Finite Group Databasebeta

← #14471457

Subgroups — #14471457

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×#65887C211yesmaximal, characteristic, complemented
2D12×Dic10C211yesmaximal, characteristic, complemented
3#11751108C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic, complemented
5#11749102C212yesmaximal, complemented
6#11748974C212yesmaximal, complemented
7#11747410C212yesmaximal, complemented
8#11747216C212yesmaximal, complemented
9#11747033C211yesmaximal, characteristic, complemented
10#11746890C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611298—31nomaximal, Hall
13C2×C3×#709—21no—
14C2×D3×Dic10—21no—
15C3×C4×C5×D4C2211yescharacteristic
16#91758C2211yescharacteristic
17C2×C5×#213C2211yescharacteristic
18C4×C5×D12C2211yescharacteristic
19C3×#4086C2212yes—
20C3×#4076—21no—
21C3×#4039C2212yes—
22C3×#4030—22no—
23C3×#4020C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91468C2212yes—
26#91417—22no—
27Dic5×D12C2212yes—
28#91365—21no—
29C2×#6652C2212yes—
30#91116C2212yes—
31#91091C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#832C2211yescharacteristic
34C5×#809C2211yescharacteristic
35C5×#807C2211yescharacteristic
36C4×C5×C3⋊C8C2211yescharacteristic
37#90982C2212yes—
38#90965C2212yes—
39#90965C2212yes—
40#90964C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83580—51nomaximal, Hall
43#65887D311yescharacteristic, complemented
44D4×Dic10—31no—
45C4×C5×D8—31no—
46#65439—32no—
47#65304—31no—
48#65296—31no—
49#65179—32no—
50#65049—32no—
51#65045—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30—21no—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C3×#709—44no—
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20C2312yes—
65C2×C3×C4×D5—22no—
66C2×C3×Dic10D411yescharacteristic
67C2×#1204—22no—
68C2×D3×Dic5—22no—
69D3×Dic10—44no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75C2×C3⋊#168C2312yes—
76C5×#213—22no—
77C5×(C2×D3)⋊C4—21no—
78C5×C4⋊Dic3C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×#685—22no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×#683D412yes—
84C3×C4×Dic5C2312yes—
85#6668—22no—
86(C2×D3)⋊Dic5—22no—
87#6652—24no—
88C3×#550—51no—
89Q8×D12—51no—
90#5072—52no—
91#5072—51no—
92#5070—52no—
93#5070—51no—
94Q8×C3⋊C8—51no—
95C4×#213—52no—
96C4×#213D511yescharacteristic, complemented
97#5007—51no—
98#5007—52no—
99C2×#709—21no—
100C22×Dic10—61no—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4086C2×D312yes—
105D4×Dic5—32no—
106C2×#686—32no—
107#4076—21no—
108#4070—61no—
109#4039C2×D312yes—
110#4034—32no—
111#4030—22no—
112#4024—62no—
113#4020C2×D311yescharacteristic
114#4015—31no—
115C4×Dic10C2×D311yescharacteristic
116C5×#107—31no—
117C5×#102—31no—
118C5×#102—31no—
119C4×C5×C8—31no—
120#3964—32no—
121#3953—32no—
122#3953—32no—
123#3946—32no—
124C8×Dic5—32no—
125#3941—32no—
126#3939—32no—
127C4⋊#168—31no—
128#3358—151noSylow
129C23×C3×C5—21no—
130C22×C5×D3—21no—
131C22×C3×D5—22no—
132C3×C5×D4—21no—
133C3×C5×D4—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—22no—
140Dic30—42no—
141C2×C5×Dic3—21no—
142C5×D12—21no—
143C5×D12#4112yescomplemented
144C4×C5×D3—42no—
145C3×C22⋊D5—44no—
146C3×C22⋊D5—82no—
147C2×C3×Dic5C2×D412yes—
148C2×C3×Dic5C2×D412yes—
149C3×D20—22no—
150C3×D20—22no—
151C3×D20—42no—
152C3×D20—81no—
153C3×C4×D5—44no—
154C3×Dic10D814yescomplemented
155#1204—44no—
156D3×Dic5—44no—
157C3⋊#168—22no—
158C5×C3⋊C8—21no—
159C5×C3⋊C8—21no—
160C2×C3×#41—101no—
161C2×D3×Q8—101no—
162C3×#127—52no—
163C3×#127—51no—
164C3×#121—102no—
165C3×#121—101no—
166C3×C4×Q8—51no—
167C3×C4×D4—52no—
168C3×C4×D4C2×D511yescharacteristic
169C2×#213—52no—
170C2×#213C2×D511yescharacteristic
