Finite Group Databasebeta

← C2×#11754751 #14481139

Subgroups — C2×#11754751 #14481139

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×#91829C211yesmaximal, characteristic, complemented
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic, complemented
4C2×#91569C212yesmaximal, complemented
5C2×#91562C212yesmaximal, complemented
6C2×#91542C212yesmaximal, complemented
7C2×#91533C212yesmaximal, complemented
8#11754751C2116yesmaximal, direct product factor
9C2×#91450C211yesmaximal, characteristic, complemented
10C2×#91428C211yesmaximal, characteristic, complemented
11C2×#91384C211yesmaximal, characteristic, complemented
12C2×#91357C211yesmaximal, characteristic, complemented
13C2×#65896—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C22×#1220C2212yes—
17C22×D60C2211yescharacteristic
18C23×C5×Dic3C2212yes—
19C22×C3×C22⋊D5C2212yes—
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1202C2212yes—
22C22×#1200C2212yes—
23#91829C2218yescomplemented
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×#217C2212yes—
26C5×D4×Dic3C2218yescomplemented
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×C22⋊Dic5C2212yes—
30C3×#4084C2218yescomplemented
31C2×C3×C4⋊Dic5C2211yescharacteristic
32#91569C22116yescomplemented
33#91562C22116yescomplemented
34C2×Dic3⋊Dic5C2212yes—
35#91542C22116yescomplemented
36C2×#6668C2212yes—
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6667C2212yes—
40C2×#6667C2212yes—
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43#91533C22116yescomplemented
44#91450C2218yescomplemented
45#91428C2218yescomplemented
46#91384C2218yescomplemented
47#91357C2218yescomplemented
48C2×#5619—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4086—31no—
51C2×#4084D311yescharacteristic, complemented
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×#4018—31no—
61C24×C3×C5C2312yes—
62C23×D15C2312yes—
63C23×C3×D5C2311yescharacteristic
64C2×C3×C5×D4—24no—
65C2×C3×C5×D4C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—44no—
68C2×#1220—44no—
69C2×#1220C2318yes—
70C2×#1220C2318yes—
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C2×D60—24no—
74C2×D60C2314yes—
75C22×C5×Dic3—44no—
76C22×C5×Dic3C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2312yes—
79C22×C5×Dic3C2318yes—
80C2×C3×C22⋊D5—44no—
81C2×C3×C22⋊D5C2318yes—
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2312yes—
84C2×C3×C4×D5—24no—
85C2×C3×C4×D5C2314yes—
86C2×#1202—44no—
87C2×#1202C2318yes—
88C2×#1200—44no—
89C2×#1200C2318yes—
90C4×Dic15C2314yes—
91C5×#217C2318yes—
92C5×C4⋊Dic3C2314yes—
93C4×C5×Dic3C2314yes—
94C3×C22⋊Dic5C2318yes—
95C3×C4⋊Dic5C2314yes—
96Dic3⋊Dic5C2318yes—
97#6668C2318yes—
98#6668C2314yes—
99#6668C2314yes—
100#6667C2318yes—
101#6667C2318yes—
102#6665C2314yes—
103#6665C2314yes—
104C2×C3×#121—51no—
105C2×#940—51no—
106C2×#939—52no—
107C2×#938—52no—
108C2×D4×Dic3D511yescharacteristic, complemented
109C2×#930—51no—
110C2×#926—51no—
111#5619—516no—
112C2×#893—51no—
113C2×#890—51no—
114C2×#886—52no—
115C2×#883—52no—
116C22×C5×D4C2×D311yescharacteristic
117C23×C4×C5—32no—
118C22×C22⋊D5—32no—
119C22×C22⋊D5—32no—
120C22×C22⋊D5C2×D312yes—
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×C5—31no—
129C2×C22⋊Dic5C2×D312yes—
130#4086—38no—
131#4084C2×D318yescomplemented
132#4076—316no—
133#4075—316no—
134C2×#685—31no—
135C2×#685—31no—
136C2×#685—32no—
137C2×#685—32no—
138C2×C4⋊Dic5—32no—
