Finite Group Databasebeta

← C2×#11747490 #14412290

Subgroups — C2×#11747490 #14412290

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D15⋊Q8C211yesmaximal, characteristic
2C2×C4⋊C4×D15C211yesmaximal, characteristic
3C22×#6648C211yesmaximal, characteristic
4C2×C5×#810C211yesmaximal, characteristic, complemented
5C2×C3×#3942C211yesmaximal, characteristic, complemented
6C2×#90973C211yesmaximal, characteristic, complemented
7C2×#90971C211yesmaximal, characteristic, complemented
8#11747490C218yesmaximal, direct product factor
9C2×D5×#103—31nomaximal, Hall
10C22×C4×D15—21no—
11C22×C4×D15C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1204—21no—
15C22×#1200—21no—
16C2×D15⋊Q8—22no—
17C2×D15⋊Q8—24no—
18C2×D15⋊Q8C418yescomplemented
19C2×D15⋊Q8C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712—21no—
23C4⋊C4×D15—22no—
24C4⋊C4×D15C2214yes—
25C22×C5×C3⋊C8C2211yescharacteristic
26C22×C3×#168C2211yescharacteristic
27C2×#6648—24no—
28C2×#6648C2214yes—
29C5×#810C2214yescomplemented
30C3×#3942C2214yescomplemented
31#90973C2214yescomplemented
32#90971C2214yescomplemented
33C2×D3×#103—51nomaximal, Hall
34C22×Q8×D5—31no—
35C22×C8×D5—31no—
36C2×D5×C4⋊C4—31no—
37C2×C5×#103—31no—
38C2×#3967—31no—
39C2×#3948—31no—
40C2×#3942D311yescharacteristic, complemented
41D5×#103—38no—
42C23×D15D411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—21no—
46C22×Dic15D411yescharacteristic
47C2×C4×D15—24no—
48C2×C4×D15—44no—
49C2×C4×D15C2×C414yes—
50C2×C4×D15D412yes—
51C2×C4×D15D414yes—
52C2×C4×D15C2312yes—
53C22×C5×Dic3—21no—
54C2×C5×Dic6—21no—
55C2×C5×Dic6—22no—
56C2×C5×Dic6C2×C414yescomplemented
57C2×C5×Dic6C2312yes—
58C22×C3×Dic5—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—22no—
61C2×C3×Dic10C2×C414yescomplemented
62C2×C3×Dic10C2312yes—
63C2×#1204—28no—
64C2×#1204—24no—
65C2×#1200—28no—
66C2×#1200—24no—
67D15⋊Q8—216no—
68D15⋊Q8—28no—
69D15⋊Q8C2×C4116yescomplemented
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74#6712—24no—
75C2×C5×C3⋊C8—22no—
76C2×C5×C3⋊C8C2312yes—
77C2×C3×#168—22no—
78C2×C3×#168C2312yes—
79#6648—28no—
80C22×D3×Q8—51no—
81C22×D3×C8—51no—
82C2×D3×C4⋊C4—51no—
83C2×C3×#103—51no—
84C2×#835—51no—
85C2×#816—51no—
86C2×#810D511yescharacteristic, complemented
87D3×#103—58no—
88C22×C5×Q8—31no—
89C2×Q8×D5—38no—
90C2×Q8×D5—34no—
91C2×Q8×D5—62no—
92C2×Q8×D5—64no—
93C22×C4×D5—31no—
94C22×C4×D5—61no—
95C22×C4×D5—61no—
96C22×Dic10—61no—
97C22×Dic10C2×D311yescharacteristic
98C22×C5×C8—31no—
99C2×C5×C4⋊C4C2×D311yescharacteristic
100C2×C4⋊Dic5—31no—
101C2×#683—61no—
102C22×#168C2×D311yescharacteristic
103C2×C8×D5—34no—
104C2×C8×D5—64no—
105D5×C4⋊C4—34no—
106D5×C4⋊C4—62no—
107C5×#103—34no—
108#3967—34no—
109#3948—34no—
110#3942C2×D314yescomplemented
111C22×#103—151noSylow
112C23×C3×C5C2×D411yescharacteristic
113C22×D15C22⋊C414yes—
114C22×D15SD1614yes—
115C22×D15Q1614yes—
116C22×D15C2×D412yes—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—42no—
119C2×C3×C4×C5C22×C412yes—
