Finite Group Databasebeta

← #14417250

Subgroups — #14417250

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×#5504C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3C2×#91309C211yesmaximal, characteristic
4#11751065C211yesmaximal, characteristic, complemented
5C2×C3×#3942C211yesmaximal, characteristic, complemented
6#11748388C211yesmaximal, characteristic
7#11748323C211yesmaximal, characteristic, complemented
8#11747267C212yesmaximal, complemented
9#11747266C212yesmaximal, complemented
10#11747265C212yesmaximal, complemented
11#11747264C212yesmaximal, complemented
12#10614302—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C4×C5×#67—22no—
19C5×#926C2211yescharacteristic
20C5×#893C2212yes—
21C5×#892—21no—
22C5×D3×C4⋊C4—21no—
23C5×#887C2212yes—
24C22×C3×#168C2211yescharacteristic
25#91528—22no—
26#91331—21no—
27#91331—21no—
28Dic3×Dic10C2212yes—
29Dic3×Dic10C2212yes—
30C2×#6661C2212yes—
31#91309C418yescomplemented
32C2×#6656C2212yes—
33#91092C2212yes—
34#91091C2212yes—
35C3×#3942C2212yes—
36C3×#3942C2212yes—
37#90973C2211yescharacteristic
38#90973C2211yescharacteristic
39#90967C2211yescharacteristic
40#90967C2211yescharacteristic
41#90953C2212yes—
42Dic3×#168C2212yes—
43#78774—51nomaximal, Hall
44C5×#520—31no—
45C2×#4097—31no—
46#65850—31no—
47#65522—31no—
48#65319—32no—
49C4×#689—32no—
50#65307—32no—
51C4×#687—32no—
52#65286—31no—
53C2×#3942D311yescharacteristic, complemented
54#65253—31no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×C5×#67—21no—
58C5×#235—22no—
59C5×#235C2×C414yes—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C4×C5×D3—22no—
63C2×C5×Dic6C2311yescharacteristic
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10C2×C414yescomplemented
68C2×C3×Dic10C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71#6719—21no—
72C4⋊Dic15C2311yescharacteristic
73C4⋊Dic15C2311yescharacteristic
74C4×Dic15—21no—
75#6710C2×C414yescomplemented
76C2×C3⋊#168C2312yes—
77C5×#217D412yes—
78C5×(C2×D3)⋊C4—22no—
79C5×C4⋊Dic3D411yescharacteristic
80C5×C4⋊Dic3D411yescharacteristic
81C5×Dic3⋊C4—22no—
82C4×C5×Dic3—22no—
83C4×C5×Dic3C2312yes—
84C2×C3×#168—22no—
85C2×C3×#168C2311yescharacteristic
86C2×C3×#168C2311yescharacteristic
87#6668—22no—
88#6668—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6661C2×C418yescomplemented
92#6656C2×C418yescomplemented
93#5812—51no—
94C2×#942—51no—
95#5504D511yescharacteristic
96C2×C3×#103—51no—
97#5113—51no—
98#5101—51no—
99#4964—51no—
100#4817—52no—
101#4790—52no—
102#4789—52no—
103#4788—52no—
104C2×C5×#41—31no—
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—61no—
112C2×C5×C4⋊C4C2×D311yescharacteristic
113#4097—38no—
114C2×#689—32no—
115C2×#687—32no—
116#4072—31no—
117C2×#681—31no—
118C22×#168C2×D311yescharacteristic
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#3942C2×D312yes—
129#3942C2×D312yes—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C5×D3—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—81no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4112yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—21no—
144C2×Dic15—21no—
145C5×#67—24no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3C2×D412yes—
148C2×C5×Dic3C2×D412yes—
149C5×D12—21no—
150C5×D12C22×C412yes—
151C4×C5×D3—24no—
152C4×C5×D3—82no—
153C5×Dic6—21no—
154C5×Dic6C22×C412yes—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C3×Dic10—24no—
158C3×Dic10—22no—
159C3×Dic10C22×C414yes—
160C3⋊#168C22×C414yes—
161C3×#168—21no—
162C3×#168—21no—
163C22×C3×Q8—51no—
164C2×#235C2×D511yescharacteristic
165C22×C3×C8—51no—
166C2×C3×C4⋊C4C2×D511yescharacteristic
167Q8×Dic3—52no—
168Q8×Dic3—52no—
169Q8×Dic3—101no—
170Q8×Dic3—101no—
171C2×#216—52no—
172#942—58no—
173C2×#215—52no—
174C4×#67—22no—
175#926—51no—
176#926—102no—
177#926C2×D511yescharacteristic
178C2×#208—51no—
179#893C2×D512yes—
180#892—21no—
181D3×C4⋊C4—21no—
182#887C2×D512yes—
183C3×#103—52no—
184C3×#103—52no—
185#821—51no—
186#821—51no—
187#816—51no—
188#816—51no—
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C5×#41—34no—
194C5×#41—62no—
195C2×C5×Q8—31no—
196C2×C5×D4—31no—
197C2×C5×D4—61no—
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×Dic10C4×D314yescomplemented
206C2×Dic10C22×D312yes—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—62no—
211C5×C4⋊C4C22×D312yes—
212C5×C22⋊C4—32no—
213C5×C22⋊C4—62no—
214C42×C5—32no—
215C42×C5—62no—
216C22⋊Dic5—61no—
217#689—38no—
218#687—38no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221#683—62no—
222#683—62no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—61no—
226#681—34no—
227C2×#168—22no—
228C2×#168—32no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231C2×#137—151no—
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—51no—
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—42no—
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—22no—
259C2×C3×Q8—54no—
260C2×C3×Q8—52no—
261C2×C3×Q8—102no—
262C2×C3×Q8—101no—
263C22×C3×C4—21no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—21no—
