Finite Group Databasebeta

← C2×#11754507 #14481148

Subgroups — C2×#11754507 #14481148

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×#91819C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic, complemented
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C2×#91558C212yesmaximal, complemented
5C2×#91557C212yesmaximal, complemented
6C2×#91451C211yesmaximal, characteristic, complemented
7#11754507C2116yesmaximal, direct product factor
8C2×#91438C212yesmaximal, complemented
9C2×#91427C212yesmaximal, complemented
10C2×#91418C211yesmaximal, characteristic, complemented
11C2×Dic5×D12C211yesmaximal, characteristic, complemented
12C2×#91388C211yesmaximal, characteristic, complemented
13C2×#65953—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2212yes—
16C22×D60C2211yescharacteristic
17C22×C5×#67C2212yes—
18C22×C5×D12C2211yescharacteristic
19C22×#1203C2212yes—
20C22×#1203C2212yes—
21C22×#1200C2212yes—
22C22×D3×Dic5C2212yes—
23#91819C2218yescomplemented
24C2×#6714C2212yes—
25C2×C4⋊Dic15C2211yescharacteristic
26C5×#930C2218yescomplemented
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C3×#4072C2218yescomplemented
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36#91558C22116yescomplemented
37#91557C22116yescomplemented
38C2×Dic3⋊Dic5C2212yes—
39C2×#6669C2212yes—
40C2×#6667C2212yes—
41C2×(C2×D3)⋊Dic5C2212yes—
42#91451C2218yescomplemented
43#91438C22116yescomplemented
44#91427C22116yescomplemented
45#91418C2218yescomplemented
46Dic5×D12C2218yescomplemented
47#91388C2218yescomplemented
48C2×#5535—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4086—31no—
51C2×#4085—32no—
52C2×#4084—32no—
53C2×D4×Dic5—31no—
54C2×#4076—31no—
55C2×#4072D311yescharacteristic, complemented
56#65953—316no—
57C2×#4039—31no—
58C2×#4036—31no—
59C2×#4032—32no—
60C2×#4029—32no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2312yes—
63C23×C5×D3C2312yes—
64C22×C3×C4×C5—24no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2314yes—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—44no—
69C2×#1220C2318yes—
70C22×Dic15C2312yes—
71C2×D60—24no—
72C2×D60C2314yes—
73C2×C5×#67—44no—
74C2×C5×#67C2318yes—
75C22×C5×Dic3C2312yes—
76C2×C5×D12—24no—
77C2×C5×D12C2314yes—
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×#1203—44no—
83C2×#1203—44no—
84C2×#1203C2318yes—
85C2×#1203C2318yes—
86C2×#1200—44no—
87C2×#1200C2318yes—
88C2×D3×Dic5—44no—
89C2×D3×Dic5C2318yes—
90#6714C2318yes—
91C4⋊Dic15C2314yes—
92C5×(C2×D3)⋊C4C2318yes—
93C5×C4⋊Dic3C2314yes—
94C3×C22⋊Dic5C2314yes—
95C3×C22⋊Dic5C2314yes—
96C3×C4⋊Dic5C2314yes—
97C3×C4⋊Dic5C2314yes—
98C3×C4×Dic5C2314yes—
99C3×C4×Dic5C2314yes—
100Dic3⋊Dic5C2318yes—
101#6669C2318yes—
102#6667C2318yes—
103(C2×D3)⋊Dic5C2318yes—
104C2×C3×#117—51no—
105C2×#930—51no—
106C2×#930D511yescharacteristic, complemented
107#5535—516no—
108C2×#894—52no—
109C2×#894—52no—
