Finite Group Databasebeta

← #14438620

Subgroups — #14438620

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4034C211yesmaximal, characteristic, complemented
2#11754572C211yesmaximal, characteristic
3#11751067C211yesmaximal, characteristic, complemented
4C5×#4966C211yesmaximal, characteristic, complemented
5#11748413C211yesmaximal, characteristic, complemented
6#11748384C211yesmaximal, characteristic, complemented
7Dic5×#208C211yesmaximal, characteristic, complemented
8#11747369C212yesmaximal, complemented
9#11747159C212yesmaximal, complemented
10#11747140C212yesmaximal, complemented
11#11747138C212yesmaximal, complemented
12#10610609—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×Dic10—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#683—21no—
21C2×C3×C4×Dic5C2211yescharacteristic
22C3×#4034—21no—
23C3×#4034—21no—
24C3×#4034C2212yes—
25C3×#4034C2212yes—
26#91566—21no—
27#91566—21no—
28#91451C2211yescharacteristic
29C4×#1203—21no—
30C4×#1203—21no—
31#91376C2211yescharacteristic
32#91375C2211yescharacteristic
33#91373C2211yescharacteristic
34#91094C2212yes—
35#91093C2212yes—
36C5×#810C2212yes—
37C5×#809C2212yes—
38#90974C2212yes—
39#90972C2212yes—
40#90968C2212yes—
41#90966C2212yes—
42#90952C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83199—51nomaximal, Hall
45#66166—31no—
46C2×#4034D311yescharacteristic, complemented
47C5×#417—31no—
48#65521—31no—
49#65422—31no—
50M16×Dic5—31no—
51#65255—31no—
52#65084—32no—
53#65081—32no—
54#65054—32no—
55#65049—32no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5—21no—
71C22×C3×Dic5D411yescharacteristic
72C22×C3×Dic5D411yescharacteristic
73C2×C3×Dic10—22no—
74C2×C3×Dic10—22no—
75C2×C3×Dic10—44no—
76C2×#1203—21no—
77C2×#1203—21no—
78C3×C5×C4⋊C4—21no—
79C3×C5×C4⋊C4C2312yes—
80#6710—22no—
81C2×C3⋊#168C2312yes—
82C5×#208—22no—
83C2×C5×C3⋊C8C2312yes—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86C3×#683—22no—
87C3×#683—22no—
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5C2311yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92#6668—21no—
93#6668—21no—
94#6667—21no—
95#6667—21no—
96(C2×D3)⋊Dic5—21no—
97(C2×D3)⋊Dic5—21no—
98C2×C3×C4⋊Q8—51no—
99#5477—51no—
100#5093—52no—
101#5089—52no—
102#5089—52no—
103#5088—52no—
104#4966—51no—
105#4966—51no—
106#4966—51no—
107#4966D511yescharacteristic, complemented
108C4×#208—51no—
109C2×C5×#41—31no—
110C2×#709—31no—
111C22×Dic10—21no—
112C2×C5×M16—31no—
113C2×C5×C4⋊C4C2×D311yescharacteristic
114#4093—31no—
115#4090—31no—
116#4086—31no—
117#4085—61no—
118#4085—61no—
119#4082—31no—
120C4×C22⋊D5—61no—
121C4×C22⋊D5—61no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C2×#683—21no—
124C2×C4×Dic5C2×D311yescharacteristic
125C2×#681—31no—
126#4034—21no—
127#4034—21no—
128#4034C2×D312yes—
129#4034C2×D312yes—
130C5×#103—32no—
131C5×#102—32no—
132#3967—32no—
133#3964—32no—
134#3953—32no—
135#3948—32no—
136#3947—32no—
137C8×Dic5—32no—
138#3942—32no—
139#3941—32no—
140#3141—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×D15—21no—
143C22×C5×D3—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—42no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5#4112yes—
