Finite Group Databasebeta

← #14460223

Subgroups — #14460223

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752710C211yesmaximal, characteristic, complemented
2#11752549C211yesmaximal, characteristic, complemented
3C8×D60C211yesmaximal, characteristic, complemented
4C4×C5×D24C211yesmaximal, characteristic, complemented
5C3×#64970C211yesmaximal, characteristic, complemented
6#11748159C212yesmaximal, complemented
7#11748145C212yesmaximal, complemented
8#11747928C212yesmaximal, complemented
9#11747692C212yesmaximal, complemented
10#11747070C211yesmaximal, characteristic, complemented
11#11746882C211yesmaximal, characteristic, complemented
12#10611341—31nomaximal, Hall
13C2×#6768C2212yes—
14C2×C8×D15C2212yes—
15C4×D60C2211yescharacteristic
16C2×C5×D24C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C4×C5×D12C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20C3×#4015C2211yescharacteristic
21#91466C2212yes—
22#91460—21no—
23#91460—21no—
24#91427—22no—
25D3×C4⋊Dic5—21no—
26#91390C2212yes—
27#91347C2212yes—
28#91338—21no—
29#91326—22no—
30C2×#6656C2212yes—
31C3×C4×C5×C8C2211yescharacteristic
32#91104C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#821C2211yescharacteristic
36C5×#818C2211yescharacteristic
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90986C2212yes—
40#90970C2212yes—
41#90966C2212yes—
42#81615—51nomaximal, Hall
43#65897—31no—
44#65889—31no—
45C4×C5×D8—31no—
46#65447—32no—
47#65308—31no—
48#65297—31no—
49#65177—32no—
50#65067—32no—
51#65061—32no—
52C8×D20—31no—
53#64970D311yescharacteristic, complemented
54C2×D60D411yescharacteristic
55C2×C4×D15C2312yes—
56C2×C5×D12C2311yescharacteristic
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C4×C5×D3—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2312yes—
62C2×#1203—22no—
63C2×#1203—22no—
64C2×D3×Dic5—22no—
65#6768—24no—
66#6768—42no—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70#6714D412yes—
71C4⋊Dic15D411yescharacteristic
72C2×C3⋊#168C2312yes—
73C8×D15—42no—
74C5×(C2×D3)⋊C4—21no—
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C5×D24—22no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83Dic3⋊Dic5—22no—
84#6667—22no—
85#6667—22no—
86(C2×D3)⋊Dic5—22no—
87Dic3×Dic5—22no—
88#6656—42no—
89#5734—51no—
90#5726—51no—
91C3×#487—51no—
92#5084—51no—
93#5083—51no—
94#4814—52no—
95#4810—52no—
96#4807—52no—
97#4804—52no—
98C4×D24D511yescharacteristic, complemented
99C8×D12—51no—
100C2×#711—32no—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4—31no—
104#4084—32no—
105C2×#687—32no—
106#4076—61no—
107#4076—61no—
108#4072—61no—
109C2×C4⋊Dic5—61no—
110C2×C8×D5—32no—
111#4043—32no—
112#4038—32no—
113#4032—62no—
114#4031—62no—
115C4×D20—31no—
116#4015C2×D311yescharacteristic
117#4015C2×D311yescharacteristic
118C5×#107—31no—
119C5×#102—31no—
120C5×#102—31no—
121C4×C5×C8C2×D311yescharacteristic
122#3964—32no—
123#3952—32no—
124#3948C2×D312yes—
125#3948C2×D312yes—
126#3942—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3303—151noSylow
130C22×D15C2×D412yes—
131C22×C5×D3—21no—
132C22×C5×D3—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15C2×D412yes—
137D60—22no—
138C4×D15—22no—
139C4×D15—22no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C5×D12—21no—
143C5×D12—21no—
144C5×D12—21no—
145C5×D12#4112yes—
146C4×C5×D3—42no—
147C4×C5×D3—42no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C3×Dic10—22no—
151C3×Dic10—22no—
152C3×Dic10—81no—
153#1203—44no—
154#1203—82no—
155D3×Dic5—44no—
156C3×C5×C8—21no—
157C3×C5×C8—21no—
158C3⋊#168—22no—
159C2×#239—52no—
160C3×C4⋊Q8—51no—
161C3×C4⋊Q8—51no—
162#947—102no—
163#946—52no—
164C2×#215—52no—
