Finite Group Databasebeta

← C2×#11752682 #14479874

Subgroups — C2×#11752682 #14479874

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×C4×Dic30C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×C42×D5C211yesmaximal, characteristic, complemented
4C2×#91449C211yesmaximal, characteristic
5C2×#91447C212yesmaximal, complemented
6C2×C4×#1201C212yesmaximal, complemented
7C2×#91388C211yesmaximal, characteristic, complemented
8C2×#91373C211yesmaximal, characteristic, complemented
9C2×#91372C212yesmaximal, complemented
10C2×#91371C212yesmaximal, complemented
11C2×#91360C211yesmaximal, characteristic, complemented
12#11752682C2116yesmaximal, direct product factor
13C2×#65891—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C4×C5×D3C2212yes—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1201C2212yes—
21C2×C3×C42×C5C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2212yes—
24C2×C4×Dic15C2212yes—
25C4×Dic30C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C4×C5×D12C2218yescomplemented
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×C42×D5C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6669C2212yes—
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×#6665C2212yes—
40#91449C2218yes—
41#91447C22116yescomplemented
42C4×#1201C22116yescomplemented
43#91388C2218yescomplemented
44#91373C2218yescomplemented
45#91372C22116yescomplemented
46#91371C22116yescomplemented
47#91360C2218yescomplemented
48C2×#5479—51nomaximal, Hall
49C2×C4×C5×D4—31no—
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×D5D311yescharacteristic, complemented
60C2×C4×Dic10—31no—
61C23×C5×D3C2312yes—
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2312yes—
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2312yes—
71C2×C5×D12—24no—
72C2×C5×D12C2314yes—
73C2×C4×C5×D3—28no—
74C2×C4×C5×D3C2318yes—
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×C4×D5—24no—
79C2×C3×C4×D5—24no—
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5C2314yes—
82C2×C3×C4×D5C2314yes—
83C2×C3×C4×D5C2314yes—
84C2×#1201—28no—
85C2×#1201C2318yes—
86C3×C42×C5C2314yes—
87C4⋊Dic15C2314yes—
88#6712C2318yes—
89C4×Dic15C2318yes—
90C5×(C2×D3)⋊C4C2318yes—
91C5×C4⋊Dic3C2314yes—
92C3×C4×Dic5C2314yes—
93C3×C4×Dic5C2314yes—
94C3×C4×Dic5C2314yes—
95Dic3⋊Dic5C2318yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101#6665C2318yes—
102C22×C3×C42—51no—
103C2×#930—51no—
104C2×#929—52no—
105C2×C4×#67—52no—
106C2×#924—51no—
107#5479—516no—
108C2×#876—52no—
109C2×#875—51no—
110C2×C4×D12D511yescharacteristic, complemented
111C2×#872—52no—
112C2×#870—51no—
113C2×C4×Dic6—51no—
114C22×C5×D4—31no—
115C23×C4×C5—32no—
116C22×C22⋊D5—32no—
117C22×C4×D5C2×D311yescharacteristic
118C22×C4×D5C2×D311yescharacteristic
119C22×C4×D5C2×D311yescharacteristic
120C22×Dic10—31no—
121C4×C5×D4—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C22⋊C4—32no—
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×Dic5C2×D311yescharacteristic
140C2×C4×Dic5C2×D311yescharacteristic
141C2×C4×Dic5C2×D311yescharacteristic
142#4043—38no—
143#4036—38no—
144#4029—316no—
145#4025—316no—
146C42×D5C2×D318yescomplemented
147C4×Dic10—38no—