148C2×C3×C4×C5#4112yes—
149C2×C3×C4×C5C2411yescharacteristic
150#1220—42no—
151C2×Dic15—21no—
152D60—21no—
153D60—21no—
154C4×D15—42no—
155Dic30—21no—
156Dic30—21no—
157C5×#67—42no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12—21no—
161C4×C5×D3—42no—
162C5×Dic6—21no—
163C5×Dic6—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—42no—
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2×D411yescharacteristic
171C2×C3×Dic5C2×D411yescharacteristic
172C3×Dic10—44no—
173C3×Dic10—44no—
174#1203—42no—
175#1203—42no—
176C3⋊#168—22no—
177C5×C3⋊C8—22no—
178C22×C3×Q8—101no—
179C2×#235—51no—
180C2×#235C2×D511yescharacteristic
181C3×C4⋊Q8—52no—
182C3×C4⋊Q8—52no—
183C3×C4⋊Q8—101no—
184C3×C4⋊Q8—101no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—101no—
187C2×C3×C4⋊C4C2×D511yescharacteristic
188C2×C3×C42—51no—
189#930—101no—
190#930—101no—
191C2×#208—51no—
192C2×#208C2×D511yescharacteristic
193#875—51no—
194#875—51no—
195#874—51no—
196C4×D12—101no—
197C4×D12—101no—
198#869—51no—
199#810—52no—
200#810—52no—
201#810—52no—
202#810C2×D512yes—
203#809—52no—
204#809—52no—
205#809—52no—
206#809C2×D512yes—
207#803—52no—
208C4×C3⋊C8—52no—
209C5×#41—62no—
210C5×#41—62no—
211C2×C5×Q8—31no—
212C2×C5×D4—31no—
213C2×C5×D4—61no—
214C22×C4×C5—21no—
215C22×C4×C5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—61no—
218C2×C22⋊D5—61no—
219C2×C22⋊D5—61no—
220C22×Dic5—21no—
221C22×Dic5#6711yescharacteristic
222C22×Dic5#6711yescharacteristic
223#709—62no—
224#709—62no—
225C2×D20—31no—
226C2×C4×D5—61no—
227C2×Dic10—22no—
228C2×Dic10—22no—
229C2×Dic10—31no—
230C2×Dic10—44no—
231C5×M16—62no—
232C2×C5×C8—32no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4C22×D312yes—
235C22⋊Dic5—61no—
236C22⋊Dic5—61no—
237#685—61no—
238#685—61no—
239C4⋊Dic5—21no—
240C4⋊Dic5C22×D312yes—
241#683—22no—
242#683—22no—
243#683—61no—
244#683—61no—
245C4×Dic5#6711yescharacteristic
246C4×Dic5#6711yescharacteristic
247C4×Dic5C22×D311yescharacteristic
248C4×Dic5C22×D311yescharacteristic
249#681—62no—
250C2×#168—32no—
251#532—151no—
252C2×C4⋊Q8—51no—
253#489—152no—
254#489—152no—
255#487—152no—
256#486—152no—
257#417—31no—
258#417—151no—
259#417—151no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5#12412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×D15—41no—
267C2×D15—41no—
268C2×D15—41no—
269C2×C5×D3—41no—
270C2×C5×D3—41no—
271C2×C5×D3—41no—
272C3×C4×C5—42no—
273C3×C4×C5#12412yes—
274C3×C4×C5C2×#4111yescharacteristic
275C3×C4×C5C2×#4111yescharacteristic
276Dic15—41no—
277C3×Dic5—21no—
278C3×Dic5—21no—
279C3×Dic5—42no—
280C3×Dic5AGL(1,ℤ/8)12yes—
281C3×Dic5#13712yes—
282C5×Dic3—41no—
283C2×C3×Q8—102no—
284C2×C3×Q8—102no—
285C2×C3×Q8—204no—
286C22×C3×C4—21no—
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—101no—
290C22×C3×C4C22×D511yescharacteristic
291C2×#67—21no—
292C2×#67—101no—
293#235—22no—
294#235—22no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×D12—101no—
299C2×D12—101no—
300C2×D12C22×D511yescharacteristic
301C2×C4×D3—21no—
302C2×C4×D3—101no—
303C2×Dic6—51no—
