Finite Group Databasebeta

← #14417283

Subgroups — #14417283

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
1C3×#65850C211yesmaximal, characteristic, complemented
2#11754513C211yesmaximal, characteristic
3C2×#91309C211yesmaximal, characteristic
4#11751096C211yesmaximal, characteristic, complemented
5C5×#5002C211yesmaximal, characteristic
6C2×#90971C211yesmaximal, characteristic, complemented
7#11748318C211yesmaximal, characteristic, complemented
8#11747263C212yesmaximal, complemented
9#11747262C212yesmaximal, complemented
10#11747218C212yesmaximal, complemented
11#11747217C212yesmaximal, complemented
12#10610552—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20C3×#4033C2212yes—
21C3×#4033C2212yes—
22C3×#4023—22no—
23C3×C4×Dic10—21no—
24C3×C4×Dic10—21no—
25#67⋊Dic5—22no—
26D3×C4⋊Dic5—21no—
27Dic5×D12C2212yes—
28#91338—21no—
29Dic5×Dic6C2212yes—
30C2×#6661C2212yes—
31#91309C418yescomplemented
32C2×#6656C2212yes—
33#91092C2212yes—
34#91091C2212yes—
35C5×#810C2211yescharacteristic
36C5×#810C2211yescharacteristic
37C5×#809C2211yescharacteristic
38C5×#809C2211yescharacteristic
39#90971C2212yes—
40#90971C2212yes—
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82547—51nomaximal, Hall
44#66161—31no—
45C2×#4097—31no—
46#65850D311yescharacteristic, complemented
47C5×#416—31no—
48C2×#3948—31no—
49#65390—31no—
50#65284—31no—
51#65079—32no—
52#65078—32no—
53#65047—32no—
54#65046—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×C5×#67—21no—
58C5×#235—22no—
59C5×#235C2×C414yes—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C5×Dic6C2311yescharacteristic
63C22×C3×Dic5—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—22no—
66C2×C3×Dic10C2×C414yescomplemented
67C2×C3×Dic10C2312yes—
68C2×D3×Dic5—22no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75#6710C2×C414yescomplemented
76C2×C3⋊#168C2312yes—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C22⋊Dic5D412yes—
81C3×C4⋊Dic5D411yescharacteristic
82C3×C4⋊Dic5D411yescharacteristic
83C3×#683—22no—
84C3×#683—22no—
85C3×C4×Dic5—22no—
86C3×C4×Dic5—22no—
87C3×C4×Dic5C2312yes—
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91#6661C2×C418yescomplemented
92#6656C2×C418yescomplemented
93C3×#519—51no—
94C2×#942—51no—
95#5523—51no—
96C2×#835—51no—
97#5030—52no—
98C4×#216—52no—
99#5026—52no—
100C4×#215—52no—
101#5002D511yescharacteristic
102#4997—51no—
103#4995—51no—
104C2×C5×#41—31no—
105C22×Dic10C2×D311yescharacteristic
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—61no—
115#4072C2×D311yescharacteristic
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—61no—
118C2×#681—31no—
119#4033C2×D312yes—
120#4033C2×D312yes—
121#4023—22no—
122C4×Dic10—21no—
123C4×Dic10—21no—
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×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—22no—
144C2×Dic15—81no—
145C5×#67—24no—
146C2×C5×Dic3—21no—
147C5×D12—21no—
148C5×D12C22×C412yes—
149C4×C5×D3—24no—
150C5×Dic6—21no—
151C5×Dic6C22×C412yes—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C2×D412yes—
155C2×C3×Dic5C2×D412yes—
156C3×Dic10—24no—
157C3×Dic10—22no—
158C3×Dic10C22×C414yes—
159D3×Dic5—82no—
160C3⋊#168C22×C414yes—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—21no—
163C22×C3×Q8—51no—
164C2×#235C2×D511yescharacteristic
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C3×#117—51no—
170C3×#117—102no—
171C3×#117C2×D511yescharacteristic
172C2×#216—52no—
173#942—58no—
174C2×#215—52no—
175C2×C4⋊Dic3—51no—
176C2×#208—51no—
177C22×C3⋊C8C2×D511yescharacteristic
178#892—101no—
179D3×C4⋊C4—101no—
180#67⋊C4—102no—
181C4×D12—52no—
182C4×Dic6—52no—
183#835—52no—
184#835—52no—
185#810C2×D511yescharacteristic
186#810C2×D511yescharacteristic
187#809C2×D511yescharacteristic
188#809C2×D511yescharacteristic
189#808—52no—
190#807—52no—
191#803—52no—
192C4×C3⋊C8—52no—
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—61no—
202C22×Dic5—62no—
203C2×Dic10—22no—
204C2×Dic10—21no—
205C2×Dic10C4×D314yescomplemented
206C2×Dic10C22×D312yes—
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—62no—
215C22⋊Dic5#6712yes—
216#689—38no—
217#687—38no—
218C4⋊Dic5—32no—
219C4⋊Dic5—61no—
220C4⋊Dic5—62no—
221C4⋊Dic5#6711yescharacteristic
222C4⋊Dic5#6711yescharacteristic
223#683—22no—
224#683—22no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C4×Dic5—62no—
228C4×Dic5C22×D312yes—
229#681—34no—
230C2×#168—32no—
231C2×#137—151no—
232#520—151no—
233#519—51no—
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×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—42no—
255C3×Dic5—24no—
256C3×Dic5—22no—
257C3×Dic5—22no—
258C5×Dic3—22no—
259C2×C3×Q8—54no—
260C2×C3×Q8—52no—
261C2×C3×Q8—101no—
262C2×C3×Q8—102no—
263C22×C3×C4—101no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—21no—
266C22×Dic3—101no—
267#235—22no—
