Finite Group Databasebeta

← #14301341

Subgroups — #14301341

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4078C211yesmaximal, characteristic
2#11754499C211yesmaximal, characteristic, complemented
3#11751316C211yesmaximal, characteristic, complemented
4C5×#5221C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic, complemented
6#11745986C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10600456—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#217—22no—
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C2×C3×#687—21no—
17C3×#4078—22no—
18C3×#4078C414yescomplemented
19C2×C3×#686—21no—
20C2×C3×#681C2211yescharacteristic
21Dic3×C22⋊D5—22no—
22#91434—21no—
23D5×C4⋊Dic3—21no—
24#91358—21no—
25#91331—21no—
26#91116—21no—
27#91116—21no—
28#90977—22no—
29#72088—51nomaximal, Hall
30C2×#4078D311yescharacteristic
31#65838—31no—
32C5×#390—31no—
33#65504—31no—
34C2×#3937—31no—
35#64750—31no—
36#64743—31no—
37C24×C3×C5—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4C2×C412yescomplemented
44C22×C3×C4×C5C2311yescharacteristic
45C22×C5×Dic3—21no—
46C22×C5×Dic3D412yes—
47C2×C3×C22⋊D5—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709C2×C412yes—
51C3×#709D412yes—
52C2×C3×D20D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×Dic10D411yescharacteristic
55C2×D5×Dic3—22no—
56#6719—21no—
57C4⋊Dic15D411yescharacteristic
58C4⋊Dic15D411yescharacteristic
59C4×Dic15—21no—
60#6710—21no—
61#6710—21no—
62C2×C3⋊#168—21no—
63C5×#217—44no—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3—21no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C3×#687—24no—
69C3×#686—24no—
70C3×#681—21no—
71C3×#681C2×C412yescomplemented
72C2×C3×#168—21no—
73#6668—22no—
74#6665—22no—
75Dic3×Dic5—22no—
76C2×C3×AGL(1,ℤ/8)—51no—
77#5827—51no—
78C2×#837—51no—
79#5221D511yescharacteristic, complemented
80#5215—51no—
81#4555—51no—
82#4554—51no—
83C22×C5×D4C2×D311yescharacteristic
84C2×#709C2×D311yescharacteristic
85C2×C5×C4⋊C4—31no—
86C2×C5×C22⋊C4—62no—
87C2×C42×C5—31no—
88C2×#687—21no—
89#4078—22no—
90#4078Dic314yescomplemented
91C2×#686—21no—
92C4×C22⋊D5—62no—
93#4072—31no—
94C2×#681—31no—
95C2×#681C2×D311yescharacteristic
96#4039—61no—
97#4038—61no—
98D5×C4⋊C4—61no—
99#4033—61no—
100#3964—61no—
101#3964—61no—
102#3937—62no—
103#1883—151noSylow
104C23×C3×C5—22no—
105C23×C3×C5—42no—
106C23×C3×C5—42no—
107C23×C3×C5—41no—
108C23×C3×C5—41no—
109C23×C3×C5C2×D411yescharacteristic
110C22×C3×D5—21no—
111C3×C5×D4—22no—
112C3×C5×D4—22no—
113C3×C5×D4—41no—
114C3×C5×D4—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C2×Dic15—21no—
122C2×Dic15—21no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—41no—
126C2×C5×Dic3—41no—
127C2×C5×Dic3—42no—
128C3×C22⋊D5—22no—
129C3×C22⋊D5—22no—
130C2×C3×Dic5—21no—
131C3×D20—21no—
132C3×D20C22⋊C412yescomplemented
133C3×C4×D5—22no—
134C3×C4×D5—22no—
135C3×Dic10—21no—
136C3×Dic10C22⋊C412yescomplemented
137D5×Dic3—82no—
138C3⋊#168—41no—
139C3×#168—22no—
140C2×C3×#41—51no—
141C22×C3×D4C2×D511yescharacteristic
142C3×AGL(1,ℤ/8)—54no—
143C3×AGL(1,ℤ/8)—102no—
144C2×C3×SD16—101no—
145C2×C3×D8—101no—
146C2×C3×M16—51no—
147C2×#217—22no—
148Q8×Dic3—101no—
149D4×Dic3—101no—
150D4×Dic3—102no—
151#926—51no—
152#926—101no—
153C2×C4⋊Dic3—101no—
154C2×C4⋊Dic3C2×D511yescharacteristic
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208—51no—
157#837—102no—
158#832—101no—
159#832—101no—
160C24×C5—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C2×Dic312yescomplemented
167C22×C4×C5—32no—
168C22×C4×C5—61no—
169C22×C4×C5C22×D311yescharacteristic
170C2×C22⋊D5—21no—
171#709—21no—
172#709—21no—
173#709C2×Dic312yes—
174#709#6712yes—
175C2×D20#6711yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—62no—
178C2×Dic10#6711yescharacteristic
