Finite Group Databasebeta

← C2×#11756453 #14483417

Subgroups — C2×#11756453 #14483417

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756453C2116yesmaximal, direct product factor
3C2×#91787C212yesmaximal, complemented
4C2×#91786C211yesmaximal, characteristic, complemented
5C2×#91786C211yesmaximal, characteristic, complemented
6C2×#91783C212yesmaximal
7C2×#91781C212yesmaximal, complemented
8C2×#91781C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
10C2×#91779C212yesmaximal, complemented
11C2×C4×D60C211yesmaximal, characteristic
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#66028—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×C4×D15C2212yes—
18C22×Dic30C2211yescharacteristic
19C3×C5×#125C2218yescomplemented
20C2×C3×C5×C4⋊C4C2212yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C42×C5C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2212yes—
28C2×#6714C2212yes—
29C2×#6714C2212yes—
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2211yescharacteristic
32C2×C4⋊Dic15C2212yes—
33C2×C4⋊Dic15C2212yes—
34C2×#6712C2212yes—
35C2×#6712C2212yes—
36C2×C4×Dic15C2212yes—
37C2×C4×Dic15C2212yes—
38#91787C22116yescomplemented
39#91786C2218yescomplemented
40#91786C2218yescomplemented
41#91783C22116yes—
42#91781C22116yescomplemented
43#91781C2218yescomplemented
44C4⋊C4×D15C2218yescomplemented
45#91779C22116yescomplemented
46C4×D60C2218yes—
47C4×Dic30C2218yescomplemented
48C2×#5694—51nomaximal, Hall
49C2×C5×#125D311yescharacteristic, complemented
50#66028—316no—
51C2×#4044—32no—
52C2×#4043—31no—
53C2×#4043—31no—
54C2×#4040—32no—
55C2×#4038—31no—
56C2×#4038—32no—
57C2×D5×C4⋊C4—31no—
58C2×#4036—32no—
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×D15C2311yescharacteristic
62C23×D15C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15C2312yes—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C22×Dic15C2311yescharacteristic
72C2×D60—24no—
73C2×D60C2314yes—
74C2×C4×D15—28no—
75C2×C4×D15—24no—
76C2×C4×D15—24no—
77C2×C4×D15C2314yes—
78C2×C4×D15C2314yes—
79C2×C4×D15C2318yes—
80C2×Dic30—24no—
81C2×Dic30C2314yes—
82C3×C5×C4⋊C4C2318yes—
83C3×C5×C4⋊C4C2314yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2318yes—
86C3×C42×C5C2314yes—
87#6714C2314yes—
88#6714C2314yes—
89#6714C2318yes—
90#6714C2318yes—
91#6714C2318yes—
92C4⋊Dic15C2314yes—
93C4⋊Dic15C2314yes—
94C4⋊Dic15C2318yes—
95C4⋊Dic15C2318yes—
96#6712C2318yes—
97#6712C2318yes—
98C4×Dic15C2318yes—
99C4×Dic15C2318yes—
100C2×C3×#125D511yescharacteristic, complemented
101#5694—516no—
102C2×#898—52no—
103C2×#897—51no—
104C2×#897—51no—
105C2×#894—52no—
106C2×#892—52no—
107C2×#892—51no—
108C2×D3×C4⋊C4—51no—
109C2×#890—52no—
110C2×C4×D12—51no—
111C2×C4×Dic6—51no—
112C22×D20—31no—
113C22×C4×D5—31no—
114C22×C4×D5—31no—
115C22×C4×D5—32no—
116C22×Dic10—31no—
117C5×#125C2×D318yescomplemented
118C2×C5×C4⋊C4C2×D312yes—
119C2×C5×C4⋊C4C2×D311yescharacteristic
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C4⋊C4C2×D312yes—
122C2×C42×C5C2×D311yescharacteristic
123C2×#685—31no—
124C2×#685—31no—
125C2×#685—32no—
126C2×#685—32no—
127C2×#685—32no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5—32no—
132C2×#683—32no—
