Finite Group Databasebeta

← #14297323

Subgroups — #14297323

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92100C211yesmaximal, characteristic
2C3×C5×#421C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic, complemented
4#11751233C211yesmaximal, characteristic, complemented
5#11751232C211yesmaximal, characteristic, complemented
6#11751107C211yesmaximal, characteristic, complemented
7#11751102C211yesmaximal, characteristic, complemented
8#10601207—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92100—22no—
11#92100—22no—
12#92100—22no—
13#92100—22no—
14C2×#6821C412yescomplemented
15C2×D4×D15—22no—
16C2×D4×D15C412yescomplemented
17C2×#6817—21no—
18C2×#6817C2211yescharacteristic
19C22×D60—21no—
20C22×D60C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic, complemented
22C3×C5×#117C2211yescharacteristic, complemented
23#91815C2211yescharacteristic, complemented
24C2×#6710C2211yescharacteristic, complemented
25C3×C5×#104—22no—
26#91121—22no—
27#91108—21no—
28#91107—21no—
29#91105—22no—
30#91093—22no—
31#91090—22no—
32#70414—51nomaximal, Hall
33C2×#4149—31no—
34C5×#421D311yescharacteristic, complemented
35#65525—31no—
36#65421—31no—
37#65420—31no—
38#65295—31no—
39#65290—31no—
40C23×D15—21no—
41C23×D15—22no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41D412yes—
45C3×C5×#41D412yes—
46C2×C3×C5×Q8C2×C411yescharacteristic
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4C2×C411yescharacteristic
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—22no—
52C2×#1220D412yes—
53#6821—24no—
54#6821—24no—
55D4×D15—28no—
56D4×D15—28no—
57D4×D15—24no—
58D4×D15—24no—
59#6817—24no—
60#6817—24no—
61#6817—21no—
62#6817—21no—
63#6817—21no—
64#6817—21no—
65C2×D60—24no—
66C2×D60—24no—
67C2×D60—22no—
68C2×D60—21no—
69C2×D60—21no—
70C2×D60—21no—
71C2×D60C2×C412yes—
72C2×D60D411yescharacteristic
73C2×D60D412yes—
74C2×D60D412yes—
75C2×C4×D15—22no—
76C2×C4×D15C2×C412yes—
77C2×Dic30D411yescharacteristic
78C3×C5×M16—21no—
79C3×C5×M16—21no—
80C2×C3×C5×C8—21no—
81C3×C5×C4⋊C4—21no—
82C3×C5×C22⋊C4—21no—
83C3×C42×C5—21no—
84#6719—21no—
85C4⋊Dic15—21no—
86C4×Dic15—21no—
87#6710—21no—
88#6710—21no—
89C2×C3⋊#168—21no—
90C2×#1009—51no—
91C3×#421D511yescharacteristic, complemented
92#5236—51no—
93#5132—51no—
94#5131—51no—
95#5006—51no—
96#5001—51no—
97C2×C5×#41C2×D311yescharacteristic
98#4149—62no—
99#4149—62no—
100#4149—62no—
101#4149—62no—
102C2×#713—32no—
103C2×D4×D5—32no—
104C2×D4×D5—62no—
105C2×#709—31no—
106C2×#709—61no—
107C22×D20—31no—
108C22×D20—61no—
109C2×C5×M16C2×D311yescharacteristic, complemented
110C5×#117C2×D311yescharacteristic, complemented
111#4072—31no—
112C2×#681—31no—
113C5×#104—22no—
114#3969—62no—
115#3956—61no—
116#3955—61no—
117#3953—62no—
118#3941—62no—
119#3938—62no—
120#1795—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5C2×D411yescharacteristic
123C22×D15—22no—
124C22×D15—28no—
125C22×D15—22no—
126C22×D15—22no—
127C22×D15—82no—
128C22×D15—84no—
129C22×D15C22⋊C412yes—
130C3×C5×Q8—21no—
131C3×C5×Q8C22⋊C412yes—
132C3×C5×D4—22no—
133C3×C5×D4—22no—
134C3×C5×D4—21no—
135C3×C5×D4C22⋊C412yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5C22×C411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146#1220—28no—
147#1220—22no—
148#1220—22no—
149C2×Dic15—41no—
150C2×Dic15C22⋊C412yes—
