Finite Group Databasebeta

← C2×#11754888 #14484746

Subgroups — C2×#11754888 #14484746

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#940C211yesmaximal, characteristic
3C2×C3×#4082C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic5C212yesmaximal, complemented
5C2×#91555C212yesmaximal, complemented
6C2×#91543C212yesmaximal, complemented
7C2×#91525C212yesmaximal, complemented
8#11754888C2116yesmaximal, direct product factor
9C2×C4×#1204C211yesmaximal, characteristic, complemented
10C2×Dic5×D12C211yesmaximal, characteristic, complemented
11C2×#91370C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
13C2×#66047—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C23×Dic15C2212yes—
16C22×C5×#67C2212yes—
17C22×C5×#67C2212yes—
18C22×C5×D12C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×D3×Dic5C2212yes—
22C2×#6719C2212yes—
23D4×Dic15C2218yescomplemented
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C5×#940C2218yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C22⋊Dic5C2212yes—
30C3×#4082C2218yescomplemented
31C2×C3×C4×Dic5C2211yescharacteristic
32#67⋊Dic5C22116yescomplemented
33#91555C22116yescomplemented
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36#91543C22116yescomplemented
37C2×#6668C2211yescharacteristic
38C2×#6668C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40C2×(C2×D3)⋊Dic5C2212yes—
41C2×(C2×D3)⋊Dic5C2212yes—
42C2×Dic3×Dic5C2212yes—
43#91525C22116yescomplemented
44C4×#1204C2218yescomplemented
45Dic5×D12C2218yescomplemented
46#91370C2218yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5681—51nomaximal, Hall
49C2×C5×#127—31no—
50C2×#4082—31no—
51C2×#4082—32no—
52C2×#4082D311yescharacteristic, complemented
53C2×#4081—32no—
54C2×#4081—32no—
55C2×D4×Dic5—31no—
56C2×D4×Dic5—31no—
57C2×D4×Dic5—32no—
58#66047—316no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C23×C5×D3C2312yes—
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15—44no—
67C22×Dic15C2312yes—
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2318yes—
71C2×C5×#67—28no—
72C2×C5×#67—44no—
73C2×C5×#67C2318yes—
74C2×C5×#67C2318yes—
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2311yescharacteristic
77C2×C5×D12—24no—
78C2×C5×D12C2314yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×C3×Dic10—24no—
83C2×C3×Dic10C2314yes—
84C2×#1204—24no—
85C2×#1204C2314yes—
86C2×D3×Dic5—44no—
87C2×D3×Dic5C2318yes—
88#6719C2318yes—
89C4⋊Dic15C2314yes—
90C4×Dic15C2314yes—
91C4×C5×Dic3C2314yes—
92C3×C22⋊Dic5C2318yes—
93C3×C22⋊Dic5C2318yes—
94C3×C4×Dic5C2314yes—
95Dic3⋊Dic5C2314yes—
96#6669C2314yes—
97#6668C2314yes—
98#6668C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×#124—51no—
104C2×#947—51no—
105C2×Q8×Dic3—51no—
