Finite Group Databasebeta

← C2×#11752713 #14481145

Subgroups — C2×#11752713 #14481145

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×C4×D60C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×#4018C211yesmaximal, characteristic, complemented
4C2×#91461C212yesmaximal, complemented
5C2×#91454C212yesmaximal, complemented
6C2×#91451C211yesmaximal, characteristic, complemented
7C2×#91450C211yesmaximal, characteristic, complemented
8C2×#91449C211yesmaximal, characteristic, complemented
9C2×#91388C211yesmaximal, characteristic, complemented
10C2×#91355C212yesmaximal, complemented
11C2×#91351C212yesmaximal, complemented
12#11752713C2116yesmaximal, direct product factor
13C2×#65896—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×D12C2211yescharacteristic
17C22×C4×C5×D3C2212yes—
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1203C2212yes—
20C22×#1203C2212yes—
21C22×#1202C2212yes—
22C22×#1201C2212yes—
23C2×C3×C42×C5C2211yescharacteristic
24C2×#6714C2212yes—
25C2×C4⋊Dic15C2211yescharacteristic
26C4×D60C2218yescomplemented
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C4×C5×D12C2218yescomplemented
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4018C2218yescomplemented
36C2×Dic3⋊Dic5C2212yes—
37C2×#6669C2212yes—
38C2×#6667C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40#91461C22116yescomplemented
41#91454C22116yescomplemented
42#91451C2218yescomplemented
43#91450C2218yescomplemented
44#91449C2218yescomplemented
45#91388C2218yescomplemented
46#91355C22116yescomplemented
47#91351C22116yescomplemented
48C2×#5535—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×#4036—31no—
57C2×#4030—32no—
58C2×#4029—32no—
59C2×C4×D20—31no—
60C2×#4018D311yescharacteristic, complemented
61C23×D15C2312yes—
62C23×C5×D3C2312yes—
63C23×C3×D5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C2×D60—24no—
69C2×D60C2314yes—
70C2×C4×D15—44no—
71C2×C4×D15C2318yes—
72C22×C5×Dic3C2312yes—
73C2×C5×D12—24no—
74C2×C5×D12C2314yes—
75C2×C4×C5×D3—44no—
76C2×C4×C5×D3C2318yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5C2314yes—
82C2×#1203—44no—
83C2×#1203—44no—
84C2×#1203C2318yes—
85C2×#1203C2318yes—
86C2×#1202—44no—
87C2×#1202C2318yes—
88C2×#1201—44no—
89C2×#1201C2318yes—
90C3×C42×C5C2314yes—
91#6714C2318yes—
92C4⋊Dic15C2314yes—
93C5×(C2×D3)⋊C4C2318yes—
94C5×C4⋊Dic3C2314yes—
95C3×#685C2314yes—
96C3×#685C2314yes—
97C3×#683C2314yes—
98C3×#683C2314yes—
99C3×C4×Dic5C2314yes—
100Dic3⋊Dic5C2318yes—
101#6669C2318yes—
102#6667C2318yes—
103(C2×D3)⋊Dic5C2318yes—
104C2×C3×#117—51no—
105C2×#930—51no—
106C2×#930—51no—
107#5535—516no—
108C2×#894—52no—
109C2×#894—52no—
110C2×#884—52no—
111C2×#884—52no—
112C2×#874—51no—
113C2×C4×D12—51no—
114C2×C4×D12D511yescharacteristic, complemented
115C2×#870—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—32no—
124C22×C4×D5C2×D311yescharacteristic
125C4×C5×D4—38no—
126C2×C5×C4⋊C4—31no—
127C2×C5×C22⋊C4—32no—
128C2×C42×C5C2×D311yescharacteristic
129C2×C22⋊Dic5—32no—
130#4086—38no—
131#4084—38no—
132#4076—316no—
133#4075—316no—
134C2×#685—32no—
135C2×#685—32no—