151D60—28no—
152D60—22no—
153D60—21no—
154D60—22no—
155D60—21no—
156D60—22no—
157D60C22⋊C414yes—
158C4×D15—28no—
159C4×D15—22no—
160C4×D15—22no—
161Dic30—21no—
162Dic30—21no—
163C3×C5×C8—41no—
164C3⋊#168—41no—
165C2×C3×#41C2×D511yescharacteristic
166#1009—102no—
167#1009—102no—
168#1009—102no—
169#1009—102no—
170C2×#239—52no—
171C2×D3×D4—52no—
172C2×D3×D4—102no—
173C2×#235—51no—
174C2×#235—101no—
175C22×D12—51no—
176C22×D12—101no—
177C2×C3×M16C2×D511yescharacteristic, complemented
178C3×#117C2×D511yescharacteristic, complemented
179#926—51no—
180C2×#208—51no—
181C3×#104—22no—
182#837—102no—
183#824—101no—
184#823—101no—
185#821—102no—
186#809—102no—
187#806—102no—
188C23×D5—62no—
189C23×D5—61no—
190C5×#41—21no—
191C5×#41—21no—
192C5×#41D1212yes—
193C5×#41#6712yes—
194C2×C5×Q8C4×D311yescharacteristic
195C2×C5×D4—21no—
196C2×C5×D4C4×D311yescharacteristic
197C22×C4×C5—21no—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—32no—
200C2×C22⋊D5—62no—
201#713—64no—
202#713—64no—
203D4×D5—64no—
204D4×D5—68no—
205D4×D5—68no—
206D4×D5—64no—
207#709—64no—
208#709—64no—
209#709—61no—
210#709—61no—
211#709—61no—
212#709—61no—
213C2×D20—32no—
214C2×D20—32no—
215C2×D20—32no—
216C2×D20—31no—
217C2×D20—62no—
218C2×D20—64no—
219C2×D20—64no—
220C2×D20—61no—
221C2×D20—61no—
222C2×D20—61no—
223C2×C4×D5—32no—
224C2×C4×D5—62no—
225C2×Dic10—31no—
226C5×M16—21no—
227C5×M16—21no—
228C2×C5×C8—21no—
229C5×C4⋊C4—21no—
230C5×C22⋊C4—21no—
231C42×C5—21no—
232C22⋊Dic5—61no—
233C4⋊Dic5—61no—
234C4×Dic5—61no—
235#681—61no—
236#681—61no—
237C2×#168—61no—
238C2×H(5,𝔽2)—151no—
239#421—151no—
240#421D1511yescharacteristic, complemented
241#418—151no—
242#418—151no—
243#413—151no—
244#410—151no—
245C22×C3×C5—22no—
246C22×C3×C5—41no—
247C22×C3×C5—42no—
248C22×C3×C5C2×C22⋊C411yescharacteristic
249C22×C3×C5#12011yescharacteristic
250C22×C3×C5#12011yescharacteristic
251C2×D15—22no—
252C2×D15—24no—
253C2×D15—44no—
254C2×D15—42no—
255C2×D15—82no—
256C2×D15—82no—
257C2×D15—88no—
258C3×C4×C5—22no—
259C3×C4×C5—81no—
260C3×C4×C5C2×C22⋊C411yescharacteristic
261C3×C4×C5C2×C22⋊C411yescharacteristic
262C3×C4×C5#12011yescharacteristic
263C3×C4×C5#12011yescharacteristic
264Dic15—22no—
265Dic15—81no—
266C23×D3—102no—
267C23×D3—101no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41D2012yes—
271C3×#41C22⋊D512yes—
272C2×C3×Q8C4×D511yescharacteristic
273C2×C3×D4—21no—
274C2×C3×D4C4×D511yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—52no—
278C2×#67—102no—
279#239—104no—
280#239—104no—
281D3×D4—104no—
282D3×D4—108no—
283D3×D4—108no—
284D3×D4—104no—
285#235—104no—
286#235—104no—
287#235—101no—
288#235—101no—
289#235—101no—
290#235—101no—
291C2×D12—52no—
292C2×D12—52no—
293C2×D12—52no—
294C2×D12—51no—
295C2×D12—102no—
296C2×D12—104no—
297C2×D12—104no—
298C2×D12—101no—
299C2×D12—101no—
300C2×D12—101no—
301C2×C4×D3—52no—
302C2×C4×D3—102no—
303C2×Dic6—51no—
304C3×M16—21no—
305C3×M16—21no—
306C2×C3×C8—21no—
307C3×C4⋊C4—21no—
308C3×C22⋊C4—21no—
309C3×C42—21no—
310#217—101no—
311C4⋊Dic3—101no—
312C4×Dic3—101no—
313#208—101no—
314#208—101no—
315C2×C3⋊C8—101no—
316C23×C5—21no—
317C23×C5D3×D411yescharacteristic
318C22×D5—32no—
319C22×D5—62no—
320C22×D5—68no—
321C22×D5—62no—
322C22×D5—62no—
323C22×D5—242no—
324C22×D5—244no—
325C5×Q8—21no—
326C5×Q8(C2×D3)⋊C412yes—
