C22×D314yes—
253#685—34no—
254#685—34no—
255#685—38no—
256#685—38no—
257#685—38no—
258#685—38no—
259C4⋊Dic5—34no—
260C4⋊Dic5—34no—
261#683—38no—
262C4×Dic5—38no—
263#553—1516no—
264C2×#126—152no—
265C2×#125D1511yescharacteristic, complemented
266C2×#123—152no—
267C2×#121—152no—
268C2×#121—151no—
269C2×#121—151no—
270C2×C4×D4—152no—
271C2×C4×D4—151no—
272C2×C4×D4—151no—
273C2×#117—151no—
274C22×C4⋊C4—151no—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5H(5,𝔽2)12yes—
278C22×C3×C5C2511yescharacteristic
279C2×D15—28no—
280C2×D15—22no—
281C2×D15—22no—
282C2×D15—22no—
283C2×D15—24no—
284C2×D15—22no—
285C2×D15—24no—
286C2×D15—24no—
287C2×D15—22no—
288C2×D15—44no—
289C2×D15—48no—
290C2×D15C2×#4114yes—
291C3×C4×C5—24no—
292C3×C4×C5—22no—
293C3×C4×C5—22no—
294C3×C4×C5—24no—
295C3×C4×C5C2×#4114yes—
296Dic15—22no—
297Dic15—22no—
298Dic15—24no—
299C23×D3—51no—
300C23×D3—51no—
301C23×D3—52no—
302C22×C3×C4C22×D512yes—
303C22×C3×C4C22×D512yes—
304C22×C3×C4C22×D511yescharacteristic
305C22×C3×C4C22×D511yescharacteristic
306C22×C3×C4C22×D511yescharacteristic
307C22×Dic3—51no—
308C22×Dic3—52no—
309C22×Dic3—51no—
310C2×D12—54no—
311C2×D12—54no—
312C2×D12—58no—
313C2×D12—58no—
314C2×D12—104no—
315C2×D12—108no—
316C2×D12—104no—
317C2×D12—204no—
318C2×C4×D3—54no—
319C2×C4×D3—54no—
320C2×C4×D3—58no—
321C2×C4×D3—58no—
322C2×C4×D3—104no—
323C2×C4×D3—104no—
324C2×C4×D3—204no—
325C2×C4×D3—204no—
326C3×C4⋊C4C22×D514yes—
327C3×C4⋊C4C22×D514yes—
328C3×C4⋊C4C22×D518yes—
329C3×C4⋊C4C22×D518yes—
330C3×C42C22×D514yes—
331(C2×D3)⋊C4—54no—
332(C2×D3)⋊C4—54no—
333(C2×D3)⋊C4—58no—
334(C2×D3)⋊C4—58no—
335(C2×D3)⋊C4—58no—
336(C2×D3)⋊C4—58no—
337C4⋊Dic3—54no—
338C4⋊Dic3—54no—
339Dic3⋊C4—58no—
340C4×Dic3—58no—
341C23×C5C23×D311yescharacteristic
342C22×D5—34no—
343C22×D5—32no—
344C22×D5—32no—
345C22×D5—34no—
346C22×D5—62no—
347C22×D5—62no—
348C22×D5—62no—
349C22×D5—64no—
350C22×D5—62no—
351C22×D5—64no—
352C22×D5—64no—
353C22×D5—62no—
354C2×C4×C5—22no—
355C2×C4×C5—24no—
356C2×C4×C5—22no—
357C2×C4×C5—24no—
358C2×C4×C5#23914yes—
359C2×C4×C5C23×D314yes—
360C2×C4×C5C23×D314yes—
361C2×C4×C5C23×D312yes—
362C2×C4×C5C23×D312yes—
363C2×C4×C5C23×D312yes—
364C2×Dic5—32no—
365C2×Dic5—34no—
366C2×Dic5—32no—
367C2×Dic5—62no—
368C2×Dic5—62no—
369C2×Dic5—64no—
370D20—68no—
371D20—616no—
372D20—68no—
373D20—128no—
374C4×D5—68no—
375C4×D5—68no—
376C4×D5—128no—
377C4×D5—128no—
378C22×D4—152no—
379C22×D4—151no—
380C22×D4—151no—
381C22×D4—152no—
382C23×C4—151no—
383C23×C4—151no—
384C23×C4—152no—
385C23×C4—152no—
386#126—1516no—
387#125C2×D1518yescomplemented
388#123—1516no—
389#121—1516no—
390#121—158no—
391#121—158no—
392C4×D4—1516no—
393C4×D4—158no—
394C4×D4—158no—
395#117—158no—
396C2×C4⋊C4—151no—
397C2×C4⋊C4—152no—
398C2×C4⋊C4—151no—
399C2×C4⋊C4—158no—
400C2×C4⋊C4C2×D1511yescharacteristic
