Finite Group Databasebeta

← #14427850

Subgroups — #14427850

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊#168C211yesmaximal, characteristic, complemented
2C5×#5791C211yesmaximal, characteristic, complemented
3C3×#66125C211yesmaximal, characteristic, complemented
4C2×#91297C211yesmaximal, characteristic, complemented
5#11748562C212yesmaximal, complemented
6#11748547C212yesmaximal, complemented
7#11748545C212yesmaximal, complemented
8#11748522C212yesmaximal, complemented
9#11748469C211yesmaximal, characteristic, complemented
10#11748382C211yesmaximal, characteristic, complemented
11#11748364C211yesmaximal, characteristic, complemented
12#10614653—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3⋊#168—24no—
17C22×C3⋊#168C2211yescharacteristic
18C22×C3⋊#168C2212yes—
19C22×C3⋊#168C2212yes—
20C22×C3⋊#168C2211yescharacteristic
21C5×#953—21no—
22C5×#930C2212yes—
23C5×#929—21no—
24C4×C5×#67—22no—
25C5×#926C2211yescharacteristic
26C5×#924C2212yes—
27C3×#4099—21no—
28C3×#4076C2212yes—
29C3×#4075—21no—
30C3×C4×C22⋊D5—22no—
31C3×#4072C2211yescharacteristic
32C3×#4070C2212yes—
33C2×#6661C2211yescharacteristic, complemented
34C2×#6656C2211yescharacteristic, complemented
35C2×#6655C2211yescharacteristic, complemented
36#91297—24no—
37C2×#6652C2211yescharacteristic, complemented
38#90989C2212yescomplemented
39#90986C2212yescomplemented
40#90972C2212yescomplemented
41#90970C2212yescomplemented
42#90966C2212yescomplemented
43#90964C2212yescomplemented
44#82922—51nomaximal, Hall
45C5×#525—31no—
46C2×#4096—31no—
47#66125D311yescharacteristic, complemented
48C23×#168—31no—
49#65522—31no—
50#65340—32no—
51#65337—32no—
52#65330—32no—
53#65327—32no—
54#65291—31no—
55#65287—31no—
56C24×C3×C5D411yescharacteristic
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5D412yes—
60C22×C3×C4×C5D411yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×C5×#67—22no—
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C2×C3×C22⋊D5—21no—
71C2×C3×C22⋊D5—22no—
72C3×#709—22no—
73C3×#709—22no—
74C2×C3×D20C2311yescharacteristic
75C2×C3×C4×D5—21no—
76C2×C3×Dic10C2311yescharacteristic
77C2×C3⋊#168—22no—
78C2×C3⋊#168—24no—
79C2×C3⋊#168—24no—
80C2×C3⋊#168D414yescomplemented
81C2×C3⋊#168C2312yes—
82C2×C3⋊#168C2311yescharacteristic
83C2×C3⋊#168C2311yescharacteristic
84C5×#217—22no—
85C5×#217—21no—
86C5×(C2×D3)⋊C4—22no—
87C5×C4⋊Dic3C2312yes—
88C5×Dic3⋊C4—22no—
89C4×C5×Dic3—21no—
90C3×C22⋊Dic5—22no—
91C3×C22⋊Dic5—21no—
92C3×#685—22no—
93C3×C4⋊Dic5C2312yes—
94C3×#683—22no—
95C3×C4×Dic5—21no—
96#6661—22no—
97#6656—22no—
98#6655—22no—
99#6652—22no—
100C3×#525—51no—
101C2×#950—51no—
102#5791D511yescharacteristic, complemented
103C23×C3⋊C8—51no—
104#5233—51no—
105#5051—52no—
106#5048—52no—
107#5041—52no—
108#5038—52no—
109#5002—51no—
110#4998—51no—
111C2×C5×#41—31no—
112C23×C4×C5C2×D311yescharacteristic
113C2×#709C2×D311yescharacteristic
114C5×#123—61no—
115C5×C22⋊Q8—32no—
116C5×#121—32no—
117C5×#120—61no—
118C4×C5×D4—62no—
119C5×#117—31no—
120#4099—21no—
121#4096—64no—
122C2×#689—31no—
123C2×#688—31no—
124C2×#687—31no—
125C2×#686—31no—
126#4076C2×D312yes—
127#4075—21no—
128C4×C22⋊D5—22no—
129#4072C2×D311yescharacteristic