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5C2411yescharacteristic
123C2×Dic15—22no—
124C2×Dic15—42no—
125C2×Dic15C22⋊C414yes—
126C2×Dic15C2×D412yes—
127C4×D15—48no—
128C4×D15C22⋊C418yes—
129C4×D15C22×C414yes—
130C4×D15C2×D414yes—
131C2×C5×Dic3—24no—
132C2×C5×Dic3—22no—
133C5×Dic6—24no—
134C5×Dic6—22no—
135C5×Dic6C22×C414yescomplemented
136C2×C3×Dic5—24no—
137C2×C3×Dic5—22no—
138C3×Dic10—24no—
139C3×Dic10—22no—
140C3×Dic10C22×C414yescomplemented
141#1204—216no—
142#1200—216no—
143C3×#168—22no—
144C5×C3⋊C8—22no—
145C22×C3×Q8—51no—
146C2×D3×Q8—58no—
147C2×D3×Q8—54no—
148C2×D3×Q8—102no—
149C2×D3×Q8—104no—
150C22×C4×D3—51no—
151C22×C4×D3—101no—
152C22×C4×D3—101no—
153C22×Dic6—101no—
154C22×Dic6C2×D511yescharacteristic
155C22×C3×C8—51no—
156C2×C3×C4⋊C4C2×D511yescharacteristic
157C2×C4⋊Dic3—51no—
158C2×Dic3⋊C4—101no—
159C22×C3⋊C8C2×D511yescharacteristic
160C2×D3×C8—54no—
161C2×D3×C8—104no—
162D3×C4⋊C4—54no—
163D3×C4⋊C4—102no—
164C3×#103—54no—
165#835—54no—
166#816—54no—
167#810C2×D514yescomplemented
168C23×D5—31no—
169C2×C5×Q8—34no—
170C2×C5×Q8—32no—
171C2×C5×Q8—62no—
172C2×C5×Q8—61no—
173C22×C4×C5—21no—
174C22×C4×C5—61no—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—21no—
177C22×Dic5—31no—
178C22×Dic5—61no—
179Q8×D5—316no—
180Q8×D5—616no—
181Q8×D5—68no—
182C2×C4×D5—34no—
183C2×C4×D5—32no—
184C2×C4×D5—34no—
185C2×C4×D5—32no—
186C2×C4×D5—68no—
187C2×C4×D5—64no—
188C2×C4×D5—64no—
189C2×C4×D5—124no—
190C2×Dic10—22no—
191C2×Dic10—21no—
192C2×Dic10—68no—
193C2×Dic10—64no—
194C2×Dic10C4×D314yescomplemented
195C2×Dic10C22×D312yes—
196C2×C5×C8—32no—
197C2×C5×C8—62no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4C22×D312yes—
200C4⋊Dic5—32no—
201C4⋊Dic5—61no—
202#683—64no—
203C2×#168—22no—
204C2×#168C22×D312yes—
205C8×D5—68no—
206C23×Q8—151no—
207C23×C8—151no—
208C22×C4⋊C4—151no—
209C2×#103—31no—
210C2×#103—51no—
211C2×#103—158no—
212C2×#103—151no—
213C2×#103—151no—
214C22×C3×C5C2×C22⋊C412yes—
215C22×C3×C5C2×SD1612yes—
216C22×C3×C5C2×Q1612yes—
217C22×C3×C5C22×D411yescharacteristic
218C2×D15#103116yescomplemented
219C2×D15C2×C22⋊C414yes—
220C2×D15C2×SD1614yes—
221C2×D15C2×Q1614yes—
222C3×C4×C5—42no—
223C3×C4×C5C2×C22⋊C412yes—
224C3×C4×C5C23×C411yescharacteristic
225C3×C4×C5C22×D411yescharacteristic
226Dic15—42no—
227Dic15C2×C22⋊C414yes—
228C3×Dic5—24no—
229C5×Dic3—24no—
230C23×D3—51no—
231C2×C3×Q8—54no—
232C2×C3×Q8—52no—
233C2×C3×Q8—102no—
234C2×C3×Q8—101no—
235C22×C3×C4—21no—
236C22×C3×C4—101no—
237C22×C3×C4C22×D511yescharacteristic
238C22×Dic3—21no—
239C22×Dic3—51no—
240C22×Dic3—101no—
241D3×Q8—516no—
242D3×Q8—108no—
243D3×Q8—1016no—
244C2×C4×D3—54no—
245C2×C4×D3—52no—
246C2×C4×D3—54no—
247C2×C4×D3—52no—
248C2×C4×D3—104no—
249C2×C4×D3—108no—
250C2×C4×D3—104no—
251C2×C4×D3—204no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6—104no—
255C2×Dic6—108no—
256C2×Dic6C4×D514yescomplemented
257C2×Dic6C22×D512yes—
258C2×C3×C8—52no—
259C2×C3×C8—102no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4C22×D512yes—
