Finite Group Databasebeta

← #14458352

Subgroups — #14458352

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
1C3×D4×D20C211yesmaximal, characteristic, complemented
2#11752532C211yesmaximal, characteristic, complemented
3#11751108C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic, complemented
5#11749021C212yesmaximal, complemented
6D5×#832C212yesmaximal, complemented
7#11747307C212yesmaximal, complemented
8#11747192C212yesmaximal, complemented
9#11747033C211yesmaximal, characteristic, complemented
10C3⋊C8×D20C211yesmaximal, characteristic, complemented
11#11746890C211yesmaximal, characteristic, complemented
12#10611339—31nomaximal, Hall
13C2×C3×D4×D5C2212yes—
14C22×C3×D20—21no—
15C2×#6765—21no—
16C3×C4×C5×D4C2211yescharacteristic
17#91758C2211yescharacteristic, complemented
18C2×C5×#213C2211yescharacteristic
19C4×C5×D12C2211yescharacteristic, complemented
20C3×#4076—21no—
21C3×#4041C2212yes—
22C3×#4028—22no—
23C3×#4020C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25#91449C2212yescomplemented
26#91414—22no—
27D5×C4⋊Dic3C2212yescomplemented
28#91365—21no—
29C2×#6652C2212yescomplemented
30C2×D5×C3⋊C8C2212yescomplemented
31#91116C2212yes—
32#91091C2212yescomplemented
33C4⋊(C3⋊#168)C2211yescharacteristic, complemented
34C5×#832C2211yescharacteristic
35C5×#809C2211yescharacteristic, complemented
36C5×#807C2211yescharacteristic, complemented
37C4×C5×C3⋊C8C2211yescharacteristic, complemented
38#90965C2212yescomplemented
39#90965C2212yescomplemented
40#90964C2212yescomplemented
41#90955C2212yescomplemented
42#83482—51nomaximal, Hall
43#65885—31no—
44D4×D20D311yescharacteristic, complemented
45C4×C5×D8—31no—
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×C3×D5—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×Dic30—21no—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×C22⋊D5—22no—
61C3×D4×D5—24no—
62C3×D4×D5—42no—
63C2×C3×D20—22no—
64C2×C3×D20—21no—
65C2×C3×D20—21no—
66C2×C3×D20—44no—
67C2×C3×D20D411yescharacteristic
68C2×C3×D20C2312yes—
69C2×C3×C4×D5C2312yes—
70C2×#1201—22no—
71C2×D5×Dic3—22no—
72#6765—44no—
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C2×C3⋊#168C2312yes—
79C5×#213—22no—
80C5×(C2×D3)⋊C4—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2311yescharacteristic
84C3×#685—22no—
85C3×#685D412yes—
86C3×C4⋊Dic5D411yescharacteristic
87#6668—22no—
88(C2×D3)⋊Dic5—22no—
89#6652—42no—
90D5×C3⋊C8—42no—
91C3×D42—51no—
92#5555—51no—
93#5217—52no—
94C2×#832—52no—
95#5072—51no—
96#5070—51no—
97#5038—52no—
98#5033—52no—
99C4×#213D511yescharacteristic, complemented
100D4×C3⋊C8—51no—
101#5007—51no—
102C2×D4×D5C2×D312yes—
103C2×#709—61no—
104C22×D20—21no—
105C2×C5×D8—31no—
106C4×C5×D4—31no—
107C4×C5×D4C2×D311yescharacteristic
108#4084—32no—
109C2×#686—32no—
110#4076—21no—
111#4070—61no—
112C2×C8×D5—32no—
113#4041C2×D312yes—
114D5×C4⋊C4—32no—
115#4029—62no—
116#4028—22no—
117#4020C2×D311yescharacteristic
118C4×D20C2×D311yescharacteristic
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#3941—32no—
129#3939—32no—
130C4⋊#168—31no—
131#3294—151noSylow
132C23×C3×C5—21no—