133C2×#683—32no—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—32no—
136#4044—316no—
137#4043—38no—
138#4043—38no—
139#4040—316no—
140#4038—316no—
141#4038—38no—
142D5×C4⋊C4—38no—
143#4036—316no—
144C4×D20—38no—
145C4×Dic10—38no—
146C2×#552—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×D15—22no—
149C22×D15—22no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15—22no—
153C22×D15#4114yes—
154C22×D15C2412yes—
155C22×D15C2412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—24no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2414yes—
163C2×C3×C4×C5C2412yes—
164C2×C3×C4×C5C2414yes—
165C2×C3×C4×C5C2412yes—
166C2×Dic15—24no—
167C2×Dic15—22no—
168C2×Dic15—22no—
169C2×Dic15—24no—
170C2×Dic15C2414yes—
171C2×Dic15C2412yes—
172C2×Dic15C2414yes—
173C2×Dic15C2412yes—
174D60—28no—
175C4×D15—216no—
176C4×D15—28no—
177C4×D15—28no—
178Dic30—28no—
179C22×D12—51no—
180C22×C4×D3—51no—
181C22×C4×D3—51no—
182C22×C4×D3—52no—
183C22×Dic6—51no—
184C3×#125C2×D518yescomplemented
185C2×C3×C4⋊C4C2×D512yes—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C4⋊C4C2×D511yescharacteristic
188C2×C3×C4⋊C4C2×D512yes—
189C2×C3×C42C2×D511yescharacteristic
190C2×(C2×D3)⋊C4—51no—
191C2×(C2×D3)⋊C4—51no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—51no—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3—52no—
203#898—516no—
204#897—58no—
205#897—58no—
206#894—516no—
207#892—516no—
208#892—58no—
209D3×C4⋊C4—58no—
210#890—516no—
211C4×D12—58no—
212C4×Dic6—58no—
213C23×D5—31no—
214C23×D5—31no—
215C22×C4×C5C22×D311yescharacteristic
216C22×C4×C5C22×D311yescharacteristic
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—32no—
221C22×Dic5—32no—
222C22×Dic5—31no—
223C22×Dic5—31no—
224C2×D20—34no—
225C2×D20—64no—
226C2×C4×D5—34no—
227C2×C4×D5—34no—
228C2×C4×D5—38no—
229C2×C4×D5—68no—
230C2×C4×D5—64no—
231C2×C4×D5—64no—
232C2×Dic10—34no—
233C2×Dic10—64no—
234C5×C4⋊C4C22×D318yes—
235C5×C4⋊C4C22×D314yes—
236C5×C4⋊C4C22×D314yes—
237C5×C4⋊C4C22×D318yes—
238C42×C5C22×D314yes—
239#685—34no—
240#685—34no—
241#685—38no—
242#685—38no—
243#685—38no—
244C4⋊Dic5—34no—
245C4⋊Dic5—34no—
246C4⋊Dic5—38no—
247C4⋊Dic5—38no—
248#683—38no—
249#683—38no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—152no—
255C2×#125D1511yescharacteristic, complemented
256C2×#123—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—151no—
262C2×#117—152no—
263C22×C4⋊C4—151no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×D15—28no—
269C2×D15—22no—
270C2×D15—22no—
271C2×D15—22no—
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—44no—
275C2×D15C2×#4114yes—
276C3×C4×C5—24no—
277C3×C4×C5—22no—
278C3×C4×C5—22no—
279C3×C4×C5—24no—
280C3×C4×C5C2×#4114yes—
281Dic15—24no—
282Dic15—22no—
283Dic15—22no—
284Dic15—24no—
285C23×D3—51no—
286C23×D3—51no—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D512yes—
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D512yes—
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—52no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—51no—
296C2×D12—54no—
297C2×D12—104no—
298C2×C4×D3—54no—
299C2×C4×D3—54no—
300C2×C4×D3—58no—
301C2×C4×D3—108no—
302C2×C4×D3—104no—
303C2×C4×D3—104no—
304C2×Dic6—54no—
305C2×Dic6—104no—
306C3×C4⋊C4C22×D518yes—
