Finite Group Databasebeta

← #14417274

Subgroups — #14417274

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
1C5×#5827C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic
3#11754188C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic
5#11749256C212yesmaximal, complemented
6Dic3×#689C212yesmaximal, complemented
7#11749010C212yesmaximal, complemented
8Dic3×#687C212yesmaximal, complemented
9#11748459C211yesmaximal, characteristic, complemented
10C2×#90970C211yesmaximal, characteristic, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10614302—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×Q8×Dic3C2212yes—
18C5×D4×Dic3—22no—
19C5×D4×Dic3C2212yes—
20C5×#926—21no—
21C5×#926C2211yescharacteristic
22C2×C5×C4⋊Dic3—21no—
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C3×#4097C418yescomplemented
25C2×C3×#689C2212yes—
26C2×C3×#687C2212yes—
27C2×C3×#681C2211yescharacteristic
28#91528—22no—
29#91331—21no—
30#91331—21no—
31Dic3×Dic10C2212yes—
32Dic3×Dic10C2212yes—
33#91119C2211yescharacteristic
34#91119C2211yescharacteristic
35#91116C2211yescharacteristic
36#91116C2211yescharacteristic
37#90988C2212yes—
38#90985C2212yes—
39#90970C2212yes—
40#90970C2212yes—
41#90953C2212yes—
42Dic3×#168C2212yes—
43#83965—51nomaximal, Hall
44C5×#520—31no—
45C2×#4097D311yescharacteristic
46#65850—31no—
47#65522—31no—
48#65319—32no—
49C4×#689—32no—
50#65307—32no—
51C4×#687—32no—
52#65286—31no—
53C2×#3942—31no—
54#65253—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yes—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C5×Dic3—21no—
63C22×C5×Dic3—22no—
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10C2×C414yescomplemented
68C2×C3×Dic10C2312yes—
69#6719—21no—
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72C4×Dic15—21no—
73C2×C3⋊#168—22no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×#217—22no—
77C5×#217D412yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3—22no—
80C5×C4⋊Dic3D411yescharacteristic
81C5×C4⋊Dic3D411yescharacteristic
82C5×C4⋊Dic3C2312yes—
83C4×C5×Dic3—22no—
84C4×C5×Dic3C2312yes—
85C3×#689C2×C418yescomplemented
86C3×#687C2×C418yescomplemented
87C3×#681C2×C414yescomplemented
88C2×C3×#168C2312yes—
89#6668—22no—
90#6668—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93C2×C3×#137—51no—
94#5827D511yescharacteristic
95#5812—51no—
96#5233—51no—
97C2×#835—51no—
98#5184—52no—
99Dic3×Q16—52no—
100#5164—52no—
101Dic3×SD16—52no—
102#5122—51no—
103#5121—51no—
104C2×C5×#41C2×D311yescharacteristic
105C22×Dic10C2×D311yescharacteristic
106C4×C5×Q8—32no—
107C4×C5×D4—32no—
108C4×C5×D4—62no—
109C5×#117—31no—
110C5×#117—61no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—61no—
113#4097Dic318yescomplemented
114C2×#689C2×D312yes—
115C2×#687C2×D312yes—
116#4072—31no—
117C2×#681C2×D311yescharacteristic
118C22×#168—31no—
119#4033—61no—
120#4033—61no—
121#4023—62no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124#3967—31no—
125#3967—31no—
126#3964—31no—
127#3964—31no—
128#3942—32no—
129#3942—32no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2947—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C3×C5×Q8—21no—
138C3×C5×Q8C22×C412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C22×C412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—82no—
152C2×C5×Dic3—81no—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C3×Dic10—24no—
158C3×Dic10—22no—
159C3×Dic10C22×C414yes—
160C3⋊#168—21no—
161C3⋊#168—21no—
162C3×#168C22×C414yes—
163C2×C3×#41C2×D511yescharacteristic
164C22×C3×Q8—51no—
165C3×#137—58no—
166C2×C3×Q16—52no—
167C2×C3×SD16—52no—
168C2×C3×M16—51no—
169Q8×Dic3—52no—
170Q8×Dic3—52no—
171Q8×Dic3—101no—
172Q8×Dic3—101no—
173Q8×Dic3C2×D512yes—
174D4×Dic3—22no—
175D4×Dic3C2×D512yes—