133C22×C5×D3—21no—
134C22×C3×D5—22no—
135C22×C3×D5—44no—
136C22×C3×D5—44no—
137C22×C3×D5—82no—
138C22×C3×D5C2×D412yes—
139C3×C5×D4—21no—
140C3×C5×D4#4112yescomplemented
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147Dic30—42no—
148C2×C5×Dic3—21no—
149C5×D12—21no—
150C5×D12—21no—
151C4×C5×D3—42no—
152C3×C22⋊D5—44no—
153C2×C3×Dic5C2×D412yes—
154C3×D20—22no—
155C3×D20—22no—
156C3×D20—44no—
157C3×D20—42no—
158C3×D20—81no—
159C3×D20D814yescomplemented
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162#1201—44no—
163D5×Dic3—44no—
164C3⋊#168—22no—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C22×C3×D4—52no—
168C22×C3×D4—101no—
169C2×#237—101no—
170C3×#127—51no—
171C3×#121—52no—
172C3×#121—101no—
173C3×#120—102no—
174C3×C4×D4—51no—
175C3×C4×D4C2×D511yescharacteristic
176C2×#213—52no—
177C2×#213C2×D511yescharacteristic
178#930—52no—
179C2×C4⋊Dic3—52no—
180C22×C3⋊C8—52no—
181#897—101no—
182#886—102no—
183C4×D12C2×D511yescharacteristic, complemented
184#869—51no—
185#832—52no—
186#832—52no—
187#832—52no—
188#832—52no—
189#832C2×D511yescharacteristic
190#830—52no—
191#809C2×D511yescharacteristic, complemented
192#807—52no—
193#807C2×D511yescharacteristic, complemented
194C4⋊(C3⋊C8)—51no—
195C4×C3⋊C8C2×D511yescharacteristic, complemented
196C23×D5—22no—
197C2×C5×D4—31no—
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—61no—
201C2×C22⋊D5—22no—
202C2×C22⋊D5—62no—
203D4×D5—24no—
204D4×D5—42no—
205#709—124no—
206C2×D20—22no—
207C2×D20—21no—
208C2×D20—21no—
209C2×D20—44no—
210C2×D20#6711yescharacteristic
211C2×D20C22×D312yes—
212C2×C4×D5—62no—
213C2×C4×D5C22×D312yes—
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—122no—
225#685—22no—
226#685#6712yes—
227C4⋊Dic5—32no—
228C4⋊Dic5—61no—
229C4⋊Dic5#6711yescharacteristic
230#683—62no—
231C2×#168—32no—
232C8×D5—122no—
233#547—151no—
234D42—51no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—31no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C22×D411yescharacteristic
248C2×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C2×C3×D5—22no—
252C2×C3×D5—22no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—88no—
257C2×C3×D5C2×D814yes—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—42no—
264C3×Dic5—22no—
265C5×Dic3—41no—
266C24×C3—102no—
267C2×C3×D4—51no—
268C2×C3×D4—52no—
269C2×C3×D4—102no—
270C2×C3×D4—102no—
271C2×C3×D4—104no—
272C2×C3×D4—101no—
273C2×C3×D4—101no—
274C2×C3×D4—204no—
275C2×C3×D4—202no—
276C2×C3×D4C22×D511yescharacteristic
277C22×C3×C4—21no—
278C22×C3×C4—52no—
279C2×#67—102no—
280C22×Dic3—102no—
281#237—204no—
282C2×D12C22×D511yescharacteristic
283C2×C4×D3—21no—
284C2×Dic6—101no—
285C3×C4⋊C4—51no—
286C3×C4⋊C4C22×D511yescharacteristic
287C3×C22⋊C4—21no—
288C3×C22⋊C4—52no—
289C3×C22⋊C4—102no—
290C3×C42C22×D511yescharacteristic
291#213—22no—
292#213—202no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—102no—
295C4⋊Dic3—52no—
296C4⋊Dic3—102no—
297C4⋊Dic3—101no—
298C4⋊Dic3C22×D511yescharacteristic
299C2×C3⋊C8—52no—
300C2×C3⋊C8—202no—
301C2×C3⋊C8C22×D511yescharacteristic
302C2×C3⋊C8C22×D511yescharacteristic
