Finite Group Databasebeta

← #14425379

Subgroups — #14425379

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×C5×2−1+4C211yesmaximal, characteristic, complemented
2#11756581C212yesmaximal, complemented
3#11756575C211yesmaximal, characteristic, complemented
4#11751347C214yesmaximal, complemented
5#11751346C214yesmaximal, complemented
6#11751337C212yesmaximal, complemented
7C2×#91120C211yesmaximal, characteristic, complemented
8#10615847—31nomaximal, Hall
9C3×C5×2−1+4—24no—
10C3×C5×2−1+4—22no—
11C3×C5×2−1+4C2214yes—
12C2×C3×C5×#41—22no—
13C2×C3×C5×#41—22no—
14C2×C3×C5×#41C2212yes—
15C22×C3×C5×Q8—22no—
16C22×C3×C5×Q8C2211yescharacteristic
17C2×#6817C2211yescharacteristic
18#91840C2214yescomplemented
19#91839—24no—
20#91838C2214yescomplemented
21#91836C2212yescomplemented
22#91835—22no—
23#91833C2212yescomplemented
24#91831—22no—
25#91821—22no—
26#91818—22no—
27#91815C2211yescharacteristic
28C2×#6710C2212yes—
29#91121C2218yescomplemented
30#91120C2214yescomplemented
31#84116—51nomaximal, Hall
32C2×C5×2−1+4D311yescharacteristic, complemented
33#66156—32no—
34#66150—31no—
35#65535—34no—
36#65534—34no—
37#65525—32no—
38C2×#3968—31no—
39C3×C5×#41—28no—
40C3×C5×#41—28no—
41C3×C5×#41—28no—
42C3×C5×#41—28no—
43C3×C5×#41—22no—
44C3×C5×#41—22no—
45C3×C5×#41D414yes—
46C3×C5×#41C2314yes—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8—28no—
49C2×C3×C5×Q8—28no—
50C2×C3×C5×Q8—22no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8D412yes—
53C2×C3×C5×Q8D412yes—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4D412yes—
58C22×C3×C4×C5—24no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5D412yes—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817—22no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68#6719—21no—
69#6718—24no—
70#6717—24no—
71#6716—24no—
72#6715—24no—
73#6714—24no—
74C4⋊Dic15—21no—
75#6712—24no—
76C4×Dic15C2312yes—
77#6710—22no—
78#6710C2314yes—
79C2×C3⋊#168—22no—
80C2×C3×2−1+4D511yescharacteristic, complemented
81#5822—52no—
82#5816—51no—
83#5246—54no—
84#5245—54no—
85#5236—52no—
86C2×#836—51no—
87C5×2−1+4—24no—
88C5×2−1+4—22no—
89C5×2−1+4C2×D314yes—
90C2×C5×#41—22no—
91C2×C5×#41—22no—
92C2×C5×#41C2×D312yes—
93C22×C5×Q8—22no—
94C22×C5×Q8C2×D311yescharacteristic
95C2×#709—31no—
96#4097—34no—
97#4096—64no—
98#4095—34no—
99#4093—32no—
100#4092—62no—
101#4090—32no—
102#4088—62no—
103#4078—62no—
104#4075—62no—
105#4072—31no—
106C2×#681—32no—
107#3969—38no—
108#3968—34no—
109#3020—151noSylow
110C23×C3×C5—22no—
111C23×C3×C5C2×D411yescharacteristic
112C22×D15—21no—
113C3×C5×Q8—28no—
114C3×C5×Q8—22no—
115C3×C5×Q8—24no—
116C3×C5×Q8—24no—
117C3×C5×Q8C2×D414yes—
118C3×C5×D4—28no—
119C3×C5×D4—24no—
120C3×C5×D4—24no—
121C3×C5×D4—22no—
122C3×C5×D4C2×D414yes—
123C2×C3×C4×C5—216no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—24no—
128C2×C3×C4×C5—24no—
129C2×C3×C4×C5C2×D414yes—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134#1220—41no—
135#1220—41no—
136C2×Dic15—22no—
137C2×Dic15—21no—
138D60—22no—
139C4×D15—42no—
140Dic30—22no—
141C3⋊#168—24no—
142C3×2−1+4—24no—
143C3×2−1+4—22no—
144C3×2−1+4C2×D514yes—
145C2×C3×#41—22no—
146C2×C3×#41—22no—
147C2×C3×#41C2×D512yes—
148C22×C3×Q8—22no—
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×#208—52no—
162#837—58no—
163#836—54no—
164C5×#41—28no—
165C5×#41—28no—
