Finite Group Databasebeta

← C2×#11754460 #14479851

Subgroups — C2×#11754460 #14479851

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic
3C2×C3×#4070C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic5C212yesmaximal, complemented
5C2×#91543C212yesmaximal, complemented
6#11754460C2116yesmaximal, direct product factor
7C2×#91435C211yesmaximal, characteristic, complemented
8C2×#91400C212yesmaximal, complemented
9C2×#91384C211yesmaximal, characteristic, complemented
10C2×#91370C211yesmaximal, characteristic, complemented
11C2×#91367C212yesmaximal, complemented
12C2×#91331C211yesmaximal, characteristic, complemented
13C2×#65934—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C23×Dic15C2211yescharacteristic
17C22×C5×#67C2212yes—
18C22×C5×D12C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×D3×Dic5C2212yes—
21C2×C4×Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C4×Dic15C2218yescomplemented
26C5×#930C2218yes—
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C3×C22⋊Dic5C2212yes—
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C3×#4070C2218yescomplemented
32C2×C3×#683C2212yes—
33#67⋊Dic5C22116yescomplemented
34C2×Dic3⋊Dic5C2212yes—
35#91543C22116yescomplemented
36C2×#6668C2212yes—
37C2×#6668C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40C2×(C2×D3)⋊Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91435C2218yescomplemented
43#91400C22116yescomplemented
44#91384C2218yescomplemented
45#91370C2218yescomplemented
46#91367C22116yescomplemented
47#91331C2218yescomplemented
48C2×#5624—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4082—31no—
51C2×#4081—32no—
52C2×D4×Dic5—31no—
53C2×D4×Dic5—32no—
54C2×#4070D311yescharacteristic, complemented
55C22×C4×Dic5—31no—
56#65934—316no—
57C2×#4036—31no—
58C2×#4033—31no—
59C2×#4025—32no—
60C2×#4023—32no—
61C24×C3×C5C2311yescharacteristic
62C23×C5×D3C2312yes—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15—24no—
68C22×Dic15—24no—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2314yes—
73C22×Dic15C2314yes—
74C22×Dic15C2311yescharacteristic
75C2×C5×#67—28no—
76C2×C5×#67C2318yes—
77C22×C5×Dic3C2312yes—
78C2×C5×D12—24no—
79C2×C5×D12C2314yes—
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C2×C3×Dic10—24no—
83C2×C3×Dic10C2314yes—
84C2×D3×Dic5—28no—
85C2×D3×Dic5C2318yes—
86C4×Dic15C2314yes—
87C4×Dic15C2314yes—
88C4×Dic15C2314yes—
89C4×Dic15C2314yes—
90C5×(C2×D3)⋊C4C2318yes—
91C5×C4⋊Dic3C2314yes—
92C3×C22⋊Dic5C2318yes—
93C3×C4⋊Dic5C2314yes—
94C3×#683C2318yes—
95Dic3⋊Dic5C2318yes—
96#6668C2318yes—
97#6668C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101Dic3×Dic5C2318yes—
102C2×C3×C22⋊Q8—51no—
103C2×#947—51no—
104C2×Q8×Dic3—51no—
105C2×#930D511yescharacteristic
106C22×C4×Dic3—51no—
107#5624—516no—
108C2×#898—52no—
109C2×#893—51no—
110C2×#892—52no—
111C2×#890—51no—
112C2×#886—52no—
113C2×#67⋊C4—52no—
114C22×C5×D4—32no—
115C22×C5×D4—31no—
116C23×C4×C5C2×D311yescharacteristic
117C23×Dic5—31no—
118C23×Dic5—31no—
119C23×Dic5—32no—
120C22×Dic10C2×D311yescharacteristic
121C5×#121—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C22⋊C4—32no—
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5C2×D312yes—
128#4082—38no—
129#4081—316no—
130D4×Dic5—316no—
131D4×Dic5—38no—
132C2×C4⋊Dic5—32no—
133C2×C4⋊Dic5C2×D311yescharacteristic
134#4070C2×D318yescomplemented
135C2×#683—32no—
