Finite Group Databasebeta

← #14417353

Subgroups — #14417353

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×D8C211yesmaximal, characteristic
2#11754910C212yesmaximal, complemented
3D8×Dic15C211yesmaximal, characteristic, complemented
4C5×Dic3×D8C211yesmaximal, characteristic, complemented
5#11748995C212yesmaximal, complemented
6#11748988C212yesmaximal, complemented
7#11748962C212yesmaximal, complemented
8#11747809C211yesmaximal, characteristic, complemented
9Dic3×D40C211yesmaximal, characteristic, complemented
10#11747672C211yesmaximal, characteristic, complemented
11#11747645C211yesmaximal, characteristic, complemented
12#10611319—31nomaximal, Hall
13C2×C3×D4×D5C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15D4×Dic15C2212yescomplemented
16C5×D4×Dic3C2212yescomplemented
17C2×C3×#686C2212yes—
18C3×D5×D8C418yescomplemented
19C2×C3×D40C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21#91559—22no—
22Dic3×C22⋊D5—22no—
23D5×#217—22no—
24C2×#6665—22no—
25#91434C2212yescomplemented
26Dic3×D20C2212yescomplemented
27#91358C2212yes—
28#91357C2211yescharacteristic
29C2×#6649C2211yescharacteristic
30#91116C2212yescomplemented
31#91102C2211yescharacteristic, complemented
32C8×Dic15C2211yescharacteristic, complemented
33C5×#832C2212yescomplemented
34C5×#818C2211yescharacteristic, complemented
35C5×C8×Dic3C2211yescharacteristic, complemented
36#90985C2212yescomplemented
37#90965C2212yescomplemented
38#90964C2212yescomplemented
39#90954C2211yescharacteristic, complemented
40#90953C2211yescharacteristic, complemented
41#83823—51nomaximal, Hall
42C2×D5×D8D311yescharacteristic
43#65879—32no—
44C4×C5×D8—31no—
45D8×Dic5—31no—
46#65303—32no—
47#65169—31no—
48#65161—31no—
49#65074—32no—
50#65059—32no—
51C4×D40—31no—
52#64978—31no—
53C23×C3×D5—22no—
54C2×C3×C5×D4C2312yes—
55C22×Dic15—22no—
56C22×C5×Dic3—22no—
57C2×C3×C22⋊D5—22no—
58C3×D4×D5—24no—
59C3×D4×D5C2×C418yescomplemented
60C2×C3×D20C2312yes—
61C2×C3×C4×D5C2311yescharacteristic
62C2×D5×Dic3—22no—
63C2×D5×Dic3—22no—
64C3×C5×D8C2×C414yescomplemented
65C2×C3×C5×C8C2311yescharacteristic
66#6719—22no—
67C4⋊Dic15C2312yes—
68C4×Dic15C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×#217—22no—
71C5×C4⋊Dic3C2312yes—
72C4×C5×Dic3C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×#686C2×C418yescomplemented
75C2×C3×#168C2311yescharacteristic
76C3×D40C2×C414yescomplemented
77C3×C8×D5C2×C414yescomplemented
78#6668D411yescharacteristic
79#6668D411yescharacteristic
80#6665—22no—
81#6665—22no—
82#6665—22no—
83#6665D411yescharacteristic
84#6665D411yescharacteristic
85Dic3×Dic5—22no—
86#6649—22no—
87C22×C3×D8—51no—
88#5798—52no—
89#5215—52no—
90#5152—52no—
91#5152—52no—
92Dic3×D8—51no—
93Dic3×D8—51no—
94Dic3×D8—51no—
95Dic3×D8D511yescharacteristic, complemented
96#5106—51no—
97#5101—51no—
98C2×D4×D5C2×D312yes—
99C2×C5×D8C2×D311yescharacteristic
100C4×C5×D4—32no—
101D4×Dic5—32no—
102C2×#686C2×D312yes—
103C4×C22⋊D5—62no—
104C2×#685—62no—
105D5×D8Dic318yescomplemented
106C2×D40C2×D311yescharacteristic
107C2×#676—31no—
108C2×C8×D5C2×D311yescharacteristic
109#4039—32no—
110#4038—32no—
111#4027—62no—
112D5×C22⋊C4—62no—
113C4×D20—32no—
114#4018—31no—
