Finite Group Databasebeta

← #14427875

Subgroups — #14427875

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#912C211yesmaximal, characteristic, complemented
2#11755065C212yesmaximal, complemented
3C2×D3×C8×D5C211yesmaximal, characteristic, complemented
4#11751258C211yesmaximal, characteristic, complemented
5C3×#65446C211yesmaximal, characteristic, complemented
6#11749121C212yesmaximal, complemented
7#11749120C212yesmaximal, complemented
8#11748965C212yesmaximal, complemented
9#11747956C211yesmaximal, characteristic, complemented
10#11747942C211yesmaximal, characteristic, complemented
11#11747682C211yesmaximal, characteristic, complemented
12#10615645—31nomaximal, Hall
13C2×C5×#237C2212yes—
14C2×C4×D3×D5C2211yescharacteristic
15C2×C3×C5×D8C2211yescharacteristic, complemented
16#91827C2212yes—
17C2×C8×D15C2211yescharacteristic
18C2×C5×#214C2212yescomplemented
19C5×#912—24no—
20C2×C5×Dic12C2211yescharacteristic, complemented
21C2×C5×D3×C8C2211yescharacteristic
22C3×#4084C2212yes—
23C2×C3×C8×D5C2211yescharacteristic
24#91577—22no—
25#91556—22no—
26#91555—22no—
27Dic3×C22⋊D5—22no—
28#91383C2212yes—
29#91359C2212yes—
30#91338C2212yes—
31C2×#6648C2211yescharacteristic
32C2×D3×#168C2211yescharacteristic
33C2×D5×C3⋊C8C2211yescharacteristic
34D3×C8×D5—24no—
35#91116C2212yescomplemented
36#91102C2211yescharacteristic, complemented
37C3×#3964C2212yescomplemented
38C3×#3950C2211yescharacteristic, complemented
39#90987C2212yescomplemented
40#90973C2212yescomplemented
41#90972C2212yescomplemented
42#80714—51nomaximal, Hall
43C2×C5×#135—31no—
44#66162—32no—
45C22×C8×D5—31no—
46#65522—32no—
47#65477—31no—
48#65477—31no—
49#65460—32no—
50#65460—32no—
51#65446—31no—
52#65446D311yescharacteristic, complemented
53#65395—31no—
54C22×D3×D5D411yescharacteristic
55C2×C3×C5×D4C2312yes—
56C2×#1220—22no—
57C2×C4×D15C2311yescharacteristic
58C2×C5×#67—22no—
59C22×C5×Dic3—22no—
60C5×#237—24no—
61C5×#237—24no—
62C2×C4×C5×D3C2311yescharacteristic
63C2×C5×Dic6C2312yes—
64C2×C3×C22⋊D5—22no—
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1200D411yescharacteristic
67C2×D3×Dic5D411yescharacteristic
68C2×D5×Dic3D411yescharacteristic
69C4×D3×D5—22no—
70C4×D3×D5—22no—
71C3×C5×D8—22no—
72C2×C3×C5×C8C2311yescharacteristic
73#6719—22no—
74C4⋊Dic15C2312yes—
75C2×C3⋊#168C2311yescharacteristic
76C8×D15—22no—
77C5×#214—24no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C5×Dic12—22no—
80C5×D3×C8D414yescomplemented
81C3×C22⋊Dic5—22no—
82C3×C4⋊Dic5C2312yes—
83C2×C3×#168C2311yescharacteristic
84C3×C8×D5—22no—
85#6669—22no—
86#6668—22no—
87#6667—22no—
88(C2×D3)⋊Dic5—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6648—22no—
92D3×#168—22no—
93D5×C3⋊C8—22no—
94C2×#912D511yescharacteristic, complemented
95C22×D3×C8—51no—
96#5606—52no—
97C3×#466—51no—
98#5157—51no—
99#5116—51no—
100#5041—52no—
101#4887—51no—
102#4880—51no—
103#4778—52no—
104#4772—52no—
105C2×C5×#41—32no—
106C22×C4×D5—31no—
107C5×#135—64no—
108C2×C5×Q16—31no—
109C2×C5×SD16—32no—
110C2×C5×D8C2×D311yescharacteristic, complemented
111C22×C5×C8—31no—
112#4092—32no—
113#4092—32no—
114#4084—32no—
115#4084C2×D312yes—
116#4083—62no—
117#4081—62no—
118C4×C22⋊D5—62no—
119C4×C22⋊D5—62no—
120#4072—32no—
121C22×#168—31no—
122C2×C8×D5—31no—
123C2×C8×D5—31no—
124C2×C8×D5—31no—
125C2×C8×D5—64no—
126C2×C8×D5C2×D311yescharacteristic
