Finite Group Databasebeta

← #14427751

Subgroups — #14427751

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91264C211yesmaximal, characteristic, complemented
2C2×D3×C8×D5C211yesmaximal, characteristic
3#11753884C212yesmaximal
4D15×#107C211yesmaximal, characteristic, complemented
5C5×#4887C211yesmaximal, characteristic, complemented
6C3×#65176C211yesmaximal, characteristic, complemented
7#11747952C211yesmaximal, characteristic, complemented
8#11747942C211yesmaximal, characteristic, complemented
9#11747490C212yesmaximal, complemented
10#11747353C212yesmaximal, complemented
11#11747341C212yesmaximal, complemented
12D5×#467—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
14C2×D15⋊Q8C2212yes—
15C2×C8×D15C2211yescharacteristic
16C4⋊C4×D15C2212yes—
17C2×C5×Dic12C2211yescharacteristic, complemented
18C2×C5×D3×C8C2211yescharacteristic
19C5×#897C2212yes—
20C2×C3×Dic20C2211yescharacteristic, complemented
21C2×C3×C8×D5C2211yescharacteristic
22C3×#4043C2212yes—
23#91473—22no—
24#91437—22no—
25#91436—22no—
26#91430—22no—
27#91369C2212yes—
28#91359C2212yes—
29C2×#6661C2212yescomplemented
30C2×#6648C2211yescharacteristic
31C2×D3×#168C2211yescharacteristic
32C2×D5×C3⋊C8C2211yescharacteristic
33#91264—24no—
34D3×C8×D5—24no—
35C3×C5×#107C2211yescharacteristic, complemented
36#91102C2211yescharacteristic, complemented
37#91091C2212yescomplemented
38C5×#810C2212yescomplemented
39C3×#3942C2212yescomplemented
40#90973C2212yescomplemented
41#90971C2212yescomplemented
42D3×#467—51nomaximal, Hall
43C2×D5×Q16—31no—
44C22×C8×D5—31no—
45D5×C22⋊Q8—32no—
46C5×#467—31no—
47#65477—31no—
48#65405—31no—
49#65340—32no—
50#65176D311yescharacteristic, complemented
51D5×#107—31no—
52#65102—32no—
53D5×#103—32no—
54C22×D3×D5D411yescharacteristic
55C2×C4×D15—22no—
56C2×C4×D15C2311yescharacteristic
57C2×C4×C5×D3C2311yescharacteristic
58C2×C5×Dic6C2312yes—
59C2×C3×C4×D5C2311yescharacteristic
60C2×C3×Dic10C2312yes—
61C2×#1204—22no—
62C2×#1200—22no—
63C2×#1200D411yescharacteristic
64C2×D3×Dic5D411yescharacteristic
65C2×D5×Dic3D411yescharacteristic
66C4×D3×D5—22no—
67C4×D3×D5—22no—
68D15⋊Q8—24no—
69D15⋊Q8—24no—
70C2×C3×C5×C8C2311yescharacteristic
71C3×C5×C4⋊C4C2312yes—
72C4⋊Dic15C2312yes—
73#6712—22no—
74C2×C3⋊#168C2311yescharacteristic
75C8×D15D414yes—
76C5×(C2×D3)⋊C4—22no—
77C5×C4⋊Dic3—22no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C5×Dic12—22no—
80C5×D3×C8—22no—
81C3×#685—22no—
82C3×C4⋊Dic5—22no—
83C2×C3×#168C2311yescharacteristic
84C3×Dic20—22no—
85C3×C8×D5—22no—
86#6669—22no—
87#6669—22no—
88(C2×D3)⋊Dic5—22no—
89#6665—22no—
90#6661—24no—
91#6648—22no—
92D3×#168—22no—
