Finite Group Databasebeta

← #14417105

Subgroups — #14417105

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756586C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic
3#11754488C211yesmaximal, characteristic, complemented
4C5×#5233C211yesmaximal, characteristic, complemented
5#11749241C212yesmaximal, complemented
6#11749239C212yesmaximal, complemented
7#11748995C212yesmaximal, complemented
8#11748993C212yesmaximal, complemented
9#11748460C211yesmaximal, characteristic, complemented
10C2×#90965C211yesmaximal, characteristic, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10610551—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15Q8×Dic15C2212yescomplemented
16D4×Dic15—22no—
17D4×Dic15C2212yescomplemented
18#91815—21no—
19#91815C2211yescharacteristic
20C2×C4⋊Dic15—21no—
21C2×C4⋊Dic15C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4095C418yescomplemented
25C2×C3×#688C2212yes—
26C2×C3×#686C2212yes—
27C2×C3×#681C2211yescharacteristic
28D5×#217—22no—
29#91434C2212yes—
30#91434C2212yes—
31Dic3×D20—21no—
32Dic3×D20—21no—
33C5×#835C2211yescharacteristic, complemented
34C5×#835C2211yescharacteristic, complemented
35C5×#832C2211yescharacteristic, complemented
36C5×#832C2211yescharacteristic, complemented
37#90988C2212yescomplemented
38#90985C2212yescomplemented
39#90965C2212yes—
40#90965C2212yes—
41#90954C2212yescomplemented
42#90951C2212yescomplemented
43#83930—51nomaximal, Hall
44#66161—31no—
45C2×#4095D311yescharacteristic
46#65855—31no—
47C5×#416—31no—
48C2×#3953—31no—
49#65390—31no—
50#65284—31no—
51#65106—32no—
52#65077—32no—
53#65074—32no—
54#65045—32no—
55C23×C3×D5—21no—
56C3×C5×#41—22no—
57C3×C5×#41C2×C414yescomplemented
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15—21no—
64C22×Dic15—22no—
65C2×C3×D20—21no—
66C2×C3×D20—22no—
67C2×C3×D20C2×C414yescomplemented
68C2×C3×D20C2312yes—
69C2×D5×Dic3—22no—
70C2×D5×Dic3—22no—
71#6719—22no—
72#6719D412yes—
73C4⋊Dic15—21no—
74C4⋊Dic15—22no—
75C4⋊Dic15D411yescharacteristic
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15C2312yes—
78C4×Dic15—22no—
79C4×Dic15C2312yes—
80C5×#217—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C5×C4⋊Dic3C2311yescharacteristic
83C4×C5×Dic3—21no—
84C2×C5×C3⋊C8—22no—
85C2×C5×C3⋊C8C2311yescharacteristic
86C2×C5×C3⋊C8C2311yescharacteristic
87C3×#688C2×C418yescomplemented
88C3×#686C2×C418yescomplemented
89C3×#681C2×C414yescomplemented
90C2×C3×#168C2312yes—
91#6665—22no—
92#6665—22no—
93C2×C3×AGL(1,ℤ/8)—51no—
94#5827—51no—
95#5798—51no—
96#5233D511yescharacteristic, complemented
97C2×#832—51no—
98#5164—52no—
99Dic3×SD16—52no—
100#5152—52no—
101Dic3×D8—52no—
102#5122—51no—
103#5121—51no—
104C2×C5×#41C2×D311yescharacteristic
105C22×D20C2×D311yescharacteristic
106C22×C5×C8—31no—
107C5×#117—31no—
108#4095Dic318yescomplemented
109Q8×Dic5—32no—
110C2×#688C2×D312yes—
111D4×Dic5—32no—
112D4×Dic5—62no—
113C2×#686C2×D312yes—
114#4072—31no—
115#4072—61no—
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—61no—
118C2×#681C2×D311yescharacteristic
119#4039—32no—
120#4039—32no—
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#103—31no—
