Finite Group Databasebeta

← #14307960

Subgroups — #14307960

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4055C211yesmaximal, characteristic
2C2×#91389C211yesmaximal, characteristic, complemented
3#11754252C211yesmaximal, characteristic
4C2×#91108C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic
6#11748399C211yesmaximal, characteristic, complemented
7C5×#4555C211yesmaximal, characteristic, complemented
8#10599561—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C3×#4055—22no—
17C3×#4055—22no—
18C2×C3×Dic20—21no—
19C2×C3×#677—21no—
20C2×Dic3⋊Dic5—22no—
21#91537—22no—
22#91389—21no—
23#91389—22no—
24#91389—22no—
25#91364—21no—
26#91360—22no—
27#91108—22no—
28#90977—22no—
29#90970—22no—
30#72108—51nomaximal, Hall
31C2×#4055D311yescharacteristic
32#65860—31no—
33C2×#4015—31no—
34C2×#3956—31no—
35#65293—31no—
36C2×#3937—31no—
37C5×#339—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15D412yes—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C22×C5×Dic3—21no—
47C2×C3×C22⋊D5—21no—
48C22×C3×Dic5—21no—
49C3×#709—21no—
50C3×#709—21no—
51C3×#709—21no—
52C3×#709—21no—
53C2×C3×D20D411yescharacteristic
54C2×C3×C4×D5—21no—
55C2×C3×Dic10—21no—
56C2×C3×Dic10—21no—
57C2×C3×Dic10—21no—
58C2×C3×Dic10—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10D412yes—
61C2×C3×Dic10D411yescharacteristic
62C3×C5×M16—21no—
63C3×C5×M16D412yes—
64C2×C3×C5×C8—21no—
65#6710—21no—
66#6710—21no—
67C2×C3⋊#168—21no—
68C5×#217—21no—
69C5×C4⋊Dic3D412yes—
70C4×C5×Dic3—21no—
71C4×C5×Dic3—21no—
72C4×C5×Dic3D412yes—
73C3×Dic20—24no—
74C3×#677—24no—
75Dic3⋊Dic5—24no—
76Dic3⋊Dic5—28no—
77#6665—24no—
78C2×C3×#137—51no—
79#5825—51no—
80C2×#944—51no—
81C2×#837—51no—
82#5225—51no—
83C2×#824—51no—
84#4555D511yescharacteristic, complemented
85C2×#709C2×D311yescharacteristic
86C22×Dic10—31no—
87C22×Dic10C2×D311yescharacteristic
88C2×C5×M16C2×D311yescharacteristic
89C5×#117—31no—
90C2×C42×C5—31no—
91C2×C4⋊Dic5—62no—
92C2×#681—31no—
93#4055—22no—
94#4055—22no—
95C2×Dic20—21no—
96C2×#677—21no—
97#4043—62no—
98#4032—62no—
99#4021—61no—
100#4015—62no—
101#4015—62no—
102#4015—61no—
103#3956—62no—
104#3942—62no—
105#3937—62no—
106#2005—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C3×D5—21no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—22no—
117C2×Dic15—22no—
118Dic30—41no—
119Dic30—41no—
120Dic30—41no—
121Dic30—41no—
122C2×C5×Dic3—24no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—22no—
125C3×C22⋊D5—41no—
126C3×C22⋊D5—41no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—41no—
130C2×C3×Dic5—41no—
131C3×D20—21no—
132C3×D20—21no—
133C3×C4×D5—41no—
134C3×C4×D5—41no—
135C3×Dic10—22no—
136C3×Dic10—21no—
137C3×Dic10—22no—
138C3×Dic10—21no—
139C3×Dic10—41no—
140C3×Dic10—41no—
141C3×C5×C8—22no—
142C3⋊#168—41no—
143C2×C3×#41—51no—
144C22×C3×Q8—51no—
145C22×Dic6—51no—
146C3×#137—102no—
147C3×#137—102no—
148C2×C3×Q16—101no—
149C2×C3×SD16—101no—
150C2×C3×M16C2×D511yescharacteristic
151#944—102no—
152#944—101no—
153#944—102no—
154#936—101no—
155#935—102no—
156#926C2×D511yescharacteristic
157#924—102no—
158C2×Dic3⋊C4—102no—
159C2×C4×Dic3C2×D511yescharacteristic
160C2×#208—51no—
161#837—102no—
162#835—102no—
163#824—102no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—21no—
167C22×Dic5—21no—
168C22×Dic5—32no—
169#709—21no—
170#709—21no—
171#709—21no—
172#709—21no—
173C2×D20#6711yescharacteristic