115C5×#107—31no—
116C5×#102—32no—
117C4×C5×C8—31no—
118#3964—32no—
119#3953—32no—
120#3950—31no—
121#3947—31no—
122C8×Dic5—31no—
123#3941—32no—
124#3940—32no—
125#3935—31no—
126#2948—151noSylow
127C23×C3×C5—22no—
128C22×C3×D5—22no—
129C22×C3×D5—28no—
130C22×C3×D5—82no—
131C22×C3×D5—82no—
132C22×C3×D5C2×D411yescharacteristic
133C3×C5×D4—22no—
134C3×C5×D4C22×C414yes—
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15—82no—
138C2×Dic15C2×D411yescharacteristic
139C2×Dic15C2×D411yescharacteristic
140C2×C5×Dic3—22no—
141C2×C5×Dic3—82no—
142C2×C5×Dic3C2×D411yescharacteristic
143C2×C5×Dic3C2×D411yescharacteristic
144C3×C22⋊D5—28no—
145C2×C3×Dic5C2×D411yescharacteristic
146C3×D20—22no—
147C3×D20C22×C414yes—
148C3×C4×D5C22×C412yes—
149C3×C4×D5#4112yes—
150D5×Dic3—82no—
151D5×Dic3—82no—
152C3×C5×C8C22×C412yes—
153C3⋊#168—21no—
154C3×#168C22×C412yes—
155C5×C3⋊C8—21no—
156C22×C3×D4—52no—
157C2×C3×D8—52no—
158C2×C3×D8—58no—
159C2×C3×D8—51no—
160C2×C3×D8C2×D511yescharacteristic
161C22×C3×C8—51no—
162C2×#217—102no—
163C2×#217—102no—
164D4×Dic3—52no—
165D4×Dic3—52no—
166D4×Dic3—52no—
167D4×Dic3—102no—
168D4×Dic3—102no—
169D4×Dic3C2×D512yescomplemented
170#926—51no—
171#926—52no—
172C2×#208—51no—
173#832—52no—
174#832—52no—
175#832—52no—
176#832C2×D512yescomplemented
177#818—51no—
178#818C2×D511yescharacteristic, complemented
179#817—52no—
180#815—51no—
181#815—51no—
182C8×Dic3—51no—
183C8×Dic3C2×D511yescharacteristic, complemented
184C23×D5—22no—
185C2×C5×D4C22×D312yes—
186C22×C4×C5—62no—
187C2×C22⋊D5—22no—
188C22×Dic5—62no—
189D4×D5—24no—
190D4×D5C2×Dic318yescomplemented
191C2×D20C22×D312yes—
192C2×C4×D5—62no—
193C2×C4×D5—62no—
194C2×C4×D5C22×D311yescharacteristic
195C5×D8C2×Dic314yescomplemented
196C2×C5×C8—31no—
197C2×C5×C8C22×D311yescharacteristic
198C5×C4⋊C4—32no—
199C5×C22⋊C4—62no—
200C42×C5—31no—
201C22⋊Dic5—62no—
202#686C2×Dic318yescomplemented
203#685—31no—
204#685—31no—
205#685—62no—
206#685—62no—
207#685—62no—
208C4⋊Dic5—32no—
209#683—31no—
210#683—31no—
211C4×Dic5—31no—
212C4×Dic5—62no—
213C2×#168—31no—
214C2×#168C22×D311yescharacteristic
215D40C2×Dic314yescomplemented
216#676—62no—
217C8×D5C2×Dic314yescomplemented
218C22×D8—51no—
219#518—152no—
220#442—152no—
221#442—152no—
222C4×D8—31no—
223C4×D8—151no—
224C4×D8—151no—
225C4×D8—151no—
226#427—151no—
227#418—152no—
228#405—151no—
229C22×C3×C5—24no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5C22×D411yescharacteristic
233C2×C3×D5—21no—
234C2×C3×D5—21no—
235C2×C3×D5—24no—
236C2×C3×D5—42no—
237C2×C3×D5—42no—
238C2×C3×D5—88no—
239C2×C3×D5C4×D412yes—
240C3×C4×C5C23×C411yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242Dic15—21no—
243Dic15—21no—
244Dic15—42no—
245C3×Dic5C4×D412yes—
246C5×Dic3—21no—
247C5×Dic3—21no—
248C5×Dic3—42no—
249C24×C3—102no—
250C2×C3×D4—58no—
251C2×C3×D4—52no—
252C2×C3×D4—104no—
253C2×C3×D4—102no—
254C2×C3×D4C22×D512yes—
255C22×C3×C4—51no—
256C22×Dic3—22no—
257C22×Dic3—102no—
258C22×Dic3—102no—
259C22×Dic3—102no—
260C3×D8—58no—
261C3×D8—54no—
262C3×D8C4×D514yescomplemented
263C2×C3×C8—51no—
264C2×C3×C8—54no—
265C2×C3×C8C22×D511yescharacteristic
266#217—22no—
267#217—51no—
268#217—51no—
269#217—102no—
