Finite Group Databasebeta

← #14417569

Subgroups — #14417569

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic12C211yesmaximal, characteristic
2#11752516C212yesmaximal
3C4×Dic60C211yesmaximal, characteristic, complemented
4C4×C5×Dic12C211yesmaximal, characteristic, complemented
5C3×#64978C211yesmaximal, characteristic
6#11748122C212yesmaximal
7#11747851C211yesmaximal, characteristic, complemented
8Dic5×Dic12C211yesmaximal, characteristic, complemented
9#11747835C212yesmaximal, complemented
10#11747672C211yesmaximal, characteristic
11#11747093C212yesmaximal, complemented
12#10611451—31nomaximal, Hall
13C2×D5×Dic6C2212yes—
14C2×Dic60C2211yescharacteristic
15C4×Dic30C2212yes—
16C2×C5×Dic12C2211yescharacteristic
17C4×C5×Dic6C2212yes—
18C2×C3×#676C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×#4018C2211yescharacteristic
21#91394—22no—
22#91393—22no—
23#91358C2212yes—
24#91333C2212yes—
25Dic5×Dic6C2212yes—
26#91325—22no—
27#91324—22no—
28C2×#6663C2212yes—
29D5×Dic12C418yescomplemented
30C3×C4×C5×C8C2211yescharacteristic
31#91102C2211yescharacteristic
32#91100C2212yes—
33C5×#818C2211yescharacteristic
34C5×#816C2212yes—
35C3×#3947C2211yescharacteristic
36C3×C8×Dic5C2211yescharacteristic
37C3×#3935C2211yescharacteristic
38#90985C2212yes—
39#90975C2212yes—
40#90973C2212yes—
41#78573—51nomaximal, Hall
42C2×D5×Q16—31no—
43#65906—32no—
44C4×C5×Q16—31no—
45Q16×Dic5—31no—
46#65319—32no—
47#65169—31no—
48#65162—31no—
49#65091—32no—
50#65078—32no—
51C4×Dic20—31no—
52#64978D311yescharacteristic
53C2×Dic30C2312yes—
54C2×C5×Dic6C2312yes—
55C2×C3×C4×D5C2311yescharacteristic
56C2×#1204—22no—
57C2×D5×Dic3—22no—
58D5×Dic6—24no—
59D5×Dic6C2×C418yes—
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15C2312yes—
64#6712—22no—
65C4×Dic15—22no—
66Dic60C2×C414yes—
67C5×C4⋊Dic3C2312yes—
68C5×Dic3⋊C4—22no—
69C4×C5×Dic3—22no—
70C5×Dic12C2×C414yes—
71C3×#685D411yescharacteristic
72C3×#685D411yescharacteristic
73C3×#683D411yescharacteristic
74C3×#683D411yescharacteristic
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78C3×#676—22no—
79C3×C8×D5C2×C414yes—
80Dic3⋊Dic5—22no—
81#6669—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6663C2×C418yes—
87C22×Dic12—51no—
88#5516—52no—
89C3×#405—51no—
90#5120—52no—
91#5106—51no—
92#4716—52no—
93#4716—52no—
94C4×Dic12—51no—
95C4×Dic12—51no—
96C4×Dic12—51no—
97C4×Dic12D511yescharacteristic, complemented
98C2×Q8×D5—32no—
99C2×C5×Q16—31no—
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#689—32no—
103D5×Q16—38no—
104C2×Dic20—31no—
105C2×#676C2×D311yescharacteristic
106C2×C8×D5C2×D311yescharacteristic
107#4038—32no—
108#4038—62no—
109#4033—32no—
110#4033—62no—
111#4018—62no—
112#4018C2×D311yescharacteristic
113C4×Dic10—32no—
114C4×Dic10—62no—
115C5×#107—31no—
116C5×#103—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3950—31no—
120#3948—32no—
121#3947C2×D311yescharacteristic
122C8×Dic5C2×D311yescharacteristic
123#3942—32no—
124#3940—32no—
125#3935C2×D311yescharacteristic
126#2950—151noSylow
127C22×C3×D5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—22no—
132C2×Dic15—22no—
133Dic30—22no—
