Finite Group Databasebeta

← #14307971

Subgroups — #14307971

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×C5×#869C211yesmaximal, characteristic, complemented
2#11754270C211yesmaximal, characteristic
3C2×#91321C211yesmaximal, characteristic
4C2×#91089C211yesmaximal, characteristic
5#11748407C211yesmaximal, characteristic, complemented
6C2×#90962C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10602588—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×C4⋊Dic3—22no—
15C5×#869—22no—
16C5×#869—22no—
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91542—22no—
20#91383—22no—
21#91376—21no—
22#91375—21no—
23#91321—22no—
24#91321—22no—
25C2×#6663—21no—
26C2×#6660—21no—
27#91089—22no—
28#90972—22no—
29#90962—22no—
30#68768—51nomaximal, Hall
31C2×C5×C4⋊Q8—31no—
32#66150—31no—
33C2×#4088—31no—
34C2×#3968—31no—
35#65514—31no—
36C2×#3937—31no—
37#64743D311yescharacteristic, complemented
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41#6817—21no—
42#6817—21no—
43#6817—21no—
44#6817—21no—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30D411yescharacteristic
48C22×C5×Dic3—21no—
49C22×C5×Dic3D412yes—
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6—21no—
54C2×C5×Dic6—21no—
55C2×C5×Dic6—21no—
56C2×C5×Dic6—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6—21no—
61C2×C5×Dic6D412yes—
62C3×C42×C5—21no—
63C3×C42×C5D412yes—
64#6710—21no—
65#6710—21no—
66C2×C3⋊#168—21no—
67C5×C4⋊Dic3—28no—
68C3×C22⋊Dic5—21no—
69C3×C4⋊Dic5D412yes—
70C3×C4×Dic5—21no—
71C3×#681—21no—
72C3×#681D412yes—
73C2×C3×#168—21no—
74#6668—24no—
75#6667—24no—
76#6663—24no—
77#6660—24no—
78C2×#909—51no—
79#5526—51no—
80C2×#869D511yescharacteristic, complemented
81C2×#824—51no—
82#5004—51no—
83C2×#805—51no—
84C3×#339—51no—
85C22×C5×Q8—31no—
86C22×C5×Q8—31no—
87C2×#709—31no—
88C5×C4⋊Q8—62no—
89C5×C4⋊Q8—62no—
90C2×C5×C4⋊C4—62no—
91C2×C42×C5C2×D311yescharacteristic
92#4093—61no—
93#4092—62no—
94#4090—61no—
95C2×#689—61no—
96#4088—62no—
97#4088—62no—
98C2×#688—61no—
99#4075—62no—
100#4072C2×D311yescharacteristic
101C2×#681—31no—
102C2×#681C2×D311yescharacteristic
103#3968—62no—
104#3967—62no—
105#3937—62no—
106#2005—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—21no—
109C2×C3×C4×C5—24no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117#1220—41no—
118#1220—41no—
119C2×Dic15—21no—
120D60—21no—
121D60—21no—
122C4×D15—41no—
123C4×D15—41no—
124Dic30—21no—
125Dic30—21no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—22no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—41no—
131C2×C5×Dic3—41no—
132C5×Dic6—22no—
133C5×Dic6—22no—
134C5×Dic6—41no—
135C5×Dic6—41no—
136C5×Dic6—41no—
137C5×Dic6—41no—
138C5×Dic6—41no—
139C5×Dic6—41no—
140C2×C3×Dic5—22no—
141C3⋊#168—41no—
142C3×#168—22no—
143C2×#235—51no—
144C22×Dic6C2×D511yescharacteristic
145C22×Dic6C2×D511yescharacteristic
146C2×C3×M16—51no—
147C3×#117—51no—
148C2×C3×C42C2×D511yescharacteristic
149C2×C4⋊Dic3—22no—
150C2×#208—51no—
151#909—102no—
152#909—102no—
153C2×Dic12—101no—
154C2×#204—101no—
155#897—102no—
156#886—102no—
157#875—101no—
158#869—22no—
159#869—22no—
160#869—101no—
161#824—102no—
162#810—102no—
163#805—102no—
164C2×C5×Q8—32no—
165C2×C5×Q8—61no—
166C2×C5×Q8—61no—
167C2×C5×Q8—61no—
168C2×C5×Q8—61no—
