Finite Group Databasebeta

← C2×#11755206 #14484099

Subgroups — C2×#11755206 #14484099

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×Q8×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#944C211yesmaximal, characteristic, complemented
3C2×C3×#4093C211yesmaximal, characteristic
4#11755206C2116yesmaximal, direct product factor
5C2×C4×#1204C211yesmaximal, characteristic, complemented
6C2×Dic3×D20C211yesmaximal, characteristic
7C2×#91422C212yesmaximal, complemented
8C2×#91394C212yesmaximal, complemented
9C2×#91368C211yesmaximal, characteristic
10C2×#91366C212yesmaximal, complemented
11C2×#91362C212yesmaximal, complemented
12C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
13C2×#66066—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×#1204C2211yescharacteristic
18C22×D5×Dic3C2212yes—
19Q8×Dic15C2218yescomplemented
20C2×C4⋊Dic15C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24C5×#944C2218yescomplemented
25C2×C5×Dic3⋊C4C2212yes—
26C2×C5×Dic3⋊C4C2212yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C3×#4093C2218yes—
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2212yes—
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6665C2212yes—
37C2×#6665C2212yes—
38C2×#6665C2212yes—
39C2×Dic3×Dic5C2212yes—
40C4×#1204C2218yescomplemented
41Dic3×D20C2218yes—
42#91422C22116yescomplemented
43#91394C22116yescomplemented
44#91368C2218yes—
45#91366C22116yescomplemented
46#91362C22116yescomplemented
47Dic5×Dic6C2218yescomplemented
48C2×#5671—51nomaximal, Hall
49C2×C5×C4⋊Q8—31no—
50C2×#4093—31no—
51C2×#4093D311yescharacteristic
52C2×Q8×Dic5—31no—
53C2×Q8×Dic5—31no—
54#66066—316no—
55C2×#4044—32no—
56C2×#4044—32no—
57C2×#4043—32no—
58C2×#4038—32no—
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×C3×D5C2312yes—
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2311yescharacteristic
72C2×C5×Dic6—24no—
73C2×C5×Dic6C2314yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×D20—24no—
77C2×C3×D20C2314yes—
78C2×#1204—24no—
79C2×#1204C2314yes—
80C2×D5×Dic3—28no—
81C2×D5×Dic3C2318yes—
82C4⋊Dic15C2318yes—
83C4⋊Dic15C2314yes—
84C4×Dic15C2318yes—
85C4×Dic15C2314yes—
86C5×Dic3⋊C4C2318yes—
87C5×Dic3⋊C4C2318yes—
88C4×C5×Dic3C2314yes—
89C3×#685C2318yes—
90C3×#685C2318yes—
91C3×C4×Dic5C2314yes—
92Dic3⋊Dic5C2314yes—
93Dic3⋊Dic5C2318yes—
94#6669C2314yes—
95#6668C2314yes—
96#6665C2318yes—
97#6665C2318yes—
98#6665C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×#124—51no—
101C2×Q8×Dic3—51no—
102C2×#944D511yescharacteristic, complemented
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×Q8—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C22×D20C2×D311yescharacteristic
115C22×C4×D5—32no—
116C22×Dic10—31no—
117C5×C4⋊Q8—38no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—32no—
120C2×C42×C5—31no—
121#4093—38no—
122#4093C2×D318yes—
123Q8×Dic5—38no—
124Q8×Dic5—38no—
125C2×#685—32no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685C2×D312yes—
129C2×#685C2×D312yes—
130C2×C4⋊Dic5—31no—
131C2×C4⋊Dic5—32no—
132C2×C4⋊Dic5—31no—
