Finite Group Databasebeta

← #14458301

Subgroups — #14458301

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756310C211yesmaximal, characteristic, complemented
2D4×D60C211yesmaximal, characteristic, complemented
3C3×C4×C5×D8C211yesmaximal, characteristic, complemented
4#11751257C212yesmaximal, complemented
5#11751116C211yesmaximal, characteristic, complemented
6#11751108C211yesmaximal, characteristic, complemented
7#11750983C212yesmaximal, complemented
8#11750876C212yesmaximal, complemented
9D15×#102C212yesmaximal, complemented
10#11750795C211yesmaximal, characteristic, complemented
11C8×D60C211yesmaximal, characteristic, complemented
12#10611339—31nomaximal, Hall
13C2×D4×D15C2212yes—
14C2×#6817—21no—
15C22×D60—21no—
16C2×C3×C5×D8C2211yescharacteristic
17C3×C4×C5×D4C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic, complemented
19#91827C2212yescomplemented
20C2×#6715C2212yescomplemented
21#91819—21no—
22#91813—21no—
23C2×C8×D15C2212yescomplemented
24#91784C2212yes—
25C4⋊C4×D15C2212yescomplemented
26#91772—22no—
27#91771—22no—
28#91763C2211yescharacteristic
29C4×D60C2211yescharacteristic
30#91758C2211yescharacteristic, complemented
31C3×C5×#107C2211yescharacteristic, complemented
32C3×C5×#102C2211yescharacteristic
33C3×C5×#102C2211yescharacteristic, complemented
34C3×C4×C5×C8C2211yescharacteristic, complemented
35#91116C2212yes—
36#91105C2212yescomplemented
37#91105C2212yescomplemented
38#91104C2212yescomplemented
39#91093C2212yescomplemented
40#91091C2212yescomplemented
41C4⋊(C3⋊#168)C2211yescharacteristic, complemented
42#79608—51nomaximal, Hall
43#65885—31no—
44D4×D20—31no—
45C4×C5×D8D311yescharacteristic, complemented
46#65445—32no—
47#65304—31no—
48#65296—31no—
49#65171—32no—
50#65064—32no—
51D5×#102—32no—
52#64983—31no—
53C8×D20—31no—
54C23×D15—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—21no—
59C2×#1220—22no—
60C2×#1220—22no—
61D4×D15—24no—
62D4×D15—42no—
63#6817—44no—
64C2×D60—22no—
65C2×D60—21no—
66C2×D60—21no—
67C2×D60—44no—
68C2×D60D411yescharacteristic
69C2×D60C2312yes—
70C2×C4×D15—22no—
71C2×C4×D15C2312yes—
72C2×Dic30—21no—
73C3×C5×D8—22no—
74C2×C3×C5×C8C2311yescharacteristic
75C2×C3×C5×C8C2311yescharacteristic
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C22⋊C4—21no—
79C3×C5×C22⋊C4—21no—
80C3×C42×C5C2311yescharacteristic
81#6719—22no—
82#6715—42no—
83#6714—22no—
84#6714D412yes—
85C4⋊Dic15—21no—
86C4⋊Dic15D411yescharacteristic
87C4⋊Dic15C2312yes—
88#6712—22no—
89C2×C3⋊#168C2312yes—
90C8×D15—42no—
91#5551—51no—
92D4×D12—51no—
93C3×C4×D8D511yescharacteristic, complemented
94#5156—52no—
95#5015—51no—
96#5007—51no—
97#4882—52no—
98#4775—52no—
99D3×#102—52no—
100#4694—51no—
101C8×D12—51no—
102C2×D4×D5—32no—
103C2×#709—61no—
104C22×D20—61no—
105C2×C5×D8C2×D311yescharacteristic
106C4×C5×D4C2×D311yescharacteristic
107C4×C5×D4C2×D311yescharacteristic, complemented
108#4084—32no—
109C2×#686—32no—
110#4076—61no—
111#4070—61no—
112C2×C8×D5—32no—
113#4041—32no—
114D5×C4⋊C4—32no—
115#4029—62no—
116#4028—62no—
117#4020—31no—
118C4×D20—31no—
119#4015—31no—
120C5×#107C2×D311yescharacteristic, complemented
121C5×#102C2×D311yescharacteristic
122C5×#102C2×D311yescharacteristic, complemented
