Finite Group Databasebeta

← C2×#11753823 #14481152

Subgroups — C2×#11753823 #14481152

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91784C211yesmaximal, characteristic, complemented
2C2×C5×#893C211yesmaximal, characteristic, complemented
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×#91466C211yesmaximal, characteristic, complemented
5C2×#91460C212yesmaximal, complemented
6C2×#91451C211yesmaximal, characteristic, complemented
7C2×#91438C212yesmaximal, complemented
8C2×#91428C211yesmaximal, characteristic, complemented
9C2×#91420C212yesmaximal, complemented
10C2×#91386C211yesmaximal, characteristic, complemented
11C2×#91351C212yesmaximal, complemented
12#11753823C2116yesmaximal, direct product factor
13C2×#65896—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×D60C2212yes—
16C22×C4×D15C2211yescharacteristic
17C22×C5×D12C2211yescharacteristic
18C22×C4×C5×D3C2212yes—
19C22×#1203C2212yes—
20C22×#1203C2212yes—
21C22×#1203C2212yes—
22C22×#1200C2212yes—
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×#6714C2212yes—
25#91784C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C5×#893C2218yescomplemented
29C2×C3×C4⋊Dic5C2212yes—
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×#683C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×#4036C2218yescomplemented
34C2×#6669C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40#91466C2218yescomplemented
41#91460C22116yescomplemented
42#91451C2218yescomplemented
43#91438C22116yescomplemented
44#91428C2218yescomplemented
45#91420C22116yescomplemented
46#91386C2218yescomplemented
47#91351C22116yescomplemented
48C2×#5697—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4086—31no—
51C2×#4084—31no—
52C2×#4076—32no—
53C2×#4075—32no—
54#65896—316no—
55C2×#4041—31no—
56C2×#4036D311yescharacteristic, complemented
57C2×#4030—32no—
58C2×#4029—32no—
59C2×C4×D20—31no—
60C2×#4018—31no—
61C23×D15C2312yes—
62C23×D15C2311yescharacteristic
63C23×C5×D3C2312yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C2×D60—24no—
68C2×D60—44no—
69C2×D60C2314yes—
70C2×D60C2318yes—
71C2×C4×D15—24no—
72C2×C4×D15C2314yes—
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2311yescharacteristic
75C2×C5×D12—24no—
76C2×C5×D12C2314yes—
77C2×C4×C5×D3—44no—
78C2×C4×C5×D3C2318yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×#1203—44no—
83C2×#1203—44no—
84C2×#1203—44no—
85C2×#1203C2318yes—
86C2×#1203C2318yes—
87C2×#1203C2318yes—
88C2×#1200—44no—
89C2×#1200C2318yes—
90C3×C5×C4⋊C4C2314yes—
91#6714C2318yes—
92C5×(C2×D3)⋊C4C2318yes—
93C4×C5×Dic3C2314yes—
94C3×C4⋊Dic5C2314yes—
95C3×C4⋊Dic5C2318yes—
96C3×#683C2318yes—
97C3×C4×Dic5C2314yes—
98#6669C2314yes—
99#6669C2314yes—
100#6667C2314yes—
101#6667C2318yes—
102#6667C2314yes—
103(C2×D3)⋊Dic5C2318yes—
104C2×C3×#125—51no—
105#5697—516no—
106C2×#895—51no—
107C2×#895—52no—
