Finite Group Databasebeta

← #14430244

Subgroups — #14430244

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6768C211yesmaximal, characteristic
2#11752484C211yesmaximal, characteristic, complemented
3D15×C4⋊C8C211yesmaximal, characteristic, complemented
4C5×#4846C211yesmaximal, characteristic, complemented
5C3×#65139C211yesmaximal, characteristic, complemented
6#11748145C212yesmaximal
7#11747878C212yesmaximal, complemented
8#11747817C212yesmaximal, complemented
9#11747690C212yesmaximal, complemented
10#11746918C211yesmaximal, characteristic, complemented
11#11746882C211yesmaximal, characteristic, complemented
12#10612695—31nomaximal, Hall
13C2×#6768C2211yescharacteristic
14C2×C8×D15C2212yes—
15C42×D15C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C4×#1203—21no—
21#91435C2211yescharacteristic
22#91406—21no—
23#91400—21no—
24C4×D3×Dic5—21no—
25#91390—21no—
26#91384C2212yes—
27#91383—21no—
28#91347C2212yes—
29#91347C2211yescharacteristic
30#91344—21no—
31#91331—21no—
32#91331C2211yescharacteristic
33C3×C5×C4⋊C8C2211yescharacteristic
34#91098C2212yes—
35C4⋊(C3⋊#168)C2211yescharacteristic
36C5×#821C2212yes—
37C5×#818C2212yes—
38C3×#3950C2212yes—
39C3×#3948C2212yes—
40#90986C2212yes—
41#90986C2212yes—
42#90970C2212yes—
43#90966C2212yes—
44#81107—51nomaximal, Hall
45#66062—31no—
46C4×#711—31no—
47C5×#474—31no—
48#65383—31no—
49#65297—31no—
50#65169—32no—
51#65166—32no—
52#65139D311yescharacteristic, complemented
53D5×C4⋊C8—31no—
54#65061—32no—
55#65055—32no—
56C2×C4×D15D411yescharacteristic
57C2×C4×D15D411yescharacteristic
58C2×C4×D15C2311yescharacteristic
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6—21no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10C2311yescharacteristic
64C2×#1203—21no—
65C2×D3×Dic5—21no—
66C2×D3×Dic5—21no—
67#6768—22no—
68#6768Q814yescomplemented
69C2×C3×C5×C8C2312yes—
70C3×C42×C5C2311yescharacteristic
71C4×Dic15D411yescharacteristic
72C4×Dic15D411yescharacteristic
73C4×Dic15C2311yescharacteristic
74C2×C3⋊#168C2312yes—
75C8×D15—24no—
76C5×(C2×D3)⋊C4—21no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C5×C4⋊Dic3C2311yescharacteristic
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2312yes—
83C3×#683—21no—
84C3×C4×Dic5—21no—
85Dic3⋊Dic5—22no—
86#6668—21no—
87#6668—22no—
88#6667—21no—
89#6667—22no—
90(C2×D3)⋊Dic5—21no—
91Dic3×Dic5—21no—
92Dic3×Dic5—21no—
93Dic3×Dic5—22no—
94#5728—51no—
95C4×#239—51no—
96C3×#477—51no—
97#5084—51no—
98#5020—51no—
99#4891—52no—
100#4880—52no—
101#4846D511yescharacteristic, complemented
102D3×C4⋊C8—51no—
103#4804—52no—
104#4796—52no—
105C2×#711—31no—
106C5×C4⋊Q8—31no—
107C4×C5×D4—31no—
108#4092—61no—
109Q8×Dic5—61no—
110D4×Dic5—31no—
111C4×C22⋊D5—61no—
112C2×C4×Dic5—61no—
113C2×C8×D5—32no—
114#4043—61no—
115#4038—32no—
116#4038—31no—
117#4036—32no—
118#4033—31no—
119#4033—61no—
120#4027—61no—
121#4023—61no—
122C42×D5—31no—
123#4015C2×D311yescharacteristic
124C4×Dic10C2×D311yescharacteristic
125C5×#107—32no—
126C5×C4⋊C8C2×D311yescharacteristic
127C5×#102—32no—
128#3964—32no—
129#3950C2×D312yes—
130#3948C2×D312yes—
131#3946—32no—
132#3942—32no—
133#3940—32no—
134#3940—32no—
135C4⋊#168—31no—
136#3076—151noSylow
137C22×D15C2×D411yescharacteristic
138C22×C5×D3—21no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15C2×D411yescharacteristic
143C2×Dic15C2×D411yescharacteristic
144C2×Dic15C2×D411yescharacteristic
145C4×D15—22no—
146C4×D15—41no—
147C4×D15C2×Q812yes—
148C4×D15#4112yes—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C5×D12—21no—
152C5×D12C2×Q812yes—
153C4×C5×D3—42no—
154C5×Dic6—42no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C3×Dic10—21no—
159C3×Dic10—42no—
160C3×Dic10C2×Q812yes—
161#1203—24no—
162D3×Dic5—24no—
