Finite Group Databasebeta

← #14417282

Subgroups — #14417282

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756275C211yesmaximal, characteristic, complemented
2#11754492C211yesmaximal, characteristic
3C2×#91322C211yesmaximal, characteristic
4C5×#5002C211yesmaximal, characteristic
5C3×#65284C211yesmaximal, characteristic, complemented
6C2×#90974C211yesmaximal, characteristic, complemented
7#11748326C211yesmaximal, characteristic, complemented
8#11747281C212yesmaximal, complemented
9#11747278C212yesmaximal, complemented
10#11747235C212yesmaximal, complemented
11#11747234C212yesmaximal, complemented
12#10610552—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16#91815C2211yescharacteristic
17#91776C2212yes—
18#91776C2212yes—
19#91766—22no—
20C4×Dic30—21no—
21C4×Dic30—21no—
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25Dic5×#67—22no—
26#91435C2212yes—
27D3×C4⋊Dic5—21no—
28#91344C2212yes—
29#91338—21no—
30#91322C418yescomplemented
31C2×#6663C2212yes—
32C2×#6659C2212yes—
33C5×#810C2211yescharacteristic
34C5×#810C2211yescharacteristic
35C5×#809C2211yescharacteristic
36C5×#809C2211yescharacteristic
37C3×#3940C2212yes—
38C3×#3939C2212yes—
39#90974C2212yes—
40#90974C2212yes—
41#90954C2212yes—
42#90951C2212yes—
43#79202—51nomaximal, Hall
44#66161—31no—
45C2×#4097—31no—
46#65850—31no—
47C5×#416—31no—
48C2×#3948—31no—
49#65390—31no—
50#65284D311yescharacteristic, complemented
51#65079—32no—
52#65078—32no—
53#65047—32no—
54#65046—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×Dic30—21no—
58C2×Dic30—22no—
59C2×Dic30C2×C414yescomplemented
60C2×Dic30C2312yes—
61C2×C5×#67—21no—
62C5×#235—22no—
63C5×#235C2×C414yes—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×D3×Dic5—22no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73#6719D412yes—
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15D411yescharacteristic
76#6712—22no—
77#6712—22no—
78C4×Dic15—22no—
79C4×Dic15—22no—
80C4×Dic15C2312yes—
81C2×C5×C3⋊C8—22no—
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2311yescharacteristic
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86C3×#681C2×C414yescomplemented
87C2×C3×#168C2312yes—
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91#6663C2×C418yescomplemented
92#6659C2×C418yescomplemented
93C2×#909—51no—
94#5516—51no—
95#5504—51no—
96C3×#428—51no—
97#5122—51no—
98#5002D511yescharacteristic
99C2×#810—51no—
100#4889—52no—
101#4873—52no—
102#4853—52no—
103#4852—52no—
104C2×C5×#41—31no—
105C22×Dic10—31no—
106C22×C5×C8—31no—
107C5×#117C2×D311yescharacteristic
108#4097—38no—
109Q8×Dic5—32no—
110C2×#689—32no—
111D4×Dic5—32no—
112D4×Dic5—62no—
113C2×#687—32no—
114#4072—31no—
115#4072—61no—
116C2×C4⋊Dic5—61no—
117C2×C4⋊Dic5C2×D311yescharacteristic
118C2×#681C2×D311yescharacteristic
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#103—31no—
125C5×#103—31no—
126C5×#102—31no—
127C5×#102—31no—
128#3948—32no—
129#3948—32no—
130#3947—32no—
131C8×Dic5—32no—
132#3940C2×D312yes—
133#3939C2×D312yes—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C5×D3—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4112yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—24no—
144C2×Dic15—22no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147Dic30—24no—
148Dic30—22no—
149Dic30C22×C414yes—
150C5×#67—24no—
151C2×C5×Dic3—21no—
152C5×D12—21no—
153C5×D12C22×C412yes—
154C4×C5×D3—24no—
155C5×Dic6—21no—
156C5×Dic6C22×C412yes—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—81no—
