Finite Group Databasebeta

← #14430088

Subgroups — #14430088

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D15C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic
3C5×#5021C211yesmaximal, characteristic, complemented
4C3×#65310C211yesmaximal, characteristic, complemented
5#11749362C212yesmaximal, complemented
6#11749203C212yesmaximal
7#11747438C212yesmaximal
8#11747182C212yesmaximal, complemented
9#11747000C211yesmaximal, characteristic
10#11746963C211yesmaximal, characteristic, complemented
11#11746917C211yesmaximal, characteristic, complemented
12D5×#477—31nomaximal, Hall
13C2×Q8×D15C2211yescharacteristic
14C2×D15⋊Q8—21no—
15C3×C4×C5×Q8C2211yescharacteristic
16Q8×Dic15C2211yescharacteristic
17C4⋊C4×D15—21no—
18C4⋊C4×D15C2211yescharacteristic
19#91776—21no—
20#91776C2211yescharacteristic
21C42×D15—21no—
22C42×D15C2211yescharacteristic
23C4×Dic30—21no—
24C4×Dic30C2211yescharacteristic
25C5×#869C2211yescharacteristic
26C3×#4015C2211yescharacteristic
27#91470—21no—
28#91470C2212yes—
29#91437—21no—
30#91437C2212yes—
31#91385—21no—
32C2×#6648C2212yes—
33C5×#835C2212yes—
34C5×#807C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3967C2212yes—
37C3×#3939C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90990C2212yes—
40#90988C2212yes—
41#90983C2212yes—
42#90975C2212yes—
43#90974C2212yes—
44D3×#477—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46C4×Q8×D5—31no—
47C5×#477—31no—
48#65380—31no—
49#65310D311yescharacteristic, complemented
50D5×#107—32no—
51#65164—32no—
52#65139—31no—
53D5×C4⋊C8—31no—
54D5×#103—32no—
55#65083—32no—
56C2×C3×C5×Q8C2311yescharacteristic
57Q8×D15—22no—
58Q8×D15Q814yescomplemented
59C2×C4×D15—21no—
60C2×C4×D15—21no—
61C2×C4×D15D411yescharacteristic
62C2×C4×D15D411yescharacteristic
63C2×C4×D15C2311yescharacteristic
64C2×Dic30—21no—
65C2×Dic30C2311yescharacteristic
66C2×C5×Dic6—21no—
67C2×C3×Dic10—21no—
68C2×#1204—22no—
69C2×#1200—22no—
70D15⋊Q8—44no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C42×C5—21no—
74C3×C42×C5C2311yescharacteristic
75C4⋊Dic15—21no—
76C4⋊Dic15C2311yescharacteristic
77#6712—21no—
78#6712—21no—
79#6712—21no—
80C4×Dic15—21no—
81C4×Dic15—21no—
82C4×Dic15—21no—
83C4×Dic15D411yescharacteristic
84C4×Dic15D411yescharacteristic
85C4×Dic15C2311yescharacteristic
86C5×C4⋊Dic3—21no—
87C5×C4⋊Dic3C2312yes—
88C2×C5×C3⋊C8C2312yes—
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2312yes—
91C2×C3×#168C2312yes—
92#6669—22no—
93#6669—22no—
94#6648—24no—
95D3×C4⋊Q8—51no—
96C4×D3×Q8—51no—
97C3×#477—51no—
98#5091—51no—
99#5021D511yescharacteristic, complemented
100D3×#107—52no—
101#4875—52no—
102#4850—51no—
103D3×C4⋊C8—51no—
104D3×#103—52no—
105#4793—52no—
106C2×Q8×D5—31no—
107C2×Q8×D5—61no—
108C5×C4⋊Q8—31no—
109C4×C5×Q8C2×D311yescharacteristic
110Q8×Dic5—31no—
111#4090—61no—
112C2×C8×D5—32no—
113D5×C4⋊C4—31no—
114D5×C4⋊C4—32no—
115D5×C4⋊C4—61no—
116D5×C4⋊C4—61no—
117#4034—32no—
