Finite Group Databasebeta

← #14484535

Subgroups — #14484535

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D15C211yesmaximal, characteristic
2C5×#5570C211yesmaximal, characteristic, complemented
3C3×#65904C211yesmaximal, characteristic, complemented
4Q8×#1200C212yesmaximal
5#11755147C212yesmaximal, complemented
6#11753620C216yesmaximal
7#11753330C216yesmaximal, complemented
8#11752562C213yesmaximal
9C4×D15⋊Q8C213yesmaximal
10#11752487C213yesmaximal, complemented
11#11752481C213yesmaximal, complemented
12D5×#557—31nomaximal, Hall
13C2×Q8×D15C2211yescharacteristic
14C2×D15⋊Q8C2213yes—
15C3×C4×C5×Q8C2211yescharacteristic
16Q8×Dic15C2211yescharacteristic
17C4⋊C4×D15C2213yes—
18#91776C2213yes—
19C42×D15C2213yes—
20C4×Dic30C2213yes—
21C5×Q8×Dic3C2212yes—
22C5×#890C2216yes—
23C5×#869C2213yes—
24C4×C5×Dic6C2213yes—
25C3×Q8×Dic5C2212yes—
26C3×#4036C2216yes—
27C3×#4015C2213yes—
28C3×C4×Dic10C2213yes—
29#91470C2216yes—
30#91470C2216yes—
31C4×#1204C2216yes—
32#91437C2211yescharacteristic
33#91437C2216yes—
34#91437C2216yes—
35#91404C2216yes—
36C4×#1200C2216yes—
37#91388C2216yes—
38#91385C2216yes—
39#91381C2216yes—
40#91344C2213yes—
41#91340C2216yes—
42#91339C22112yes—
43#91336C22112yes—
44#91333C2216yes—
45#91331C2213yes—
46#91325C2216yes—
47D3×#557—51nomaximal, Hall
48C5×#557—31no—
49D5×C4⋊Q8—33no—
50#66055—33no—
51D5×#125—36no—
52#66019—36no—
53C4×Q8×D5—32no—
54C4×Q8×D5—33no—
55C4×Q8×D5—31no—
56#65904D311yescharacteristic, complemented
57#65903—32no—
58#65901—33no—
59C2×C3×C5×Q8C2311yescharacteristic
60Q8×D15Q818yescomplemented
61C2×C4×D15C2313yes—
62C2×C4×D15C2313yes—
63C2×C4×D15C2311yescharacteristic
64C2×Dic30C2313yes—
65C2×C5×Dic6C2313yes—
66C2×C3×Dic10C2313yes—
67C2×#1204C2316yes—
68C2×#1200C2312yes—
69C2×#1200C2316yes—
70D15⋊Q8—212no—
71C3×C5×C4⋊C4C2313yes—
72C3×C42×C5C2313yes—
73C4⋊Dic15C2313yes—
74#6712C2316yes—
75C4×Dic15C2313yes—
76C4×Dic15C2313yes—
77C4×Dic15C2313yes—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×C4⋊Dic3C2316yes—
80C5×C4⋊Dic3C2316yes—
81C5×Dic3⋊C4C2316yes—
82C4×C5×Dic3C2316yes—
83C3×C4⋊Dic5C2316yes—
84C3×C4⋊Dic5C2316yes—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×#683C2316yes—
87C3×C4×Dic5C2316yes—
88Dic3⋊Dic5C2316yes—
89#6669C2312yes—
90#6669C23112yes—
91#6669C23112yes—
92#6668C2316yes—
93Dic3×Dic5C2316yes—
94Dic3×Dic5C2316yes—
95C3×#557—51no—
96D3×C4⋊Q8—53no—
97#5721—53no—
98D3×#125—56no—
99#5685—56no—
100C4×D3×Q8—51no—
101C4×D3×Q8—52no—
102C4×D3×Q8—53no—
103#5570D511yescharacteristic, complemented
104#5569—52no—
105#5567—53no—
106C2×Q8×D5—31no—
107C2×Q8×D5—33no—
108C5×C4⋊Q8—33no—
109C5×#125—36no—
110C4×C5×Q8—32no—
111C4×C5×Q8—33no—
112C4×C5×Q8C2×D311yescharacteristic