130#4070C2×D312yes—
131C22×#168—31no—
132C22×#168—31no—
133C22×#168—32no—
134C22×#168—32no—
135C22×#168—64no—
136#3967—32no—
137#3964—32no—
138#3942—32no—
139#3941—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5—22no—
144C23×C3×C5—24no—
145C23×C3×C5C2×D411yescharacteristic
146C23×C3×C5C2×D412yes—
147C22×C5×D3—21no—
148C22×C3×D5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—24no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158C5×#67—42no—
159C5×#67—44no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—21no—
162C5×D12—21no—
163C5×D12—21no—
164C4×C5×D3—42no—
165C5×Dic6—21no—
166C5×Dic6—21no—
167C3×C22⋊D5—42no—
168C3×C22⋊D5—44no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—21no—
171C3×D20—21no—
172C3×D20—21no—
173C3×C4×D5—42no—
174C3×Dic10—21no—
175C3×Dic10—21no—
176C3⋊#168—22no—
177C3⋊#168C2×D412yes—
178C3⋊#168C2×D412yes—
179C2×C3×#41—51no—
180C23×C3×C4C2×D511yescharacteristic
181C2×#235C2×D511yescharacteristic
182C3×#123—101no—
183C3×C22⋊Q8—52no—
184C3×#121—52no—
185C3×#120—101no—
186C3×C4×D4—102no—
187C3×#117—51no—
188#953—21no—
189#950—104no—
190C2×#216—51no—
191C2×#215—51no—
192C2×#214—51no—
193C2×#213—51no—
194#930C2×D512yes—
195#929—21no—
196C4×#67—22no—
197#926C2×D511yescharacteristic
198#924C2×D512yes—
199C22×C3⋊C8—51no—
200C22×C3⋊C8—51no—
201C22×C3⋊C8—52no—
202C22×C3⋊C8—52no—
203C22×C3⋊C8—104no—
204#835—52no—
205#832—52no—
206#810—52no—
207#809—52no—
208#808—52no—
209#807—52no—
210C24×C5#6711yescharacteristic
211C5×#41—62no—
212C5×#41—62no—
213C2×C5×Q8—31no—
214C2×C5×D4—31no—
215C2×C5×D4—62no—
216C2×C5×D4—61no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—61no—
220C22×C4×C5#6712yes—
221C22×C4×C5#6711yescharacteristic
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—22no—
226#709—22no—
227#709—22no—
228C2×D20C22×D311yescharacteristic
229C2×C4×D5—21no—
230C2×Dic10C22×D311yescharacteristic
231C5×C4⋊C4—32no—
232C5×C4⋊C4—62no—
233C5×C22⋊C4—61no—
234C5×C22⋊C4—62no—
235C5×C22⋊C4—62no—
236C42×C5—61no—
237C22⋊Dic5—22no—
238C22⋊Dic5—21no—
239#689—62no—
240#688—62no—
241#687—62no—
242#686—62no—
243#685—22no—
244C4⋊Dic5C22×D312yes—
245#683—22no—
246C4×Dic5—21no—
247C2×#168—34no—
248C2×#168—31no—
249C2×#168—31no—
250C2×#168—32no—
251C2×#168—64no—
252C2×#168—64no—
253C2×#168—62no—
254C2×#135—151no—
255C23×C8—151no—
256#525—31no—
257#525—51no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—151no—
264#416—151no—
265C22×C3×C5—28no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5#12112yes—
270C22×C3×C5#13514yescomplemented
271C22×C3×C5C22×D411yescharacteristic
272C2×C5×D3—41no—
273C2×C5×D3—42no—
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5—22no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280C3×Dic5—41no—
281C3×Dic5—42no—
282C5×Dic3—41no—
283C5×Dic3—42no—
284C24×C3C22⋊D511yescharacteristic
285C3×#41—102no—
286C3×#41—102no—
287C2×C3×Q8—51no—
288C2×C3×D4—51no—
289C2×C3×D4—102no—
290C2×C3×D4—101no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—101no—
294C22×C3×C4C22⋊D512yes—
295C22×C3×C4C22⋊D511yescharacteristic
296C22×C3×C4C22×D512yes—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—22no—
