Finite Group Databasebeta

← #14471828

Subgroups — #14471828

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65877C211yesmaximal, characteristic, complemented
2#11752662C211yesmaximal, characteristic, complemented
3#11751116C211yesmaximal, characteristic
4C4×C5×#214C211yesmaximal, characteristic, complemented
5#11749068C212yesmaximal, complemented
6#11748975C212yesmaximal, complemented
7#11747244C212yesmaximal, complemented
8#11747145C212yesmaximal, complemented
9#11746959C211yesmaximal, characteristic, complemented
10#11746910C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611352—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6715C2212yes—
15#91763C2211yescharacteristic
16C2×C5×#214C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×D4×Dic5C2212yes—
19C2×C3×C4⋊Dic5—21no—
20C3×#4070—21no—
21C3×#4036C2212yes—
22C3×#4024—22no—
23C3×#4015C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91433—22no—
26#91428—21no—
27#91418C2212yes—
28#91375C2212yes—
29#91374—21no—
30#91093C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C5×#832C2211yescharacteristic
33C5×#810C2211yescharacteristic
34C5×#808C2211yescharacteristic
35C4×C5×C3⋊C8C2211yescharacteristic
36#90989C2212yes—
37#90982C2212yes—
38#90972C2212yes—
39#90968C2212yes—
40#90968C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83643—51nomaximal, Hall
43#65919—31no—
44#65877D311yescharacteristic, complemented
45C4×C5×SD16—31no—
46#65454—32no—
47#65310—31no—
48#65304—31no—
49#65160—32no—
50#65089—32no—
51#65045—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×D60—21no—
57C2×D60—21no—
58C2×D60C2312yes—
59C2×C5×Dic6C2311yescharacteristic
60C22×C3×Dic5—22no—
61C2×C3×Dic10—21no—
62C2×C3×Dic10D411yescharacteristic
63C2×#1200—22no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C22⋊C4—21no—
66C3×C42×C5C2311yescharacteristic
67#6715—24no—
68C2×C3⋊#168C2312yes—
69C5×#214—22no—
70C5×C4⋊Dic3C2311yescharacteristic
71C5×Dic3⋊C4—21no—
72C4×C5×Dic3—21no—
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C3×C22⋊Dic5—22no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5—22no—
78C3×C4⋊Dic5D411yescharacteristic
79C3×C4⋊Dic5C2312yes—
80C3×#683—22no—
81C3×#683D412yes—
82C3×C4×Dic5C2312yes—
83#6667—22no—
84#6667—22no—
85#6667—22no—
86C3×#554—51no—
87#5585—51no—
88#5091—51no—
89#5088—51no—
90#5068—52no—
91#5066—52no—
92Q8×C3⋊C8—51no—
93C4×#214D511yescharacteristic, complemented
94#5016—52no—
95#5015—51no—
96C4×#213—52no—
97C2×C5×SD16—31no—
98C4×C5×Q8—31no—
99C4×C5×D4C2×D311yescharacteristic
100#4093—32no—
101D4×Dic5C2×D312yes—
102C2×#686—32no—
103C2×C4⋊Dic5—21no—
104#4070—21no—
105#4040—62no—
106#4039—32no—
107#4036C2×D312yes—
108#4024—22no—
109#4021—61no—
110#4020—31no—
111C4×D20—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×#106—31no—
115C5×#103—31no—
116C5×#102—31no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—32no—
120#3953—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3361—151noSylow
127C23×C3×C5—21no—
128C22×D15—22no—
129C3×C5×D4—21no—
130C3×C5×D4#4112yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136D60—22no—
137D60—22no—
138D60—42no—
139D60—81no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C5×Dic6—21no—
143C5×Dic6—21no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—82no—
146C2×C3×Dic5C2×D412yes—
147C2×C3×Dic5C2×D412yes—
148C3×Dic10—22no—
149C3×Dic10—81no—
150#1200—82no—