327C5×D4—22no—
328C5×D4—22no—
329C5×D4—21no—
330C5×D4(C2×D3)⋊C412yes—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—41no—
335C2×C4×C5C2×C4×D311yescharacteristic
336C2×C4×C5C2×D1211yescharacteristic
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5D3×D411yescharacteristic
339C2×C4×C5D3×D411yescharacteristic
340C2×C4×C5C2×#6711yescharacteristic
341C22⋊D5—68no—
342C22⋊D5—62no—
343C22⋊D5—62no—
344C2×Dic5—32no—
345C2×Dic5—121no—
346D20—34no—
347D20—68no—
348D20—62no—
349D20—61no—
350D20—62no—
351D20—62no—
352D20—61no—
353C4×D5—68no—
354C4×D5—62no—
355C4×D5—62no—
356Dic10—61no—
357Dic10—61no—
358C5×C8—41no—
359#168—121no—
360H(5,𝔽2)—302no—
361H(5,𝔽2)—302no—
362H(5,𝔽2)—302no—
363H(5,𝔽2)—302no—
364C2×#41—151no—
365C2×#41—152no—
366C2×#41—301no—
367C2×#41C2×D1511yescharacteristic
368C22×D4—152no—
369C22×D4—151no—
370C22×D4—301no—
371C22×D4—302no—
372C2×M16—151no—
373C2×M16C2×D1511yescharacteristic, complemented
374#117—151no—
375#117C2×D1511yescharacteristic, complemented
376#104—22no—
377#104—302no—
378#102—302no—
379#102—302no—
380#101—301no—
381#100—301no—
382#99—302no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5—21no—
386C2×C3×C5—42no—
387C2×C3×C5#37911yescharacteristic
388D15—44no—
389D15—42no—
390C23×C3—21no—
391C23×C3D4×D511yescharacteristic
392C22×D3—52no—
393C22×D3—102no—
394C22×D3—108no—
395C22×D3—102no—
396C22×D3—102no—
397C22×D3—402no—
398C22×D3—404no—
399C3×Q8—21no—
400C3×Q8#68512yes—
401C3×D4—22no—
402C3×D4—22no—
403C3×D4—21no—
404C3×D4#68512yes—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—41no—
409C2×C3×C4C2×C4×D511yescharacteristic
410C2×C3×C4C2×D2011yescharacteristic
411C2×C3×C4D4×D511yescharacteristic
412C2×C3×C4D4×D511yescharacteristic
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4C2×C22⋊D511yescharacteristic
415#67—108no—
416#67—102no—
417#67—102no—
418C2×Dic3—52no—
419C2×Dic3—201no—
420D12—54no—
421D12—108no—
422D12—102no—
423D12—101no—
424D12—102no—
425D12—102no—
426D12—101no—
427C4×D3—108no—
428C4×D3—102no—
429C4×D3—102no—
430Dic6—101no—
431Dic6—101no—
432C3×C8—41no—
433C3⋊C8—201no—
434C22×C5—22no—
435C22×C5—41no—
436C22×C5—42no—
437C22×C5D3×C22⋊C411yescharacteristic
438C22×C5#88211yescharacteristic
439C22×C5#93711yescharacteristic
440C2×D5—64no—
441C2×D5—62no—
442C2×D5—124no—
443C2×D5—122no—
444C2×D5—242no—
445C2×D5—242no—
446C2×D5—248no—
447C4×C5—22no—
448C4×C5—81no—
449C4×C5D3×C22⋊C411yescharacteristic
450C4×C5#88211yescharacteristic
451C4×C5C2×(C2×D3)⋊C411yescharacteristic
452C4×C5#93711yescharacteristic
453Dic5—62no—
454Dic5—241no—
455C24—302no—
456C24—301no—
457#41—21no—
458#41—21no—
459#41—304no—
460#41—304no—
461#41—304no—
462#41—304no—
463#41—301no—
464#41—301no—
465#41—301no—
466#41—301no—
467#41D6012yes—
468#41#122012yes—
469C2×Q8—151no—
470C2×Q8C4×D1511yescharacteristic
471C2×D4—21no—
472C2×D4—152no—
473C2×D4—152no—
474C2×D4—152no—
475C2×D4—152no—
476C2×D4—151no—
477C2×D4—302no—
478C2×D4—304no—
479C2×D4—304no—
480C2×D4—302no—
481C2×D4—304no—
482C2×D4—308no—
483C2×D4—308no—
484C2×D4—304no—
485C2×D4—301no—
486C2×D4—301no—
487C2×D4—301no—
488C2×D4C4×D1511yescharacteristic
489C22×C4—21no—
490C22×C4—152no—
491C22×C4—302no—
492C22×C4C22×D1511yescharacteristic
493M16—21no—
494M16—21no—
495M16—301no—
496M16—301no—
497C2×C8—21no—
498C2×C8—301no—