108C2×#895—51no—
109C2×#895—52no—
110C2×#894—52no—
111C2×#894—52no—
112C2×#893—51no—
113C2×#893D511yescharacteristic, complemented
114C2×#874—51no—
115C2×#872—51no—
116C22×C5×D4—31no—
117C23×C4×C5—32no—
118C22×C22⋊D5—32no—
119C22×C22⋊D5—32no—
120C22×C22⋊D5—32no—
121C22×D20—31no—
122C22×D20—32no—
123C22×C4×D5—31no—
124C22×C4×D5—32no—
125C4×C5×D4—38no—
126C2×C5×C4⋊C4C2×D311yescharacteristic
127C2×C5×C22⋊C4—32no—
128C2×C42×C5—31no—
129C2×C22⋊Dic5—32no—
130#4086—38no—
131#4084—38no—
132#4076—316no—
133#4075—316no—
134C2×#685—32no—
135C2×#685—31no—
136C2×#685—31no—
137C2×#685—32no—
138C2×C4⋊Dic5C2×D311yescharacteristic
139C2×C4⋊Dic5C2×D312yes—
140C2×#683—31no—
141C2×#683—31no—
142C2×#683C2×D312yes—
143C2×C4×Dic5C2×D311yescharacteristic
144#4041—38no—
145#4036C2×D318yescomplemented
146#4030—316no—
147#4029—316no—
148C4×D20—38no—
149#4018—38no—
150C2×#540—151noSylow
151C23×C3×C5C2411yescharacteristic
152C22×D15—22no—
153C22×D15—24no—
154C22×D15—24no—
155C22×D15—22no—
156C22×D15—24no—
157C22×D15—22no—
158C22×D15C2412yes—
159C22×D15C2414yes—
160C22×C5×D3—24no—
161C22×C5×D3—24no—
162C22×C5×D3—24no—
163C22×C5×D3C2414yes—
164C2×C3×C4×C5—24no—
165C2×C3×C4×C5#4114yes—
166C2×C3×C4×C5C2414yes—
167C2×C3×C4×C5C2412yes—
168C2×Dic15—22no—
169C2×Dic15C2412yes—
170D60—28no—
171D60—48no—
172C4×D15—28no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3C2412yes—
176C2×C5×Dic3C2412yes—
177C5×D12—28no—
178C4×C5×D3—48no—
179C2×C3×Dic5—24no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5—22no—
182C2×C3×Dic5C2414yes—
183C2×C3×Dic5C2412yes—
184C2×C3×Dic5C2412yes—
185#1203—48no—
186#1203—48no—
187#1203—48no—
188#1200—48no—
189C22×D12—51no—
190C22×D12—52no—
191C22×D12—52no—
192C22×D12—52no—
193C22×D12—52no—
194C22×D12C2×D511yescharacteristic
195C22×C4×D3—51no—
196C22×C4×D3—52no—
197C22×C4×D3C2×D512yes—
198C3×#125—58no—
199C2×C3×C4⋊C4—51no—
200C2×C3×C4⋊C4—52no—
201C2×C3×C4⋊C4—52no—
202C2×C3×C4⋊C4C2×D511yescharacteristic
203C2×C3×C42—51no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—52no—
206C2×(C2×D3)⋊C4—51no—
207C2×(C2×D3)⋊C4—51no—
208C2×(C2×D3)⋊C4—52no—
209C2×(C2×D3)⋊C4C2×D512yes—
210C2×Dic3⋊C4—51no—
211C2×Dic3⋊C4—51no—
212C2×C4×Dic3C2×D511yescharacteristic
213#895—58no—
214#895—516no—
215#895—58no—
216#895—516no—
217#894—516no—
218#894—516no—
219#893—58no—
220#893C2×D518yescomplemented
221#874—58no—
222#872—58no—
223C24×C5—32no—
224C23×D5—31no—
225C23×D5—32no—
226C2×C5×D4—34no—
227C2×C5×D4—64no—
228C22×C4×C5—31no—
229C22×C4×C5—31no—
230C22×C4×C5—38no—
231C22×C4×C5—124no—
232C22×C4×C5C22×D312yes—
233C22×C4×C5C22×D311yescharacteristic
234C2×C22⋊D5—38no—
235C2×C22⋊D5—38no—
236C2×C22⋊D5—38no—
237C2×C22⋊D5—124no—
238C2×C22⋊D5—124no—
239C2×C22⋊D5—124no—
240C22×Dic5—31no—
241C22×Dic5C22×D312yes—
242C22×Dic5C22×D311yescharacteristic
243C22×Dic5C22×D311yescharacteristic
244C2×D20—34no—
