Finite Group Databasebeta

← #14458390

Subgroups — #14458390

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#11756485C211yesmaximal, characteristic, complemented
2#11752745C211yesmaximal, characteristic, complemented
3C5×#5087C211yesmaximal, characteristic, complemented
4C3×#65377C211yesmaximal, characteristic, complemented
5#11747485C212yesmaximal, complemented
6#11747478C212yesmaximal, complemented
7#11747330C212yesmaximal, complemented
8#11747329C212yesmaximal, complemented
9#11747043C211yesmaximal, characteristic, complemented
10C4×#6654C211yesmaximal, characteristic, complemented
11#11746988C211yesmaximal, characteristic, complemented
12#10612711—31nomaximal, Hall
13C2×#6821—21no—
14C2×#6777C2212yes—
15C2×D3×D20—21no—
16C3×C5×C4⋊Q8C2211yescharacteristic, complemented
17#91835—21no—
18#91784C2212yescomplemented
19#91783—22no—
20C4⋊C4×D15C2212yescomplemented
21C4×D60C2211yescharacteristic
22C4×D60C2211yescharacteristic, complemented
23C4×C5×D12C2211yescharacteristic
24C3×#4020C2211yescharacteristic
25#91474—22no—
26#91465C2212yes—
27#91456—21no—
28C2×#6654C2211yescharacteristic
29C2×#6653C2212yescomplemented
30C2×#6648C2212yescomplemented
31C5×#809C2212yes—
32C5×#807C2212yescomplemented
33C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
34C3×#3941C2212yescomplemented
35C3×#3941C2212yescomplemented
36C3×C4×#168C2211yescharacteristic, complemented
37#90988C2211yescharacteristic, complemented
38#90969C2211yescharacteristic, complemented
39#90967C2211yescharacteristic
40#90965C2212yescomplemented
41#90957C2212yescomplemented
42#81576—51nomaximal, Hall
43#66060—31no—
44D4×D20—31no—
45C5×#474—31no—
46#65377D311yescharacteristic, complemented
47C4×#686—31no—
48#65172—32no—
49#65171—32no—
50#65132—31no—
51#65123—31no—
52#65062—32no—
53D5×#102—32no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8—21no—
56#6821—44no—
57C2×D60—22no—
58C2×D60D411yescharacteristic
59C2×D60C2311yescharacteristic
60C2×C4×D15—22no—
61C2×C4×D15—21no—
62C2×C4×D15C2312yes—
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C3×D20—21no—
66C2×C3×D20—21no—
67C2×C3×D20C2312yes—
68C2×#1202—22no—
69C2×#1201—22no—
70#6777—24no—
71#6777—42no—
72D3×D20—44no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—22no—
78#6714D412yes—
79C4⋊Dic15D411yescharacteristic
80C4⋊Dic15C2311yescharacteristic
81#6712—22no—
82C5×(C2×D3)⋊C4—21no—
83C5×C4⋊Dic3C2311yescharacteristic
84C2×C5×C3⋊C8C2312yes—
85C2×C3×#168C2311yescharacteristic
86C2×C3×#168C2311yescharacteristic
87#6665—22no—
88#6654—22no—
89#6653—42no—
90#6648—42no—
91#5726—51no—
92#5717—51no—
93C3×#486—51no—
94#5087D511yescharacteristic, complemented
95#5072—51no—
96#4775—52no—
97#4774—52no—
98#4773—52no—
99D3×#102—52no—
100C4×D24—51no—
101C8×D12—51no—
102C2×#713—61no—
103C2×D4×D5—32no—
104C22×D20—61no—
105C5×C4⋊Q8C2×D311yescharacteristic, complemented
106C4×C5×D4—31no—
107#4092—61no—
108C2×#686—31no—
109#4076—61no—
110C2×D40—32no—
111C2×C8×D5—32no—
112#4041—32no—
113#4041—32no—
114#4040—62no—
115D5×C4⋊C4—32no—
116#4028—62no—
117#4020C2×D311yescharacteristic
118C4×D20—31no—
119C4×D20—31no—
120C5×#107—32no—
121C5×C4⋊C8—31no—
122C5×#102—32no—
