Finite Group Databasebeta

← #14417254

Subgroups — #14417254

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
1C2×#91831C211yesmaximal, characteristic
2C3×#66146C211yesmaximal, characteristic, complemented
3#11754506C211yesmaximal, characteristic
4C2×C5×#835C211yesmaximal, characteristic, complemented
5#11749250C212yesmaximal, complemented
6#11749244C212yesmaximal, complemented
7#11749225C212yesmaximal, complemented
8#11749221C212yesmaximal, complemented
9#11748472C211yesmaximal, characteristic, complemented
10#11748411C211yesmaximal, characteristic
11#11748318C211yesmaximal, characteristic, complemented
12#10610505—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×#6718C2212yes—
16#91831C418yescomplemented
17C2×#6717C2212yes—
18C2×#6710C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C22×C5×C3⋊C8C2211yescharacteristic
21C3×Q8×Dic5—21no—
22C3×Q8×Dic5—21no—
23C3×Q8×Dic5C2212yes—
24C3×Q8×Dic5C2212yes—
25C3×#4072—22no—
26C3×#4072C2211yescharacteristic
27C3×#4072C2211yescharacteristic
28#91556—22no—
29#91437—21no—
30#91418C2212yes—
31#91347—21no—
32#91333C2212yes—
33C5×#835C2212yes—
34C5×#835C2212yes—
35#90989C2212yes—
36#90986C2212yes—
37#90974C2211yescharacteristic
38#90974C2211yescharacteristic
39#90968C2211yescharacteristic
40#90968C2211yescharacteristic
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82547—51nomaximal, Hall
44#66146D311yescharacteristic, complemented
45C2×#4088—31no—
46#65838—31no—
47C2×C5×#103—31no—
48#65402—31no—
49#65390—31no—
50#65253—31no—
51#65106—32no—
52#65079—32no—
53#65078—32no—
54#65077—32no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×Q8—22no—
57C2×C3×C5×Q8C2×C414yescomplemented
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×#1220—21no—
62#6817—22no—
63#6817C2×C414yes—
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×Dic30C2311yescharacteristic
67C22×C5×Dic3—21no—
68C2×#1200—22no—
69#6718C2×C418yescomplemented
70#6717C2×C418yescomplemented
71#6710C2×C414yescomplemented
72C2×C3⋊#168C2312yes—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3C2312yes—
75C2×C5×C3⋊C8—22no—
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×C22⋊Dic5—21no—
79C3×C22⋊Dic5D412yes—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4×Dic5—21no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5—22no—
89C3×C4×Dic5C2312yes—
90#6669—22no—
91#6667—22no—
92Dic3×Dic5—22no—
93C3×#519—51no—
94C2×#942—51no—
95#5523—51no—
96C2×#835D511yescharacteristic, complemented
97#5030—52no—
98C4×#216—52no—
99#5026—52no—
100C4×#215—52no—
101#5002—51no—
102#4997—51no—
103#4995—51no—
104C22×C5×Q8C2×D311yescharacteristic
105C2×#709—31no—
106C22×C5×C8—31no—
107C2×C5×C4⋊C4—31no—
108Q8×Dic5—21no—
109Q8×Dic5—21no—
110Q8×Dic5C2×D312yes—
111Q8×Dic5C2×D312yes—
112C2×#689—32no—
113#4088—38no—
114C2×#688—32no—
115C4×C22⋊D5—62no—
116#4072—22no—
117#4072C2×D311yescharacteristic
118#4072C2×D311yescharacteristic
119C2×#681—31no—
120#4039—32no—
121#4038—61no—
122D5×C4⋊C4—61no—
123#4033—32no—
124C5×#103—32no—
125C5×#103—32no—
126#3953—31no—
127#3953—31no—
128#3948—31no—
129#3948—31no—
130#3947—32no—
131C8×Dic5—32no—
132#3940—32no—
133#3939—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C3×C5×Q8—24no—
138C3×C5×Q8—22no—
139C3×C5×Q8C22×C414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148D60—21no—