125C5×#103—31no—
126C5×#102—31no—
127C5×#102—31no—
128#3953—32no—
129#3953—32no—
130#3947—32no—
131C8×Dic5—32no—
132#3940—32no—
133#3939—32no—
134#2946—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C22×C3×D5—22no—
138C22×C3×D5—24no—
139C22×C3×D5—81no—
140C22×C3×D5—81no—
141C3×C5×Q8—21no—
142C3×C5×Q8C22×C412yes—
143C3×C5×D4—24no—
144C3×C5×D4—21no—
145C3×C5×D4C22×C412yes—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—24no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15—22no—
153C2×Dic15—82no—
154C2×Dic15—81no—
155C2×Dic15C2×D412yes—
156C2×Dic15C2×D412yes—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C3×D20—24no—
160C3×D20—22no—
161C3×D20C22×C414yes—
162D5×Dic3—82no—
163D5×Dic3—82no—
164C3×#168C22×C414yes—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C2×C3×#41C2×D511yescharacteristic
168C22×C3×D4—51no—
169C3×AGL(1,ℤ/8)—58no—
170C2×C3×SD16—52no—
171C2×C3×D8—52no—
172C2×C3×M16—51no—
173C2×#217—102no—
174Q8×Dic3—52no—
175D4×Dic3—52no—
176D4×Dic3—52no—
177D4×Dic3—52no—
178D4×Dic3—101no—
179D4×Dic3—101no—
180D4×Dic3—102no—
181#926—51no—
182#926—101no—
183#926C2×D511yescharacteristic
184C2×C4⋊Dic3—51no—
185C2×C4⋊Dic3—101no—
186C22×C3⋊C8C2×D511yescharacteristic
187#835C2×D511yescharacteristic, complemented
188#835C2×D511yescharacteristic, complemented
189#832—52no—
190#832—52no—
191#832C2×D511yescharacteristic, complemented
192#832C2×D511yescharacteristic, complemented
193#818—52no—
194#817—52no—
195#815—52no—
196C8×Dic3—52no—
197C23×D5—21no—
198C5×#41—22no—
199C5×#41C2×Dic314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—62no—
206C22×Dic5—61no—
207C2×D20—21no—
208C2×D20—22no—
209C2×D20C2×Dic314yescomplemented
210C2×D20C22×D312yes—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C5×C8—31no—
214C2×C5×C8—31no—
215C2×C5×C8—62no—
216C5×C4⋊C4—31no—
217C5×C4⋊C4—31no—
218C5×C22⋊C4—61no—
219C42×C5—61no—
220C22⋊Dic5—32no—
221C22⋊Dic5—62no—
222#688C2×Dic318yescomplemented
223#686C2×Dic318yescomplemented
224#685—62no—
225#685—62no—
226C4⋊Dic5—31no—
227C4⋊Dic5—31no—
228C4⋊Dic5—32no—
229C4⋊Dic5—62no—
230C4⋊Dic5—61no—
231C4×Dic5—32no—
232C4×Dic5—62no—
233#681C2×Dic314yescomplemented
234C2×#168C22×D312yes—
235C2×AGL(1,ℤ/8)—51no—
236#520—151no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—31no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5C4×D412yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C3×D5—24no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—84no—
257C3×C4×C5—22no—
258C3×C4×C5C4×D412yes—
259C3×C4×C5C23×C411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261Dic15—22no—
262Dic15—22no—
263Dic15—42no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C24×C3—101no—
267C3×#41—22no—
268C3×#41C4×D514yescomplemented
269C2×C3×Q8C22×D511yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4—54no—
272C2×C3×D4—52no—
273C2×C3×D4—101no—
274C2×C3×D4—102no—
275C2×C3×D4C22×D511yescharacteristic
276C22×C3×C4—21no—
277C22×C3×C4C22×D511yescharacteristic
278C22×Dic3—102no—
279C22×Dic3—102no—
280C22×Dic3—102no—
281C22×Dic3—101no—
282C3×SD16—58no—
283C3×D8—58no—
284C3×M16—54no—
285C2×C3×C8—52no—
286#217—21no—