307C3×C4⋊C4C22×D514yes—
308C3×C4⋊C4C22×D514yes—
309C3×C4⋊C4C22×D518yes—
310C3×C42C22×D514yes—
311(C2×D3)⋊C4—54no—
312(C2×D3)⋊C4—54no—
313(C2×D3)⋊C4—58no—
314(C2×D3)⋊C4—58no—
315(C2×D3)⋊C4—58no—
316C4⋊Dic3—54no—
317C4⋊Dic3—54no—
318C4⋊Dic3—58no—
319C4⋊Dic3—58no—
320Dic3⋊C4—58no—
321Dic3⋊C4—58no—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5C23×D311yescharacteristic
325C22×D5—34no—
326C22×D5—32no—
327C22×D5—32no—
328C22×D5—62no—
329C22×D5—62no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C2×C4×C5—24no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—24no—
337C2×C4×C5#23914yes—
338C2×C4×C5C23×D312yes—
339C2×C4×C5C23×D314yes—
340C2×C4×C5C23×D312yes—
341C2×C4×C5C23×D314yes—
342C2×C4×C5C23×D312yes—
343C2×Dic5—34no—
344C2×Dic5—32no—
345C2×Dic5—34no—
346C2×Dic5—32no—
347C2×Dic5—64no—
348C2×Dic5—62no—
349C2×Dic5—62no—
350C2×Dic5—64no—
351D20—68no—
352C4×D5—616no—
353C4×D5—68no—
354C4×D5—68no—
355Dic10—68no—
356C22×Q8—151no—
357C22×D4—151no—
358C23×C4—152no—
359C23×C4—151no—
360C23×C4—151no—
361#126—1516no—
362#125—1516no—
363#125C2×D1518yescomplemented
364#123—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—158no—
369#117—158no—
370#117—1516no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—151no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—158no—
378C2×C4⋊C4C2×D1511yescharacteristic
379C2×C4⋊C4C2×D1511yescharacteristic
380C2×C4⋊C4C2×D1512yes—
381C2×C4⋊C4C2×D1512yes—
382C2×C22⋊C4—151no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—152no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42C2×D1511yescharacteristic
390C2×C3×C5#55214yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394D15—24no—
395D15—42no—
396C23×C3C23×D511yescharacteristic
397C22×D3—54no—
398C22×D3—52no—
399C22×D3—52no—
400C22×D3—102no—
401C22×D3—102no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3—102no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—24no—
409C2×C3×C4#71314yes—
410C2×C3×C4C23×D512yes—
411C2×C3×C4C23×D514yes—
412C2×C3×C4C23×D512yes—
413C2×C3×C4C23×D514yes—
414C2×C3×C4C23×D512yes—
415C2×Dic3—54no—
416C2×Dic3—52no—
417C2×Dic3—54no—
418C2×Dic3—52no—
419C2×Dic3—104no—
420C2×Dic3—102no—
421C2×Dic3—102no—
422C2×Dic3—104no—
423D12—108no—
424C4×D3—1016no—
425C4×D3—108no—
426C4×D3—108no—
427Dic6—108no—
428C22×C5C2×#23912yes—
429C22×C5D3×#4112yes—
430C22×C5#101012yes—
431C22×C5C24×D311yescharacteristic
432C2×D5—34no—
433C2×D5—68no—
434C2×D5—62no—
435C2×D5—62no—
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—24no—
441C4×C5—22no—
442C4×C5—22no—
443C4×C5—24no—
444C4×C5C2×#23914yes—
445Dic5—64no—
446Dic5—62no—
447Dic5—62no—
448Dic5—64no—
449C24—151no—
450C24—151no—
451C2×Q8—154no—
452C2×Q8—304no—
453C2×D4—154no—
454C2×D4—304no—
455C22×C4—151no—
456C22×C4—152no—
457C22×C4—152no—
458C22×C4—151no—
459C22×C4—158no—
460C22×C4—154no—
461C22×C4—154no—
462C22×C4—308no—
463C22×C4—304no—
464C22×C4—304no—
465C22×C4C22×D1511yescharacteristic
466C22×C4C22×D1512yes—
467C22×C4C22×D1511yescharacteristic
468C22×C4C22×D1512yes—
469C22×C4C22×D1511yescharacteristic
470C4⋊C4—154no—
471C4⋊C4—158no—
472C4⋊C4—158no—
473C4⋊C4—154no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4C22×D1514yes—