136C2×#685C2×D311yescharacteristic
137C2×#685C2×D311yescharacteristic
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—32no—
140C2×#683—32no—
141C2×#683C2×D311yescharacteristic
142C2×#683C2×D311yescharacteristic
143C2×C4×Dic5C2×D311yescharacteristic
144#4041—38no—
145#4036—38no—
146#4030—316no—
147#4029—316no—
148C4×D20—38no—
149#4018C2×D318yescomplemented
150C2×#540—151noSylow
151C23×C3×C5C2411yescharacteristic
152C22×D15—24no—
153C22×D15—24no—
154C22×D15—24no—
155C22×D15C2414yes—
156C22×C5×D3—24no—
157C22×C5×D3—24no—
158C22×C5×D3—24no—
159C22×C5×D3C2414yes—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5C2412yes—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5#4114yes—
167C2×C3×C4×C5C2412yes—
168C2×C3×C4×C5C2412yes—
169C2×C3×C4×C5C2412yes—
170C2×Dic15—24no—
171C2×Dic15C2414yes—
172D60—28no—
173C4×D15—48no—
174C2×C5×Dic3—24no—
175C2×C5×Dic3C2414yes—
176C5×D12—28no—
177C4×C5×D3—48no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5C2412yes—
182C2×C3×Dic5C2412yes—
183C2×C3×Dic5C2412yes—
184C3×C4×D5—28no—
185#1203—48no—
186#1203—48no—
187#1202—48no—
188#1201—48no—
189C23×C3×C4—51no—
190C22×#67—52no—
191C22×#67—52no—
192C22×D12—51no—
193C22×D12—52no—
194C22×D12—52no—
195C22×D12C2×D511yescharacteristic
196C22×C4×D3—52no—
197C22×C4×D3C2×D512yes—
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×C42C2×D511yescharacteristic
205#930—58no—
206#930—58no—
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×D12C2×D518yescomplemented
222#870—58no—
223C24×C5—32no—
224C23×D5—32no—
225C23×D5C22×D311yescharacteristic
226C2×C5×D4—34no—
227C2×C5×D4—64no—
228C22×C4×C5—32no—
229C22×C4×C5—38no—
230C22×C4×C5—124no—
231C22×C4×C5C22×D311yescharacteristic
232C22×C4×C5C22×D311yescharacteristic
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—32no—
241C22×Dic5C22×D311yescharacteristic
242C22×Dic5C22×D311yescharacteristic
243C22×Dic5C22×D311yescharacteristic
244C2×D20—34no—
245C2×D20—38no—
246C2×D20—64no—
247C2×D20—124no—
248C2×C4×D5—24no—
249C2×C4×D5—38no—
250C2×C4×D5—124no—
251C2×C4×D5C22×D314yes—
252C5×C4⋊C4—34no—
253C5×C22⋊C4—38no—
254C42×C5C22×D314yes—
255C22⋊Dic5—38no—
256#685—38no—
257#685—38no—
258#685C22×D314yes—
259#685C22×D314yes—
260C4⋊Dic5—34no—
261C4⋊Dic5—38no—
262#683—38no—
263#683C22×D314yes—
264#683C22×D314yes—
265C4×Dic5C22×D314yes—
266#540—1516no—
267C2×#127—151no—
268C2×#125—151no—
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—51no—
278C22×C3×C5C2×#4112yes—
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C5H(5,𝔽2)12yes—
281C22×C3×C5C2511yescharacteristic
282C2×D15—24no—
283C2×D15—24no—
284C2×D15—24no—
285C2×D15—48no—
286C2×C5×D3—24no—
287C2×C5×D3—24no—
288C2×C5×D3—24no—
289C2×C5×D3—48no—
290C2×C3×D5—22no—
291C2×C3×D5—22no—
292C2×C3×D5—22no—
293C2×C3×D5—44no—
294C3×C4×C5—22no—
295C3×C4×C5—22no—
296C3×C4×C5C2×#4114yes—
297Dic15—24no—
298C3×Dic5—22no—
299C3×Dic5—22no—
300C3×Dic5—22no—
301C5×Dic3—24no—
302C24×C3—51no—
303C23×D3—52no—
304C23×D3C22×D512yes—
305C22×C3×C4—51no—
306C22×C3×C4—51no—
307C22×C3×C4—51no—
308C22×C3×C4—54no—
309C22×C3×C4—104no—
