Finite Group Databasebeta

← #14458405

Subgroups — #14458405

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#11752737C211yesmaximal, characteristic, complemented
3C5×#5015C211yesmaximal, characteristic, complemented
4C3×C4×#686C211yesmaximal, characteristic, complemented
5#11749153C212yesmaximal, complemented
6#11749038C212yesmaximal, complemented
7#11747478C212yesmaximal, complemented
8#11747331C212yesmaximal, complemented
9#11746988C211yesmaximal, characteristic, complemented
10#11746906C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10612083—31nomaximal, Hall
13C2×#6817—21no—
14C2×#6777C2212yes—
15C2×D5×D12—21no—
16C3×C4×C5×D4C2211yescharacteristic, complemented
17#91827C2212yescomplemented
18#91813—21no—
19C4⋊C4×D15C2212yescomplemented
20#91772—22no—
21C4×D60C2211yescharacteristic
22#91758C2211yescharacteristic, complemented
23C2×C5×#213C2212yescomplemented
24C5×#874C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×C4×D20C2211yescharacteristic
27#91475—22no—
28#91466C2212yes—
29#91449—21no—
30C2×#6648C2212yescomplemented
31C5×#809C2212yescomplemented
32C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×#3964C2211yescharacteristic, complemented
34C3×#3941C2211yescharacteristic
35C3×#3939C2211yescharacteristic, complemented
36C3×C4×#168C2211yescharacteristic, complemented
37#90990C2212yescomplemented
38#90967C2212yescomplemented
39#90967C2212yescomplemented
40#90965C2212yes—
41#90957C2212yescomplemented
42#79608—51nomaximal, Hall
43#66051—31no—
44#65885—31no—
45C5×#459—31no—
46#65446—32no—
47#65445—32no—
48#65359—31no—
49C4×#686D311yescharacteristic, complemented
50#65135—31no—
51#65123—31no—
52#65063—32no—
53D5×#102—32no—
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×D12—21no—
64C2×C5×D12—21no—
65C2×C5×D12C2312yes—
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C2×#1203—22no—
69C2×#1201—22no—
70#6777—24no—
71#6777—42no—
72D5×D12—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—42no—
83C2×C5×C3⋊C8C2312yes—
84C3×#686—22no—
85C3×#685—21no—
86C3×C4⋊Dic5C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88C2×C3×#168C2311yescharacteristic
89(C2×D3)⋊Dic5—22no—
90#6648—42no—
91#5551—51no—
92D4×D12—51no—
93C3×C4×D8—51no—
94#5156—52no—
95#5015D511yescharacteristic, complemented
96#5007—51no—
97#4882—52no—
98#4775—52no—
99D3×#102—52no—
100#4694—51no—
101C8×D12—51no—
102C2×D4×D5—32no—
103C2×D4×D5—61no—
104C2×#709—61no—
105C2×C5×D8—32no—
106C5×#127—31no—
107C4×C5×D4C2×D311yescharacteristic, complemented
108#4084—32no—
109#4084—32no—
110#4084—61no—
111#4083—62no—
112C2×#686C2×D311yescharacteristic
113#4070—61no—
114C2×C8×D5—32no—
115D5×C4⋊C4—32no—
116#4029—62no—
117C4×D20—31no—
118C4×D20C2×D311yescharacteristic
119#4015—31no—
120C5×C4⋊C8—31no—
121C5×#102—32no—
122#3964—32no—
123#3964—32no—
124#3964C2×D311yescharacteristic, complemented
125#3953—32no—
126#3952—32no—
127#3950—32no—
128#3941C2×D311yescharacteristic
129#3939C2×D311yescharacteristic, complemented
130C4×#168C2×D311yescharacteristic, complemented
131#3294—151noSylow
132C23×C3×C5—21no—
133C22×D15C2×D412yes—
134C22×C5×D3—22no—
135C22×C3×D5—21no—
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—
154C5×D12—22no—
155C5×D12—22no—
156C5×D12—42no—
157C5×D12—81no—
158C2×C3×Dic5—21no—
159C3×D20—21no—
160C3×D20#4112yescomplemented
161C3×C4×D5—42no—
162#1203—44no—
163#1201—44no—
164C3×#168—21no—
165C3×#168—21no—
166C5×C3⋊C8—22no—
167C2×D3×D4—52no—
168C2×#235—101no—
169C22×D12—101no—
170C2×C3×D8—51no—
171C3×C4×D4—51no—
172C3×C4×D4C2×D511yescharacteristic, complemented
173#938—52no—
174C2×#213C2×D512yescomplemented
175#930—101no—
176#924—101no—
177C2×D3×C8—52no—
178#895—52no—
179D3×C4⋊C4—52no—
180#883—102no—
181#882—102no—
182#874C2×D511yescharacteristic
183C4×D12—51no—
184#869—51no—
185C3×#107—51no—
186C3×#102—51no—
187C3×#102—51no—
188C3×C4×C8—51no—