123C4×C5×C8C2×D311yescharacteristic, complemented
124#3964—32no—
125#3953—32no—
126#3953—32no—
127#3952—32no—
128#3941—32no—
129#3939—32no—
130C4⋊#168—31no—
131#3294—151noSylow
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C22×D15—22no—
135C22×D15—44no—
136C22×D15—44no—
137C22×D15—82no—
138C22×D15C2×D412yes—
139C3×C5×D4—21no—
140C3×C5×D4—21no—
141C3×C5×D4—21no—
142C3×C5×D4#4112yescomplemented
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—42no—
146C2×C3×C4×C5—42no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150#1220—44no—
151#1220—44no—
152C2×Dic15—22no—
153C2×Dic15C2×D412yes—
154D60—22no—
155D60—22no—
156D60—44no—
157D60—42no—
158D60—81no—
159D60D814yescomplemented
160C4×D15—22no—
161C4×D15—22no—
162C4×D15—44no—
163Dic30—42no—
164C3×C5×C8—21no—
165C3×C5×C8—21no—
166C3⋊#168—22no—
167C2×D3×D4—52no—
168C2×#235—101no—
169C22×D12—101no—
170C2×C3×D8C2×D511yescharacteristic
171C3×C4×D4C2×D511yescharacteristic
172C3×C4×D4C2×D511yescharacteristic, complemented
173#938—52no—
174C2×#213—52no—
175#930—101no—
176#924—101no—
177C2×D3×C8—52no—
178#895—52no—
179D3×C4⋊C4—52no—
180#883—102no—
181#882—102no—
182#874—51no—
183C4×D12—51no—
184#869—51no—
185C3×#107C2×D511yescharacteristic, complemented
186C3×#102C2×D511yescharacteristic
187C3×#102C2×D511yescharacteristic, complemented
188C3×C4×C8C2×D511yescharacteristic, complemented
189#832—52no—
190#821—52no—
191#821—52no—
192(C2×D3)⋊C8—52no—
193#809—52no—
194#807—52no—
195C4⋊(C3⋊C8)—51no—
196C23×D5—62no—
197C2×C5×D4C22×D311yescharacteristic
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C2×C22⋊D5—62no—
202C2×C22⋊D5—62no—
203D4×D5—64no—
204D4×D5—122no—
205#709—124no—
206C2×D20—31no—
207C2×D20—32no—
208C2×D20—62no—
209C2×D20—61no—
210C2×D20—61no—
211C2×D20—124no—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×Dic10—61no—
215C5×D8—22no—
216C2×C5×C8C22×D311yescharacteristic
217C2×C5×C8C22×D311yescharacteristic
218C5×C4⋊C4C22×D311yescharacteristic
219C5×C4⋊C4C22×D311yescharacteristic
220C5×C22⋊C4—21no—
221C5×C22⋊C4—21no—
222C42×C5C22×D311yescharacteristic
223C22⋊Dic5—62no—
224#686—122no—
225#685—32no—
226#685—62no—
227C4⋊Dic5—31no—
228C4⋊Dic5—32no—
229C4⋊Dic5—61no—
230#683—62no—
231C2×#168—32no—
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8D1511yescharacteristic, complemented
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5C22×D411yescharacteristic
251C2×D15—22no—
252C2×D15—22no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—88no—
257C2×D15C2×D814yes—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5—41no—
261C3×C4×C5C2×D812yes—
262C3×C4×C5C2×#4111yescharacteristic
263C3×C4×C5H(5,𝔽2)11yescharacteristic
264Dic15—22no—
265Dic15—42no—
266C23×D3—102no—
267C2×C3×D4C22×D511yescharacteristic
268C2×C3×D4C22×D511yescharacteristic
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C2×#67—102no—
272C2×#67—102no—
273D3×D4—104no—
274D3×D4—202no—
275#235—204no—
276C2×D12—51no—
277C2×D12—52no—
278C2×D12—102no—
279C2×D12—101no—
280C2×D12—101no—
281C2×D12—204no—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×Dic6—101no—
285C3×D8—22no—
286C2×C3×C8C22×D511yescharacteristic
287C2×C3×C8C22×D511yescharacteristic
288C3×C4⋊C4C22×D511yescharacteristic