106C2×#940D511yescharacteristic
107C2×D4×Dic3—51no—
108#5681—516no—
109C2×#886—52no—
110C2×#885—52no—
111C2×#883—52no—
112C2×#67⋊C4—52no—
113C2×C4×D12—51no—
114C2×C4×Dic6—51no—
115C22×C5×D4—32no—
116C22×C5×D4—32no—
117C22×C5×D4—31no—
118C22×C5×D4C2×D311yescharacteristic
119C23×Dic5—32no—
120C23×Dic5—32no—
121C22×Dic10—31no—
122C22×Dic10C2×D311yescharacteristic
123C5×#127—38no—
124C2×C42×C5—31no—
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5—32no—
129C2×C22⋊Dic5C2×D312yes—
130C2×C22⋊Dic5C2×D312yes—
131#4082—38no—
132#4082—316no—
133#4082C2×D318yescomplemented
134#4081—316no—
135#4081—316no—
136D4×Dic5—38no—
137D4×Dic5—316no—
138D4×Dic5—38no—
139C2×C4⋊Dic5—31no—
140C2×C4⋊Dic5—31no—
141C2×#683—31no—
142C2×#683—32no—
143C2×#683—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5—32no—
146C2×C4×Dic5C2×D311yescharacteristic
147C4×Dic10—38no—
148C4×Dic10—38no—
149C2×#559—151noSylow
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5—24no—
153C23×C3×C5C2414yes—
154C23×C3×C5C2411yescharacteristic
155C22×C5×D3—24no—
156C22×C5×D3—24no—
157C22×C5×D3—24no—
158C22×C5×D3C2414yes—
159C3×C5×D4—28no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15—22no—
165C2×Dic15—48no—
166C2×Dic15C2414yes—
167C2×Dic15C2412yes—
168C2×Dic15C2412yes—
169C5×#67—216no—
170C5×#67—48no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3#4114yes—
173C2×C5×Dic3C2412yes—
174C2×C5×Dic3C2412yes—
175C5×D12—28no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—24no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2412yes—
181C2×C3×Dic5C2412yes—
182C3×Dic10—28no—
183#1204—28no—
184D3×Dic5—48no—
185C22×C3×Q8—51no—
186C22×C3×D4C2×D511yescharacteristic
187C22×#67C2×D512yes—
188C22×#67C2×D512yes—
189C23×Dic3—52no—
190C22×D12C2×D511yescharacteristic
191C22×C4×D3—52no—
192C22×Dic6—51no—
193C3×#124—58no—
194C2×C3×C22⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C42—51no—
197C2×#217—52no—
198#947—58no—
199Q8×Dic3—58no—
200#940C2×D518yes—
201D4×Dic3—58no—
202C2×(C2×D3)⋊C4—52no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×C4⋊Dic3—51no—
206C2×C4⋊Dic3—51no—
207C2×C4⋊Dic3—52no—
208C2×Dic3⋊C4—51no—
209C2×Dic3⋊C4—51no—
210C2×C4×Dic3—51no—
211C2×C4×Dic3—52no—
212C2×C4×Dic3C2×D511yescharacteristic
213#886—516no—
214#885—516no—
215#883—516no—
216#67⋊C4—516no—
217C4×D12—58no—
218C4×Dic6—58no—
219C24×C5—32no—
220C24×C5C22×D312yes—
221C2×C5×D4—24no—
222C2×C5×D4—38no—
223C2×C5×D4—38no—
224C2×C5×D4—34no—
225C2×C5×D4—68no—
226C2×C5×D4—64no—
227C2×C5×D4—124no—
228C2×C5×D4C22×D314yes—
229C22×C4×C5—31no—
230C22×C4×C5—31no—
231C22×C4×C5C22×D311yescharacteristic
232C22×Dic5—31no—
233C22×Dic5—32no—
234C22×Dic5—31no—
235C22×Dic5—38no—
236C22×Dic5—38no—
237C22×Dic5—124no—
238C22×Dic5—124no—