268#235C4×D514yes—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—102no—
272C2×Dic6C22×D511yescharacteristic
273C3×C4⋊C4—51no—
274C3×C4⋊C4—51no—
275C3×C4⋊C4—102no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C4⋊C4C22×D511yescharacteristic
279C3×C22⋊C4—21no—
280C3×C22⋊C4—52no—
281C3×C42—21no—
282C3×C42—52no—
283C3×C42—102no—
284C3×C42—102no—
285#216—58no—
286#215—58no—
287(C2×D3)⋊C4—102no—
288C4⋊Dic3—52no—
289C4⋊Dic3—101no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292#208—54no—
293C2×C3⋊C8—22no—
294C2×C3⋊C8—52no—
295C2×C3⋊C8C22×D511yescharacteristic
296C2×C3⋊C8C22×D511yescharacteristic
297C23×C5—61no—
298C23×C5C2×#6711yescharacteristic
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×C5#23512yes—
310C2×C4×C5C2×#6711yescharacteristic
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—24no—
313C2×Dic5—22no—
314C2×Dic5—62no—
315C2×Dic5—242no—
316C2×Dic5—241no—
317C2×Dic5C2×#6712yes—
318C2×Dic5C2×#6712yes—
319Dic10—24no—
320Dic10—22no—
321Dic10C2×C4×D314yes—
322C5×C8—61no—
323C5×C8—61no—
324#168—34no—
325C2×#41—31no—
326C22×Q8—51no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8—31no—
332C4×Q8—52no—
333C4×Q8—52no—
334C4×Q8—101no—
335C4×Q8—101no—
336C4×Q8—152no—
337C4×D4—152no—
338C4×D4—302no—
339#117—51no—
340#117—102no—
341#117—301no—
342#117D3×D511yescharacteristic
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×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C5×D3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—21no—
362C3×Q8—54no—
363C3×Q8—102no—
364C3×Q8—104no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—52no—
368C2×C3×C4—52no—
369C2×C3×C4—102no—
370C2×C3×C4—104no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71112yes—
374C2×C3×C4C23×D511yescharacteristic
375#67—24no—
376C2×Dic3—21no—
377C2×Dic3—102no—
378C2×Dic3—401no—
379D12—21no—
380D12C2×C4×D512yes—
381C4×D3—24no—
382C4×D3—402no—
383Dic6—21no—
384Dic6C2×C4×D512yes—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5C4×#6712yes—
394C22×C5C22×#6711yescharacteristic
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—62no—
398C4×C5C4×#6712yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23511yescharacteristic
401Dic5—24no—
402Dic5—22no—
403Dic5—22no—
404Dic5—122no—
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—61no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—62no—
425C2×C8—152no—
426C4⋊C4—51no—
427C4⋊C4—51no—
428C4⋊C4—102no—
429C4⋊C4—102no—
430C4⋊C4—152no—
431C4⋊C4—302no—
432C4⋊C4—301no—
433C4⋊C4C2×D3×D511yescharacteristic
434C4⋊C4C2×D3×D511yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—52no—
437C22⋊C4—302no—
438C42—21no—
439C42—52no—
440C42—102no—
441C42—102no—
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—104no—
454C3×C4—102no—
455C3×C4—102no—
456C3×C4#402712yes—
457C3×C4C22×C4×D511yescharacteristic
458C3×C4C2×#71111yescharacteristic
459Dic3—22no—
460Dic3—202no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×C4×#6711yescharacteristic
464C2×C5#583711yescharacteristic
465C2×C5#583811yescharacteristic
466C23—61no—
467C23D5×#6711yescharacteristic
468Q8—32no—
469Q8—54no—
470Q8—61no—
471Q8—104no—
472Q8—102no—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—52no—
479C2×C4—52no—
480C2×C4—61no—
481C2×C4—64no—
482C2×C4—104no—
483C2×C4—102no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4#677212yes—
488C2×C4C4×D3×D512yes—
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—61no—
492C8—61no—
493C8—154no—
494C2×C3—22no—
495C2×C3C2×#402711yescharacteristic
496C2×C3#6610411yescharacteristic
497C2×C3#6610511yescharacteristic
498D3—42no—
499C5#8254711yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22#9144012yes—
506C22C2×D5×#6711yescharacteristic
507C4—41no—
508C4—41no—
509C4—62no—
510C4—104no—
511C4—102no—
512C4—102no—
513C4—602no—
514C4#9144012yes—
515C4C2×#677211yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061055211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2C2×#9144011yescharacteristic
521C2#1175531911yescharacteristic
522C2#1175533811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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. C3×#65850C2semidirect
4. #11751096C2semidirect
6. C2×#90971C2semidirect
7. #11748318C2semidirect
8. #11747263C2semidirect
9. #11747262C2semidirect
10. #11747218C2semidirect
11. #11747217C2semidirect
31. #91309C4semidirect
46. #65850D3semidirect
66. C2×C3×Dic10C2×C4semidirect
75. #6710C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
205. C2×Dic10C4×D3semidirect
443. C3×C5#2947semidirect
499. C5#82547semidirect
517. C3#10610552semidirect

Maximal subgroups

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

subgroupindex
C3×#658502
#117545132
C2×#913092
#117510962
C5×#50022
C2×#909712
#117483182
#117472632
#117472622
#117472182
#117472172
#106105523
#825475