401C2×C4⋊C4C2×D1511yescharacteristic
402C2×C4⋊C4C2×D1512yes—
403C2×C4⋊C4C2×D1512yes—
404C2×C22⋊C4—152no—
405C2×C22⋊C4—151no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—151no—
409C2×C22⋊C4—152no—
410C2×C42—152no—
411C2×C42C2×D1511yescharacteristic
412C2×C3×C5#55314yescomplemented
413C2×C3×C5C22×#4111yescharacteristic
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
416D15—24no—
417D15—42no—
418D15—44no—
419C23×C3C23×D511yescharacteristic
420C22×D3—54no—
421C22×D3—52no—
422C22×D3—52no—
423C22×D3—54no—
424C22×D3—102no—
425C22×D3—102no—
426C22×D3—102no—
427C22×D3—104no—
428C22×D3—102no—
429C22×D3—104no—
430C22×D3—104no—
431C22×D3—102no—
432C2×C3×C4—24no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—24no—
436C2×C3×C4#71314yes—
437C2×C3×C4C23×D514yes—
438C2×C3×C4C23×D514yes—
439C2×C3×C4C23×D512yes—
440C2×C3×C4C23×D512yes—
441C2×C3×C4C23×D512yes—
442C2×Dic3—52no—
443C2×Dic3—54no—
444C2×Dic3—52no—
445C2×Dic3—102no—
446C2×Dic3—102no—
447C2×Dic3—104no—
448D12—108no—
449D12—1016no—
450D12—108no—
451D12—208no—
452C4×D3—108no—
453C4×D3—108no—
454C4×D3—208no—
455C4×D3—208no—
456C22×C5C2×#23912yes—
457C22×C5D3×#4112yes—
458C22×C5#100912yes—
459C22×C5C24×D311yescharacteristic
460C2×D5—34no—
461C2×D5—68no—
462C2×D5—62no—
463C2×D5—62no—
464C2×D5—62no—
465C2×D5—64no—
466C2×D5—62no—
467C2×D5—64no—
468C2×D5—64no—
469C2×D5—62no—
470C2×D5—124no—
471C2×D5—128no—
472C4×C5—24no—
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—24no—
476C4×C5C2×#23914yes—
477Dic5—62no—
478Dic5—62no—
479Dic5—64no—
480C24—151no—
481C24—151no—
482C24—152no—
483C2×D4—158no—
484C2×D4—154no—
485C2×D4—154no—
486C2×D4—158no—
487C2×D4—308no—
488C2×D4—304no—
489C2×D4—304no—
490C2×D4—604no—
491C22×C4—151no—
492C22×C4—152no—
493C22×C4—151no—
494C22×C4—154no—
495C22×C4—154no—
496C22×C4—158no—
497C22×C4—158no—
498C22×C4—304no—
499C22×C4—304no—
500C22×C4—604no—
501C22×C4—604no—
502C22×C4C22×D1512yes—
503C22×C4C22×D1511yescharacteristic
504C22×C4C22×D1511yescharacteristic
505C22×C4C22×D1512yes—
506C22×C4C22×D1511yescharacteristic
507C4⋊C4—154no—
508C4⋊C4—158no—
509C4⋊C4—154no—
510C4⋊C4C22×D1514yes—
511C4⋊C4C22×D1514yes—
512C4⋊C4C22×D1518yes—
513C4⋊C4C22×D1518yes—
514C22⋊C4—158no—
515C22⋊C4—154no—
516C22⋊C4—158no—
517C22⋊C4—158no—
518C22⋊C4—154no—
519C22⋊C4—158no—
520C42—158no—
521C42C22×D1514yes—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3C2×#71312yes—
524C22×C3D5×#4112yes—
525C22×C3#414912yes—
526C22×C3C24×D511yescharacteristic
527C2×D3—54no—
528C2×D3—102no—
529C2×D3—102no—
530C2×D3—108no—
531C2×D3—102no—
532C2×D3—104no—
533C2×D3—102no—
534C2×D3—104no—
535C2×D3—104no—
536C2×D3—102no—
537C2×D3—204no—
538C2×D3—208no—
539C3×C4—24no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—24no—
543C3×C4C2×#71314yes—
544Dic3—102no—
545Dic3—102no—
546Dic3—104no—