93D5×C3⋊C8—22no—
94C2×D3×Q16—51no—
95C22×D3×C8—51no—
96D3×C22⋊Q8—52no—
97C3×#467—51no—
98#5188—51no—
99#5116—51no—
100#5051—52no—
101#4887D511yescharacteristic, complemented
102D3×#107—51no—
103#4813—52no—
104D3×#103—52no—
105C2×Q8×D5—32no—
106C22×C4×D5—31no—
107C2×C5×Q16—31no—
108C22×C5×C8—31no—
109C5×C22⋊Q8—32no—
110#4092—32no—
111C2×#689—32no—
112#4070—32no—
113C22×#168—31no—
114D5×Q16—64no—
115C2×Dic20C2×D311yescharacteristic, complemented
116C2×C8×D5—31no—
117C2×C8×D5—31no—
118C2×C8×D5—31no—
119C2×C8×D5—64no—
120C2×C8×D5C2×D311yescharacteristic
121#4043C2×D312yes—
122#4042—62no—
123D5×C4⋊C4—32no—
124D5×C4⋊C4—62no—
125D5×C22⋊C4—62no—
126#4024—62no—
127C5×#107C2×D311yescharacteristic, complemented
128C5×#103—32no—
129#3967—32no—
130#3950—31no—
131#3948—32no—
132#3942C2×D312yescomplemented
133#3939—32no—
134C2×#467—151noSylow
135C22×D15C2×D411yescharacteristic
136C22×C5×D3C2×D411yescharacteristic
137C22×C3×D5C2×D411yescharacteristic
138C2×D3×D5—22no—
139C2×D3×D5—22no—
140C2×D3×D5Q1614yescomplemented
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—22no—
144C2×Dic15C2×D411yescharacteristic
145C4×D15—44no—
146C4×D15C2×D412yes—
147C4×D15#4112yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C2×D411yescharacteristic
150C4×C5×D3—21no—
151C4×C5×D3—21no—
152C5×Dic6—22no—
153C5×Dic6—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5C2×D411yescharacteristic
156C3×C4×D5—21no—
157C3×C4×D5—21no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160#1204—44no—
161#1200—22no—
162#1200—44no—
163D3×Dic5—22no—
164D5×Dic3—22no—
165C3×C5×C8C2×D412yes—
166C3⋊#168C2×D412yes—
167C3×#168—21no—
168C5×C3⋊C8—21no—
169C2×D3×Q8—52no—
170C22×C4×D3—51no—
171C2×C3×Q16—51no—
172C22×C3×C8—51no—
173C3×C22⋊Q8—52no—
174#946—52no—
175C2×#216—52no—
176#924—52no—
177C22×C3⋊C8—51no—
178D3×Q16—104no—
179C2×Dic12C2×D511yescharacteristic, complemented
180C2×D3×C8—51no—
181C2×D3×C8—51no—
182C2×D3×C8—51no—
183C2×D3×C8—104no—
184C2×D3×C8C2×D511yescharacteristic
185#897C2×D512yes—
186#896—102no—
187D3×C4⋊C4—52no—
188D3×C4⋊C4—102no—
189D3×C22⋊C4—102no—
190#878—102no—
191C3×#107C2×D511yescharacteristic, complemented
192C3×#103—52no—
193#835—52no—
194#818—51no—
195#816—52no—
196#810C2×D512yescomplemented
197#807—52no—
198C23×D5—31no—
199C2×C5×Q8—32no—
200C22×C4×C5—31no—
201C22×Dic5—31no—
202Q8×D5—64no—
203Q8×D5—64no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C2×C4×D5—62no—
210C2×C4×D5—62no—
211C2×C4×D5C22×D311yescharacteristic
212C2×Dic10—62no—
213C2×Dic10C22×D312yes—
214C5×Q16—62no—
215C2×C5×C8—31no—
216C2×C5×C8—62no—
217C2×C5×C8C22×D311yescharacteristic
218C5×C4⋊C4—62no—