310C22×C3×C4C22×D511yescharacteristic
311C22×C3×C4C22×D511yescharacteristic
312C22×C3×C4C22×D511yescharacteristic
313C2×#67—58no—
314C2×#67—58no—
315C2×#67—204no—
316C2×#67—204no—
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—44no—
328C2×C4×D3—58no—
329C2×C4×D3—204no—
330C2×C4×D3C22×D518yes—
331C3×C4⋊C4—54no—
332C3×C4⋊C4—54no—
333C3×C22⋊C4—54no—
334C3×C22⋊C4—54no—
335C3×C42—54no—
336C3×C42C22×D514yes—
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—34no—
346C23×C5—64no—
347C23×C5—64no—
348C23×C5—64no—
349C23×C5C23×D311yescharacteristic
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—34no—
354C22×D5—64no—
355C22×D5—64no—
356C22×D5—64no—
357C22×D5C23×D312yes—
358C5×D4—68no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—34no—
362C2×C4×C5—64no—
363C2×C4×C5—128no—
364C2×C4×C5#23514yes—
365C2×C4×C5C23×D312yes—
366C2×C4×C5C23×D312yes—
367C2×C4×C5C23×D312yes—
368C22⋊D5—128no—
369C22⋊D5—128no—
370C22⋊D5—128no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—34no—
375C2×Dic5—64no—
376C2×Dic5C23×D312yes—
377C2×Dic5C23×D312yes—
378C2×Dic5C23×D312yes—
379D20—68no—
380D20—128no—
381C4×D5—28no—
382C4×D5—128no—
383C22×D4—31no—
384C22×D4—152no—
385C22×D4—152no—
386C22×D4—152no—
387C22×D4—152no—
388C22×D4—151no—
389C23×C4—32no—
390C23×C4—51no—
391C23×C4—152no—
392#127—158no—
393#125—158no—
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—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×C42D3×D511yescharacteristic
417C2×C3×C5#54014yescomplemented
418C2×C3×C5C22×#4111yescharacteristic
419C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
420C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
421D15—44no—
422C3×D5—42no—
423C5×D3—44no—
424C23×C3—52no—
425C23×C3—102no—
426C23×C3—102no—
427C23×C3—102no—
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—22no—
439C2×C3×C4—52no—
440C2×C3×C4—52no—
441C2×C3×C4—52no—
442C2×C3×C4—102no—
443C2×C3×C4—102no—
444C2×C3×C4—102no—
445C2×C3×C4—108no—
446C2×C3×C4#70914yes—
447C2×C3×C4C23×D512yes—
448C2×C3×C4C23×D512yes—
449C2×C3×C4C23×D512yes—
450#67—208no—
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—48no—
461C4×D3—208no—
462C22×C5—64no—
463C22×C5—64no—
464C22×C5—64no—
465C22×C5—128no—
466C22×C5C2×#23512yes—
467C22×C5#100912yes—
468C22×C5#100912yes—
469C22×C5C24×D311yescharacteristic
470C2×D5—22no—
471C2×D5—22no—
472C2×D5—22no—
473C2×D5—44no—
474C2×D5—64no—
475C2×D5—64no—
476C2×D5—64no—
477C2×D5—128no—
478C4×C5—22no—
479C4×C5—22no—
480C4×C5—64no—
481C4×C5C2×#23514yes—
482Dic5—22no—
483Dic5—22no—
484Dic5—22no—
485Dic5—64no—
486C24—32no—
487C24—51no—
488C24—152no—
489C2×D4—34no—
490C2×D4—64no—
491C2×D4—158no—
492C2×D4—158no—
493C2×D4—158no—
494C2×D4—158no—
495C2×D4—154no—
496C2×D4—304no—
497C2×D4—604no—
498C2×D4—604no—
499C2×D4—604no—
500C2×D4—604no—
501C22×C4—32no—
502C22×C4—38no—
503C22×C4—51no—
504C22×C4—51no—
505C22×C4—51no—
506C22×C4—54no—
507C22×C4—104no—
508C22×C4—124no—
509C22×C4—152no—
510C22×C4—158no—
511C22×C4—604no—
512C22×C4C2×D3×D511yescharacteristic
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—
528C42C2×D3×D514yes—
