Finite Group Databasebeta

← C2×#11752609 #14483561

Subgroups — C2×#11752609 #14483561

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×#91759C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#91423C212yesmaximal
6C2×#91398C212yesmaximal, complemented
7C2×#91372C212yesmaximal, complemented
8C2×#91369C211yesmaximal, characteristic, complemented
9C2×#91369C211yesmaximal, characteristic, complemented
10C2×#91338C211yesmaximal, characteristic, complemented
11C2×#91336C212yesmaximal, complemented
12#11752609C2116yesmaximal, direct product factor
13C2×#65875—31nomaximal, Hall
14C22×C5×D12C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C4×C5×D3C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×D3×Dic5C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712C2212yes—
23C2×#6712C2212yes—
24#91759C2218yescomplemented
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C4×C5×D12C2218yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2212yes—
32C3×C4×Dic10C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40D3×C4⋊Dic5C2218yescomplemented
41#91423C22116yes—
42#91398C22116yescomplemented
43#91372C22116yescomplemented
44#91369C2218yescomplemented
45#91369C2218yescomplemented
46#91338C2218yescomplemented
47#91336C22116yescomplemented
48C2×#5581—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4081—32no—
51C2×#4072—31no—
52C22×C4⋊Dic5—31no—
53C2×#4070—31no—
54C2×#4070—31no—
55#65875—316no—
56C2×#4035—32no—
57C2×#4025—32no—
58C2×#4023—32no—
59C2×#4016—31no—
60C2×C4×Dic10D311yescharacteristic, complemented
61C23×C5×D3C2311yescharacteristic
62C23×C5×D3C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2312yes—
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2311yescharacteristic
70C2×C5×D12—24no—
71C2×C5×D12C2314yes—
72C2×C4×C5×D3—24no—
73C2×C4×C5×D3—24no—
74C2×C4×C5×D3C2314yes—
75C2×C4×C5×D3C2314yes—
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2312yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×D3×Dic5—28no—
81C2×D3×Dic5C2318yes—
82C3×C42×C5C2314yes—
83C4⋊Dic15C2314yes—
84C4⋊Dic15C2314yes—
85#6712C2318yes—
86#6712C2318yes—
87C5×(C2×D3)⋊C4C2314yes—
88C5×(C2×D3)⋊C4C2314yes—
89C5×C4⋊Dic3C2314yes—
90C3×C4⋊Dic5C2314yes—
91C3×#683C2318yes—
92C3×C4×Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94#6669C2318yes—
95#6669C2318yes—
96(C2×D3)⋊Dic5C2318yes—
97(C2×D3)⋊Dic5C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C4×Q8—51no—
101C2×#946—51no—
102C2×#946—51no—
103#5581—516no—
104C2×#894—52no—
105C2×#892—51no—
106C2×D3×C4⋊C4—51no—
107C2×#889—52no—
108C2×#876—52no—
109C2×C4×D12D511yescharacteristic
110C2×#872—52no—
111C2×#870—51no—
112C22×C5×D4—31no—
113C23×C4×C5—31no—
114C23×C4×C5—31no—
115C23×Dic5—32no—
116C22×Dic10C2×D311yescharacteristic
117C4×C5×D4—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C22⋊C4—31no—
120C2×C5×C22⋊C4—31no—
121C2×C42×C5C2×D311yescharacteristic
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125#4081—316no—
126#4072—38no—
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—38no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132#4070—38no—
133#4070—38no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683C2×D312yes—
139C2×C4×Dic5—32no—
140C2×C4×Dic5C2×D312yes—
141#4035—316no—
142#4025—316no—
143#4023—316no—
144#4016—38no—
145C4×Dic10C2×D318yescomplemented
146C2×#552—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C5×D3—22no—
149C22×C5×D3—22no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3#4114yes—
154C22×C5×D3C2412yes—
155C22×C5×D3C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—24no—
163C2×Dic15—24no—
164C2×Dic15C2414yes—
165C2×Dic15C2414yes—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3C2412yes—
169C2×C5×Dic3C2412yes—
170C5×D12—28no—
171C4×C5×D3—28no—
172C4×C5×D3—28no—
173C2×C3×Dic5—24no—
174C2×C3×Dic5—24no—
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2414yes—
177C3×Dic10—28no—
178D3×Dic5—216no—
179C22×C3×Q8—51no—
180C22×D12C2×D511yescharacteristic
181C22×C4×D3—52no—
182C22×C4×D3C2×D511yescharacteristic
183C22×C4×D3C2×D511yescharacteristic
184C3×C4×Q8—58no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C42—52no—
