Finite Group Databasebeta

← C2×#11756300 #14483423

Subgroups — C2×#11756300 #14483423

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×C4×C5×D4C211yesmaximal, characteristic
2C2×#91824C212yesmaximal
3C2×#91815C211yesmaximal, characteristic, complemented
4C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
5C2×#91813C211yesmaximal, characteristic, complemented
6C2×#91813C211yesmaximal, characteristic, complemented
7#11756300C2116yesmaximal, direct product factor
8C2×#91778C212yesmaximal, complemented
9C2×#91768C212yesmaximal, complemented
10C2×#91766C212yesmaximal, complemented
11C2×#91759C211yesmaximal, characteristic, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#65875—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C23×Dic15C2212yes—
18C22×Dic30C2211yescharacteristic
19C3×C4×C5×D4C2218yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×#6719C2212yes—
25C2×#6719C2212yes—
26C2×#6719C2212yes—
27#91824C22116yes—
28#91815C2218yescomplemented
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2212yes—
32C2×C4⋊Dic15C2211yescharacteristic
33C2×C4⋊Dic15C2218yescomplemented
34#91813C2218yescomplemented
35#91813C2218yescomplemented
36C2×#6712C2212yes—
37C2×#6712C2212yes—
38C2×#6712C2212yes—
39C2×#6712C2212yes—
40C2×#6712C2212yes—
41C2×C4×Dic15C2212yes—
42C2×C4×Dic15C2212yes—
43#91778C22116yescomplemented
44#91768C22116yescomplemented
45#91766C22116yescomplemented
46#91759C2218yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5541—51nomaximal, Hall
49C2×C4×C5×D4D311yescharacteristic
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×Dic10—31no—
61C24×C3×C5C2311yescharacteristic
62C24×C3×C5C2311yescharacteristic
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5—24no—
66C22×C3×C4×C5—24no—
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2314yes—
72C22×C3×C4×C5C2314yes—
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15—28no—
75C22×Dic15C2318yes—
76C22×Dic15C2312yes—
77C22×Dic15C2312yes—
78C22×Dic15C2312yes—
79C22×Dic15C2312yes—
80C2×Dic30—24no—
81C2×Dic30C2314yes—
82C3×C5×C4⋊C4C2314yes—
83C3×C5×C22⋊C4C2314yes—
84C3×C5×C22⋊C4C2314yes—
85C3×C42×C5C2314yes—
86#6719C2318yes—
87#6719C2318yes—
88#6719C2318yes—
89C4⋊Dic15C2314yes—
90C4⋊Dic15C2314yes—
91C4⋊Dic15C2314yes—
92C4⋊Dic15C2318yes—
93#6712C2318yes—
94#6712C2318yes—
95#6712C2318yes—
96#6712C2318yes—
97#6712C2318yes—
98C4×Dic15C2318yes—
99C4×Dic15C2318yes—
100C2×C3×C4×D4D511yescharacteristic
101C2×#935—52no—
102C2×#926—51no—
103C22×C4⋊Dic3—51no—
104C2×#924—51no—
105C2×#924—51no—
106#5541—516no—
107C2×#889—52no—
108C2×#879—52no—
109C2×#877—52no—
110C2×#870—51no—
111C2×C4×Dic6—51no—
112C22×C5×D4C2×D311yescharacteristic
113C23×C4×C5C2×D311yescharacteristic
114C23×C4×C5C2×D311yescharacteristic
115C23×Dic5—32no—
116C22×Dic10—31no—
117C4×C5×D4C2×D318yes—
118C2×C5×C4⋊C4C2×D311yescharacteristic
119C2×C5×C22⋊C4C2×D311yescharacteristic
120C2×C5×C22⋊C4C2×D311yescharacteristic
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—31no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5—38no—
132#4070—38no—
133#4070—38no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683—32no—