127#3967—32no—
128#3967—32no—
129#3964—32no—
130#3964C2×D312yescomplemented
131#3950—31no—
132#3950C2×D311yescharacteristic, complemented
133#3949—32no—
134#3050—151noSylow
135C23×C3×C5—22no—
136C22×D15C2×D411yescharacteristic
137C22×C5×D3C2×D411yescharacteristic
138C22×C3×D5C2×D411yescharacteristic
139C2×D3×D5—22no—
140C2×D3×D5—22no—
141C2×D3×D5—22no—
142C3×C5×D4—22no—
143C3×C5×D4—22no—
144C2×C3×C4×C5C2411yescharacteristic
145#1220—44no—
146C2×Dic15—22no—
147C2×Dic15C2×D411yescharacteristic
148C4×D15—21no—
149C4×D15—21no—
150C5×#67—44no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—44no—
153C2×C5×Dic3C2×D411yescharacteristic
154C4×C5×D3C2×D412yes—
155C4×C5×D3#4112yes—
156C5×Dic6—22no—
157C5×Dic6—22no—
158C3×C22⋊D5—44no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C2×D411yescharacteristic
161C3×C4×D5—21no—
162C3×C4×D5—21no—
163#1200—22no—
164D3×Dic5—22no—
165D5×Dic3—22no—
166C3×C5×C8C2×D412yes—
167C3⋊#168—21no—
168C3×#168—21no—
169C5×C3⋊C8C2×D412yes—
170C2×#237C2×D512yes—
171C22×C4×D3—51no—
172C2×C3×D8C2×D511yescharacteristic, complemented
173C22×C3×C8—51no—
174C3×#121—52no—
175#938—52no—
176#937—102no—
177D4×Dic3—102no—
178C2×#214C2×D512yescomplemented
179#924—52no—
180C22×C3⋊C8—51no—
181#912—24no—
182C2×Dic12C2×D511yescharacteristic, complemented
183C2×D3×C8—51no—
184C2×D3×C8—51no—
185C2×D3×C8—51no—
186C2×D3×C8—104no—
187C2×D3×C8C2×D511yescharacteristic
188#897—52no—
189#892—52no—
190#883—102no—
191#67⋊C4—102no—
192C3×#107—51no—
193C3×#102—52no—
194#832—52no—
195#818—51no—
196#816—52no—
197#810—52no—
198#808—52no—
199C23×D5—31no—
200C5×#41—64no—
201C5×#41—64no—
202C2×C5×Q8—32no—
203C2×C5×D4—62no—
204C2×C5×D4C22×D312yes—
205C22×C4×C5—31no—
206C22×C4×C5—62no—
207C2×C22⋊D5—22no—
208C2×C22⋊D5—62no—
209C22×Dic5—31no—
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—62no—
214C2×C4×D5—62no—
215C2×C4×D5C22×D311yescharacteristic
216C5×Q16—62no—
217C5×SD16—64no—
218C5×D8—22no—
219C2×C5×C8—31no—
220C2×C5×C8—34no—
221C2×C5×C8C22×D311yescharacteristic
222C22⋊Dic5—22no—
223C22⋊Dic5—62no—
224C22⋊Dic5—62no—
225#685—62no—
226#685—62no—
227C4⋊Dic5—32no—
228C4⋊Dic5C22×D312yes—
229#683—62no—
230#683—62no—
231C4×Dic5—62no—
232C2×#168—31no—
233C2×#168—62no—
234C2×#168C22×D311yescharacteristic
235C8×D5—22no—
236C8×D5—62no—
237C8×D5—62no—
238C8×D5—62no—
239C2×#135—31no—
240C23×C8—151no—
241#525—152no—
242#467—151no—
243#467—151no—
244#466—51no—
245#466—151no—
246#465—152no—
247#465—152no—
248#427—151no—
249#416—152no—
250C22×C3×C5—42no—
251C22×C3×C5—42no—
252C22×C3×C5—42no—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—21no—
255C2×D15—21no—
256C2×D15#13512yescomplemented
257C2×C5×D3—21no—
258C2×C5×D3—21no—
259C2×C5×D3#12112yes—
260C2×C3×D5—21no—
261C2×C3×D5—21no—
262C2×C3×D5#13512yescomplemented
263D3×D5—28no—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C2×#4111yescharacteristic
266Dic15—21no—
267Dic15—42no—
268C3×Dic5—21no—
269C3×Dic5—42no—
270C5×Dic3—42no—
271C5×Dic3#12112yes—
272C23×D3—51no—
273C2×C3×D4—102no—
274C2×C3×D4C22×D512yes—
275C22×C3×C4—51no—
276C2×#67—22no—
277C2×#67—102no—
278C22×Dic3—22no—
279C22×Dic3—51no—
280#237—24no—
281#237—24no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—51no—
285C2×C4×D3—102no—
286C2×C4×D3—102no—
287C2×C4×D3C22×D511yescharacteristic
288C2×Dic6C22×D512yes—
289C3×D8—22no—
290C2×C3×C8—51no—
291C2×C3×C8—102no—
