Finite Group Databasebeta

← #14413429

Subgroups — #14413429

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×#117C211yesmaximal, characteristic
2D3×#4072C211yesmaximal, characteristic
3C22×#6650C211yesmaximal, characteristic
4#11751099C211yesmaximal, characteristic, complemented
5C3×#65287C211yesmaximal, characteristic, complemented
6#11748469C211yesmaximal, characteristic, complemented
7#11748458C211yesmaximal, characteristic, complemented
8#11747455C212yesmaximal, complemented
9#11747454C212yesmaximal, complemented
10#11747191C212yesmaximal, complemented
11#11747190C212yesmaximal, complemented
12#10613938—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C5×#892C2212yes—
19C5×D3×C4⋊C4C2212yes—
20C5×D3×C22⋊C4—21no—
21C5×#877—21no—
22C5×#872—21no—
23C42×C5×D3—21no—
24C3×#4072C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26D3×C22⋊Dic5—21no—
27#91529—21no—
28D3×C4⋊Dic5C2212yes—
29C4×D3×Dic5—21no—
30#91371—21no—
31#91338C2212yes—
32C2×#6650C418yescomplemented
33C2×#6650C2211yescharacteristic
34C2×#6650C2211yescharacteristic
35C2×#6650C2211yescharacteristic
36C2×#6650C2211yescharacteristic
37#91092C2212yescomplemented
38#91091C2212yescomplemented
39C3×#3940C2212yescomplemented
40C3×#3939C2212yescomplemented
41#90989C2212yescomplemented
42#90988C2212yescomplemented
43#90986C2212yescomplemented
44#90985C2212yescomplemented
45#79177—51nomaximal, Hall
46C2×C5×#117—31no—
47C2×#4072—31no—
48C22×#681—31no—
49#65287—31no—
50#65287—31no—
51#65287—31no—
52#65287D311yescharacteristic, complemented
53#65284—32no—
54#65284—32no—
55#65253—32no—
56#65253—32no—
57C23×C5×D3D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C5×Dic3D411yescharacteristic
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3C2×C414yes—
62C2×C4×C5×D3D411yescharacteristic
63C2×C4×C5×D3D411yescharacteristic
64C2×C4×C5×D3Q814yes—
65C2×C4×C5×D3C2311yescharacteristic
66C2×C4×C5×D3C2311yescharacteristic
67C2×D3×Dic5—22no—
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—21no—
70C3×C42×C5—21no—
71#6719—21no—
72C4⋊Dic15C2312yes—
73C4×Dic15—21no—
74C2×C3⋊#168C2×C414yescomplemented
75C2×C3⋊#168C2311yescharacteristic
76C2×C3⋊#168C2311yescharacteristic
77C5×#217—21no—
78C5×(C2×D3)⋊C4—22no—
79C5×C4⋊Dic3C2312yes—
80C5×Dic3⋊C4—22no—
81C4×C5×Dic3—21no—
82C4×C5×Dic3—22no—
83C3×C22⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85C3×C4×Dic5—21no—
86C2×C3×#168C2×C414yescomplemented
87C2×C3×#168C2311yescharacteristic
88C2×C3×#168C2311yescharacteristic
89Dic3⋊Dic5—22no—
90(C2×D3)⋊Dic5—22no—
91Dic3×Dic5—22no—
92#6650C2×C414yescomplemented
93#6650C2×C414yescomplemented
94#6650C2×C414yescomplemented
95#6650C2×C414yescomplemented
96C22×ΓL(1,𝔽25)—51no—
97D3×#117—51no—
98D3×#117D511yescharacteristic
99C3×#427—51no—
100#5106—51no—
101#4998—51no—
102#4998—51no—
103#4881—52no—
104#4881—52no—
105#4861—52no—
106#4861—52no—
107C23×C4×C5—31no—
108C5×#117—31no—
109C5×#117—32no—
110C5×#117—61no—
111C5×#117—61no—
112C5×#117C2×D311yescharacteristic
113C2×C5×C4⋊C4—32no—
114C2×C5×C22⋊C4—61no—
115C2×C42×C5—61no—
116C2×C22⋊Dic5—61no—
117#4072—31no—
118#4072—32no—
119#4072—61no—
120#4072—61no—
121#4072C2×D311yescharacteristic