239C22×Dic5C22×D311yescharacteristic
240C22×Dic5C22×D312yes—
241C22×Dic5C22×D311yescharacteristic
242C2×Dic10—24no—
243C2×Dic10—34no—
244C2×Dic10—64no—
245C2×Dic10C22×D314yes—
246C42×C5—34no—
247C22⋊Dic5—38no—
248C22⋊Dic5—38no—
249C22⋊Dic5—38no—
250C22⋊Dic5—38no—
251C22⋊Dic5C22×D318yes—
252C22⋊Dic5C22×D318yes—
253C4⋊Dic5—34no—
254C4⋊Dic5—34no—
255#683—38no—
256#683—34no—
257#683—34no—
258C4×Dic5—34no—
259C4×Dic5—38no—
260C4×Dic5C22×D314yes—
261#559—1516no—
262C2×#127—31no—
263C2×#124—51no—
264C2×#124—152no—
265C2×#124—151no—
266C2×#123—152no—
267C2×#123—152no—
268C2×C4×Q8—151no—
269C2×C4×Q8—151no—
270C2×C4×D4—151no—
271C2×C4×D4—152no—
272C2×C4×D4—151no—
273C22×C3×C5—24no—
274C22×C3×C5—24no—
275C22×C3×C5—24no—
276C22×C3×C5—48no—
277C22×C3×C5C2×#4112yes—
278C22×C3×C5C2×#4112yes—
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C5C2511yescharacteristic
281C2×C5×D3—24no—
282C2×C5×D3—24no—
283C2×C5×D3—24no—
284C2×C5×D3—48no—
285C3×C4×C5C2×#4114yes—
286Dic15—22no—
287Dic15—24no—
288Dic15—22no—
289C3×Dic5—22no—
290C3×Dic5—24no—
291C3×Dic5—22no—
292C5×Dic3—22no—
293C5×Dic3C2×#4114yes—
294C24×C3C22×D512yes—
295C23×D3C22×D512yes—
296C2×C3×Q8—54no—
297C2×C3×Q8—104no—
298C2×C3×D4—24no—
299C2×C3×D4C22×D514yes—
300C22×C3×C4—52no—
301C22×C3×C4—51no—
302C22×C3×C4—51no—
303C22×C3×C4C22×D511yescharacteristic
304C2×#67—28no—
305C2×#67—44no—
306C2×#67C22×D518yes—
307C2×#67C22×D518yes—
308C22×Dic3—51no—
309C22×Dic3—51no—
310C22×Dic3—52no—
311C22×Dic3—58no—
312C22×Dic3—204no—
313C22×Dic3C22×D511yescharacteristic
314C22×Dic3C22×D511yescharacteristic
315C2×D12—24no—
316C2×D12C22×D514yes—
317C2×C4×D3—58no—
318C2×C4×D3—204no—
319C2×Dic6—54no—
320C2×Dic6—104no—
321C3×C22⋊C4—58no—
322C3×C22⋊C4—58no—
323C3×C42—54no—
324#217—58no—
325(C2×D3)⋊C4—58no—
326(C2×D3)⋊C4—58no—
327(C2×D3)⋊C4—58no—
328C4⋊Dic3—54no—
329C4⋊Dic3—54no—
330C4⋊Dic3—58no—
331Dic3⋊C4—54no—
332Dic3⋊C4—54no—
333C4×Dic3—54no—
334C4×Dic3—58no—
335C4×Dic3C22×D514yes—
336C23×C5—24no—
337C23×C5—24no—
338C23×C5—24no—
339C23×C5—34no—
340C23×C5—64no—
341C23×C5—64no—
342C23×C5—64no—
343C23×C5C23×D314yes—
344C23×C5C23×D311yescharacteristic
345C5×D4—28no—
346C5×D4—616no—
347C5×D4—68no—
348C5×D4—128no—
349C2×C4×C5—34no—
350C2×C4×C5—32no—
351C2×C4×C5—32no—
352C2×C4×C5—62no—
353C2×C4×C5#23714yes—
354C2×C4×C5C23×D312yes—
355C2×Dic5—24no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—32no—
359C2×Dic5—34no—
360C2×Dic5—32no—
361C2×Dic5—62no—
362C2×Dic5—64no—
363C2×Dic5—62no—
364C2×Dic5—128no—
365C2×Dic5—128no—
366C2×Dic5C23×D314yes—
367C2×Dic5C23×D312yes—
368C2×Dic5C23×D312yes—
369Dic10—28no—
370Dic10—68no—
371C22×Q8—51no—
372C22×Q8—151no—
373C22×D4—32no—
374C22×D4—32no—
375C22×D4—31no—
376C22×D4D3×D511yescharacteristic
377C23×C4—152no—
