Finite Group Databasebeta

← C2×#11756430 #14483993

Subgroups — C2×#11756430 #14483993

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#124C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×#91833C211yesmaximal, characteristic, complemented
4C2×#91825C211yesmaximal, characteristic
5C2×D4×Dic15C211yesmaximal, characteristic
6#11756430C2116yesmaximal, direct product factor
7C2×#91768C212yesmaximal, complemented
8C2×#91768C212yesmaximal, complemented
9C2×#91767C212yesmaximal, complemented
10C2×#91766C212yesmaximal, complemented
11C2×C4×Dic30C211yesmaximal, characteristic, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#66005—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C3×C5×D4C2211yescharacteristic
16C23×Dic15C2212yes—
17C22×Dic30C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C3×C5×#124C2218yes—
20C2×C3×C5×C22⋊C4C2212yes—
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C42×C5C2211yescharacteristic
23C2×#6719C2212yes—
24C2×#6719C2212yes—
25C2×#6719C2212yes—
26Q8×Dic15C2218yescomplemented
27#91833C2218yescomplemented
28#91825C2218yes—
29D4×Dic15C2218yes—
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2212yes—
32C2×C4⋊Dic15C2211yescharacteristic
33C2×#6712C2212yes—
34C2×#6712C2212yes—
35C2×#6712C2211yescharacteristic
36C2×#6712C2212yes—
37C2×#6712C2211yescharacteristic
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2211yescharacteristic
40C2×C4×Dic15C2212yes—
41C2×C4×Dic15C2212yes—
42#91768C22116yescomplemented
43#91768C22116yescomplemented
44#91767C22116yescomplemented
45#91766C22116yescomplemented
46C4×Dic30C2218yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5671—51nomaximal, Hall
49C2×C5×#124D311yescharacteristic
50C2×Q8×Dic5—31no—
51C2×#4090—31no—
52C2×#4082—31no—
53C2×D4×Dic5—31no—
54#66005—316no—
55C2×#4025—32no—
56C2×#4025—32no—
57C2×#4024—32no—
58C2×#4023—32no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C2×C3×C5×D4—24no—
65C2×C3×C5×D4C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×Dic15—28no—
71C22×Dic15C2318yes—
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2312yes—
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2312yes—
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C2×Dic30—24no—
79C2×Dic30—24no—
80C2×Dic30C2314yes—
81C2×Dic30C2314yes—
82C3×C5×C22⋊C4C2318yes—
83C3×C5×C22⋊C4C2318yes—
84C3×C42×C5C2314yes—
85#6719C2318yes—
86#6719C2318yes—
87#6719C2318yes—
88C4⋊Dic15C2314yes—
89C4⋊Dic15C2314yes—
90C4⋊Dic15C2318yes—
91#6712C2314yes—
92#6712C2318yes—
93#6712C2314yes—
94#6712C2318yes—
95#6712C2318yes—
96C4×Dic15C2318yes—
97C4×Dic15C2314yes—
98C4×Dic15C2314yes—
99C4×Dic15C2318yes—
100C2×C3×#124D511yescharacteristic
101C2×Q8×Dic3—51no—
102C2×#944—51no—
103C2×#936—51no—
104C2×D4×Dic3—51no—
105#5671—516no—
106C2×#879—52no—
107C2×#879—52no—
108C2×#878—52no—
109C2×#877—52no—
110C2×C4×Dic6—51no—
111C2×C4×Dic6—51no—
112C22×C5×Q8C2×D311yescharacteristic
113C22×C5×D4C2×D311yescharacteristic
114C23×Dic5—32no—
115C22×Dic10—31no—
116C22×Dic10—31no—
117C5×#124C2×D318yes—
118C2×C5×C22⋊C4C2×D312yes—
119C2×C5×C22⋊C4C2×D312yes—
120C2×C42×C5C2×D311yescharacteristic