219C5×C4⋊C4C22×D312yes—
220C5×C22⋊C4—62no—
221C22⋊Dic5—62no—
222#689—64no—
223#685—22no—
224#685—62no—
225C4⋊Dic5—22no—
226C4⋊Dic5—32no—
227#683—62no—
228#683—62no—
229#683—62no—
230C2×#168—31no—
231C2×#168—62no—
232C2×#168C22×D311yescharacteristic
233Dic20—22no—
234C8×D5—22no—
235C8×D5—34no—
236C8×D5—62no—
237C8×D5—62no—
238C22×Q16—151no—
239C23×C8—151no—
240C2×C22⋊Q8—152no—
241#467—31no—
242#467—51no—
243#467—152no—
244#467—152no—
245#467—151no—
246#467—151no—
247C2×#107—151no—
248C2×#103—152no—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15#12112yes—
251C2×D15C2×Q1612yes—
252C2×D15#13512yes—
253C2×C5×D3—21no—
254C2×C5×D3—21no—
255C2×C5×D3C2×Q1612yescomplemented
256C2×C3×D5—21no—
257C2×C3×D5—21no—
258C2×C3×D5C2×Q1612yescomplemented
259D3×D5—28no—
260C3×C4×C5—42no—
261C3×C4×C5C22×D411yescharacteristic
262C3×C4×C5C2×#4111yescharacteristic
263Dic15—42no—
264Dic15#12112yes—
265C3×Dic5—21no—
266C3×Dic5—42no—
267C5×Dic3—21no—
268C5×Dic3—42no—
269C23×D3—51no—
270C2×C3×Q8—52no—
271C22×C3×C4—51no—
272C22×Dic3—51no—
273D3×Q8—104no—
274D3×Q8—104no—
275C2×C4×D3—51no—
276C2×C4×D3—51no—
277C2×C4×D3—51no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C2×C4×D3C22×D511yescharacteristic
283C2×Dic6—102no—
284C2×Dic6C22×D512yes—
285C3×Q16—102no—
286C2×C3×C8—51no—
287C2×C3×C8—102no—
288C2×C3×C8C22×D511yescharacteristic
289C3×C4⋊C4—102no—
290C3×C4⋊C4C22×D512yes—
291C3×C22⋊C4—102no—
292#217—102no—
293#216—104no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3—22no—
297C4⋊Dic3—52no—
298Dic3⋊C4—102no—
299Dic3⋊C4—102no—
300Dic3⋊C4—102no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—102no—
303C2×C3⋊C8C22×D511yescharacteristic
304Dic12—22no—
305D3×C8—22no—
306D3×C8—54no—
307D3×C8—102no—
308D3×C8—102no—
309C23×C5—31no—
310C22×D5—31no—
311C22×D5—34no—
312C22×D5—62no—
313C22×D5—62no—
314C22×D5D3×D411yescharacteristic
315C5×Q8—62no—
316C5×Q8—62no—
317C2×C4×C5—22no—
318C2×C4×C5—31no—
319C2×C4×C5—61no—
320C2×C4×C5—61no—
321C2×C4×C5—62no—
322C2×C4×C5C23×D311yescharacteristic
323C2×Dic5—22no—
324C2×Dic5—31no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5D3×D411yescharacteristic
328C4×D5—21no—
329C4×D5—21no—
330C4×D5—32no—
331C4×D5—32no—
332C4×D5—62no—
333C4×D5—62no—
334C4×D5—124no—
335C4×D5—124no—
336Dic10—22no—
337Dic10—22no—
338Dic10—124no—
339C5×C8—61no—
340C5×C8D3×D412yes—
341#168—21no—
342#168—32no—
343C22×Q8—152no—
344C23×C4—151no—
345C2×Q16—31no—
346C2×Q16—51no—
347C2×Q16—152no—
348C2×Q16—304no—
349C22×C8—31no—
350C22×C8—51no—
351C22×C8—151no—
352C22×C8—151no—
353C22×C8—151no—
354C22×C8—151no—
355C22×C8—304no—
356C22⋊Q8—32no—
357C22⋊Q8—52no—
358C22⋊Q8—152no—