378C23×C4—152no—
379#127—38no—
380#124—58no—
381#124—1516no—
382#124—158no—
383#123—1516no—
384#123—1516no—
385C4×Q8—158no—
386C4×Q8—158no—
387C4×D4—158no—
388C4×D4—1516no—
389C4×D4—158no—
390C2×C4⋊C4—151no—
391C2×C4⋊C4—151no—
392C2×C4⋊C4—151no—
393C2×C4⋊C4—152no—
394C2×C4⋊C4—151no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—152no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C42—31no—
402C2×C42—51no—
403C2×C42—152no—
404C2×C42—151no—
405C2×C3×C5—44no—
406C2×C3×C5#55914yescomplemented
407C2×C3×C5C22×#4111yescharacteristic
408C2×C3×C5C22×#4111yescharacteristic
409C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
410C5×D3—44no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3C23×D514yes—
415C23×C3C23×D511yescharacteristic
416C22×D3—24no—
417C22×D3—24no—
418C22×D3—24no—
419C22×D3C23×D514yes—
420C3×Q8—108no—
421C3×D4—28no—
422C2×C3×C4—54no—
423C2×C3×C4—52no—
424C2×C3×C4—52no—
425C2×C3×C4—102no—
426C2×C3×C4—104no—
427C2×C3×C4—102no—
428C2×C3×C4#71114yes—
429C2×C3×C4C23×D512yes—
430#67—216no—
431#67—48no—
432C2×Dic3—22no—
433C2×Dic3—52no—
434C2×Dic3—52no—
435C2×Dic3—54no—
436C2×Dic3—102no—
437C2×Dic3—104no—
438C2×Dic3—102no—
439C2×Dic3—208no—
440C2×Dic3#71114yes—
441C2×Dic3C23×D512yes—
442C2×Dic3C23×D512yes—
443D12—28no—
444C4×D3—208no—
445Dic6—108no—
446C22×C5—24no—
447C22×C5—24no—
448C22×C5—24no—
449C22×C5—48no—
450C22×C5—64no—
451C22×C5—64no—
452C22×C5—64no—
453C22×C5—128no—
454C22×C5C2×#23712yes—
455C22×C5D3×#4112yes—
456C22×C5#100912yes—
457C22×C5C24×D311yescharacteristic
458C4×C5—34no—
459C4×C5—62no—
460C4×C5C2×#23714yes—
461Dic5—24no—
462Dic5—22no—
463Dic5—22no—
464Dic5—62no—
465Dic5—64no—
466Dic5—62no—
467C24—32no—
468C24C2×D3×D512yes—
469C2×Q8—54no—
470C2×Q8—104no—
471C2×Q8—154no—
472C2×Q8—304no—
473C2×D4—24no—
474C2×D4—38no—
475C2×D4—38no—
476C2×D4—34no—
477C2×D4—68no—
478C2×D4—64no—
479C2×D4—124no—
480C2×D4C2×D3×D514yes—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—51no—
484C22×C4—51no—
485C22×C4—52no—
486C22×C4—158no—
487C22×C4—151no—
488C22×C4—152no—
489C22×C4—151no—
490C22×C4—158no—
491C22×C4—604no—
492C22×C4—604no—
493C22×C4C2×D3×D511yescharacteristic
494C4⋊C4—154no—
495C4⋊C4—154no—
496C4⋊C4—154no—
497C4⋊C4—158no—
498C4⋊C4—154no—
499C22⋊C4—58no—
500C22⋊C4—58no—
501C22⋊C4—158no—
502C22⋊C4—158no—
503C22⋊C4—158no—
504C22⋊C4—158no—
505C42—34no—
506C42—54no—
507C42—158no—
508C42—154no—
509C3×C5C2×#55911yescharacteristic, complemented, Hall
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—48no—
514C22×C3C2×#71112yes—
515C22×C3C2×#71112yes—
516C22×C3#414412yes—
517C22×C3C24×D511yescharacteristic
518C2×D3—24no—
519C2×D3—24no—
520C2×D3—24no—
521C2×D3—48no—
522C3×C4—102no—
523C3×C4—104no—
524C3×C4—102no—