121C2×C22⋊Dic5—32no—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124Q8×Dic5—38no—
125#4090—38no—
126#4082—38no—
127D4×Dic5—38no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—31no—
134C2×#683—32no—
135C2×#683—32no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—32no—
140#4025—316no—
141#4025—316no—
142#4024—316no—
143#4023—316no—
144C4×Dic10—38no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5—24no—
148C23×C3×C5—24no—
149C23×C3×C5—24no—
150C23×C3×C5C2414yes—
151C23×C3×C5C2411yescharacteristic
152C3×C5×Q8—28no—
153C3×C5×D4—28no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—24no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5#4114yes—
158C2×C3×C4×C5C2412yes—
159C2×C3×C4×C5C2414yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—24no—
163C2×Dic15—22no—
164C2×Dic15—24no—
165C2×Dic15—22no—
166C2×Dic15—22no—
167C2×Dic15—216no—
168C2×Dic15#4114yes—
169C2×Dic15C2412yes—
170C2×Dic15C2414yes—
171C2×Dic15C2412yes—
172C2×Dic15C2414yes—
173C2×Dic15C2412yes—
174C2×Dic15C2412yes—
175Dic30—28no—
176Dic30—28no—
177C22×C3×Q8C2×D511yescharacteristic
178C22×C3×D4C2×D511yescharacteristic
179C23×Dic3—52no—
180C22×Dic6—51no—
181C22×Dic6—51no—
182C3×#124C2×D518yes—
183C2×C3×C22⋊C4C2×D512yes—
184C2×C3×C22⋊C4C2×D512yes—
185C2×C3×C42C2×D511yescharacteristic
186C2×#217—52no—
187C2×#217—52no—
188C2×#217—52no—
189Q8×Dic3—58no—
190#944—58no—
191#936—58no—
192D4×Dic3—58no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×Dic3⋊C4—51no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—52no—
205#879—516no—
206#879—516no—
207#878—516no—
208#877—516no—
209C4×Dic6—58no—
210C4×Dic6—58no—
211C24×C5C22×D312yes—
212C2×C5×Q8—24no—
213C2×C5×Q8C22×D314yes—
214C2×C5×D4—24no—
215C2×C5×D4C22×D314yes—
216C22×C4×C5C22×D311yescharacteristic
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—31no—
221C22×Dic5—32no—
222C22×Dic5—31no—
223C22×Dic5—31no—
224C22×Dic5—31no—
225C22×Dic5—32no—
226C22×Dic5—38no—
227C22×Dic5—68no—
228C2×Dic10—34no—
229C2×Dic10—34no—
230C2×Dic10—64no—
231C2×Dic10—64no—
232C5×C22⋊C4C22×D318yes—
233C5×C22⋊C4C22×D318yes—
234C42×C5C22×D314yes—
235C22⋊Dic5—38no—
236C22⋊Dic5—38no—
237C22⋊Dic5—38no—
238C4⋊Dic5—34no—
239C4⋊Dic5—34no—
240C4⋊Dic5—38no—
241#683—34no—
242#683—38no—
243#683—34no—
244#683—38no—
245#683—38no—
246C4×Dic5—38no—
247C4×Dic5—34no—
248C4×Dic5—34no—
249C4×Dic5—38no—
250#556—1516no—
251C2×C4⋊Q8—151no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—151no—
255C2×#124D1511yescharacteristic
256C2×C22⋊Q8—152no—
257C2×C4×Q8—151no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C22×C3×C5—24no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—48no—
266C22×C3×C5C2×#4112yes—
267C22×C3×C5C2×#4112yes—
268C22×C3×C52−1+412yes—
269C22×C3×C5C2511yescharacteristic
270C3×C4×C5—22no—
271C3×C4×C5—24no—
272C3×C4×C5—22no—
273C3×C4×C5C2×#4114yes—
274Dic15—24no—
275Dic15—22no—
276Dic15—24no—
277Dic15—22no—
278Dic15—22no—
279Dic15C2×#4114yes—
280C24×C3C22×D512yes—
281C2×C3×Q8—24no—
282C2×C3×Q8C22×D514yes—
283C2×C3×D4—24no—
284C2×C3×D4C22×D514yes—
285C22×C3×C4C22×D511yescharacteristic