287#217—52no—
288#217—102no—
289#217—102no—
290#217—102no—
291C4⋊Dic3—51no—
292C4⋊Dic3—51no—
293C4⋊Dic3—52no—
294C4⋊Dic3—102no—
295C4⋊Dic3—101no—
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298C4×Dic3—21no—
299C4×Dic3—52no—
300C4×Dic3—102no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D511yescharacteristic
303C2×C3⋊C8C22×D511yescharacteristic
304C23×C5—21no—
305C23×C5D3×D411yescharacteristic
306C22×D5—22no—
307C22×D5—24no—
308C22×D5—81no—
309C22×D5—81no—
310C5×Q8—21no—
311C5×Q8C22×Dic312yes—
312C5×D4—24no—
313C5×D4—21no—
314C5×D4C22×Dic312yes—
315C2×C4×C5—21no—
316C2×C4×C5—24no—
317C2×C4×C5—61no—
318C2×C4×C5—61no—
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5#23712yes—
321C2×C4×C5C22×Dic312yes—
322C2×C4×C5C23×D311yescharacteristic
323C2×Dic5—32no—
324C2×Dic5—32no—
325C2×Dic5—62no—
326C2×Dic5—242no—
327C2×Dic5—241no—
328D20—24no—
329D20—22no—
330D20C22×Dic314yes—
331C4×D5—242no—
332C4×D5—242no—
333C5×C8—61no—
334C5×C8—61no—
335#168C22×Dic314yes—
336C2×#41D3×D511yescharacteristic
337C22×D4—51no—
338AGL(1,ℤ/8)—58no—
339C2×SD16—52no—
340C2×D8—52no—
341C2×M16—51no—
342C22×C8—31no—
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—301no—
348C4×D4—301no—
349C4×D4—302no—
350#117—31no—
351#117—151no—
352#117—301no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—302no—
356#107—152no—
357#106—152no—
358#103—31no—
359#103—31no—
360#102—31no—
361#102—31no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371C3×D5—44no—
372C23×C3—21no—
373C23×C3—102no—
374C23×C3—104no—
375C23×C3—401no—
376C23×C3—401no—
377C23×C3D4×D511yescharacteristic
378C3×Q8—21no—
379C3×Q8C2×C4×D512yes—
380C3×D4—24no—
381C3×D4—21no—
382C3×D4—54no—
383C3×D4—102no—
384C3×D4—104no—
385C3×D4C2×C4×D512yes—
386C2×C3×C4—21no—
387C2×C3×C4—24no—
388C2×C3×C4C2×C4×D512yes—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4#71112yes—
391C2×C3×C4C23×D511yescharacteristic
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—52no—
395C2×Dic3—52no—
396C2×Dic3—102no—
397C2×Dic3—402no—
398C2×Dic3—402no—
399C2×Dic3—402no—
400C2×Dic3—401no—
401C3×C8—54no—
402C3⋊C8—21no—
403C3⋊C8—21no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—22no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5D4×Dic312yes—
410C22×C5C2×D3×D411yescharacteristic
411C2×D5—24no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—84no—
415C4×C5—22no—
416C4×C5—121no—
417C4×C5—121no—
418C4×C5D4×Dic312yes—
419C4×C5C2×#23711yescharacteristic
420C4×C5C23×Dic311yescharacteristic
421Dic5—62no—
422Dic5—62no—
423Dic5—122no—
424C24—101no—
425#41—22no—
426#41D5×Dic314yescomplemented
427C2×Q8C2×D3×D511yescharacteristic
428C2×D4—21no—
429C2×D4—54no—
430C2×D4—52no—
431C2×D4—102no—
432C2×D4—101no—
433C2×D4C2×D3×D511yescharacteristic
434C22×C4—21no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—58no—
441D8—58no—
442M16—54no—
443C2×C8—31no—
444C2×C8—31no—
445C2×C8—52no—
446C2×C8—62no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—151no—
450C4⋊C4—151no—
451C4⋊C4—152no—
452C4⋊C4—302no—
453C4⋊C4—301no—
454C22⋊C4—61no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—61no—
