Finite Group Databasebeta

← #14417106

Subgroups — #14417106

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91838C211yesmaximal, characteristic
2C3×#66161C211yesmaximal, characteristic, complemented
3#11754515C211yesmaximal, characteristic, complemented
4C5×#5233C211yesmaximal, characteristic, complemented
5#11749225C212yesmaximal, complemented
6#11749221C212yesmaximal, complemented
7#11748979C212yesmaximal, complemented
8#11748975C212yesmaximal, complemented
9#11748470C211yesmaximal, characteristic, complemented
10C2×#90968C211yesmaximal, characteristic, complemented
11#11748318C211yesmaximal, characteristic, complemented
12#10610551—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15#91838C418yescomplemented
16C2×#6717C2212yes—
17C2×#6715C2212yes—
18C2×#6710C2211yescharacteristic
19C5×#926C2211yescharacteristic
20C22×C5×C3⋊C8C2211yescharacteristic
21C3×Q8×Dic5C2212yescomplemented
22C3×D4×Dic5—22no—
23C3×D4×Dic5C2212yescomplemented
24C3×#4072—21no—
25C3×#4072C2211yescharacteristic
26C2×C3×C4⋊Dic5—21no—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28#91561—22no—
29#91428—21no—
30#91428—21no—
31#91418C2212yes—
32#91418C2212yes—
33C5×#835C2211yescharacteristic, complemented
34C5×#835C2211yescharacteristic, complemented
35C5×#832C2211yescharacteristic, complemented
36C5×#832C2211yescharacteristic, complemented
37#90989C2212yescomplemented
38#90986C2212yescomplemented
39#90968C2212yes—
40#90968C2212yes—
41#90952C2212yescomplemented
42Dic5×C3⋊C8C2212yescomplemented
43#82564—51nomaximal, Hall
44#66161D311yescharacteristic, complemented
45C2×#4095—31no—
46#65855—31no—
47C5×#416—31no—
48C2×#3953—31no—
49#65390—31no—
50#65284—31no—
51#65106—32no—
52#65077—32no—
53#65074—32no—
54#65045—32no—
55C23×D15—21no—
56C3×C5×#41—22no—
57C3×C5×#41C2×C414yescomplemented
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×D60—21no—
64C2×D60—22no—
65C2×D60C2×C414yescomplemented
66C2×D60C2312yes—
67C22×C3×Dic5—21no—
68C22×C3×Dic5—22no—
69C2×#1200—22no—
70C2×#1200—22no—
71#6717C2×C418yescomplemented
72#6715C2×C418yescomplemented
73#6710C2×C414yescomplemented
74C2×C3⋊#168C2312yes—
75C5×#217—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C4×C5×Dic3—21no—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C3×C22⋊Dic5—22no—
83C3×C22⋊Dic5D412yes—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5—22no—
86C3×C4⋊Dic5D411yescharacteristic
87C3×C4⋊Dic5D411yescharacteristic
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—22no—
90C3×C4×Dic5C2312yes—
91#6667—22no—
92#6667—22no—
93C3×#520—51no—
94C2×#949—51no—
95#5521—51no—
96#5233D511yescharacteristic, complemented
97#5026—52no—
98C4×#215—52no—
99#5014—52no—
100C4×#213—52no—
101#4997—51no—
102C2×#809—51no—
103#4964—51no—
104C2×C5×#41C2×D311yescharacteristic
105C22×D20—31no—
106C22×C5×C8—31no—
107C5×#117—31no—
108#4095—38no—
109Q8×Dic5C2×D312yescomplemented
110C2×#688—32no—
111D4×Dic5—22no—
112D4×Dic5C2×D312yescomplemented
113C2×#686—32no—
114#4072—21no—
115#4072C2×D311yescharacteristic
116C2×C4⋊Dic5—21no—
117C2×C4⋊Dic5C2×D311yescharacteristic
118C2×#681—31no—
119#4039—32no—
120#4039—32no—
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#103—31no—
125C5×#103—31no—
126C5×#102—31no—
127C5×#102—31no—
128#3953—32no—
129#3953—32no—
130#3947—32no—
131C8×Dic5—32no—
132#3940—32no—
133#3939—32no—
134#2946—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C22×D15—22no—
138C22×D15—24no—
139C22×D15—81no—
140C22×D15—81no—
141C3×C5×Q8—21no—
142C3×C5×Q8C22×C412yes—
143C3×C5×D4—24no—
144C3×C5×D4—21no—
145C3×C5×D4C22×C412yes—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—24no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5C2411yescharacteristic
152D60—24no—
153D60—22no—
154D60C22×C414yes—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—82no—
159C2×C3×Dic5—81no—
160C2×C3×Dic5C2×D412yes—
161C2×C3×Dic5C2×D412yes—
162#1200—82no—
163#1200—82no—
164C3⋊#168C22×C414yes—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C2×C3×#41C2×D511yescharacteristic
168C22×D12—51no—
169C3×C4×Q8—52no—
170C3×C4×D4—52no—
171C3×C4×D4—102no—
172C3×#117—51no—
173C3×#117—101no—
174C2×C3×C4⋊C4—51no—
175C2×C3×C4⋊C4—101no—