149D60C22×C412yes—
150C4×D15—24no—
151Dic30—21no—
152Dic30C22×C412yes—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—81no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×D412yes—
159#1200—82no—
160C3⋊#168C22×C414yes—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—21no—
163C22×C3×Q8C2×D511yescharacteristic
164C2×#235—51no—
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C3×#117—51no—
170C3×#117—51no—
171C3×#117—102no—
172C2×#216—52no—
173#942—58no—
174C2×#215—52no—
175C2×C4⋊Dic3C2×D511yescharacteristic
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#835C2×D512yes—
184#835C2×D512yes—
185#810—51no—
186#810—51no—
187#809—51no—
188#809—51no—
189#808—52no—
190#807—52no—
191#803—52no—
192C4×C3⋊C8—52no—
193C2×C5×Q8—22no—
194C2×C5×Q8—21no—
195C2×C5×Q8C4×D314yescomplemented
196C2×C5×Q8C22×D312yes—
197C22×C4×C5—21no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201#709—34no—
202#709—62no—
203C2×D20—31no—
204C2×C4×D5—61no—
205C2×C4×D5—62no—
206C2×Dic10—31no—
207C2×C5×C8—31no—
208C2×C5×C8—31no—
209C2×C5×C8—62no—
210C5×C4⋊C4—32no—
211C5×C4⋊C4—61no—
212C22⋊Dic5—21no—
213C22⋊Dic5#6712yes—
214#689—38no—
215#688—38no—
216#685—62no—
217C4⋊Dic5—22no—
218C4⋊Dic5—22no—
219C4⋊Dic5#6711yescharacteristic
220C4⋊Dic5#6711yescharacteristic
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D311yescharacteristic
223#683—62no—
224C4×Dic5—21no—
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—151no—
240C2×#103—31no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5—24no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—22no—
254C3×Dic5—22no—
255C3×Dic5—22no—
256C3×Dic5—41no—
257C3×Dic5—41no—
258C5×Dic3—42no—
259C2×C3×Q8—21no—
260C2×C3×Q8—22no—
261C2×C3×Q8C4×D514yescomplemented
262C2×C3×Q8C22×D512yes—
263C22×C3×C4—21no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—101no—
266C22×Dic3—21no—
267#235—54no—
268#235—102no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×C4×D3—102no—
272C2×Dic6—51no—
273C3×C4⋊C4—51no—
274C3×C4⋊C4—51no—
275C3×C4⋊C4—51no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—102no—
278C3×C4⋊C4—102no—
279C3×C22⋊C4—52no—
280C3×C22⋊C4—101no—
281C3×C42—52no—
282C3×C42—102no—
283C3×C42—102no—
284C3×C42—101no—
285#216—58no—
286#215—58no—
287(C2×D3)⋊C4—102no—
288C4⋊Dic3—21no—
289C4⋊Dic3C22×D512yes—
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×C5C2×#6711yescharacteristic
298C22×D5—61no—
299C5×Q8—24no—
300C5×Q8—22no—
301C5×Q8C2×C4×D314yes—
302C2×C4×C5—24no—
303C2×C4×C5—22no—
304C2×C4×C5—62no—
305C2×C4×C5—241no—
306C2×C4×C5C2×C4×D312yes—
307C2×C4×C5#23512yes—
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—64no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—61no—
314C2×Dic5C2×#6712yes—
315C2×Dic5C2×#6712yes—
316D20—32no—
317D20—61no—
318C4×D5—64no—
319C4×D5—242no—
320Dic10—32no—
321Dic10—61no—
322C5×C8—61no—
323C5×C8—61no—
324#168—34no—
325C2×#41—151no—
326C22×Q8D3×D511yescharacteristic
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—51no—
341#117—102no—
342#117—301no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—32no—
348#103—32no—
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
359D15—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—101no—
362C3×Q8—22no—
363C3×Q8—24no—
364C3×Q8C2×C4×D514yes—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—52no—
