Finite Group Databasebeta

← #14417276

Subgroups — #14417276

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#11756586C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic
3#11754188C211yesmaximal, characteristic, complemented
4C5×#5233C211yesmaximal, characteristic
5#11749264C212yesmaximal, complemented
6#11749263C212yesmaximal, complemented
7#11749018C212yesmaximal, complemented
8#11749017C212yesmaximal, complemented
9#11748460C211yesmaximal, characteristic, complemented
10C2×#90971C211yesmaximal, characteristic, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10610552—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15Q8×Dic15C2212yes—
16D4×Dic15—22no—
17D4×Dic15C2212yes—
18#91815—21no—
19#91815C2211yescharacteristic
20C2×C4⋊Dic15—21no—
21C2×C4⋊Dic15C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4097C418yescomplemented
25C2×C3×#689C2212yes—
26C2×C3×#687C2212yes—
27C2×C3×#681C2211yescharacteristic
28#91528—22no—
29#91331C2212yes—
30#91331C2212yes—
31Dic3×Dic10—21no—
32Dic3×Dic10—21no—
33C5×#835C2211yescharacteristic
34C5×#835C2211yescharacteristic
35C5×#832C2211yescharacteristic
36C5×#832C2211yescharacteristic
37#90988C2212yes—
38#90985C2212yes—
39#90971C2212yes—
40#90971C2212yes—
41#90954C2212yes—
42#90951C2212yes—
43#83965—51nomaximal, Hall
44#66161—31no—
45C2×#4097D311yescharacteristic
46#65850—31no—
47C5×#416—31no—
48C2×#3948—31no—
49#65390—31no—
50#65284—31no—
51#65079—32no—
52#65078—32no—
53#65047—32no—
54#65046—32no—
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×Dic15—21no—
63C22×Dic15—22no—
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10C2×C414yescomplemented
68C2×C3×Dic10C2312yes—
69#6719—22no—
70#6719D412yes—
71C4⋊Dic15—21no—
72C4⋊Dic15—22no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15C2312yes—
76C4×Dic15—22no—
77C4×Dic15C2312yes—
78C5×#217—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C4×C5×Dic3—21no—
82C2×C5×C3⋊C8—22no—
83C2×C5×C3⋊C8C2311yescharacteristic
84C2×C5×C3⋊C8C2311yescharacteristic
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#5827—51no—
95#5812—51no—
96#5233D511yescharacteristic
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
106C22×C5×C8—31no—
107C5×#117—31no—
108#4097Dic318yescomplemented
109Q8×Dic5—32no—
110C2×#689C2×D312yes—
111D4×Dic5—32no—
112D4×Dic5—62no—
113C2×#687C2×D312yes—
114#4072—31no—
115#4072—61no—
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—61no—
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#3940—32no—
133#3939—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—22no—
149C2×Dic15—82no—
150C2×Dic15—81no—
151C2×Dic15C2×D412yes—
152C2×Dic15C2×D412yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C3×Dic10—24no—
158C3×Dic10—22no—
159C3×Dic10C22×C414yes—
160C3×#168C22×C414yes—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—21no—
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—52no—
172Q8×Dic3—101no—
173Q8×Dic3—101no—
174D4×Dic3—52no—
175D4×Dic3—102no—
176#926—51no—
177#926—101no—
178#926—102no—
179#926C2×D511yescharacteristic
180C2×C4⋊Dic3—51no—
181C2×C4⋊Dic3—101no—
182C22×C3⋊C8C2×D511yescharacteristic
183#835—52no—
184#835—52no—
185#835C2×D511yescharacteristic
186#835C2×D511yescharacteristic
187#832C2×D511yescharacteristic
188#832C2×D511yescharacteristic
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×C5C22×D311yescharacteristic
200C22×Dic5—21no—
201C22×Dic5—62no—
202C22×Dic5—61no—
203C2×Dic10—21no—
204C2×Dic10—22no—
205C2×Dic10C2×Dic314yescomplemented
206C2×Dic10C22×D312yes—
207C2×C5×C8—31no—
208C2×C5×C8—31no—
209C2×C5×C8—62no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—31no—
212C5×C22⋊C4—61no—
213C42×C5—61no—
214C22⋊Dic5—32no—
215C22⋊Dic5—62no—
216#689C2×Dic318yescomplemented
217#687C2×Dic318yescomplemented
218C4⋊Dic5—31no—
219C4⋊Dic5—31no—
220C4⋊Dic5—32no—
221C4⋊Dic5—62no—
222C4⋊Dic5—61no—
223#683—62no—
224#683—62no—
225C4×Dic5—32no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—62no—
229#681C2×Dic314yescomplemented
230C2×#168C22×D312yes—
231C2×#137—51no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—31no—
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—22no—
254Dic15—22no—
255Dic15—42no—
256C3×Dic5—24no—
257C5×Dic3—41no—
258C5×Dic3—41no—
259C3×#41—22no—
260C3×#41C4×D514yes—
261C2×C3×Q8—54no—
262C2×C3×Q8—52no—
263C2×C3×Q8—101no—
264C2×C3×Q8—102no—
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—102no—
272C22×Dic3—101no—
273C3×Q16—58no—
274C3×SD16—58no—
275C3×M16—54no—
276C2×C3×C8—52no—
277#217—21no—