299C2×#67—21no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6C22×D511yescharacteristic
305C3×C4⋊C4—52no—
306C3×C4⋊C4—102no—
307C3×C22⋊C4—101no—
308C3×C22⋊C4—102no—
309C3×C22⋊C4—102no—
310C3×C42—101no—
311#217—22no—
312#217—21no—
313#216—102no—
314#215—102no—
315#214—102no—
316#213—102no—
317(C2×D3)⋊C4—22no—
318C4⋊Dic3C22×D512yes—
319Dic3⋊C4—22no—
320C4×Dic3—21no—
321C2×C3⋊C8—54no—
322C2×C3⋊C8—51no—
323C2×C3⋊C8—51no—
324C2×C3⋊C8—52no—
325C2×C3⋊C8—104no—
326C2×C3⋊C8—104no—
327C2×C3⋊C8—102no—
328C23×C5—22no—
329C23×C5—24no—
330C23×C5—61no—
331C23×C5C2×#6711yescharacteristic
332C23×C5C2×#6712yes—
333C22×D5—21no—
334C5×Q8—61no—
335C5×Q8—61no—
336C5×D4—61no—
337C5×D4—61no—
338C5×D4—122no—
339C5×D4—124no—
340C2×C4×C5—22no—
341C2×C4×C5—24no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—62no—
345C2×C4×C5—61no—
346C2×C4×C5—122no—
347C2×C4×C5D3×D412yes—
348C2×C4×C5#23712yes—
349C2×C4×C5C2×#6712yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—42no—
353C22⋊D5—44no—
354C2×Dic5—22no—
355C2×Dic5—21no—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359Dic10—21no—
360Dic10—21no—
361#168—32no—
362#168—32no—
363#168—62no—
364C2×#41—31no—
365C2×#41—51no—
366C23×C4D3×D511yescharacteristic
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—151no—
373C22×C8—151no—
374C22×C8—152no—
375C22×C8—152no—
376C22×C8—304no—
377#123—61no—
378#123—101no—
379C22⋊Q8—32no—
380C22⋊Q8—52no—
381#121—32no—
382#121—52no—
383#120—61no—
384#120—101no—
385C4×D4—62no—
386C4×D4—102no—
387#117—31no—
388#117—51no—
389#107—152no—
390#106—152no—
391#103—152no—
392#103—152no—
393#102—152no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5—24no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399C3×D5—81no—
400C5×D3—81no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3—101no—
404C23×C3C2×C22⋊D512yes—
405C23×C3C2×C22⋊D511yescharacteristic
406C22×D3—21no—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—101no—
410C3×D4—101no—
411C3×D4—204no—
412C3×D4—202no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—102no—
418C2×C3×C4—101no—
419C2×C3×C4—202no—
420C2×C3×C4D4×D512yes—
421C2×C3×C4#71112yes—
422C2×C3×C4C2×C22⋊D512yes—
423C2×C3×C4C2×C22⋊D511yescharacteristic
424C2×C3×C4C23×D511yescharacteristic
425#67—44no—
426#67—42no—
427C2×Dic3—22no—
428C2×Dic3—21no—
429D12—21no—
430D12—21no—
431C4×D3—42no—
432Dic6—21no—
433Dic6—21no—
434C3⋊C8—52no—
435C3⋊C8—52no—
436C3⋊C8—102no—
437C22×C5—28no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—121no—
442C22×C5—122no—
443C22×C5#93912yes—
444C22×C5#95014yescomplemented
445C22×C5C22×#6711yescharacteristic
446C2×D5—41no—
447C2×D5—42no—
448C4×C5—22no—
449C4×C5—121no—
450C4×C5—122no—
451C4×C5#93912yes—
452C4×C5C2×D3×D411yescharacteristic
453C4×C5C2×#23711yescharacteristic
454Dic5—41no—
455Dic5—42no—
456C24#120111yescharacteristic
457#41—62no—
458#41—62no—
459#41—102no—
460#41—102no—
461C2×Q8—31no—
462C2×Q8—51no—
463C2×D4—31no—
464C2×D4—51no—
465C2×D4—62no—
466C2×D4—61no—
467C2×D4—102no—
468C2×D4—101no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—61no—
472C22×C4—101no—
473C22×C4#120111yescharacteristic
474C22×C4#120112yes—
475C22×C4C2×D3×D512yes—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—154no—
