Finite Group Databasebeta

← #14458402

Subgroups — #14458402

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
2#11752745C211yesmaximal, characteristic, complemented
3C4×C5×#213C211yesmaximal, characteristic, complemented
4C3×#65304C211yesmaximal, characteristic, complemented
5#11749153C212yesmaximal, complemented
6#11749031C212yesmaximal, complemented
7#11747478C212yesmaximal, complemented
8#11747330C212yesmaximal, complemented
9#11746994C211yesmaximal, characteristic, complemented
10#11746964C211yesmaximal, characteristic, complemented
11#11746890C211yesmaximal, characteristic, complemented
12#10611339—31nomaximal, Hall
13C2×#6817—21no—
14C2×#6777C2212yes—
15C2×D3×D20—21no—
16C3×C4×C5×D4C2211yescharacteristic, complemented
17#91827C2212yescomplemented
18#91813—21no—
19C4⋊C4×D15C2212yescomplemented
20#91772—22no—
21C4×D60C2211yescharacteristic
22#91758C2211yescharacteristic, complemented
23C2×C5×#213C2211yescharacteristic
24C4×C5×D12C2211yescharacteristic
25C2×C3×#686C2212yescomplemented
26C3×#4020C2211yescharacteristic
27#91474—22no—
28#91465C2212yes—
29#91456—21no—
30C2×#6648C2212yescomplemented
31C5×#832C2211yescharacteristic, complemented
32C5×#809C2211yescharacteristic
33C5×#807C2211yescharacteristic, complemented
34C4×C5×C3⋊C8C2211yescharacteristic, complemented
35C3×#3941C2212yescomplemented
36C3×C4⋊#168C2211yescharacteristic, complemented
37#90988C2212yescomplemented
38#90967C2212yes—
39#90965C2212yescomplemented
40#90965C2212yescomplemented
41#90957C2212yescomplemented
42#80352—51nomaximal, Hall
43#65885—31no—
44D4×D20—31no—
45C4×C5×D8—31no—
46#65445—32no—
47#65304D311yescharacteristic, complemented
48#65296—31no—
49#65171—32no—
50#65064—32no—
51D5×#102—32no—
52#64983—31no—
53C8×D20—31no—
54C22×D3×D5—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58#6817—44no—
59C2×D60D411yescharacteristic
60C2×C4×D15—22no—
61C2×C4×D15C2312yes—
62C2×Dic30—21no—
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⋊C4C2311yescharacteristic
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76#6719—22no—
77#6714D412yes—
78C4⋊Dic15—21no—
79C4⋊Dic15D411yescharacteristic
80C4⋊Dic15C2312yes—
81#6712—22no—
82C5×#213—22no—
83C5×(C2×D3)⋊C4—21no—
84C5×C4⋊Dic3C2311yescharacteristic
85C2×C5×C3⋊C8C2311yescharacteristic
86C2×C5×C3⋊C8C2311yescharacteristic
87C3×#686—42no—
88C2×C3×#168C2312yes—
89#6665—22no—
90#6648—42no—
91#5717—51no—
92#5551—51no—
93C3×#459—51no—
94#5157—52no—
95#5156—52no—
96#5070—51no—
97C4×#213D511yescharacteristic, complemented
98#4846—51no—
99#4834—51no—
100#4774—52no—
101D3×#102—52no—
102C2×D4×D5—32no—
103C2×#709—61no—
104C22×D20—61no—
105C2×C5×D8—31no—
106C4×C5×D4—31no—
107C4×C5×D4C2×D311yescharacteristic, complemented
108#4084—32no—
109C2×#686C2×D312yescomplemented
110#4076—61no—
111#4070—61no—
112C2×C8×D5—32no—
113#4041—32no—
114D5×C4⋊C4—32no—
115#4029—62no—
116#4028—62no—
117#4020C2×D311yescharacteristic
118C4×D20—31no—
119#4015—31no—
120C5×#107—31no—
121C5×#102—31no—
122C5×#102—31no—
123C4×C5×C8—31no—
124#3964—32no—
125#3953—32no—
126#3953—32no—
127#3952—32no—
128#3941C2×D312yescomplemented
129#3939—32no—
130C4⋊#168C2×D311yescharacteristic, complemented
131#3294—151noSylow
132C23×C3×C5—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×D4—21no—
140C3×C5×D4—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—44no—
147C2×Dic15—22no—
148C2×Dic15C2×D412yes—
149D60D814yescomplemented
150C4×D15—22no—
151C4×D15—22no—
152C4×D15—44no—
153Dic30—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—22no—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C2×D3×D4—52no—
168C2×D3×D4—101no—
169C2×#235—101no—
170C2×C3×D8—52no—
171C3×#127—51no—
172C3×C4×D4C2×D511yescharacteristic, complemented
173#938—52no—
174#938—52no—
175#938—101no—
176#937—102no—
177C2×#213C2×D511yescharacteristic
178#924—101no—
179C2×D3×C8—52no—
180D3×C4⋊C4—52no—
181#883—102no—
182C4×D12—51no—
183C4×D12C2×D511yescharacteristic
184#869—51no—
185C3×C4⋊C8—51no—
186C3×#102—52no—
187#832—52no—