139C2×C4⋊Dic5C2×D311yescharacteristic
140C2×#683—31no—
141C2×#683—31no—
142C2×#683—32no—
143C2×C4×Dic5—31no—
144#4041—38no—
145#4036—38no—
146#4030—316no—
147#4029—316no—
148C4×D20—38no—
149#4018—38no—
150C2×#540—151noSylow
151C23×C3×C5—24no—
152C23×C3×C5—24no—
153C23×C3×C5—24no—
154C23×C3×C5C2414yes—
155C23×C3×C5C2411yescharacteristic
156C22×D15—24no—
157C22×D15—24no—
158C22×D15—24no—
159C22×D15C2414yes—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5C2412yes—
164C3×C5×D4—28no—
165C2×C3×C4×C5#4114yes—
166C2×C3×C4×C5C2412yes—
167#1220—48no—
168#1220—48no—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15C2412yes—
172C2×Dic15C2412yes—
173D60—28no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3—24no—
176C2×C5×Dic3—22no—
177C2×C5×Dic3—48no—
178C2×C5×Dic3C2412yes—
179C2×C5×Dic3C2412yes—
180C2×C5×Dic3C2414yes—
181C3×C22⋊D5—48no—
182C2×C3×Dic5—22no—
183C2×C3×Dic5—24no—
184C2×C3×Dic5C2412yes—
185C2×C3×Dic5C2414yes—
186C3×C4×D5—28no—
187#1202—48no—
188#1200—48no—
189C22×C3×D4—52no—
190C22×C3×D4C2×D511yescharacteristic
191C23×C3×C4—51no—
192C22×#67—52no—
193C22×#67—52no—
194C22×#67—52no—
195C23×Dic3C2×D512yes—
196C22×D12—51no—
197C22×C4×D3—52no—
198C3×#121—58no—
199C2×C3×C4⋊C4—51no—
200C2×C3×C22⋊C4—52no—
201C2×#217—51no—
202C2×#217—51no—
203C2×#217C2×D512yes—
204#940—58no—
205#939—516no—
206#938—516no—
207D4×Dic3C2×D518yescomplemented
208#930—58no—
209C2×(C2×D3)⋊C4—52no—
210C2×(C2×D3)⋊C4—52no—
211#926—58no—
212C2×C4⋊Dic3—51no—
213C2×C4⋊Dic3—51no—
214C2×C4⋊Dic3—52no—
215C2×C4⋊Dic3C2×D511yescharacteristic
216C2×Dic3⋊C4—52no—
217C2×C4×Dic3—51no—
218C2×C4×Dic3C2×D511yescharacteristic
219#893—58no—
220#890—58no—
221#886—516no—
222#883—516no—
223C24×C5C22×D312yes—
224C23×D5—32no—
225C23×D5C22×D311yescharacteristic
226C2×C5×D4—24no—
227C2×C5×D4C22×D314yes—
228C22×C4×C5—31no—
229C22×C4×C5—31no—
230C22×C4×C5—32no—
231C22×C4×C5—38no—
232C22×C4×C5—124no—
233C22×C4×C5C22×D311yescharacteristic
234C2×C22⋊D5—38no—
235C2×C22⋊D5—38no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—124no—
238C2×C22⋊D5—124no—
239C2×C22⋊D5C22×D318yes—
240C22×Dic5—31no—
241C22×Dic5—31no—
242C22×Dic5C22×D311yescharacteristic
243C22×Dic5C22×D312yes—
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×C5—34no—
255C22⋊Dic5C22×D318yes—
256#685—34no—
257#685—34no—
258#685—38no—
259#685—38no—
260C4⋊Dic5—38no—
261C4⋊Dic5C22×D314yes—
262#683—34no—
263#683—34no—
264#683—38no—
265C4×Dic5—34no—
266#540—1516no—
267C2×#127—151no—
268C2×#125—151no—
269C2×#123—152no—
270C2×#123—152no—
271C2×#121—51no—
272C2×#121—152no—
273C2×#121—151no—
274C2×#121—152no—
275C2×C4×D4—31no—
276C2×C4×D4—151no—
277C2×#117—151no—
278C22×C3×C5—24no—
279C22×C3×C5—24no—
280C22×C3×C5—24no—
281C22×C3×C5—48no—
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×C3×D5—22no—
291C2×C3×D5—22no—
292C2×C3×D5—22no—
293C2×C3×D5—44no—
294C3×C4×C5C2×#4114yes—
295Dic15—22no—
296Dic15—22no—
297C3×Dic5—22no—
298C3×Dic5—24no—
299C5×Dic3—22no—
300C5×Dic3—24no—
301C5×Dic3—22no—
302C24×C3—51no—
303C24×C3C22×D512yes—
304C23×D3—52no—
305C2×C3×D4—24no—
306C2×C3×D4—58no—
307C2×C3×D4—204no—
308C2×C3×D4C22×D514yes—
309C22×C3×C4—52no—
310C22×C3×C4—51no—
311C22×C3×C4—54no—
312C22×C3×C4—104no—
313C22×C3×C4C22×D511yescharacteristic
314C2×#67—58no—
315C2×#67—58no—
316C2×#67—58no—
317C2×#67—204no—
318C2×#67—204no—
319C2×#67—204no—
320C22×Dic3—44no—
321C22×Dic3—51no—
322C22×Dic3—51no—
323C22×Dic3C22×D511yescharacteristic