134Dic30C22×C414yes—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—22no—
137C5×Dic6—22no—
138C5×Dic6C22×C414yes—
139C2×C3×Dic5C2×D411yescharacteristic
140C2×C3×Dic5C2×D411yescharacteristic
141C2×C3×Dic5C2×D411yescharacteristic
142C3×C4×D5C22×C412yes—
143C3×C4×D5#4112yes—
144#1204—28no—
145D5×Dic3—28no—
146C3×C5×C8—21no—
147C3×C5×C8C22×C412yes—
148C3×#168—21no—
149C3×#168C22×C412yes—
150C22×Dic6—52no—
151C2×C3×M16—51no—
152C22×C3×C8—51no—
153C3×#117—51no—
154#926—52no—
155C2×Dic12—52no—
156C2×Dic12—51no—
157C2×Dic12—58no—
158C2×Dic12C2×D511yescharacteristic
159#887—102no—
160#887—102no—
161#877—102no—
162#877—102no—
163C4×Dic6—52no—
164C4×Dic6—52no—
165C4×Dic6—52no—
166C4×Dic6C2×D512yes—
167C3×#97—51no—
168C3×#97—51no—
169C3×C4×C8—51no—
170C3×C4×C8C2×D511yescharacteristic
171#818—51no—
172#818C2×D511yescharacteristic
173#817—52no—
174#816—52no—
175#816—52no—
176#816—52no—
177#816C2×D512yes—
178C2×C5×Q8—32no—
179Q8×D5—38no—
180Q8×D5—64no—
181C2×C4×D5—62no—
182C2×C4×D5C22×D311yescharacteristic
183C2×Dic10—32no—
184C2×Dic10—62no—
185C5×Q16—34no—
186C2×C5×C8C22×D311yescharacteristic
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—32no—
189C5×C4⋊C4—62no—
190C42×C5—62no—
191C42×C5C22×D311yescharacteristic
192#689—38no—
193#685—62no—
194#685D1211yescharacteristic
195#685D1211yescharacteristic
196C4⋊Dic5—32no—
197C4⋊Dic5—62no—
198#683—62no—
199#683—62no—
200#683D1211yescharacteristic
201#683D1211yescharacteristic
202C4×Dic5—62no—
203C4×Dic5—62no—
204C4×Dic5—62no—
205C4×Dic5—62no—
206C4×Dic5C22×D311yescharacteristic
207C2×#168C22×D311yescharacteristic
208C2×#168C22×D311yescharacteristic
209Dic20—34no—
210#676—22no—
211C8×D5C4×D314yes—
212C22×Q16—151no—
213#519—152no—
214#441—152no—
215#441—152no—
216C4×Q16—31no—
217C4×Q16—151no—
218C4×Q16—151no—
219C4×Q16—151no—
220#427—151no—
221#419—152no—
222#405—51no—
223C22×C3×C5C22×D411yescharacteristic
224C2×C3×D5—21no—
225C2×C3×D5—21no—
226C2×C3×D5C4×D412yes—
227C3×C4×C5—21no—
228C3×C4×C5—21no—
229C3×C4×C5C23×C411yescharacteristic
230C3×C4×C5C2×#4111yescharacteristic
231Dic15—24no—
232Dic15—42no—
233C3×Dic5—21no—
234C3×Dic5—21no—
235C3×Dic5C4×D412yes—
236C5×Dic3—24no—
237C5×Dic3—42no—
238C22×C3×C4—51no—
239C22×Dic3—102no—
240C2×Dic6—52no—
241C2×Dic6—58no—
242C2×Dic6—104no—
243C2×Dic6—102no—
244C2×Dic6C22×D512yes—
245C3×M16—102no—
246C2×C3×C8—51no—
247C2×C3×C8—54no—
248C2×C3×C8—51no—
249C2×C3×C8C22×D511yescharacteristic
250C2×C3×C8C22×D511yescharacteristic
251C3×C4⋊C4—51no—
252C3×C4⋊C4—51no—
253C3×C22⋊C4—51no—
254C3×C22⋊C4—51no—
255C3×C42—51no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258C4⋊Dic3—52no—
259C4⋊Dic3C22×D512yes—
260Dic3⋊C4—22no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—102no—
264C4×Dic3—22no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C4×Dic3—102no—
268C4×Dic3—102no—
269Dic12—58no—
270Dic12—54no—
271Dic12C4×D514yes—
272C22×D5C2×D1211yescharacteristic
273C5×Q8—34no—
274C5×Q8—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5C2×D1211yescharacteristic
278C2×C4×C5C2×D1211yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5C2×D1211yescharacteristic
283C2×Dic5C2×D1211yescharacteristic
284C2×Dic5C2×D1211yescharacteristic