303C23×C5—21no—
304C23×C5—61no—
305C22×D5—22no—
306C22×D5—44no—
307C22×D5—44no—
308C22×D5—82no—
309C22×D5C2×#6712yes—
310C5×D4—21no—
311C5×D4—61no—
312C5×D4—61no—
313C5×D4#23712yescomplemented
314C2×C4×C5—21no—
315C2×C4×C5—42no—
316C2×C4×C5—61no—
317C2×C4×C5—122no—
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—44no—
322C22⋊D5—124no—
323C2×Dic5—62no—
324C2×Dic5C2×#6712yes—
325D20—22no—
326D20—22no—
327D20—44no—
328D20—42no—
329D20—81no—
330D20#21314yescomplemented
331C4×D5—22no—
332C4×D5—22no—
333C4×D5—124no—
334Dic10—122no—
335C5×C8—61no—
336C5×C8—61no—
337#168—62no—
338C2×#41—301no—
339C22×D4—52no—
340C22×D4—101no—
341C2×D8—31no—
342C2×D8—152no—
343C22×C8—152no—
344C4⋊Q8—151no—
345#127—51no—
346#123—302no—
347C22⋊Q8—301no—
348#121—52no—
349#121—101no—
350#121—152no—
351#120—102no—
352C4×D4—31no—
353C4×D4—51no—
354C4×D4D3×D511yescharacteristic
355C2×C4⋊C4—152no—
356#107—31no—
357#107—152no—
358C4⋊C8—151no—
359#102—31no—
360#102—31no—
361#102—152no—
362#102—152no—
363#102—152no—
364#102—152no—
365C22⋊C8—152no—
366C4×C8—31no—
367C2×C3×C5—42no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371C3×D5—24no—
372C3×D5—82no—
373C5×D3—81no—
374C23×C3—21no—
375C23×C3—52no—
376C23×C3—102no—
377C23×C3—204no—
378C23×C3—204no—
379C23×C3—402no—
380C22×D3—21no—
381C3×D4—21no—
382C3×D4—54no—
383C3×D4—102no—
384C3×D4—102no—
385C3×D4—204no—
386C3×D4—204no—
387C3×D4—202no—
388C3×D4—401no—
389C3×D4#70912yescomplemented
390C2×C3×C4—21no—
391C2×C3×C4—42no—
392C2×C3×C4—52no—
393C2×C3×C4—102no—
394C2×C3×C4—102no—
395C2×C3×C4D4×D511yescharacteristic
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398#67—204no—
399C2×Dic3—21no—
400C2×Dic3—102no—
401C2×Dic3—204no—
402D12—21no—
403D12—21no—
404C4×D3—42no—
405Dic6—202no—
406C3⋊C8—21no—
407C3⋊C8—21no—
408C3⋊C8—102no—
409C22×C5—22no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5—121no—
415C22×C5C22×#6711yescharacteristic
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—42no—
419C2×D5—42no—
420C2×D5—42no—
421C2×D5—88no—
422C2×D5C2×#21314yes—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5—121no—
426C4×C5C2×#21312yes—
427C4×C5C2×#23711yescharacteristic
428C4×C5#100411yescharacteristic
429Dic5—22no—
430Dic5—122no—
431C24—102no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—31no—
435C2×D4—51no—
436C2×D4—52no—
437C2×D4—102no—
438C2×D4—102no—
439C2×D4—104no—
440C2×D4—101no—
441C2×D4—101no—
442C2×D4—204no—
443C2×D4—202no—
444C2×D4—302no—
445C2×D4C2×D3×D511yescharacteristic
446C22×C4—21no—
447C22×C4—52no—
448C22×C4—61no—
449C22×C4—302no—
450D8—62no—
451D8—602no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—152no—
455C2×C8—602no—
456C4⋊C4—31no—
457C4⋊C4—51no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—301no—
461C4⋊C4C2×D3×D511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—52no—
464C22⋊C4—61no—
465C22⋊C4—102no—
466C22⋊C4—302no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—54no—
473C22×C3—102no—
474C22×C3—102no—
475C22×C3—202no—
476C22×C3—202no—
477C22×C3—202no—
478C22×C3—408no—
479C22×C3C2×D4×D511yescharacteristic