118#4034—61no—
119#4033—31no—
120#4033—61no—
121C42×D5—31no—
122C42×D5—61no—
123#4015C2×D311yescharacteristic
124C4×Dic10—31no—
125C4×Dic10—61no—
126C5×#107—32no—
127C5×C4⋊C8—31no—
128C5×#103—32no—
129#3967C2×D312yes—
130#3950—32no—
131#3948—32no—
132#3946—32no—
133#3942—32no—
134#3939—32no—
135#3939C2×D312yes—
136C4⋊#168C2×D311yescharacteristic
137C2×#477—151noSylow
138C22×D15C2×D411yescharacteristic
139C3×C5×Q8—21no—
140C3×C5×Q8C2×Q812yescomplemented
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15C2×D411yescharacteristic
149C2×Dic15C2×D411yescharacteristic
150C2×Dic15C2×D411yescharacteristic
151C4×D15—24no—
152C4×D15—22no—
153C4×D15—42no—
154C4×D15Q1614yes—
155C4×D15C2×Q812yes—
156C4×D15#4112yes—
157Dic30—21no—
158Dic30—24no—
159Dic30C2×Q812yescomplemented
160C2×C5×Dic3—22no—
161C5×Dic6—42no—
162C2×C3×Dic5—22no—
163C3×Dic10—42no—
164#1204—44no—
165#1200—44no—
166C3×#168—22no—
167C5×C3⋊C8—22no—
168C2×D3×Q8—51no—
169C2×D3×Q8—101no—
170C3×C4⋊Q8—51no—
171C3×C4×Q8C2×D511yescharacteristic
172Q8×Dic3—51no—
173#944—101no—
174C2×D3×C8—52no—
175D3×C4⋊C4—51no—
176D3×C4⋊C4—52no—
177D3×C4⋊C4—101no—
178D3×C4⋊C4—101no—
179#888—52no—
180#888—101no—
181#887—51no—
182#887—101no—
183C42×D3—51no—
184C42×D3—101no—
185#869C2×D511yescharacteristic
186C4×Dic6—51no—
187C4×Dic6—101no—
188C3×#107—52no—
189C3×C4⋊C8—51no—
190C3×#103—52no—
191#835C2×D512yes—
192#818—52no—
193#816—52no—
194Dic3⋊C8—52no—
195#810—52no—
196#807—52no—
197#807C2×D512yes—
198C4⋊(C3⋊C8)C2×D511yescharacteristic
199C2×C5×Q8—61no—
200C2×C5×Q8C22×D311yescharacteristic
201Q8×D5—34no—
202Q8×D5—62no—
203Q8×D5—124no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—61no—
208C2×C4×D5—62no—
209C2×C4×D5—61no—
210C2×Dic10—21no—
211C2×Dic10—31no—
212C2×Dic10—61no—
213C2×Dic10—62no—
214C2×C5×C8—32no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—32no—
217C5×C4⋊C4—61no—
218C5×C4⋊C4C22×D311yescharacteristic
219C42×C5—21no—
220C42×C5C22×D311yescharacteristic
221C4⋊Dic5—21no—
222C4⋊Dic5—31no—
223C4⋊Dic5—61no—
224C4⋊Dic5C22×D312yes—
225#683—62no—
226#683—62no—
227#683—61no—
228#683—61no—
229#683—61no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—31no—
233C4×Dic5—61no—
234C4×Dic5—61no—
235C4×Dic5—61no—
236C2×#168C22×D312yes—
237C8×D5—64no—
238C2×C4⋊Q8—151no—
239C2×C4×Q8—151no—
240#477—31no—
241#477—51no—
242#477—152no—
243#477—151no—
244#477—151no—
245#477—152no—
246C2×#107—152no—
247C2×C4⋊C8—151no—
248C2×#103—152no—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15C22⋊Q812yes—
251C2×D15C2×Q1612yes—
252C2×D15AGL(1,ℤ/8)12yes—
253C3×C4×C5—22no—
254C3×C4×C5—21no—
255C3×C4×C5—41no—
256C3×C4×C5C2×Q1612yes—
257C3×C4×C5C22×Q811yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—22no—
260Dic15—21no—
261Dic15—41no—
262Dic15C22⋊Q812yes—
263Dic15C2×Q1612yes—
264C3×Dic5—42no—
265C5×Dic3—42no—
266C2×C3×Q8—101no—
267C2×C3×Q8C22×D511yescharacteristic
268D3×Q8—54no—
269D3×Q8—102no—
270D3×Q8—204no—