262C4⋊Dic3—52no—
263C4⋊Dic3—101no—
264Dic3⋊C4—104no—
265C2×C3⋊C8—22no—
266C2×C3⋊C8C22×D512yes—
267D3×C8—108no—
268C23×C5D3×D411yescharacteristic
269C22×D5—34no—
270C22×D5—34no—
271C22×D5—34no—
272C22×D5—32no—
273C5×Q8—34no—
274C5×Q8—64no—
275C5×Q8—62no—
276C2×C4×C5—22no—
277C2×C4×C5—42no—
278C2×C4×C5—64no—
279C2×C4×C5—62no—
280C2×C4×C5C2×C4×D312yes—
281C2×C4×C5D3×D412yes—
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—24no—
285C2×Dic5—22no—
286C2×Dic5—34no—
287C2×Dic5—32no—
288C2×Dic5—62no—
289C2×Dic5—122no—
290C4×D5—38no—
291C4×D5—34no—
292C4×D5—34no—
293C4×D5—616no—
294C4×D5—128no—
295Dic10—24no—
296Dic10—22no—
297Dic10—616no—
298Dic10C2×C4×D314yescomplemented
299C5×C8—62no—
300#168—22no—
301C22×Q8—31no—
302C22×Q8—51no—
303C22×Q8—154no—
304C22×Q8—158no—
305C22×Q8—301no—
306C22×Q8—304no—
307C22×Q8—302no—
308C23×C4—151no—
309C23×C4—301no—
310C23×C4—301no—
311C22×C8—31no—
312C22×C8—51no—
313C22×C8—154no—
314C22×C8—304no—
315C2×C4⋊C4—151no—
316C2×C4⋊C4—154no—
317C2×C4⋊C4—302no—
318C2×C4⋊C4—301no—
319C2×C4⋊C4D3×D511yescharacteristic
320#103—34no—
321#103—54no—
322#103—154no—
323#103—154no—
324C2×C3×C5C2×#10314yescomplemented
325C2×C3×C5C22×C22⋊C411yescharacteristic
326C2×C3×C5C22×SD1611yescharacteristic
327C2×C3×C5C22×Q1611yescharacteristic
328D15C2×#10318yescomplemented
329C23×C3D4×D511yescharacteristic
330C22×D3—52no—
331C22×D3—54no—
332C22×D3—54no—
333C22×D3—54no—
334C3×Q8—54no—
335C3×Q8—102no—
336C3×Q8—104no—
337C2×C3×C4—22no—
338C2×C3×C4—42no—
339C2×C3×C4—102no—
340C2×C3×C4—104no—
341C2×C3×C4C2×C4×D512yes—
342C2×C3×C4D4×D512yes—
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—24no—
347C2×Dic3—52no—
348C2×Dic3—54no—
349C2×Dic3—102no—
350C2×Dic3—202no—
351C4×D3—54no—
352C4×D3—54no—
353C4×D3—58no—
354C4×D3—1016no—
355C4×D3—208no—
356Dic6—22no—
357Dic6—24no—
358Dic6—1016no—
359Dic6C2×C4×D514yescomplemented
360C3×C8—102no—
361C3⋊C8—22no—
362C22×C5D3×C22⋊C412yes—
363C22×C5D3×SD1612yes—
364C22×C5D3×Q1612yes—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—34no—
367C2×D5—34no—
368C2×D5—34no—
369C2×D5—316no—
370C4×C5—42no—
371C4×C5—64no—
372C4×C5D3×C22⋊C412yes—
373C4×C5C22×C4×D311yescharacteristic
374C4×C5C2×D3×D411yescharacteristic
375Dic5—24no—
376Dic5—34no—
377Dic5—122no—
378C24—151no—
379C2×Q8—34no—
380C2×Q8—32no—
381C2×Q8—54no—
382C2×Q8—52no—
383C2×Q8—62no—
384C2×Q8—61no—
385C2×Q8—102no—
386C2×Q8—101no—
387C2×Q8—1516no—
388C2×Q8—308no—
389C2×Q8—304no—
390C2×Q8—3016no—
391C2×Q8—308no—
392C22×C4—21no—
393C22×C4—61no—
394C22×C4—101no—
395C22×C4—151no—
396C22×C4—154no—
397C22×C4—154no—
398C22×C4—152no—
399C22×C4—152no—
400C22×C4—304no—
401C22×C4—308no—
402C22×C4—304no—
403C22×C4—301no—
404C22×C4—604no—
405C22×C4C2×D3×D511yescharacteristic
406C2×C8—32no—
407C2×C8—52no—
408C2×C8—62no—
409C2×C8—102no—
410C2×C8—308no—
411C4⋊C4—21no—
412C4⋊C4—152no—
413C4⋊C4—304no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D512yes—
416C3×C5C22×#10311yescharacteristic, complemented, Hall