139C2×C4×Dic5—32no—
140C2×C4×Dic5—32no—
141#4035—316no—
142#4025—316no—
143#4023—316no—
144#4016—38no—
145C4×Dic10—38no—
146C2×#552—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5—22no—
152C23×C3×C5#4114yes—
153C23×C3×C5C2412yes—
154C23×C3×C5C2412yes—
155C23×C3×C5C2411yescharacteristic
156C3×C5×D4—28no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—28no—
162C2×C3×C4×C5—28no—
163C2×C3×C4×C5#4114yes—
164C2×C3×C4×C5C2412yes—
165C2×C3×C4×C5C2412yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168C2×C3×C4×C5C2412yes—
169C2×Dic15—24no—
170C2×Dic15—216no—
171C2×Dic15—24no—
172C2×Dic15—24no—
173C2×Dic15—24no—
174C2×Dic15C2414yes—
175C2×Dic15C2414yes—
176C2×Dic15C2414yes—
177C2×Dic15C2414yes—
178Dic30—28no—
179C22×C3×D4C2×D511yescharacteristic
180C23×C3×C4C2×D511yescharacteristic
181C23×C3×C4C2×D511yescharacteristic
182C23×Dic3—52no—
183C22×Dic6—51no—
184C3×C4×D4C2×D518yes—
185C2×C3×C4⋊C4C2×D511yescharacteristic
186C2×C3×C22⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4C2×D511yescharacteristic
188C2×C3×C42C2×D511yescharacteristic
189C2×#217—52no—
190C2×#217—52no—
191C2×#217—52no—
192#935—516no—
193#926—58no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—51no—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3—58no—
199#924—58no—
200#924—58no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—52no—
207C2×C4×Dic3—52no—
208#889—516no—
209#879—516no—
210#877—516no—
211#870—58no—
212C4×Dic6—58no—
213C24×C5C22×D311yescharacteristic
214C24×C5C22×D311yescharacteristic
215C2×C5×D4—24no—
216C2×C5×D4C22×D314yes—
217C22×C4×C5—24no—
218C22×C4×C5—24no—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D314yes—
224C22×C4×C5C22×D314yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—32no—
227C22×Dic5—32no—
228C22×Dic5—32no—
229C22×Dic5—32no—
230C22×Dic5—38no—
231C22×Dic5—68no—
232C2×Dic10—34no—
233C2×Dic10—64no—
234C5×C4⋊C4C22×D314yes—
235C5×C22⋊C4C22×D314yes—
236C5×C22⋊C4C22×D314yes—
237C42×C5C22×D314yes—
238C22⋊Dic5—38no—
239C22⋊Dic5—38no—
240C22⋊Dic5—38no—
241C4⋊Dic5—34no—
242C4⋊Dic5—34no—
243C4⋊Dic5—34no—
244C4⋊Dic5—38no—
245#683—38no—
246#683—38no—
247#683—38no—
248#683—38no—
249#683—38no—
250C4×Dic5—38no—
251C4×Dic5—38no—
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—151no—
260C2×C4×D4D1511yescharacteristic
261C2×#117—151no—
262C2×#117—152no—
263C22×C4⋊C4—151no—
264C22×C3×C5—28no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5—22no—
270C22×C3×C5—44no—
271C22×C3×C5C2×#4114yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2×#4112yes—
274C22×C3×C52−1+412yes—
275C22×C3×C5C2511yescharacteristic
276C3×C4×C5—22no—
277C3×C4×C5—22no—
278C3×C4×C5—22no—
279C3×C4×C5—22no—
280C3×C4×C5C2×#4114yes—
281Dic15—24no—
282Dic15—24no—
283Dic15—24no—
284Dic15—24no—
285C24×C3C22×D511yescharacteristic
286C24×C3C22×D511yescharacteristic
287C2×C3×D4—24no—
288C2×C3×D4C22×D514yes—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D511yescharacteristic
294C22×C3×C4C22×D511yescharacteristic
295C22×C3×C4C22×D514yes—
296C22×C3×C4C22×D514yes—
297C22×C3×C4C22×D511yescharacteristic
298C22×Dic3—58no—
299C22×Dic3—52no—
300C22×Dic3—52no—
301C22×Dic3—52no—