113Q8×Dic5—31no—
114Q8×Dic5—33no—
115Q8×Dic5C2×D312yes—
116#4090—36no—
117D5×C4⋊C4—33no—
118D5×C4⋊C4—36no—
119D5×C4⋊C4—36no—
120D5×C4⋊C4—31no—
121D5×C4⋊C4—36no—
122#4036—36no—
123#4036C2×D316yes—
124#4035—312no—
125#4035—312no—
126#4034—36no—
127#4034—36no—
128#4033—33no—
129#4033—33no—
130#4033—36no—
131#4033—36no—
132C42×D5—33no—
133C42×D5—36no—
134#4016—36no—
135#4015C2×D313yes—
136C4×Dic10—33no—
137C4×Dic10—36no—
138C4×Dic10—36no—
139C4×Dic10C2×D313yes—
140C2×#557—151noSylow
141C22×D15C2411yescharacteristic
142C3×C5×Q8C2×Q814yescomplemented
143C2×C3×C4×C5C2413yes—
144C2×C3×C4×C5C2413yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15C2413yes—
147C2×Dic15C2413yes—
148C2×Dic15C2411yescharacteristic
149C4×D15—26no—
150C4×D15C2×Q8112yes—
151C4×D15#4114yes—
152Dic30C2×Q8112yescomplemented
153C2×C5×Dic3C2412yes—
154C2×C5×Dic3C2416yes—
155C5×Dic6—26no—
156C2×C3×Dic5C2412yes—
157C2×C3×Dic5C2416yes—
158C3×Dic10—26no—
159#1204—212no—
160#1200—212no—
161#1200—24no—
162C2×D3×Q8—51no—
163C2×D3×Q8—53no—
164C3×C4⋊Q8—53no—
165C3×#125—56no—
166C3×C4×Q8—52no—
167C3×C4×Q8—53no—
168C3×C4×Q8C2×D511yescharacteristic
169Q8×Dic3—51no—
170Q8×Dic3—53no—
171Q8×Dic3C2×D512yes—
172#944—56no—
173D3×C4⋊C4—53no—
174D3×C4⋊C4—56no—
175D3×C4⋊C4—56no—
176D3×C4⋊C4—51no—
177D3×C4⋊C4—56no—
178#890—56no—
179#890C2×D516yes—
180#889—512no—
181#889—512no—
182#888—56no—
183#888—56no—
184#887—53no—
185#887—53no—
186#887—56no—
187#887—56no—
188C42×D3—53no—
189C42×D3—56no—
190#870—56no—
191#869C2×D513yes—
192C4×Dic6—53no—
193C4×Dic6—56no—
194C4×Dic6—56no—
195C4×Dic6C2×D513yes—
196C2×C5×Q8—33no—
197C2×C5×Q8C22×D311yescharacteristic
198Q8×D5—38no—
199Q8×D5—612no—
200C2×C4×D5—31no—
201C2×C4×D5—33no—
202C2×C4×D5—33no—
203C2×C4×D5—36no—
204C2×C4×D5—32no—
205C2×Dic10—33no—
206C2×Dic10—36no—
207C2×Dic10C22×D313yes—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—36no—
210C5×C4⋊C4—36no—
211C5×C4⋊C4—36no—
212C5×C4⋊C4C22×D313yes—
213C42×C5—36no—
214C42×C5C22×D313yes—
215C4⋊Dic5—33no—
216C4⋊Dic5—36no—
217C4⋊Dic5C22×D316yes—
218C4⋊Dic5C22×D311yescharacteristic
219C4⋊Dic5C22×D316yes—
220#683—36no—
221#683—36no—
222#683—32no—
223#683—312no—
224#683—312no—
225#683C22×D316yes—
226C4×Dic5—33no—
227C4×Dic5—33no—
228C4×Dic5—33no—
229C4×Dic5—36no—
230C4×Dic5—36no—
231C4×Dic5C22×D316yes—
232#557—31no—
233#557—51no—
234#557—152no—
235#557—153no—
236#557—153no—
237#557—156no—
238C2×C4⋊Q8—153no—
239C2×#125—156no—
240C2×C4×Q8—152no—
241C2×C4×Q8—153no—
242C2×C4×Q8—151no—
243C22×C3×C5C2511yescharacteristic
244C2×D15C22×Q812yes—
245C2×D15C2×#4112yes—
246C2×D152−1+412yes—
247C3×C4×C5—23no—
248C3×C4×C5C22×Q816yes—
249C3×C4×C5C2×#4112yes—
250Dic15—23no—
