Finite Group Databasebeta

← #14471485

Subgroups — #14471485

Order 1920.

852 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66061C211yesmaximal, characteristic, complemented
2#11752538C211yesmaximal, characteristic, complemented
3#11751189C211yesmaximal, characteristic, complemented
4C5×#5087C211yesmaximal, characteristic, complemented
5#11747399C212yesmaximal, complemented
6#11747238C212yesmaximal, complemented
7#11747223C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11747028C211yesmaximal, characteristic, complemented
10C4×#6652C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612723—31nomaximal, Hall
13C2×C3×Q8×D5—21no—
14C2×#6769—21no—
15C3×C5×C4⋊Q8C2211yescharacteristic
16#91763C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C3×#4092—21no—
19C3×#4042—22no—
20C3×#4039C2212yes—
21C3×#4034C2212yes—
22C3×C4×D20C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91460—21no—
25#91451C2212yes—
26#91420—22no—
27#91418C2212yes—
28C2×#6653C2212yes—
29C2×#6652C2211yescharacteristic
30#91093C2212yes—
31#91093C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C5×#809C2212yes—
34C5×#807C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36#90989C2211yescharacteristic
37#90982C2212yes—
38#90968C2212yes—
39#90966C2211yescharacteristic
40#90964C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83562—51nomaximal, Hall
43#66061D311yescharacteristic, complemented
44#65887—31no—
45C5×#474—31no—
46#65377—31no—
47C4×#686—31no—
48#65179—32no—
49#65161—32no—
50#65132—31no—
51#65119—31no—
52#65075—32no—
53#65049—32no—
54C2×C3×C5×Q8—21no—
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C3×Q8×D5—44no—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5—22no—
64C2×C3×Dic10—22no—
65C2×C3×Dic10D411yescharacteristic
66C2×#1203—22no—
67C2×#1203—22no—
68C2×#1200—22no—
69#6769—44no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C42×C5C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C2×C5×C3⋊C8C2312yes—
78C3×#685—21no—
79C3×#685—22no—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—22no—
83C3×#683D412yes—
84C3×C4×Dic5C2312yes—
85#6667—22no—
86#6653—24no—
87#6652—22no—
88C3×D4×Q8—51no—
89#5577—51no—
90#5088—51no—
91#5088—52no—
92#5087—52no—
93#5087D511yescharacteristic, complemented
94Q8×C3⋊C8—51no—
95#5015—52no—
96#5015—51no—
97C4×#213—51no—
98C4×#213—52no—
99C2×Q8×D5—21no—
100C2×#709—61no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C4×C5×D4—31no—
103#4092—21no—
104#4086—32no—
105C2×#686—31no—
106#4076—61no—
107C2×D40—32no—
108#4042—22no—
109#4039—32no—
110#4039C2×D312yes—
111#4034C2×D312yes—
112#4030—62no—
113#4020—31no—
114C4×D20C2×D311yescharacteristic
115C4×Dic10C2×D311yescharacteristic
116C5×#107—32no—
117C5×C4⋊C8—31no—
118C5×#102—32no—
119#3964—31no—
120#3953—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—31no—
124#3941—32no—
125#3941—32no—
126#3939—31no—
127C4×#168—31no—
128#3358—151noSylow
129C22×D15—22no—
130C22×C5×D3—21no—
131C22×C3×D5—21no—
132C3×C5×Q8—42no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137D60—22no—
138D60—22no—
139D60—42no—
140D60—81no—
141C2×C5×Dic3—21no—
142C5×D12—21no—
143C5×D12—21no—
144C4×C5×D3—42no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5C2×D412yes—
147C2×C3×Dic5C2×D412yes—
148C3×D20—21no—
149C3×D20#4112yescomplemented
150C3×C4×D5—42no—
151C3×C4×D5—44no—
152C3×Dic10—44no—
153C3×Dic10D814yescomplemented
154#1203—44no—
155#1203—82no—
156#1200—44no—
157C3⋊#168—21no—
158C3⋊#168—21no—
159C5×C3⋊C8—22no—
160C22×C3×Q8—101no—
161C2×#239—101no—
162C3×C4⋊Q8—52no—
163C3×C4⋊Q8C2×D511yescharacteristic
164C3×C22⋊Q8—102no—
165C3×C22⋊Q8—101no—
166C3×C4×Q8—51no—
167C3×C4×D4—52no—
168C3×C4×D4—51no—
169C2×#213—51no—
170C2×#213—52no—
171#895—102no—