189#832—52no—
190#821—52no—
191#821—52no—
192(C2×D3)⋊C8—52no—
193#809C2×D512yescomplemented
194#807—52no—
195C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
196C23×D5—62no—
197C2×C5×D4—32no—
198C2×C5×D4—61no—
199C2×C5×D4—61no—
200C2×C5×D4C22×D311yescharacteristic
201C22×C4×C5—21no—
202C2×C22⋊D5—62no—
203C2×C22⋊D5—62no—
204C2×C22⋊D5—62no—
205D4×D5—64no—
206D4×D5—124no—
207D4×D5—122no—
208#709—124no—
209C2×D20—31no—
210C2×D20C22×D311yescharacteristic
211C2×C4×D5—21no—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×Dic10—61no—
215C5×D8—122no—
216C2×C5×C8—32no—
217C5×C4⋊C4C22×D311yescharacteristic
218C5×C22⋊C4—21no—
219C42×C5C22×D311yescharacteristic
220C22⋊Dic5—62no—
221C22⋊Dic5—62no—
222#686—22no—
223#685—21no—
224#685—32no—
225C4⋊Dic5—31no—
226C4⋊Dic5—32no—
227C4⋊Dic5—61no—
228C4⋊Dic5C22×D311yescharacteristic
229#683—62no—
230C2×#168C22×D311yescharacteristic
231C2×#168C22×D311yescharacteristic
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—31no—
240#447—152no—
241C4×D8—51no—
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—42no—
252C2×C5×D3—42no—
253C2×C5×D3—42no—
254C2×C3×D5—22no—
255C2×C3×D5—41no—
256C2×C3×D5—41no—
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—
265C3×Dic5—41no—
266C23×D3—102no—
267C2×C3×D4—51no—
268C2×C3×D4C22×D511yescharacteristic
269C22×C3×C4—21no—
270C22×C3×C4—101no—
271C2×#67—102no—
272C2×#67—102no—
273D3×D4—104no—
274D3×D4—202no—
275#235—204no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—51no—
279C2×D12—102no—
280C2×D12—204no—
281C2×D12C22×D512yes—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×Dic6—101no—
285C3×D8—102no—
286C2×C3×C8—51no—
287C2×C3×C8—51no—
288C3×C4⋊C4—51no—
289C3×C4⋊C4C22×D511yescharacteristic
290C3×C22⋊C4—21no—
291C3×C22⋊C4—101no—
292C3×C42C22×D511yescharacteristic
293#217—102no—
294#213—42no—
295(C2×D3)⋊C4—52no—
296(C2×D3)⋊C4—102no—
297C4⋊Dic3—51no—
298C4⋊Dic3—52no—
299C4⋊Dic3—101no—
300Dic3⋊C4—102no—
301C2×C3⋊C8C22×D512yes—
302D3×C8—202no—
303C23×C5—21no—
304C23×C5—62no—
305C22×D5—21no—
306C22×D5—32no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×D4—21no—
311C5×D4—21no—
312C5×D4—62no—
313C5×D4—62no—
314C5×D4—122no—
315C5×D4—241no—
316C2×C4×C5—21no—
317C2×C4×C5—42no—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—124no—
322C22⋊D5—124no—
323C22⋊D5—124no—
324C2×Dic5—21no—
325C2×Dic5—32no—
326C2×Dic5—62no—
327D20—21no—
328D20—34no—
329D20#23512yescomplemented
330C4×D5—42no—
331C4×D5—62no—
332C4×D5—62no—
333C4×D5—124no—
334Dic10—122no—
335C5×C8—62no—
336#168—21no—
337#168—21no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—32no—
342C2×D8—51no—
343C22×C8—152no—
344C4⋊Q8—151no—
345#127—31no—
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—51no—
353C4×D4—151no—
354C4×D4D3×D511yescharacteristic, complemented
355C2×C4⋊C4—152no—
356#107—51no—
357#107—152no—
358C4⋊C8—31no—
359#102—32no—
360#102—51no—
361#102—51no—
362#102—152no—
363#102—152no—
364#102—152no—
365C22⋊C8—152no—
366C4×C8—51no—
367C2×C3×C5—81no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—24no—
372C3×D5—42no—
373C5×D3—82no—
374C23×C3—21no—
375C23×C3—101no—
376C22×D3—22no—
377C22×D3—52no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×D4—21no—
382C3×D4—21no—
383C3×D4—52no—
384C3×D4—101no—
385C2×C3×C4—21no—
386C2×C3×C4—42no—
387C2×C3×C4—101no—
388C2×C3×C4—202no—
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—22no—
397D12—22no—
398D12—42no—
399D12—54no—
400D12—81no—
401D12—204no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—204no—
405Dic6—202no—
406C3×C8—101no—
407C3×C8—101no—
408C3⋊C8—22no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—122no—
413C22×C5—122no—
414C22×C5—122no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—22no—
417C2×D5—34no—
418C2×D5—41no—
419C2×D5—41no—
420C2×D5—62no—
421C2×D5—62no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5D3×D812yes—