286C22×C3×C4C22×D512yes—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—58no—
291C22×Dic3—51no—
292C22×Dic3—52no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—51no—
296C22×Dic3—108no—
297C2×Dic6—54no—
298C2×Dic6—54no—
299C2×Dic6—104no—
300C2×Dic6—104no—
301C3×C22⋊C4C22×D518yes—
302C3×C22⋊C4C22×D518yes—
303C3×C42C22×D514yes—
304#217—58no—
305#217—58no—
306#217—58no—
307C4⋊Dic3—54no—
308C4⋊Dic3—54no—
309C4⋊Dic3—58no—
310Dic3⋊C4—54no—
311Dic3⋊C4—58no—
312Dic3⋊C4—54no—
313Dic3⋊C4—58no—
314Dic3⋊C4—58no—
315C4×Dic3—58no—
316C4×Dic3—54no—
317C4×Dic3—54no—
318C4×Dic3—58no—
319C23×C5—24no—
320C23×C5—24no—
321C23×C5—24no—
322C23×C5C23×D314yes—
323C23×C5C23×D311yescharacteristic
324C5×Q8—28no—
325C5×D4—28no—
326C2×C4×C5—24no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5#23714yes—
330C2×C4×C5C23×D312yes—
331C2×C4×C5C23×D314yes—
332C2×C4×C5C23×D312yes—
333C2×C4×C5C23×D312yes—
334C2×Dic5—34no—
335C2×Dic5—32no—
336C2×Dic5—32no—
337C2×Dic5—34no—
338C2×Dic5—32no—
339C2×Dic5—34no—
340C2×Dic5—32no—
341C2×Dic5—616no—
342C2×Dic5—64no—
343C2×Dic5—62no—
344C2×Dic5—64no—
345C2×Dic5—62no—
346C2×Dic5—62no—
347Dic10—68no—
348Dic10—68no—
349C22×Q8—151no—
350C22×Q8—151no—
351C22×Q8C2×D1511yescharacteristic
352C22×D4C2×D1511yescharacteristic
353C23×C4—152no—
354C4⋊Q8—158no—
355#126—1516no—
356#126—1516no—
357#124—158no—
358#124C2×D1518yes—
359C22⋊Q8—1516no—
360C4×Q8—158no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—158no—
364#117—1516no—
365C2×C4⋊C4—151no—
366C2×C4⋊C4—152no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—152no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—152no—
373C2×C22⋊C4—152no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4C2×D1512yes—
377C2×C22⋊C4C2×D1512yes—
378C2×C42—152no—
379C2×C42—152no—
380C2×C42—151no—
381C2×C42—151no—
382C2×C42C2×D1511yescharacteristic
383C2×C3×C5—44no—
384C2×C3×C5#55614yescomplemented
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C22×#4111yescharacteristic
387C2×C3×C5C2×2−1+411yescharacteristic
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3C23×D514yes—
392C23×C3C23×D511yescharacteristic
393C3×Q8—28no—
394C3×D4—28no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4#71114yes—
399C2×C3×C4C23×D512yes—
400C2×C3×C4C23×D514yes—
401C2×C3×C4C23×D512yes—
402C2×C3×C4C23×D512yes—
403C2×Dic3—54no—
404C2×Dic3—52no—
405C2×Dic3—52no—
406C2×Dic3—54no—
407C2×Dic3—52no—
408C2×Dic3—54no—
409C2×Dic3—52no—
410C2×Dic3—1016no—
411C2×Dic3—104no—
412C2×Dic3—102no—
413C2×Dic3—104no—
414C2×Dic3—102no—
415C2×Dic3—102no—
416Dic6—108no—
417Dic6—108no—
418C22×C5—24no—
419C22×C5—24no—
420C22×C5—24no—
421C22×C5—48no—
422C22×C5C2×#23712yes—
423C22×C5D3×#4112yes—
424C22×C5#101012yes—
425C22×C5C24×D311yescharacteristic
426C4×C5—24no—
427C4×C5—22no—
428C4×C5—22no—
429C4×C5C2×#23714yes—
430Dic5—34no—
431Dic5—64no—
432Dic5—62no—
433Dic5—64no—
434Dic5—62no—
435Dic5—62no—
436C24C22×D1512yes—
437C2×Q8—24no—
438C2×Q8—154no—
439C2×Q8—154no—
440C2×Q8—304no—
441C2×Q8—304no—
442C2×Q8C22×D1514yes—
443C2×D4—24no—
444C2×D4C22×D1514yes—
445C22×C4—151no—
446C22×C4—158no—
447C22×C4—151no—
448C22×C4—152no—
449C22×C4—151no—