289C3×C4⋊C4C22×D511yescharacteristic
290C3×C22⋊C4—21no—
291C3×C22⋊C4—21no—
292C3×C42C22×D511yescharacteristic
293#217—102no—
294#213—202no—
295(C2×D3)⋊C4—52no—
296(C2×D3)⋊C4—102no—
297C4⋊Dic3—51no—
298C4⋊Dic3—52no—
299C4⋊Dic3—101no—
300Dic3⋊C4—102no—
301C2×C3⋊C8—52no—
302D3×C8—202no—
303C23×C5—21no—
304C23×C5—21no—
305C22×D5—32no—
306C22×D5—62no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×D4—21no—
311C5×D4—21no—
312C5×D4—21no—
313C5×D4#23512yescomplemented
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—124no—
322C22⋊D5—124no—
323C2×Dic5—32no—
324C2×Dic5—62no—
325D20—34no—
326D20—62no—
327D20—62no—
328D20—124no—
329D20—122no—
330D20—241no—
331C4×D5—62no—
332C4×D5—62no—
333C4×D5—124no—
334Dic10—122no—
335C5×C8—21no—
336C5×C8—21no—
337#168—62no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—152no—
342C2×D8C2×D1511yescharacteristic
343C22×C8—152no—
344C4⋊Q8—151no—
345#127—151no—
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—151no—
353C4×D4C2×D1511yescharacteristic
354C4×D4C2×D1511yescharacteristic, complemented
355C2×C4⋊C4—152no—
356#107—152no—
357#107C2×D1511yescharacteristic, complemented
358C4⋊C8—151no—
359#102—152no—
360#102—152no—
361#102—152no—
362#102—152no—
363#102C2×D1511yescharacteristic
364#102C2×D1511yescharacteristic, complemented
365C22⋊C8—152no—
366C4×C8C2×D1511yescharacteristic, complemented
367C2×C3×C5—42no—
368C2×C3×C5—81no—
369C2×C3×C5#54611yescharacteristic
370C2×C3×C5C22×D811yescharacteristic
371C2×C3×C5#57711yescharacteristic
372D15—24no—
373D15—82no—
374C23×C3—21no—
375C23×C3—21no—
376C22×D3—52no—
377C22×D3—102no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×D4—21no—
382C3×D4—21no—
383C3×D4—21no—
384C3×D4#70912yescomplemented
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—204no—
393#67—204no—
394C2×Dic3—52no—
395C2×Dic3—102no—
396D12—54no—
397D12—102no—
398D12—102no—
399D12—204no—
400D12—202no—
401D12—401no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—204no—
405Dic6—202no—
406C3×C8—21no—
407C3×C8—21no—
408C3⋊C8—102no—
409C22×C5—22no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—34no—
417C2×D5—62no—
418C2×D5—62no—
419C2×D5—122no—
420C2×D5—122no—
421C2×D5—122no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5—41no—
426C4×C5D3×D812yes—
427C4×C5C2×#23511yescharacteristic
428C4×C5#100911yescharacteristic
429Dic5—62no—
430Dic5—122no—
431C24—302no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—151no—
435C2×D4—152no—
436C2×D4—302no—
437C2×D4—302no—
438C2×D4—304no—
439C2×D4—302no—
440C2×D4—301no—
441C2×D4—301no—
442C2×D4—604no—
443C2×D4—602no—
444C2×D4C22×D1511yescharacteristic
445C2×D4C22×D1511yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—152no—
449C22×C4—302no—
450D8—22no—
451D8—602no—
452C2×C8—152no—
453C2×C8—602no—
454C2×C8C22×D1511yescharacteristic
455C2×C8C22×D1511yescharacteristic
456C4⋊C4—151no—
457C4⋊C4—152no—
458C4⋊C4—302no—
459C4⋊C4—301no—
460C4⋊C4C22×D1511yescharacteristic
461C4⋊C4C22×D1511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—152no—
465C22⋊C4—302no—
466C22⋊C4—302no—
467C42C22×D1511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—54no—
477C2×D3—102no—
478C2×D3—102no—