245C2×D20—38no—
246C2×D20—64no—
247C2×D20—124no—
248C2×C4×D5—34no—
249C2×C4×D5—38no—
250C2×C4×D5—64no—
251C2×C4×D5—124no—
252C5×C4⋊C4C22×D314yes—
253C5×C22⋊C4—38no—
254C42×C5—34no—
255C22⋊Dic5—38no—
256#685—38no—
257#685—34no—
258#685—34no—
259#685—38no—
260C4⋊Dic5C22×D314yes—
261C4⋊Dic5C22×D318yes—
262#683—34no—
263#683—34no—
264#683C22×D318yes—
265C4×Dic5C22×D314yes—
266#540—1516no—
267C2×#127—151no—
268C2×#125—51no—
269C2×#123—152no—
270C2×#123—152no—
271C2×#121—152no—
272C2×#121—152no—
273C2×#121—151no—
274C2×#121—151no—
275C2×C4×D4—31no—
276C2×C4×D4—151no—
277C2×#117—151no—
278C22×C3×C5C2×#4112yes—
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C5H(5,𝔽2)12yes—
281C22×C3×C5C2511yescharacteristic
282C2×D15—22no—
283C2×D15—24no—
284C2×D15—24no—
285C2×D15—22no—
286C2×D15—24no—
287C2×D15—22no—
288C2×D15—44no—
289C2×D15—48no—
290C2×C5×D3—24no—
291C2×C5×D3—24no—
292C2×C5×D3—24no—
293C2×C5×D3—48no—
294C3×C4×C5—24no—
295C3×C4×C5C2×#4114yes—
296Dic15—22no—
297C3×Dic5—24no—
298C3×Dic5—22no—
299C3×Dic5—22no—
300C5×Dic3—22no—
301C5×Dic3—22no—
302C23×D3—51no—
303C23×D3—52no—
304C23×D3C22×D512yes—
305C22×C3×C4—51no—
306C22×C3×C4—51no—
307C22×C3×C4—52no—
308C22×C3×C4C22×D512yes—
309C22×C3×C4C22×D511yescharacteristic
310C22×Dic3—51no—
311C22×Dic3C22×D511yescharacteristic
312C22×Dic3C22×D511yescharacteristic
313C2×D12—24no—
314C2×D12—54no—
315C2×D12—58no—
316C2×D12—58no—
317C2×D12—58no—
318C2×D12—58no—
319C2×D12—104no—
320C2×D12—204no—
321C2×D12—204no—
322C2×D12—204no—
323C2×D12—204no—
324C2×D12C22×D514yes—
325C2×C4×D3—44no—
326C2×C4×D3—54no—
327C2×C4×D3—58no—
328C2×C4×D3—104no—
329C2×C4×D3—204no—
330C2×C4×D3C22×D518yes—
331C3×C4⋊C4—58no—
332C3×C4⋊C4—54no—
333C3×C4⋊C4—58no—
334C3×C4⋊C4C22×D514yes—
335C3×C42—54no—
336(C2×D3)⋊C4—58no—
337(C2×D3)⋊C4—58no—
338(C2×D3)⋊C4—54no—
339(C2×D3)⋊C4—54no—
340(C2×D3)⋊C4—58no—
341(C2×D3)⋊C4C22×D518yes—
342Dic3⋊C4—54no—
343Dic3⋊C4—54no—
344C4×Dic3C22×D514yes—
345C23×C5—34no—
346C23×C5—64no—
347C23×C5—64no—
348C23×C5—64no—
349C23×C5C23×D311yescharacteristic
350C22×D5—32no—
351C22×D5—34no—
352C22×D5—62no—
353C22×D5—64no—
354C22×D5—64no—
355C22×D5—62no—
356C22×D5—64no—
357C22×D5—62no—
358C5×D4—68no—
359C2×C4×C5—24no—
360C2×C4×C5—32no—
361C2×C4×C5—32no—
362C2×C4×C5—62no—
363C2×C4×C5—62no—
364C2×C4×C5—128no—
365C2×C4×C5#23914yes—
366C2×C4×C5C23×D314yes—
367C2×C4×C5C23×D312yes—
368C22⋊D5—128no—
369C22⋊D5—128no—
370C22⋊D5—128no—
371C2×Dic5—24no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—32no—
375C2×Dic5—62no—
376C2×Dic5C23×D312yes—
377C2×Dic5C23×D312yes—
378C2×Dic5C23×D314yes—
379D20—68no—
380D20—128no—
381C4×D5—68no—
382C4×D5—128no—
383C22×D4—31no—
384C22×D4—152no—
385C22×D4—152no—
386C22×D4—152no—
387C22×D4—151no—
388C22×D4—152no—
389C23×C4—32no—
390C23×C4—152no—
391C23×C4—151no—
392#127—158no—
393#125—58no—
394#123—1516no—
395#123—1516no—
