Finite Group Databasebeta

← C2×#11754432 #14483474

Subgroups — C2×#11754432 #14483474

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91813C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C2×#91555C212yesmaximal
5C2×#91530C212yesmaximal, complemented
6#11754432C2116yesmaximal, direct product factor
7C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#91398C212yesmaximal, complemented
9C2×#91381C211yesmaximal, characteristic, complemented
10C2×#91378C212yesmaximal, complemented
11C2×#91365C211yesmaximal, characteristic, complemented
12C2×#91340C211yesmaximal, characteristic, complemented
13C2×#65875—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C5×#67C2211yescharacteristic
17C22×C4×C5×D3C2211yescharacteristic
18C22×D3×Dic5C2212yes—
19C2×#6719C2212yes—
20C2×C4⋊Dic15C2211yescharacteristic
21#91813C2218yescomplemented
22C2×#6712C2212yes—
23C2×C5×#217C2211yescharacteristic
24C4×C5×#67C2218yes—
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C3×#4072C2218yescomplemented
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2212yes—
33#91555C22116yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6669C2212yes—
36C2×#6669C2212yes—
37C2×#6668C2212yes—
38C2×#6668C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40#91530C22116yescomplemented
41C2×Dic3×Dic5C2212yes—
42D3×C4⋊Dic5C2218yescomplemented
43#91398C22116yescomplemented
44#91381C2218yescomplemented
45#91378C22116yescomplemented
46#91365C2218yescomplemented
47#91340C2218yescomplemented
48C2×#5529—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4081—32no—
51C2×#4072D311yescharacteristic, complemented
52C22×C4⋊Dic5—31no—
53C2×#4070—31no—
54C2×#4070—31no—
55#65875—316no—
56C2×#4035—32no—
57C2×#4025—32no—
58C2×#4023—32no—
59C2×#4016—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2311yescharacteristic
62C23×C5×D3C2311yescharacteristic
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2312yes—
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C2×C5×#67—24no—
72C2×C5×#67C2314yes—
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2311yescharacteristic
75C22×C5×Dic3C2311yescharacteristic
76C2×C4×C5×D3—24no—
77C2×C4×C5×D3C2314yes—
78C22×C3×Dic5C2312yes—
79C22×C3×Dic5C2312yes—
80C2×D3×Dic5—28no—
81C2×D3×Dic5C2318yes—
82#6719C2318yes—
83C4⋊Dic15C2314yes—
84#6712C2318yes—
85C5×#217C2314yes—
86C5×(C2×D3)⋊C4C2314yes—
87C5×Dic3⋊C4C2314yes—
88C4×C5×Dic3C2314yes—
89C3×C22⋊Dic5C2318yes—
90C3×C4⋊Dic5C2314yes—
91C3×C4⋊Dic5C2314yes—
92C3×C4×Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94#6669C2318yes—
95#6669C2318yes—
96#6668C2318yes—
97#6668C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×#117—51no—
101C2×C4×#67D511yescharacteristic
102C2×#924—51no—
103#5529—516no—
104C2×#897—51no—
105C2×D3×C4⋊C4—51no—
106C2×#890—51no—
107C2×#887—51no—
108C2×#883—52no—
109C2×#879—52no—
110C2×#872—52no—
111C2×#870—52no—
112C22×C5×D4—31no—
113C23×C4×C5—31no—
114C23×C4×C5C2×D311yescharacteristic
115C23×Dic5—32no—
116C22×Dic10—31no—
117C4×C5×D4—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C22⋊C4—31no—
120C2×C5×C22⋊C4—31no—
121C2×C42×C5—31no—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5C2×D312yes—
125#4081—316no—
126#4072C2×D318yescomplemented