270#217—102no—
271#217—102no—
272#217—102no—
273C4⋊Dic3—51no—
274C4⋊Dic3—51no—
275C4⋊Dic3—52no—
276C4⋊Dic3C22×D512yes—
277C4×Dic3—51no—
278C4×Dic3—102no—
279C4×Dic3C22×D511yescharacteristic
280#208—102no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8C22×D511yescharacteristic
283C23×C5—22no—
284C22×D5—22no—
285C22×D5—28no—
286C22×D5—82no—
287C22×D5—82no—
288C22×D5D3×D411yescharacteristic
289C5×D4—22no—
290C5×D4C22×Dic314yes—
291C2×C4×C5—31no—
292C2×C4×C5—31no—
293C2×C4×C5—62no—
294C2×C4×C5—242no—
295C2×C4×C5C23×D311yescharacteristic
296C22⋊D5—28no—
297C2×Dic5—31no—
298C2×Dic5—31no—
299C2×Dic5—62no—
300C2×Dic5—242no—
301C2×Dic5D3×D411yescharacteristic
302D20—22no—
303D20C22×Dic314yes—
304C4×D5—242no—
305C4×D5—242no—
306C4×D5#23712yes—
307C4×D5C22×Dic312yes—
308C5×C8—61no—
309C5×C8C22×Dic312yes—
310#168—61no—
311#168C22×Dic312yes—
312C22×D4—52no—
313C2×D8—52no—
314C2×D8—58no—
315C2×D8—51no—
316C2×D8D3×D511yescharacteristic
317C2×M16—151no—
318C22×C8—51no—
319C4×D4—32no—
320C4×D4—152no—
321C4×D4—152no—
322C4×D4—152no—
323C4×D4—302no—
324C4×D4—302no—
325#117—151no—
326#117—152no—
327C2×C22⋊C4—302no—
328C2×C22⋊C4—302no—
329#107—31no—
330#107—151no—
331#106—152no—
332#102—32no—
333#102—152no—
334#102—152no—
335#102—152no—
336#97—151no—
337#97—151no—
338C4×C8—31no—
339C4×C8—151no—
340C2×C3×C5—44no—
341C2×C3×C5C2×C4×D411yescharacteristic
342C2×C3×C5#57611yescharacteristic
343C2×C3×C5#57611yescharacteristic
344C3×D5—22no—
345C3×D5—44no—
346C23×C3—22no—
347C23×C3—51no—
348C23×C3—108no—
349C23×C3—102no—
350C23×C3—402no—
351C23×C3—402no—
352C3×D4—22no—
353C3×D4—54no—
354C3×D4—108no—
355C3×D4—102no—
356C3×D4C2×C4×D514yes—
357C2×C3×C4—51no—
358C2×C3×C4—52no—
359C2×C3×C4—52no—
360C2×C3×C4C23×D511yescharacteristic
361C2×Dic3—22no—
362C2×Dic3—51no—
363C2×Dic3—51no—
364C2×Dic3—82no—
365C2×Dic3—102no—
366C2×Dic3—402no—
367C2×Dic3—402no—
368C2×Dic3—402no—
369C2×Dic3D4×D511yescharacteristic
370C2×Dic3D4×D511yescharacteristic
371C3×C8—52no—
372C3×C8C2×C4×D512yes—
373C3⋊C8—21no—
374C3⋊C8—101no—
375C22×C5—24no—
376C22×C5—42no—
377C22×C5—42no—
378C22×C5C2×D3×D411yescharacteristic
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—24no—
382C2×D5—42no—
383C2×D5—42no—
384C2×D5—88no—
385C2×D5D4×Dic312yes—
386C4×C5—61no—
387C4×C5—61no—
388C4×C5—122no—
389C4×C5C2×#23711yescharacteristic
390C4×C5C23×Dic311yescharacteristic
391Dic5—61no—
392Dic5—61no—
393Dic5—122no—
394Dic5D4×Dic312yes—
395C24—102no—
396C2×D4—58no—
397C2×D4—52no—
398C2×D4—104no—
399C2×D4—102no—
400C2×D4C2×D3×D512yes—
401C22×C4—51no—
402C22×C4—62no—
403C22×C4—302no—
404C22×C4—302no—
405C22×C4—302no—
406D8—58no—
407D8—54no—
408D8D5×Dic314yescomplemented
409M16—302no—
410C2×C8—31no—
411C2×C8—51no—
412C2×C8—54no—
413C2×C8—151no—
414C2×C8C2×D3×D511yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—151no—
417C4⋊C4—151no—
418C4⋊C4—152no—
419C22⋊C4—62no—
420C22⋊C4—151no—
421C22⋊C4—151no—
422C22⋊C4—302no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C22⋊C4—302no—
426C42—31no—
427C42—151no—
428C42—302no—
429C3×C5#294811yescharacteristic, complemented, Hall
430C22×C3—24no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—52no—
434C22×C3—101no—