172#895—101no—
173#874—52no—
174#874—51no—
175C4×D12—52no—
176C4×D12C2×D511yescharacteristic
177#832—51no—
178#809—51no—
179#809—52no—
180#809—52no—
181#809—52no—
182#809C2×D512yes—
183#807—51no—
184#807C2×D512yes—
185C4⋊(C3⋊C8)—52no—
186C4⋊(C3⋊C8)C2×D511yescharacteristic
187C4×C3⋊C8—51no—
188C4×C3⋊C8—52no—
189C2×C5×Q8—21no—
190C2×C5×D4—31no—
191C22×C4×C5—61no—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194Q8×D5—44no—
195#709—124no—
196C2×D20—32no—
197C2×D20—61no—
198C2×D20—61no—
199C2×D20C22×D311yescharacteristic
200C2×C4×D5—21no—
201C2×C4×D5—22no—
202C2×C4×D5—62no—
203C2×Dic10—22no—
204C2×Dic10#6711yescharacteristic
205C2×C5×C8—32no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—31no—
208C5×C4⋊C4C22×D312yes—
209C5×C22⋊C4—61no—
210C42×C5C22×D311yescharacteristic
211#686—62no—
212#685—21no—
213#685—22no—
214#685—62no—
215C4⋊Dic5#6711yescharacteristic
216C4⋊Dic5C22×D311yescharacteristic
217#683—22no—
218#683#6712yes—
219C4×Dic5C22×D312yes—
220C2×#168—31no—
221C2×#168—31no—
222D40—64no—
223#550—151no—
224D4×Q8—51no—
225#486—152no—
226#486—151no—
227#474—31no—
228#474—152no—
229#459—152no—
230#459—151no—
231C8×Q8—151no—
232C4×D8—152no—
233C4×D8—151no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—42no—
236C2×D15—42no—
237C2×D15—42no—
238C2×C5×D3—41no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C3×D5—22no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5C2×D812yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C52−1+411yescharacteristic
249C3×Dic5—22no—
250C3×Dic5—41no—
251C3×Dic5C2×D814yes—
252C5×Dic3—41no—
253C2×C3×Q8—21no—
254C2×C3×Q8—51no—
255C2×C3×Q8—102no—
256C2×C3×Q8—204no—
257C2×C3×D4—51no—
258C22×C3×C4—102no—
259C22×C3×C4—101no—
260#239—204no—
261C2×D12—52no—
262C2×D12—102no—
263C2×D12—101no—
264C2×D12—102no—
265C2×D12—101no—
266C2×D12C22×D511yescharacteristic
267C2×C4×D3—21no—
268C2×C4×D3—102no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—52no—
271C3×C4⋊C4—51no—
272C3×C4⋊C4—51no—
273C3×C4⋊C4—102no—
274C3×C4⋊C4C22×D512yes—
275C3×C22⋊C4—102no—
276C3×C22⋊C4—101no—
277C3×C42—52no—
278C3×C42C22×D511yescharacteristic
279#213—104no—
280#213—102no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3C22×D511yescharacteristic
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8C22×D512yes—
287C23×C5—61no—
288C22×D5—21no—
289C22×D5—62no—
290C5×Q8—42no—
291C5×D4—61no—
292C5×D4—61no—
293C2×C4×C5—22no—
294C2×C4×C5—61no—
295C2×C4×C5—122no—
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—124no—
300C22⋊D5—242no—
301C2×Dic5—21no—
302C2×Dic5C2×#6712yes—
303C2×Dic5C2×#6712yes—
304D20—21no—
305D20—62no—
306D20—62no—
307D20—122no—
308D20—241no—
309D20#23912yescomplemented
310C4×D5—42no—
311C4×D5—44no—
312C4×D5—124no—
313Dic10—44no—
314Dic10#21314yescomplemented
315C5×C8—62no—
316#168—61no—
317#168—61no—
318C2×#41—301no—
319C22×Q8—101no—
320C2×D8—152no—
321C2×D8—151no—
322C4⋊Q8—52no—
323C4⋊Q8D3×D511yescharacteristic
324#127—152no—
325#127—151no—
326C22⋊Q8—102no—
327C22⋊Q8—101no—
328#121—302no—
329#121—301no—
330C4×Q8—51no—
331C4×D4—31no—
332C4×D4—52no—
333C4×D4—51no—
334C4×D4—152no—
335#107—32no—
336#107—151no—
337C4⋊C8—31no—
338C4⋊C8—152no—
339#102—32no—
340#102—151no—
341#102—152no—
342#102—151no—
343#102—152no—
344#102—152no—
345C4×C8—152no—
346C4×C8—151no—
347C2×C3×C5#54811yescharacteristic
348C2×C3×C5C22×D811yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—82no—
351C3×D5—42no—
352C5×D3—81no—
353C23×C3—101no—
354C22×D3—21no—
355C22×D3—102no—
356C3×Q8—42no—
357C3×Q8—54no—
358C3×Q8—204no—
359C3×D4—52no—
360C3×D4—101no—
361C2×C3×C4—22no—
362C2×C3×C4—52no—
363C2×C3×C4—52no—
364C2×C3×C4—101no—
365C2×C3×C4—204no—
366C2×C3×C4—202no—
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4C23×D511yescharacteristic