499C4⋊C4—21no—
500C4⋊C4—301no—
501C22⋊C4—21no—
502C22⋊C4—301no—
503C42—21no—
504C42—301no—
505C3×C5#179511yescharacteristic, complemented, Hall
506C22×C3—22no—
507C22×C3—41no—
508C22×C3—42no—
509C22×C3D5×C22⋊C411yescharacteristic
510C22×C3#402811yescharacteristic
511C22×C3#408311yescharacteristic
512C2×D3—104no—
513C2×D3—102no—
514C2×D3—204no—
515C2×D3—202no—
516C2×D3—402no—
517C2×D3—402no—
518C2×D3—408no—
519C3×C4—22no—
520C3×C4—81no—
521C3×C4D5×C22⋊C411yescharacteristic
522C3×C4#402811yescharacteristic
523C3×C4C2×#68511yescharacteristic
524C3×C4#408311yescharacteristic
525Dic3—102no—
526Dic3—401no—
527C2×C5—21no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—42no—
531C2×C5#495511yescharacteristic
532D5—124no—
533D5—122no—
534C23—21no—
535C23—152no—
536C23—308no—
537C23—302no—
538C23—302no—
539C23—302no—
540C23—1202no—
541C23—1204no—
542C23D4×D1511yescharacteristic
543Q8—21no—
544Q8—301no—
545Q8—301no—
546Q8#671412yes—
547D4—22no—
548D4—22no—
549D4—21no—
550D4—154no—
551D4—308no—
552D4—308no—
553D4—302no—
554D4—302no—
555D4—302no—
556D4—301no—
557D4—302no—
558D4—302no—
559D4—301no—
560D4#671412yes—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—152no—
566C2×C4—308no—
567C2×C4—302no—
568C2×C4—302no—
569C2×C4—601no—
570C2×C4C2×C4×D1511yescharacteristic
571C2×C4C2×D6011yescharacteristic
572C2×C4D4×D1511yescharacteristic
573C2×C4D4×D1511yescharacteristic
574C2×C4D4×D1511yescharacteristic
575C2×C4C2×#122011yescharacteristic
576C8—41no—
577C8—601no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—42no—
582C2×C3#6524411yescharacteristic
583D3—204no—
584D3—202no—
585C5#7041411yescharacteristic, complemented, Sylow
586C22—22no—
587C22—41no—
588C22—42no—
589C22—304no—
590C22—302no—
591C22—602no—
592C22—604no—
593C22—1202no—
594C22—1202no—
595C22—1208no—
596C22C22⋊C4×D1511yescharacteristic
597C22#9177111yescharacteristic
598C22#9182611yescharacteristic
599C4—22no—
600C4—81no—
601C4—302no—
602C4—1201no—
603C4C22⋊C4×D1511yescharacteristic
604C4#9177111yescharacteristic
605C4C2×#671411yescharacteristic
606C4#9182611yescharacteristic
607C3#1060120711yescharacteristic, complemented, Sylow
608C2—21no—
609C2—21no—
610C2—21no—
611C2—42no—
612C2—604no—
613C2—602no—
614C2#1175105611yescharacteristic
subgroupG/H
centerC2#11751056
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#379
prime radicalC2×#92100C2
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1795
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C3×C5×#421C2semidirect
3. #11751337C2semidirect
4. #11751233C2semidirect
5. #11751232C2semidirect
6. #11751107C2semidirect
7. #11751102C2semidirect
14. C2×#6821C4semidirect
16. C2×D4×D15C4semidirect
21. C2×C3×C5×M16C22semidirect
22. C3×C5×#117C22semidirect
23. #91815C22semidirect
24. C2×#6710C22semidirect
34. C5×#421D3semidirect
91. C3×#421D5semidirect
109. C2×C5×M16C2×D3semidirect
110. C5×#117C2×D3semidirect
177. C2×C3×M16C2×D5semidirect
178. C3×#117C2×D5semidirect
240. #421D15semidirect
373. C2×M16C2×D15semidirect
375. #117C2×D15semidirect
505. C3×C5#1795semidirect
585. C5#70414semidirect
607. C3#10601207semidirect

Maximal subgroups

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

subgroupindex
C2×#921002
C3×C5×#4212
#117513372
#117512332
#117512322
#117511072
#117511022
#106012073
#704145