271C2×C4×D3—51no—
272C2×C4×D3—51no—
273C2×C4×D3—51no—
274C2×C4×D3—101no—
275C2×C4×D3—102no—
276C2×C4×D3—101no—
277C2×Dic6—21no—
278C2×Dic6—51no—
279C2×Dic6—101no—
280C2×Dic6—102no—
281C2×C3×C8—52no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—52no—
284C3×C4⋊C4—101no—
285C3×C4⋊C4C22×D511yescharacteristic
286C3×C42—21no—
287C3×C42C22×D511yescharacteristic
288C4⋊Dic3—21no—
289C4⋊Dic3—51no—
290C4⋊Dic3—101no—
291C4⋊Dic3C22×D512yes—
292Dic3⋊C4—102no—
293Dic3⋊C4—102no—
294Dic3⋊C4—101no—
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—51no—
298C4×Dic3—51no—
299C4×Dic3—51no—
300C4×Dic3—101no—
301C4×Dic3—101no—
302C4×Dic3—101no—
303C2×C3⋊C8C22×D512yes—
304D3×C8—104no—
305C22×D5—31no—
306C5×Q8—21no—
307C5×Q8—122no—
308C5×Q8D3×Q812yescomplemented
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—62no—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—22no—
316C2×Dic5—31no—
317C2×Dic5—31no—
318C2×Dic5—31no—
319C2×Dic5—61no—
320C2×Dic5—61no—
321C4×D5—34no—
322C4×D5—32no—
323C4×D5—32no—
324C4×D5—62no—
325C4×D5—64no—
326C4×D5—124no—
327C4×D5—122no—
328Dic10—32no—
329Dic10—42no—
330Dic10—64no—
331Dic10—61no—
332Dic10—124no—
333C5×C8—62no—
334#168—22no—
335C22×Q8—151no—
336C22×Q8—301no—
337C22×C8—152no—
338C4⋊Q8—31no—
339C4⋊Q8—51no—
340C4⋊Q8—152no—
341C4⋊Q8—301no—
342C4⋊Q8—301no—
343C4×Q8—151no—
344C4×Q8—151no—
345C4×Q8—151no—
346C4×Q8—301no—
347C4×Q8—301no—
348C4×Q8D3×D511yescharacteristic
349C2×C4⋊C4—152no—
350C2×C4⋊C4—151no—
351C2×C4⋊C4—301no—
352C2×C4⋊C4—301no—
353C2×C42—151no—
354C2×C42—301no—
355#107—32no—
356#107—52no—
357#107—152no—
358#107—152no—
359C4⋊C8—31no—
360C4⋊C8—51no—
361C4⋊C8—152no—
362#103—32no—
363#103—52no—
364#103—152no—
365#103—152no—
366C2×C3×C5C2×C22⋊Q811yescharacteristic
367C2×C3×C5C22×Q1611yescharacteristic
368C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
369D15#47714yescomplemented
370C22×D3—51no—
371C3×Q8—21no—
372C3×Q8—202no—
373C3×Q8Q8×D512yescomplemented
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—102no—
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380C2×Dic3—22no—
381C2×Dic3—51no—
382C2×Dic3—51no—
383C2×Dic3—51no—
384C2×Dic3—101no—
385C2×Dic3—101no—
386C4×D3—52no—
387C4×D3—52no—
388C4×D3—54no—
389C4×D3—102no—
390C4×D3—104no—
391C4×D3—204no—
392C4×D3—202no—
393Dic6—42no—
394Dic6—52no—
395Dic6—104no—
396Dic6—101no—
397Dic6—204no—
398C3×C8—102no—
399C3⋊C8—22no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—32no—
402C2×D5—32no—
403C2×D5—32no—
404C4×C5—21no—
405C4×C5—22no—
406C4×C5—41no—
407C4×C5—122no—
408C4×C5D3×Q1612yes—
409C4×C5C2×D3×Q811yescharacteristic
410C4×C5D3×#4111yescharacteristic
411Dic5—32no—
412Dic5—32no—
413Dic5—42no—
414Dic5—61no—
415Dic5—62no—
416Dic5—121no—
417C2×Q8—61no—
418C2×Q8—101no—
419C2×Q8—154no—
420C2×Q8—151no—
421C2×Q8—301no—
422C2×Q8—302no—
423C2×Q8—302no—
424C2×Q8—604no—
425C2×Q8C2×D3×D511yescharacteristic
426C22×C4—151no—
427C22×C4—151no—
