Finite Group Databasebeta

← #14301283

Subgroups — #14301283

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4055C211yesmaximal, characteristic
2#11754509C211yesmaximal, characteristic
3#11748609C211yesmaximal, characteristic, complemented
4C2×#90977C211yesmaximal, characteristic
5#11748399C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7C5×#4555C211yesmaximal, characteristic, complemented
8#10599568—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C3×#4055—22no—
17C3×#4055C414yescomplemented
18C2×C3×Dic20—21no—
19C2×C3×#677—21no—
20#91559—22no—
21Dic3×D20—21no—
22D5×C4⋊Dic3—21no—
23#91358—21no—
24Dic3×Dic10—21no—
25#90994—22no—
26#90977—22no—
27#90970—21no—
28#90970—21no—
29#72100—51nomaximal, Hall
30C2×#4055D311yescharacteristic
31#65857—31no—
32#65293—31no—
33#65218—31no—
34C2×#3937—31no—
35C5×#339—31no—
36#64774—31no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15D412yes—
39C22×C5×Dic3—21no—
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709C2×C412yes—
45C3×#709D412yes—
46C2×C3×D20D411yescharacteristic
47C2×C3×C4×D5—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10C2×C412yescomplemented
54C2×C3×Dic10D411yescharacteristic
55C2×D5×Dic3—22no—
56C3×C5×M16—21no—
57C3×C5×M16C2×C412yescomplemented
58C2×C3×C5×C8—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61#6710—21no—
62#6710—21no—
63C2×C3⋊#168—21no—
64C5×#217—21no—
65C5×C4⋊Dic3D411yescharacteristic
66C5×C4⋊Dic3D411yescharacteristic
67C4×C5×Dic3—21no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3—21no—
70C3×Dic20—24no—
71C3×#677—24no—
72#6668—22no—
73#6665—22no—
74Dic3×Dic5—22no—
75C2×C3×#137—51no—
76#5827—51no—
77C2×#837—51no—
78#5229—51no—
79#5225—51no—
80#4555D511yescharacteristic, complemented
81#4554—51no—
82C2×#709C2×D311yescharacteristic
83C22×Dic10C2×D311yescharacteristic
84C2×C5×M16C2×D311yescharacteristic
85C5×#117—31no—
86C2×C42×C5—31no—
87C2×C4⋊Dic5—31no—
88C2×#681—31no—
89#4055—22no—
90#4055Dic314yescomplemented
91C2×Dic20—21no—
92C2×#677—21no—
93#4038—61no—
94D5×C4⋊C4—61no—
95#4027—62no—
96C4×D20—61no—
97C4×Dic10—61no—
98#3963—62no—
99#3942—61no—
100#3942—61no—
101#3937—62no—
102#1882—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—21no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—42no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3—41no—
118C3×C22⋊D5—22no—
119C3×C22⋊D5—22no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5—41no—
124C3×D20—21no—
125C3×D20C22⋊C412yes—
126C3×C4×D5—22no—
127C3×C4×D5—22no—
128C3×Dic10—21no—
129C3×Dic10—22no—
130C3×Dic10—22no—
131C3×Dic10—41no—
132C3×Dic10—41no—
133C3×Dic10C22⋊C412yes—
134D5×Dic3—82no—
135C3×C5×C8—22no—
136C3⋊#168—41no—
137C2×C3×#41—51no—
138C22×C3×Q8—51no—
139C3×#137—54no—
140C3×#137—102no—
141C2×C3×Q16—101no—
142C2×C3×SD16—101no—
143C2×C3×M16C2×D511yescharacteristic
144Q8×Dic3—101no—
145D4×Dic3—101no—
146D4×Dic3—102no—
147#926—101no—
148#926C2×D511yescharacteristic
149C2×C4⋊Dic3—51no—
150C2×C4⋊Dic3—101no—
151C2×C4×Dic3C2×D511yescharacteristic
152C2×#208—51no—
153#837—102no—
154#835—101no—
155#835—101no—
156C3⋊#95—102no—
157C22×C4×C5—61no—
158C22×C4×C5C22×D311yescharacteristic
159C2×C22⋊D5—21no—
160C22×Dic5—21no—
161C22×Dic5—32no—
162#709—21no—
163#709—21no—
164#709C2×Dic312yes—
165#709#6712yes—
166C2×D20#6711yescharacteristic
167C2×C4×D5—21no—
168C2×C4×D5—62no—
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10—21no—
172C2×Dic10—21no—
173C2×Dic10—21no—
174C2×Dic10C2×Dic312yescomplemented