110C2×#884—52no—
111C2×#884—52no—
112C2×#874—51no—
113C2×C4×D12—51no—
114C2×C4×D12—51no—
115C2×#870—51no—
116C22×C5×D4—32no—
117C22×C5×D4—31no—
118C23×C4×C5C2×D311yescharacteristic
119C22×C22⋊D5—32no—
120C22×C22⋊D5—32no—
121C22×C22⋊D5—32no—
122C23×Dic5—32no—
123C22×D20—31no—
124C22×C4×D5—32no—
125C5×#121—38no—
126C2×C5×C4⋊C4—31no—
127C2×C5×C22⋊C4—32no—
128C2×C22⋊Dic5—32no—
129C2×C22⋊Dic5C2×D311yescharacteristic
130C2×C22⋊Dic5C2×D311yescharacteristic
131#4086—38no—
132#4085—316no—
133#4084—316no—
134D4×Dic5—38no—
135#4076—38no—
136C2×#685—32no—
137C2×#685—32no—
138#4072C2×D318yescomplemented
139C2×C4⋊Dic5—31no—
140C2×C4⋊Dic5—32no—
141C2×C4⋊Dic5C2×D311yescharacteristic
142C2×C4⋊Dic5C2×D311yescharacteristic
143C2×#683—32no—
144C2×C4×Dic5C2×D311yescharacteristic
145C2×C4×Dic5C2×D311yescharacteristic
146#4039—38no—
147#4036—38no—
148#4032—316no—
149#4029—316no—
150C2×#540—151noSylow
151C23×C3×C5—22no—
152C23×C3×C5—22no—
153C23×C3×C5—22no—
154C23×C3×C5C2412yes—
155C23×C3×C5C2411yescharacteristic
156C22×D15—24no—
157C22×D15—24no—
158C22×D15—24no—
159C22×D15C2414yes—
160C22×C5×D3—24no—
161C22×C5×D3—24no—
162C22×C5×D3—24no—
163C22×C5×D3C2414yes—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—28no—
166C2×C3×C4×C5#4114yes—
167C2×C3×C4×C5C2412yes—
168C2×C3×C4×C5C2412yes—
169#1220—48no—
170C2×Dic15—24no—
171C2×Dic15C2414yes—
172D60—28no—
173C5×#67—48no—
174C2×C5×Dic3—24no—
175C2×C5×Dic3C2414yes—
176C5×D12—28no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5C2412yes—
182C2×C3×Dic5C2412yes—
183C2×C3×Dic5C2412yes—
184C2×C3×Dic5C2412yes—
185#1203—48no—
186#1203—48no—
187#1200—48no—
188D3×Dic5—48no—
189C23×C3×C4C2×D511yescharacteristic
190C22×#67—52no—
191C22×#67C2×D512yes—
192C22×D12—51no—
193C22×D12—52no—
194C22×D12—52no—
195C22×D12C2×D511yescharacteristic
196C22×C4×D3—52no—
197C22×C4×D3—52no—
198C3×#117—58no—
199C2×C3×C4⋊C4—51no—
200C2×C3×C4⋊C4—51no—
201C2×C3×C22⋊C4—51no—
202C2×C3×C22⋊C4—51no—
203C2×C3×C42—51no—
204C2×C3×C42—51no—
205#930—58no—
206#930C2×D518yescomplemented
207C2×(C2×D3)⋊C4—52no—
208C2×(C2×D3)⋊C4—52no—
209C2×(C2×D3)⋊C4—52no—
210C2×(C2×D3)⋊C4C2×D512yes—
211C2×C4⋊Dic3—51no—
212C2×C4⋊Dic3C2×D511yescharacteristic
213C2×Dic3⋊C4—52no—
214C2×Dic3⋊C4—52no—
215#894—516no—
216#894—516no—
217#884—516no—
218#884—516no—
219#874—58no—
220C4×D12—58no—
221C4×D12—58no—
222#870—58no—
223C24×C5—32no—
224C24×C5C22×D311yescharacteristic
225C23×D5—32no—
226C2×C5×D4—38no—
227C2×C5×D4—34no—
228C2×C5×D4—64no—
229C2×C5×D4—124no—
230C22×C4×C5—24no—
231C22×C4×C5—32no—
232C22×C4×C5C22×D311yescharacteristic
233C22×C4×C5C22×D314yes—
234C22×C4×C5C22×D311yescharacteristic
235C2×C22⋊D5—38no—
236C2×C22⋊D5—38no—
237C2×C22⋊D5—38no—
238C2×C22⋊D5—124no—
239C2×C22⋊D5—124no—
240C2×C22⋊D5—124no—
241C22×Dic5—32no—
242C22×Dic5—38no—
243C22×Dic5—124no—
244C22×Dic5C22×D311yescharacteristic
