Finite Group Databasebeta

← #14425433

Subgroups — #14425433

Order 1920.

1396 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4147C211yesmaximal, characteristic, complemented
2#11756575C211yesmaximal, characteristic, complemented
3#11754154C212yesmaximal, complemented
4C2×C5×#836C211yesmaximal, characteristic, complemented
5#11749391C214yesmaximal, complemented
6#11749384C214yesmaximal, complemented
7#11748420C212yesmaximal, complemented
8#10610440—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C3×#4147—22no—
12C3×#4147—24no—
13C3×#4147C2214yes—
14C2×C3×#713—22no—
15C2×C3×Q8×D5—22no—
16C2×C3×#709—22no—
17C2×C3×#709C2212yes—
18#91836C2212yescomplemented
19#91835—22no—
20#91833C2212yescomplemented
21#91818—22no—
22#91815C2211yescharacteristic
23C2×C5×#208C2212yes—
24#91315—22no—
25#91313C2214yescomplemented
26#91312—22no—
27#91311—24no—
28#91301C2214yescomplemented
29C5×#836C2214yescomplemented
30#90976C2218yescomplemented
31#84116—51nomaximal, Hall
32C2×#4147D311yescharacteristic, complemented
33#66150—31no—
34#66082—32no—
35C2×C5×#101—31no—
36#65428—32no—
37#65042—34no—
38#65041—34no—
39C2×C3×C5×Q8—22no—
40C2×C3×C5×Q8—22no—
41C2×C3×C5×Q8D412yes—
42C2×C3×C5×Q8C2312yes—
43C22×C3×C4×C5D412yes—
44C22×C3×C4×C5C2311yescharacteristic
45C2×#1220—21no—
46#6817—22no—
47#6817—22no—
48C2×D60C2311yescharacteristic
49C2×C4×D15—21no—
50C2×Dic30C2311yescharacteristic
51C2×C3×C22⋊D5—22no—
52C3×#713—28no—
53C3×#713—28no—
54C3×Q8×D5—28no—
55C3×Q8×D5—28no—
56C3×#709—28no—
57C3×#709—28no—
58C3×#709—22no—
59C3×#709—22no—
60C3×#709D414yes—
61C3×#709C2314yes—
62C2×C3×D20—22no—
63C2×C3×D20D412yes—
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5—22no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10D412yes—
68#6719—21no—
69#6714—24no—
70C4⋊Dic15—21no—
71#6712—24no—
72C4×Dic15C2312yes—
73C5×#208—22no—
74C5×#208C2314yes—
75C2×C5×C3⋊C8—22no—
76#6662—24no—
77#6658—24no—
78#6657—24no—
79#6653—24no—
80C2×C3×2−1+4—51no—
81#5822—52no—
82#5816—51no—
83#5246—54no—
84#5245—54no—
85#5236—52no—
86C2×#836D511yescharacteristic, complemented
87C22×C5×Q8C2×D311yescharacteristic
88#4147—22no—
89#4147—24no—
90#4147C2×D314yes—
91C2×#713—22no—
92C2×Q8×D5—22no—
93C2×#709—22no—
94C2×#709—31no—
95C2×#709C2×D312yes—
96C2×C5×M16—32no—
97#4093—32no—
98#4092—62no—
99#4090—32no—
100#4075—62no—
101#4072—31no—
102#4055—34no—
103#4055—62no—
104#4054—34no—
105#4054—62no—
106#4050—64no—
107C5×#101—34no—
108#3957—38no—
109#3020—151noSylow
110C23×C3×C5C2×D411yescharacteristic
111C22×D15—21no—
112C22×C3×D5—22no—
113C3×C5×Q8—24no—
114C3×C5×Q8—24no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5C2×D414yes—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D412yes—
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2411yescharacteristic
122#1220—41no—
123#1220—41no—
124C2×Dic15—22no—
125C2×Dic15—21no—
126D60—22no—
127C4×D15—42no—
128Dic30—22no—
129C3×C22⋊D5—24no—
130C3×C22⋊D5—24no—
131C2×C3×Dic5—22no—
132C3×D20—28no—
133C3×D20—22no—
134C3×D20C2×D414yes—
135C3×C4×D5—216no—
136C3×C4×D5—24no—
137C3×C4×D5—24no—
138C3×Dic10—28no—
139C3×Dic10—22no—
140C3×Dic10C2×D414yes—
141C5×C3⋊C8—24no—
142C3×2−1+4—54no—
143C3×2−1+4—104no—
144C3×2−1+4—102no—
145C2×C3×#41—52no—
146C2×C3×#41—102no—
147C2×C3×#41—102no—
148C22×C3×Q8—102no—
149C22×C3×Q8C2×D511yescharacteristic
150C2×#235—51no—
151#951—54no—
152#950—104no—
153#949—54no—
154#947—52no—
155#946—102no—
156#944—52no—
157#942—102no—
158#932—102no—
159#929—102no—
160#926—51no—
161C2×#208C2×D512yes—