133C2×C4⋊Dic5—32no—
134C2×#683—31no—
135C2×#683—31no—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5C2×D311yescharacteristic
140#4044—316no—
141#4044—316no—
142#4043—316no—
143#4038—316no—
144C4×D20—38no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C3×D5—24no—
149C22×C3×D5—24no—
150C22×C3×D5—24no—
151C22×C3×D5C2414yes—
152C3×C5×Q8—28no—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5#4114yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—24no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15C2414yes—
161C2×Dic15C2412yes—
162C2×Dic15C2412yes—
163C2×C5×Dic3—24no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3#4114yes—
166C2×C5×Dic3C2414yes—
167C2×C5×Dic3C2412yes—
168C2×C5×Dic3C2412yes—
169C5×Dic6—28no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5C2412yes—
173C2×C3×Dic5C2412yes—
174C3×D20—28no—
175#1204—28no—
176D5×Dic3—216no—
177C22×C3×Q8C2×D511yescharacteristic
178C22×C3×D4—51no—
179C23×Dic3—52no—
180C22×Dic6—51no—
181C22×Dic6C2×D511yescharacteristic
182C3×#124—58no—
183C2×C3×C22⋊C4—52no—
184C2×C3×C22⋊C4—52no—
185C2×C3×C42—51no—
186C2×#217—52no—
187C2×#217—52no—
188C2×#217—52no—
189Q8×Dic3—58no—
190#944C2×D518yescomplemented
191#936—58no—
192D4×Dic3—58no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—52no—
195C2×C4⋊Dic3—51no—
196C2×Dic3⋊C4—51no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4C2×D512yes—
200C2×Dic3⋊C4C2×D512yes—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3C2×D511yescharacteristic
205#879—516no—
206#879—516no—
207#878—516no—
208#877—516no—
209C4×Dic6—58no—
210C4×Dic6—58no—
211C23×D5C22×D312yes—
212C2×C5×Q8—24no—
213C2×C5×Q8—34no—
214C2×C5×Q8—64no—
215C2×C5×Q8C22×D314yes—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—32no—
219C22×C4×C5C22×D312yes—
220C22×C4×C5C22×D311yescharacteristic
221C22×Dic5—31no—
222C22×Dic5—32no—
223C22×Dic5—31no—
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D311yescharacteristic
226C2×D20—24no—
227C2×D20C22×D314yes—
228C2×C4×D5—38no—
229C2×C4×D5—68no—
230C2×Dic10—34no—
231C2×Dic10—64no—
232C5×C4⋊C4—38no—
233C5×C4⋊C4—38no—
234C42×C5—34no—
235#685—38no—
236#685—38no—
237#685—38no—
238#685C22×D318yes—
239#685C22×D318yes—
240C4⋊Dic5—34no—
241C4⋊Dic5—38no—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244#683—34no—
245#683—34no—
246C4×Dic5—34no—
247C4×Dic5—38no—
248C4×Dic5—38no—
249C4×Dic5C22×D314yes—
250#556—1516no—
251C2×C4⋊Q8—31no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—51no—
255C2×#124—151no—
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×C5C2×#4112yes—
263C22×C3×C5C2×#4112yes—
264C22×C3×C52−1+412yes—
265C22×C3×C5C2511yescharacteristic
266C2×C3×D5—24no—
267C2×C3×D5—24no—
268C2×C3×D5—24no—
269C2×C3×D5—48no—
270C3×C4×C5—24no—
271C3×C4×C5C2×#4114yes—
272Dic15—24no—
273Dic15—22no—
274Dic15—22no—
275C3×Dic5—22no—
276C3×Dic5—22no—
277C5×Dic3—24no—
278C5×Dic3—22no—
279C5×Dic3C2×#4114yes—
280C24×C3—52no—
281C2×C3×Q8—24no—
282C2×C3×Q8C22×D514yes—
283C2×C3×D4—54no—