174C2×C4×D5—21no—
175C2×Dic10—21no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10—61no—
181C2×Dic10—61no—
182C2×Dic10—61no—
183C2×Dic10—61no—
184C2×Dic10—61no—
185C2×Dic10—61no—
186C2×Dic10#6712yes—
187C2×Dic10#6711yescharacteristic
188C5×M16—21no—
189C5×M16#6712yes—
190C2×C5×C8—21no—
191C5×C4⋊C4—32no—
192C5×C22⋊C4—61no—
193C42×C5—32no—
194C42×C5—61no—
195C42×C5—61no—
196#685—64no—
197C4⋊Dic5—68no—
198C4⋊Dic5—64no—
199#681—61no—
200#681—61no—
201C2×#168—61no—
202Dic20—24no—
203#677—24no—
204C2×#137—51no—
205#536—151no—
206C2×C4⋊Q8—151no—
207C2×#104—151no—
208#419—151no—
209C2×#101—151no—
210#339—31no—
211C22×C3×C5—22no—
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12011yescharacteristic
214C22×C3×C5#12111yescharacteristic
215C2×C3×D5—41no—
216C2×C3×D5—42no—
217C3×C4×C5#12011yescharacteristic
218C3×C4×C5#12111yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12711yescharacteristic
221Dic15—42no—
222C3×Dic5—42no—
223C3×Dic5—41no—
224C5×Dic3—24no—
225C5×Dic3—42no—
226C3×#41—101no—
227C3×#41—101no—
228C3×#41—101no—
229C3×#41—101no—
230C2×C3×Q8—51no—
231C2×C3×Q8—52no—
232C2×C3×Q8—101no—
233C2×C3×Q8—101no—
234C2×C3×Q8—101no—
235C2×C3×Q8—101no—
236C2×C3×Q8—101no—
237C2×C3×D4—51no—
238C2×C3×D4—101no—
239C22×C3×C4—101no—
240C22×C3×C4—101no—
241C22×C3×C4C22×D511yescharacteristic
242C22×Dic3—21no—
243C22×Dic3—52no—
244C2×Dic6—101no—
245C2×Dic6—101no—
246C2×Dic6—101no—
247C2×Dic6—101no—
248C2×Dic6—101no—
249C2×Dic6—101no—
250C3×Q16—104no—
251C3×SD16—104no—
252C3×M16—21no—
253C3×M16D2012yes—
254C2×C3×C8—21no—
255#217—21no—
256#217—104no—
257C4⋊Dic3D2012yes—
258Dic3⋊C4—108no—
259Dic3⋊C4—104no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3D2012yes—
263#208—101no—
264#208—101no—
265C2×C3⋊C8—101no—
266C23×C5D3×D411yescharacteristic
267C22×D5—21no—
268C2×C4×C5—64no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5#23711yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C22⋊D5—41no—
278C22⋊D5—41no—
279C2×Dic5—22no—
280C2×Dic5—21no—
281C2×Dic5—41no—
282C2×Dic5—41no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286D20—21no—
287D20—21no—
288C4×D5—41no—
289C4×D5—41no—
290Dic10—22no—
291Dic10—21no—
292Dic10—22no—
293Dic10—21no—
294Dic10—41no—
295Dic10—41no—
296Dic10—121no—
297Dic10—121no—
298Dic10—121no—
299Dic10—121no—
300C5×C8—22no—
301#168—121no—
302C2×#41—51no—
303C22×Q8—51no—
304C22×Q8—151no—
305#137—102no—
306#137—102no—
307C2×Q16—101no—
308C2×SD16—101no—
309C2×M16—151no—
310C2×M16D3×D511yescharacteristic
311C4⋊Q8—302no—
312C4⋊Q8—302no—
313C4⋊Q8—301no—
314#124—301no—
315#123—302no—
316C22⋊Q8—302no—
317#117—31no—
318C2×C4⋊C4—302no—
319C2×C42—31no—
320#104—302no—
321#103—302no—
322#101—302no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#39211yescharacteristic
326C2×C3×C5#45612yes—
327C3×D5—81no—
328C23×C3—101no—
329C23×C3D4×D511yescharacteristic
330C3×Q8—102no—
331C3×Q8—101no—
332C3×Q8—102no—
333C3×Q8—101no—
334C3×Q8—201no—
335C3×Q8—201no—
336C3×D4—101no—
337C3×D4—101no—
338C3×D4—201no—
339C3×D4—201no—
340C2×C3×C4—101no—
341C2×C3×C4—102no—
342C2×C3×C4—201no—
343C2×C3×C4—201no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4C2×D2011yescharacteristic
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4C2×D2011yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4#71311yescharacteristic
352C2×Dic3—24no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—102no—