547C2×C5#569514yescomplemented
548C2×C5C22×#23911yescharacteristic
549C2×C5C2×D3×#4111yescharacteristic
550C2×C5C2×#100911yescharacteristic
551D5—64no—
552D5—122no—
553D5—124no—
554C23—154no—
555C23—152no—
556C23—152no—
557C23—154no—
558C23—302no—
559C23—302no—
560C23—302no—
561C23—304no—
562C23—302no—
563C23—304no—
564C23—304no—
565C23—302no—
566C23C23×D1511yescharacteristic
567D4—3016no—
568D4—308no—
569D4—308no—
570D4—608no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—152no—
576C2×C4—154no—
577C2×C4—152no—
578C2×C4—302no—
579C2×C4—302no—
580C2×C4—304no—
581C2×C4—308no—
582C2×C4—308no—
583C2×C4—608no—
584C2×C4—608no—
585C2×C4#682114yes—
586C2×C4C23×D1514yes—
587C2×C4C23×D1512yes—
588C2×C4C23×D1512yes—
589C2×C4C23×D1514yes—
590C2×C4C23×D1512yes—
591C2×C3#6602914yescomplemented
592C2×C3C22×#71311yescharacteristic
593C2×C3C2×D5×#4111yescharacteristic
594C2×C3C2×#414911yescharacteristic
595D3—104no—
596D3—202no—
597D3—204no—
598C5C2×#569511yescharacteristic, complemented, Sylow
599C22—154no—
600C22—302no—
601C22—302no—
602C22—308no—
603C22—302no—
604C22—304no—
605C22—302no—
606C22—304no—
607C22—304no—
608C22—302no—
609C22—604no—
610C22—608no—
611C22C2×#682112yes—
612C22#41×D1512yes—
613C22#9210012yes—
614C22C24×D1511yescharacteristic
615C4—24no—
616C4—22no—
617C4—22no—
618C4—24no—
619C4—302no—
620C4—302no—
621C4—304no—
622C4C2×#682114yes—
623C3C2×#6602911yescharacteristic, complemented, Sylow
624C2—304no—
625C2—602no—
626C2—604no—
627C2#1175645414yesdirect product factor
628C2C22×#682111yescharacteristic
629C2C2×#41×D1511yescharacteristic
630C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
hypercenterC2×#125D15
hypocenterC3×C5C2×#553
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. #11756454C2direct (N × H)
3. C2×#91787C2semidirect
4. C2×#91784C2semidirect
5. C2×#91784C2semidirect
6. C2×#91784C2semidirect
7. C2×#91783C2semidirect
8. C2×#91782C2semidirect
9. C2×#91781C2semidirect
10. C2×C4⋊C4×D15C2semidirect
11. C2×C4×D60C2semidirect
12. C2×C4×D60C2semidirect
22. C3×C5×#125C22semidirect
38. #91787C22semidirect
39. #91784C22semidirect
40. #91784C22semidirect
41. #91784C22semidirect
42. #91783C22semidirect
43. #91782C22semidirect
44. #91781C22semidirect
45. C4⋊C4×D15C22semidirect
46. C4×D60C22semidirect
47. C4×D60C22semidirect
49. C2×C5×#125D3semidirect
103. C2×C3×#125D5semidirect
123. C5×#125C2×D3semidirect
195. C3×#125C2×D5semidirect
265. C2×#125D15semidirect
387. #125C2×D15semidirect
412. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
547. C2×C5#5695semidirect
591. C2×C3#66029semidirect
598. C5C2×#5695semidirect
623. C3C2×#66029semidirect
627. C2#11756454direct (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
#117564542
C2×#917872
C2×#917842
C2×#917832
C2×#917822
C2×#917812
C2×C4⋊C4×D152
C2×C4×D602
C2×#660293
C2×#56955