Finite Group Databasebeta

← C2×#11756316 #14479783

Subgroups — C2×#11756316 #14479783

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×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×#91827C211yesmaximal, characteristic
3C2×#91825C211yesmaximal, characteristic, complemented
4C2×C4×#1220C212yesmaximal, complemented
5C2×#91815C212yesmaximal, complemented
6#11756316C2116yesmaximal, direct product factor
7C2×#91786C211yesmaximal, characteristic, complemented
8C2×#91779C211yesmaximal, characteristic, complemented
9C2×#91772C212yesmaximal, complemented
10C2×#91768C212yesmaximal, complemented
11C2×C42×D15C211yesmaximal, characteristic, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#65891—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2212yes—
16C22×#1220C2212yes—
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic
21C3×C4×C5×D4C2218yescomplemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C42×C5C2211yescharacteristic
25C2×#6719C2212yes—
26C2×#6719C2212yes—
27C2×#6719C2212yes—
28#91827C2218yes—
29#91825C2218yescomplemented
30C4×#1220C22116yescomplemented
31C2×#6714C2212yes—
32#91815C22116yescomplemented
33C2×C4⋊Dic15C2212yes—
34C2×C4⋊Dic15C2212yes—
35C2×C4⋊Dic15C2211yescharacteristic
36C2×#6712C2212yes—
37C2×#6712C2212yes—
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2212yes—
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91786C2218yescomplemented
43#91779C2218yescomplemented
44#91772C22116yescomplemented
45#91768C22116yescomplemented
46C42×D15C2218yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5557—51nomaximal, Hall
49C2×C4×C5×D4D311yescharacteristic, complemented
50C2×#4084—31no—
51C2×#4082—31no—
52C2×C4×C22⋊D5—32no—
53C2×#4072—32no—
54#65891—316no—
55C2×#4043—31no—
56C2×#4036—31no—
57C2×#4029—32no—
58C2×#4025—32no—
59C2×C42×D5—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C23×D15C2311yescharacteristic
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5—28no—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2318yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C2×#1220—28no—
72C2×#1220C2318yes—
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2312yes—
77C22×Dic15C2312yes—
78C2×C4×D15—24no—
79C2×C4×D15—24no—
80C2×C4×D15—24no—
81C2×C4×D15C2314yes—
82C2×C4×D15C2314yes—
83C2×C4×D15C2314yes—
84C2×Dic30—24no—
85C2×Dic30C2314yes—
86C3×C5×C4⋊C4C2314yes—
87C3×C5×C22⋊C4C2318yes—
88C3×C42×C5C2314yes—
89#6719C2318yes—
90#6719C2318yes—
91#6719C2318yes—
92#6714C2318yes—
93C4⋊Dic15C2314yes—
94C4⋊Dic15C2318yes—
95C4⋊Dic15C2318yes—
96#6712C2318yes—
97#6712C2318yes—
98C4×Dic15C2318yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C4×Dic15C2314yes—
102C2×C3×C4×D4D511yescharacteristic, complemented
103C2×#938—51no—
104C2×#936—51no—
105C2×C4×#67—52no—
106C2×#926—52no—
107#5557—516no—
108C2×#897—51no—
109C2×#890—51no—
110C2×#883—52no—
111C2×#879—52no—
112C2×C42×D3—51no—
113C2×C4×Dic6—51no—
114C22×C5×D4C2×D311yescharacteristic
115C23×C4×C5C2×D312yes—
116C22×C22⋊D5—32no—
117C22×C4×D5—31no—
118C22×C4×D5—31no—
119C22×C4×D5—31no—
120C22×Dic10—31no—
121C4×C5×D4C2×D318yescomplemented
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C5×C22⋊C4C2×D312yes—
124C2×C42×C5C2×D311yescharacteristic
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5—32no—
128#4084—38no—
129#4082—38no—
130C4×C22⋊D5—316no—
131C2×#685—32no—
132#4072—316no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—32no—