324C22×Dic3C22×D511yescharacteristic
325C22×Dic3C22×D512yes—
326C22×Dic3C22×D518yes—
327C2×D12—54no—
328C2×D12—104no—
329C2×C4×D3—58no—
330C2×C4×D3—204no—
331C3×C4⋊C4—54no—
332C3×C22⋊C4—58no—
333#217—54no—
334#217—54no—
335#217C22×D518yes—
336(C2×D3)⋊C4—58no—
337(C2×D3)⋊C4—58no—
338C4⋊Dic3—54no—
339C4⋊Dic3—54no—
340C4⋊Dic3—58no—
341C4⋊Dic3C22×D514yes—
342Dic3⋊C4—58no—
343C4×Dic3—54no—
344C4×Dic3C22×D514yes—
345C23×C5—24no—
346C23×C5—24no—
347C23×C5—24no—
348C23×C5C23×D314yes—
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—28no—
359C2×C4×C5—34no—
360C2×C4×C5—32no—
361C2×C4×C5—32no—
362C2×C4×C5—62no—
363C2×C4×C5—64no—
364C2×C4×C5—62no—
365C2×C4×C5—128no—
366C2×C4×C5#23714yes—
367C2×C4×C5C23×D312yes—
368C22⋊D5—48no—
369C22⋊D5—128no—
370C22⋊D5—128no—
371C2×Dic5—22no—
372C2×Dic5—24no—
373C2×Dic5—32no—
374C2×Dic5—32no—
375C2×Dic5—62no—
376C2×Dic5—62no—
377C2×Dic5C23×D312yes—
378C2×Dic5C23×D314yes—
379D20—68no—
380D20—128no—
381C4×D5—28no—
382C4×D5—128no—
383C22×D4—52no—
384C22×D4—152no—
385C22×D4—152no—
386C22×D4—152no—
387C22×D4—151no—
388C22×D4D3×D511yescharacteristic
389C23×C4—32no—
390C23×C4—51no—
391C23×C4—152no—
392#127—158no—
393#125—158no—
394#123—1516no—
395#123—1516no—
396#121—58no—
397#121—1516no—
398#121—158no—
399#121—1516no—
400C4×D4—38no—
401C4×D4—158no—
402#117—158no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—51no—
405C2×C4⋊C4—151no—
406C2×C4⋊C4—151no—
407C2×C4⋊C4—152no—
408C2×C4⋊C4—152no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—52no—
411C2×C22⋊C4—152no—
412C2×C22⋊C4—152no—
413C2×C22⋊C4—151no—
414C2×C22⋊C4—151no—
415C2×C42—31no—
416C2×C42—151no—
417C2×C3×C5—44no—
418C2×C3×C5#54014yescomplemented
419C2×C3×C5C22×#4111yescharacteristic
420C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
421C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
422D15—44no—
423C3×D5—42no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—52no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3C23×D514yes—
432C23×C3C23×D511yescharacteristic
433C22×D3—54no—
434C22×D3—104no—
435C22×D3—104no—
436C22×D3—104no—
437C3×D4—28no—
438C3×D4—208no—
439C2×C3×C4—54no—
440C2×C3×C4—52no—
441C2×C3×C4—102no—
442C2×C3×C4—104no—
443C2×C3×C4—108no—
444C2×C3×C4#70914yes—
445C2×C3×C4C23×D512yes—
446#67—208no—
447#67—208no—
448#67—208no—
449C2×Dic3—22no—
450C2×Dic3—24no—
451C2×Dic3—22no—
452C2×Dic3—48no—
453C2×Dic3—52no—
454C2×Dic3—52no—
455C2×Dic3—102no—
456C2×Dic3—102no—
457C2×Dic3C23×D512yes—
458C2×Dic3C23×D512yes—
459C2×Dic3C23×D514yes—
460D12—108no—
461C4×D3—208no—
462C22×C5—24no—
463C22×C5—24no—
464C22×C5—24no—
465C22×C5—48no—
466C22×C5C2×#23712yes—
467C22×C5#100412yes—
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—62no—
479C4×C5—64no—
480C4×C5—62no—
481C4×C5C2×#23714yes—
482Dic5—22no—
483Dic5—24no—
484Dic5—62no—
485Dic5—62no—
486C24—51no—
487C24—152no—
488C24C2×D3×D512yes—
489C2×D4—24no—
490C2×D4—58no—
491C2×D4—158no—
492C2×D4—158no—
493C2×D4—158no—
494C2×D4—154no—
495C2×D4—204no—
496C2×D4—304no—
497C2×D4—604no—
498C2×D4—604no—
499C2×D4—604no—
500C2×D4C2×D3×D514yes—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—32no—
504C22×C4—38no—
505C22×C4—51no—
506C22×C4—52no—
507C22×C4—54no—
508C22×C4—104no—
509C22×C4—124no—
510C22×C4—158no—
511C22×C4—151no—
512C22×C4—151no—
513C22×C4—604no—
514C22×C4C2×D3×D511yescharacteristic
515C4⋊C4—34no—
516C4⋊C4—54no—
517C4⋊C4—154no—