176#926—21no—
177#926—51no—
178#926—102no—
179#926C2×D511yescharacteristic
180C2×C4⋊Dic3—21no—
181C2×C4⋊Dic3C2×D511yescharacteristic
182C22×C3⋊C8—51no—
183#835—51no—
184#835—51no—
185#835—52no—
186#835—52no—
187#832—51no—
188#832—51no—
189#818—52no—
190#817—52no—
191#815—52no—
192C8×Dic3—52no—
193C5×#41—22no—
194C5×#41C2×Dic314yes—
195C2×C5×Q8C22×D311yescharacteristic
196C2×C5×D4—21no—
197C2×C5×D4C22×D311yescharacteristic
198C22×C4×C5—21no—
199C22×C4×C5—62no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—21no—
203C2×Dic10—21no—
204C2×Dic10—22no—
205C2×Dic10C2×Dic314yescomplemented
206C2×Dic10C22×D312yes—
207C5×C4⋊C4—31no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—62no—
211C5×C4⋊C4—61no—
212C5×C22⋊C4—32no—
213C5×C22⋊C4—62no—
214C42×C5—32no—
215C42×C5—62no—
216C22⋊Dic5—61no—
217#689C2×Dic318yescomplemented
218#687C2×Dic318yescomplemented
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221#683—62no—
222#683—62no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—61no—
226#681C2×Dic314yescomplemented
227C2×#168—31no—
228C2×#168—31no—
229C2×#168—62no—
230C2×#168C22×D312yes—
231C2×#137—51no—
232#520—31no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C4×D412yes—
248C22×C3×C5C22×D411yescharacteristic
249C3×C4×C5—22no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—41no—
254Dic15—41no—
255C3×Dic5—24no—
256C5×Dic3—22no—
257C5×Dic3—22no—
258C5×Dic3—42no—
259C3×#41—22no—
260C3×#41C4×D514yes—
261C2×C3×Q8—54no—
262C2×C3×Q8—52no—
263C2×C3×Q8—102no—
264C2×C3×Q8—101no—
265C2×C3×Q8C22×D511yescharacteristic
266C2×C3×D4—21no—
267C2×C3×D4C22×D511yescharacteristic
268C22×C3×C4—21no—
269C22×C3×C4—101no—
270C22×C3×C4C22×D511yescharacteristic
271C22×Dic3—21no—
272C22×Dic3—22no—
273C3×Q16—58no—
274C3×SD16—58no—
275C3×M16—54no—
276C2×C3×C8—52no—
277#217—22no—
278#217—101no—
279#217C22⋊D512yes—
280C4⋊Dic3—21no—
281C4⋊Dic3—22no—
282C4⋊Dic3—51no—
283C4⋊Dic3—51no—
284C4⋊Dic3—102no—
285C4⋊Dic3—102no—
286C4⋊Dic3C22⋊D511yescharacteristic
287C4⋊Dic3C22⋊D511yescharacteristic
288C4⋊Dic3C22×D512yes—
289C4×Dic3—22no—
290C4×Dic3—101no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3C22×D512yes—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—51no—
296C2×C3⋊C8—102no—
297C23×C5—21no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—21no—
300C5×Q8C22×Dic312yes—
301C5×D4—24no—
302C5×D4—21no—
303C5×D4C22×Dic312yes—
304C2×C4×C5—21no—
305C2×C4×C5—24no—
306C2×C4×C5—32no—
307C2×C4×C5—32no—
308C2×C4×C5—62no—
309C2×C4×C5—242no—
310C2×C4×C5—241no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5#23712yes—
313C2×C4×C5C22×Dic312yes—
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—24no—
316C2×Dic5—22no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319Dic10—24no—
320Dic10—22no—
321Dic10C22×Dic314yes—
322#168—61no—
323#168—61no—
324#168C22×Dic314yes—
325C2×#41D3×D511yescharacteristic
326C22×Q8—51no—
327#137—58no—
328C2×Q16—52no—
329C2×SD16—52no—
330C2×M16—51no—
331C22×C8—151no—
332C4×Q8—32no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—32no—
338C4×D4—62no—
339#117—31no—
340#117—61no—
341#117—151no—
342#117—302no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—61no—
345#107—152no—
346#106—152no—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5—42no—
357C2×C3×C5C2×C4×D411yescharacteristic
358C2×C3×C5#57711yescharacteristic
359C2×C3×C5#57811yescharacteristic
360C23×C3—21no—
361C23×C3C2×C22⋊D511yescharacteristic
362C3×Q8—21no—
363C3×Q8—54no—
364C3×Q8—102no—
365C3×Q8—104no—
366C3×Q8C2×C4×D512yes—
367C3×D4—24no—
368C3×D4—21no—
369C3×D4C2×C4×D512yes—
370C2×C3×C4—21no—
371C2×C3×C4—24no—
372C2×C3×C4—102no—
373C2×C3×C4—104no—
374C2×C3×C4C2×C4×D512yes—
375C2×C3×C4#70912yes—