188C2×C3×C42C2×D511yescharacteristic
189#946—58no—
190#946—58no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4C2×D511yescharacteristic
195C2×(C2×D3)⋊C4C2×D511yescharacteristic
196C2×C4⋊Dic3—51no—
197C2×C4⋊Dic3—51no—
198C2×C4⋊Dic3C2×D511yescharacteristic
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×C4×Dic3—52no—
205#894—516no—
206#892—58no—
207D3×C4⋊C4—58no—
208#889—516no—
209#876—516no—
210C4×D12C2×D518yes—
211#872—516no—
212#870—58no—
213C24×C5—31no—
214C24×C5—31no—
215C2×C5×D4—34no—
216C2×C5×D4—64no—
217C22×C4×C5—31no—
218C22×C4×C5—31no—
219C22×C4×C5—34no—
220C22×C4×C5—34no—
221C22×C4×C5—64no—
222C22×C4×C5—64no—
223C22×C4×C5C22×D311yescharacteristic
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—32no—
227C22×Dic5—32no—
228C22×Dic5—38no—
229C22×Dic5—68no—
230C22×Dic5C22×D312yes—
231C22×Dic5C22×D312yes—
232C2×Dic10—24no—
233C2×Dic10C22×D314yes—
234C5×C4⋊C4—34no—
235C5×C22⋊C4—34no—
236C5×C22⋊C4—34no—
237C42×C5C22×D314yes—
238C22⋊Dic5—38no—
239C22⋊Dic5—38no—
240C22⋊Dic5—38no—
241C4⋊Dic5—34no—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244C4⋊Dic5C22×D314yes—
245#683—38no—
246#683—38no—
247#683—38no—
248#683—38no—
249#683C22×D318yes—
250C4×Dic5—38no—
251C4×Dic5C22×D318yes—
252#552—1516no—
253C2×#126—152no—
254C2×#125—152no—
255C2×#125—151no—
256C2×#123—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—51no—
260C2×C4×D4—31no—
261C2×#117—152no—
262C2×#117—151no—
263C22×C4⋊C4—151no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×C5×D3—28no—
269C2×C5×D3—22no—
270C2×C5×D3—22no—
271C2×C5×D3—22no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3—44no—
275C2×C5×D3C2×#4114yes—
276C3×C4×C5—22no—
277C3×C4×C5—22no—
278C3×C4×C5C2×#4114yes—
279Dic15—24no—
280Dic15—24no—
281C3×Dic5—24no—
282C3×Dic5—24no—
283C5×Dic3—22no—
284C5×Dic3—22no—
285C23×D3C22×D511yescharacteristic
286C23×D3C22×D511yescharacteristic
287C2×C3×Q8—54no—
288C2×C3×Q8—104no—
289C22×C3×C4—52no—
290C22×C3×C4—52no—
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—52no—
295C22×Dic3—52no—
296C22×Dic3C22×D511yescharacteristic
297C22×Dic3C22×D511yescharacteristic
298C2×D12—24no—
299C2×D12C22×D514yes—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—58no—
303C2×C4×D3—108no—
304C2×C4×D3C22×D514yes—
305C2×C4×D3C22×D514yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C42—58no—
309C3×C42C22×D514yes—
310(C2×D3)⋊C4—58no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4C22×D514yes—
314(C2×D3)⋊C4C22×D514yes—
315C4⋊Dic3—54no—
316C4⋊Dic3—54no—
317C4⋊Dic3C22×D514yes—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321Dic3⋊C4—58no—
322Dic3⋊C4—58no—
323C4×Dic3—58no—
324C23×C5—34no—
325C23×C5—32no—
326C23×C5—32no—
327C23×C5—62no—
328C23×C5—62no—
329C23×C5—62no—
330C23×C5—62no—
331C23×C5—62no—
332C23×C5C23×D311yescharacteristic
333C5×D4—68no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—62no—
339C2×C4×C5—62no—
340C2×C4×C5—68no—
341C2×C4×C5—68no—
342C2×C4×C5#23514yes—
343C2×C4×C5C23×D312yes—
344C2×C4×C5C23×D312yes—
345C2×C4×C5C23×D312yes—
346C2×Dic5—24no—
347C2×Dic5—24no—
348C2×Dic5—34no—
349C2×Dic5—34no—
350C2×Dic5—616no—
351C2×Dic5—64no—
352C2×Dic5—64no—
353C2×Dic5C23×D314yes—
354C2×Dic5C23×D314yes—
355Dic10—28no—
356C22×Q8—51no—
357C22×D4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—152no—
361#126—1516no—
362#125—1516no—
363#125—158no—
364#123—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—58no—
368C4×D4—38no—
369#117—1516no—
370#117—158no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—52no—
374C2×C4⋊C4—158no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—152no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—152no—
386C2×C22⋊C4—152no—
387C2×C42—52no—
388C2×C42—152no—
389C2×C42D3×D511yescharacteristic
390C2×C3×C5#55214yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394C5×D3—24no—
395C5×D3—42no—
396C23×C3C23×D511yescharacteristic
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3#70914yes—
403C22×D3C23×D512yes—
404C22×D3C23×D512yes—
405C3×Q8—108no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—54no—
409C2×C3×C4—54no—
410C2×C3×C4—104no—
411C2×C3×C4—104no—
412C2×C3×C4#71114yes—