188#832—52no—
189#832C2×D511yescharacteristic, complemented
190#821—52no—
191(C2×D3)⋊C8—52no—
192#818—52no—
193#809C2×D511yescharacteristic
194#807C2×D511yescharacteristic, complemented
195C4×C3⋊C8C2×D511yescharacteristic, complemented
196C23×D5—62no—
197C2×C5×D4—31no—
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—61no—
201C2×C22⋊D5—62no—
202C2×C22⋊D5—62no—
203D4×D5—64no—
204D4×D5—122no—
205#709—124no—
206C2×D20—21no—
207C2×D20—21no—
208C2×D20—31no—
209C2×D20—62no—
210C2×D20—124no—
211C2×D20C22×D312yes—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×Dic10—61no—
215C5×D8—62no—
216C2×C5×C8—31no—
217C2×C5×C8—31no—
218C5×C4⋊C4—31no—
219C5×C4⋊C4C22×D311yescharacteristic
220C5×C22⋊C4—21no—
221C5×C22⋊C4—61no—
222C42×C5C22×D311yescharacteristic
223C22⋊Dic5—62no—
224#686—42no—
225#685—32no—
226#685—62no—
227C4⋊Dic5—31no—
228C4⋊Dic5—32no—
229C4⋊Dic5—61no—
230#683—62no—
231C2×#168C22×D312yes—
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—51no—
240#447—152no—
241C4×D8—31no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—41no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—22no—
249C2×D15—22no—
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—41no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—22no—
264Dic15—42no—
265C5×Dic3—41no—
266C23×D3—102no—
267C2×C3×D4—52no—
268C2×C3×D4—101no—
269C2×C3×D4—101no—
270C2×C3×D4C22×D511yescharacteristic
271C22×C3×C4—21no—
272C2×#67—102no—
273C2×#67—102no—
274C2×#67—102no—
275D3×D4—104no—
276D3×D4—204no—
277D3×D4—202no—
278#235—204no—
279C2×D12—51no—
280C2×D12C22×D511yescharacteristic
281C2×C4×D3—21no—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×Dic6—101no—
285C3×D8—202no—
286C2×C3×C8—52no—
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C22⋊C4—21no—
289C3×C42C22×D511yescharacteristic
290#217—102no—
291#217—102no—
292#213—22no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—52no—
295C4⋊Dic3—51no—
296C4⋊Dic3—52no—
297C4⋊Dic3—101no—
298C4⋊Dic3C22×D511yescharacteristic
299Dic3⋊C4—102no—
300C2×C3⋊C8C22×D511yescharacteristic
301C2×C3⋊C8C22×D511yescharacteristic
302D3×C8—202no—
303C23×C5—21no—
304C23×C5—61no—
305C22×D5—22no—
306C22×D5—32no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×D4—21no—
311C5×D4—21no—
312C5×D4—32no—
313C5×D4—61no—
314C2×C4×C5—21no—
315C2×C4×C5—42no—
316C2×C4×C5—61no—
317C2×C4×C5—122no—
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—22no—
326D20—22no—
327D20—34no—
328D20—42no—
329D20—81no—
330D20—124no—
331C4×D5—62no—
332C4×D5—62no—
333C4×D5—124no—
334Dic10—122no—
335C5×C8—61no—
336C5×C8—61no—
337#168—22no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—31no—
342C2×D8—52no—
343C22×C8—152no—
344C4⋊Q8—151no—
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×D4D3×D511yescharacteristic, complemented
355C2×C4⋊C4—152no—
356#107—31no—
357#107—152no—
358C4⋊C8—51no—
359#102—31no—
360#102—31no—
361#102—52no—
362#102—152no—
363#102—152no—
364#102—152no—
365C22⋊C8—152no—
366C4×C8—31no—
367C2×C3×C5—81no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—24no—
372C3×D5—82no—
373C5×D3—42no—
374C23×C3—21no—
375C23×C3—102no—
376C22×D3—21no—
377C22×D3—52no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×D4—21no—
382C3×D4—21no—
383C3×D4—102no—
384C3×D4—102no—
385C3×D4—202no—
386C3×D4—401no—
387C2×C3×C4—21no—
388C2×C3×C4—42no—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—204no—
393#67—204no—
394#67—204no—
395C2×Dic3—21no—
396C2×Dic3—52no—
397C2×Dic3—102no—
398D12—21no—
399D12—54no—
400D12#70912yescomplemented
401C4×D3—42no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—204no—
405Dic6—202no—
406C3×C8—102no—
407C3⋊C8—21no—
408C3⋊C8—21no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—62no—
413C22×C5—121no—
414C22×C5—121no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—34no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—42no—
420C2×D5—62no—
421C2×D5—62no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5—121no—
426C4×C5D3×D812yes—