159D3×Dic5—82no—
160C3×#168C22×C414yes—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—21no—
163C2×#235C2×D511yescharacteristic
164C22×Dic6—51no—
165C2×C3×M16—51no—
166C3×#117C2×D511yescharacteristic
167C2×C3×C4⋊C4—51no—
168C4×#67—102no—
169#926—51no—
170C22×C3⋊C8C2×D511yescharacteristic
171#909—58no—
172C2×Dic12—52no—
173C2×#204—52no—
174#893—52no—
175#892—101no—
176D3×C4⋊C4—101no—
177#887—52no—
178#887—52no—
179#887—52no—
180#877—102no—
181C4×Dic6—101no—
182C4×Dic6—101no—
183C3×#107—52no—
184C3×#106—52no—
185#815—52no—
186C8×Dic3—52no—
187#810—52no—
188#810—52no—
189#810C2×D511yescharacteristic
190#810C2×D511yescharacteristic
191#809C2×D511yescharacteristic
192#809C2×D511yescharacteristic
193C5×#41—34no—
194C5×#41—62no—
195C2×C5×Q8—31no—
196C2×C5×D4—31no—
197C2×C5×D4—61no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—21no—
201C22×Dic5—62no—
202C22×Dic5—61no—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C2×C5×C8—31no—
208C2×C5×C8—31no—
209C2×C5×C8—62no—
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C22⋊C4—21no—
213C42×C5—21no—
214C22⋊Dic5—32no—
215C22⋊Dic5—62no—
216#689—38no—
217#687—38no—
218C4⋊Dic5—21no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D312yes—
223#683—62no—
224#683—62no—
225C4×Dic5—32no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—62no—
229#681C4×D314yescomplemented
230C2×#168C22×D312yes—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—51no—
239#416—31no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—41no—
249C3×C4×C5—41no—
250C3×C4×C5—41no—
251C3×C4×C5C4×D412yes—
252C3×C4×C5C23×C411yescharacteristic
253C3×C4×C5C2×#4111yescharacteristic
254Dic15—24no—
255Dic15—22no—
256Dic15—22no—
257C3×Dic5—42no—
258C5×Dic3—22no—
259C22×C3×C4—101no—
260C22×C3×C4C22×D511yescharacteristic
261C2×#67—21no—
262C22×Dic3—101no—
263#235—22no—
264#235C4×D514yes—
265C2×D12C22×D511yescharacteristic
266C2×C4×D3—21no—
267C2×C4×D3—102no—
268C2×Dic6—54no—
269C2×Dic6—52no—
270C2×Dic6—101no—
271C2×Dic6—102no—
272C2×Dic6C22×D511yescharacteristic
273C3×M16—54no—
274C2×C3×C8—52no—
275C3×C4⋊C4—52no—
276C3×C4⋊C4—101no—
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C4⋊C4C22×D511yescharacteristic
279C3×C22⋊C4—21no—
280C3×C42—21no—
281#217—52no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285Dic3⋊C4—102no—
286Dic3⋊C4—102no—
287Dic3⋊C4—102no—
288C4×Dic3—52no—
289C4×Dic3—102no—
290C4×Dic3—102no—
291C4×Dic3—102no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8C22×D511yescharacteristic
294C2×C3⋊C8C22×D511yescharacteristic
295Dic12—58no—
296#204—58no—
297C23×C5—61no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—32no—
300C5×Q8—61no—
301C5×D4—32no—
302C5×D4—64no—
303C5×D4—61no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—61no—
307C2×C4×C5—64no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5#23912yes—
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—22no—
313C2×Dic5—32no—
314C2×Dic5—32no—
315C2×Dic5—64no—
316C2×Dic5—62no—
317C2×Dic5—81no—
318C2×Dic5—242no—
319Dic10—34no—
320Dic10—64no—
321Dic10—62no—
322C5×C8—61no—
323C5×C8—61no—
324#168C2×C4×D314yes—
325C2×#41—31no—
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—51no—
331C22×C8—31no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—151no—
340#117—302no—
341#117—301no—
342#117D3×D511yescharacteristic
343C2×C4⋊C4—51no—
344C2×C4⋊C4—301no—
345#107—52no—
346#106—52no—
347#103—31no—
348#103—31no—