136C2×#683—32no—
137C2×#683C2×D312yes—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—38no—
143C2×C4×Dic5—32no—
144#4036—38no—
145#4033—38no—
146#4025—316no—
147#4023—316no—
148C2×#529—151noSylow
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5#4114yes—
152C23×C3×C5C2412yes—
153C23×C3×C5C2411yescharacteristic
154C22×C5×D3—24no—
155C22×C5×D3—24no—
156C22×C5×D3—24no—
157C22×C5×D3C2414yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—28no—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15—22no—
167C2×Dic15—28no—
168C2×Dic15#4114yes—
169C2×Dic15C2412yes—
170C2×Dic15C2412yes—
171C2×Dic15C2412yes—
172C2×Dic15C2412yes—
173C5×#67—216no—
174C2×C5×Dic3—24no—
175C2×C5×Dic3C2414yes—
176C5×D12—28no—
177C2×C3×Dic5—24no—
178C2×C3×Dic5—24no—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2414yes—
181C3×Dic10—28no—
182D3×Dic5—216no—
183C22×C3×Q8—51no—
184C23×C3×C4C2×D511yescharacteristic
185C22×#67C2×D512yes—
186C23×Dic3—51no—
187C23×Dic3—51no—
188C22×D12C2×D511yescharacteristic
189C22×C4×D3—52no—
190C3×C22⋊Q8—58no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4—52no—
193C2×C3×C22⋊C4—52no—
194#947—58no—
195Q8×Dic3—58no—
196#930C2×D518yes—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4C2×D512yes—
201C2×C4⋊Dic3—52no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204C2×Dic3⋊C4—52no—
205C2×C4×Dic3—51no—
206C2×C4×Dic3—51no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—58no—
210C2×C4×Dic3—52no—
211#898—516no—
212#893—58no—
213#892—516no—
214#890—58no—
215#886—516no—
216#67⋊C4—516no—
217C24×C5—32no—
218C24×C5C22×D311yescharacteristic
219C2×C5×D4—38no—
220C2×C5×D4—34no—
221C2×C5×D4—68no—
222C2×C5×D4—64no—
223C22×C4×C5—24no—
224C22×C4×C5—32no—
225C22×C4×C5C22×D311yescharacteristic
226C22×C4×C5C22×D314yes—
227C22×C4×C5C22×D311yescharacteristic
228C22×Dic5—31no—
229C22×Dic5—31no—
230C22×Dic5—31no—
231C22×Dic5—31no—
232C22×Dic5—34no—
233C22×Dic5—34no—
234C22×Dic5—38no—
235C22×Dic5—68no—
236C22×Dic5—64no—
237C22×Dic5—64no—
238C22×Dic5C22×D312yes—
239C22×Dic5C22×D312yes—
240C2×Dic10—24no—
241C2×Dic10C22×D314yes—
242C5×C4⋊C4—34no—
243C5×C22⋊C4—38no—
244C22⋊Dic5—38no—
245C22⋊Dic5—38no—
246C22⋊Dic5—38no—
247C22⋊Dic5C22×D318yes—
248C4⋊Dic5—38no—
249C4⋊Dic5C22×D314yes—
250#683—38no—
251#683—38no—
252#683C22×D318yes—
253C4×Dic5—34no—
254C4×Dic5—34no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5—38no—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—51no—
264C2×#121—31no—
265C2×C4×Q8—151no—
266C2×C4×D4—152no—
267C2×C4×D4—151no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5—28no—
271C22×C3×C5—22no—
272C22×C3×C5—22no—
273C22×C3×C5C2×#4112yes—
274C22×C3×C5C2×#4114yes—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5C2511yescharacteristic
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—24no—
281C2×C5×D3—48no—
282C3×C4×C5—22no—
283C3×C4×C5C2×#4114yes—
284Dic15—22no—
285Dic15—22no—
286Dic15—22no—
287Dic15C2×#4114yes—
288C3×Dic5—24no—
289C3×Dic5—24no—
290C5×Dic3—24no—
291C24×C3C22×D511yescharacteristic
292C23×D3C22×D512yes—
293C2×C3×Q8—54no—
294C2×C3×Q8—104no—
295C22×C3×C4—24no—
296C22×C3×C4—52no—
297C22×C3×C4—52no—
298C22×C3×C4C22×D511yescharacteristic
299C22×C3×C4C22×D514yes—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—28no—
302C2×#67C22×D518yes—
303C22×Dic3—51no—
304C22×Dic3—54no—
305C22×Dic3—54no—
306C22×Dic3—51no—