171#897—102no—
172#897—101no—
173C4×D12—52no—
174C4×D12C2×D511yescharacteristic
175#869—51no—
176#869—52no—
177#832—52no—
178#832—52no—
179#832—52no—
180#832—52no—
181#832C2×D511yescharacteristic
182#809C2×D511yescharacteristic
183#807—52no—
184#807C2×D511yescharacteristic
185C4⋊(C3⋊C8)—51no—
186C4⋊(C3⋊C8)—52no—
187C4×C3⋊C8—52no—
188C4×C3⋊C8C2×D511yescharacteristic
189C2×C5×D4—31no—
190C2×C5×D4C22×D311yescharacteristic
191C22×C4×C5—21no—
192C22×C4×C5—61no—
193C2×C22⋊D5—22no—
194C2×C22⋊D5—22no—
195C22×Dic5—62no—
196#709—44no—
197C2×D20—21no—
198C2×D20—21no—
199C2×D20C22×D312yes—
200C2×C4×D5—22no—
201C2×Dic10—61no—
202C2×Dic10—62no—
203C2×Dic10—124no—
204C2×Dic10#6711yescharacteristic
205C5×D8—62no—
206C2×C5×C8—31no—
207C2×C5×C8—31no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4C22×D311yescharacteristic
210C5×C22⋊C4—21no—
211C5×C22⋊C4—61no—
212C42×C5C22×D311yescharacteristic
213C22⋊Dic5—62no—
214#686—64no—
215#685—22no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218C4⋊Dic5#6711yescharacteristic
219#683—62no—
220#683#6712yes—
221C4×Dic5C22×D312yes—
222C2×#168—32no—
223#550—51no—
224D4×Q8—151no—
225#486—151no—
226#486—152no—
227#474—152no—
228#474—151no—
229#459—151no—
230#459—152no—
231C8×Q8—151no—
232C4×D8—31no—
233C4×D8—152no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5C2×D812yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C52−1+411yescharacteristic
249Dic15—42no—
250C3×Dic5—22no—
251C3×Dic5C2×D814yes—
252C5×Dic3—41no—
253C3×#41—204no—
254C2×C3×Q8—51no—
255C2×C3×D4—52no—
256C2×C3×D4—102no—
257C2×C3×D4—102no—
258C2×C3×D4—101no—
259C2×C3×D4—101no—
260C2×C3×D4C22×D511yescharacteristic
261C22×C3×C4—21no—
262C22×C3×C4—102no—
263D3×Q8—204no—
264C2×D12C22×D511yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3—102no—
267C2×Dic6—102no—
268C2×Dic6—101no—
269C3×C4⋊C4—52no—
270C3×C4⋊C4—51no—
271C3×C4⋊C4C22×D511yescharacteristic
272C3×C22⋊C4—21no—
273C3×C22⋊C4—102no—
274C3×C42—52no—
275C3×C42C22×D511yescharacteristic
276#213—22no—
277#213—104no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—102no—
280C4⋊Dic3—52no—
281C4⋊Dic3—102no—
282C4⋊Dic3—101no—
283C4⋊Dic3C22×D511yescharacteristic
284C2×C3⋊C8—52no—
285C2×C3⋊C8C22×D511yescharacteristic
286C2×C3⋊C8C22×D511yescharacteristic
287C23×C5—21no—
288C23×C5—61no—
289C22×D5—22no—
290C5×D4—21no—
291C5×D4—21no—
292C5×D4—32no—
293C5×D4—61no—
294C2×C4×C5—21no—
295C2×C4×C5—42no—
296C2×C4×C5—61no—
297C2×C4×C5—122no—
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—44no—
302C22⋊D5—82no—
303C2×Dic5—62no—
304C2×Dic5—124no—
305C2×Dic5C2×#6712yes—
306C2×Dic5C2×#6712yes—
307D20—22no—
308D20—22no—
309D20—42no—
310D20—81no—
311C4×D5—44no—
312Dic10—122no—
313Dic10—124no—
314Dic10#21314yescomplemented
315C5×C8—61no—
316C5×C8—61no—
317#168—62no—
318C2×#41—101no—
319C22×Q8—301no—
320C2×D8—31no—
321C2×D8—152no—
322C4⋊Q8—152no—
323C4⋊Q8—151no—
324#127—52no—
325#127—51no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—102no—
329#121—101no—
330C4×Q8—51no—
331C4×D4—31no—
332C4×D4—52no—
333C4×D4—152no—
334C4×D4D3×D511yescharacteristic
335#107—31no—
336#107—152no—
337C4⋊C8—152no—
338C4⋊C8—151no—
339#102—31no—
340#102—31no—
341#102—152no—
342#102—152no—
343#102—152no—
344#102—152no—
345C4×C8—31no—
346C4×C8—152no—
347C2×C3×C5—81no—
348C2×C3×C5#54811yescharacteristic
349C2×C3×C5C22×D811yescharacteristic
350C2×C3×C5#57711yescharacteristic
351C3×D5—82no—
352C5×D3—42no—
353C23×C3—21no—
354C23×C3—102no—
355C22×D3—21no—
356C3×Q8—54no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—204no—
362C3×D4—202no—
363C3×D4—401no—
364C3×D4—402no—
365C2×C3×C4—21no—
366C2×C3×C4—42no—
367C2×C3×C4—52no—
368C2×C3×C4—52no—