428C22×C4—151no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4—302no—
432C2×C8—32no—
433C2×C8—52no—
434C2×C8—304no—
435C4⋊C4—21no—
436C4⋊C4—32no—
437C4⋊C4—52no—
438C4⋊C4—61no—
439C4⋊C4—101no—
440C4⋊C4—151no—
441C4⋊C4—301no—
442C4⋊C4—301no—
443C4⋊C4—301no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—301no—
447C4⋊C4C2×D3×D511yescharacteristic
448C42—21no—
449C42—151no—
450C42—151no—
451C42—151no—
452C42—301no—
453C42—301no—
454C42—301no—
455C42C2×D3×D511yescharacteristic
456C3×C5C2×#47711yescharacteristic, complemented, Hall
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—52no—
459C2×D3—52no—
460C2×D3—52no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—202no—
465C3×C4D5×Q1612yes—
466C3×C4C2×Q8×D511yescharacteristic
467C3×C4D5×#4111yescharacteristic
468Dic3—42no—
469Dic3—52no—
470Dic3—52no—
471Dic3—101no—
472Dic3—102no—
473Dic3—201no—
474C2×C5D3×C22⋊Q811yescharacteristic
475C2×C5C2×D3×Q1611yescharacteristic
476C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
477D5—34no—
478C23—151no—
479Q8—21no—
480Q8—122no—
481Q8—152no—
482Q8—202no—
483Q8—304no—
484Q8—301no—
485Q8—604no—
486Q8D15⋊Q812yescomplemented
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—62no—
490C2×C4—102no—
491C2×C4—151no—
492C2×C4—151no—
493C2×C4—152no—
494C2×C4—152no—
495C2×C4—154no—
496C2×C4—151no—
497C2×C4—302no—
498C2×C4—304no—
499C2×C4—301no—
500C2×C4—301no—
501C2×C4—602no—
502C2×C4—604no—
503C2×C4#679011yescharacteristic
504C2×C4#679011yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—62no—
507C8—102no—
508C2×C3D5×C22⋊Q811yescharacteristic
509C2×C3C2×D5×Q1611yescharacteristic
510C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
511D3—54no—
512C5D3×#47711yescharacteristic, complemented, Sylow
513C22—152no—
514C22—152no—
515C22—152no—
516C22C2×#679011yescharacteristic
517C4—21no—
518C4—22no—
519C4—41no—
520C4—122no—
521C4—152no—
522C4—152no—
523C4—202no—
524C4—301no—
525C4—302no—
526C4—601no—
527C4#9151112yes—
528C4C2×D15⋊Q811yescharacteristic
529C4#9201611yescharacteristic
530C3D5×#47711yescharacteristic, complemented, Sylow
531C2—154no—
532C2#1175438311yescharacteristic
533C2C2×#9151111yescharacteristic
534C2#1175532711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#477
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C5×#5021C2semidirect
4. C3×#65310C2semidirect
5. #11749362C2semidirect
8. #11747182C2semidirect
10. #11746963C2semidirect
11. #11746917C2semidirect
49. #65310D3semidirect
58. Q8×D15Q8semidirect
99. #5021D5semidirect
140. C3×C5×Q8C2×Q8semidirect
159. Dic30C2×Q8semidirect
308. C5×Q8D3×Q8semidirect
369. D15#477semidirect
373. C3×Q8Q8×D5semidirect
456. C3×C5C2×#477semidirect
486. Q8D15⋊Q8semidirect
512. C5D3×#477semidirect
530. C3D5×#477semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D152
#117525622
C5×#50212
C3×#653102
#117493622
#117492032
#117474382
#117471822
#117470002
#117469632
#117469172
D5×#4773
D3×#4775