359C22⋊Q8—152no—
360C22⋊Q8—302no—
361C22⋊Q8—302no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4—302no—
364C2×C22⋊C4—302no—
365#107—151no—
366#107—152no—
367#107D3×D511yescharacteristic, complemented
368#103—32no—
369#103—52no—
370#103—152no—
371#103—152no—
372C2×C3×C5C2×#12111yescharacteristic
373C2×C3×C5C22×Q1611yescharacteristic
374C2×C3×C5C2×#13511yescharacteristic
375D15#46714yescomplemented
376C3×D5—22no—
377C5×D3—22no—
378C23×C3—51no—
379C22×D3—51no—
380C22×D3—54no—
381C22×D3—102no—
382C22×D3—102no—
383C22×D3D4×D511yescharacteristic
384C3×Q8—102no—
385C3×Q8—102no—
386C2×C3×C4—22no—
387C2×C3×C4—51no—
388C2×C3×C4—101no—
389C2×C3×C4—101no—
390C2×C3×C4—102no—
391C2×C3×C4C23×D511yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—51no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3D4×D511yescharacteristic
397C4×D3—21no—
398C4×D3—21no—
399C4×D3—52no—
400C4×D3—52no—
401C4×D3—102no—
402C4×D3—102no—
403C4×D3—204no—
404C4×D3—204no—
405Dic6—22no—
406Dic6—22no—
407Dic6—204no—
408C3×C8—101no—
409C3×C8D4×D512yes—
410C3⋊C8—21no—
411C3⋊C8—52no—
412C22×C5—32no—
413C22×C5—61no—
414C22×C5—61no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—21no—
417C2×D5—21no—
418C2×D5—32no—
419C2×D5—32no—
420C2×D5—32no—
421C2×D5—68no—
422C2×D5D3×Q1612yescomplemented
423C4×C5—42no—
424C4×C5—61no—
425C4×C5—122no—
426C4×C5C2×D3×D411yescharacteristic
427C4×C5D3×#4111yescharacteristic
428Dic5—21no—
429Dic5—32no—
430Dic5—42no—
431Dic5—122no—
432C24—151no—
433C2×Q8—32no—
434C2×Q8—52no—
435C2×Q8—302no—
436C2×Q8—304no—
437C2×Q8—304no—
438C22×C4—31no—
439C22×C4—51no—
440C22×C4—151no—
441C22×C4—151no—
442C22×C4—151no—
443C22×C4—151no—
444C22×C4—302no—
445C22×C4—302no—
446C22×C4—302no—
447C22×C4—302no—
448Q16—62no—
449Q16—102no—
450Q16—304no—
451C2×C8—31no—
452C2×C8—51no—
453C2×C8—62no—
454C2×C8—102no—
455C2×C8—151no—
456C2×C8—154no—
457C2×C8—302no—
458C2×C8—302no—
459C2×C8—302no—
460C2×C8C2×D3×D511yescharacteristic
461C4⋊C4—62no—
462C4⋊C4—102no—
463C4⋊C4—152no—
464C4⋊C4—302no—
465C4⋊C4—302no—
466C4⋊C4—302no—
467C4⋊C4C2×D3×D512yes—
468C22⋊C4—62no—
469C22⋊C4—102no—
470C22⋊C4—302no—
471C22⋊C4—302no—
472C3×C5C2×#46711yescharacteristic, complemented, Hall
473C22×C3—52no—
474C22×C3—101no—
475C22×C3—101no—
476C22×C3C2×D4×D511yescharacteristic
477C2×D3—21no—
478C2×D3—21no—
479C2×D3—52no—
480C2×D3—52no—
481C2×D3—52no—
482C2×D3—108no—
483C2×D3D5×Q1612yescomplemented
484C3×C4—42no—
485C3×C4—101no—
486C3×C4—202no—
487C3×C4C2×D4×D511yescharacteristic
488C3×C4D5×#4111yescharacteristic
489Dic3—21no—
490Dic3—42no—
491Dic3—52no—
492Dic3—202no—
493C2×C5—62no—
494C2×C5D3×#12111yescharacteristic