135C2×C4⋊Dic5—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142#4043—38no—
143#4036—38no—
144#4029—316no—
145#4025—316no—
146C42×D5—38no—
147C4×Dic10—38no—
148C2×#529—151noSylow
149C23×C3×C5—24no—
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5C2414yes—
153C23×C3×C5C2411yescharacteristic
154C22×D15—22no—
155C22×D15—22no—
156C22×D15#4114yes—
157C22×D15C2412yes—
158C3×C5×D4—28no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—24no—
161C2×C3×C4×C5—216no—
162C2×C3×C4×C5#4114yes—
163C2×C3×C4×C5#4114yes—
164C2×C3×C4×C5C2412yes—
165C2×C3×C4×C5C2414yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168#1220—216no—
169C2×Dic15—24no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—22no—
173C2×Dic15—24no—
174C2×Dic15C2412yes—
175C2×Dic15C2412yes—
176C2×Dic15C2412yes—
177C2×Dic15C2414yes—
178C2×Dic15C2414yes—
179C4×D15—28no—
180C4×D15—28no—
181C4×D15—28no—
182Dic30—28no—
183C22×C3×D4C2×D511yescharacteristic
184C23×C3×C4C2×D512yes—
185C22×#67—52no—
186C22×C4×D3—51no—
187C22×C4×D3—51no—
188C22×C4×D3—51no—
189C22×Dic6—51no—
190C3×C4×D4C2×D518yescomplemented
191C2×C3×C4⋊C4C2×D511yescharacteristic
192C2×C3×C22⋊C4C2×D512yes—
193C2×C3×C42C2×D511yescharacteristic
194C2×#217—52no—
195C2×#217—52no—
196C2×#217—52no—
197#938—58no—
198#936—58no—
199C4×#67—516no—
200C2×(C2×D3)⋊C4—52no—
201#926—516no—
202C2×C4⋊Dic3—51no—
203C2×C4⋊Dic3—52no—
204C2×C4⋊Dic3—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×C4×Dic3—52no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—51no—
211#897—58no—
212#890—58no—
213#883—516no—
214#879—516no—
215C42×D3—58no—
216C4×Dic6—58no—
217C24×C5C22×D312yes—
218C23×D5—31no—
219C2×C5×D4—24no—
220C2×C5×D4C22×D314yes—
221C22×C4×C5—28no—
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D312yes—
224C22×C4×C5C22×D318yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—38no—
228C2×C22⋊D5—68no—
229C22×Dic5—32no—
230C22×Dic5—31no—
231C22×Dic5—31no—
232C22×Dic5—31no—
233C22×Dic5—32no—
234C2×C4×D5—34no—
235C2×C4×D5—34no—
236C2×C4×D5—34no—
237C2×C4×D5—64no—
238C2×C4×D5—64no—
239C2×C4×D5—64no—
240C2×Dic10—34no—
241C2×Dic10—64no—
242C5×C4⋊C4C22×D314yes—
243C5×C22⋊C4C22×D318yes—
244C42×C5C22×D314yes—
245C22⋊Dic5—38no—
246C22⋊Dic5—38no—
247C22⋊Dic5—38no—
248#685—38no—
249C4⋊Dic5—34no—
250C4⋊Dic5—38no—
251C4⋊Dic5—38no—
252#683—38no—
253#683—38no—
254C4×Dic5—38no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5—34no—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—151no—
265C2×C4×Q8—151no—
266C2×C4×D4—152no—
267C2×C4×D4D1511yescharacteristic, complemented
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5—24no—
271C22×C3×C5—24no—
272C22×C3×C5—24no—
273C22×C3×C5—48no—
274C22×C3×C5C2×#4112yes—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5C2511yescharacteristic
278C2×D15—28no—
279C2×D15—22no—
280C2×D15—22no—
281C2×D15C2×#4114yes—
282C3×C4×C5—22no—
283C3×C4×C5—24no—
284C3×C4×C5C2×#4114yes—
285C3×C4×C5C2×#4114yes—
286Dic15—24no—
287Dic15—22no—
288Dic15—22no—
289Dic15—22no—
290Dic15—24no—
291C24×C3C22×D512yes—
292C23×D3—51no—
293C2×C3×D4—24no—
294C2×C3×D4C22×D514yes—
295C22×C3×C4—28no—
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D512yes—
298C22×C3×C4C22×D518yes—
299C22×C3×C4C22×D511yescharacteristic
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—58no—
302C2×#67—108no—
303C22×Dic3—51no—
304C22×Dic3—51no—
305C22×Dic3—51no—