477C4⋊C4C22×D1514yes—
478C4⋊C4C22×D1518yes—
479C4⋊C4C22×D1518yes—
480C22⋊C4—154no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4—154no—
484C22⋊C4—158no—
485C42—158no—
486C42—158no—
487C42C22×D1514yes—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3C2×#71312yes—
490C22×C3D5×#4112yes—
491C22×C3#415012yes—
492C22×C3C24×D511yescharacteristic
493C2×D3—54no—
494C2×D3—102no—
495C2×D3—102no—
496C2×D3—108no—
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—24no—
502C3×C4—22no—
503C3×C4—22no—
504C3×C4—24no—
505C3×C4C2×#71314yes—
506Dic3—104no—
507Dic3—102no—
508Dic3—102no—
509Dic3—104no—
510C2×C5#569414yescomplemented
511C2×C5C22×#23911yescharacteristic
512C2×C5C2×D3×#4111yescharacteristic
513C2×C5C2×#101011yescharacteristic
514D5—64no—
515D5—122no—
516C23—154no—
517C23—152no—
518C23—152no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23—302no—
523C23—302no—
524C23C23×D1511yescharacteristic
525Q8—308no—
526D4—308no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—152no—
532C2×C4—154no—
533C2×C4—154no—
534C2×C4—152no—
535C2×C4—3016no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—304no—
539C2×C4—304no—
540C2×C4—308no—
541C2×C4—308no—
542C2×C4#682114yes—
543C2×C4C23×D1512yes—
544C2×C4C23×D1514yes—
545C2×C4C23×D1512yes—
546C2×C4C23×D1514yes—
547C2×C4C23×D1512yes—
548C2×C3#6602814yescomplemented
549C2×C3C22×#71311yescharacteristic
550C2×C3C2×D5×#4111yescharacteristic
551C2×C3C2×#415011yescharacteristic
552D3—104no—
553D3—202no—
554C5C2×#569411yescharacteristic, complemented, Sylow
555C22—154no—
556C22—302no—
557C22—302no—
558C22—308no—
559C22—302no—
560C22—302no—
561C22—302no—
562C22—604no—
563C22C2×#682112yes—
564C22#41×D1512yes—
565C22#9210112yes—
566C22C24×D1511yescharacteristic
567C4—24no—
568C4—22no—
569C4—22no—
570C4—24no—
571C4—302no—
572C4—302no—
573C4—304no—
574C4—304no—
575C4C2×#682114yes—
576C3C2×#6602811yescharacteristic, complemented, Sylow
577C2—304no—
578C2—602no—
579C2#1175645314yesdirect product factor
580C2C22×#682111yescharacteristic
581C2C2×#41×D1511yescharacteristic
582C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×#125D15
hypocenterC3×C5C2×#552
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. #11756453C2direct (N × H)
3. C2×#91787C2semidirect
4. C2×#91786C2semidirect
5. C2×#91786C2semidirect
7. C2×#91781C2semidirect
8. C2×#91781C2semidirect
9. C2×C4⋊C4×D15C2semidirect
10. C2×#91779C2semidirect
12. C2×C4×Dic30C2semidirect
19. C3×C5×#125C22semidirect
38. #91787C22semidirect
39. #91786C22semidirect
40. #91786C22semidirect
42. #91781C22semidirect
43. #91781C22semidirect
44. C4⋊C4×D15C22semidirect
45. #91779C22semidirect
47. C4×Dic30C22semidirect
49. C2×C5×#125D3semidirect
100. C2×C3×#125D5semidirect
117. C5×#125C2×D3semidirect
184. C3×#125C2×D5semidirect
255. C2×#125D15semidirect
363. #125C2×D15semidirect
390. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
510. C2×C5#5694semidirect
548. C2×C3#66028semidirect
554. C5C2×#5694semidirect
576. C3C2×#66028semidirect
579. C2#11756453direct (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
#117564532
C2×#917872
C2×#917862
C2×#917832
C2×#917812
C2×C4⋊C4×D152
C2×#917792
C2×C4×D602
C2×C4×Dic302
C2×#660283
C2×#56945