307C22×Dic3—51no—
308C22×Dic3—51no—
309C22×Dic3—104no—
310C22×Dic3—104no—
311C22×Dic3C22×D512yes—
312C2×D12—24no—
313C2×D12C22×D514yes—
314C2×C4×D3—58no—
315C2×C4×D3—108no—
316C3×C4⋊C4—58no—
317C3×C4⋊C4—54no—
318C3×C22⋊C4—58no—
319(C2×D3)⋊C4—58no—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4C22×D518yes—
323C4⋊Dic3—58no—
324C4⋊Dic3—58no—
325C4⋊Dic3C22×D514yes—
326Dic3⋊C4—58no—
327C4×Dic3—54no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3—58no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—34no—
335C23×C5—64no—
336C23×C5—64no—
337C23×C5—64no—
338C23×C5#23914yes—
339C23×C5C23×D312yes—
340C23×C5C23×D311yescharacteristic
341C5×D4—616no—
342C5×D4—68no—
343C2×C4×C5—22no—
344C2×C4×C5—28no—
345C2×C4×C5—34no—
346C2×C4×C5—64no—
347C2×C4×C5#23714yes—
348C2×C4×C5C23×D312yes—
349C2×C4×C5C23×D312yes—
350C2×Dic5—24no—
351C2×Dic5—24no—
352C2×Dic5—34no—
353C2×Dic5—32no—
354C2×Dic5—32no—
355C2×Dic5—32no—
356C2×Dic5—32no—
357C2×Dic5—616no—
358C2×Dic5—68no—
359C2×Dic5—68no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5—62no—
363C2×Dic5C23×D314yes—
364C2×Dic5C23×D314yes—
365Dic10—28no—
366C22×Q8—51no—
367C22×D4—32no—
368C22×D4—31no—
369C23×C4—152no—
370C23×C4—151no—
371C23×C4—151no—
372C23×C4D3×D511yescharacteristic
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—58no—
378#121—38no—
379C4×Q8—158no—
380C4×D4—1516no—
381C4×D4—158no—
382#117—1516no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—52no—
385C2×C4⋊C4—51no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—152no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—52no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—152no—
395C2×C42—151no—
396C2×C42—151no—
397C2×C42—151no—
398C2×C42—151no—
399C2×C42—158no—
400C2×C3×C5—24no—
401C2×C3×C5#52914yescomplemented
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C22×#4111yescharacteristic
405C5×D3—44no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3#71114yes—
409C23×C3C23×D512yes—
410C23×C3C23×D511yescharacteristic
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3C23×D514yes—
415C3×Q8—108no—
416C2×C3×C4—22no—
417C2×C3×C4—28no—
418C2×C3×C4—54no—
419C2×C3×C4—54no—
420C2×C3×C4—104no—
421C2×C3×C4—104no—
422C2×C3×C4#71114yes—
423C2×C3×C4C23×D512yes—
424C2×C3×C4C23×D512yes—
425#67—216no—
426C2×Dic3—24no—
427C2×Dic3—54no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—52no—
431C2×Dic3—52no—
432C2×Dic3—108no—
433C2×Dic3—108no—
434C2×Dic3—102no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3C23×D514yes—
438D12—28no—
439C4×D3—1016no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—28no—
443C22×C5—64no—
444C22×C5—64no—
445C22×C5—64no—
446C22×C5—128no—
447C22×C5C2×#23712yes—
448C22×C5C2×#23914yes—
449C22×C5C2×#23912yes—
450C22×C5D3×#4112yes—
451C22×C5C24×D311yescharacteristic
452C4×C5—22no—
453C4×C5—64no—
454C4×C5C2×#23714yes—
455Dic5—24no—
456Dic5—24no—
457Dic5—34no—
458Dic5—62no—
459Dic5—62no—
460Dic5—62no—
461C24—32no—
462C24C2×D3×D511yescharacteristic
463C2×Q8—54no—
464C2×Q8—104no—
465C2×D4—38no—
466C2×D4—34no—
467C2×D4—68no—
468C2×D4—64no—
469C22×C4—24no—
470C22×C4—32no—
471C22×C4—52no—
472C22×C4—52no—
473C22×C4—158no—
474C22×C4—151no—
475C22×C4—154no—
476C22×C4—154no—
477C22×C4—151no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—308no—
481C22×C4—304no—
482C22×C4—304no—
483C22×C4C2×D3×D514yes—