482C2×C8—151no—
483C2×C8—151no—
484C2×C8—152no—
485C2×C8—304no—
486C2×C8—304no—
487C2×C8—302no—
488C4⋊C4—32no—
489C4⋊C4—52no—
490C4⋊C4—62no—
491C4⋊C4—102no—
492C22⋊C4—61no—
493C22⋊C4—62no—
494C22⋊C4—62no—
495C22⋊C4—101no—
496C22⋊C4—102no—
497C22⋊C4—102no—
498C42—61no—
499C42—101no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—28no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—201no—
506C22×C3—202no—
507C22×C3#408512yes—
508C22×C3#409614yescomplemented
509C22×C3C22×C22⋊D511yescharacteristic
510C2×D3—41no—
511C2×D3—42no—
512C3×C4—22no—
513C3×C4—201no—
514C3×C4—202no—
515C3×C4#408512yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C2×#71111yescharacteristic
518Dic3—41no—
519Dic3—42no—
520C2×C5—22no—
521C2×C5—24no—
522C2×C5—241no—
523C2×C5C2×#93911yescharacteristic
524C2×C5C2×#95012yes—
525D5—81no—
526C23—24no—
527C23—22no—
528C23—61no—
529C23—101no—
530C23C2×#120112yes—
531C23C2×#120111yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—101no—
535Q8—101no—
536D4—61no—
537D4—61no—
538D4—101no—
539D4—101no—
540D4—124no—
541D4—122no—
542D4—204no—
543D4—202no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—102no—
551C2×C4—101no—
552C2×C4—122no—
553C2×C4—202no—
554C2×C4#678012yes—
555C2×C4C2×#120112yes—
556C2×C4C2×#120111yescharacteristic
557C2×C4#679012yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—152no—
560C8—152no—
561C8—302no—
562C2×C3—24no—
563C2×C3—22no—
564C2×C3—401no—
565C2×C3C2×#408511yescharacteristic
566C2×C3C2×#409612yes—
567D3—81no—
568C5#8292211yescharacteristic, complemented, Sylow
569C22—28no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—122no—
574C22—121no—
575C22—202no—
576C22—201no—
577C22#9129714yescomplemented
578C22#9157112yes—
579C22C22×#120111yescharacteristic
580C4—22no—
581C4—122no—
582C4—121no—
583C4—202no—
584C4—201no—
585C4#9157112yes—
586C4C2×#678011yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061465311yescharacteristic, complemented, Sylow
589C2—24no—
590C2—22no—
591C2—241no—
592C2—401no—
593C2C2×#9129712yes—
594C2C2×#9157111yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C22×D4
hypercenterC23×C4D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊#168C2semidirect
2. C5×#5791C2semidirect
3. C3×#66125C2semidirect
4. C2×#91297C2semidirect
5. #11748562C2semidirect
6. #11748547C2semidirect
7. #11748545C2semidirect
8. #11748522C2semidirect
9. #11748469C2semidirect
10. #11748382C2semidirect
11. #11748364C2semidirect
33. C2×#6661C22semidirect
34. C2×#6656C22semidirect
35. C2×#6655C22semidirect
37. C2×#6652C22semidirect
38. #90989C22semidirect
39. #90986C22semidirect
40. #90972C22semidirect
41. #90970C22semidirect
42. #90966C22semidirect
43. #90964C22semidirect
47. #66125D3semidirect
80. C2×C3⋊#168D4semidirect
102. #5791D5semidirect
270. C22×C3×C5#135semidirect
444. C22×C5#950semidirect
500. C3×C5#3050semidirect
508. C22×C3#4096semidirect
568. C5#82922semidirect
577. C22#91297semidirect
588. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
C23×C3⋊#1682
C5×#57912
C3×#661252
C2×#912972
#117485622
#117485472
#117485452
#117485222
#117484692
#117483822
#117483642
#106146533
#829225