151C3⋊#168—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C3×C4⋊Q8—51no—
155C3×#125—52no—
156C3×C22⋊Q8—102no—
157C3×C22⋊Q8—101no—
158C3×C4×Q8—51no—
159C3×C4×D4—52no—
160C3×C4×D4C2×D511yescharacteristic
161C2×C3×C4⋊C4—101no—
162#947—101no—
163C2×#214C2×D511yescharacteristic
164C2×#213—52no—
165#894—102no—
166#893—101no—
167#875—52no—
168#874—51no—
169C4×D12—52no—
170C4×Dic6C2×D511yescharacteristic
171#832C2×D511yescharacteristic
172#810—52no—
173#810C2×D511yescharacteristic
174#809—52no—
175#809—52no—
176#809—52no—
177#808C2×D511yescharacteristic
178#807—52no—
179C4⋊(C3⋊C8)—51no—
180C4⋊(C3⋊C8)—52no—
181C4×C3⋊C8—52no—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8—31no—
184C2×C5×D4C22×D311yescharacteristic
185C22×C4×C5—21no—
186C22×Dic5—22no—
187C2×D20—32no—
188C2×D20—61no—
189C2×D20—61no—
190C2×C4×D5—62no—
191C2×Dic10—21no—
192C2×Dic10#6711yescharacteristic
193C5×SD16—62no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—61no—
198C5×C4⋊C4C22×D311yescharacteristic
199C5×C22⋊C4—21no—
200C42×C5—61no—
201C42×C5C22×D311yescharacteristic
202C22⋊Dic5—22no—
203#686—64no—
204#685—62no—
205#685—62no—
206#685—62no—
207C4⋊Dic5—21no—
208C4⋊Dic5—22no—
209C4⋊Dic5#6711yescharacteristic
210C4⋊Dic5C22×D312yes—
211#683—22no—
212#683#6712yes—
213C4×Dic5C22×D312yes—
214C2×#168—32no—
215#559—151no—
216#554—51no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—31no—
225C4×D8—152no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238C3×Dic5—22no—
239C3×Dic5—22no—
240C3×Dic5—42no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×Q8—51no—
244C2×C3×Q8—101no—
245C2×C3×D4C22×D511yescharacteristic
246C22×C3×C4—21no—
247C22×C3×C4—102no—
248C2×D12—52no—
249C2×D12—101no—
250C2×D12—101no—
251C2×C4×D3—102no—
252C2×Dic6C22×D511yescharacteristic
253C3×C4⋊C4—52no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—52no—
256C3×C4⋊C4—102no—
257C3×C4⋊C4—102no—
258C3×C4⋊C4—101no—
259C3×C4⋊C4C22×D511yescharacteristic
260C3×C22⋊C4—21no—
261C3×C22⋊C4—102no—
262C3×C42—52no—
263C3×C42C22×D511yescharacteristic
264#214—22no—
265#213—104no—
266(C2×D3)⋊C4—102no—
267(C2×D3)⋊C4—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3C22×D511yescharacteristic
270Dic3⋊C4—21no—
271C4×Dic3—21no—
272C2×C3⋊C8—52no—
273C2×C3⋊C8C22×D511yescharacteristic
274C2×C3⋊C8C22×D511yescharacteristic
275C23×C5—21no—
276C22×D5—62no—
277C5×Q8—61no—
278C5×Q8—61no—
279C5×D4—21no—
280C5×D4#23912yes—
281C2×C4×C5—21no—
282C2×C4×C5—42no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6711yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—82no—
290C2×Dic5C2×#6712yes—
291C2×Dic5C2×#6712yes—
292D20—62no—
293D20—62no—
294D20—122no—
295D20—241no—
296C4×D5—242no—
297Dic10—22no—
298Dic10—81no—
299C5×C8—61no—
300C5×C8—61no—
301#168—62no—
302C2×SD16—31no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—151no—
306#125—52no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—102no—
311C22⋊Q8—101no—
312C4×Q8—31no—
313C4×Q8—51no—
314C4×D4—52no—
315C4×D4—152no—
316C4×D4—301no—
317C4×D4D3×D511yescharacteristic
318C2×C4⋊C4—101no—
319#107—152no—
320#106—31no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—31no—
324#103—152no—
325#102—31no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—31no—
330C4×C8—152no—
331C2×C3×C5—42no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335D15—82no—
336C23×C3—21no—
337C22×D3—102no—
338C3×Q8—102no—
339C3×Q8—401no—
340C3×D4—21no—