123#3964—31no—
124#3953—32no—
125#3952—32no—
126#3941—31no—
127#3941C2×D312yescomplemented
128#3941C2×D312yescomplemented
129#3939—31no—
130C4×#168C2×D311yescharacteristic, complemented
131#3294—151noSylow
132C22×D15—21no—
133C22×D15C2×D412yes—
134C22×C5×D3—21no—
135C22×C3×D5—22no—
136C2×D3×D5—44no—
137C2×D3×D5—44no—
138C2×D3×D5—82no—
139C3×C5×Q8—42no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15C2×D412yes—
146D60—21no—
147D60—21no—
148D60—44no—
149D60D814yescomplemented
150C4×D15—22no—
151C4×D15—22no—
152C4×D15—44no—
153C4×D15—42no—
154C2×C5×Dic3—21no—
155C5×D12—21no—
156C5×D12#4112yescomplemented
157C4×C5×D3—42no—
158C3×D20—22no—
159C3×D20—22no—
160C3×D20—42no—
161C3×D20—81no—
162#1202—44no—
163#1201—44no—
164C3×#168—21no—
165C3×#168—21no—
166C5×C3⋊C8—22no—
167C2×#239—101no—
168C2×D3×D4—52no—
169C2×D3×D4—101no—
170C3×C4⋊Q8C2×D511yescharacteristic, complemented
171C3×#127—51no—
172#946—101no—
173#938—52no—
174#938—101no—
175#937—102no—
176C2×#213—52no—
177C2×D24—51no—
178C2×D3×C8—52no—
179#895—52no—
180#894—102no—
181D3×C4⋊C4—52no—
182C4×D12—51no—
183C4×D12—51no—
184C4×D12C2×D511yescharacteristic
185C3×#102—52no—
186C3×#102—52no—
187C3×C4×C8—51no—
188#832—52no—
189#821—51no—
190#821—51no—
191(C2×D3)⋊C8—52no—
192#818—51no—
193#809C2×D512yes—
194#807C2×D512yescomplemented
195C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
196C23×D5—62no—
197C2×C5×Q8—21no—
198C2×C5×D4—31no—
199C22×C4×C5—61no—
200C2×C22⋊D5—62no—
201#713—124no—
202D4×D5—64no—
203D4×D5—122no—
204C2×D20—21no—
205C2×D20—21no—
206C2×D20—31no—
207C2×D20—31no—
208C2×D20—62no—
209C2×D20—62no—
210C2×D20—124no—
211C2×D20C22×D312yes—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×C4×D5—61no—
215C2×C5×C8—32no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—31no—
218C5×C4⋊C4C22×D312yes—
219C5×C22⋊C4—61no—
220C42×C5C22×D311yescharacteristic
221#686—62no—
222#685—32no—
223#685—62no—
224#685—62no—
225#685—61no—
226C4⋊Dic5—31no—
227C4⋊Dic5—31no—
228#683—62no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231D40—122no—
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—51no—
236#480—152no—
237#474—31no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—151no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—22no—
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C2×D15—41no—
250C2×D15C2×D814yes—
251C2×C5×D3—22no—
252C2×C5×D3—41no—
253C2×C5×D3—41no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—42no—
257D3×D5—88no—
258C3×C4×C5—21no—
259C3×C4×C5—42no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—22no—
264Dic15—41no—
265C5×Dic3—41no—
266C23×D3—102no—
267C2×C3×Q8—21no—
268C2×C3×D4—52no—
269C2×C3×D4—101no—
270C2×C3×D4—101no—
271C2×#67—102no—
272C2×#67—102no—
273#239—204no—
274D3×D4—104no—
275D3×D4—204no—
276D3×D4—202no—
277C2×D12—51no—
278C2×D12—51no—
279C2×D12—102no—
280C2×D12C22×D511yescharacteristic
281C2×C4×D3—21no—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×C4×D3—101no—
285C2×C3×C8—51no—
286C2×C3×C8—51no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4C22×D512yes—
289C3×C42C22×D511yescharacteristic
290#217—102no—