292C2×C3×C8C22×D511yescharacteristic
293C3×C4⋊C4—52no—
294C3×C22⋊C4—102no—
295#217—102no—
296#217—102no—
297#214—24no—
298(C2×D3)⋊C4—102no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—52no—
301C4⋊Dic3—102no—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—102no—
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12—22no—
308D3×C8—102no—
309D3×C8—102no—
310D3×C8—102no—
311D3×C8C22⋊D514yescomplemented
312C23×C5—22no—
313C23×C5—31no—
314C22×D5—31no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5D3×D411yescharacteristic
319C5×Q8—62no—
320C5×Q8—62no—
321C5×D4—22no—
322C5×D4—22no—
323C5×D4—124no—
324C2×C4×C5—31no—
325C2×C4×C5—32no—
326C2×C4×C5—32no—
327C2×C4×C5—62no—
328C2×C4×C5—124no—
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—44no—
331C22⋊D5—124no—
332C2×Dic5—22no—
333C2×Dic5—31no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5D3×D411yescharacteristic
337C4×D5—21no—
338C4×D5—21no—
339C4×D5—62no—
340C4×D5—62no—
341C4×D5—61no—
342C4×D5—61no—
343C5×C8—32no—
344C5×C8D3×D412yes—
345#168—21no—
346#168—61no—
347C2×#41—32no—
348C23×C4—151no—
349#135—64no—
350C2×Q16—31no—
351C2×SD16—32no—
352C2×D8D3×D511yescharacteristic, complemented
353C22×C8—31no—
354C22×C8—51no—
355C22×C8—151no—
356C22×C8—151no—
357C22×C8—151no—
358C22×C8—151no—
359C22×C8—304no—
360#123—302no—
361C22⋊Q8—152no—
362C22⋊Q8—152no—
363#121—52no—
364#121—152no—
365#120—302no—
366C4×D4—302no—
367C4×D4—302no—
368#117—152no—
369#107—51no—
370#107—151no—
371#106—152no—
372#103—152no—
373#103—152no—
374#102—52no—
375#102—152no—
376C2×C3×C5—82no—
377C2×C3×C5C2×#12111yescharacteristic
378C2×C3×C5C2×#13511yescharacteristic
379C2×C3×C5C2×#13511yescharacteristic
380D15—22no—
381C3×D5—22no—
382C5×D3—22no—
383C23×C3—22no—
384C23×C3—51no—
385C22×D3—51no—
386C22×D3—102no—
387C22×D3—102no—
388C22×D3—102no—
389C22×D3D4×D511yescharacteristic
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—204no—
393C2×C3×C4—51no—
394C2×C3×C4—101no—
395C2×C3×C4—101no—
396C2×C3×C4—102no—
397C2×C3×C4C23×D511yescharacteristic
398#67—44no—
399#67—204no—
400C2×Dic3—22no—
401C2×Dic3—44no—
402C2×Dic3—51no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3D4×D511yescharacteristic
406C4×D3—102no—
407C4×D3—101no—
408C4×D3—101no—
409C4×D3—102no—
410C4×D3#71112yes—
411C4×D3C2×C22⋊D512yes—
412Dic6—22no—
413Dic6—22no—
414C3×C8—101no—
415C3×C8C2×C22⋊D512yes—
416C3⋊C8—101no—
417C3⋊C8C2×C22⋊D512yes—
418C22×C5—32no—
419C22×C5—42no—
420C22×C5—42no—
421C22×C5—42no—
422C22×C5—61no—
423C22×C5—61no—
424C22×C5C2×D3×D411yescharacteristic
425C2×D5—21no—
426C2×D5—21no—
427C2×D5—32no—
428C2×D5—68no—
429C2×D5—61no—
430C2×D5—61no—
431C2×D5#91212yescomplemented
432C4×C5—32no—
433C4×C5—122no—
434C4×C5C2×D3×D411yescharacteristic
435C4×C5D3×#4111yescharacteristic
436Dic5—21no—
437Dic5—42no—
438Dic5—61no—
439Dic5—122no—
440C24—151no—
441#41—64no—
442#41—64no—
443C2×Q8—32no—
444C2×D4—62no—
445C2×D4—102no—
446C2×D4—302no—
447C2×D4C2×D3×D512yes—
448C22×C4—31no—
449C22×C4—51no—
450C22×C4—62no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—151no—
455C22×C4—302no—
456C22×C4—302no—
457Q16—62no—
458SD16—64no—
459D8—22no—
460C2×C8—31no—
461C2×C8—34no—
462C2×C8—51no—
463C2×C8—102no—
464C2×C8—151no—
465C2×C8—302no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—52no—
471C4⋊C4—152no—
472C4⋊C4—302no—
473C4⋊C4—302no—