122C2×C4⋊Dic5—32no—
123C2×C4×Dic5—61no—
124C2×#681—38no—
125C2×#681—31no—
126C2×#681—31no—
127C2×#681—31no—
128C2×#681—31no—
129C22×#168—31no—
130C22×#168C2×D311yescharacteristic
131#3940—32no—
132#3940—32no—
133#3940—32no—
134#3940C2×D312yescomplemented
135#3939—32no—
136#3939—32no—
137#3939—32no—
138#3939C2×D312yescomplemented
139#2911—151noSylow
140C23×C3×C5C2×D411yescharacteristic
141C22×C5×D3—42no—
142C22×C5×D3C4⋊C414yes—
143C22×C5×D3C2×D411yescharacteristic
144C22×C5×D3C2×D411yescharacteristic
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×Q812yes—
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3C4⋊C414yes—
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C4×C5×D3—44no—
156C4×C5×D3C4⋊C414yes—
157C4×C5×D3C4⋊C414yes—
158C4×C5×D3C22×C412yes—
159C4×C5×D3C22×C412yes—
160C4×C5×D3C2×Q812yes—
161C4×C5×D3C2×Q812yes—
162C2×C3×Dic5—22no—
163D3×Dic5—44no—
164C3⋊#168C22×C412yes—
165C3⋊#168C22×C412yes—
166C3×#168C22×C412yes—
167C3×#168C22×C412yes—
168C22×C4×D3C2×D511yescharacteristic
169C22×C3×C8—51no—
170C3×#117—51no—
171C3×#117C2×D511yescharacteristic
172#926—51no—
173#926C2×D511yescharacteristic
174C22×C3⋊C8—51no—
175C2×ΓL(1,𝔽25)—58no—
176C2×ΓL(1,𝔽25)—51no—
177C2×ΓL(1,𝔽25)—51no—
178C2×ΓL(1,𝔽25)—51no—
179C2×ΓL(1,𝔽25)—51no—
180#892—52no—
181#892C2×D512yes—
182D3×C4⋊C4—52no—
183D3×C4⋊C4C2×D512yes—
184D3×C22⋊C4—21no—
185D3×C22⋊C4—101no—
186#877—21no—
187#877—101no—
188#872—21no—
189#872—101no—
190C42×D3—21no—
191C42×D3—101no—
192C3×#107—52no—
193C3×#106—52no—
194#818—52no—
195#817—52no—
196#808—52no—
197#808—52no—
198#807—52no—
199#807—52no—
200C24×C5—31no—
201C22×C4×C5—31no—
202C22×C4×C5—34no—
203C22×C4×C5—31no—
204C22×C4×C5—31no—
205C22×C4×C5—34no—
206C22×C4×C5—31no—
207C22×C4×C5—31no—
208C22×C4×C5—62no—
209C22×C4×C5C22×D311yescharacteristic
210C22×Dic5—62no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—62no—
213C5×C4⋊C4C22×D312yes—
214C5×C22⋊C4—21no—
215C5×C22⋊C4—62no—
216C5×C22⋊C4—61no—
217C42×C5—21no—
218C42×C5—62no—
219C42×C5—61no—
220C22⋊Dic5—21no—
221C22⋊Dic5—62no—
222C22⋊Dic5—61no—
223C4⋊Dic5—32no—
224C4⋊Dic5—62no—
225C4⋊Dic5C22×D312yes—
226C4×Dic5—21no—
227C4×Dic5—62no—
228C4×Dic5—61no—
229#681—34no—
230#681—34no—
231#681—34no—
232#681—34no—
233C2×#168—34no—
234C2×#168—31no—
235C2×#168—31no—
236C2×#168C4×D314yescomplemented
237C2×#168C22×D311yescharacteristic
238C2×#168C22×D311yescharacteristic
239C22×M16—151no—
240C2×#117—31no—
241C2×#117—151no—
242#428—152no—
243#428—152no—
244#428—152no—
245#428—152no—
246#427—51no—
247#427—151no—
248#427—151no—
249#427—151no—
250C22×C3×C5—22no—
251C22×C3×C5C2×C4⋊C412yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—22no—
255C2×C5×D3—44no—
256C2×C5×D3C2×C4⋊C412yes—
257C2×C5×D3C2×C4⋊C412yes—
258C3×C4×C5—42no—
259C3×C4×C5C2×C4⋊C412yes—
260C3×C4×C5C23×C411yescharacteristic
261C3×C4×C5C22×Q811yescharacteristic
262Dic15—42no—
263C3×Dic5—42no—
264C5×Dic3—42no—
265C5×Dic3C2×C4⋊C412yes—
266C5×Dic3C2×C4⋊C412yes—
267C23×D3C22⋊D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3C22⋊D511yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—102no—
272C2×C4×D3Dic1014yes—
273C2×C4×D3C4×D514yes—