495C2×C5C2×D3×Q1611yescharacteristic
496C2×C5D3×#13511yescharacteristic
497D5—22no—
498D5—34no—
499C23—31no—
500C23—51no—
501C23—154no—
502C23—151no—
503C23—302no—
504C23—302no—
505Q8—62no—
506Q8—62no—
507Q8—102no—
508Q8—102no—
509Q8—604no—
510C2×C4—22no—
511C2×C4—31no—
512C2×C4—51no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—102no—
519C2×C4—151no—
520C2×C4—152no—
521C2×C4—152no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4—604no—
528C2×C4C22×D3×D511yescharacteristic
529C8—61no—
530C8—101no—
531C8—152no—
532C8#677712yes—
533C2×C3—102no—
534C2×C3D5×#12111yescharacteristic
535C2×C3C2×D5×Q1611yescharacteristic
536C2×C3D5×#13511yescharacteristic
537D3—22no—
538D3—54no—
539C5D3×#46711yescharacteristic, complemented, Sylow
540C22—32no—
541C22—52no—
542C22—61no—
543C22—61no—
544C22—101no—
545C22—101no—
546C22—152no—
547C22—152no—
548C22—152no—
549C22—308no—
550C22D3×D4×D511yescharacteristic
551C4—42no—
552C4—61no—
553C4—101no—
554C4—122no—
555C4—152no—
556C4—202no—
557C4—602no—
558C4C2×#677711yescharacteristic
559C4#9203411yescharacteristic
560C3D5×#46711yescharacteristic, complemented, Sylow
561C2—62no—
562C2—102no—
563C2—154no—
564C2#1175385011yescharacteristic
565C2#1175405311yescharacteristic
566C2D3×D5×Q1611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC22×D3×D5D4
hypercenter#107D3×D5
hypocenterC3×C5C2×#467
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#91264C2semidirect
4. D15×#107C2semidirect
5. C5×#4887C2semidirect
6. C3×#65176C2semidirect
7. #11747952C2semidirect
8. #11747942C2semidirect
9. #11747490C2semidirect
10. #11747353C2semidirect
11. #11747341C2semidirect
17. C2×C5×Dic12C22semidirect
20. C2×C3×Dic20C22semidirect
29. C2×#6661C22semidirect
35. C3×C5×#107C22semidirect
36. #91102C22semidirect
37. #91091C22semidirect
38. C5×#810C22semidirect
39. C3×#3942C22semidirect
40. #90973C22semidirect
41. #90971C22semidirect
50. #65176D3semidirect
101. #4887D5semidirect
115. C2×Dic20C2×D3semidirect
127. C5×#107C2×D3semidirect
132. #3942C2×D3semidirect
140. C2×D3×D5Q16semidirect
179. C2×Dic12C2×D5semidirect
191. C3×#107C2×D5semidirect
196. #810C2×D5semidirect
255. C2×C5×D3C2×Q16semidirect
258. C2×C3×D5C2×Q16semidirect
367. #107D3×D5semidirect
375. D15#467semidirect
422. C2×D5D3×Q16semidirect
472. C3×C5C2×#467semidirect
483. C2×D3D5×Q16semidirect
539. C5D3×#467semidirect
560. C3D5×#467semidirect

Maximal subgroups

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

subgroupindex
C2×#912642
C2×D3×C8×D52
#117538842
D15×#1072
C5×#48872
C3×#651762
#117479522
#117479422
#117474902
#117473532
#117473412
D5×#4673
D3×#4675