179C5×C4⋊C4—61no—
180C5×C4⋊C4—61no—
181C5×C22⋊C4—124no—
182C42×C5—61no—
183C42×C5—61no—
184C22⋊Dic5—61no—
185#687—24no—
186#686—24no—
187#685—62no—
188C4⋊Dic5—31no—
189C4⋊Dic5—31no—
190#683—62no—
191C4×Dic5—62no—
192C4×Dic5—61no—
193#681—21no—
194#681—61no—
195#681—61no—
196#681C2×Dic312yescomplemented
197C2×#168—21no—
198C2×#168—61no—
199C2×AGL(1,ℤ/8)—51no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—31no—
204#343—151no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5—44no—
209C22×C3×C5—42no—
210C22×C3×C5—82no—
211C22×C3×C5—81no—
212C22×C3×C5—81no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×C3×D5—22no—
217C2×C3×D5—41no—
218C2×C3×D5—41no—
219C3×C4×C5C2×C22⋊C411yescharacteristic
220C3×C4×C5C4×D411yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5#12311yescharacteristic
223Dic15—41no—
224Dic15—41no—
225C3×Dic5—22no—
226C5×Dic3—42no—
227C5×Dic3—42no—
228C24×C3—21no—
229C3×#41—52no—
230C3×#41—52no—
231C3×#41—101no—
232C3×#41—101no—
233C2×C3×Q8—51no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—51no—
240C2×C3×D4—101no—
241C2×C3×D4C4×D512yescomplemented
242C22×C3×C4—101no—
243C22×C3×C4C22×D511yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—102no—
246C22×Dic3C22⋊D512yes—
247C3×SD16—104no—
248C3×D8—104no—
249C3×M16—52no—
250C3×M16—101no—
251C2×C3×C8—101no—
252#217—44no—
253#217—102no—
254#217—101no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—51no—
258C4⋊Dic3—51no—
259C4⋊Dic3—102no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—102no—
263C4×Dic3—101no—
264#208—101no—
265#208—101no—
266C2×C3⋊C8—101no—
267C23×C5—22no—
268C23×C5—42no—
269C23×C5—42no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5D3×D411yescharacteristic
273C22×D5—21no—
274C5×D4—22no—
275C5×D4—22no—
276C5×D4—41no—
277C5×D4—41no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—122no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5#23711yescharacteristic
285C2×C4×C5#23711yescharacteristic
286C2×C4×C5C22×Dic311yescharacteristic
287C2×C4×C5C2×#6711yescharacteristic
288C2×C4×C5C2×#6711yescharacteristic
289C22⋊D5—22no—
290C22⋊D5—22no—
291C2×Dic5—21no—
292C2×Dic5—61no—
293C2×Dic5—61no—
294D20—21no—
295D20#21712yescomplemented
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—242no—
299Dic10—21no—
300Dic10#21712yescomplemented
301#168—22no—
302#168—121no—
303C2×#41—51no—
304C22×D4D3×D511yescharacteristic
305AGL(1,ℤ/8)—54no—
306AGL(1,ℤ/8)—102no—
307C2×SD16—101no—
308C2×D8—101no—
309C2×M16—51no—
310C2×M16—151no—
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—151no—
315#117—301no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—62no—
319C2×C42—31no—
320#104—302no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5—82no—
326C2×C3×C5#38611yescharacteristic
327C2×C3×C5#45311yescharacteristic
328C2×C3×C5#45411yescharacteristic
329C3×D5—42no—
330C23×C3—22no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—101no—
336C23×C3C2×C22⋊D511yescharacteristic
337C3×Q8—52no—
338C3×Q8—101no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—52no—
344C3×D4—102no—
345C3×D4—102no—
346C3×D4—101no—
347C2×C3×C4—101no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4C2×C4×D511yescharacteristic
351C2×C3×C4#70911yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4#71111yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—42no—
361C2×Dic3—101no—
362C2×Dic3—101no—
363C2×Dic3—402no—
364C3×C8—102no—
365C3⋊C8—201no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—44no—
369C22×C5—42no—
370C22×C5—82no—
371C22×C5—81no—
372C22×C5—81no—
373C22×C5D4×Dic311yescharacteristic
374C22×C5#93711yescharacteristic
375C22×C5#93911yescharacteristic
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—122no—
380C4×C5—122no—