306C22×Dic3—52no—
307C22×Dic3—52no—
308C2×C4×D3—54no—
309C2×C4×D3—54no—
310C2×C4×D3—54no—
311C2×C4×D3—104no—
312C2×C4×D3—104no—
313C2×C4×D3—104no—
314C2×Dic6—54no—
315C2×Dic6—104no—
316C3×C4⋊C4C22×D514yes—
317C3×C22⋊C4C22×D518yes—
318C3×C42C22×D514yes—
319#217—58no—
320#217—58no—
321#217—58no—
322(C2×D3)⋊C4—58no—
323C4⋊Dic3—54no—
324C4⋊Dic3—58no—
325C4⋊Dic3—58no—
326Dic3⋊C4—58no—
327Dic3⋊C4—58no—
328C4×Dic3—58no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C23×C5—24no—
333C23×C5—24no—
334C23×C5—24no—
335C23×C5C23×D314yes—
336C23×C5C23×D311yescharacteristic
337C22×D5—34no—
338C22×D5—32no—
339C22×D5—62no—
340C22×D5—62no—
341C5×D4—28no—
342C2×C4×C5—24no—
343C2×C4×C5—22no—
344C2×C4×C5—216no—
345C2×C4×C5#23514yes—
346C2×C4×C5#23714yes—
347C2×C4×C5C23×D312yes—
348C2×C4×C5C23×D314yes—
349C2×C4×C5C23×D312yes—
350C2×C4×C5C23×D312yes—
351C22⋊D5—616no—
352C2×Dic5—32no—
353C2×Dic5—32no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—34no—
357C2×Dic5—64no—
358C2×Dic5—62no—
359C2×Dic5—62no—
360C2×Dic5—62no—
361C2×Dic5—64no—
362C4×D5—68no—
363C4×D5—68no—
364C4×D5—68no—
365Dic10—68no—
366C22×Q8—151no—
367C22×D4—152no—
368C22×D4C2×D1511yescharacteristic
369C23×C4—151no—
370C23×C4—151no—
371C23×C4—151no—
372C23×C4C2×D1512yes—
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—158no—
379C4×Q8—158no—
380C4×D4—1516no—
381C4×D4C2×D1518yescomplemented
382#117—1516no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—151no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4C2×D1511yescharacteristic
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4C2×D1512yes—
394C2×C42—151no—
395C2×C42—151no—
396C2×C42—151no—
397C2×C42—152no—
398C2×C42—158no—
399C2×C42C2×D1511yescharacteristic
400C2×C3×C5—44no—
401C2×C3×C5#52914yescomplemented
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C22×#4111yescharacteristic
405D15—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3C23×D514yes—
410C23×C3C23×D511yescharacteristic
411C22×D3—54no—
412C22×D3—52no—
413C22×D3—102no—
414C22×D3—102no—
415C3×D4—28no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—216no—
419C2×C3×C4#70914yes—
420C2×C3×C4#71114yes—
421C2×C3×C4C23×D512yes—
422C2×C3×C4C23×D514yes—
423C2×C3×C4C23×D512yes—
424C2×C3×C4C23×D512yes—
425#67—1016no—
426C2×Dic3—52no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—54no—
430C2×Dic3—54no—
431C2×Dic3—104no—
432C2×Dic3—102no—
433C2×Dic3—102no—
434C2×Dic3—102no—
435C2×Dic3—104no—
436C4×D3—108no—
437C4×D3—108no—
438C4×D3—108no—
439Dic6—108no—
440C22×C5—24no—
441C22×C5—24no—
442C22×C5—24no—
443C22×C5—48no—
444C22×C5C2×#23512yes—
445C22×C5C2×#23712yes—
446C22×C5D3×#4112yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—34no—
449C2×D5—62no—
450C2×D5—62no—
451C2×D5—68no—
452C4×C5—24no—
453C4×C5—22no—
454C4×C5C2×#23514yes—
455C4×C5C2×#23714yes—
456Dic5—64no—
457Dic5—62no—
458Dic5—62no—
459Dic5—62no—
460Dic5—64no—
461C24—151no—
462C24C22×D1512yes—
463C2×Q8—154no—
464C2×Q8—304no—
465C2×D4—24no—
466C2×D4—158no—
467C2×D4—308no—
468C2×D4C22×D1514yes—
469C22×C4—28no—
470C22×C4—151no—
471C22×C4—151no—
472C22×C4—151no—
473C22×C4—152no—
474C22×C4—152no—
475C22×C4—154no—
476C22×C4—154no—
477C22×C4—154no—
478C22×C4—304no—
479C22×C4—304no—
480C22×C4—304no—
481C22×C4C22×D1511yescharacteristic
482C22×C4C22×D1512yes—
483C22×C4C22×D1518yes—
484C22×C4C22×D1511yescharacteristic
485C22×C4C22×D1511yescharacteristic
486C4⋊C4—158no—