165C2×D24C2×D511yescharacteristic
166C2×D3×C8—52no—
167#895—52no—
168#895—101no—
169#895—101no—
170#894—102no—
171#892—52no—
172#892—101no—
173D3×C4⋊C4—101no—
174C4×D12—51no—
175C4×D12C2×D511yescharacteristic
176C4×D12C2×D511yescharacteristic
177C3×#103—52no—
178C3×#103—52no—
179C3×C4×C8C2×D511yescharacteristic
180#835—52no—
181#821C2×D511yescharacteristic
182#821C2×D511yescharacteristic
183(C2×D3)⋊C8—52no—
184#818C2×D511yescharacteristic
185#809—52no—
186#808—52no—
187C4⋊(C3⋊C8)—51no—
188C2×C5×D4—31no—
189C2×C5×D4—31no—
190C22×C4×C5—61no—
191C22×C4×C5—61no—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194C22×Dic5—62no—
195#711—64no—
196#711—122no—
197C2×D20—31no—
198C2×C4×D5—32no—
199C2×Dic10—21no—
200C2×Dic10C22×D312yes—
201C5×D8—62no—
202C2×C5×C8C22×D311yescharacteristic
203C2×C5×C8C22×D311yescharacteristic
204C5×C4⋊C4—31no—
205C5×C4⋊C4—31no—
206C5×C22⋊C4—61no—
207C5×C22⋊C4—61no—
208C42×C5C22×D311yescharacteristic
209C22⋊Dic5—62no—
210#687—122no—
211#685—32no—
212#685—62no—
213#685—62no—
214C4⋊Dic5—21no—
215C4⋊Dic5—21no—
216C4⋊Dic5—21no—
217C4⋊Dic5—31no—
218C4⋊Dic5—62no—
219C4⋊Dic5C22×D312yes—
220C4×Dic5—62no—
221C2×#168—32no—
222C8×D5—122no—
223#555—151no—
224#547—151no—
225#487—51no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—31no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—22no—
236C2×D15—22no—
237C2×D15—22no—
238C2×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C5×D3—41no—
242C2×C5×D3—41no—
243C2×C5×D3—41no—
244C3×C4×C5—21no—
245C3×C4×C5#13512yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C5H(5,𝔽2)11yescharacteristic
248Dic15—22no—
249C3×Dic5—42no—
250C3×Dic5—42no—
251C5×Dic3—41no—
252C5×Dic3—41no—
253C2×C3×Q8—52no—
254C2×C3×Q8—101no—
255#239—104no—
256#239—202no—
257C2×D12—51no—
258C2×D12—102no—
259C2×D12—102no—
260C2×D12C22×D511yescharacteristic
261C2×D12C22×D511yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—52no—
265C2×C4×D3—102no—
266C2×C3×C8C22×D511yescharacteristic
267C2×C3×C8C22×D511yescharacteristic
268C3×C4⋊C4—52no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4—101no—
271C3×C4⋊C4—101no—
272C3×C42C22×D511yescharacteristic
273#215—202no—
274(C2×D3)⋊C4—21no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—52no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—102no—
279(C2×D3)⋊C4—102no—
280C4⋊Dic3—51no—
281C4⋊Dic3C22×D511yescharacteristic
282C4⋊Dic3C22×D511yescharacteristic
283Dic3⋊C4—102no—
284C4×Dic3—102no—
285C2×C3⋊C8—52no—
286D24—22no—
287D3×C8—202no—
288C23×C5—61no—
289C23×C5—61no—
290C22×D5—32no—
291C5×D4—32no—
292C5×D4—61no—
293C5×D4—61no—
294C5×D4—61no—
295C2×C4×C5—61no—
296C2×C4×C5—61no—
297C2×C4×C5—122no—
298C2×C4×C5—122no—
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C22⋊D5—124no—
303C22⋊D5—242no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—32no—
307C2×Dic5—124no—
308D20—62no—
309C4×D5—62no—
310C4×D5—62no—
311Dic10—22no—
312Dic10—22no—
313Dic10—81no—
314C5×C8—21no—
315C5×C8—21no—
316#168—62no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—31no—
320C22×C8—152no—
321C4⋊Q8—51no—
322C4⋊Q8—51no—
323#124—302no—
324#123—302no—
325C22⋊Q8—152no—
326#121—152no—
327#121—301no—
328#121—301no—
329C4×D4—31no—
330C4×D4—31no—
331C4×D4—151no—
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—31no—
336#106—152no—
337C4⋊C8—151no—
338#103—52no—
339#103—52no—
340#103—152no—
341#102—31no—
342#102—31no—
343#102—152no—
344C22⋊C8—152no—
345C4×C8D3×D511yescharacteristic
346C2×C3×C5#54611yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5#57711yescharacteristic
349D15—42no—
350C5×D3—42no—
351C5×D3—81no—
352C22×D3—21no—
353C22×D3—21no—
354C22×D3—52no—
355C3×Q8—102no—