349#103—152no—
350#103—152no—
351#102—31no—
352#102—31no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C5×D3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—102no—
365C2×C3×C4—401no—
366C2×C3×C4C2×C4×D512yes—
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4#71112yes—
369C2×C3×C4C23×D511yescharacteristic
370#67—24no—
371C2×Dic3—21no—
372C2×Dic3—52no—
373C2×Dic3—52no—
374C2×Dic3—102no—
375C2×Dic3—104no—
376D12—21no—
377D12C2×C4×D512yes—
378C4×D3—24no—
379C4×D3—402no—
380Dic6—21no—
381Dic6—54no—
382Dic6—102no—
383Dic6—104no—
384Dic6C2×C4×D512yes—
385C3×C8—54no—
386C3⋊C8—21no—
387C3⋊C8—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5#89312yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—62no—
398C4×C5#89312yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23911yescharacteristic
401Dic5—42no—
402Dic5—64no—
403Dic5—62no—
404Dic5—62no—
405#41—34no—
406#41—62no—
407C2×Q8—31no—
408C2×Q8—154no—
409C2×Q8—152no—
410C2×Q8—302no—
411C2×Q8—301no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—54no—
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—52no—
425C2×C8—62no—
426C4⋊C4—52no—
427C4⋊C4—101no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4C2×D3×D511yescharacteristic
434C4⋊C4C2×D3×D511yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—21no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#402712yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—202no—
454C3×C4#402712yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#71111yescharacteristic
457Dic3—22no—
458Dic3—104no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×#89311yescharacteristic
464C2×C5#577511yescharacteristic
465C2×C5#577911yescharacteristic
466C23—61no—
467C23#679011yescharacteristic
468Q8—32no—
469Q8—61no—
470Q8—154no—
471Q8—304no—
472Q8—302no—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—61no—
479C2×C4—64no—
480C2×C4—102no—
481C2×C4—152no—
482C2×C4—152no—
483C2×C4—304no—
484C2×C4—302no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4#676812yes—
488C2×C4C4×D3×D512yes—
489C2×C4#679011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—54no—
492C8—61no—
493C8—61no—
494C2×C3—22no—
495C2×C3C2×#402711yescharacteristic
496C2×C3#6610411yescharacteristic
497C2×C3#6610511yescharacteristic
498D3—42no—
499C5#7920211yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22#9140612yes—
506C22C2×#679011yescharacteristic
507C4—41no—
508C4—41no—
509C4—62no—
510C4—202no—
511C4—304no—
512C4—302no—
513C4—302no—
514C4#9140612yes—
515C4C2×#676811yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061055211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2C2×#9140611yescharacteristic
521C2#1175533111yescharacteristic
522C2#1175535311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756275C2semidirect
5. C3×#65284C2semidirect
6. C2×#90974C2semidirect
7. #11748326C2semidirect
8. #11747281C2semidirect
9. #11747278C2semidirect
10. #11747235C2semidirect
11. #11747234C2semidirect
30. #91322C4semidirect
50. #65284D3semidirect
59. C2×Dic30C2×C4semidirect
86. C3×#681C2×C4semidirect
91. #6663C2×C4semidirect
92. #6659C2×C4semidirect
229. #681C4×D3semidirect
443. C3×C5#2947semidirect
499. C5#79202semidirect
517. C3#10610552semidirect

Maximal subgroups

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

subgroupindex
#117562752
#117544922
C2×#913222
C5×#50022
C3×#652842
C2×#909742
#117483262
#117472812
#117472782
#117472352
#117472342
#106105523
#792025