487C4⋊C4—158no—
488C4⋊C4—158no—
489C4⋊C4—154no—
490C4⋊C4—158no—
491C4⋊C4C22×D1514yes—
492C22⋊C4—158no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4C22×D1518yes—
497C42—154no—
498C42—154no—
499C42—154no—
500C42—158no—
501C42C22×D1514yes—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—48no—
507C22×C3C2×#70912yes—
508C22×C3C2×#71112yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—54no—
512C2×D3—108no—
513C2×D3—102no—
514C2×D3—102no—
515C3×C4—24no—
516C3×C4—22no—
517C3×C4C2×#70914yes—
518C3×C4C2×#71114yes—
519Dic3—104no—
520Dic3—102no—
521Dic3—102no—
522Dic3—102no—
523Dic3—104no—
524C2×C5—44no—
525C2×C5#555714yescomplemented
526C2×C5C22×#23511yescharacteristic
527C2×C5C22×#23711yescharacteristic
528C2×C5C2×D3×#4111yescharacteristic
529D5—64no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—154no—
534C23—152no—
535C23—302no—
536C23—302no—
537C23C23×D1514yes—
538C23C23×D1511yescharacteristic
539Q8—308no—
540D4—28no—
541D4—3016no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—216no—
545C2×C4—152no—
546C2×C4—152no—
547C2×C4—152no—
548C2×C4—154no—
549C2×C4—154no—
550C2×C4—308no—
551C2×C4—302no—
552C2×C4—304no—
553C2×C4—302no—
554C2×C4—302no—
555C2×C4—304no—
556C2×C4—308no—
557C2×C4—308no—
558C2×C4#681714yes—
559C2×C4#681914yes—
560C2×C4C23×D1512yes—
561C2×C4C23×D1514yes—
562C2×C4C23×D1512yes—
563C2×C4C23×D1512yes—
564C2×C3—44no—
565C2×C3#6589114yescomplemented
566C2×C3C22×#70911yescharacteristic
567C2×C3C22×#71111yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—104no—
570C5C2×#555711yescharacteristic, complemented, Sylow
571C22—24no—
572C22—24no—
573C22—24no—
574C22—48no—
575C22—154no—
576C22—308no—
577C22—302no—
578C22—302no—
579C22C2×#681712yes—
580C22C2×#681912yes—
581C22#41×D1512yes—
582C22C24×D1511yescharacteristic
583C4—24no—
584C4—22no—
585C4—302no—
586C4—304no—
587C4—302no—
588C4—302no—
589C4—304no—
590C4C2×#681714yes—
591C4C2×#681914yes—
592C3C2×#6589111yescharacteristic, complemented, Sylow
593C2—44no—
594C2—304no—
595C2#1175631614yesdirect product factor
596C2C22×#681711yescharacteristic
597C2C22×#681911yescharacteristic
598C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC22×C4C22×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×#91827C2
hypercenterC2×C4×D4D15
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C2×#91825C2semidirect
4. C2×C4×#1220C2semidirect
5. C2×#91815C2semidirect
6. #11756316C2direct (N × H)
7. C2×#91786C2semidirect
8. C2×#91779C2semidirect
9. C2×#91772C2semidirect
10. C2×#91768C2semidirect
11. C2×C42×D15C2semidirect
12. C2×C4×Dic30C2semidirect
21. C3×C4×C5×D4C22semidirect
29. #91825C22semidirect
30. C4×#1220C22semidirect
32. #91815C22semidirect
42. #91786C22semidirect
43. #91779C22semidirect
44. #91772C22semidirect
45. #91768C22semidirect
46. C42×D15C22semidirect
47. C4×Dic30C22semidirect
49. C2×C4×C5×D4D3semidirect
102. C2×C3×C4×D4D5semidirect
121. C4×C5×D4C2×D3semidirect
190. C3×C4×D4C2×D5semidirect
267. C2×C4×D4D15semidirect
381. C4×D4C2×D15semidirect
401. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
525. C2×C5#5557semidirect
565. C2×C3#65891semidirect
570. C5C2×#5557semidirect
592. C3C2×#65891semidirect
595. C2#11756316direct (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×#918272
C2×#918252
C2×C4×#12202
C2×#918152
#117563162
C2×#917862
C2×#917792
C2×#917722
C2×#917682
C2×C42×D152
C2×C4×Dic302
C2×#658913
C2×#55575