518C4⋊C4—154no—
519C4⋊C4—158no—
520C4⋊C4—158no—
521C22⋊C4—38no—
522C22⋊C4—58no—
523C22⋊C4—158no—
524C22⋊C4—158no—
525C22⋊C4—154no—
526C22⋊C4—154no—
527C42—34no—
528C42—154no—
529C3×C5C2×#54011yescharacteristic, complemented, Hall
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—48no—
534C22×C3—102no—
535C22×C3—102no—
536C22×C3—102no—
537C22×C3—204no—
538C22×C3C2×#70912yes—
539C22×C3#414412yes—
540C22×C3#414912yes—
541C22×C3C24×D511yescharacteristic
542C2×D3—104no—
543C2×D3—104no—
544C2×D3—104no—
545C2×D3—208no—
546C3×C4—102no—
547C3×C4—104no—
548C3×C4C2×#70914yes—
549Dic3—22no—
550Dic3—24no—
551Dic3—22no—
552Dic3—102no—
553Dic3—102no—
554C2×C5—44no—
555C2×C5#561914yescomplemented
556C2×C5C22×#23711yescharacteristic
557C2×C5C2×#100411yescharacteristic
558C2×C5C2×#100911yescharacteristic
559D5—42no—
560D5—124no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—52no—
565C23—102no—
566C23—102no—
567C23—102no—
568C23—154no—
569C23—304no—
570C23—304no—
571C23—304no—
572C23C22×D3×D514yes—
573C23C22×D3×D511yescharacteristic
574D4—28no—
575D4—208no—
576D4—308no—
577D4—608no—
578D4—608no—
579D4—608no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—34no—
583C2×C4—52no—
584C2×C4—54no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—64no—
588C2×C4—104no—
589C2×C4—102no—
590C2×C4—108no—
591C2×C4—128no—
592C2×C4—152no—
593C2×C4—152no—
594C2×C4—302no—
595C2×C4—302no—
596C2×C4—608no—
597C2×C4#677914yes—
598C2×C4C22×D3×D512yes—
599C2×C3—44no—
600C2×C3—202no—
601C2×C3#6589614yescomplemented
602C2×C3C22×#70911yescharacteristic
603C2×C3C2×#414411yescharacteristic
604C2×C3C2×#414911yescharacteristic
605D3—204no—
606C5C2×#561911yescharacteristic, complemented, Sylow
607C22—24no—
608C22—24no—
609C22—24no—
610C22—48no—
611C22—102no—
612C22—102no—
613C22—102no—
614C22—204no—
615C22—304no—
616C22—304no—
617C22—304no—
618C22—608no—
619C22#9202612yes—
620C22#9202712yes—
621C22C2×#677912yes—
622C22C23×D3×D511yescharacteristic
623C4—62no—
624C4—62no—
625C4—64no—
626C4—102no—
627C4—104no—
628C4—302no—
629C4—302no—
630C4C2×#677914yes—
631C3C2×#6589611yescharacteristic, complemented, Sylow
632C2—44no—
633C2—202no—
634C2—604no—
635C2#1175475114yesdirect product factor
636C2C2×#9202611yescharacteristic
637C2C2×#9202711yescharacteristic
638C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91829C2semidirect
2. C2×C5×D4×Dic3C2semidirect
3. C2×C3×#4084C2semidirect
4. C2×#91569C2semidirect
5. C2×#91562C2semidirect
6. C2×#91542C2semidirect
7. C2×#91533C2semidirect
8. #11754751C2direct (N × H)
9. C2×#91450C2semidirect
10. C2×#91428C2semidirect
11. C2×#91384C2semidirect
12. C2×#91357C2semidirect
23. #91829C22semidirect
26. C5×D4×Dic3C22semidirect
30. C3×#4084C22semidirect
32. #91569C22semidirect
33. #91562C22semidirect
35. #91542C22semidirect
43. #91533C22semidirect
44. #91450C22semidirect
45. #91428C22semidirect
46. #91384C22semidirect
47. #91357C22semidirect
51. C2×#4084D3semidirect
108. C2×D4×Dic3D5semidirect
131. #4084C2×D3semidirect
207. D4×Dic3C2×D5semidirect
418. C2×C3×C5#540semidirect
529. C3×C5C2×#540semidirect
555. C2×C5#5619semidirect
601. C2×C3#65896semidirect
606. C5C2×#5619semidirect
631. C3C2×#65896semidirect
635. C2#11754751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C5×D4×Dic32
C2×C3×#40842
C2×#915692
C2×#915622
C2×#915422
C2×#915332
#117547512
C2×#914502
C2×#914282
C2×#913842
C2×#913572
C2×#658963
C2×#56195