479C2×D3—202no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4D5×D812yes—
487C3×C4C2×#70911yescharacteristic
488C3×C4#414911yescharacteristic
489Dic3—102no—
490Dic3—202no—
491C2×C5—42no—
492C2×C5—81no—
493C2×C5#555011yescharacteristic
494C2×C5C2×D3×D811yescharacteristic
495C2×C5#577011yescharacteristic
496D5—64no—
497D5—242no—
498C23—21no—
499C23—21no—
500C23—152no—
501C23—302no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—602no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—154no—
510D4—302no—
511D4—302no—
512D4—604no—
513D4—604no—
514D4—604no—
515D4—602no—
516D4—1201no—
517D4#681712yescomplemented
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—152no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4D4×D1511yescharacteristic
528C2×C4D4×D1511yescharacteristic
529C2×C4C23×D1511yescharacteristic
530C8—21no—
531C8—21no—
532C8—302no—
533C2×C3—42no—
534C2×C3—81no—
535C2×C3#6588411yescharacteristic
536C2×C3C2×D5×D811yescharacteristic
537C2×C3#6610411yescharacteristic
538D3—104no—
539D3—402no—
540C5#7960811yescharacteristic, complemented, Sylow
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—154no—
548C22—302no—
549C22—302no—
550C22—602no—
551C22—602no—
552C22—602no—
553C22—1208no—
554C22C2×D4×D1511yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—302no—
559C4—602no—
560C4D8×D1512yes—
561C4C2×#681711yescharacteristic
562C4#9210011yescharacteristic
563C3#1061133911yescharacteristic, complemented, Sylow
564C2—42no—
565C2—81no—
566C2—304no—
567C2—1202no—
568C2#1175630911yescharacteristic
569C2C2×D8×D1511yescharacteristic
570C2#1175652911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
hypercenterC4×D8D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11756310C2semidirect
2. D4×D60C2semidirect
3. C3×C4×C5×D8C2semidirect
4. #11751257C2semidirect
5. #11751116C2semidirect
6. #11751108C2semidirect
7. #11750983C2semidirect
8. #11750876C2semidirect
9. D15×#102C2semidirect
10. #11750795C2semidirect
11. C8×D60C2semidirect
18. C3×C4×C5×D4C22semidirect
19. #91827C22semidirect
20. C2×#6715C22semidirect
23. C2×C8×D15C22semidirect
25. C4⋊C4×D15C22semidirect
30. #91758C22semidirect
31. C3×C5×#107C22semidirect
33. C3×C5×#102C22semidirect
34. C3×C4×C5×C8C22semidirect
36. #91105C22semidirect
37. #91105C22semidirect
38. #91104C22semidirect
39. #91093C22semidirect
40. #91091C22semidirect
41. C4⋊(C3⋊#168)C22semidirect
45. C4×C5×D8D3semidirect
93. C3×C4×D8D5semidirect
107. C4×C5×D4C2×D3semidirect
120. C5×#107C2×D3semidirect
122. C5×#102C2×D3semidirect
123. C4×C5×C8C2×D3semidirect
142. C3×C5×D4#41semidirect
159. D60D8semidirect
172. C3×C4×D4C2×D5semidirect
185. C3×#107C2×D5semidirect
187. C3×#102C2×D5semidirect
188. C3×C4×C8C2×D5semidirect
241. C4×D8D15semidirect
313. C5×D4#235semidirect
354. C4×D4C2×D15semidirect
357. #107C2×D15semidirect
364. #102C2×D15semidirect
366. C4×C8C2×D15semidirect
384. C3×D4#709semidirect
468. C3×C5#3294semidirect
517. D4#6817semidirect
540. C5#79608semidirect
563. C3#10611339semidirect

Maximal subgroups

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

subgroupindex
#117563102
D4×D602
C3×C4×C5×D82
#117512572
#117511162
#117511082
#117509832
#117508762
D15×#1022
#117507952
C8×D602
#106113393
#796085