176#949—58no—
177C2×#215—52no—
178C2×#213—52no—
179#926C2×D511yescharacteristic
180C2×#208—51no—
181C22×C3⋊C8C2×D511yescharacteristic
182#893—101no—
183#893—101no—
184D3×C22⋊C4—102no—
185C4×D12—52no—
186C4×D12—52no—
187#835C2×D511yescharacteristic, complemented
188#835C2×D511yescharacteristic, complemented
189#832C2×D511yescharacteristic, complemented
190#832C2×D511yescharacteristic, complemented
191#809—52no—
192#809—52no—
193#808—52no—
194#807—52no—
195#803—52no—
196C4×C3⋊C8—52no—
197C23×D5—61no—
198C5×#41—22no—
199C5×#41C4×D314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—21no—
206C22×Dic5—22no—
207C2×D20—34no—
208C2×D20—32no—
209C2×D20—62no—
210C2×D20—61no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C5×C8—31no—
214C2×C5×C8—31no—
215C2×C5×C8—62no—
216C5×C4⋊C4—31no—
217C5×C4⋊C4—31no—
218C5×C22⋊C4—61no—
219C42×C5—61no—
220C22⋊Dic5—22no—
221C22⋊Dic5#6712yes—
222#688—38no—
223#686—38no—
224#685—62no—
225#685—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5—22no—
228C4⋊Dic5#6711yescharacteristic
229C4⋊Dic5#6711yescharacteristic
230C4⋊Dic5C22×D312yes—
231C4×Dic5—22no—
232C4×Dic5C22×D312yes—
233#681—34no—
234C2×#168—32no—
235C2×AGL(1,ℤ/8)—151no—
236#520—51no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—31no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5C4×D412yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×D15—24no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—84no—
257C3×C4×C5—22no—
258C3×C4×C5C4×D412yes—
259C3×C4×C5C23×C411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261C3×Dic5—22no—
262C3×Dic5—22no—
263C3×Dic5—42no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C23×D3—101no—
267C3×#41—22no—
268C3×#41C4×D514yescomplemented
269C2×C3×Q8C22×D511yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4C22×D511yescharacteristic
272C22×C3×C4—21no—
273C22×C3×C4—102no—
274C22×C3×C4—101no—
275C22×C3×C4C22×D511yescharacteristic
276C2×D12—54no—
277C2×D12—52no—
278C2×D12—101no—
279C2×D12—102no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C3×C4⋊C4—51no—
283C3×C4⋊C4—51no—
284C3×C4⋊C4—52no—
285C3×C4⋊C4—102no—
286C3×C4⋊C4—101no—
287C3×C22⋊C4—52no—
288C3×C22⋊C4—102no—
289C3×C42—52no—
290C3×C42—102no—
291#217—21no—
292#215—58no—
293#213—58no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298C4×Dic3—21no—
299#208—54no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—52no—
302C2×C3⋊C8C22×D511yescharacteristic
303C2×C3⋊C8C22×D511yescharacteristic
304C23×C5—21no—
305C23×C5C2×#6711yescharacteristic
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C5×Q8—21no—
311C5×Q8C2×C4×D312yes—
312C5×D4—24no—
313C5×D4—21no—
314C5×D4C2×C4×D312yes—
315C2×C4×C5—21no—
316C2×C4×C5—24no—
317C2×C4×C5—61no—
318C2×C4×C5—61no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5#23512yes—
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C23×D311yescharacteristic
323C2×Dic5—22no—
324C2×Dic5—82no—
325C2×Dic5—81no—
326C2×Dic5C2×#6712yes—
327C2×Dic5C2×#6712yes—
328D20—34no—
329D20—64no—
330D20—62no—
331C4×D5—242no—
332C4×D5—242no—
333C5×C8—61no—
334C5×C8—61no—
335#168—34no—
336C2×#41D3×D511yescharacteristic
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—151no—
342C22×C8—31no—
343C4×Q8—52no—
344C4×D4—52no—
345C4×D4—102no—
346C4×D4—152no—
347C4×D4—152no—
348C4×D4—301no—
349C4×D4—301no—
350#117—31no—
351#117—51no—
352#117—101no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—101no—
355C2×C22⋊C4—302no—
356#107—152no—
357#106—152no—
358#103—31no—
359#103—31no—
360#102—31no—
361#102—31no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—44no—
372C23×C3—21no—
373C23×C3D4×D511yescharacteristic
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C3×Q8—21no—
379C3×Q8C2×C4×D512yes—
380C3×D4—24no—
381C3×D4—21no—
382C3×D4C2×C4×D512yes—
383C2×C3×C4—21no—
384C2×C3×C4—24no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—102no—
388C2×C3×C4—402no—
389C2×C3×C4—401no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4D4×D511yescharacteristic
392C2×C3×C4#71112yes—
393C2×C3×C4C23×D511yescharacteristic
394C2×Dic3—21no—
395C2×Dic3—21no—
396D12—54no—
397D12—102no—
398D12—104no—
399C4×D3—402no—