396#121—1516no—
397#121—1516no—
398#121—158no—
399#121—158no—
400C4×D4—38no—
401C4×D4—158no—
402#117—158no—
403C2×C4⋊C4—51no—
404C2×C4⋊C4—52no—
405C2×C4⋊C4—52no—
406C2×C4⋊C4—151no—
407C2×C4⋊C4—151no—
408C2×C4⋊C4D3×D511yescharacteristic
409C2×C22⋊C4—32no—
410C2×C22⋊C4—151no—
411C2×C22⋊C4—151no—
412C2×C22⋊C4—152no—
413C2×C22⋊C4—152no—
414C2×C22⋊C4—152no—
415C2×C42—31no—
416C2×C42—51no—
417C2×C3×C5#54014yescomplemented
418C2×C3×C5C22×#4111yescharacteristic
419C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
420C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
421D15—42no—
422D15—44no—
423C5×D3—44no—
424C23×C3C23×D511yescharacteristic
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—52no—
429C22×D3—54no—
430C22×D3—102no—
431C22×D3—104no—
432C22×D3—104no—
433C22×D3—102no—
434C22×D3—104no—
435C22×D3—102no—
436C22×D3C23×D514yes—
437C2×C3×C4—24no—
438C2×C3×C4—52no—
439C2×C3×C4—52no—
440C2×C3×C4—54no—
441C2×C3×C4—102no—
442C2×C3×C4—104no—
443C2×C3×C4—102no—
444C2×C3×C4#70914yes—
445C2×C3×C4C23×D514yes—
446C2×C3×C4C23×D512yes—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—52no—
450C2×Dic3—102no—
451C2×Dic3C23×D512yes—
452C2×Dic3C23×D512yes—
453D12—28no—
454D12—108no—
455D12—208no—
456D12—208no—
457D12—208no—
458D12—208no—
459C4×D3—48no—
460C4×D3—108no—
461C4×D3—208no—
462C22×C5—64no—
463C22×C5—64no—
464C22×C5—64no—
465C22×C5—128no—
466C22×C5C2×#23912yes—
467C22×C5#100912yes—
468C22×C5#100912yes—
469C22×C5C24×D311yescharacteristic
470C2×D5—62no—
471C2×D5—64no—
472C2×D5—64no—
473C2×D5—62no—
474C2×D5—64no—
475C2×D5—62no—
476C2×D5—124no—
477C2×D5—128no—
478C4×C5—24no—
479C4×C5—62no—
480C4×C5—62no—
481C4×C5C2×#23914yes—
482Dic5—24no—
483Dic5—22no—
484Dic5—22no—
485Dic5—62no—
486C24—32no—
487C24—151no—
488C24—152no—
489C2×D4—34no—
490C2×D4—64no—
491C2×D4—158no—
492C2×D4—158no—
493C2×D4—158no—
494C2×D4—154no—
495C2×D4—158no—
496C2×D4—304no—
497C2×D4—604no—
498C2×D4—604no—
499C2×D4—604no—
500C2×D4—604no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—38no—
504C22×C4—51no—
505C22×C4—51no—
506C22×C4—52no—
507C22×C4—124no—
508C22×C4—158no—
509C22×C4—151no—
510C22×C4—154no—
511C22×C4—304no—
512C22×C4—604no—
513C22×C4C2×D3×D512yes—
514C22×C4C2×D3×D511yescharacteristic
515C4⋊C4—54no—
516C4⋊C4—58no—
517C4⋊C4—58no—
518C4⋊C4—154no—
519C4⋊C4—154no—
520C4⋊C4C2×D3×D514yes—
521C22⋊C4—38no—
522C22⋊C4—154no—
523C22⋊C4—154no—
524C22⋊C4—158no—
525C22⋊C4—158no—
526C22⋊C4—158no—
527C42—34no—
528C42—54no—
529C3×C5C2×#54011yescharacteristic, complemented, Hall
530C22×C3C2×#70912yes—
531C22×C3#414412yes—
532C22×C3#414912yes—
533C22×C3C24×D511yescharacteristic
534C2×D3—24no—
535C2×D3—24no—
536C2×D3—24no—
537C2×D3—48no—
538C2×D3—102no—
539C2×D3—104no—
540C2×D3—104no—
541C2×D3—102no—
542C2×D3—104no—
543C2×D3—102no—
544C2×D3—204no—
545C2×D3—208no—
546C3×C4—24no—
547C3×C4—102no—