251Dic15C22×Q816yes—
252Dic15C2×#4112yes—
253C3×Dic5—26no—
254C3×Dic5—22no—
255C5×Dic3—26no—
256C5×Dic3—22no—
257C2×C3×Q8—53no—
258C2×C3×Q8C22×D511yescharacteristic
259D3×Q8—58no—
260D3×Q8—1012no—
261C2×C4×D3—53no—
262C2×C4×D3—51no—
263C2×C4×D3—53no—
264C2×C4×D3—52no—
265C2×C4×D3—56no—
266C2×Dic6—53no—
267C2×Dic6—56no—
268C2×Dic6C22×D513yes—
269C3×C4⋊C4—56no—
270C3×C4⋊C4—51no—
271C3×C4⋊C4—56no—
272C3×C4⋊C4—56no—
273C3×C4⋊C4C22×D513yes—
274C3×C42—56no—
275C3×C42C22×D513yes—
276C4⋊Dic3—53no—
277C4⋊Dic3—56no—
278C4⋊Dic3C22×D516yes—
279C4⋊Dic3C22×D511yescharacteristic
280C4⋊Dic3C22×D516yes—
281Dic3⋊C4—56no—
282Dic3⋊C4—52no—
283Dic3⋊C4—512no—
284Dic3⋊C4—512no—
285Dic3⋊C4—56no—
286Dic3⋊C4C22×D516yes—
287C4×Dic3—53no—
288C4×Dic3—53no—
289C4×Dic3—53no—
290C4×Dic3—56no—
291C4×Dic3—56no—
292C4×Dic3C22×D516yes—
293C22×D5—31no—
294C5×Q8—66no—
295C5×Q8D3×Q814yescomplemented
296C2×C4×C5—32no—
297C2×C4×C5—36no—
298C2×C4×C5C23×D313yes—
299C2×C4×C5C23×D313yes—
300C2×C4×C5C23×D311yescharacteristic
301C2×Dic5—33no—
302C2×Dic5—31no—
303C2×Dic5—33no—
304C2×Dic5C23×D312yes—
305C2×Dic5C23×D316yes—
306C4×D5—312no—
307C4×D5—34no—
308C4×D5—64no—
309C4×D5—612no—
310C4×D5—66no—
311Dic10—26no—
312Dic10—312no—
313Dic10—612no—
314C22×Q8—153no—
315C22×Q8—151no—
316C4⋊Q8—33no—
317C4⋊Q8—53no—
318C4⋊Q8—156no—
319C4⋊Q8—156no—
320C4⋊Q8—156no—
321#125—36no—
322#125—56no—
323#125—156no—
324#125—156no—
325#125—1512no—
326#125—1512no—
327C4×Q8—32no—
328C4×Q8—33no—
329C4×Q8—52no—
330C4×Q8—53no—
331C4×Q8—156no—
332C4×Q8—156no—
333C4×Q8—156no—
334C4×Q8—156no—
335C4×Q8—153no—
336C4×Q8—153no—
337C4×Q8—151no—
338C4×Q8—153no—
339C4×Q8—153no—
340C4×Q8D3×D511yescharacteristic
341C2×C4⋊C4—151no—
342C2×C4⋊C4—156no—
343C2×C4⋊C4—156no—
344C2×C4⋊C4—156no—
345C2×C4⋊C4—153no—
346C2×C42—156no—
347C2×C42—153no—
348C2×C3×C5C23×Q811yescharacteristic
349C2×C3×C5C22×#4111yescharacteristic
350C2×C3×C5C2×2−1+411yescharacteristic
351D15#55714yescomplemented
352C22×D3—51no—
353C3×Q8—106no—
354C3×Q8Q8×D514yescomplemented
355C2×C3×C4—52no—
356C2×C3×C4—56no—
357C2×C3×C4C23×D513yes—
358C2×C3×C4C23×D513yes—
359C2×C3×C4C23×D511yescharacteristic
360C2×Dic3—53no—
361C2×Dic3—51no—
362C2×Dic3—53no—
363C2×Dic3C23×D512yes—
364C2×Dic3C23×D516yes—
365C4×D3—512no—
366C4×D3—54no—
367C4×D3—104no—
368C4×D3—1012no—
369C4×D3—106no—
370Dic6—26no—
371Dic6—512no—
372Dic6—1012no—
373C22×C5C24×D311yescharacteristic
374C2×D5—32no—
375C2×D5—32no—
376C2×D5—32no—
377C4×C5—23no—
378C4×C5—66no—
379C4×C5—62no—
380C4×C5C2×D3×Q816yes—
381C4×C5D3×#4112yes—
382Dic5—26no—
383Dic5—22no—
384Dic5—36no—
385Dic5—32no—
386Dic5—63no—
387C2×Q8—33no—
388C2×Q8—53no—
389C2×Q8—156no—
390C2×Q8—158no—