148C2×#529—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×C5×D3—24no—
151C22×C5×D3—24no—
152C22×C5×D3—24no—
153C22×C5×D3C2414yes—
154C22×C3×D5—22no—
155C22×C3×D5—22no—
156C22×C3×D5#4114yes—
157C22×C3×D5C2412yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×C3×C4×C5C2412yes—
164C2×Dic15—24no—
165C2×Dic15—24no—
166C2×Dic15C2414yes—
167C2×Dic15C2414yes—
168Dic30—28no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3C2414yes—
171C5×D12—28no—
172C4×C5×D3—216no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2412yes—
177C2×C3×Dic5C2412yes—
178C2×C3×Dic5C2412yes—
179C3×C4×D5—28no—
180C3×C4×D5—28no—
181C3×C4×D5—28no—
182#1201—216no—
183C23×C3×C4—51no—
184C23×C3×C4—51no—
185C23×C3×C4—51no—
186C22×#67—52no—
187C22×D12C2×D511yescharacteristic
188C22×C4×D3C2×D512yes—
189C22×Dic6—51no—
190C2×C3×C42—51no—
191C2×C3×C42—51no—
192C2×C3×C42—51no—
193C2×C3×C42—58no—
194C2×C3×C42C2×D511yescharacteristic
195C2×#217—52no—
196#930—58no—
197#929—516no—
198C4×#67—516no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4—52no—
201C2×(C2×D3)⋊C4—52no—
202C2×(C2×D3)⋊C4C2×D512yes—
203C2×C4⋊Dic3—51no—
204C2×C4⋊Dic3C2×D511yescharacteristic
205#924—58no—
206C2×Dic3⋊C4—52no—
207C2×Dic3⋊C4—52no—
208C2×Dic3⋊C4—52no—
209C2×Dic3⋊C4—52no—
210C2×C4×Dic3—52no—
211#876—516no—
212#875—58no—
213C4×D12C2×D518yescomplemented
214#872—516no—
215#870—58no—
216C4×Dic6—58no—
217C24×C5—32no—
218C23×D5C22×D311yescharacteristic
219C2×C5×D4—34no—
220C2×C5×D4—64no—
221C22×C4×C5—32no—
222C22×C4×C5—38no—
223C22×C4×C5—68no—
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—38no—
228C2×C22⋊D5—68no—
229C22×Dic5—32no—
230C22×Dic5—32no—
231C22×Dic5C22×D311yescharacteristic
232C22×Dic5C22×D311yescharacteristic
233C22×Dic5C22×D311yescharacteristic
234C2×C4×D5—24no—
235C2×C4×D5—24no—
236C2×C4×D5—24no—
237C2×C4×D5C22×D314yes—
238C2×C4×D5C22×D314yes—
239C2×C4×D5C22×D314yes—
240C2×Dic10—34no—
241C2×Dic10—64no—
242C5×C4⋊C4—34no—
243C5×C22⋊C4—38no—
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×Dic5C22×D314yes—
256C4×Dic5C22×D314yes—
257C4×Dic5C22×D314yes—
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—31no—
267C2×C4×D4—152no—
268C2×#117—152no—
269C22×C42—51no—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2511yescharacteristic
274C2×C5×D3—24no—
275C2×C5×D3—24no—
276C2×C5×D3—24no—
277C2×C5×D3—48no—
278C2×C3×D5—28no—
279C2×C3×D5—22no—
280C2×C3×D5—22no—
281C2×C3×D5C2×#4114yes—
282C3×C4×C5—22no—
283C3×C4×C5C2×#4114yes—
284C3×C4×C5C2×#4114yes—
285Dic15—24no—
286Dic15—24no—
287C3×Dic5—22no—
288C3×Dic5—22no—
289C3×Dic5—22no—
290C5×Dic3—24no—
291C24×C3—51no—
292C23×D3C22×D512yes—
293C22×C3×C4—51no—
294C22×C3×C4—51no—
295C22×C3×C4—51no—
296C22×C3×C4—54no—
297C22×C3×C4—54no—
298C22×C3×C4—54no—
299C22×C3×C4—104no—
300C22×C3×C4—104no—
301C22×C3×C4—104no—
302C22×C3×C4C22×D511yescharacteristic
303C22×C3×C4C22×D511yescharacteristic
304C22×C3×C4C22×D511yescharacteristic
305C2×#67—58no—
306C2×#67—108no—
307C22×Dic3—52no—
308C22×Dic3—52no—
309C22×Dic3C22×D512yes—
310C2×D12—24no—
311C2×D12C22×D514yes—
312C2×C4×D3—28no—
313C2×C4×D3C22×D518yes—
314C2×Dic6—54no—
315C2×Dic6—104no—
316C3×C42—54no—