525C3×C4C2×#71114yes—
526Dic3—22no—
527Dic3—102no—
528Dic3—104no—
529Dic3—102no—
530Dic3C2×#71114yes—
531C2×C5—44no—
532C2×C5—124no—
533C2×C5#568114yescomplemented
534C2×C5C22×#23711yescharacteristic
535C2×C5C2×D3×#4111yescharacteristic
536C2×C5C2×#100911yescharacteristic
537C23—24no—
538C23—24no—
539C23—24no—
540C23—34no—
541C23—64no—
542C23—64no—
543C23—64no—
544C23C22×D3×D514yes—
545C23C22×D3×D511yescharacteristic
546Q8—108no—
547Q8—308no—
548D4—28no—
549D4—616no—
550D4—68no—
551D4—128no—
552C2×C4—34no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—54no—
558C2×C4—62no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—104no—
562C2×C4—152no—
563C2×C4—154no—
564C2×C4—152no—
565C2×C4—302no—
566C2×C4—304no—
567C2×C4—302no—
568C2×C4—608no—
569C2×C4—608no—
570C2×C4#678014yes—
571C2×C4C22×D3×D512yes—
572C2×C3—44no—
573C2×C3#6604714yescomplemented
574C2×C3C22×#71111yescharacteristic
575C2×C3C22×#71111yescharacteristic
576C2×C3C2×#414411yescharacteristic
577D3—44no—
578C5C2×#568111yescharacteristic, complemented, Sylow
579C22—24no—
580C22—24no—
581C22—24no—
582C22—48no—
583C22—64no—
584C22—64no—
585C22—64no—
586C22—128no—
587C22D3×#71112yes—
588C22#9202712yes—
589C22C2×#678012yes—
590C22C23×D3×D511yescharacteristic
591C4—34no—
592C4—62no—
593C4—104no—
594C4—102no—
595C4—102no—
596C4—302no—
597C4—304no—
598C4—302no—
599C4C2×#678014yes—
600C3C2×#6604711yescharacteristic, complemented, Sylow
601C2—44no—
602C2—124no—
603C2#1175488814yesdirect product factor
604C2C2×D3×#71111yescharacteristic
605C2C2×#9202711yescharacteristic
606C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C5×#940C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#559
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×D4×Dic15C2semidirect
3. C2×C3×#4082C2semidirect
4. C2×#67⋊Dic5C2semidirect
5. C2×#91555C2semidirect
6. C2×#91543C2semidirect
7. C2×#91525C2semidirect
8. #11754888C2direct (N × H)
9. C2×C4×#1204C2semidirect
10. C2×Dic5×D12C2semidirect
11. C2×#91370C2semidirect
12. C2×Dic3×Dic10C2semidirect
23. D4×Dic15C22semidirect
30. C3×#4082C22semidirect
32. #67⋊Dic5C22semidirect
33. #91555C22semidirect
36. #91543C22semidirect
43. #91525C22semidirect
44. C4×#1204C22semidirect
45. Dic5×D12C22semidirect
46. #91370C22semidirect
47. Dic3×Dic10C22semidirect
52. C2×#4082D3semidirect
133. #4082C2×D3semidirect
406. C2×C3×C5#559semidirect
509. C3×C5C2×#559semidirect
533. C2×C5#5681semidirect
573. C2×C3#66047semidirect
578. C5C2×#5681semidirect
600. C3C2×#66047semidirect
603. C2#11754888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×C5×#9402
C2×C3×#40822
C2×#67⋊Dic52
C2×#915552
C2×#915432
C2×#915252
#117548882
C2×C4×#12042
C2×Dic5×D122
C2×#913702
C2×Dic3×Dic102
C2×#660473
C2×#56815