426C4×C5C2×#23511yescharacteristic
427C4×C5#100911yescharacteristic
428Dic5—41no—
429Dic5—62no—
430Dic5—122no—
431C24—302no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—32no—
435C2×D4—51no—
436C2×D4—61no—
437C2×D4—61no—
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—101no—
448C22×C4—152no—
449C22×C4—302no—
450D8—102no—
451D8—122no—
452C2×C8—32no—
453C2×C8—51no—
454C2×C8—51no—
455C2×C8—602no—
456C4⋊C4—51no—
457C4⋊C4—151no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—301no—
461C4⋊C4C2×D3×D511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—101no—
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—102no—
473C22×C3—201no—
474C22×C3—201no—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3—54no—
480C2×D3—102no—
481C2×D3—102no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—201no—
486C3×C4D5×D812yes—
487C3×C4#414411yescharacteristic
488C3×C4D5×#4111yescharacteristic
489Dic3—102no—
490Dic3—202no—
491C2×C5—81no—
492C2×C5—242no—
493C2×C5#555011yescharacteristic
494C2×C5C2×D3×D811yescharacteristic
495C2×C5#577011yescharacteristic
496D5—42no—
497D5—64no—
498C23—21no—
499C23—62no—
500C23—101no—
501C23—152no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—602no—
506D4—21no—
507D4—21no—
508D4—52no—
509D4—62no—
510D4—62no—
511D4—101no—
512D4—122no—
513D4—154no—
514D4—241no—
515D4—604no—
516D4—604no—
517D4—604no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—101no—
521C2×C4—152no—
522C2×C4—202no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4#679011yescharacteristic
528C2×C4#679011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—62no—
531C8—101no—
532C8—101no—
533C2×C3—81no—
534C2×C3—202no—
535C2×C3#6594611yescharacteristic
536C2×C3C2×D5×D811yescharacteristic
537C2×C3#6610911yescharacteristic
538D3—82no—
539D3—104no—
540C5#7960811yescharacteristic, complemented, Sylow
541C22—41no—
542C22—41no—
543C22—41no—
544C22—102no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—154no—
549C22—201no—
550C22—201no—
551C22—302no—
552C22—302no—
553C22—1208no—
554C22C2×#679011yescharacteristic
555C4—21no—
556C4—41no—
557C4—201no—
558C4—302no—
559C4—602no—
560C4#9148112yes—
561C4D5×#23511yescharacteristic
562C4#9201811yescharacteristic
563C3#1061208311yescharacteristic, complemented, Sylow
564C2—81no—
565C2—202no—
566C2—242no—
567C2—304no—
568C2#1175466511yescharacteristic
569C2C2×#9148111yescharacteristic
570C2#1175533311yescharacteristic
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. #11752737C2semidirect
3. C5×#5015C2semidirect
4. C3×C4×#686C2semidirect
5. #11749153C2semidirect
6. #11749038C2semidirect
7. #11747478C2semidirect
8. #11747331C2semidirect
9. #11746988C2semidirect
10. #11746906C2semidirect
11. #11746889C2semidirect
16. C3×C4×C5×D4C22semidirect
17. #91827C22semidirect
19. C4⋊C4×D15C22semidirect
22. #91758C22semidirect
23. C2×C5×#213C22semidirect
30. C2×#6648C22semidirect
31. C5×#809C22semidirect
32. C5×C4⋊(C3⋊C8)C22semidirect
33. C3×#3964C22semidirect
35. C3×#3939C22semidirect
36. C3×C4×#168C22semidirect
37. #90990C22semidirect
38. #90967C22semidirect
39. #90967C22semidirect
41. #90957C22semidirect
49. C4×#686D3semidirect
95. #5015D5semidirect
107. C4×C5×D4C2×D3semidirect
124. #3964C2×D3semidirect
129. #3939C2×D3semidirect
130. C4×#168C2×D3semidirect
149. D60D8semidirect
160. C3×D20#41semidirect
172. C3×C4×D4C2×D5semidirect
174. C2×#213C2×D5semidirect
193. #809C2×D5semidirect
195. C4⋊(C3⋊C8)C2×D5semidirect
329. D20#235semidirect
354. C4×D4D3×D5semidirect
468. C3×C5#3294semidirect
540. C5#79608semidirect
563. C3#10612083semidirect

Maximal subgroups

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

subgroupindex
#117563102
#117527372
C5×#50152
C3×C4×#6862
#117491532
#117490382
#117474782
#117473312
#117469882
#117469062
#117468892
#106120833
#796085