162#837—58no—
163#836C2×D514yescomplemented
164C2×C5×Q8—22no—
165C2×C5×Q8—22no—
166C2×C5×Q8#6712yes—
167C2×C5×Q8C22×D312yes—
168C22×C4×C5#6712yes—
169C22×C4×C5C22×D311yescharacteristic
170C2×C22⋊D5—22no—
171C2×C22⋊D5—61no—
172#713—28no—
173#713—28no—
174Q8×D5—28no—
175Q8×D5—28no—
176#709—28no—
177#709—28no—
178#709—22no—
179#709—22no—
180#709—62no—
181#709—62no—
182#709#6714yes—
183#709C22×D314yes—
184C2×D20—22no—
185C2×D20—31no—
186C2×D20#6712yes—
187C2×C4×D5—24no—
188C2×C4×D5—22no—
189C2×C4×D5—61no—
190C2×Dic10—22no—
191C2×Dic10—31no—
192C2×Dic10#6712yes—
193C5×M16—34no—
194C5×M16—62no—
195C2×C5×C8—62no—
196C22⋊Dic5—61no—
197#685—64no—
198C4⋊Dic5—61no—
199#683—64no—
200C4×Dic5—32no—
201Dic20—64no—
202D40—64no—
203#677—64no—
204#677—64no—
205C2×2−1+4—51no—
206#575—152no—
207#536—151no—
208#456—154no—
209#454—154no—
210#421—152no—
211C2×#101—31no—
212C22×C3×C5—41no—
213C22×C3×C5#12011yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5C22×D411yescharacteristic
216C2×D15—42no—
217C2×D15—41no—
218C2×C3×D5—24no—
219C2×C3×D5—44no—
220C3×C4×C5—24no—
221C3×C4×C5#12012yes—
222C3×C4×C5C22×D412yes—
223Dic15—42no—
224Dic15—41no—
225C3×Dic5—24no—
226C3×#41—54no—
227C3×#41—54no—
228C3×#41—108no—
229C3×#41—108no—
230C3×#41—108no—
231C3×#41—102no—
232C3×#41—108no—
233C3×#41—102no—
234C2×C3×Q8—22no—
235C2×C3×Q8—22no—
236C2×C3×Q8—52no—
237C2×C3×Q8—102no—
238C2×C3×Q8—108no—
239C2×C3×Q8—108no—
240C2×C3×Q8D2012yes—
241C2×C3×Q8C22×D512yes—
242C2×C3×D4—52no—
243C2×C3×D4—102no—
244C2×C3×D4—102no—
245C22×C3×C4—104no—
246C22×C3×C4—102no—
247C22×C3×C4D2012yes—
248C22×C3×C4C22×D511yescharacteristic
249C2×#67—101no—
250#235—102no—
251#235—102no—
252C2×D12—51no—
253C2×C4×D3—101no—
254C2×Dic6—51no—
255#217—101no—
256#216—104no—
257#215—104no—
258#214—104no—
259#213—104no—
260(C2×D3)⋊C4—104no—
261C4⋊Dic3—101no—
262Dic3⋊C4—104no—
263C4×Dic3—52no—
264#208—22no—
265#208C22×D514yes—
266C2×C3⋊C8—22no—
267C23×C5C2×#6711yescharacteristic
268C22×D5—22no—
269C22×D5—61no—
270C5×Q8—24no—
271C5×Q8—24no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5C2×#6714yes—
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6712yes—
277C2×C4×C5C2×#6712yes—
278C2×C4×C5C23×D311yescharacteristic
279C22⋊D5—24no—
280C22⋊D5—24no—
281C22⋊D5—121no—
282C22⋊D5—121no—
283C2×Dic5—22no—
284C2×Dic5—62no—
285C2×Dic5—61no—
286D20—28no—
287D20—22no—
288D20—62no—
289D20C2×#6714yes—
290C4×D5—216no—
291C4×D5—24no—
292C4×D5—24no—
293C4×D5—122no—
294Dic10—28no—
295Dic10—22no—
296Dic10—62no—
297Dic10C2×#6714yes—
298C5×C8—64no—
2992−1+4—54no—
3002−1+4—104no—
3012−1+4—102no—
302C2×#41—52no—
303C2×#41—102no—
304C2×#41—102no—
305C2×#41—151no—
306C22×Q8—102no—
307C22×Q8D3×D511yescharacteristic
308#137—154no—
309#137—302no—
310AGL(1,ℤ/8)—154no—
311AGL(1,ℤ/8)—302no—
312#135—304no—
313C2×M16—32no—
314C4⋊Q8—152no—
315#124—152no—
316#123—302no—
317C22⋊Q8—302no—
318#117—151no—
319#104—158no—
320#101—34no—
321C2×C3×C5—21no—
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5C2×#12011yescharacteristic
325D15—81no—
326C3×D5—44no—
327C23×C3—102no—
328C23×C3C2×D2011yescharacteristic
329C22×D3—101no—
330C3×Q8—24no—
331C3×Q8—24no—
332C3×Q8—54no—
333C3×Q8—108no—
334C3×Q8—102no—
335C3×D4—54no—
336C3×D4—108no—
337C3×D4—104no—
338C3×D4—104no—
339C3×D4—102no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—1016no—
343C2×C3×C4—102no—
344C2×C3×C4—104no—
345C2×C3×C4—104no—
346C2×C3×C4C2×D2014yes—
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4D4×D512yes—
349C2×C3×C4D4×D512yes—