274C2×C4×D3C22⋊D511yescharacteristic
275C2×C4×D3C22⋊D511yescharacteristic
276C2×C4×D3C22×D511yescharacteristic
277C2×C4×D3C22×D511yescharacteristic
278C2×C3×C8—54no—
279C2×C3×C8—51no—
280C2×C3×C8—51no—
281C3×C4⋊C4—52no—
282C3×C4⋊C4C22×D512yes—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—101no—
285C3×C42—21no—
286C3×C42—101no—
287#217—21no—
288#217—101no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—102no—
291C4⋊Dic3—52no—
292C4⋊Dic3C22×D512yes—
293Dic3⋊C4—22no—
294Dic3⋊C4—102no—
295C4×Dic3—21no—
296C4×Dic3—22no—
297C4×Dic3—101no—
298C4×Dic3—102no—
299C2×C3⋊C8—54no—
300C2×C3⋊C8—51no—
301C2×C3⋊C8—51no—
302ΓL(1,𝔽25)—54no—
303ΓL(1,𝔽25)—54no—
304ΓL(1,𝔽25)—54no—
305ΓL(1,𝔽25)—54no—
306C23×C5—31no—
307C23×C5—31no—
308C23×C5—34no—
309C23×C5—122no—
310C23×C5D3×D411yescharacteristic
311C2×C4×C5—22no—
312C2×C4×C5—34no—
313C2×C4×C5—31no—
314C2×C4×C5—31no—
315C2×C4×C5—34no—
316C2×C4×C5—34no—
317C2×C4×C5—32no—
318C2×C4×C5—32no—
319C2×C4×C5—32no—
320C2×C4×C5—32no—
321C2×C4×C5—62no—
322C2×C4×C5—124no—
323C2×C4×C5C2×C4×D312yes—
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5D3×Q812yes—
326C2×C4×C5C23×D311yescharacteristic
327C2×Dic5—22no—
328C2×Dic5—62no—
329C2×Dic5—124no—
330#168—32no—
331#168—32no—
332#168C2×C4×D312yes—
333#168C2×C4×D312yes—
334C23×C4—31no—
335C2×M16—151no—
336C2×M16—151no—
337C2×M16—151no—
338C2×M16—151no—
339C2×M16—158no—
340C22×C8—51no—
341C22×C8—151no—
342#117—31no—
343#117—32no—
344#117—51no—
345#117—61no—
346#117—61no—
347#117—152no—
348#117—151no—
349#117—301no—
350#117—301no—
351#117D3×D511yescharacteristic
352C2×C4⋊C4—32no—
353C2×C4⋊C4—152no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—301no—
356C2×C42—61no—
357C2×C42—301no—
358#107—52no—
359#107—152no—
360#107—152no—
361#107—152no—
362#106—52no—
363#106—152no—
364#106—152no—
365#106—152no—
366C2×C3×C5—22no—
367C2×C3×C5C22×C4⋊C411yescharacteristic
368C2×C3×C5#57512yes—
369C5×D3—22no—
370C5×D3—22no—
371C23×C3C2×C22⋊D511yescharacteristic
372C22×D3—42no—
373C22×D3#68314yes—
374C22×D3C2×C22⋊D511yescharacteristic
375C22×D3C2×C22⋊D511yescharacteristic
376C2×C3×C4—22no—
377C2×C3×C4—102no—
378C2×C3×C4C2×Dic1012yes—
379C2×C3×C4C2×C4×D512yes—
380C2×C3×C4C2×C22⋊D511yescharacteristic
381C2×C3×C4C23×D511yescharacteristic
382C2×Dic3—22no—
383C2×Dic3—102no—
384C2×Dic3#68314yes—
385C2×Dic3C2×C22⋊D511yescharacteristic
386C2×Dic3C2×C22⋊D511yescharacteristic
387C4×D3—44no—
388C4×D3—204no—
389C4×D3#68314yes—
390C4×D3#68314yes—
391C4×D3C2×Dic1012yes—
392C4×D3C2×Dic1012yes—
393C4×D3C2×C4×D512yes—
394C4×D3C2×C4×D512yes—
395C3×C8—52no—
396C3×C8—52no—
397C3⋊C8—52no—
398C3⋊C8—52no—
399C22×C5—22no—
400C22×C5—32no—
401C22×C5—32no—
402C22×C5—62no—
403C22×C5—62no—
404C22×C5—124no—
405C22×C5D3×C4⋊C412yes—
406C22×C5C2×D3×D411yescharacteristic
407C4×C5—32no—
408C4×C5—32no—
409C4×C5—42no—
410C4×C5—122no—
411C4×C5D3×C4⋊C412yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×D3×Q811yescharacteristic
414Dic5—42no—
415Dic5—122no—
416C24—31no—
417C22×C4—31no—
418C22×C4—34no—
419C22×C4—34no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—62no—
425C22×C4—302no—
426C22×C4C2×D3×D511yescharacteristic
427M16—154no—