291#213—202no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—52no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—101no—
296C4⋊Dic3—51no—
297C4⋊Dic3—51no—
298C4⋊Dic3C22×D511yescharacteristic
299Dic3⋊C4—102no—
300C2×C3⋊C8C22×D512yes—
301D24—102no—
302D3×C8—202no—
303C23×C5—61no—
304C22×D5—22no—
305C22×D5—32no—
306C22×D5—61no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×Q8—42no—
311C5×D4—32no—
312C5×D4—61no—
313C2×C4×C5—22no—
314C2×C4×C5—61no—
315C2×C4×C5—122no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C22⋊D5—124no—
320C2×Dic5—32no—
321C2×Dic5—61no—
322D20—22no—
323D20—22no—
324D20—34no—
325D20—42no—
326D20—61no—
327D20—61no—
328D20—81no—
329D20—124no—
330D20—124no—
331C4×D5—62no—
332C4×D5—62no—
333C4×D5—124no—
334C4×D5—122no—
335C5×C8—62no—
336#168—21no—
337#168—21no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—152no—
342C2×D8—151no—
343C22×C8—152no—
344C4⋊Q8D3×D511yescharacteristic, complemented
345#127—51no—
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—31no—
353C4×D4—151no—
354C4×D4—151no—
355C2×C4⋊C4—152no—
356#107—32no—
357#107—151no—
358C4⋊C8—31no—
359#102—32no—
360#102—52no—
361#102—52no—
362#102—151no—
363#102—152no—
364#102—151no—
365C22⋊C8—152no—
366C4×C8—51no—
367C2×C3×C5#54611yescharacteristic
368C2×C3×C5C22×D811yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—24no—
371D15—81no—
372C3×D5—82no—
373C5×D3—42no—
374C23×C3—102no—
375C22×D3—21no—
376C22×D3—52no—
377C22×D3—101no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×Q8—42no—
382C3×D4—102no—
383C3×D4—102no—
384C3×D4—202no—
385C3×D4—401no—
386C2×C3×C4—22no—
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4C23×D511yescharacteristic
390#67—204no—
391#67—204no—
392C2×Dic3—21no—
393C2×Dic3—52no—
394C2×Dic3—101no—
395D12—21no—
396D12—54no—
397D12—101no—
398D12—101no—
399D12—204no—
400D12#71312yescomplemented
401C4×D3—42no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—204no—
405C4×D3—202no—
406C3×C8—101no—
407C3×C8—101no—
408C3⋊C8—22no—
409C22×C5—62no—
410C22×C5—121no—
411C22×C5—121no—
412C22×C5C2×D3×D411yescharacteristic
413C2×D5—34no—
414C2×D5—42no—
415C2×D5—42no—
416C2×D5—42no—
417C2×D5—62no—
418C2×D5—62no—
419C2×D5—121no—
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—42no—
425C4×C5—121no—
426C4×C5D3×D812yes—
427C4×C5D3×#4111yescharacteristic
428C4×C5#100911yescharacteristic
429Dic5—62no—
430Dic5—121no—
431C24—302no—
432#41—604no—
433C2×Q8—21no—
434C2×D4—31no—
435C2×D4—52no—
436C2×D4—101no—
437C2×D4—101no—
438C2×D4—151no—
439C2×D4—151no—
440C2×D4—302no—
441C2×D4—302no—
442C2×D4—302no—
443C2×D4—304no—
444C2×D4—604no—
445C2×D4—602no—
446C22×C4—61no—
447C22×C4—152no—
448C22×C4—302no—
449C22×C4—301no—
450D8—302no—
451D8—602no—
452C2×C8—32no—
453C2×C8—51no—
454C2×C8—51no—
455C2×C8—602no—
456C4⋊C4—21no—
457C4⋊C4—31no—
458C4⋊C4—151no—
459C4⋊C4—151no—
460C4⋊C4—302no—
461C4⋊C4C2×D3×D512yes—
462C22⋊C4—61no—
463C22⋊C4—152no—
464C22⋊C4—302no—
465C22⋊C4—302no—
466C22⋊C4—301no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—202no—
470C22×C3—202no—
471C22×C3—202no—
472C22×C3C2×D4×D511yescharacteristic
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—54no—
477C2×D3—102no—
478C2×D3—102no—