175C2×Dic10#6711yescharacteristic
176C5×M16—21no—
177C5×M16C2×Dic312yescomplemented
178C2×C5×C8—21no—
179C5×C4⋊C4—31no—
180C5×C4⋊C4—31no—
181C5×C22⋊C4—61no—
182C42×C5—61no—
183C42×C5—61no—
184C42×C5—61no—
185#685—62no—
186C4⋊Dic5—61no—
187C4⋊Dic5—61no—
188#683—62no—
189C4×Dic5—62no—
190#681—61no—
191#681—61no—
192C2×#168—61no—
193Dic20—24no—
194#677—24no—
195C2×#137—51no—
196#520—151no—
197C2×#104—151no—
198#419—151no—
199#391—151no—
200#343—151no—
201#339—31no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×C3×D5—22no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C3×C4×C5C2×C22⋊C411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12111yescharacteristic
213C3×C4×C5#12311yescharacteristic
214Dic15—42no—
215C3×Dic5—22no—
216C3×Dic5—42no—
217C5×Dic3—42no—
218C5×Dic3—41no—
219C5×Dic3—41no—
220C3×#41—52no—
221C3×#41—52no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—52no—
225C2×C3×Q8—51no—
226C2×C3×Q8—101no—
227C2×C3×Q8—101no—
228C2×C3×Q8—101no—
229C2×C3×Q8—101no—
230C2×C3×Q8—101no—
231C2×C3×D4—51no—
232C2×C3×D4—101no—
233C22×C3×C4—101no—
234C22×C3×C4—101no—
235C22×C3×C4C22×D511yescharacteristic
236C22×Dic3—21no—
237C22×Dic3—52no—
238C22×Dic3—102no—
239C3×Q16—104no—
240C3×SD16—104no—
241C3×M16—21no—
242C3×M16C4×D512yescomplemented
243C2×C3×C8—21no—
244#217—21no—
245#217—102no—
246C4⋊Dic3—102no—
247C4⋊Dic3—101no—
248C4⋊Dic3—101no—
249C4⋊Dic3D2011yescharacteristic
250C4⋊Dic3D2011yescharacteristic
251C4×Dic3—21no—
252C4×Dic3—21no—
253C4×Dic3—21no—
254C4×Dic3—102no—
255#208—101no—
256#208—101no—
257C2×C3⋊C8—101no—
258C23×C5D3×D411yescharacteristic
259C22×D5—21no—
260C2×C4×C5—62no—
261C2×C4×C5—61no—
262C2×C4×C5—61no—
263C2×C4×C5—121no—
264C2×C4×C5—121no—
265C2×C4×C5D3×D411yescharacteristic
266C2×C4×C5#23711yescharacteristic
267C2×C4×C5#23711yescharacteristic
268C2×C4×C5C22×Dic311yescharacteristic
269C2×C4×C5C2×#6711yescharacteristic
270C2×C4×C5C2×#6711yescharacteristic
271C22⋊D5—22no—
272C22⋊D5—22no—
273C2×Dic5—21no—
274C2×Dic5—22no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—62no—
278C2×Dic5—122no—
279D20—21no—
280D20#21712yes—
281C4×D5—22no—
282C4×D5—22no—
283C4×D5—242no—
284Dic10—21no—
285Dic10—22no—
286Dic10—22no—
287Dic10—41no—
288Dic10—41no—
289Dic10#21712yes—
290C5×C8—22no—
291#168—121no—
292C2×#41—51no—
293C22×Q8—51no—
294#137—54no—
295#137—102no—
296C2×Q16—101no—
297C2×SD16—101no—
298C2×M16—151no—
299C2×M16D3×D511yescharacteristic
300C4×Q8—301no—
301C4×D4—301no—
302C4×D4—302no—
303#117—31no—
304#117—301no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—301no—
307C2×C42—31no—
308#104—302no—
309#103—301no—
310#103—301no—
311#95—302no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317C3×D5—42no—
318C23×C3—101no—
319C23×C3D4×D511yescharacteristic
320C3×Q8—52no—
321C3×Q8—101no—
322C3×Q8—102no—
323C3×Q8—102no—
324C3×Q8—201no—
325C3×Q8—201no—
326C3×D4—52no—
327C3×D4—102no—
328C3×D4—102no—
329C3×D4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—201no—
335C2×C3×C4—201no—
336C2×C3×C4C2×C4×D511yescharacteristic
337C2×C3×C4C2×D2011yescharacteristic
338C2×C3×C4#70911yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4#71311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—102no—
348C2×Dic3—202no—
349C2×Dic3—402no—
350C3×C8—22no—
351C3⋊C8—201no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5D4×Dic311yescharacteristic
355C22×C5#93711yescharacteristic
356C22×C5#93911yescharacteristic
357C2×D5—22no—
358C2×D5—41no—
359C2×D5—41no—
360C4×C5—122no—
361C4×C5—121no—