304C2×Dic6C22×D511yescharacteristic
305C3×C4⋊C4—21no—
306C3×C4⋊C4—52no—
307C3×C4⋊C4—102no—
308C3×C4⋊C4—102no—
309C3×C4⋊C4—101no—
310C3×C4⋊C4C22×D512yes—
311C3×C42—51no—
312C3×C42—51no—
313C3×C42—51no—
314C3×C42—51no—
315(C2×D3)⋊C4—101no—
316(C2×D3)⋊C4—101no—
317(C2×D3)⋊C4—101no—
318(C2×D3)⋊C4—101no—
319C4⋊Dic3—101no—
320C4⋊Dic3—101no—
321#208—22no—
322#208—102no—
323C2×C3⋊C8—52no—
324C2×C3⋊C8C22×D512yes—
325C23×C5—61no—
326C23×C5C2×#6711yescharacteristic
327C22×D5—61no—
328C5×Q8—61no—
329C5×Q8—61no—
330C5×D4—61no—
331C5×D4—61no—
332C5×D4—122no—
333C2×C4×C5—22no—
334C2×C4×C5—42no—
335C2×C4×C5—61no—
336C2×C4×C5—122no—
337C2×C4×C5#23912yes—
338C2×C4×C5#23912yes—
339C2×C4×C5C2×#6711yescharacteristic
340C2×C4×C5C23×D311yescharacteristic
341C22⋊D5—122no—
342C22⋊D5—122no—
343C22⋊D5—122no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—42no—
348C2×Dic5—61no—
349C2×Dic5C2×#6711yescharacteristic
350C2×Dic5C2×#6711yescharacteristic
351C2×Dic5C2×#6711yescharacteristic
352C2×Dic5C2×#6711yescharacteristic
353D20—61no—
354D20—61no—
355C4×D5—122no—
356Dic10—44no—
357Dic10—44no—
358Dic10—61no—
359Dic10—61no—
360C5×C8—62no—
361#168—62no—
362C2×#41—31no—
363C2×#41—151no—
364C22×Q8—101no—
365C2×M16—31no—
366C2×M16—151no—
367C4⋊Q8—52no—
368C4⋊Q8—52no—
369C4⋊Q8—101no—
370C4⋊Q8—101no—
371C4⋊Q8—151no—
372#127—151no—
373#124—151no—
374#124—151no—
375#121—301no—
376#121—301no—
377C4×D4—301no—
378C4×D4—301no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C42—51no—
383#103—32no—
384#103—152no—
385#103—152no—
386#103—152no—
387#102—32no—
388#102—152no—
389#102—152no—
390#102—152no—
391#97—152no—
392C4×C8—152no—
393C2×C3×C5—22no—
394C2×C3×C5C2×#12411yescharacteristic
395C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C3×C5C2×#13711yescharacteristic
397D15—81no—
398C5×D3—81no—
399C23×C3D4×D511yescharacteristic
400C22×D3—21no—
401C22×D3—101no—
402C3×Q8—204no—
403C3×Q8—204no—
404C2×C3×C4—22no—
405C2×C3×C4—42no—
406C2×C3×C4—51no—
407C2×C3×C4—51no—
408C2×C3×C4—51no—
409C2×C3×C4—51no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4—202no—
414C2×C3×C4#70912yes—
415C2×C3×C4D4×D511yescharacteristic
416C2×C3×C4#71112yes—
417C2×C3×C4C23×D511yescharacteristic
418#67—42no—
419#67—202no—
420C2×Dic3—21no—
421C2×Dic3—101no—
422D12—21no—
423D12—21no—
424D12—101no—
425D12—101no—
426D12—202no—
427D12—202no—
428C4×D3—42no—
429C4×D3—202no—
430Dic6—21no—
431Dic6—21no—
432Dic6—101no—
433Dic6—101no—
434C3⋊C8—22no—
435C3⋊C8—102no—
436C22×C5—21no—
437C22×C5—21no—
438C22×C5—121no—
439C22×C5—121no—
440C22×C5—121no—
441C22×C5#94712yes—
442C22×C5C22×#6711yescharacteristic
443C2×D5—121no—
444C2×D5—121no—
445C2×D5—121no—
446C4×C5—42no—
447C4×C5—121no—
448C4×C5#94712yes—
449C4×C5C2×#23911yescharacteristic
450C4×C5C2×#23911yescharacteristic
451Dic5—21no—
452Dic5—21no—
453Dic5—42no—
454Dic5—121no—
455Dic5#93212yes—
456Dic5#94212yes—
457#41—62no—
458#41—62no—
459#41—302no—
460#41—302no—
461C2×Q8—31no—
462C2×Q8—102no—
463C2×Q8—102no—
464C2×Q8—151no—
465C2×Q8—204no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—151no—
469C2×D4—301no—
470C2×D4—301no—