317C3×C42—54no—
318C3×C42—54no—
319C3×C42C22×D514yes—
320#217—58no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323(C2×D3)⋊C4—58no—
324(C2×D3)⋊C4C22×D518yes—
325C4⋊Dic3—54no—
326C4⋊Dic3C22×D514yes—
327Dic3⋊C4—58no—
328Dic3⋊C4—58no—
329Dic3⋊C4—58no—
330Dic3⋊C4—58no—
331C4×Dic3—58no—
332C23×C5—34no—
333C23×C5—64no—
334C23×C5—64no—
335C23×C5—64no—
336C23×C5C23×D311yescharacteristic
337C22×D5—22no—
338C22×D5—22no—
339C22×D5#23514yes—
340C22×D5C23×D312yes—
341C5×D4—68no—
342C2×C4×C5—22no—
343C2×C4×C5—34no—
344C2×C4×C5—64no—
345C2×C4×C5—616no—
346C2×C4×C5#23514yes—
347C2×C4×C5#23514yes—
348C2×C4×C5C23×D312yes—
349C2×C4×C5C23×D312yes—
350C2×C4×C5C23×D312yes—
351C22⋊D5—616no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—34no—
356C2×Dic5—34no—
357C2×Dic5—64no—
358C2×Dic5—64no—
359C2×Dic5C23×D312yes—
360C2×Dic5C23×D312yes—
361C2×Dic5C23×D312yes—
362C4×D5—28no—
363C4×D5—28no—
364C4×D5—28no—
365Dic10—68no—
366C22×Q8—151no—
367C22×D4—31no—
368C22×D4—152no—
369C23×C4—32no—
370C23×C4—51no—
371C23×C4—51no—
372C23×C4—51no—
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—158no—
379C4×Q8—158no—
380C4×D4—38no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—151no—
388C2×C4⋊C4—152no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—51no—
395C2×C42—51no—
396C2×C42—51no—
397C2×C42—58no—
398C2×C42—152no—
399C2×C42D3×D511yescharacteristic
400C2×C3×C5#52914yescomplemented
401C2×C3×C5C22×#4111yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C3×D5—24no—
405C5×D3—44no—
406C23×C3—54no—
407C23×C3—52no—
408C23×C3—102no—
409C23×C3—102no—
410C23×C3C23×D511yescharacteristic
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3C23×D514yes—
415C2×C3×C4—22no—
416C2×C3×C4—52no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—108no—
420C2×C3×C4—102no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—108no—
424C2×C3×C4—108no—
425C2×C3×C4#70914yes—
426C2×C3×C4#71114yes—
427C2×C3×C4C23×D512yes—
428C2×C3×C4C23×D512yes—
429C2×C3×C4C23×D512yes—
430#67—1016no—
431C2×Dic3—24no—
432C2×Dic3—54no—
433C2×Dic3—54no—
434C2×Dic3—104no—
435C2×Dic3—104no—
436C2×Dic3C23×D514yes—
437D12—28no—
438C4×D3—216no—
439Dic6—108no—
440C22×C5—64no—
441C22×C5—64no—
442C22×C5—64no—
443C22×C5—128no—
444C22×C5C2×#23512yes—
445C22×C5C2×#23512yes—
446C22×C5C2×#23512yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—22no—
449C2×D5—22no—
450C2×D5—28no—
451C2×D5C2×#23514yes—
452C4×C5—22no—
453C4×C5—64no—
454C4×C5C2×#23514yes—
455C4×C5C2×#23514yes—
456Dic5—22no—
457Dic5—22no—
458Dic5—22no—
459Dic5—64no—
460Dic5—64no—
461C24—32no—
462C24—51no—
463C2×Q8—154no—
464C2×Q8—304no—
465C2×D4—34no—
466C2×D4—64no—
467C2×D4—158no—
468C2×D4—308no—
469C22×C4—32no—
470C22×C4—38no—
471C22×C4—51no—
472C22×C4—51no—
473C22×C4—51no—
474C22×C4—54no—
475C22×C4—54no—
476C22×C4—54no—
477C22×C4—68no—
478C22×C4—104no—
479C22×C4—104no—
480C22×C4—104no—
481C22×C4—152no—
482C22×C4—152no—
483C22×C4C2×D3×D511yescharacteristic
484C22×C4C2×D3×D511yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—158no—
488C4⋊C4—158no—
489C4⋊C4—158no—
490C4⋊C4—154no—
491C4⋊C4—158no—
492C22⋊C4—38no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—54no—