166C5×#41—28no—
167C5×#41—28no—
168C5×#41—22no—
169C5×#41—22no—
170C5×#41#6714yes—
171C5×#41C22×D314yes—
172C2×C5×Q8—22no—
173C2×C5×Q8—28no—
174C2×C5×Q8—28no—
175C2×C5×Q8—22no—
176C2×C5×Q8—22no—
177C2×C5×Q8#6712yes—
178C2×C5×Q8#6712yes—
179C2×C5×Q8C22×D312yes—
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4#6712yes—
183C22×C4×C5—24no—
184C22×C4×C5—22no—
185C22×C4×C5#6712yes—
186C22×C4×C5C22×D311yescharacteristic
187C2×C22⋊D5—61no—
188#709—62no—
189#709—62no—
190C2×D20—31no—
191C2×C4×D5—61no—
192C2×Dic10—31no—
193C22⋊Dic5—61no—
194#689—64no—
195#688—64no—
196#687—64no—
197#686—64no—
198#685—64no—
199C4⋊Dic5—61no—
200#683—64no—
201C4×Dic5—32no—
202#681—34no—
203#681—62no—
204C2×#168—62no—
205C2×2−1+4D1511yescharacteristic, complemented
206#575—152no—
207#536—151no—
208#456—154no—
209#454—154no—
210#421—152no—
211C2×#101—151no—
212C22×C3×C5—24no—
213C22×C3×C5—41no—
214C22×C3×C5—44no—
215C22×C3×C5#12011yescharacteristic
216C22×C3×C5#12011yescharacteristic
217C22×C3×C5C22×D411yescharacteristic
218C2×D15—42no—
219C2×D15—41no—
220C3×C4×C5—24no—
221C3×C4×C5—24no—
222C3×C4×C5#12012yes—
223C3×C4×C5C22×D412yes—
224Dic15—42no—
225Dic15—41no—
226C3×#41—28no—
227C3×#41—28no—
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—22no—
231C3×#41—22no—
232C3×#41C22⋊D514yes—
233C3×#41C22×D514yes—
234C2×C3×Q8—22no—
235C2×C3×Q8—28no—
236C2×C3×Q8—28no—
237C2×C3×Q8—22no—
238C2×C3×Q8—22no—
239C2×C3×Q8C22⋊D512yes—
240C2×C3×Q8C22⋊D512yes—
241C2×C3×Q8C22×D512yes—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4C22⋊D512yes—
245C22×C3×C4—24no—
246C22×C3×C4—22no—
247C22×C3×C4C22⋊D512yes—
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—54no—
265#208—102no—
266C2×C3⋊C8—102no—
267C23×C5—22no—
268C23×C5C2×#6711yescharacteristic
269C22×D5—61no—
270C5×Q8—28no—
271C5×Q8—22no—
272C5×Q8—24no—
273C5×Q8—24no—
274C5×Q8C2×#6714yes—
275C5×D4—28no—
276C5×D4—24no—
277C5×D4—24no—
278C5×D4—22no—
279C5×D4C2×#6714yes—
280C2×C4×C5—216no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5C2×#6714yes—
287C2×C4×C5C2×#6711yescharacteristic
288C2×C4×C5C2×#6712yes—
289C2×C4×C5C2×#6712yes—
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—121no—
292C22⋊D5—121no—
293C2×Dic5—62no—
294C2×Dic5—61no—
295D20—62no—
296C4×D5—122no—
297Dic10—62no—
298#168—64no—
2992−1+4—24no—
3002−1+4—22no—
3012−1+4C2×D1514yes—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—151no—
305C2×#41C2×D1512yes—
306C22×Q8—22no—
307C22×Q8C2×D1511yescharacteristic
308#137—154no—
309#137—302no—
310AGL(1,ℤ/8)—154no—
311AGL(1,ℤ/8)—302no—
312#135—304no—
313C2×M16—152no—
314C4⋊Q8—152no—
315#124—152no—
316#123—302no—
317C22⋊Q8—302no—
318#117—151no—
319#104—158no—
320#101—154no—
321C2×C3×C5—21no—
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5—44no—
325C2×C3×C5C2×#12011yescharacteristic
326D15—81no—
327C23×C3—22no—
328C23×C3C2×C22⋊D511yescharacteristic
329C22×D3—101no—
330C3×Q8—28no—
331C3×Q8—22no—
332C3×Q8—24no—
333C3×Q8—24no—
334C3×Q8C2×C22⋊D514yes—
335C3×D4—28no—
336C3×D4—24no—
337C3×D4—24no—
338C3×D4—22no—
339C3×D4C2×C22⋊D514yes—
340C2×C3×C4—216no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4C2×C22⋊D514yes—
347C2×C3×C4C2×C22⋊D511yescharacteristic
348C2×C3×C4C2×C22⋊D512yes—
349C2×C3×C4C2×C22⋊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—104no—
359C22×C5—24no—
360C22×C5—41no—