302C22×Dic3—52no—
303C22×Dic3—108no—
304C2×Dic6—54no—
305C2×Dic6—104no—
306C3×C4⋊C4C22×D514yes—
307C3×C22⋊C4C22×D514yes—
308C3×C22⋊C4C22×D514yes—
309C3×C42C22×D514yes—
310#217—58no—
311#217—58no—
312#217—58no—
313C4⋊Dic3—54no—
314C4⋊Dic3—54no—
315C4⋊Dic3—54no—
316C4⋊Dic3—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321Dic3⋊C4—58no—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5#23514yes—
330C23×C5C23×D312yes—
331C23×C5C23×D312yes—
332C23×C5C23×D311yescharacteristic
333C5×D4—28no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—28no—
339C2×C4×C5—28no—
340C2×C4×C5#23714yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C2×C4×C5C23×D312yes—
344C2×C4×C5C23×D312yes—
345C2×C4×C5C23×D312yes—
346C2×Dic5—34no—
347C2×Dic5—34no—
348C2×Dic5—34no—
349C2×Dic5—34no—
350C2×Dic5—616no—
351C2×Dic5—64no—
352C2×Dic5—64no—
353C2×Dic5—64no—
354C2×Dic5—64no—
355Dic10—68no—
356C22×Q8—151no—
357C22×D4C2×D1511yescharacteristic
358C23×C4—152no—
359C23×C4C2×D1511yescharacteristic
360C23×C4C2×D1511yescharacteristic
361#126—1516no—
362#125—1516no—
363#125—158no—
364#123—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4C2×D1518yes—
369#117—158no—
370#117—1516no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—151no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—158no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4C2×D1511yescharacteristic
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4C2×D1511yescharacteristic
386C2×C22⋊C4C2×D1511yescharacteristic
387C2×C42—152no—
388C2×C42—152no—
389C2×C42C2×D1511yescharacteristic
390C2×C3×C5—24no—
391C2×C3×C5—42no—
392C2×C3×C5#55214yescomplemented
393C2×C3×C5C22×#4111yescharacteristic
394C2×C3×C5C22×#4111yescharacteristic
395C2×C3×C5C2×2−1+411yescharacteristic
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3#70914yes—
402C23×C3C23×D512yes—
403C23×C3C23×D512yes—
404C23×C3C23×D511yescharacteristic
405C3×D4—28no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—28no—
411C2×C3×C4—28no—
412C2×C3×C4#71114yes—
413C2×C3×C4C23×D512yes—
414C2×C3×C4C23×D512yes—
415C2×C3×C4C23×D512yes—
416C2×C3×C4C23×D512yes—
417C2×C3×C4C23×D512yes—
418C2×Dic3—54no—
419C2×Dic3—54no—
420C2×Dic3—54no—
421C2×Dic3—54no—
422C2×Dic3—1016no—
423C2×Dic3—104no—
424C2×Dic3—104no—
425C2×Dic3—104no—
426C2×Dic3—104no—
427Dic6—108no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—28no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—44no—
435C22×C5C2×#23514yes—
436C22×C5C2×#23512yes—
437C22×C5C2×#23712yes—
438C22×C5#101012yes—
439C22×C5C24×D311yescharacteristic
440C4×C5—22no—
441C4×C5—22no—
442C4×C5—22no—
443C4×C5—22no—
444C4×C5C2×#23714yes—
445Dic5—64no—
446Dic5—64no—
447Dic5—64no—
448Dic5—64no—
449C24C22×D1511yescharacteristic
450C24C22×D1511yescharacteristic
451C2×Q8—154no—
452C2×Q8—304no—
453C2×D4—24no—
454C2×D4C22×D1514yes—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—158no—
458C22×C4—152no—
459C22×C4—152no—
460C22×C4—152no—
461C22×C4—152no—
462C22×C4—308no—
463C22×C4C22×D1514yes—
464C22×C4C22×D1514yes—
465C22×C4C22×D1511yescharacteristic
466C22×C4C22×D1511yescharacteristic
467C22×C4C22×D1511yescharacteristic