435C22×C3—101no—
436C22×C3—104no—
437C22×C3—202no—
438C22×C3—202no—
439C22×C3—408no—
440C22×C3C2×D4×D511yescharacteristic
441C3×C4—52no—
442C3×C4C22×C4×D511yescharacteristic
443C3×C4D5×#4111yescharacteristic
444Dic3—21no—
445Dic3—21no—
446Dic3—42no—
447Dic3—101no—
448Dic3—101no—
449Dic3—202no—
450C2×C5—44no—
451C2×C5#575711yescharacteristic
452C2×C5#575711yescharacteristic
453C2×C5C2×D4×Dic311yescharacteristic
454D5—22no—
455D5—44no—
456C23—22no—
457C23—51no—
458C23—108no—
459C23—102no—
460C23—402no—
461C23—402no—
462D4—22no—
463D4—54no—
464D4—108no—
465D4—102no—
466D4C2×D5×Dic314yes—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—51no—
470C2×C4—52no—
471C2×C4—52no—
472C2×C4—62no—
473C2×C4—151no—
474C2×C4—151no—
475C2×C4—242no—
476C2×C4—302no—
477C2×C4—1202no—
478C2×C4—1202no—
479C2×C4—1202no—
480C2×C4C22×D3×D511yescharacteristic
481C8—52no—
482C8—61no—
483C8—301no—
484C8C2×D5×Dic312yes—
485C2×C3—44no—
486C2×C3—102no—
487C2×C3—204no—
488C2×C3C4×D4×D511yescharacteristic
489C2×C3#6609111yescharacteristic
490C2×C3#6610311yescharacteristic
491C5#8382311yescharacteristic, complemented, Sylow
492C22—24no—
493C22—42no—
494C22—42no—
495C22—52no—
496C22—101no—
497C22—101no—
498C22—104no—
499C22—202no—
500C22—202no—
501C22—408no—
502C22D3×D4×D511yescharacteristic
503C4—52no—
504C4—61no—
505C4—61no—
506C4—122no—
507C4—301no—
508C4—301no—
509C4—602no—
510C4D5×#23711yescharacteristic
511C4C22×D5×Dic311yescharacteristic
512C3#1061131911yescharacteristic, complemented, Sylow
513C2—44no—
514C2—102no—
515C2—204no—
516C2#1175405411yescharacteristic
517C2#1175405811yescharacteristic
518C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D5×D8C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5#2948
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11754910C2semidirect
3. D8×Dic15C2semidirect
4. C5×Dic3×D8C2semidirect
5. #11748995C2semidirect
6. #11748988C2semidirect
7. #11748962C2semidirect
8. #11747809C2semidirect
9. Dic3×D40C2semidirect
10. #11747672C2semidirect
11. #11747645C2semidirect
15. D4×Dic15C22semidirect
16. C5×D4×Dic3C22semidirect
18. C3×D5×D8C4semidirect
25. #91434C22semidirect
26. Dic3×D20C22semidirect
30. #91116C22semidirect
31. #91102C22semidirect
32. C8×Dic15C22semidirect
33. C5×#832C22semidirect
34. C5×#818C22semidirect
35. C5×C8×Dic3C22semidirect
36. #90985C22semidirect
37. #90965C22semidirect
38. #90964C22semidirect
39. #90954C22semidirect
40. #90953C22semidirect
59. C3×D4×D5C2×C4semidirect
64. C3×C5×D8C2×C4semidirect
74. C3×#686C2×C4semidirect
76. C3×D40C2×C4semidirect
77. C3×C8×D5C2×C4semidirect
95. Dic3×D8D5semidirect
105. D5×D8Dic3semidirect
169. D4×Dic3C2×D5semidirect
176. #832C2×D5semidirect
178. #818C2×D5semidirect
183. C8×Dic3C2×D5semidirect
190. D4×D5C2×Dic3semidirect
195. C5×D8C2×Dic3semidirect
202. #686C2×Dic3semidirect
215. D40C2×Dic3semidirect
217. C8×D5C2×Dic3semidirect
262. C3×D8C4×D5semidirect
408. D8D5×Dic3semidirect
429. C3×C5#2948semidirect
491. C5#83823semidirect
512. C3#10611319semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×D82
#117549102
D8×Dic152
C5×Dic3×D82
#117489952
#117489882
#117489622
#117478092
Dic3×D402
#117476722
#117476452
#106113193
#838235