169C2×C5×Q8—61no—
170C2×C5×Q8—61no—
171C2×C5×Q8—61no—
172C2×C5×Q8—61no—
173C2×C5×Q8—61no—
174C2×C5×Q8—61no—
175C2×C5×Q8—61no—
176C22×C4×C5—21no—
177C22×C4×C5—32no—
178C22×C4×C5—61no—
179C22×C4×C5C22×D311yescharacteristic
180C2×C22⋊D5—61no—
181#709—61no—
182#709—61no—
183#709—61no—
184#709—61no—
185C2×D20—31no—
186C2×C4×D5—61no—
187C2×Dic10—31no—
188C5×C4⋊C4—68no—
189C42×C5—21no—
190C42×C5D1212yes—
191C22⋊Dic5—21no—
192#689—64no—
193#688—64no—
194#685—64no—
195C4⋊Dic5D1212yes—
196#683—64no—
197C4×Dic5—21no—
198#681—21no—
199#681—61no—
200#681—61no—
201#681D1212yes—
202C2×#168—21no—
203C2×#168—61no—
204C2×#137—151no—
205#536—151no—
206C2×C4⋊Q8—31no—
207C2×#104—151no—
208#419—151no—
209C2×#101—151no—
210#339—51no—
211C22×C3×C5—22no—
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12011yescharacteristic
214C22×C3×C5#12111yescharacteristic
215C2×D15—41no—
216C2×D15—42no—
217C3×C4×C5—24no—
218C3×C4×C5#12011yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12111yescharacteristic
221C3×C4×C5#12711yescharacteristic
222Dic15—41no—
223C3×Dic5—42no—
224C5×Dic3—42no—
225C5×Dic3—42no—
226C22×C3×C4—21no—
227C22×C3×C4C22×D511yescharacteristic
228C2×#67—101no—
229C22×Dic3—21no—
230C22×Dic3C22⋊D512yes—
231#235—101no—
232#235—101no—
233#235—101no—
234#235—101no—
235C2×D12—51no—
236C2×C4×D3—101no—
237C2×Dic6—21no—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6—21no—
244C2×Dic6—21no—
245C2×Dic6—21no—
246C2×Dic6—21no—
247C2×Dic6—21no—
248C2×Dic6—51no—
249C2×Dic6C22⋊D512yes—
250C3×M16—52no—
251C3×M16—101no—
252C2×C3×C8—101no—
253C3×C4⋊C4—52no—
254C3×C22⋊C4—101no—
255C3×C42—21no—
256C3×C42—101no—
257C3×C42C22⋊D512yes—
258(C2×D3)⋊C4—104no—
259C4⋊Dic3—28no—
260C4⋊Dic3—104no—
261#208—101no—
262#208—101no—
263C2×C3⋊C8—101no—
264Dic12—104no—
265#204—104no—
266C23×C5D3×D411yescharacteristic
267C22×D5—61no—
268C5×Q8—62no—
269C5×Q8—62no—
270C5×Q8—121no—
271C5×Q8—121no—
272C5×Q8—121no—
273C5×Q8—121no—
274C5×Q8—121no—
275C5×Q8—121no—
276C2×C4×C5—24no—
277C2×C4×C5—22no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5C2×D1211yescharacteristic
285C2×C4×C5C2×D1211yescharacteristic
286C2×C4×C5C2×D1211yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5#23911yescharacteristic
290C22⋊D5—121no—
291C22⋊D5—121no—
292C2×Dic5—22no—
293C2×Dic5—61no—
294D20—61no—
295D20—61no—
296C4×D5—121no—
297C4×D5—121no—
298Dic10—61no—
299Dic10—61no—
300#168—22no—
301#168—121no—
302C2×#41—151no—
303C22×Q8—31no—
304C22×Q8—31no—
305#137—302no—
306#137—302no—
307C2×Q16—301no—
308C2×SD16—301no—
309C2×M16—51no—
310C2×M16—151no—
311C4⋊Q8—62no—
312C4⋊Q8—62no—
313C4⋊Q8—301no—
314#124—301no—
315#123—302no—
316C22⋊Q8—302no—
317#117—51no—
318C2×C4⋊C4—62no—
319C2×C42D3×D511yescharacteristic
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—
327D15—81no—
328C23×C3C2×C22⋊D511yescharacteristic
329C22×D3—101no—
330C2×C3×C4—24no—
331C2×C3×C4—22no—
332C2×C3×C4—102no—
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4C2×C22⋊D511yescharacteristic
338C2×C3×C4C2×C22⋊D511yescharacteristic
339#67—201no—
340#67—201no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—101no—
348D12—101no—
349D12—101no—
350C4×D3—201no—
351C4×D3—201no—
352Dic6—22no—
353Dic6—22no—
354Dic6—41no—
355Dic6—41no—
356Dic6—41no—