428M16—154no—
429M16—154no—
430M16—154no—
431C2×C8—54no—
432C2×C8—51no—
433C2×C8—51no—
434C2×C8—154no—
435C2×C8—151no—
436C2×C8—151no—
437C4⋊C4—32no—
438C4⋊C4—52no—
439C4⋊C4—62no—
440C4⋊C4—152no—
441C4⋊C4—302no—
442C4⋊C4C2×D3×D512yes—
443C22⋊C4—21no—
444C22⋊C4—62no—
445C22⋊C4—61no—
446C22⋊C4—101no—
447C22⋊C4—302no—
448C22⋊C4—301no—
449C42—21no—
450C42—62no—
451C42—61no—
452C42—101no—
453C42—302no—
454C42—301no—
455C3×C5#291111yescharacteristic, complemented, Hall
456C22×C3—22no—
457C22×C3C2×#68312yes—
458C22×C3C22×C22⋊D511yescharacteristic
459C2×D3—22no—
460C2×D3—22no—
461C2×D3—44no—
462C2×D3C2×#68312yes—
463C2×D3C2×#68312yes—
464C3×C4—42no—
465C3×C4—202no—
466C3×C4C2×#68312yes—
467C3×C4C22×Dic1011yescharacteristic
468C3×C4C22×C4×D511yescharacteristic
469Dic3—42no—
470Dic3—202no—
471Dic3C2×#68312yes—
472Dic3C2×#68312yes—
473C2×C5—22no—
474C2×C5—62no—
475C2×C5—62no—
476C2×C5C2×D3×C4⋊C411yescharacteristic
477C2×C5#576812yes—
478C23—31no—
479C23—31no—
480C23—34no—
481C23—122no—
482C23D3×C22⋊D511yescharacteristic
483C2×C4—22no—
484C2×C4—34no—
485C2×C4—31no—
486C2×C4—31no—
487C2×C4—34no—
488C2×C4—34no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—62no—
494C2×C4—102no—
495C2×C4—124no—
496C2×C4—302no—
497C2×C4—604no—
498C2×C4D3×Dic1012yes—
499C2×C4C4×D3×D512yes—
500C2×C4D3×C22⋊D511yescharacteristic
501C2×C4C22×D3×D511yescharacteristic
502C8—52no—
503C8—52no—
504C8—152no—
505C8—152no—
506C2×C3—22no—
507C2×C3C22×#68311yescharacteristic
508C2×C3#6615612yes—
509D3—22no—
510D3—22no—
511C5#7917711yescharacteristic, complemented, Sylow
512C22—22no—
513C22—32no—
514C22—32no—
515C22—62no—
516C22—62no—
517C22—124no—
518C22D3×#68312yes—
519C22C2×D3×C22⋊D511yescharacteristic
520C4—32no—
521C4—32no—
522C4—42no—
523C4—122no—
524C4—202no—
525C4—602no—
526C4D3×#68312yes—
527C4C2×D3×Dic1011yescharacteristic
528C4C2×C4×D3×D511yescharacteristic
529C3#1061393811yescharacteristic, complemented, Sylow
530C2—22no—
531C2—62no—
532C2—62no—
533C2C2×D3×#68311yescharacteristic
534C2#1175532212yes—
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC23×C5×D3D4
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2911
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11751099C2semidirect
5. C3×#65287C2semidirect
6. #11748469C2semidirect
7. #11748458C2semidirect
8. #11747455C2semidirect
9. #11747454C2semidirect
10. #11747191C2semidirect
11. #11747190C2semidirect
32. C2×#6650C4semidirect
37. #91092C22semidirect
38. #91091C22semidirect
39. C3×#3940C22semidirect
40. C3×#3939C22semidirect
41. #90989C22semidirect
42. #90988C22semidirect
43. #90986C22semidirect
44. #90985C22semidirect
52. #65287D3semidirect
74. C2×C3⋊#168C2×C4semidirect
86. C2×C3×#168C2×C4semidirect
92. #6650C2×C4semidirect
93. #6650C2×C4semidirect
94. #6650C2×C4semidirect
95. #6650C2×C4semidirect
134. #3940C2×D3semidirect
138. #3939C2×D3semidirect
236. C2×#168C4×D3semidirect
455. C3×C5#2911semidirect
511. C5#79177semidirect
529. C3#10613938semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1172
D3×#40722
C22×#66502
#117510992
C3×#652872
#117484692
#117484582
#117474552
#117474542
#117471912
#117471902
#106139383
#791775