381C4×C5D4×Dic311yescharacteristic
382C4×C5#93511yescharacteristic
383C4×C5#93911yescharacteristic
384C4×C5C2×#21711yescharacteristic
385Dic5—22no—
386Dic5—121no—
387Dic5—121no—
388C24—21no—
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—51no—
400C2×D4—101no—
401C2×D4D5×Dic312yescomplemented
402C22×C4—32no—
403C22×C4—61no—
404C22×C4—101no—
405C22×C4—302no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—104no—
408D8—104no—
409M16—52no—
410M16—101no—
411M16—301no—
412M16—301no—
413C2×C8—101no—
414C2×C8—301no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—151no—
418C4⋊C4—151no—
419C4⋊C4—302no—
420C22⋊C4—124no—
421C22⋊C4—302no—
422C22⋊C4—301no—
423C42—61no—
424C42—61no—
425C42—302no—
426C42—301no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—44no—
431C22×C3—42no—
432C22×C3—82no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—102no—
436C22×C3—201no—
437C22×C3—201no—
438C22×C3C4×C22⋊D511yescharacteristic
439C22×C3#408311yescharacteristic
440C22×C3#408411yescharacteristic
441C3×C4—102no—
442C3×C4D5×C22⋊C411yescharacteristic
443C3×C4#402711yescharacteristic
444C3×C4#402911yescharacteristic
445C3×C4#403011yescharacteristic
446Dic3—42no—
447Dic3—42no—
448Dic3—201no—
449Dic3—201no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—82no—
453C2×C5#519811yescharacteristic
454C2×C5#520111yescharacteristic
455C2×C5#522011yescharacteristic
456D5—42no—
457C23—22no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—101no—
463C23D3×C22⋊D511yescharacteristic
464Q8—52no—
465Q8—101no—
466D4—22no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—52no—
471D4—102no—
472D4—102no—
473D4—101no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—101no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—122no—
482C2×C4—301no—
483C2×C4—301no—
484C2×C4—1202no—
485C2×C4C2×D5×Dic311yescharacteristic
486C2×C4#677911yescharacteristic
487C2×C4#678011yescharacteristic
488C2×C4D5×#6711yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4#679011yescharacteristic
491C8—102no—
492C8—601no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—82no—
496C2×C3—202no—
497C2×C3#6524511yescharacteristic
498C2×C3#6535111yescharacteristic
499C2×C3#6536611yescharacteristic
500C5#7208811yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—44no—
504C22—42no—
505C22—82no—
506C22—81no—
507C22—81no—
508C22—102no—
509C22—201no—
510C22—201no—
511C22#9154911yescharacteristic
512C22Dic3×C22⋊D511yescharacteristic
513C22#9157711yescharacteristic
514C4—102no—
515C4—122no—
516C4—122no—
517C4—601no—
518C4—601no—
519C4D5×#21711yescharacteristic
520C4#9154811yescharacteristic
521C4#9155011yescharacteristic
522C4#9155911yescharacteristic
523C3#1060045611yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—82no—
527C2—202no—
528C2#1174916511yescharacteristic
529C2#1174916711yescharacteristic
530C2#1174951811yescharacteristic
subgroupG/H
centerC22#91577
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×#4078C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11754499C2semidirect
3. #11751316C2semidirect
4. C5×#5221C2semidirect
5. C2×#90977C2semidirect
6. #11745986C2semidirect
7. #11745976C2semidirect
18. C3×#4078C4semidirect
43. C2×C3×C5×D4C2×C4semidirect
71. C3×#681C2×C4semidirect
79. #5221D5semidirect
90. #4078Dic3semidirect
132. C3×D20C22⋊C4semidirect
136. C3×Dic10C22⋊C4semidirect
166. C2×C5×D4C2×Dic3semidirect
196. #681C2×Dic3semidirect
241. C2×C3×D4C4×D5semidirect
295. D20#217semidirect
300. Dic10#217semidirect
401. C2×D4D5×Dic3semidirect
427. C3×C5#1883semidirect
500. C5#72088semidirect
523. C3#10600456semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40782
#117544992
#117513162
C5×#52212
C2×#909772
#117459862
#117459762
#106004563
#720885