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—38no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131C2×C4⋊Dic5C2×D311yescharacteristic
132#4070—38no—
133#4070—38no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683—32no—
139C2×C4×Dic5—32no—
140C2×C4×Dic5C2×D312yes—
141#4035—316no—
142#4025—316no—
143#4023—316no—
144#4016—38no—
145C4×Dic10—38no—
146C2×#552—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5C2412yes—
151C23×C3×C5C2411yescharacteristic
152C22×C5×D3—22no—
153C22×C5×D3—22no—
154C22×C5×D3#4114yes—
155C22×C5×D3C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×Dic15—24no—
162C2×Dic15—24no—
163C2×Dic15C2414yes—
164C2×Dic15C2414yes—
165Dic30—28no—
166C5×#67—28no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2412yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2412yes—
173C4×C5×D3—28no—
174C2×C3×Dic5—24no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2414yes—
177C2×C3×Dic5C2414yes—
178D3×Dic5—216no—
179C23×C3×C4C2×D511yescharacteristic
180C22×#67C2×D511yescharacteristic
181C22×C4×D3—52no—
182C22×C4×D3C2×D511yescharacteristic
183C22×Dic6—51no—
184C3×#117—58no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C22⋊C4—52no—
188C2×C3×C42—52no—
189C2×#217—52no—
190C2×#217C2×D511yescharacteristic
191C4×#67C2×D518yes—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D511yescharacteristic
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—52no—
197#924—58no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4C2×D511yescharacteristic
203C2×C4×Dic3—52no—
204C2×C4×Dic3C2×D511yescharacteristic
205#897—58no—
206D3×C4⋊C4—58no—
207#890—58no—
208#887—58no—
209#883—516no—
210#879—516no—
211#872—516no—
212#870—516no—
213C24×C5—31no—
214C24×C5C22×D311yescharacteristic
215C2×C5×D4—34no—
216C2×C5×D4—64no—
217C22×C4×C5—24no—
218C22×C4×C5—31no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—34no—
222C22×C4×C5—64no—
223C22×C4×C5C22×D311yescharacteristic
224C22×C4×C5C22×D314yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—32no—
227C22×Dic5—32no—
228C22×Dic5—38no—
229C22×Dic5—68no—
230C22×Dic5C22×D312yes—
231C22×Dic5C22×D312yes—
232C2×Dic10—34no—
233C2×Dic10—64no—
234C5×C4⋊C4—34no—
235C5×C22⋊C4—34no—
236C5×C22⋊C4—34no—
237C42×C5—34no—
238C22⋊Dic5—38no—
239C22⋊Dic5—38no—
240C22⋊Dic5C22×D318yes—
241C4⋊Dic5—34no—
242C4⋊Dic5—38no—
243C4⋊Dic5C22×D314yes—
244C4⋊Dic5C22×D314yes—
245#683—38no—
246#683—38no—
247#683—38no—
248#683—38no—
249#683—38no—
250C4×Dic5—38no—
251C4×Dic5C22×D318yes—
252#552—1516no—
253C2×#126—152no—
254C2×#125—151no—
255C2×#125—152no—
256C2×#123—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—31no—
261C2×#117—51no—
262C2×#117—152no—
263C22×C4⋊C4—151no—
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—44no—
268C22×C3×C5C2×#4112yes—
269C22×C3×C5C2×#4112yes—
270C22×C3×C52−1+412yes—
271C22×C3×C5C2511yescharacteristic
272C2×C5×D3—28no—
273C2×C5×D3—22no—
274C2×C5×D3—22no—
275C2×C5×D3C2×#4114yes—
276C3×C4×C5—22no—
277C3×C4×C5C2×#4114yes—
278Dic15—24no—
279Dic15—24no—
280C3×Dic5—24no—
281C3×Dic5—24no—
282C5×Dic3—22no—
283C5×Dic3—22no—
284C5×Dic3—22no—
285C24×C3C22×D511yescharacteristic
286C23×D3C22×D511yescharacteristic
287C22×C3×C4—24no—
288C22×C3×C4—52no—
289C22×C3×C4—52no—
290C22×C3×C4C22×D511yescharacteristic