245C22×Dic5C22×D311yescharacteristic
246C22×Dic5C22×D311yescharacteristic
247C22×Dic5C22×D311yescharacteristic
248C2×D20—34no—
249C2×D20—64no—
250C2×C4×D5—38no—
251C2×C4×D5—124no—
252C5×C4⋊C4—34no—
253C5×C22⋊C4—38no—
254C22⋊Dic5—38no—
255C22⋊Dic5C22×D314yes—
256C22⋊Dic5C22×D314yes—
257#685—38no—
258#685—38no—
259C4⋊Dic5—34no—
260C4⋊Dic5—38no—
261C4⋊Dic5C22×D314yes—
262C4⋊Dic5C22×D314yes—
263#683—38no—
264C4×Dic5C22×D314yes—
265C4×Dic5C22×D314yes—
266#540—1516no—
267C2×#127—151no—
268C2×#125—151no—
269C2×#123—152no—
270C2×#123—152no—
271C2×#121—31no—
272C2×#121—152no—
273C2×#121—152no—
274C2×#121—151no—
275C2×C4×D4—151no—
276C2×C4×D4—151no—
277C2×#117—51no—
278C22×C3×C5—22no—
279C22×C3×C5—22no—
280C22×C3×C5—22no—
281C22×C3×C5—44no—
282C22×C3×C5C2×#4112yes—
283C22×C3×C5H(5,𝔽2)12yes—
284C22×C3×C5H(5,𝔽2)12yes—
285C22×C3×C5C2511yescharacteristic
286C2×D15—24no—
287C2×D15—24no—
288C2×D15—24no—
289C2×D15—48no—
290C2×C5×D3—24no—
291C2×C5×D3—24no—
292C2×C5×D3—24no—
293C2×C5×D3—48no—
294C3×C4×C5—22no—
295C3×C4×C5C2×#4114yes—
296Dic15—24no—
297C3×Dic5—22no—
298C3×Dic5—22no—
299C3×Dic5—22no—
300C3×Dic5—22no—
301C5×Dic3—24no—
302C24×C3C22×D511yescharacteristic
303C23×D3—52no—
304C23×D3C22×D512yes—
305C22×C3×C4—24no—
306C22×C3×C4—51no—
307C22×C3×C4—51no—
308C22×C3×C4—51no—
309C22×C3×C4—51no—
310C22×C3×C4C22×D511yescharacteristic
311C22×C3×C4C22×D514yes—
312C22×C3×C4C22×D511yescharacteristic
313C2×#67—44no—
314C2×#67—58no—
315C2×#67—204no—
316C2×#67C22×D518yes—
317C22×Dic3—52no—
318C22×Dic3C22×D512yes—
319C2×D12—24no—
320C2×D12—54no—
321C2×D12—58no—
322C2×D12—58no—
323C2×D12—104no—
324C2×D12—204no—
325C2×D12—204no—
326C2×D12C22×D514yes—
327C2×C4×D3—58no—
328C2×C4×D3—58no—
329C2×C4×D3—204no—
330C2×C4×D3—204no—
331C3×C4⋊C4—54no—
332C3×C4⋊C4—54no—
333C3×C22⋊C4—54no—
334C3×C22⋊C4—54no—
335C3×C42—54no—
336C3×C42—54no—
337(C2×D3)⋊C4—58no—
338(C2×D3)⋊C4—58no—
339(C2×D3)⋊C4—58no—
340(C2×D3)⋊C4C22×D518yes—
341C4⋊Dic3—54no—
342C4⋊Dic3C22×D514yes—
343Dic3⋊C4—58no—
344Dic3⋊C4—58no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—34no—
349C23×C5—64no—
350C23×C5—64no—
351C23×C5—64no—
352C23×C5C23×D312yes—
353C23×C5C23×D311yescharacteristic
354C22×D5—34no—
355C22×D5—64no—
356C22×D5—64no—
357C22×D5—64no—
358C5×D4—68no—
359C5×D4—128no—
360C2×C4×C5—22no—
361C2×C4×C5—28no—
362C2×C4×C5—34no—
363C2×C4×C5—64no—
364C2×C4×C5#23514yes—
365C2×C4×C5C23×D312yes—
366C2×C4×C5C23×D312yes—
367C22⋊D5—128no—
368C22⋊D5—128no—
369C22⋊D5—128no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—34no—
375C2×Dic5—64no—
376C2×Dic5—128no—
377C2×Dic5C23×D312yes—
378C2×Dic5C23×D312yes—
379C2×Dic5C23×D312yes—
380C2×Dic5C23×D312yes—
381D20—68no—
382C4×D5—128no—
383C22×D4—32no—
384C22×D4—31no—
385C22×D4—152no—
386C22×D4—152no—
387C22×D4—152no—
388C22×D4—151no—
389C23×C4—152no—
390C23×C4—152no—
391C23×C4D3×D511yescharacteristic
392#127—158no—
393#125—158no—