284C2×C3×D4—104no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4C22×D512yes—
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—52no—
291C22×Dic3—51no—
292C22×Dic3—58no—
293C22×Dic3—108no—
294C22×Dic3C22×D512yes—
295C22×Dic3C22×D511yescharacteristic
296C22×Dic3C22×D511yescharacteristic
297C2×Dic6—24no—
298C2×Dic6—54no—
299C2×Dic6—104no—
300C2×Dic6C22×D514yes—
301C3×C22⋊C4—58no—
302C3×C22⋊C4—58no—
303C3×C42—54no—
304#217—58no—
305#217—58no—
306#217—58no—
307C4⋊Dic3—54no—
308C4⋊Dic3—58no—
309C4⋊Dic3—54no—
310Dic3⋊C4—54no—
311Dic3⋊C4—54no—
312Dic3⋊C4—58no—
313Dic3⋊C4C22×D518yes—
314Dic3⋊C4C22×D518yes—
315C4×Dic3—54no—
316C4×Dic3—58no—
317C4×Dic3—58no—
318C4×Dic3C22×D514yes—
319C23×C5C23×D311yescharacteristic
320C22×D5—24no—
321C22×D5—24no—
322C22×D5—24no—
323C22×D5C23×D314yes—
324C5×Q8—28no—
325C5×Q8—68no—
326C2×C4×C5—24no—
327C2×C4×C5—34no—
328C2×C4×C5—32no—
329C2×C4×C5—34no—
330C2×C4×C5—32no—
331C2×C4×C5—64no—
332C2×C4×C5—62no—
333C2×C4×C5#23714yes—
334C2×C4×C5C23×D314yes—
335C2×C4×C5C23×D312yes—
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—32no—
339C2×Dic5—34no—
340C2×Dic5—32no—
341C2×Dic5—62no—
342C2×Dic5—64no—
343C2×Dic5—62no—
344C2×Dic5C23×D312yes—
345C2×Dic5C23×D312yes—
346D20—28no—
347C4×D5—616no—
348Dic10—68no—
349C22×Q8—31no—
350C22×Q8—151no—
351C22×Q8D3×D511yescharacteristic
352C22×D4—51no—
353C23×C4—152no—
354C4⋊Q8—38no—
355#126—1516no—
356#126—1516no—
357#124—58no—
358#124—158no—
359C22⋊Q8—1516no—
360C4×Q8—158no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—158no—
364#117—1516no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—152no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C22⋊C4—152no—
378C2×C42—31no—
379C2×C42—51no—
380C2×C42—152no—
381C2×C42—152no—
382C2×C42—151no—
383C2×C3×C5#55614yescomplemented
384C2×C3×C5C22×#4111yescharacteristic
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C2×2−1+411yescharacteristic
387C3×D5—44no—
388C23×C3—54no—
389C23×C3—104no—
390C23×C3—104no—
391C23×C3—104no—
392C23×C3C23×D511yescharacteristic
393C3×Q8—28no—
394C3×D4—108no—
395C2×C3×C4—24no—
396C2×C3×C4—52no—
397C2×C3×C4—52no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4#71114yes—
401C2×C3×C4C23×D514yes—
402C2×C3×C4C23×D512yes—
403C2×Dic3—24no—
404C2×Dic3—22no—
405C2×Dic3—52no—
406C2×Dic3—54no—
407C2×Dic3—52no—
408C2×Dic3—102no—
409C2×Dic3—104no—
410C2×Dic3—102no—
411C2×Dic3—1016no—
412C2×Dic3#71314yes—
413C2×Dic3C23×D514yes—
414C2×Dic3C23×D512yes—
415C2×Dic3C23×D512yes—
416Dic6—28no—
417Dic6—108no—
418C22×C5C2×#23712yes—
419C22×C5D3×#4112yes—
420C22×C5#101012yes—
421C22×C5C24×D311yescharacteristic
422C2×D5—24no—
423C2×D5—24no—
424C2×D5—24no—
425C2×D5—48no—
426C4×C5—24no—
427C4×C5—34no—
428C4×C5—64no—
429C4×C5—62no—
430C4×C5C2×#23714yes—
431Dic5—22no—
432Dic5—22no—
433Dic5—62no—
434Dic5—64no—
435Dic5—62no—
436C24—52no—
437C2×Q8—24no—
438C2×Q8—34no—
439C2×Q8—64no—
440C2×Q8—154no—
441C2×Q8—304no—
442C2×Q8C2×D3×D514yes—
443C2×D4—54no—
444C2×D4—104no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—158no—
451C22×C4—151no—