361C22×C5—44no—
362C22×C5#95311yescharacteristic
363C22×C5#95311yescharacteristic
364C22×C5C22×#6711yescharacteristic
365C2×D5—122no—
366C2×D5—121no—
367C4×C5—24no—
368C4×C5—24no—
369C4×C5#95312yes—
370C4×C5C22×#6712yes—
371Dic5—122no—
372Dic5—121no—
373#41—28no—
374#41—28no—
375#41—28no—
376#41—28no—
377#41—22no—
378#41—22no—
379#41—302no—
380#41—302no—
381#41#122014yes—
382#41C22×D1514yes—
383C2×Q8—22no—
384C2×Q8—28no—
385C2×Q8—28no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—151no—
389C2×Q8#122012yes—
390C2×Q8#122012yes—
391C2×Q8C22×D1512yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—151no—
395C2×D4—301no—
396C2×D4#122012yes—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—301no—
400C22×C4#122012yes—
401C22×C4C22×D1511yescharacteristic
402Q16—304no—
403SD16—304no—
404SD16—304no—
405D8—304no—
406M16—154no—
407M16—302no—
408C2×C8—302no—
409C4⋊C4—301no—
410C4⋊C4—304no—
411C22⋊C4—301no—
412C22⋊C4—304no—
413C42—152no—
414C3×C5#302011yescharacteristic, complemented, Hall
415C22×C3—24no—
416C22×C3—41no—
417C22×C3—44no—
418C22×C3#409911yescharacteristic
419C22×C3#409911yescharacteristic
420C22×C3C22×C22⋊D511yescharacteristic
421C2×D3—202no—
422C2×D3—201no—
423C3×C4—24no—
424C3×C4—24no—
425C3×C4#409912yes—
426C3×C4C22×C22⋊D512yes—
427Dic3—202no—
428Dic3—201no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—44no—
433C2×C5C2×#95311yescharacteristic
434D5—241no—
435C23—22no—
436C23—301no—
437C23C2×#122011yescharacteristic
438Q8—28no—
439Q8—22no—
440Q8—24no—
441Q8—24no—
442Q8—302no—
443Q8C2×#122014yes—
444D4—28no—
445D4—24no—
446D4—24no—
447D4—22no—
448D4—302no—
449D4—601no—
450D4—601no—
451D4C2×#122014yes—
452C2×C4—216no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—302no—
459C2×C4—301no—
460C2×C4—602no—
461C2×C4C2×#122014yes—
462C2×C4C2×#122011yescharacteristic
463C2×C4C2×#122012yes—
464C2×C4C2×#122012yes—
465C2×C4C23×D1511yescharacteristic
466C8—304no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—44no—
471C2×C3C2×#409911yescharacteristic
472D3—401no—
473C5#8411611yescharacteristic, complemented, Sylow
474C22—24no—
475C22—41no—
476C22—44no—
477C22—602no—
478C22—601no—
479C22#9184211yescharacteristic
480C22#9184211yescharacteristic
481C22C22×#122011yescharacteristic
482C4—24no—
483C4—24no—
484C4—602no—
485C4—601no—
486C4#9184212yes—
487C4C22×#122012yes—
488C3#1061584711yescharacteristic, complemented, Sylow
489C2—21no—
490C2—21no—
491C2—21no—
492C2—44no—
493C2—1201no—
494C2C2×#9184211yescharacteristic
subgroupG/H
centerC2C2×#91842
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×2−1+4C2
socleC2×C3×C5C2×#120
hypercenterC2×2−1+4D15
hypocenterC3×C5#3020
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×2−1+4C2semidirect
2. #11756581C2semidirect
3. #11756575C2semidirect
4. #11751347C2semidirect
5. #11751346C2semidirect
6. #11751337C2semidirect
7. C2×#91120C2semidirect
18. #91840C22semidirect
20. #91838C22semidirect
21. #91836C22semidirect
23. #91833C22semidirect
29. #91121C22semidirect
30. #91120C22semidirect
32. C2×C5×2−1+4D3semidirect
80. C2×C3×2−1+4D5semidirect
205. C2×2−1+4D15semidirect
414. C3×C5#3020semidirect
473. C5#84116semidirect
488. C3#10615847semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×2−1+42
#117565812
#117565752
#117513472
#117513462
#117513372
C2×#911202
#106158473
#841165