163D3×Dic5—42no—
164C3×C5×C8—22no—
165C3⋊#168—22no—
166C2×#239—51no—
167C3×C4⋊Q8—51no—
168C3×C4×Q8—51no—
169#946—101no—
170Q8×Dic3—51no—
171Q8×Dic3—101no—
172C2×D3×C8—52no—
173#897—101no—
174#893—51no—
175#893—101no—
176#892—51no—
177#892—52no—
178#892—101no—
179#890—52no—
180#887—101no—
181C4×D12—101no—
182C4×D12C2×D511yescharacteristic
183C42×D3—51no—
184C42×D3—101no—
185#869C2×D511yescharacteristic
186C3×#107—52no—
187C3×C4⋊C8C2×D511yescharacteristic
188C3×#103—52no—
189#835—52no—
190#821C2×D512yes—
191#818C2×D512yes—
192Dic3⋊C8—52no—
193#809—52no—
194#808—52no—
195#808—52no—
196C4⋊(C3⋊C8)—51no—
197C2×C5×Q8—61no—
198C2×C5×D4—31no—
199C22×C4×C5—61no—
200C2×C22⋊D5—61no—
201C22×Dic5—61no—
202C22×Dic5—61no—
203#711—34no—
204#711—62no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—31no—
208C2×Dic10—21no—
209C2×Dic10C22×D311yescharacteristic
210C2×C5×C8C22×D312yes—
211C5×C4⋊C4—31no—
212C5×C4⋊C4—32no—
213C5×C4⋊C4—61no—
214C5×C22⋊C4—61no—
215C42×C5C22×D311yescharacteristic
216C22⋊Dic5—61no—
217#685—61no—
218#685—62no—
219C4⋊Dic5—21no—
220C4⋊Dic5—62no—
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D312yes—
223#683—21no—
224#683—61no—
225#683—62no—
226C4×Dic5—21no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—31no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C4×Dic5—62no—
233C2×#168—32no—
234C8×D5—64no—
235#533—151no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—51no—
240#476—151no—
241#475—151no—
242#474—31no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—21no—
248C2×D15—21no—
249C2×D15C22⋊Q812yes—
250C2×C5×D3—22no—
251C2×C5×D3—41no—
252C2×C5×D3—41no—
253C3×C4×C5—21no—
254C3×C4×C5#13512yes—
255C3×C4×C5C22×Q811yescharacteristic
256C3×C4×C5C2×#4111yescharacteristic
257Dic15—21no—
258Dic15—21no—
259Dic15C22⋊Q812yes—
260C3×Dic5—22no—
261C3×Dic5—41no—
262C3×Dic5—42no—
263C5×Dic3—42no—
264C5×Dic3—41no—
265C2×C3×Q8—51no—
266C2×C3×Q8—101no—
267#239—54no—
268#239—102no—
269C2×D12—101no—
270C2×D12C22×D511yescharacteristic
271C2×C4×D3—21no—
272C2×C4×D3—51no—
273C2×C4×D3—51no—
274C2×C4×D3—51no—
275C2×C4×D3—101no—
276C2×C4×D3—101no—
277C2×Dic6—21no—
278C2×C3×C8C22×D512yes—
279C3×C4⋊C4—51no—
280C3×C4⋊C4—52no—
281C3×C4⋊C4—101no—
282C3×C4⋊C4—101no—
283C3×C42—101no—
284C3×C42C22×D511yescharacteristic
285(C2×D3)⋊C4—21no—
286(C2×D3)⋊C4—101no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4—101no—
289C4⋊Dic3—21no—
290C4⋊Dic3—101no—
291C4⋊Dic3—102no—
292C4⋊Dic3C22×D511yescharacteristic
293C4⋊Dic3C22×D512yes—
294Dic3⋊C4—102no—
295C4×Dic3—51no—
296C4×Dic3—51no—
297C4×Dic3—51no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C4×Dic3—102no—
301C2×C3⋊C8—52no—
302D3×C8—104no—
303C23×C5—61no—
304C22×D5—31no—
305C5×Q8—122no—
306C5×D4—32no—
307C5×D4—61no—
308C2×C4×C5—61no—
309C2×C4×C5—62no—
310C2×C4×C5—122no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—64no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5—31no—
319C2×Dic5—31no—
320C2×Dic5—31no—
321C2×Dic5—64no—
322C2×Dic5—122no—
323C4×D5—32no—
324C4×D5—32no—
325C4×D5—62no—
326C4×D5—121no—
327Dic10—21no—
328Dic10—42no—
329Dic10D3×Q812yes—
330C5×C8—22no—
331#168—62no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8—31no—
335C4⋊Q8—51no—
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—51no—
340C4×Q8—151no—
341C4×Q8—301no—
342C4×Q8—301no—
343C4×D4—31no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—151no—
348#117—152no—
349#117—301no—
350C2×C42—151no—
351C2×C42—301no—
352#107—32no—
353#107—52no—
354#106—152no—
355#106—152no—
356C4⋊C8—152no—
357C4⋊C8—151no—
358C4⋊C8D3×D511yescharacteristic
359#103—52no—
360#103—152no—
361#102—32no—
362#102—152no—
363C2×C3×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366D15—22no—
367C5×D3—42no—