450C22×C4—152no—
451C22×C4—151no—
452C22×C4—308no—
453C22×C4C22×D1511yescharacteristic
454C22×C4C22×D1512yes—
455C22×C4C22×D1511yescharacteristic
456C22×C4C22×D1511yescharacteristic
457C4⋊C4—154no—
458C4⋊C4—158no—
459C4⋊C4—154no—
460C4⋊C4—158no—
461C4⋊C4—158no—
462C4⋊C4—154no—
463C4⋊C4—154no—
464C4⋊C4—158no—
465C22⋊C4—158no—
466C22⋊C4—158no—
467C22⋊C4—158no—
468C22⋊C4C22×D1518yes—
469C22⋊C4C22×D1518yes—
470C42—158no—
471C42—158no—
472C42—154no—
473C42—154no—
474C42C22×D1514yes—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—48no—
480C22×C3C2×#71112yes—
481C22×C3D5×#4112yes—
482C22×C3#415012yes—
483C22×C3C24×D511yescharacteristic
484C3×C4—24no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4C2×#71114yes—
488Dic3—54no—
489Dic3—104no—
490Dic3—102no—
491Dic3—104no—
492Dic3—102no—
493Dic3—102no—
494C2×C5—44no—
495C2×C5#567114yescomplemented
496C2×C5C22×#23711yescharacteristic
497C2×C5C2×D3×#4111yescharacteristic
498C2×C5C2×#101011yescharacteristic
499C23—24no—
500C23—24no—
501C23—24no—
502C23C23×D1514yes—
503C23C23×D1511yescharacteristic
504Q8—28no—
505Q8—308no—
506Q8—308no—
507D4—28no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—154no—
512C2×C4—152no—
513C2×C4—152no—
514C2×C4—154no—
515C2×C4—152no—
516C2×C4—154no—
517C2×C4—152no—
518C2×C4—3016no—
519C2×C4—304no—
520C2×C4—304no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4#681914yes—
525C2×C4C23×D1512yes—
526C2×C4C23×D1514yes—
527C2×C4C23×D1512yes—
528C2×C4C23×D1512yes—
529C2×C3—44no—
530C2×C3#6600514yescomplemented
531C2×C3C22×#71111yescharacteristic
532C2×C3C2×D5×#4111yescharacteristic
533C2×C3C2×#415011yescharacteristic
534C5C2×#567111yescharacteristic, complemented, Sylow
535C22—24no—
536C22—24no—
537C22—24no—
538C22—48no—
539C22C2×#681912yes—
540C22#41×D1512yes—
541C22#9210112yes—
542C22C24×D1511yescharacteristic
543C4—24no—
544C4—22no—
545C4—22no—
546C4—154no—
547C4—304no—
548C4—304no—
549C4—302no—
550C4—302no—
551C4—302no—
552C4C2×#681914yes—
553C3C2×#6600511yescharacteristic, complemented, Sylow
554C2—44no—
555C2#1175643014yesdirect product factor
556C2C22×#681911yescharacteristic
557C2C2×#41×D1511yescharacteristic
558C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#124C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×#124D15
hypocenterC3×C5C2×#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×#91833C2semidirect
6. #11756430C2direct (N × H)
7. C2×#91768C2semidirect
8. C2×#91768C2semidirect
9. C2×#91767C2semidirect
10. C2×#91766C2semidirect
11. C2×C4×Dic30C2semidirect
12. C2×C4×Dic30C2semidirect
26. Q8×Dic15C22semidirect
27. #91833C22semidirect
42. #91768C22semidirect
43. #91768C22semidirect
44. #91767C22semidirect
45. #91766C22semidirect
46. C4×Dic30C22semidirect
47. C4×Dic30C22semidirect
384. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
495. C2×C5#5671semidirect
530. C2×C3#66005semidirect
534. C5C2×#5671semidirect
553. C3C2×#66005semidirect
555. C2#11756430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1242
C2×Q8×Dic152
C2×#918332
C2×#918252
C2×D4×Dic152
#117564302
C2×#917682
C2×#917672
C2×#917662
C2×C4×Dic302
C2×#660053
C2×#56715