291C22×C3×C4C22×D514yes—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—24no—
294C2×#67C22×D514yes—
295C22×Dic3—52no—
296C22×Dic3—52no—
297C22×Dic3C22×D511yescharacteristic
298C22×Dic3C22×D511yescharacteristic
299C22×Dic3C22×D511yescharacteristic
300C2×C4×D3—24no—
301C2×C4×D3—58no—
302C2×C4×D3—108no—
303C2×C4×D3C22×D514yes—
304C2×Dic6—54no—
305C2×Dic6—104no—
306C3×C4⋊C4—54no—
307C3×C4⋊C4—54no—
308C3×C22⋊C4—58no—
309C3×C42—58no—
310#217—58no—
311#217C22×D514yes—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4C22×D514yes—
314C4⋊Dic3—54no—
315C4⋊Dic3—58no—
316C4⋊Dic3—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321Dic3⋊C4C22×D514yes—
322C4×Dic3—58no—
323C4×Dic3C22×D514yes—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—34no—
328C23×C5—32no—
329C23×C5—62no—
330C23×C5—62no—
331C23×C5C23×D312yes—
332C23×C5C23×D311yescharacteristic
333C5×D4—68no—
334C2×C4×C5—22no—
335C2×C4×C5—28no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—32no—
339C2×C4×C5—62no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5—68no—
343C2×C4×C5#23514yes—
344C2×C4×C5C23×D312yes—
345C2×C4×C5C23×D312yes—
346C2×Dic5—24no—
347C2×Dic5—24no—
348C2×Dic5—34no—
349C2×Dic5—34no—
350C2×Dic5—616no—
351C2×Dic5—64no—
352C2×Dic5—64no—
353C2×Dic5C23×D314yes—
354C2×Dic5C23×D314yes—
355Dic10—68no—
356C22×Q8—151no—
357C22×D4—31no—
358C23×C4—31no—
359C23×C4—152no—
360C23×C4D3×D511yescharacteristic
361#126—1516no—
362#125—158no—
363#125—1516no—
364#123—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—38no—
369#117—58no—
370#117—1516no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—158no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—152no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—52no—
385C2×C22⋊C4—152no—
386C2×C22⋊C4—152no—
387C2×C42—31no—
388C2×C42—52no—
389C2×C42—152no—
390C2×C3×C5—42no—
391C2×C3×C5#55214yescomplemented
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C22×#4111yescharacteristic
394C2×C3×C5C2×2−1+411yescharacteristic
395C5×D3—24no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3C23×D512yes—
400C23×C3C23×D511yescharacteristic
401C22×D3—22no—
402C22×D3—22no—
403C22×D3#70914yes—
404C22×D3C23×D512yes—
405C2×C3×C4—22no—
406C2×C3×C4—28no—
407C2×C3×C4—54no—
408C2×C3×C4—54no—
409C2×C3×C4—104no—
410C2×C3×C4—104no—
411C2×C3×C4#71114yes—
412C2×C3×C4C23×D512yes—
413C2×C3×C4C23×D512yes—
414#67—28no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—54no—
419C2×Dic3—54no—
420C2×Dic3—104no—
421C2×Dic3—104no—
422C2×Dic3C23×D512yes—
423C2×Dic3C23×D512yes—
424C2×Dic3C23×D512yes—
425C4×D3—28no—
426C4×D3—1016no—
427Dic6—108no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—34no—
432C22×C5—44no—
433C22×C5—62no—
434C22×C5—62no—
435C22×C5—68no—
436C22×C5C2×#23512yes—
437C22×C5D3×#4112yes—
438C22×C5#101012yes—
439C22×C5C24×D311yescharacteristic
440C4×C5—22no—
441C4×C5—62no—
442C4×C5—62no—
443C4×C5—62no—
444C4×C5C2×#23514yes—
445Dic5—24no—
446Dic5—24no—
447Dic5—64no—
448Dic5—64no—
449C24—31no—
450C24C2×D3×D511yescharacteristic
451C2×Q8—154no—
452C2×Q8—304no—
453C2×D4—34no—
454C2×D4—64no—
455C22×C4—24no—
456C22×C4—31no—
457C22×C4—31no—
458C22×C4—31no—
459C22×C4—34no—
460C22×C4—52no—
461C22×C4—52no—
462C22×C4—64no—