400C4×D3—402no—
401C3⋊C8—21no—
402C3⋊C8—21no—
403C3⋊C8—54no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—22no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5C4×#6712yes—
410C22×C5C22×#6711yescharacteristic
411C2×D5—64no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—244no—
415C4×C5—22no—
416C4×C5—121no—
417C4×C5—121no—
418C4×C5C4×#6712yes—
419C4×C5C22×C4×D311yescharacteristic
420C4×C5C2×#23511yescharacteristic
421Dic5—22no—
422Dic5—22no—
423Dic5—42no—
424C24—301no—
425#41—22no—
426#41#120014yescomplemented
427C2×Q8C2×D3×D511yescharacteristic
428C2×D4—21no—
429C2×D4—154no—
430C2×D4—152no—
431C2×D4—302no—
432C2×D4—301no—
433C2×D4C2×D3×D511yescharacteristic
434C22×C4—21no—
435C22×C4—102no—
436C22×C4—101no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—154no—
443C2×C8—31no—
444C2×C8—31no—
445C2×C8—62no—
446C2×C8—152no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—51no—
450C4⋊C4—51no—
451C4⋊C4—52no—
452C4⋊C4—102no—
453C4⋊C4—101no—
454C22⋊C4—52no—
455C22⋊C4—61no—
456C22⋊C4—102no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—52no—
460C42—61no—
461C42—102no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3#402712yes—
469C22×C3C2×D4×D511yescharacteristic
470C2×D3—104no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—404no—
474C3×C4—22no—
475C3×C4—102no—
476C3×C4—102no—
477C3×C4—202no—
478C3×C4#402712yes—
479C3×C4C22×C4×D511yescharacteristic
480C3×C4C2×#71111yescharacteristic
481Dic3—41no—
482Dic3—41no—
483C2×C5—22no—
484C2×C5—42no—
485C2×C5C2×C4×#6711yescharacteristic
486C2×C5#583511yescharacteristic
487C2×C5#583711yescharacteristic
488D5—124no—
489C23—21no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23D5×#6711yescharacteristic
495Q8—21no—
496Q8C2×#120012yes—
497D4—24no—
498D4—21no—
499D4—154no—
500D4—302no—
501D4—304no—
502D4C2×#120012yes—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—52no—
506C2×C4—52no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—102no—
510C2×C4—402no—
511C2×C4—401no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#678212yes—
515C2×C4C2×#120012yes—
516C2×C4D5×#6711yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—61no—
519C8—61no—
520C8—154no—
521C2×C3—22no—
522C2×C3—42no—
523C2×C3C2×#402711yescharacteristic
524C2×C3#6610311yescharacteristic
525C2×C3#6610411yescharacteristic
526D3—204no—
527C5#8256411yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—304no—
534C22—602no—
535C22—602no—
536C22—1204no—
537C22#9155212yes—
538C22C2×D5×#6711yescharacteristic
539C4—22no—
540C4—102no—
541C4—102no—
542C4—121no—
543C4—121no—
544C4—202no—
545C4#9155212yes—
546C4C2×#678211yescharacteristic
547C4C22×#120011yescharacteristic
548C3#1061055111yescharacteristic, complemented, Sylow
549C2—22no—
550C2—42no—
551C2—604no—
552C2#1175531811yescharacteristic
553C2#1175531911yescharacteristic
554C2C2×#9155211yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91838C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#66161C2semidirect
3. #11754515C2semidirect
4. C5×#5233C2semidirect
5. #11749225C2semidirect
6. #11749221C2semidirect
7. #11748979C2semidirect
8. #11748975C2semidirect
9. #11748470C2semidirect
10. C2×#90968C2semidirect
11. #11748318C2semidirect
15. #91838C4semidirect
21. C3×Q8×Dic5C22semidirect
23. C3×D4×Dic5C22semidirect
33. C5×#835C22semidirect
34. C5×#835C22semidirect
35. C5×#832C22semidirect
36. C5×#832C22semidirect
37. #90989C22semidirect
38. #90986C22semidirect
41. #90952C22semidirect
42. Dic5×C3⋊C8C22semidirect
44. #66161D3semidirect
57. C3×C5×#41C2×C4semidirect
65. C2×D60C2×C4semidirect
71. #6717C2×C4semidirect
72. #6715C2×C4semidirect
73. #6710C2×C4semidirect
96. #5233D5semidirect
109. Q8×Dic5C2×D3semidirect
112. D4×Dic5C2×D3semidirect
187. #835C2×D5semidirect
188. #835C2×D5semidirect
189. #832C2×D5semidirect
190. #832C2×D5semidirect
199. C5×#41C4×D3semidirect
268. C3×#41C4×D5semidirect
426. #41#1200semidirect
462. C3×C5#2946semidirect
527. C5#82564semidirect
548. C3#10610551semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C3×#661612
#117545152
C5×#52332
#117492252
#117492212
#117489792
#117489752
#117484702
C2×#909682
#117483182
#106105513
#825645