479C2×D3—201no—
480C2×D3—201no—
481C2×D3—201no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—42no—
485C3×C4D5×D812yes—
486C3×C4C2×#71311yescharacteristic
487C3×C4#414911yescharacteristic
488Dic3—41no—
489Dic3—102no—
490Dic3—201no—
491C2×C5—122no—
492C2×C5#567611yescharacteristic
493C2×C5C2×D3×D811yescharacteristic
494C2×C5#576211yescharacteristic
495D5—64no—
496D5—82no—
497D5—241no—
498C23—61no—
499C23—102no—
500C23—152no—
501C23—301no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—42no—
506D4—32no—
507D4—61no—
508D4—102no—
509D4—102no—
510D4—154no—
511D4—202no—
512D4—301no—
513D4—301no—
514D4—401no—
515D4—604no—
516D4—604no—
517D4—604no—
518C2×C4—22no—
519C2×C4—61no—
520C2×C4—122no—
521C2×C4—152no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—301no—
525C2×C4—604no—
526C2×C4—602no—
527C2×C4#679011yescharacteristic
528C2×C4#679011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—62no—
531C8—101no—
532C8—101no—
533C2×C3—402no—
534C2×C3#6596411yescharacteristic
535C2×C3C2×D5×D811yescharacteristic
536C2×C3#6611211yescharacteristic
537D3—42no—
538D3—104no—
539D3—401no—
540C5#8157611yescharacteristic, complemented, Sylow
541C22—62no—
542C22—121no—
543C22—121no—
544C22—154no—
545C22—202no—
546C22—202no—
547C22—202no—
548C22—302no—
549C22—302no—
550C22—601no—
551C22—601no—
552C22—601no—
553C22—1208no—
554C22C2×#679011yescharacteristic
555C4—21no—
556C4—42no—
557C4—121no—
558C4—302no—
559C4—601no—
560C4#9148112yes—
561C4D3×#71311yescharacteristic
562C4#9203511yescharacteristic
563C3#1061271111yescharacteristic, complemented, Sylow
564C2—122no—
565C2—304no—
566C2—402no—
567C2—1201no—
568C2C2×#9148111yescharacteristic
569C2#1175509711yescharacteristic
570C2#1175528411yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3294
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. #11756485C2semidirect
2. #11752745C2semidirect
3. C5×#5087C2semidirect
4. C3×#65377C2semidirect
5. #11747485C2semidirect
6. #11747478C2semidirect
7. #11747330C2semidirect
8. #11747329C2semidirect
9. #11747043C2semidirect
10. C4×#6654C2semidirect
11. #11746988C2semidirect
16. C3×C5×C4⋊Q8C22semidirect
18. #91784C22semidirect
20. C4⋊C4×D15C22semidirect
22. C4×D60C22semidirect
29. C2×#6653C22semidirect
30. C2×#6648C22semidirect
32. C5×#807C22semidirect
33. C5×C4⋊(C3⋊C8)C22semidirect
34. C3×#3941C22semidirect
35. C3×#3941C22semidirect
36. C3×C4×#168C22semidirect
37. #90988C22semidirect
38. #90969C22semidirect
40. #90965C22semidirect
41. #90957C22semidirect
46. #65377D3semidirect
94. #5087D5semidirect
105. C5×C4⋊Q8C2×D3semidirect
127. #3941C2×D3semidirect
128. #3941C2×D3semidirect
130. C4×#168C2×D3semidirect
149. D60D8semidirect
156. C5×D12#41semidirect
170. C3×C4⋊Q8C2×D5semidirect
194. #807C2×D5semidirect
195. C4⋊(C3⋊C8)C2×D5semidirect
344. C4⋊Q8D3×D5semidirect
400. D12#713semidirect
468. C3×C5#3294semidirect
540. C5#81576semidirect
563. C3#10612711semidirect

Maximal subgroups

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

subgroupindex
#117564852
#117527452
C5×#50872
C3×#653772
#117474852
#117474782
#117473302
#117473292
#117470432
C4×#66542
#117469882
#106127113
#815765