529C3×C5C2×#54011yescharacteristic, complemented, Hall
530C22×C3—102no—
531C22×C3—102no—
532C22×C3—102no—
533C22×C3—204no—
534C22×C3C2×#70912yes—
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—22no—
548C3×C4—102no—
549C3×C4—102no—
550C3×C4—102no—
551C3×C4C2×#70914yes—
552Dic3—24no—
553Dic3—104no—
554C2×C5—124no—
555C2×C5#553514yescomplemented
556C2×C5C22×#23511yescharacteristic
557C2×C5C2×#100911yescharacteristic
558C2×C5C2×#100911yescharacteristic
559D5—42no—
560D5—124no—
561C23—34no—
562C23—52no—
563C23—64no—
564C23—64no—
565C23—64no—
566C23—102no—
567C23—102no—
568C23—102no—
569C23—154no—
570C23—304no—
571C23—304no—
572C23—304no—
573C23C22×D3×D511yescharacteristic
574D4—68no—
575D4—308no—
576D4—608no—
577D4—608no—
578D4—608no—
579D4—608no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—34no—
583C2×C4—52no—
584C2×C4—52no—
585C2×C4—52no—
586C2×C4—64no—
587C2×C4—102no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—108no—
591C2×C4—128no—
592C2×C4—154no—
593C2×C4—304no—
594C2×C4—608no—
595C2×C4#677114yes—
596C2×C4C22×D3×D512yes—
597C2×C4C22×D3×D512yes—
598C2×C4C22×D3×D512yes—
599C2×C3—202no—
600C2×C3#6589614yescomplemented
601C2×C3C22×#70911yescharacteristic
602C2×C3C2×#414411yescharacteristic
603C2×C3C2×#414911yescharacteristic
604D3—44no—
605D3—204no—
606C5C2×#553511yescharacteristic, complemented, Sylow
607C22—64no—
608C22—64no—
609C22—64no—
610C22—102no—
611C22—102no—
612C22—102no—
613C22—128no—
614C22—204no—
615C22—304no—
616C22—304no—
617C22—304no—
618C22—608no—
619C22C2×#677112yes—
620C22#9201812yes—
621C22#9201912yes—
622C22C23×D3×D511yescharacteristic
623C4—22no—
624C4—22no—
625C4—64no—
626C4—102no—
627C4—102no—
628C4—102no—
629C4—304no—
630C4C2×#677114yes—
631C3C2×#6589611yescharacteristic, complemented, Sylow
632C2—124no—
633C2—202no—
634C2—604no—
635C2#1175271314yesdirect product factor
636C2C22×#677111yescharacteristic
637C2C2×#9201811yescharacteristic
638C2C2×#9201911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×D60C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×#4018C2semidirect
4. C2×#91461C2semidirect
5. C2×#91454C2semidirect
6. C2×#91451C2semidirect
7. C2×#91450C2semidirect
8. C2×#91449C2semidirect
9. C2×#91388C2semidirect
10. C2×#91355C2semidirect
11. C2×#91351C2semidirect
12. #11752713C2direct (N × H)
26. C4×D60C22semidirect
29. C4×C5×D12C22semidirect
35. C3×#4018C22semidirect
40. #91461C22semidirect
41. #91454C22semidirect
42. #91451C22semidirect
43. #91450C22semidirect
44. #91449C22semidirect
45. #91388C22semidirect
46. #91355C22semidirect
47. #91351C22semidirect
60. C2×#4018D3semidirect
114. C2×C4×D12D5semidirect
149. #4018C2×D3semidirect
221. C4×D12C2×D5semidirect
417. C2×C3×C5#540semidirect
529. C3×C5C2×#540semidirect
555. C2×C5#5535semidirect
600. C2×C3#65896semidirect
606. C5C2×#5535semidirect
631. C3C2×#65896semidirect
635. C2#11752713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D602
C2×C4×C5×D122
C2×C3×#40182
C2×#914612
C2×#914542
C2×#914512
C2×#914502
C2×#914492
C2×#913882
C2×#913552
C2×#913512
#117527132
C2×#658963
C2×#55355