548C3×C4—104no—
549C3×C4—102no—
550C3×C4C2×#70914yes—
551Dic3—22no—
552Dic3—22no—
553Dic3—102no—
554C2×C5—124no—
555C2×C5#569714yescomplemented
556C2×C5C22×#23911yescharacteristic
557C2×C5C2×#100911yescharacteristic
558C2×C5C2×#100911yescharacteristic
559D5—122no—
560D5—124no—
561C23—34no—
562C23—64no—
563C23—64no—
564C23—64no—
565C23—152no—
566C23—154no—
567C23—302no—
568C23—304no—
569C23—302no—
570C23—304no—
571C23—304no—
572C23—302no—
573C23C22×D3×D511yescharacteristic
574D4—68no—
575D4—308no—
576D4—608no—
577D4—608no—
578D4—608no—
579D4—608no—
580C2×C4—24no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—52no—
584C2×C4—52no—
585C2×C4—54no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—102no—
589C2×C4—104no—
590C2×C4—102no—
591C2×C4—128no—
592C2×C4—152no—
593C2×C4—302no—
594C2×C4—308no—
595C2×C4—608no—
596C2×C4#676914yes—
597C2×C4C22×D3×D514yes—
598C2×C4C22×D3×D512yes—
599C2×C3#6589614yescomplemented
600C2×C3C22×#70911yescharacteristic
601C2×C3C2×#414411yescharacteristic
602C2×C3C2×#414911yescharacteristic
603D3—44no—
604D3—202no—
605D3—204no—
606C5C2×#569711yescharacteristic, complemented, Sylow
607C22—64no—
608C22—64no—
609C22—64no—
610C22—128no—
611C22—302no—
612C22—304no—
613C22—302no—
614C22—304no—
615C22—304no—
616C22—302no—
617C22—604no—
618C22—608no—
619C22C2×#676912yes—
620C22#9202712yes—
621C22#9203512yes—
622C22C23×D3×D511yescharacteristic
623C4—24no—
624C4—62no—
625C4—62no—
626C4—102no—
627C4—104no—
628C4—102no—
629C4—302no—
630C4C2×#676914yes—
631C3C2×#6589611yescharacteristic, complemented, Sylow
632C2—124no—
633C2—602no—
634C2—604no—
635C2#1175382314yesdirect product factor
636C2C22×#676911yescharacteristic
637C2C2×#9202711yescharacteristic
638C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91784C2semidirect
2. C2×C5×#893C2semidirect
3. C2×C3×#4036C2semidirect
4. C2×#91466C2semidirect
5. C2×#91460C2semidirect
6. C2×#91451C2semidirect
7. C2×#91438C2semidirect
8. C2×#91428C2semidirect
9. C2×#91420C2semidirect
10. C2×#91386C2semidirect
11. C2×#91351C2semidirect
12. #11753823C2direct (N × H)
25. #91784C22semidirect
28. C5×#893C22semidirect
33. C3×#4036C22semidirect
40. #91466C22semidirect
41. #91460C22semidirect
42. #91451C22semidirect
43. #91438C22semidirect
44. #91428C22semidirect
45. #91420C22semidirect
46. #91386C22semidirect
47. #91351C22semidirect
56. C2×#4036D3semidirect
113. C2×#893D5semidirect
145. #4036C2×D3semidirect
220. #893C2×D5semidirect
417. C2×C3×C5#540semidirect
529. C3×C5C2×#540semidirect
555. C2×C5#5697semidirect
599. C2×C3#65896semidirect
606. C5C2×#5697semidirect
631. C3C2×#65896semidirect
635. C2#11753823direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917842
C2×C5×#8932
C2×C3×#40362
C2×#914662
C2×#914602
C2×#914512
C2×#914382
C2×#914282
C2×#914202
C2×#913862
C2×#913512
#117538232
C2×#658963
C2×#56975