368C2×C3×C4—52no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71112yes—
374C2×C3×C4C23×D511yescharacteristic
375#67—104no—
376C2×Dic3—22no—
377C2×Dic3—81no—
378C2×Dic3—101no—
379D12—52no—
380D12—101no—
381C4×D3—104no—
382C4×D3—402no—
383Dic6—52no—
384Dic6—101no—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5C4×#6712yes—
391C22×C5C22×#6711yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—24no—
396C4×C5—122no—
397C4×C5C4×#6712yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23511yescharacteristic
400Dic5—22no—
401Dic5—22no—
402Dic5—41no—
403Dic5—41no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—151no—
410C2×Q8#120014yescomplemented
411C2×Q8C2×D3×D512yes—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—61no—
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—32no—
427C4⋊C4—51no—
428C4⋊C4—51no—
429C4⋊C4—51no—
430C4⋊C4—51no—
431C4⋊C4—61no—
432C4⋊C4—102no—
433C4⋊C4—102no—
434C4⋊C4—302no—
435C22⋊C4—52no—
436C22⋊C4—101no—
437C22⋊C4—302no—
438C42—52no—
439C42—102no—
440C42—102no—
441C42—101no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#402712yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—24no—
452C3×C4—102no—
453C3×C4—102no—
454C3×C4—201no—
455C3×C4—201no—
456C3×C4#402712yes—
457C3×C4C22×C4×D511yescharacteristic
458C3×C4C2×#71111yescharacteristic
459Dic3—42no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×C4×#6711yescharacteristic
463C2×C5#583711yescharacteristic
464C2×C5#583811yescharacteristic
465D5—122no—
466C23—301no—
467C23D5×#6711yescharacteristic
468Q8—22no—
469Q8—24no—
470Q8—152no—
471Q8—301no—
472Q8C2×#120014yes—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—52no—
479C2×C4—52no—
480C2×C4—62no—
481C2×C4—101no—
482C2×C4—101no—
483C2×C4—241no—
484C2×C4—301no—
485C2×C4—304no—
486C2×C4—1202no—
487C2×C4#678212yes—
488C2×C4C2×#120012yes—
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—61no—
492C8—61no—
493C8—154no—
494C2×C3—22no—
495C2×C3C2×#402711yescharacteristic
496C2×C3#6609611yescharacteristic
497C2×C3#6610011yescharacteristic
498D3—202no—
499C5#8254711yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9155212yes—
506C22C2×D5×#6711yescharacteristic
507C4—24no—
508C4—102no—
509C4—102no—
510C4—122no—
511C4—201no—
512C4—201no—
513C4—302no—
514C4#9155212yes—
515C4C2×#678211yescharacteristic
516C4C22×#120011yescharacteristic
517C3#1061050511yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2#1175508511yescharacteristic
521C2#1175510111yescharacteristic
522C2C2×#9155211yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#66146C2semidirect
4. C2×C5×#835C2semidirect
5. #11749250C2semidirect
6. #11749244C2semidirect
7. #11749225C2semidirect
8. #11749221C2semidirect
9. #11748472C2semidirect
11. #11748318C2semidirect
16. #91831C4semidirect
44. #66146D3semidirect
57. C2×C3×C5×Q8C2×C4semidirect
69. #6718C2×C4semidirect
70. #6717C2×C4semidirect
71. #6710C2×C4semidirect
96. C2×#835D5semidirect
195. C2×C5×Q8C4×D3semidirect
261. C2×C3×Q8C4×D5semidirect
410. C2×Q8#1200semidirect
443. C3×C5#2947semidirect
499. C5#82547semidirect
517. C3#10610505semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C3×#661462
#117545062
C2×C5×#8352
#117492502
#117492442
#117492252
#117492212
#117484722
#117484112
#117483182
#106105053
#825475