362C4×C5—121no—
363C4×C5D4×Dic311yescharacteristic
364C4×C5#93511yescharacteristic
365C4×C5#93911yescharacteristic
366C4×C5C2×#21711yescharacteristic
367Dic5—22no—
368Dic5—42no—
369Dic5—122no—
370#41—52no—
371#41—52no—
372#41—101no—
373#41—101no—
374C2×Q8—52no—
375C2×Q8—51no—
376C2×Q8—101no—
377C2×Q8—101no—
378C2×Q8—101no—
379C2×Q8—101no—
380C2×Q8—101no—
381C2×D4—51no—
382C2×D4—101no—
383C22×C4—61no—
384C22×C4—101no—
385C22×C4—101no—
386C22×C4—152no—
387C22×C4—302no—
388C22×C4C2×D3×D511yescharacteristic
389Q16—104no—
390SD16—104no—
391M16—21no—
392M16—301no—
393M16—301no—
394M16D5×Dic312yescomplemented
395C2×C8—21no—
396C2×C8—301no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—302no—
400C4⋊C4—301no—
401C4⋊C4—301no—
402C22⋊C4—61no—
403C22⋊C4—302no—
404C42—61no—
405C42—61no—
406C42—61no—
407C42—302no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—102no—
412C22×C3—201no—
413C22×C3—201no—
414C22×C3#402811yescharacteristic
415C22×C3#403011yescharacteristic
416C22×C3#403911yescharacteristic
417C3×C4—102no—
418C3×C4—202no—
419C3×C4C4×D2011yescharacteristic
420C3×C4D5×C22⋊C411yescharacteristic
421C3×C4#404011yescharacteristic
422C3×C4#404111yescharacteristic
423Dic3—42no—
424Dic3—41no—
425Dic3—41no—
426Dic3—202no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5#520211yescharacteristic
430C2×C5#520511yescharacteristic
431C2×C5#522011yescharacteristic
432D5—42no—
433C23—101no—
434C23#677711yescharacteristic
435Q8—52no—
436Q8—101no—
437Q8—102no—
438Q8—102no—
439Q8—201no—
440Q8—201no—
441D4—52no—
442D4—102no—
443D4—102no—
444D4—101no—
445C2×C4—62no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—101no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—121no—
453C2×C4—121no—
454C2×C4—201no—
455C2×C4—201no—
456C2×C4—302no—
457C2×C4—602no—
458C2×C4—1202no—
459C2×C4#676511yescharacteristic
460C2×C4#676611yescharacteristic
461C2×C4D3×D2011yescharacteristic
462C2×C4C2×D5×Dic311yescharacteristic
463C2×C4D5×#6711yescharacteristic
464C2×C4D5×#6711yescharacteristic
465C8—22no—
466C8—601no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—202no—
470C2×C3#6495411yescharacteristic
471C2×C3#6511411yescharacteristic
472C2×C3#6511511yescharacteristic
473C5#7210011yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—102no—
477C22—201no—
478C22—201no—
479C22#9140811yescharacteristic
480C22#9143411yescharacteristic
481C22#9147411yescharacteristic
482C4—102no—
483C4—122no—
484C4—121no—
485C4—121no—
486C4—202no—
487C4—602no—
488C4#9140711yescharacteristic
489C4#9140911yescharacteristic
490C4Dic3×D2011yescharacteristic
491C4D5×#21711yescharacteristic
492C3#1059956811yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—202no—
496C2#1174824011yescharacteristic
497C2#1174825211yescharacteristic
498C2#1174889611yescharacteristic
subgroupG/H
centerC22#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1882
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #11748609C2semidirect
5. #11748399C2semidirect
6. #11746375C2semidirect
7. C5×#4555C2semidirect
17. C3×#4055C4semidirect
53. C2×C3×Dic10C2×C4semidirect
57. C3×C5×M16C2×C4semidirect
80. #4555D5semidirect
90. #4055Dic3semidirect
174. C2×Dic10C2×Dic3semidirect
177. C5×M16C2×Dic3semidirect
242. C3×M16C4×D5semidirect
394. M16D5×Dic3semidirect
408. C3×C5#1882semidirect
473. C5#72100semidirect
492. C3#10599568semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40552
#117545092
#117486092
C2×#909772
#117483992
#117463752
C5×#45552
#105995683
#721005