468C22×C4C22×D1511yescharacteristic
469C22×C4C22×D1511yescharacteristic
470C4⋊C4—154no—
471C4⋊C4—154no—
472C4⋊C4—158no—
473C4⋊C4—158no—
474C4⋊C4—154no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—158no—
479C4⋊C4C22×D1514yes—
480C22⋊C4—158no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4C22×D1514yes—
484C22⋊C4C22×D1514yes—
485C42—158no—
486C42—158no—
487C42C22×D1514yes—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—28no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—44no—
496C22×C3C2×#70914yes—
497C22×C3C2×#70912yes—
498C22×C3C2×#71112yes—
499C22×C3#415012yes—
500C22×C3C24×D511yescharacteristic
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4C2×#71114yes—
506Dic3—104no—
507Dic3—104no—
508Dic3—104no—
509Dic3—104no—
510C2×C5—24no—
511C2×C5—42no—
512C2×C5#554114yescomplemented
513C2×C5C22×#23511yescharacteristic
514C2×C5C22×#23711yescharacteristic
515C2×C5C2×#101011yescharacteristic
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23#681714yes—
522C23C23×D1512yes—
523C23C23×D1512yes—
524C23C23×D1511yescharacteristic
525Q8—308no—
526D4—28no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—28no—
533C2×C4—154no—
534C2×C4—154no—
535C2×C4—154no—
536C2×C4—154no—
537C2×C4—3016no—
538C2×C4—304no—
539C2×C4—304no—
540C2×C4—304no—
541C2×C4—304no—
542C2×C4#681914yes—
543C2×C4C23×D1512yes—
544C2×C4C23×D1512yes—
545C2×C4C23×D1512yes—
546C2×C4C23×D1512yes—
547C2×C4C23×D1512yes—
548C2×C3—24no—
549C2×C3—42no—
550C2×C3#6587514yescomplemented
551C2×C3C22×#70911yescharacteristic
552C2×C3C22×#71111yescharacteristic
553C2×C3C2×#415011yescharacteristic
554C5C2×#554111yescharacteristic, complemented, Sylow
555C22—28no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—44no—
562C22C2×#681714yes—
563C22C2×#681712yes—
564C22C2×#681912yes—
565C22#9210112yes—
566C22C24×D1511yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—304no—
572C4—304no—
573C4—304no—
574C4—304no—
575C4C2×#681914yes—
576C3C2×#6587511yescharacteristic, complemented, Sylow
577C2—24no—
578C2—42no—
579C2#1175630014yesdirect product factor
580C2C22×#681711yescharacteristic
581C2C22×#681911yescharacteristic
582C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×C4×D4D15
hypocenterC3×C5C2×#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#91815C2semidirect
4. C22×C4⋊Dic15C2semidirect
5. C2×#91813C2semidirect
6. C2×#91813C2semidirect
7. #11756300C2direct (N × H)
8. C2×#91778C2semidirect
9. C2×#91768C2semidirect
10. C2×#91766C2semidirect
11. C2×#91759C2semidirect
12. C2×C4×Dic30C2semidirect
28. #91815C22semidirect
33. C2×C4⋊Dic15C22semidirect
34. #91813C22semidirect
35. #91813C22semidirect
43. #91778C22semidirect
44. #91768C22semidirect
45. #91766C22semidirect
46. #91759C22semidirect
47. C4×Dic30C22semidirect
392. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
512. C2×C5#5541semidirect
550. C2×C3#65875semidirect
554. C5C2×#5541semidirect
576. C3C2×#65875semidirect
579. C2#11756300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×#918242
C2×#918152
C22×C4⋊Dic152
C2×#918132
#117563002
C2×#917782
C2×#917682
C2×#917662
C2×#917592
C2×C4×Dic302
C2×#658753
C2×#55415