498C42—54no—
499C42—54no—
500C42—158no—
501C42C2×D3×D514yes—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—54no—
504C22×C3—108no—
505C22×C3—102no—
506C22×C3—102no—
507C22×C3C2×#70912yes—
508C22×C3C2×#71112yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—24no—
512C2×D3—24no—
513C2×D3—24no—
514C2×D3—48no—
515C3×C4—22no—
516C3×C4—102no—
517C3×C4—102no—
518C3×C4—102no—
519C3×C4C2×#70914yes—
520C3×C4C2×#71114yes—
521Dic3—24no—
522Dic3—104no—
523Dic3—104no—
524C2×C5—124no—
525C2×C5#547914yescomplemented
526C2×C5C22×#23511yescharacteristic
527C2×C5C22×#23511yescharacteristic
528C2×C5C22×#23511yescharacteristic
529D5—24no—
530C23—34no—
531C23—54no—
532C23—52no—
533C23—64no—
534C23—64no—
535C23—64no—
536C23—102no—
537C23—102no—
538C23C22×D3×D511yescharacteristic
539Q8—308no—
540D4—68no—
541D4—3016no—
542C2×C4—22no—
543C2×C4—34no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—64no—
548C2×C4—616no—
549C2×C4—108no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—108no—
554C2×C4—108no—
555C2×C4—154no—
556C2×C4—154no—
557C2×C4—304no—
558C2×C4—304no—
559C2×C4#677114yes—
560C2×C4#677214yes—
561C2×C4C22×D3×D512yes—
562C2×C4C22×D3×D512yes—
563C2×C4C22×D3×D512yes—
564C2×C3—104no—
565C2×C3#6589114yescomplemented
566C2×C3C22×#70911yescharacteristic
567C2×C3C22×#71111yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—44no—
570C5C2×#547911yescharacteristic, complemented, Sylow
571C22—54no—
572C22—64no—
573C22—64no—
574C22—64no—
575C22—102no—
576C22—102no—
577C22—108no—
578C22—128no—
579C22C2×#677112yes—
580C22C2×#677212yes—
581C22D5×#23512yes—
582C22C23×D3×D511yescharacteristic
583C4—22no—
584C4—64no—
585C4—102no—
586C4—102no—
587C4—102no—
588C4—304no—
589C4—304no—
590C4C2×#677114yes—
591C4C2×#677214yes—
592C3C2×#6589111yescharacteristic, complemented, Sylow
593C2—104no—
594C2—124no—
595C2#1175268214yesdirect product factor
596C2C22×#677111yescharacteristic
597C2C22×#677211yescharacteristic
598C2C2×D5×#23511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91449C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic30C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×C42×D5C2semidirect
5. C2×#91447C2semidirect
6. C2×C4×#1201C2semidirect
7. C2×#91388C2semidirect
8. C2×#91373C2semidirect
9. C2×#91372C2semidirect
10. C2×#91371C2semidirect
11. C2×#91360C2semidirect
12. #11752682C2direct (N × H)
25. C4×Dic30C22semidirect
28. C4×C5×D12C22semidirect
32. C3×C42×D5C22semidirect
41. #91447C22semidirect
42. C4×#1201C22semidirect
43. #91388C22semidirect
44. #91373C22semidirect
45. #91372C22semidirect
46. #91371C22semidirect
47. #91360C22semidirect
59. C2×C42×D5D3semidirect
110. C2×C4×D12D5semidirect
146. C42×D5C2×D3semidirect
213. C4×D12C2×D5semidirect
400. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
525. C2×C5#5479semidirect
565. C2×C3#65891semidirect
570. C5C2×#5479semidirect
592. C3C2×#65891semidirect
595. C2#11752682direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C4×C5×D122
C2×C3×C42×D52
C2×#914492
C2×#914472
C2×C4×#12012
C2×#913882
C2×#913732
C2×#913722
C2×#913712
C2×#913602
#117526822
C2×#658913
C2×#54795