267#235—22no—
268#235C4×D514yes—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—22no—
272C2×Dic6C22×D511yescharacteristic
273C2×C3×C8—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C22×D512yes—
278#217—101no—
279#217C22⋊D512yes—
280#216—58no—
281#215—58no—
282(C2×D3)⋊C4—22no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285C4⋊Dic3—102no—
286C4⋊Dic3—102no—
287C4⋊Dic3C22⋊D511yescharacteristic
288C4⋊Dic3C22⋊D511yescharacteristic
289Dic3⋊C4—22no—
290C4×Dic3—22no—
291C4×Dic3—101no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3C22×D512yes—
295#208—54no—
296C2×C3⋊C8—52no—
297C23×C5—61no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—32no—
300C5×Q8—61no—
301C5×D4—32no—
302C5×D4—64no—
303C5×D4—61no—
304C2×C4×C5—22no—
305C2×C4×C5—32no—
306C2×C4×C5—32no—
307C2×C4×C5—61no—
308C2×C4×C5—64no—
309C2×C4×C5—81no—
310C2×C4×C5—242no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5#23712yes—
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—24no—
316C2×Dic5—22no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319Dic10—24no—
320Dic10—22no—
321Dic10C2×C4×D314yes—
322#168—21no—
323#168—21no—
324#168—34no—
325C2×#41—31no—
326C22×Q8—51no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8—51no—
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—61no—
344C2×C4⋊C4D3×D511yescharacteristic
345#107—152no—
346#106—152no—
347#103—52no—
348#103—52no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
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×C3C2×C22⋊D511yescharacteristic
361C22×D3—21no—
362C3×Q8—54no—
363C3×Q8—102no—
364C3×Q8—104no—
365C2×C3×C4—22no—
366C2×C3×C4—81no—
367C2×C3×C4—102no—
368C2×C3×C4—104no—
369C2×C3×C4C2×C4×D512yes—
370C2×C3×C4#70912yes—
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—24no—
374C2×Dic3—21no—
375C2×Dic3—101no—
376C2×Dic3—101no—
377C2×Dic3C2×C22⋊D512yes—
378C2×Dic3C2×C22⋊D512yes—
379D12—21no—
380D12C2×C4×D512yes—
381C4×D3—24no—
382C4×D3—82no—
383Dic6—21no—
384Dic6C2×C4×D512yes—
385C3×C8—101no—
386C3×C8—101no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5#67⋊C412yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—42no—
396C4×C5—62no—
397C4×C5—62no—
398C4×C5—62no—
399C4×C5#67⋊C412yes—
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×#23711yescharacteristic
402Dic5—24no—
403Dic5—121no—
404Dic5—121no—
405#41—34no—
406#41—62no—
407C2×Q8—31no—
408C2×Q8—54no—
409C2×Q8—52no—
410C2×Q8—102no—
411C2×Q8—101no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—21no—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—101no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—51no—
423C2×C8—51no—
424C2×C8—102no—
425C2×C8—152no—
426C4⋊C4—21no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—62no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4C2×D3×D512yes—
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×C3C4×C22⋊D512yes—
447C22×C3C22×C22⋊D511yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—42no—
452C3×C4—104no—
453C3×C4C4×C22⋊D512yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#70911yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—22no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#576211yescharacteristic
465C2×C5#576611yescharacteristic
466C23—61no—
467C23D3×C22⋊D511yescharacteristic
468Q8—32no—
469Q8—54no—
470Q8—61no—
471Q8—104no—
472Q8—102no—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—22no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—61no—
480C2×C4—64no—
481C2×C4—81no—
482C2×C4—104no—
483C2×C4—102no—
484C2×C4—242no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4#676512yes—
488C2×C4C4×D3×D512yes—
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—101no—
492C8—101no—
493C8—154no—
494C2×C3—22no—
495C2×C3C2×C4×C22⋊D511yescharacteristic
496C2×C3#6617011yescharacteristic
497C2×C3#6617211yescharacteristic
498D3—42no—
499C5#7877411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22#9144112yes—
506C22C2×D3×C22⋊D511yescharacteristic
507C4—42no—
508C4—62no—
509C4—62no—
510C4—62no—
511C4—104no—
512C4—601no—
513C4—601no—
514C4#9144112yes—
515C4C2×#676511yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061430211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2C2×#9144111yescharacteristic
521C2#1175471111yescharacteristic
522C2#1175510511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
4. #11751065C2semidirect
5. C2×C3×#3942C2semidirect
7. #11748323C2semidirect
8. #11747267C2semidirect
9. #11747266C2semidirect
10. #11747265C2semidirect
11. #11747264C2semidirect
31. #91309C4semidirect
53. C2×#3942D3semidirect
67. C2×C3×Dic10C2×C4semidirect
75. #6710C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
205. C2×Dic10C4×D3semidirect
443. C3×C5#2947semidirect
499. C5#78774semidirect
517. C3#10614302semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
#117541882
C2×#913092
#117510652
C2×C3×#39422
#117483882
#117483232
#117472672
#117472662
#117472652
#117472642
#106143023
#787745