368C22×D3—21no—
369C22×D3—51no—
370C3×Q8—52no—
371C3×Q8—101no—
372C3×Q8—202no—
373C2×C3×C4—101no—
374C2×C3×C4—102no—
375C2×C3×C4—101no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—51no—
382C2×Dic3—51no—
383C2×Dic3—51no—
384D12—21no—
385D12—104no—
386D12Q8×D512yes—
387C4×D3—42no—
388C4×D3—52no—
389C4×D3—52no—
390C4×D3—104no—
391C4×D3—102no—
392C4×D3—201no—
393C4×D3—202no—
394Dic6—42no—
395C3×C8—22no—
396C3⋊C8—102no—
397C22×C5—62no—
398C22×C5—121no—
399C22×C5—121no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—32no—
402C2×D5—61no—
403C2×D5—61no—
404C4×C5—21no—
405C4×C5—121no—
406C4×C5—122no—
407C4×C5#91912yes—
408C4×C5C2×D3×Q811yescharacteristic
409C4×C5D3×#4111yescharacteristic
410Dic5—22no—
411Dic5—32no—
412Dic5—42no—
413Dic5—41no—
414Dic5—61no—
415Dic5—61no—
416#41—154no—
417#41—302no—
418C2×Q8—51no—
419C2×Q8—61no—
420C2×Q8—101no—
421C2×D4—31no—
422C2×D4—301no—
423C22×C4—61no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—152no—
430C2×C8—304no—
431C2×C8C2×D3×D512yes—
432C4⋊C4—32no—
433C4⋊C4—31no—
434C4⋊C4—52no—
435C4⋊C4—51no—
436C4⋊C4—61no—
437C4⋊C4—101no—
438C4⋊C4—101no—
439C4⋊C4—301no—
440C4⋊C4—302no—
441C4⋊C4—302no—
442C22⋊C4—61no—
443C22⋊C4—301no—
444C22⋊C4—302no—
445C22⋊C4—301no—
446C42—101no—
447C42—151no—
448C42—151no—
449C42—151no—
450C42—301no—
451C42—301no—
452C42—302no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3C2×D4×D511yescharacteristic
456C2×D3—22no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—52no—
460C2×D3—101no—
461C2×D3—101no—
462C3×C4—21no—
463C3×C4—102no—
464C3×C4—201no—
465C3×C4—202no—
466C3×C4#405812yes—
467C3×C4C2×Q8×D511yescharacteristic
468C3×C4D5×#4111yescharacteristic
469Dic3—42no—
470Dic3—41no—
471Dic3—52no—
472Dic3—101no—
473Dic3—101no—
474C2×C5—122no—
475C2×C5D3×C22⋊Q811yescharacteristic
476C2×C5C2×#91911yescharacteristic
477C2×C5#577311yescharacteristic
478D5—62no—
479C23—61no—
480C23—151no—
481Q8—52no—
482Q8—101no—
483Q8—122no—
484Q8—202no—
485D4—32no—
486D4—61no—
487D4—304no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—102no—
493C2×C4—122no—
494C2×C4—151no—
495C2×C4—152no—
496C2×C4—152no—
497C2×C4—151no—
498C2×C4—151no—
499C2×C4—304no—
500C2×C4—302no—
501C2×C4—601no—
502C2×C4—602no—
503C2×C4#677711yescharacteristic
504C2×C4#677711yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—22no—
507C8—302no—
508C2×C3D5×C22⋊Q811yescharacteristic
509C2×C3C2×#405811yescharacteristic
510C2×C3#6611111yescharacteristic
511D3—42no—
512D3—102no—
513C5#8110711yescharacteristic, complemented, Sylow
514C22—62no—
515C22—121no—
516C22—121no—
517C22—152no—
518C22—301no—
519C22—301no—
520C22C2×#677711yescharacteristic
521C4—21no—
522C4—102no—
523C4—121no—
524C4—122no—
525C4—152no—
526C4—201no—
527C4—202no—
528C4—301no—
529C4—301no—
530C4#9127912yes—
531C4#9202411yescharacteristic
532C4D3×Q8×D511yescharacteristic
533C3#1061269511yescharacteristic, complemented, Sylow
534C2—122no—
535C2—302no—
536C2#1175388411yescharacteristic
537C2C2×#9127911yescharacteristic
538C2#1175403611yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6768C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752484C2semidirect
3. D15×C4⋊C8C2semidirect
4. C5×#4846C2semidirect
5. C3×#65139C2semidirect
7. #11747878C2semidirect
8. #11747817C2semidirect
9. #11747690C2semidirect
10. #11746918C2semidirect
11. #11746882C2semidirect
52. #65139D3semidirect
68. #6768Q8semidirect
101. #4846D5semidirect
454. C3×C5#3076semidirect
513. C5#81107semidirect
533. C3#10612695semidirect

Maximal subgroups

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

subgroupindex
C4×#67682
#117524842
D15×C4⋊C82
C5×#48462
C3×#651392
#117481452
#117478782
#117478172
#117476902
#117469182
#117468822
#106126953
#811075