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C23×D511yescharacteristic
378C2×Dic3—22no—
379C2×Dic3—82no—
380C2×Dic3—81no—
381C2×Dic3—101no—
382C2×Dic3—101no—
383C2×Dic3C2×C22⋊D512yes—
384C2×Dic3C2×C22⋊D512yes—
385C3×C8—54no—
386C3⋊C8—101no—
387C3⋊C8—101no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—22no—
391C22×C5—41no—
392C22×C5—41no—
393C22×C5D4×Dic312yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—22no—
396C4×C5—62no—
397C4×C5—62no—
398C4×C5—122no—
399C4×C5D4×Dic312yes—
400C4×C5C2×#23711yescharacteristic
401C4×C5C23×Dic311yescharacteristic
402Dic5—24no—
403Dic5—121no—
404Dic5—121no—
405#41—22no—
406#41D5×Dic314yes—
407C2×Q8—54no—
408C2×Q8—52no—
409C2×Q8—102no—
410C2×Q8—101no—
411C2×Q8C2×D3×D511yescharacteristic
412C2×D4—21no—
413C2×D4C2×D3×D511yescharacteristic
414C22×C4—21no—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—101no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—58no—
420SD16—58no—
421M16—54no—
422C2×C8—52no—
423C2×C8—151no—
424C2×C8—151no—
425C2×C8—302no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—32no—
429C4⋊C4—62no—
430C4⋊C4—61no—
431C4⋊C4—151no—
432C4⋊C4—151no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—32no—
436C22⋊C4—62no—
437C22⋊C4—301no—
438C42—32no—
439C42—62no—
440C42—302no—
441C42—302no—
442C42—301no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3C4×C22⋊D512yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C3×C4—22no—
452C3×C4—104no—
453C3×C4C4×C22⋊D512yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#70911yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—42no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5—42no—
463C2×C5#577811yescharacteristic
464C2×C5#577911yescharacteristic
465C2×C5C2×D4×Dic311yescharacteristic
466C23—21no—
467C23D3×C22⋊D511yescharacteristic
468Q8—21no—
469Q8—54no—
470Q8—102no—
471Q8—104no—
472Q8C2×D5×Dic312yes—
473D4—24no—
474D4—21no—
475D4C2×D5×Dic312yes—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—62no—
481C2×C4—102no—
482C2×C4—104no—
483C2×C4—242no—
484C2×C4—241no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4C2×D5×Dic312yes—
488C2×C4#677912yes—
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—54no—
492C8—301no—
493C8—301no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3C2×C4×C22⋊D511yescharacteristic
497C2×C3#6617011yescharacteristic
498C2×C3#6617211yescharacteristic
499C5#8396511yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22Dic3×C22⋊D512yes—
506C22C2×D3×C22⋊D511yescharacteristic
507C4—22no—
508C4—62no—
509C4—62no—
510C4—104no—
511C4—122no—
512C4—601no—
513C4—601no—
514C4Dic3×C22⋊D512yes—
515C4C22×D5×Dic311yescharacteristic
516C4C2×#677911yescharacteristic
517C3#1061430211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—42no—
520C2#1175534011yescharacteristic
521C2#1175534111yescharacteristic
522C2C2×Dic3×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2947
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
3. #11754188C2semidirect
5. #11749256C2semidirect
6. Dic3×#689C2semidirect
7. #11749010C2semidirect
8. Dic3×#687C2semidirect
9. #11748459C2semidirect
10. C2×#90970C2semidirect
11. #11748327C2semidirect
24. C3×#4097C4semidirect
67. C2×C3×Dic10C2×C4semidirect
85. C3×#689C2×C4semidirect
86. C3×#687C2×C4semidirect
87. C3×#681C2×C4semidirect
113. #4097Dic3semidirect
205. C2×Dic10C2×Dic3semidirect
217. #689C2×Dic3semidirect
218. #687C2×Dic3semidirect
226. #681C2×Dic3semidirect
443. C3×C5#2947semidirect
499. C5#83965semidirect
517. C3#10614302semidirect

Maximal subgroups

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

subgroupindex
C5×#58272
C2×C3×#40972
#117541882
#117513342
#117492562
Dic3×#6892
#117490102
Dic3×#6872
#117484592
C2×#909702
#117483272
#106143023
#839655