480C2×D3—41no—
481C2×D3—41no—
482C2×D3—41no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—102no—
486C3×C4D5×D812yes—
487C3×C4C2×#70911yescharacteristic
488C3×C4#414911yescharacteristic
489Dic3—41no—
490Dic3—202no—
491C2×C5—42no—
492C2×C5—241no—
493C2×C5C22×#21311yescharacteristic
494C2×C5#580611yescharacteristic
495C2×C5#583611yescharacteristic
496D5—24no—
497D5—82no—
498C23—21no—
499C23—52no—
500C23—61no—
501C23—102no—
502C23—204no—
503C23—204no—
504C23—402no—
505Q8—602no—
506D4—21no—
507D4—54no—
508D4—61no—
509D4—61no—
510D4—102no—
511D4—102no—
512D4—204no—
513D4—204no—
514D4—202no—
515D4—401no—
516D4—604no—
517D4#676512yescomplemented
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—52no—
521C2×C4—61no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—122no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4D5×#6711yescharacteristic
528C2×C4D5×#6711yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—61no—
531C8—61no—
532C8—302no—
533C2×C3—42no—
534C2×C3—104no—
535C2×C3—402no—
536C2×C3#6588411yescharacteristic
537C2×C3C2×D5×D811yescharacteristic
538C2×C3#6610411yescharacteristic
539D3—81no—
540C5#8348211yescharacteristic, complemented, Sylow
541C22—22no—
542C22—41no—
543C22—41no—
544C22—54no—
545C22—102no—
546C22—102no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22—202no—
551C22—202no—
552C22—202no—
553C22—408no—
554C22C2×D5×#6711yescharacteristic
555C4—21no—
556C4—41no—
557C4—102no—
558C4—121no—
559C4—602no—
560C4D5×#21312yes—
561C4C2×#676511yescharacteristic
562C4#9201711yescharacteristic
563C3#1061133911yescharacteristic, complemented, Sylow
564C2—42no—
565C2—104no—
566C2—241no—
567C2—402no—
568C2#1175430511yescharacteristic
569C2C2×D5×#21311yescharacteristic
570C2#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#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. C3×D4×D20C2semidirect
2. #11752532C2semidirect
3. #11751108C2semidirect
4. C4×C5×#213C2semidirect
5. #11749021C2semidirect
6. D5×#832C2semidirect
7. #11747307C2semidirect
8. #11747192C2semidirect
9. #11747033C2semidirect
10. C3⋊C8×D20C2semidirect
11. #11746890C2semidirect
17. #91758C22semidirect
19. C4×C5×D12C22semidirect
25. #91449C22semidirect
27. D5×C4⋊Dic3C22semidirect
29. C2×#6652C22semidirect
30. C2×D5×C3⋊C8C22semidirect
32. #91091C22semidirect
33. C4⋊(C3⋊#168)C22semidirect
35. C5×#809C22semidirect
36. C5×#807C22semidirect
37. C4×C5×C3⋊C8C22semidirect
38. #90965C22semidirect
39. #90965C22semidirect
40. #90964C22semidirect
41. #90955C22semidirect
44. D4×D20D3semidirect
99. C4×#213D5semidirect
140. C3×C5×D4#41semidirect
159. C3×D20D8semidirect
183. C4×D12C2×D5semidirect
191. #809C2×D5semidirect
193. #807C2×D5semidirect
195. C4×C3⋊C8C2×D5semidirect
313. C5×D4#237semidirect
330. D20#213semidirect
389. C3×D4#709semidirect
468. C3×C5#3294semidirect
517. D4#6765semidirect
540. C5#83482semidirect
563. C3#10611339semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D202
#117525322
#117511082
C4×C5×#2132
#117490212
D5×#8322
#117473072
#117471922
#117470332
C3⋊C8×D202
#117468902
#106113393
#834825