357Dic6—41no—
358Dic6—41no—
359Dic6—41no—
360Dic6—101no—
361Dic6—101no—
362C3×C8—102no—
363C3⋊C8—201no—
364C22×C5—22no—
365C22×C5#88211yescharacteristic
366C22×C5#88211yescharacteristic
367C22×C5#89511yescharacteristic
368C2×D5—121no—
369C2×D5—122no—
370C4×C5—24no—
371C4×C5—122no—
372C4×C5—122no—
373C4×C5#87411yescharacteristic
374C4×C5#88211yescharacteristic
375C4×C5#89511yescharacteristic
376C4×C5#89511yescharacteristic
377Dic5—42no—
378Dic5—121no—
379#41—301no—
380#41—301no—
381#41—301no—
382#41—301no—
383C2×Q8—32no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—151no—
396C2×D4—151no—
397C2×D4—301no—
398C22×C4—21no—
399C22×C4—32no—
400C22×C4—61no—
401C22×C4—301no—
402C22×C4C2×D3×D511yescharacteristic
403Q16—304no—
404SD16—304no—
405M16—52no—
406M16—101no—
407M16—301no—
408M16—301no—
409C2×C8—101no—
410C2×C8—301no—
411C4⋊C4—52no—
412C4⋊C4—68no—
413C4⋊C4—304no—
414C22⋊C4—101no—
415C22⋊C4—304no—
416C42—21no—
417C42—101no—
418C42#120312yes—
419C3×C5#200511yescharacteristic, complemented, Hall
420C22×C3—22no—
421C22×C3#408311yescharacteristic
422C22×C3#408511yescharacteristic
423C22×C3#409911yescharacteristic
424C2×D3—202no—
425C2×D3—201no—
426C3×C4—24no—
427C3×C4—202no—
428C3×C4#408311yescharacteristic
429C3×C4#408411yescharacteristic
430C3×C4#408511yescharacteristic
431C3×C4#408611yescharacteristic
432Dic3—42no—
433Dic3—42no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#467111yescharacteristic
438C2×C5#482612yes—
439D5—241no—
440C23—301no—
441C23D3×C22⋊D511yescharacteristic
442Q8—62no—
443Q8—62no—
444Q8—121no—
445Q8—121no—
446Q8—121no—
447Q8—121no—
448Q8—121no—
449Q8—121no—
450Q8—301no—
451Q8—301no—
452D4—301no—
453D4—301no—
454D4—601no—
455D4—601no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—102no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—301no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4#676811yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4D5×D1211yescharacteristic
471C2×C4#677711yescharacteristic
472C2×C4C2×#120311yescharacteristic
473C2×C4D3×C22⋊D511yescharacteristic
474C8—102no—
475C8—601no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3#6538412yes—
479C2×C3#6551211yescharacteristic
480D3—401no—
481C5#6876811yescharacteristic, complemented, Sylow
482C22—22no—
483C22—602no—
484C22—601no—
485C22#9141611yescharacteristic
486C22#9147511yescharacteristic
487C22#9157011yescharacteristic
488C4—24no—
489C4—122no—
490C4—122no—
491C4—202no—
492C4—601no—
493C4#9141611yescharacteristic
494C4#9145111yescharacteristic
495C4#9146611yescharacteristic
496C4#9147511yescharacteristic
497C3#1060258811yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—1201no—
501C2#1174712212yes—
502C2#1174892911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC2×#6817C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2005
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C5×#869C2semidirect
5. #11748407C2semidirect
6. C2×#90962C2semidirect
7. C3×#64743C2semidirect
37. #64743D3semidirect
80. C2×#869D5semidirect
419. C3×C5#2005semidirect
481. C5#68768semidirect
497. C3#10602588semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8692
#117542702
C2×#913212
C2×#910892
#117484072
C2×#909622
C3×#647432
#106025883
#687685