369C2×C3×C4—204no—
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373C2×Dic3—21no—
374C2×Dic3—102no—
375D12—21no—
376D12#70912yescomplemented
377C4×D3—42no—
378C4×D3—204no—
379Dic6—204no—
380Dic6—202no—
381C3⋊C8—21no—
382C3⋊C8—21no—
383C3⋊C8—102no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5—62no—
388C22×C5—121no—
389C22×C5—121no—
390C22×C5C22×#6711yescharacteristic
391C2×D5—42no—
392C2×D5—42no—
393C2×D5—42no—
394C4×C5—21no—
395C4×C5—41no—
396C4×C5—121no—
397C4×C5C2×#21312yes—
398C4×C5D3×#4111yescharacteristic
399C4×C5#101011yescharacteristic
400Dic5—22no—
401Dic5—122no—
402Dic5C2×#21314yes—
403#41—204no—
404C2×Q8—51no—
405C2×Q8—302no—
406C2×Q8—301no—
407C2×Q8—604no—
408C2×D4—31no—
409C2×D4—52no—
410C2×D4—102no—
411C2×D4—102no—
412C2×D4—101no—
413C2×D4—101no—
414C2×D4C2×D3×D511yescharacteristic
415C22×C4—21no—
416C22×C4—61no—
417C22×C4—102no—
418C22×C4—302no—
419D8—62no—
420D8—304no—
421C2×C8—31no—
422C2×C8—31no—
423C2×C8—152no—
424C4⋊C4—31no—
425C4⋊C4—52no—
426C4⋊C4—51no—
427C4⋊C4—152no—
428C4⋊C4—302no—
429C4⋊C4—301no—
430C4⋊C4C2×D3×D511yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—61no—
433C22⋊C4—102no—
434C22⋊C4—302no—
435C42—52no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—202no—
442C22×C3—202no—
443C22×C3—202no—
444C22×C3C2×D4×D511yescharacteristic
445C2×D3—22no—
446C2×D3—41no—
447C2×D3—41no—
448C3×C4—21no—
449C3×C4—41no—
450C3×C4—54no—
451C3×C4—102no—
452C3×C4D5×D812yes—
453C3×C4C2×#70911yescharacteristic
454C3×C4#415011yescharacteristic
455Dic3—41no—
456Dic3—202no—
457C2×C5—81no—
458C2×C5—122no—
459C2×C5C22×#21311yescharacteristic
460C2×C5#583111yescharacteristic
461C2×C5#583611yescharacteristic
462D5—82no—
463C23—21no—
464C23—61no—
465C23—102no—
466Q8—54no—
467Q8—604no—
468Q8—602no—
469D4—21no—
470D4—21no—
471D4—32no—
472D4—61no—
473D4—102no—
474D4—102no—
475D4—204no—
476D4—202no—
477D4—401no—
478D4—402no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—61no—
484C2×C4—122no—
485C2×C4—204no—
486C2×C4—302no—
487C2×C4—604no—
488C2×C4D5×#6711yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—61no—
492C8—61no—
493C8—302no—
494C2×C3—81no—
495C2×C3—402no—
496C2×C3#6588611yescharacteristic
497C2×C3C2×D5×D811yescharacteristic
498C2×C3#6610411yescharacteristic
499D3—42no—
500C5#8358011yescharacteristic, complemented, Sylow
501C22—41no—
502C22—41no—
503C22—41no—
504C22—62no—
505C22—121no—
506C22—121no—
507C22—202no—
508C22—202no—
509C22—202no—
510C22C2×D5×#6711yescharacteristic
511C4—21no—
512C4—41no—
513C4—54no—
514C4—102no—
515C4—121no—
516C4—602no—
517C4D5×#21312yes—
518C4#9200111yescharacteristic
519C4D3×#70911yescharacteristic
520C3#1061129811yescharacteristic, complemented, Sylow
521C2—81no—
522C2—122no—
523C2—402no—
524C2#1175452811yescharacteristic
525C2C2×D5×#21311yescharacteristic
526C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3358
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×#65887C2semidirect
2. D12×Dic10C2semidirect
3. #11751108C2semidirect
4. C4×C5×#213C2semidirect
5. #11749102C2semidirect
6. #11748974C2semidirect
7. #11747410C2semidirect
8. #11747216C2semidirect
9. #11747033C2semidirect
10. #11746890C2semidirect
11. C3⋊C8×Dic10C2semidirect
43. #65887D3semidirect
96. C4×#213D5semidirect
143. C5×D12#41semidirect
154. C3×Dic10D8semidirect
314. Dic10#213semidirect
376. D12#709semidirect
437. C3×C5#3358semidirect
500. C5#83580semidirect
520. C3#10611298semidirect

Maximal subgroups

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

subgroupindex
C3×#658872
D12×Dic102
#117511082
C4×C5×#2132
#117491022
#117489742
#117474102
#117472162
#117470332
#117468902
C3⋊C8×Dic102
#106112983
#835805