460C42—152no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—104no—
469C22×C3—202no—
470C22×C3—202no—
471C22×C3—404no—
472C22×C3#402712yes—
473C22×C3C2×D4×D511yescharacteristic
474C3×C4—22no—
475C3×C4#402712yes—
476C3×C4C22×C4×D511yescharacteristic
477C3×C4C2×#71111yescharacteristic
478Dic3—41no—
479Dic3—41no—
480Dic3—102no—
481Dic3—102no—
482Dic3—202no—
483C2×C5—22no—
484C2×C5—42no—
485C2×C5#577411yescharacteristic
486C2×C5#577511yescharacteristic
487C2×C5C2×D4×Dic311yescharacteristic
488D5—44no—
489C23—21no—
490C23—102no—
491C23—104no—
492C23—401no—
493C23—401no—
494C23#679011yescharacteristic
495Q8—21no—
496Q8C2×D5×Dic312yes—
497D4—24no—
498D4—21no—
499D4—54no—
500D4—102no—
501D4—104no—
502D4C2×D5×Dic312yes—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—152no—
508C2×C4—152no—
509C2×C4—302no—
510C2×C4—1202no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1201no—
514C2×C4C2×D5×Dic312yes—
515C2×C4#678012yes—
516C2×C4#679011yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—54no—
519C8—61no—
520C8—61no—
521C2×C3—22no—
522C2×C3—42no—
523C2×C3—204no—
524C2×C3C2×#402711yescharacteristic
525C2×C3#6610311yescharacteristic
526C2×C3#6610411yescharacteristic
527C5#8393011yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—104no—
534C22—202no—
535C22—202no—
536C22—404no—
537C22#9155912yes—
538C22C2×#679011yescharacteristic
539C4—22no—
540C4—121no—
541C4—121no—
542C4—302no—
543C4—302no—
544C4—602no—
545C4#9155912yes—
546C4C22×D5×Dic311yescharacteristic
547C4C2×#678011yescharacteristic
548C3#1061055111yescharacteristic, complemented, Sylow
549C2—22no—
550C2—42no—
551C2—204no—
552C2#1175533011yescharacteristic
553C2#1175533111yescharacteristic
554C2C2×#9155911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4095C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756586C2semidirect
3. #11754488C2semidirect
4. C5×#5233C2semidirect
5. #11749241C2semidirect
6. #11749239C2semidirect
7. #11748995C2semidirect
8. #11748993C2semidirect
9. #11748460C2semidirect
10. C2×#90965C2semidirect
11. #11748326C2semidirect
15. Q8×Dic15C22semidirect
17. D4×Dic15C22semidirect
24. C3×#4095C4semidirect
33. C5×#835C22semidirect
34. C5×#835C22semidirect
35. C5×#832C22semidirect
36. C5×#832C22semidirect
37. #90988C22semidirect
38. #90985C22semidirect
41. #90954C22semidirect
42. #90951C22semidirect
57. C3×C5×#41C2×C4semidirect
67. C2×C3×D20C2×C4semidirect
87. C3×#688C2×C4semidirect
88. C3×#686C2×C4semidirect
89. C3×#681C2×C4semidirect
96. #5233D5semidirect
108. #4095Dic3semidirect
187. #835C2×D5semidirect
188. #835C2×D5semidirect
191. #832C2×D5semidirect
192. #832C2×D5semidirect
199. C5×#41C2×Dic3semidirect
209. C2×D20C2×Dic3semidirect
222. #688C2×Dic3semidirect
223. #686C2×Dic3semidirect
233. #681C2×Dic3semidirect
268. C3×#41C4×D5semidirect
426. #41D5×Dic3semidirect
462. C3×C5#2946semidirect
527. C5#83930semidirect
548. C3#10610551semidirect

Maximal subgroups

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

subgroupindex
#117565862
C2×C3×#40952
#117544882
C5×#52332
#117492412
#117492392
#117489952
#117489932
#117484602
C2×#909652
#117483262
#106105513
#839305