341C3×D4#70912yes—
342C2×C3×C4—21no—
343C2×C3×C4—42no—
344C2×C3×C4—52no—
345C2×C3×C4—52no—
346C2×C3×C4—102no—
347C2×C3×C4—402no—
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4C23×D511yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—21no—
353D12—102no—
354D12—102no—
355D12—202no—
356D12—401no—
357C4×D3—402no—
358Dic6—21no—
359Dic6—21no—
360C3⋊C8—21no—
361C3⋊C8—21no—
362C3⋊C8—102no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5C22×#6711yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—121no—
373C4×C5—121no—
374C4×C5#95012yes—
375C4×C5C2×#23911yescharacteristic
376C4×C5#100711yescharacteristic
377Dic5—22no—
378Dic5—22no—
379Dic5—42no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×Q8—101no—
383C2×D4—152no—
384C2×D4—301no—
385C2×D4—301no—
386C2×D4C2×D3×D511yescharacteristic
387C22×C4—21no—
388C22×C4—102no—
389C22×C4—302no—
390SD16—62no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—152no—
395C4⋊C4—31no—
396C4⋊C4—51no—
397C4⋊C4—52no—
398C4⋊C4—52no—
399C4⋊C4—61no—
400C4⋊C4—102no—
401C4⋊C4—102no—
402C4⋊C4—101no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—102no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—52no—
410C42—61no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—22no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—102no—
423C3×C4—102no—
424C3×C4—202no—
425C3×C4#406212yes—
426C3×C4C2×#70911yescharacteristic
427C3×C4#415011yescharacteristic
428Dic3—41no—
429Dic3—41no—
430C2×C5—42no—
431C2×C5#581711yescharacteristic
432C2×C5C2×#95011yescharacteristic
433C2×C5#583511yescharacteristic
434D5—242no—
435C23—21no—
436C23—302no—
437Q8—61no—
438Q8—61no—
439Q8—102no—
440Q8—401no—
441D4—21no—
442D4—302no—
443D4—302no—
444D4—602no—
445D4—1201no—
446D4#676912yes—
447C2×C4—21no—
448C2×C4—42no—
449C2×C4—52no—
450C2×C4—52no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—102no—
454C2×C4—402no—
455C2×C4—1202no—
456C2×C4D5×#6711yescharacteristic
457C2×C4D5×#6711yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—61no—
461C8—302no—
462C2×C3—42no—
463C2×C3#6588611yescharacteristic
464C2×C3C2×#406211yescharacteristic
465C2×C3#6610311yescharacteristic
466D3—402no—
467C5#8364311yescharacteristic, complemented, Sylow
468C22—22no—
469C22—41no—
470C22—41no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×D5×#6711yescharacteristic
475C4—21no—
476C4—41no—
477C4—102no—
478C4—102no—
479C4—121no—
480C4—121no—
481C4—202no—
482C4#9149212yes—
483C4#9200411yescharacteristic
484C4C2×#676911yescharacteristic
485C3#1061135211yescharacteristic, complemented, Sylow
486C2—42no—
487C2—1202no—
488C2#1175432111yescharacteristic
489C2C2×#9149211yescharacteristic
490C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11751116C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65877C2semidirect
2. #11752662C2semidirect
4. C4×C5×#214C2semidirect
5. #11749068C2semidirect
6. #11748975C2semidirect
7. #11747244C2semidirect
8. #11747145C2semidirect
9. #11746959C2semidirect
10. #11746910C2semidirect
11. C3⋊C8×Dic10C2semidirect
44. #65877D3semidirect
93. C4×#214D5semidirect
412. C3×C5#3361semidirect
467. C5#83643semidirect
485. C3#10611352semidirect

Maximal subgroups

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

subgroupindex
C3×#658772
#117526622
#117511162
C4×C5×#2142
#117490682
#117489752
#117472442
#117471452
#117469592
#117469102
C3⋊C8×Dic102
#106113523
#836435