391C2×Q8—153no—
392C2×Q8—3012no—
393C2×Q8C2×D3×D511yescharacteristic
394C22×C4—152no—
395C22×C4—156no—
396C22×C4—153no—
397C22×C4—151no—
398C22×C4—153no—
399C4⋊C4—31no—
400C4⋊C4—36no—
401C4⋊C4—36no—
402C4⋊C4—36no—
403C4⋊C4—51no—
404C4⋊C4—56no—
405C4⋊C4—56no—
406C4⋊C4—56no—
407C4⋊C4—152no—
408C4⋊C4—156no—
409C4⋊C4—156no—
410C4⋊C4—1512no—
411C4⋊C4—1512no—
412C4⋊C4—156no—
413C4⋊C4—153no—
414C4⋊C4C2×D3×D513yes—
415C42—36no—
416C42—56no—
417C42—156no—
418C42—156no—
419C42—153no—
420C42—153no—
421C42—153no—
422C42C2×D3×D513yes—
423C3×C5C2×#55711yescharacteristic, complemented, Hall
424C22×C3C24×D511yescharacteristic
425C2×D3—52no—
426C2×D3—52no—
427C2×D3—52no—
428C3×C4—23no—
429C3×C4—106no—
430C3×C4—102no—
431C3×C4C2×Q8×D516yes—
432C3×C4D5×#4112yes—
433Dic3—26no—
434Dic3—22no—
435Dic3—56no—
436Dic3—52no—
437Dic3—103no—
438C2×C5C22×D3×Q811yescharacteristic
439C2×C5C2×D3×#4111yescharacteristic
440C2×C5D3×2−1+411yescharacteristic
441D5—34no—
442C23—151no—
443Q8—66no—
444Q8—106no—
445Q8—1512no—
446Q8—3012no—
447Q8D15⋊Q814yescomplemented
448C2×C4—32no—
449C2×C4—36no—
450C2×C4—52no—
451C2×C4—56no—
452C2×C4—153no—
453C2×C4—151no—
454C2×C4—1512no—
455C2×C4—154no—
456C2×C4—153no—
457C2×C4—306no—
458C2×C4—3012no—
459C2×C4—304no—
460C2×C4C22×D3×D513yes—
461C2×C4C22×D3×D513yes—
462C2×C4C22×D3×D511yescharacteristic
463C2×C3C22×Q8×D511yescharacteristic
464C2×C3C2×D5×#4111yescharacteristic
465C2×C3D5×2−1+411yescharacteristic
466D3—54no—
467C5D3×#55711yescharacteristic, complemented, Sylow
468C22—152no—
469C22—152no—
470C22—152no—
471C22C23×D3×D511yescharacteristic
472C4—23no—
473C4—62no—
474C4—66no—
475C4—102no—
476C4—106no—
477C4—156no—
478C4—152no—
479C4—303no—
480C4C2×D15⋊Q816yes—
481C4#9203412yes—
482C3D5×#55711yescharacteristic, complemented, Sylow
483C2—154no—
484C2C22×D15⋊Q811yescharacteristic
485C2C2×#9203411yescharacteristic
486C2#1175705711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC22×D15C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#557
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5570C2semidirect
3. C3×#65904C2semidirect
5. #11755147C2semidirect
7. #11753330C2semidirect
10. #11752487C2semidirect
11. #11752481C2semidirect
56. #65904D3semidirect
60. Q8×D15Q8semidirect
103. #5570D5semidirect
142. C3×C5×Q8C2×Q8semidirect
152. Dic30C2×Q8semidirect
295. C5×Q8D3×Q8semidirect
351. D15#557semidirect
354. C3×Q8Q8×D5semidirect
423. C3×C5C2×#557semidirect
447. Q8D15⋊Q8semidirect
467. C5D3×#557semidirect
482. C3D5×#557semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D152
C5×#55702
C3×#659042
Q8×#12002
#117551472
#117536202
#117533302
#117525622
C4×D15⋊Q82
#117524872
#117524812
D5×#5573
D3×#5575