370C2×Dic3—21no—
371D12—21no—
372D12—21no—
373D12—102no—
374D12—102no—
375D12—204no—
376D12—202no—
377D12—401no—
378D12—402no—
379C4×D3—42no—
380C4×D3—204no—
381C3⋊C8—22no—
382C3⋊C8—101no—
383C3⋊C8—101no—
384C22×C5—121no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C22×#6711yescharacteristic
388C2×D5—22no—
389C2×D5—41no—
390C2×D5—41no—
391C2×D5—122no—
392C2×D5—122no—
393C2×D5—122no—
394C4×C5—21no—
395C4×C5—42no—
396C4×C5—121no—
397C4×C5C2×#21312yes—
398C4×C5C2×#23911yescharacteristic
399C4×C5#100711yescharacteristic
400Dic5—22no—
401Dic5—41no—
402Dic5C2×#21314yes—
403#41—604no—
404C2×Q8—21no—
405C2×Q8—51no—
406C2×Q8—102no—
407C2×Q8—204no—
408C2×D4—31no—
409C2×D4—51no—
410C2×D4—152no—
411C2×D4—302no—
412C2×D4—302no—
413C2×D4—301no—
414C2×D4—301no—
415C22×C4—61no—
416C22×C4—102no—
417C22×C4—101no—
418C22×C4—302no—
419D8—304no—
420D8—302no—
421C2×C8—32no—
422C2×C8—151no—
423C2×C8—151no—
424C4⋊C4—21no—
425C4⋊C4—31no—
426C4⋊C4—52no—
427C4⋊C4—51no—
428C4⋊C4—51no—
429C4⋊C4—102no—
430C4⋊C4C2×D3×D512yes—
431C22⋊C4—61no—
432C22⋊C4—102no—
433C22⋊C4—101no—
434C22⋊C4—302no—
435C42—52no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—102no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3C2×D4×D511yescharacteristic
442C2×D3—41no—
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—202no—
446C2×D3—202no—
447C2×D3—202no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—54no—
451C3×C4—102no—
452C3×C4—201no—
453C3×C4D5×D812yes—
454C3×C4#414711yescharacteristic
455C3×C4D5×#4111yescharacteristic
456Dic3—41no—
457C2×C5—241no—
458C2×C5C22×#21311yescharacteristic
459C2×C5#581711yescharacteristic
460C2×C5#583711yescharacteristic
461D5—42no—
462D5—242no—
463C23—61no—
464C23—101no—
465C23—302no—
466Q8—42no—
467Q8—54no—
468Q8—204no—
469D4—52no—
470D4—61no—
471D4—61no—
472D4—101no—
473D4—302no—
474D4—302no—
475D4—604no—
476D4—602no—
477D4—1201no—
478D4—1202no—
479C2×C4—22no—
480C2×C4—52no—
481C2×C4—52no—
482C2×C4—61no—
483C2×C4—101no—
484C2×C4—122no—
485C2×C4—204no—
486C2×C4—202no—
487C2×C4—604no—
488C2×C4D5×#6711yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—62no—
492C8—301no—
493C8—301no—
494C2×C3—202no—
495C2×C3#6596711yescharacteristic
496C2×C3C2×D5×D811yescharacteristic
497C2×C3#6611211yescharacteristic
498D3—81no—
499D3—402no—
500C5#8356211yescharacteristic, complemented, Sylow
501C22—102no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—201no—
506C22—201no—
507C22—602no—
508C22—602no—
509C22—602no—
510C22C2×D5×#6711yescharacteristic
511C4—21no—
512C4—42no—
513C4—54no—
514C4—102no—
515C4—121no—
516C4—201no—
517C4D5×#21312yes—
518C4#9202911yescharacteristic
519C4D5×#23911yescharacteristic
520C3#1061272311yescharacteristic, complemented, Sylow
521C2—202no—
522C2—241no—
523C2—1202no—
524C2C2×D5×#21311yescharacteristic
525C2#1175508611yescharacteristic
526C2#1175522711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3358
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66061C2semidirect
2. #11752538C2semidirect
3. #11751189C2semidirect
4. C5×#5087C2semidirect
5. #11747399C2semidirect
6. #11747238C2semidirect
7. #11747223C2semidirect
8. #11747138C2semidirect
9. #11747028C2semidirect
10. C4×#6652C2semidirect
11. #11746846C2semidirect
43. #66061D3semidirect
93. #5087D5semidirect
149. C3×D20#41semidirect
153. C3×Dic10D8semidirect
309. D20#239semidirect
314. Dic10#213semidirect
437. C3×C5#3358semidirect
500. C5#83562semidirect
520. C3#10612723semidirect

Maximal subgroups

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

subgroupindex
C3×#660612
#117525382
#117511892
C5×#50872
#117473992
#117472382
#117472232
#117471382
#117470282
C4×#66522
#117468462
#106127233
#835625