278#217—52no—
279#217—102no—
280C4⋊Dic3—51no—
281C4⋊Dic3—51no—
282C4⋊Dic3—52no—
283C4⋊Dic3—102no—
284C4⋊Dic3—102no—
285C4⋊Dic3—102no—
286C4⋊Dic3—101no—
287C4⋊Dic3C22×D511yescharacteristic
288C4⋊Dic3C22×D511yescharacteristic
289C4×Dic3—21no—
290C4×Dic3—52no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C2×C3⋊C8—22no—
295C2×C3⋊C8C22×D511yescharacteristic
296C2×C3⋊C8C22×D511yescharacteristic
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—61no—
307C2×C4×C5—61no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5#23712yes—
310C2×C4×C5C22×Dic312yes—
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—24no—
313C2×Dic5—22no—
314C2×Dic5—32no—
315C2×Dic5—32no—
316C2×Dic5—62no—
317C2×Dic5—242no—
318C2×Dic5—241no—
319Dic10—24no—
320Dic10—22no—
321Dic10C22×Dic314yes—
322C5×C8—61no—
323C5×C8—61no—
324#168C22×Dic314yes—
325C2×#41D3×D511yescharacteristic
326C22×Q8—51no—
327#137—58no—
328C2×Q16—52no—
329C2×SD16—52no—
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—31no—
340#117—151no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
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×C5—42no—
357C2×C3×C5C2×C4×D411yescharacteristic
358C2×C3×C5#57711yescharacteristic
359C2×C3×C5#57811yescharacteristic
360C23×C3—21no—
361C23×C3D4×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×C4D4×D511yescharacteristic
376C2×C3×C4#71112yes—
377C2×C3×C4C23×D511yescharacteristic
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—52no—
381C2×Dic3—52no—
382C2×Dic3—102no—
383C2×Dic3—402no—
384C2×Dic3—401no—
385C3×C8—54no—
386C3⋊C8—21no—
387C3⋊C8—21no—
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—121no—
397C4×C5—121no—
398C4×C5D4×Dic312yes—
399C4×C5C2×#23711yescharacteristic
400C4×C5C23×Dic311yescharacteristic
401Dic5—24no—
402Dic5—62no—
403Dic5—62no—
404Dic5—122no—
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—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—58no—
420SD16—58no—
421M16—54no—
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—52no—
425C2×C8—62no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—152no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—301no—
435C22⋊C4—61no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—61no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3#402712yes—
450C22×C3C2×D4×D511yescharacteristic
451C3×C4—22no—
452C3×C4—104no—
453C3×C4#402712yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#71111yescharacteristic
456Dic3—41no—
457Dic3—41no—
458Dic3—102no—
459Dic3—102no—
460Dic3—202no—
461C2×C5—22no—
462C2×C5—42no—
463C2×C5#577811yescharacteristic
464C2×C5#577911yescharacteristic
465C2×C5C2×D4×Dic311yescharacteristic
466C23—21no—
467C23#679011yescharacteristic
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—61no—
479C2×C4—61no—
480C2×C4—102no—
481C2×C4—104no—
482C2×C4—152no—
483C2×C4—152no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4C2×D5×Dic312yes—
488C2×C4#678012yes—
489C2×C4#679011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—54no—
492C8—61no—
493C8—61no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3C2×#402711yescharacteristic
497C2×C3#6610411yescharacteristic
498C2×C3#6610511yescharacteristic
499C5#8396511yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22#9155912yes—
506C22C2×#679011yescharacteristic
507C4—22no—
508C4—104no—
509C4—121no—
510C4—121no—
511C4—302no—
512C4—302no—
513C4—602no—
514C4#9155912yes—
515C4C22×D5×Dic311yescharacteristic
516C4C2×#678011yescharacteristic
517C3#1061055211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—42no—
520C2#1175535311yescharacteristic
521C2#1175535411yescharacteristic
522C2C2×#9155911yescharacteristic
subgroupG/H
centerC22C2×#6790
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. #11749264C2semidirect
6. #11749263C2semidirect
7. #11749018C2semidirect
8. #11749017C2semidirect
9. #11748460C2semidirect
10. C2×#90971C2semidirect
11. #11748326C2semidirect
24. C3×#4097C4semidirect
67. C2×C3×Dic10C2×C4semidirect
85. C3×#689C2×C4semidirect
86. C3×#687C2×C4semidirect
87. C3×#681C2×C4semidirect
108. #4097Dic3semidirect
205. C2×Dic10C2×Dic3semidirect
216. #689C2×Dic3semidirect
217. #687C2×Dic3semidirect
229. #681C2×Dic3semidirect
443. C3×C5#2947semidirect
499. C5#83965semidirect
517. C3#10610552semidirect

Maximal subgroups

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

subgroupindex
#117565862
C2×C3×#40972
#117541882
C5×#52332
#117492642
#117492632
#117490182
#117490172
#117484602
C2×#909712
#117483262
#106105523
#839655