413C2×C3×C4C23×D512yes—
414C2×C3×C4C23×D512yes—
415C2×C3×C4C23×D512yes—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—54no—
419C2×Dic3—54no—
420C2×Dic3—104no—
421C2×Dic3—104no—
422C2×Dic3C23×D512yes—
423C2×Dic3C23×D512yes—
424D12—28no—
425C4×D3—28no—
426C4×D3—28no—
427C4×D3—1016no—
428C22×C5—34no—
429C22×C5—62no—
430C22×C5—62no—
431C22×C5—68no—
432C22×C5—62no—
433C22×C5—62no—
434C22×C5—62no—
435C22×C5—124no—
436C22×C5C2×#23512yes—
437C22×C5#100712yes—
438C22×C5D3×#4112yes—
439C22×C5C24×D311yescharacteristic
440C4×C5—22no—
441C4×C5—22no—
442C4×C5—62no—
443C4×C5—62no—
444C4×C5C2×#23514yes—
445Dic5—24no—
446Dic5—24no—
447Dic5—64no—
448Dic5—64no—
449C24—31no—
450C24—31no—
451C2×Q8—54no—
452C2×Q8—104no—
453C2×D4—34no—
454C2×D4—64no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—34no—
458C22×C4—34no—
459C22×C4—52no—
460C22×C4—52no—
461C22×C4—64no—
462C22×C4—64no—
463C22×C4—158no—
464C22×C4—152no—
465C22×C4—152no—
466C22×C4—308no—
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—54no—
472C4⋊C4—58no—
473C4⋊C4—158no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—154no—
477C4⋊C4—154no—
478C4⋊C4—158no—
479C4⋊C4—158no—
480C22⋊C4—34no—
481C22⋊C4—34no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C22⋊C4—158no—
485C42—58no—
486C42—158no—
487C42C2×D3×D514yes—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3C2×#70912yes—
490C22×C3C2×#71112yes—
491C22×C3#415012yes—
492C22×C3C24×D511yescharacteristic
493C2×D3—28no—
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—44no—
500C2×D3C2×#70914yes—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—104no—
504C3×C4—104no—
505C3×C4C2×#71114yes—
506Dic3—22no—
507Dic3—22no—
508Dic3—104no—
509Dic3—104no—
510C2×C5—64no—
511C2×C5—122no—
512C2×C5#558114yescomplemented
513C2×C5C22×#23511yescharacteristic
514C2×C5C2×#100711yescharacteristic
515C2×C5C2×D3×#4111yescharacteristic
516C23—34no—
517C23—32no—
518C23—32no—
519C23—62no—
520C23—62no—
521C23—62no—
522C23—62no—
523C23—62no—
524C23C22×D3×D511yescharacteristic
525Q8—108no—
526D4—68no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—54no—
532C2×C4—54no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—68no—
536C2×C4—68no—
537C2×C4—104no—
538C2×C4—104no—
539C2×C4—154no—
540C2×C4—154no—
541C2×C4—3016no—
542C2×C4—304no—
543C2×C4—304no—
544C2×C4#677214yes—
545C2×C4C22×D3×D512yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3#6587514yescomplemented
549C2×C3C22×#70911yescharacteristic
550C2×C3C22×#71111yescharacteristic
551C2×C3C2×#415011yescharacteristic
552D3—24no—
553D3—42no—
554C5C2×#558111yescharacteristic, complemented, Sylow
555C22—34no—
556C22—68no—
557C22—62no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22—62no—
562C22—124no—
563C22#9200412yes—
564C22C2×#677212yes—
565C22D3×#70912yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—22no—
569C4—62no—
570C4—62no—
571C4—104no—
572C4—104no—
573C4—304no—
574C4—304no—
575C4C2×#677214yes—
576C3C2×#6587511yescharacteristic, complemented, Sylow
577C2—64no—
578C2—122no—
579C2#1175260914yesdirect product factor
580C2C2×#9200411yescharacteristic
581C2C22×#677211yescharacteristic
582C2C2×D3×#70911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91759C2semidirect
3. C2×C3×C4×Dic10C2semidirect
4. C2×D3×C4⋊Dic5C2semidirect
6. C2×#91398C2semidirect
7. C2×#91372C2semidirect
8. C2×#91369C2semidirect
9. C2×#91369C2semidirect
10. C2×#91338C2semidirect
11. C2×#91336C2semidirect
12. #11752609C2direct (N × H)
24. #91759C22semidirect
32. C3×C4×Dic10C22semidirect
40. D3×C4⋊Dic5C22semidirect
42. #91398C22semidirect
43. #91372C22semidirect
44. #91369C22semidirect
45. #91369C22semidirect
46. #91338C22semidirect
47. #91336C22semidirect
60. C2×C4×Dic10D3semidirect
145. C4×Dic10C2×D3semidirect
390. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
512. C2×C5#5581semidirect
548. C2×C3#65875semidirect
554. C5C2×#5581semidirect
576. C3C2×#65875semidirect
579. C2#11752609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917592
C2×C4×C5×D122
C2×C3×C4×Dic102
C2×D3×C4⋊Dic52
C2×#914232
C2×#913982
C2×#913722
C2×#913692
C2×#913382
C2×#913362
#117526092
C2×#658753
C2×#55815