427C4×C5#100411yescharacteristic
428C4×C5D3×#4111yescharacteristic
429Dic5—62no—
430Dic5—122no—
431C24—302no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—31no—
435C2×D4—52no—
436C2×D4—101no—
437C2×D4—101no—
438C2×D4—151no—
439C2×D4—302no—
440C2×D4—302no—
441C2×D4—304no—
442C2×D4—302no—
443C2×D4—604no—
444C2×D4—602no—
445C2×D4C2×D3×D511yescharacteristic
446C22×C4—21no—
447C22×C4—61no—
448C22×C4—152no—
449C22×C4—302no—
450D8—62no—
451D8—202no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—52no—
455C2×C8—602no—
456C4⋊C4—31no—
457C4⋊C4—151no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—301no—
461C4⋊C4C2×D3×D511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—61no—
464C22⋊C4—152no—
465C22⋊C4—302no—
466C22⋊C4—302no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—22no—
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—54no—
480C2×D3—102no—
481C2×D3—102no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4D5×D812yes—
486C3×C4C2×#70911yescharacteristic
487C3×C4#414911yescharacteristic
488Dic3—41no—
489Dic3—102no—
490Dic3—202no—
491C2×C5—81no—
492C2×C5—122no—
493C2×C5#561211yescharacteristic
494C2×C5C2×D3×D811yescharacteristic
495C2×C5#577511yescharacteristic
496D5—64no—
497D5—82no—
498C23—21no—
499C23—61no—
500C23—102no—
501C23—152no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—602no—
506D4—21no—
507D4—21no—
508D4—32no—
509D4—61no—
510D4—102no—
511D4—102no—
512D4—154no—
513D4—202no—
514D4—401no—
515D4—604no—
516D4—604no—
517D4—604no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—61no—
521C2×C4—122no—
522C2×C4—152no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4#679011yescharacteristic
528C2×C4#679011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—61no—
531C8—61no—
532C8—102no—
533C2×C3—81no—
534C2×C3—402no—
535C2×C3#6588411yescharacteristic
536C2×C3C2×D5×D811yescharacteristic
537C2×C3#6610411yescharacteristic
538D3—42no—
539D3—104no—
540C5#8035211yescharacteristic, complemented, Sylow
541C22—41no—
542C22—41no—
543C22—41no—
544C22—62no—
545C22—121no—
546C22—121no—
547C22—154no—
548C22—202no—
549C22—202no—
550C22—202no—
551C22—302no—
552C22—302no—
553C22—1208no—
554C22C2×#679011yescharacteristic
555C4—21no—
556C4—41no—
557C4—121no—
558C4—302no—
559C4—602no—
560C4#9148112yes—
561C4D3×#70911yescharacteristic
562C4#9201711yescharacteristic
563C3#1061133911yescharacteristic, complemented, Sylow
564C2—81no—
565C2—122no—
566C2—304no—
567C2—402no—
568C2#1175466711yescharacteristic
569C2C2×#9148111yescharacteristic
570C2#1175533111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3294
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. #11756310C2semidirect
2. #11752745C2semidirect
3. C4×C5×#213C2semidirect
4. C3×#65304C2semidirect
5. #11749153C2semidirect
6. #11749031C2semidirect
7. #11747478C2semidirect
8. #11747330C2semidirect
9. #11746994C2semidirect
10. #11746964C2semidirect
11. #11746890C2semidirect
16. C3×C4×C5×D4C22semidirect
17. #91827C22semidirect
19. C4⋊C4×D15C22semidirect
22. #91758C22semidirect
25. C2×C3×#686C22semidirect
30. C2×#6648C22semidirect
31. C5×#832C22semidirect
33. C5×#807C22semidirect
34. C4×C5×C3⋊C8C22semidirect
35. C3×#3941C22semidirect
36. C3×C4⋊#168C22semidirect
37. #90988C22semidirect
39. #90965C22semidirect
40. #90965C22semidirect
41. #90957C22semidirect
47. #65304D3semidirect
97. C4×#213D5semidirect
107. C4×C5×D4C2×D3semidirect
109. C2×#686C2×D3semidirect
128. #3941C2×D3semidirect
130. C4⋊#168C2×D3semidirect
149. D60D8semidirect
156. C5×D12#41semidirect
172. C3×C4×D4C2×D5semidirect
189. #832C2×D5semidirect
194. #807C2×D5semidirect
195. C4×C3⋊C8C2×D5semidirect
354. C4×D4D3×D5semidirect
400. D12#709semidirect
468. C3×C5#3294semidirect
540. C5#80352semidirect
563. C3#10611339semidirect

Maximal subgroups

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

subgroupindex
#117563102
#117527452
C4×C5×#2132
C3×#653042
#117491532
#117490312
#117474782
#117473302
#117469942
#117469642
#117468902
#106113393
#803525