452C22×C4—152no—
453C22×C4—151no—
454C22×C4—308no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—38no—
458C4⋊C4—38no—
459C4⋊C4—154no—
460C4⋊C4—158no—
461C4⋊C4—154no—
462C4⋊C4—154no—
463C4⋊C4—154no—
464C4⋊C4—158no—
465C22⋊C4—58no—
466C22⋊C4—58no—
467C22⋊C4—158no—
468C22⋊C4—158no—
469C22⋊C4—158no—
470C42—34no—
471C42—54no—
472C42—158no—
473C42—158no—
474C42—154no—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3—104no—
477C22×C3—104no—
478C22×C3—104no—
479C22×C3—208no—
480C22×C3C2×#71112yes—
481C22×C3C2×#71312yes—
482C22×C3#414712yes—
483C22×C3C24×D511yescharacteristic
484C3×C4—24no—
485C3×C4—102no—
486C3×C4—102no—
487C3×C4C2×#71114yes—
488Dic3—24no—
489Dic3—22no—
490Dic3—102no—
491Dic3—104no—
492Dic3—102no—
493Dic3C2×#71314yes—
494C2×C5#567114yescomplemented
495C2×C5C22×#23711yescharacteristic
496C2×C5C2×D3×#4111yescharacteristic
497C2×C5C2×#101011yescharacteristic
498D5—44no—
499C23—54no—
500C23—104no—
501C23—104no—
502C23—104no—
503C23C22×D3×D511yescharacteristic
504Q8—28no—
505Q8—68no—
506Q8—308no—
507D4—108no—
508C2×C4—24no—
509C2×C4—34no—
510C2×C4—32no—
511C2×C4—32no—
512C2×C4—34no—
513C2×C4—52no—
514C2×C4—52no—
515C2×C4—62no—
516C2×C4—64no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—152no—
520C2×C4—154no—
521C2×C4—152no—
522C2×C4—3016no—
523C2×C4—302no—
524C2×C4—304no—
525C2×C4—302no—
526C2×C4#678014yes—
527C2×C4C22×D3×D514yes—
528C2×C4C22×D3×D512yes—
529C2×C3—204no—
530C2×C3#6606614yescomplemented
531C2×C3C22×#71111yescharacteristic
532C2×C3C22×#71311yescharacteristic
533C2×C3C2×#414711yescharacteristic
534C5C2×#567111yescharacteristic, complemented, Sylow
535C22—104no—
536C22—104no—
537C22—104no—
538C22—208no—
539C22#9202812yes—
540C22D3×#71312yes—
541C22C2×#678012yes—
542C22C23×D3×D511yescharacteristic
543C4—24no—
544C4—34no—
545C4—64no—
546C4—62no—
547C4—102no—
548C4—102no—
549C4—302no—
550C4—304no—
551C4—302no—
552C4C2×#678014yes—
553C3C2×#6606611yescharacteristic, complemented, Sylow
554C2—204no—
555C2#1175520614yesdirect product factor
556C2C2×#9202811yescharacteristic
557C2C2×D3×#71311yescharacteristic
558C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic15C2semidirect
2. C2×C5×#944C2semidirect
4. #11755206C2direct (N × H)
5. C2×C4×#1204C2semidirect
7. C2×#91422C2semidirect
8. C2×#91394C2semidirect
10. C2×#91366C2semidirect
11. C2×#91362C2semidirect
12. C2×Dic5×Dic6C2semidirect
19. Q8×Dic15C22semidirect
24. C5×#944C22semidirect
40. C4×#1204C22semidirect
42. #91422C22semidirect
43. #91394C22semidirect
45. #91366C22semidirect
46. #91362C22semidirect
47. Dic5×Dic6C22semidirect
102. C2×#944D5semidirect
190. #944C2×D5semidirect
383. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
494. C2×C5#5671semidirect
530. C2×C3#66066semidirect
534. C5C2×#5671semidirect
553. C3C2×#66066semidirect
555. C2#11755206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic152
C2×C5×#9442
C2×C3×#40932
#117552062
C2×C4×#12042
C2×Dic3×D202
C2×#914222
C2×#913942
C2×#913682
C2×#913662
C2×#913622
C2×Dic5×Dic62
C2×#660663
C2×#56715