463C22×C4—158no—
464C22×C4—152no—
465C22×C4—152no—
466C22×C4—308no—
467C22×C4C2×D3×D514yes—
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—54no—
472C4⋊C4—54no—
473C4⋊C4—158no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—154no—
479C4⋊C4—158no—
480C22⋊C4—34no—
481C22⋊C4—34no—
482C22⋊C4—58no—
483C22⋊C4—158no—
484C22⋊C4—158no—
485C42—34no—
486C42—58no—
487C42—158no—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—44no—
493C22×C3C2×#70912yes—
494C22×C3C2×#71112yes—
495C22×C3#415012yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—28no—
498C2×D3—22no—
499C2×D3—22no—
500C2×D3C2×#70914yes—
501C3×C4—22no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4C2×#71114yes—
505Dic3—22no—
506Dic3—22no—
507Dic3—22no—
508Dic3—104no—
509Dic3—104no—
510C2×C5—42no—
511C2×C5—64no—
512C2×C5#552914yescomplemented
513C2×C5C22×#23511yescharacteristic
514C2×C5C2×D3×#4111yescharacteristic
515C2×C5C2×#101011yescharacteristic
516C23—22no—
517C23—22no—
518C23—22no—
519C23—34no—
520C23—32no—
521C23—62no—
522C23—62no—
523C23C22×D3×D512yes—
524C23C22×D3×D511yescharacteristic
525Q8—308no—
526D4—68no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—32no—
532C2×C4—54no—
533C2×C4—54no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—68no—
538C2×C4—104no—
539C2×C4—104no—
540C2×C4—154no—
541C2×C4—154no—
542C2×C4—3016no—
543C2×C4—304no—
544C2×C4—304no—
545C2×C4#678214yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3—42no—
549C2×C3#6587514yescomplemented
550C2×C3C22×#70911yescharacteristic
551C2×C3C22×#71111yescharacteristic
552C2×C3C2×#415011yescharacteristic
553D3—24no—
554C5C2×#552911yescharacteristic, complemented, Sylow
555C22—22no—
556C22—22no—
557C22—22no—
558C22—34no—
559C22—44no—
560C22—62no—
561C22—68no—
562C22—62no—
563C22#9200112yes—
564C22D3×#70912yes—
565C22C2×#678212yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—62no—
569C4—62no—
570C4—62no—
571C4—104no—
572C4—104no—
573C4—304no—
574C4—304no—
575C4C2×#678214yes—
576C3C2×#6587511yescharacteristic, complemented, Sylow
577C2—42no—
578C2—64no—
579C2#1175443214yesdirect product factor
580C2C2×#9200111yescharacteristic
581C2C2×D3×#70911yescharacteristic
582C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#552
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×#91813C2semidirect
3. C2×C3×#4072C2semidirect
5. C2×#91530C2semidirect
6. #11754432C2direct (N × H)
7. C2×D3×C4⋊Dic5C2semidirect
8. C2×#91398C2semidirect
9. C2×#91381C2semidirect
10. C2×#91378C2semidirect
11. C2×#91365C2semidirect
12. C2×#91340C2semidirect
21. #91813C22semidirect
29. C3×#4072C22semidirect
40. #91530C22semidirect
42. D3×C4⋊Dic5C22semidirect
43. #91398C22semidirect
44. #91381C22semidirect
45. #91378C22semidirect
46. #91365C22semidirect
47. #91340C22semidirect
51. C2×#4072D3semidirect
126. #4072C2×D3semidirect
391. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
512. C2×C5#5529semidirect
549. C2×C3#65875semidirect
554. C5C2×#5529semidirect
576. C3C2×#65875semidirect
579. C2#11754432direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918132
C2×C4×C5×#672
C2×C3×#40722
C2×#915552
C2×#915302
#117544322
C2×D3×C4⋊Dic52
C2×#913982
C2×#913812
C2×#913782
C2×#913652
C2×#913402
C2×#658753
C2×#55295