394#123—1516no—
395#123—1516no—
396#121—38no—
397#121—1516no—
398#121—1516no—
399#121—158no—
400C4×D4—158no—
401C4×D4—158no—
402#117—58no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—51no—
405C2×C4⋊C4—51no—
406C2×C4⋊C4—152no—
407C2×C4⋊C4—152no—
408C2×C4⋊C4—151no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—51no—
411C2×C22⋊C4—51no—
412C2×C22⋊C4—152no—
413C2×C22⋊C4—152no—
414C2×C22⋊C4—152no—
415C2×C42—51no—
416C2×C42—51no—
417C2×C3×C5—42no—
418C2×C3×C5#54014yescomplemented
419C2×C3×C5C22×#4111yescharacteristic
420C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
421C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
422D15—44no—
423C5×D3—44no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3C23×D512yes—
428C23×C3C23×D511yescharacteristic
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—54no—
433C22×D3—104no—
434C22×D3—104no—
435C22×D3—104no—
436C22×D3C23×D514yes—
437C2×C3×C4—22no—
438C2×C3×C4—28no—
439C2×C3×C4—52no—
440C2×C3×C4—52no—
441C2×C3×C4—52no—
442C2×C3×C4—52no—
443C2×C3×C4—102no—
444C2×C3×C4—102no—
445C2×C3×C4—102no—
446C2×C3×C4—102no—
447C2×C3×C4#71114yes—
448C2×C3×C4C23×D512yes—
449C2×C3×C4C23×D512yes—
450#67—48no—
451#67—208no—
452C2×Dic3—24no—
453C2×Dic3—54no—
454C2×Dic3—104no—
455C2×Dic3C23×D514yes—
456D12—28no—
457D12—108no—
458D12—208no—
459D12—208no—
460C4×D3—208no—
461C4×D3—208no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5—44no—
466C22×C5—64no—
467C22×C5—64no—
468C22×C5—64no—
469C22×C5—128no—
470C22×C5C2×#23512yes—
471C22×C5#100912yes—
472C22×C5#100912yes—
473C22×C5C24×D311yescharacteristic
474C2×D5—64no—
475C2×D5—64no—
476C2×D5—64no—
477C2×D5—128no—
478C4×C5—22no—
479C4×C5—64no—
480C4×C5C2×#23514yes—
481Dic5—22no—
482Dic5—22no—
483Dic5—22no—
484Dic5—22no—
485Dic5—64no—
486C24—32no—
487C24—152no—
488C24C2×D3×D511yescharacteristic
489C2×D4—38no—
490C2×D4—34no—
491C2×D4—64no—
492C2×D4—124no—
493C2×D4—158no—
494C2×D4—158no—
495C2×D4—158no—
496C2×D4—154no—
497C2×D4—304no—
498C2×D4—604no—
499C2×D4—604no—
500C2×D4—604no—
501C22×C4—24no—
502C22×C4—32no—
503C22×C4—51no—
504C22×C4—51no—
505C22×C4—51no—
506C22×C4—51no—
507C22×C4—158no—
508C22×C4—158no—
509C22×C4—152no—
510C22×C4—604no—
511C22×C4—604no—
512C22×C4C2×D3×D514yes—
513C22×C4C2×D3×D511yescharacteristic
514C22×C4C2×D3×D511yescharacteristic
515C4⋊C4—34no—
516C4⋊C4—54no—
517C4⋊C4—54no—
518C4⋊C4—158no—
519C4⋊C4—158no—
520C4⋊C4—154no—
521C22⋊C4—38no—
522C22⋊C4—54no—
523C22⋊C4—54no—
524C22⋊C4—158no—
525C22⋊C4—158no—
526C22⋊C4—158no—
527C42—54no—
528C42—54no—
529C3×C5C2×#54011yescharacteristic, complemented, Hall
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—44no—
534C22×C3C2×#71112yes—
535C22×C3#414412yes—
536C22×C3#414912yes—
537C22×C3C24×D511yescharacteristic
538C2×D3—24no—
539C2×D3—24no—
540C2×D3—24no—
541C2×D3—48no—
542C2×D3—104no—
543C2×D3—104no—
544C2×D3—104no—