417C22×C3D5×C22⋊C412yes—
418C22×C3D5×SD1612yes—
419C22×C3D5×Q1612yes—
420C22×C3C2×D4×D511yescharacteristic
421C2×D3—54no—
422C2×D3—54no—
423C2×D3—54no—
424C2×D3—516no—
425C3×C4—42no—
426C3×C4—104no—
427C3×C4D5×C22⋊C412yes—
428C3×C4C22×C4×D511yescharacteristic
429C3×C4C2×D4×D511yescharacteristic
430Dic3—24no—
431Dic3—54no—
432Dic3—202no—
433C2×C5D3×#10314yescomplemented
434C2×C5C2×D3×C22⋊C411yescharacteristic
435C2×C5C2×D3×SD1611yescharacteristic
436C2×C5C2×D3×Q1611yescharacteristic
437D5—38no—
438C23—154no—
439C23—154no—
440C23—154no—
441C23—152no—
442C23#679011yescharacteristic
443Q8—34no—
444Q8—54no—
445Q8—64no—
446Q8—62no—
447Q8—104no—
448Q8—102no—
449Q8—3016no—
450C2×C4—22no—
451C2×C4—42no—
452C2×C4—64no—
453C2×C4—62no—
454C2×C4—104no—
455C2×C4—102no—
456C2×C4—154no—
457C2×C4—152no—
458C2×C4—158no—
459C2×C4—154no—
460C2×C4—154no—
461C2×C4—3016no—
462C2×C4—302no—
463C2×C4—608no—
464C2×C4—602no—
465C2×C4C4×D3×D512yes—
466C2×C4#677712yes—
467C2×C4#679011yescharacteristic
468C2×C4C22×D3×D511yescharacteristic
469C8—62no—
470C8—102no—
471C2×C3D5×#10314yescomplemented
472C2×C3C2×D5×C22⋊C411yescharacteristic
473C2×C3C2×D5×SD1611yescharacteristic
474C2×C3C2×D5×Q1611yescharacteristic
475D3—58no—
476C5C2×D3×#10311yescharacteristic, complemented, Sylow
477C22—154no—
478C22—154no—
479C22—1516no—
480C22—154no—
481C22#9147312yes—
482C22#9148712yes—
483C22#9151112yes—
484C22C2×#679011yescharacteristic
485C4—42no—
486C4—64no—
487C4—104no—
488C4—154no—
489C4—602no—
490C4#9147312yes—
491C4C2×C4×D3×D511yescharacteristic
492C4C2×#677711yescharacteristic
493C3C2×D5×#10311yescharacteristic, complemented, Sylow
494C2—158no—
495C2#1174749014yesdirect product factor
496C2C2×#9147311yescharacteristic
497C2C2×#9148711yescharacteristic
498C2C2×#9151111yescharacteristic
subgroupG/H
centerC23#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C22×#103
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C5×#810C2semidirect
5. C2×C3×#3942C2semidirect
6. C2×#90973C2semidirect
7. C2×#90971C2semidirect
8. #11747490C2direct (N × H)
18. C2×D15⋊Q8C4semidirect
29. C5×#810C22semidirect
30. C3×#3942C22semidirect
31. #90973C22semidirect
32. #90971C22semidirect
40. C2×#3942D3semidirect
56. C2×C5×Dic6C2×C4semidirect
61. C2×C3×Dic10C2×C4semidirect
69. D15⋊Q8C2×C4semidirect
86. C2×#810D5semidirect
110. #3942C2×D3semidirect
135. C5×Dic6C22×C4semidirect
140. C3×Dic10C22×C4semidirect
167. #810C2×D5semidirect
194. C2×Dic10C4×D3semidirect
218. C2×D15#103semidirect
256. C2×Dic6C4×D5semidirect
298. Dic10C2×C4×D3semidirect
324. C2×C3×C5C2×#103semidirect
328. D15C2×#103semidirect
359. Dic6C2×C4×D5semidirect
416. C3×C5C22×#103semidirect
433. C2×C5D3×#103semidirect
471. C2×C3D5×#103semidirect
476. C5C2×D3×#103semidirect
493. C3C2×D5×#103semidirect
495. C2#11747490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D15⋊Q82
C2×C4⋊C4×D152
C22×#66482
C2×C5×#8102
C2×C3×#39422
C2×#909732
C2×#909712
#117474902
C2×D5×#1033
C2×D3×#1035