471C2×D4—301no—
472C22×C4—21no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—61no—
476C22×C4—101no—
477C22×C4—301no—
478C22×C4C2×D3×D511yescharacteristic
479M16—62no—
480M16—302no—
481C2×C8—32no—
482C2×C8—152no—
483C4⋊C4—21no—
484C4⋊C4—52no—
485C4⋊C4—102no—
486C4⋊C4—102no—
487C4⋊C4—101no—
488C4⋊C4—301no—
489C4⋊C4—301no—
490C4⋊C4C2×D3×D512yes—
491C22⋊C4—301no—
492C22⋊C4—301no—
493C22⋊C4—301no—
494C22⋊C4—301no—
495C42—51no—
496C42—51no—
497C42—51no—
498C42—51no—
499C3×C5#314111yescharacteristic, complemented, Hall
500C22×C3—21no—
501C22×C3—21no—
502C22×C3#403112yes—
503C22×C3C2×D4×D511yescharacteristic
504C2×D3—41no—
505C2×D3—41no—
506C2×D3—41no—
507C2×D3—201no—
508C2×D3—201no—
509C2×D3—201no—
510C3×C4—42no—
511C3×C4—52no—
512C3×C4—52no—
513C3×C4—101no—
514C3×C4—101no—
515C3×C4—202no—
516C3×C4#403112yes—
517C3×C4C2×#70911yescharacteristic
518C3×C4C2×#71111yescharacteristic
519Dic3—41no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5C2×#93211yescharacteristic
524C2×C5C2×#94211yescharacteristic
525C2×C5C2×#94711yescharacteristic
526D5—241no—
527C23—61no—
528C23—301no—
529C23D5×#6711yescharacteristic
530Q8—61no—
531Q8—61no—
532Q8—204no—
533Q8—204no—
534Q8—301no—
535Q8—301no—
536D4—61no—
537D4—61no—
538D4—122no—
539D4—301no—
540D4—301no—
541D4—602no—
542D4—602no—
543D4—602no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—51no—
547C2×C4—51no—
548C2×C4—51no—
549C2×C4—51no—
550C2×C4—61no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—122no—
555C2×C4—202no—
556C2×C4—301no—
557C2×C4—602no—
558C2×C4#676812yes—
559C2×C4#676912yes—
560C2×C4D5×#6711yescharacteristic
561C2×C4C22×D3×D511yescharacteristic
562C8—62no—
563C8—302no—
564C2×C3—22no—
565C2×C3C2×#403111yescharacteristic
566C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
567C2×C3D5×#13711yescharacteristic
568D3—81no—
569D3—401no—
570C5#8319911yescharacteristic, complemented, Sylow
571C22—21no—
572C22—21no—
573C22—121no—
574C22—121no—
575C22—121no—
576C22—601no—
577C22—601no—
578C22—601no—
579C22#9132612yes—
580C22C2×D5×#6711yescharacteristic
581C4—42no—
582C4—52no—
583C4—52no—
584C4—101no—
585C4—101no—
586C4—121no—
587C4—202no—
588C4—601no—
589C4#9132612yes—
590C4C2×#676811yescharacteristic
591C4C2×#676911yescharacteristic
592C3#1061060911yescharacteristic, complemented, Sylow
593C2—22no—
594C2—241no—
595C2—1201no—
596C2C2×#9132611yescharacteristic
597C2D5×#93211yescharacteristic
598C2D5×#94211yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#11754572C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4034C2semidirect
3. #11751067C2semidirect
4. C5×#4966C2semidirect
5. #11748413C2semidirect
6. #11748384C2semidirect
7. Dic5×#208C2semidirect
8. #11747369C2semidirect
9. #11747159C2semidirect
10. #11747140C2semidirect
11. #11747138C2semidirect
46. C2×#4034D3semidirect
107. #4966D5semidirect
499. C3×C5#3141semidirect
570. C5#83199semidirect
592. C3#10610609semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40342
#117545722
#117510672
C5×#49662
#117484132
#117483842
Dic5×#2082
#117473692
#117471592
#117471402
#117471382
#106106093
#831995