545C2×D3—208no—
546C3×C4—22no—
547C3×C4—102no—
548C3×C4—102no—
549C3×C4—102no—
550C3×C4—102no—
551C3×C4C2×#71114yes—
552Dic3—24no—
553Dic3—104no—
554C2×C5—42no—
555C2×C5—124no—
556C2×C5#553514yescomplemented
557C2×C5C22×#23511yescharacteristic
558C2×C5C2×#100911yescharacteristic
559C2×C5C2×#100911yescharacteristic
560D5—124no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—34no—
565C23—64no—
566C23—64no—
567C23—64no—
568C23—154no—
569C23—304no—
570C23—304no—
571C23—304no—
572C23C22×D3×D512yes—
573C23C22×D3×D511yescharacteristic
574D4—68no—
575D4—128no—
576D4—308no—
577D4—608no—
578D4—608no—
579D4—608no—
580C2×C4—22no—
581C2×C4—28no—
582C2×C4—34no—
583C2×C4—52no—
584C2×C4—52no—
585C2×C4—52no—
586C2×C4—52no—
587C2×C4—64no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4—154no—
593C2×C4—304no—
594C2×C4—608no—
595C2×C4—608no—
596C2×C4#678214yes—
597C2×C4C22×D3×D512yes—
598C2×C4C22×D3×D512yes—
599C2×C3—42no—
600C2×C3#6595314yescomplemented
601C2×C3C22×#71111yescharacteristic
602C2×C3C2×#414411yescharacteristic
603C2×C3C2×#414911yescharacteristic
604D3—44no—
605D3—204no—
606C5C2×#553511yescharacteristic, complemented, Sylow
607C22—22no—
608C22—22no—
609C22—22no—
610C22—44no—
611C22—64no—
612C22—64no—
613C22—64no—
614C22—128no—
615C22—304no—
616C22—304no—
617C22—304no—
618C22—608no—
619C22#9201812yes—
620C22#9201912yes—
621C22C2×#678212yes—
622C22C23×D3×D511yescharacteristic
623C4—22no—
624C4—64no—
625C4—102no—
626C4—102no—
627C4—102no—
628C4—102no—
629C4—304no—
630C4C2×#678214yes—
631C3C2×#6595311yescharacteristic, complemented, Sylow
632C2—42no—
633C2—124no—
634C2—604no—
635C2#1175450714yesdirect product factor
636C2C2×#9201811yescharacteristic
637C2C2×#9201911yescharacteristic
638C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91819C2semidirect
2. C2×C5×#930C2semidirect
3. C2×C3×#4072C2semidirect
4. C2×#91558C2semidirect
5. C2×#91557C2semidirect
6. C2×#91451C2semidirect
7. #11754507C2direct (N × H)
8. C2×#91438C2semidirect
9. C2×#91427C2semidirect
10. C2×#91418C2semidirect
11. C2×Dic5×D12C2semidirect
12. C2×#91388C2semidirect
23. #91819C22semidirect
26. C5×#930C22semidirect
31. C3×#4072C22semidirect
36. #91558C22semidirect
37. #91557C22semidirect
42. #91451C22semidirect
43. #91438C22semidirect
44. #91427C22semidirect
45. #91418C22semidirect
46. Dic5×D12C22semidirect
47. #91388C22semidirect
55. C2×#4072D3semidirect
106. C2×#930D5semidirect
138. #4072C2×D3semidirect
206. #930C2×D5semidirect
418. C2×C3×C5#540semidirect
529. C3×C5C2×#540semidirect
556. C2×C5#5535semidirect
600. C2×C3#65953semidirect
606. C5C2×#5535semidirect
631. C3C2×#65953semidirect
635. C2#11754507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918192
C2×C5×#9302
C2×C3×#40722
C2×#915582
C2×#915572
C2×#914512
#117545072
C2×#914382
C2×#914272
C2×#914182
C2×Dic5×D122
C2×#913882
C2×#659533
C2×#55355