474C22⋊C4—102no—
475C22⋊C4—302no—
476C22⋊C4—302no—
477C22⋊C4—302no—
478C22⋊C4—302no—
479C42—302no—
480C3×C5#305011yescharacteristic, complemented, Hall
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—52no—
485C22×C3—101no—
486C22×C3—101no—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—21no—
489C2×D3—21no—
490C2×D3—52no—
491C2×D3—108no—
492C2×D3—101no—
493C2×D3—101no—
494C2×D3#408412yes—
495C3×C4—101no—
496C3×C4—202no—
497C3×C4C2×#71111yescharacteristic
498C3×C4C22×C22⋊D511yescharacteristic
499Dic3—42no—
500Dic3—101no—
501Dic3—202no—
502Dic3#408412yes—
503C2×C5—62no—
504C2×C5—82no—
505C2×C5D3×#12111yescharacteristic
506C2×C5C2×#91211yescharacteristic
507C2×C5D3×#13511yescharacteristic
508D5—22no—
509D5—62no—
510C23—22no—
511C23—31no—
512C23—51no—
513C23—151no—
514C23—302no—
515C23—302no—
516C23—302no—
517Q8—62no—
518Q8—62no—
519D4—22no—
520D4—22no—
521D4—124no—
522D4—204no—
523D4—604no—
524C2×C4—31no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—51no—
528C2×C4—62no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—102no—
532C2×C4—124no—
533C2×C4—151no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—301no—
538C2×C4—301no—
539C2×C4—302no—
540C2×C4C22×D3×D511yescharacteristic
541C8—32no—
542C8—101no—
543C8—301no—
544C8D3×C22⋊D512yes—
545C2×C3—82no—
546C2×C3—102no—
547C2×C3D5×#13511yescharacteristic
548C2×C3D5×#13511yescharacteristic
549C2×C3C2×#408411yescharacteristic
550D3—22no—
551D3—102no—
552C5#8071411yescharacteristic, complemented, Sylow
553C22—32no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—52no—
558C22—61no—
559C22—61no—
560C22—101no—
561C22—101no—
562C22—152no—
563C22—308no—
564C22—301no—
565C22—301no—
566C22D3×D4×D511yescharacteristic
567C4—32no—
568C4—101no—
569C4—122no—
570C4—202no—
571C4—301no—
572C4—602no—
573C4D3×#71111yescharacteristic
574C4C2×D3×C22⋊D511yescharacteristic
575C3#1061564511yescharacteristic, complemented, Sylow
576C2—62no—
577C2—82no—
578C2—102no—
579C2—302no—
580C2D5×#91211yescharacteristic
581C2#1175405311yescharacteristic
582C2D3×#408411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
hypercenterC2×D8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C5×#912C2semidirect
2. #11755065C2semidirect
3. C2×D3×C8×D5C2semidirect
4. #11751258C2semidirect
5. C3×#65446C2semidirect
6. #11749121C2semidirect
7. #11749120C2semidirect
8. #11748965C2semidirect
9. #11747956C2semidirect
10. #11747942C2semidirect
11. #11747682C2semidirect
15. C2×C3×C5×D8C22semidirect
18. C2×C5×#214C22semidirect
20. C2×C5×Dic12C22semidirect
35. #91116C22semidirect
36. #91102C22semidirect
37. C3×#3964C22semidirect
38. C3×#3950C22semidirect
39. #90987C22semidirect
40. #90973C22semidirect
41. #90972C22semidirect
52. #65446D3semidirect
80. C5×D3×C8D4semidirect
94. C2×#912D5semidirect
110. C2×C5×D8C2×D3semidirect
130. #3964C2×D3semidirect
132. #3950C2×D3semidirect
172. C2×C3×D8C2×D5semidirect
178. C2×#214C2×D5semidirect
182. C2×Dic12C2×D5semidirect
256. C2×D15#135semidirect
262. C2×C3×D5#135semidirect
311. D3×C8C22⋊D5semidirect
352. C2×D8D3×D5semidirect
431. C2×D5#912semidirect
480. C3×C5#3050semidirect
552. C5#80714semidirect
575. C3#10615645semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9122
#117550652
C2×D3×C8×D52
#117512582
C3×#654462
#117491212
#117491202
#117489652
#117479562
#117479422
#117476822
#106156453
#807145