356C3×Q8—102no—
357C3×Q8—401no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—52no—
366D12—21no—
367D12—21no—
368D12—21no—
369D12—102no—
370D12—204no—
371D12—402no—
372D12#70912yes—
373C4×D3—42no—
374C4×D3—42no—
375C4×D3—102no—
376C4×D3—102no—
377C4×D3—204no—
378C3×C8—21no—
379C3×C8—21no—
380C3⋊C8—102no—
381C22×C5—62no—
382C22×C5—121no—
383C22×C5—121no—
384C22×C5—121no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C2×D3×D411yescharacteristic
388C2×D5—62no—
389C2×D5—62no—
390C2×D5—62no—
391C4×C5—21no—
392C4×C5—121no—
393C4×C5—121no—
394C4×C5#91912yes—
395C4×C5D3×#4111yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—42no—
398Dic5—42no—
399Dic5—62no—
400#41—304no—
401#41—602no—
402C2×Q8—52no—
403C2×Q8—101no—
404C2×D4—31no—
405C2×D4—31no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4—302no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—152no—
412C22×C4—302no—
413SD16—602no—
414D8—62no—
415C2×C8—152no—
416C2×C8—602no—
417C2×C8C2×D3×D511yescharacteristic
418C2×C8C2×D3×D511yescharacteristic
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—52no—
422C4⋊C4—101no—
423C4⋊C4—101no—
424C4⋊C4—101no—
425C4⋊C4—151no—
426C4⋊C4—302no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C22⋊C4—152no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C22⋊C4—302no—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3C2×D4×D511yescharacteristic
437C2×D3—22no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—102no—
444C2×D3—102no—
445C2×D3—102no—
446C3×C4—21no—
447C3×C4—202no—
448C3×C4—202no—
449C3×C4#405812yes—
450C3×C4C2×#70911yescharacteristic
451C3×C4#414911yescharacteristic
452Dic3—41no—
453Dic3—41no—
454Dic3—102no—
455C2×C5—122no—
456C2×C5—241no—
457C2×C5#567611yescharacteristic
458C2×C5#576211yescharacteristic
459C2×C5C2×#91911yescharacteristic
460D5—122no—
461C23—61no—
462C23—61no—
463C23—152no—
464Q8—102no—
465Q8—102no—
466Q8—401no—
467D4—32no—
468D4—61no—
469D4—61no—
470D4—61no—
471D4—302no—
472D4—604no—
473D4—1202no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—102no—
477C2×C4—102no—
478C2×C4—122no—
479C2×C4—122no—
480C2×C4—152no—
481C2×C4—302no—
482C2×C4—302no—
483C2×C4—604no—
484C2×C4#677711yescharacteristic
485C2×C4#677711yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—21no—
488C8—21no—
489C8—302no—
490C2×C3#6588411yescharacteristic
491C2×C3C2×#405811yescharacteristic
492C2×C3#6610411yescharacteristic
493D3—42no—
494D3—81no—
495D3—202no—
496C5#8161511yescharacteristic, complemented, Sylow
497C22—62no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22—302no—
504C22—302no—
505C22—302no—
506C22C2×#677711yescharacteristic
507C4—21no—
508C4—121no—
509C4—121no—
510C4—202no—
511C4—202no—
512C4—302no—
513C4#9127912yes—
514C4D3×#70911yescharacteristic
515C4#9201911yescharacteristic
516C3#1061134111yescharacteristic, complemented, Sylow
517C2—122no—
518C2—241no—
519C2—602no—
520C2#1175274911yescharacteristic
521C2#1175398011yescharacteristic
522C2C2×#9127911yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752710C2semidirect
2. #11752549C2semidirect
3. C8×D60C2semidirect
4. C4×C5×D24C2semidirect
5. C3×#64970C2semidirect
6. #11748159C2semidirect
7. #11748145C2semidirect
8. #11747928C2semidirect
9. #11747692C2semidirect
10. #11747070C2semidirect
11. #11746882C2semidirect
53. #64970D3semidirect
98. C4×D24D5semidirect
435. C3×C5#3303semidirect
496. C5#81615semidirect
516. C3#10611341semidirect

Maximal subgroups

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

subgroupindex
#117527102
#117525492
C8×D602
C4×C5×D242
C3×#649702
#117481592
#117481452
#117479282
#117476922
#117470702
#117468822
#106113413
#816155