356C2×Dic3—102no—
357C2×Dic3—102no—
358Dic6—201no—
359Dic6—201no—
360Dic6—201no—
361Dic6—201no—
362C3×C8—22no—
363C3⋊C8—201no—
364C22×C5—22no—
365C22×C5#93711yescharacteristic
366C22×C5#93711yescharacteristic
367C22×C5#93811yescharacteristic
368C2×D5—42no—
369C2×D5—41no—
370C4×C5—64no—
371C4×C5—122no—
372C4×C5#93911yescharacteristic
373C4×C5#93911yescharacteristic
374C4×C5#94011yescharacteristic
375C4×C5#95311yescharacteristic
376Dic5—42no—
377Dic5—41no—
378Dic5—122no—
379#41—101no—
380#41—101no—
381#41—101no—
382#41—101no—
383C2×Q8—51no—
384C2×Q8—52no—
385C2×Q8—101no—
386C2×Q8—101no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×Q8—301no—
391C2×Q8—301no—
392C2×Q8—301no—
393C2×Q8—301no—
394C2×Q8—301no—
395C2×Q8—301no—
396C2×D4—51no—
397C2×D4—101no—
398C22×C4—61no—
399C22×C4—101no—
400C22×C4—101no—
401C22×C4—152no—
402C22×C4C2×D3×D511yescharacteristic
403Q16—104no—
404SD16—104no—
405M16—21no—
406M16—301no—
407M16—301no—
408M16#120212yes—
409C2×C8—21no—
410C2×C8—301no—
411C4⋊C4—32no—
412C4⋊C4—308no—
413C4⋊C4—304no—
414C22⋊C4—61no—
415C22⋊C4—304no—
416C42—32no—
417C42—61no—
418C42—61no—
419C3×C5#200511yescharacteristic, complemented, Hall
420C22×C3—22no—
421C22×C3—202no—
422C22×C3—201no—
423C22×C3#402811yescharacteristic
424C22×C3#402811yescharacteristic
425C22×C3#404111yescharacteristic
426C3×C4—201no—
427C3×C4—202no—
428C3×C4#402011yescharacteristic
429C3×C4#402811yescharacteristic
430C3×C4#404111yescharacteristic
431C3×C4#404111yescharacteristic
432Dic3—24no—
433Dic3—42no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#520512yes—
438C2×C5#522311yescharacteristic
439D5—81no—
440C23—101no—
441C23#677711yescharacteristic
442Q8—102no—
443Q8—101no—
444Q8—102no—
445Q8—101no—
446Q8—201no—
447Q8—201no—
448Q8—601no—
449Q8—601no—
450Q8—601no—
451Q8—601no—
452D4—101no—
453D4—101no—
454D4—201no—
455D4—201no—
456C2×C4—64no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—102no—
460C2×C4—101no—
461C2×C4—201no—
462C2×C4—201no—
463C2×C4—201no—
464C2×C4—201no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4#676611yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4D3×D2011yescharacteristic
471C2×C4C2×#120211yescharacteristic
472C2×C4D5×#6711yescharacteristic
473C2×C4D5×#6711yescharacteristic
474C8—22no—
475C8—601no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—401no—
479C2×C3#6496011yescharacteristic
480C2×C3#6511512yes—
481C5#7210811yescharacteristic, complemented, Sylow
482C22—22no—
483C22—201no—
484C22—202no—
485C22#9146511yescharacteristic
486C22#9147411yescharacteristic
487C22#9147411yescharacteristic
488C4—64no—
489C4—122no—
490C4—201no—
491C4—202no—
492C4—602no—
493C4#9140911yescharacteristic
494C4#9140911yescharacteristic
495C4#9145811yescharacteristic
496C4#9156411yescharacteristic
497C3#1059956111yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—401no—
501C2#1174825212yes—
502C2#1174892311yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#2005
LCSG ▷ C22×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
2. C2×#91389C2semidirect
4. C2×#91108C2semidirect
6. #11748399C2semidirect
7. C5×#4555C2semidirect
84. #4555D5semidirect
419. C3×C5#2005semidirect
481. C5#72108semidirect
497. C3#10599561semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40552
C2×#913892
#117542522
C2×#911082
C2×#909772
#117483992
C5×#45552
#105995613
#721085