350C2×C3×C4C23×D511yescharacteristic
351#67—201no—
352#67—201no—
353C2×Dic3—102no—
354C2×Dic3—101no—
355D12—102no—
356C4×D3—202no—
357Dic6—102no—
358C3⋊C8—24no—
359C22×C5—41no—
360C22×C5#95311yescharacteristic
361C22×C5#95311yescharacteristic
362C22×C5C22×#6711yescharacteristic
363C2×D5—24no—
364C2×D5—44no—
365C2×D5—122no—
366C2×D5—121no—
367C4×C5—24no—
368C4×C5#95312yes—
369C4×C5C22×#6712yes—
370Dic5—24no—
371Dic5—122no—
372Dic5—121no—
373#41—54no—
374#41—54no—
375#41—108no—
376#41—108no—
377#41—108no—
378#41—102no—
379#41—108no—
380#41—102no—
381#41—302no—
382#41—302no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—52no—
386C2×Q8—102no—
387C2×Q8—108no—
388C2×Q8—108no—
389C2×Q8—151no—
390C2×Q8#120212yes—
391C2×Q8C2×D3×D512yes—
392C2×D4—52no—
393C2×D4—102no—
394C2×D4—102no—
395C2×D4—151no—
396C2×D4—301no—
397C22×C4—104no—
398C22×C4—102no—
399C22×C4—301no—
400C22×C4#120212yes—
401C22×C4C2×D3×D511yescharacteristic
402Q16—304no—
403SD16—304no—
404SD16—304no—
405D8—304no—
406M16—34no—
407M16—62no—
408C2×C8—62no—
409C4⋊C4—301no—
410C4⋊C4—304no—
411C22⋊C4—301no—
412C22⋊C4—304no—
413C42—152no—
414C3×C5#302011yescharacteristic, complemented, Hall
415C22×C3—41no—
416C22×C3—104no—
417C22×C3—204no—
418C22×C3#402811yescharacteristic
419C22×C3#402811yescharacteristic
420C22×C3C22×D2011yescharacteristic
421C2×D3—202no—
422C2×D3—201no—
423C3×C4—24no—
424C3×C4—104no—
425C3×C4#402812yes—
426C3×C4C2×D4×D512yes—
427Dic3—202no—
428Dic3—201no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5C2×#95311yescharacteristic
433D5—44no—
434D5—241no—
435C23—102no—
436C23—301no—
437C23C2×#120211yescharacteristic
438Q8—24no—
439Q8—24no—
440Q8—54no—
441Q8—108no—
442Q8—102no—
443Q8—302no—
444D4—54no—
445D4—108no—
446D4—104no—
447D4—104no—
448D4—102no—
449D4—302no—
450D4—601no—
451D4—601no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—1016no—
455C2×C4—102no—
456C2×C4—104no—
457C2×C4—104no—
458C2×C4—302no—
459C2×C4—301no—
460C2×C4—602no—
461C2×C4C2×#120214yes—
462C2×C4C2×#120211yescharacteristic
463C2×C4D5×#6712yes—
464C2×C4D5×#6712yes—
465C2×C4C22×D3×D511yescharacteristic
466C8—64no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—204no—
471C2×C3C2×#402811yescharacteristic
472D3—401no—
473C5#8411611yescharacteristic, complemented, Sylow
474C22—41no—
475C22—104no—
476C22—204no—
477C22—602no—
478C22—601no—
479C22#9156411yescharacteristic
480C22#9156411yescharacteristic
481C22C22×#120211yescharacteristic
482C4—24no—
483C4—104no—
484C4—602no—
485C4—601no—
486C4#9156412yes—
487C4C2×D5×#6712yes—
488C3#1061044011yescharacteristic, complemented, Sylow
489C2—21no—
490C2—21no—
491C2—21no—
492C2—204no—
493C2—1201no—
494C2C2×#9156411yescharacteristic
subgroupG/H
centerC2C2×#91564
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC2×C3×C5C2×#120
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3020
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4147C2semidirect
2. #11756575C2semidirect
3. #11754154C2semidirect
4. C2×C5×#836C2semidirect
5. #11749391C2semidirect
6. #11749384C2semidirect
7. #11748420C2semidirect
18. #91836C22semidirect
20. #91833C22semidirect
25. #91313C22semidirect
28. #91301C22semidirect
29. C5×#836C22semidirect
30. #90976C22semidirect
32. C2×#4147D3semidirect
86. C2×#836D5semidirect
163. #836C2×D5semidirect
414. C3×C5#3020semidirect
473. C5#84116semidirect
488. C3#10610440semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41472
#117565752
#117541542
C2×C5×#8362
#117493912
#117493842
#117484202
#106104403
#841165