484C22×C4C2×D3×D511yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—58no—
488C4⋊C4—54no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—158no—
492C22⋊C4—38no—
493C22⋊C4—58no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—158no—
498C42—154no—
499C42—154no—
500C42—154no—
501C42—154no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—28no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3C2×#71114yes—
507C22×C3C2×#71112yes—
508C22×C3C2×#71112yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—24no—
512C2×D3—24no—
513C2×D3—24no—
514C2×D3—48no—
515C3×C4—22no—
516C3×C4—104no—
517C3×C4—104no—
518C3×C4C2×#71114yes—
519Dic3—24no—
520Dic3—54no—
521Dic3—102no—
522Dic3—102no—
523Dic3—102no—
524C2×C5—24no—
525C2×C5—124no—
526C2×C5#562414yescomplemented
527C2×C5C22×#23711yescharacteristic
528C2×C5C22×#23911yescharacteristic
529C2×C5C2×D3×#4111yescharacteristic
530C23—22no—
531C23—22no—
532C23—34no—
533C23—64no—
534C23—64no—
535C23—64no—
536C23#676814yes—
537C23C22×D3×D512yes—
538C23C22×D3×D511yescharacteristic
539Q8—108no—
540D4—616no—
541D4—68no—
542C2×C4—22no—
543C2×C4—28no—
544C2×C4—34no—
545C2×C4—54no—
546C2×C4—54no—
547C2×C4—64no—
548C2×C4—104no—
549C2×C4—104no—
550C2×C4—154no—
551C2×C4—152no—
552C2×C4—152no—
553C2×C4—152no—
554C2×C4—152no—
555C2×C4—3016no—
556C2×C4—308no—
557C2×C4—308no—
558C2×C4—302no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4#678014yes—
562C2×C4C22×D3×D512yes—
563C2×C4C22×D3×D512yes—
564C2×C3—24no—
565C2×C3#6593414yescomplemented
566C2×C3C22×#71111yescharacteristic
567C2×C3C22×#71111yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—44no—
570C5C2×#562411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—22no—
573C22—28no—
574C22—64no—
575C22—64no—
576C22—64no—
577C22—128no—
578C22C2×#676814yes—
579C22C2×#676812yes—
580C22#9201612yes—
581C22C2×#678012yes—
582C22C23×D3×D511yescharacteristic
583C4—22no—
584C4—64no—
585C4—104no—
586C4—104no—
587C4—154no—
588C4—302no—
589C4—302no—
590C4—302no—
591C4C2×#678014yes—
592C3C2×#6593411yescharacteristic, complemented, Sylow
593C2—24no—
594C2—124no—
595C2#1175446014yesdirect product factor
596C2C22×#676811yescharacteristic
597C2C2×#9201611yescharacteristic
598C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC2×C5×#930C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#529
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. C22×C4×Dic15C2semidirect
3. C2×C3×#4070C2semidirect
4. C2×#67⋊Dic5C2semidirect
5. C2×#91543C2semidirect
6. #11754460C2direct (N × H)
7. C2×#91435C2semidirect
8. C2×#91400C2semidirect
9. C2×#91384C2semidirect
10. C2×#91370C2semidirect
11. C2×#91367C2semidirect
12. C2×#91331C2semidirect
25. C2×C4×Dic15C22semidirect
31. C3×#4070C22semidirect
33. #67⋊Dic5C22semidirect
35. #91543C22semidirect
42. #91435C22semidirect
43. #91400C22semidirect
44. #91384C22semidirect
45. #91370C22semidirect
46. #91367C22semidirect
47. #91331C22semidirect
54. C2×#4070D3semidirect
134. #4070C2×D3semidirect
401. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
526. C2×C5#5624semidirect
565. C2×C3#65934semidirect
570. C5C2×#5624semidirect
592. C3C2×#65934semidirect
595. C2#11754460direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic152
C2×C5×#9302
C2×C3×#40702
C2×#67⋊Dic52
C2×#915432
#117544602
C2×#914352
C2×#914002
C2×#913842
C2×#913702
C2×#913672
C2×#913312
C2×#659343
C2×#56245