285C4×D5—68no—
286C4×D5C2×C4×D312yes—
287C4×D5#23512yes—
288Dic10—34no—
289Dic10—62no—
290Dic10—68no—
291C5×C8—21no—
292C5×C8C2×C4×D312yes—
293#168—21no—
294#168C2×C4×D312yes—
295C22×Q8—152no—
296C2×Q16—31no—
297C2×Q16—158no—
298C2×Q16—152no—
299C2×Q16—151no—
300C2×M16—51no—
301C22×C8—51no—
302C4×Q8—32no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—302no—
307C4×Q8—302no—
308#117—51no—
309#117—152no—
310#117—302no—
311#117—302no—
312#107—31no—
313#107—151no—
314#106—152no—
315#103—32no—
316#103—152no—
317#103—152no—
318#103—152no—
319#97—51no—
320#97—51no—
321C4×C8—51no—
322C4×C8D3×D511yescharacteristic
323C2×C3×C5C2×C4×D411yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C2×C3×C5#57811yescharacteristic
326C3×D5—22no—
327C23×C3—51no—
328C2×C3×C4—51no—
329C2×C3×C4—52no—
330C2×C3×C4—52no—
331C2×C3×C4—51no—
332C2×C3×C4—51no—
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4C23×D511yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—108no—
339C2×Dic3—102no—
340C2×Dic3—102no—
341Dic6—22no—
342Dic6—54no—
343Dic6—108no—
344Dic6—102no—
345Dic6C2×C4×D514yes—
346C3×C8—21no—
347C3×C8—52no—
348C3×C8—101no—
349C3×C8C2×C4×D512yes—
350C22×C5C22×D1211yescharacteristic
351C2×D5—21no—
352C2×D5—21no—
353C2×D5C4×D1212yes—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—64no—
357C4×C5—122no—
358C4×C5C22×C4×D311yescharacteristic
359C4×C5C2×#23511yescharacteristic
360Dic5—21no—
361Dic5—21no—
362Dic5—64no—
363Dic5—122no—
364Dic5C4×D1212yes—
365C2×Q8—32no—
366C2×Q8—158no—
367C2×Q8—152no—
368C2×Q8—302no—
369C2×Q8—304no—
370C22×C4—51no—
371C22×C4—302no—
372Q16—34no—
373Q16—158no—
374Q16—154no—
375M16—102no—
376C2×C8—51no—
377C2×C8—54no—
378C2×C8—51no—
379C2×C8C2×D3×D511yescharacteristic
380C2×C8C2×D3×D511yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—51no—
383C4⋊C4—51no—
384C4⋊C4—62no—
385C4⋊C4—152no—
386C4⋊C4—302no—
387C4⋊C4—302no—
388C4⋊C4—302no—
389C22⋊C4—51no—
390C22⋊C4—51no—
391C22⋊C4—302no—
392C42—51no—
393C42—62no—
394C42—302no—
395C42—302no—
396C42—302no—
397C42—302no—
398C42C2×D3×D511yescharacteristic
399C3×C5#295011yescharacteristic, complemented, Hall
400C22×C3—52no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3C2×D4×D511yescharacteristic
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—52no—
407C3×C4—101no—
408C3×C4—101no—
409C3×C4C22×C4×D511yescharacteristic
410C3×C4D5×#4111yescharacteristic
411Dic3—24no—
412Dic3—42no—
413Dic3—104no—
414Dic3—202no—
415C2×C5C2×C4×D1211yescharacteristic
416C2×C5#575311yescharacteristic
417C2×C5#575311yescharacteristic
418D5—22no—
419C23—51no—
420Q8—34no—
421Q8—62no—
422Q8—154no—
423Q8—308no—
424Q8—302no—
425C2×C4—51no—
426C2×C4—52no—
427C2×C4—52no—
428C2×C4—51no—
429C2×C4—51no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—308no—
433C2×C4—302no—
434C2×C4—302no—
435C2×C4D5×D1211yescharacteristic
436C2×C4D5×D1211yescharacteristic
437C2×C4C22×D3×D511yescharacteristic
438C8—21no—
439C8—52no—
440C8—101no—
441C8C4×D3×D512yes—
442C2×C3—102no—
443C2×C3C4×D4×D511yescharacteristic
444C2×C3#6610011yescharacteristic
445C2×C3#6610511yescharacteristic
446C5#7857311yescharacteristic, complemented, Sylow
447C22—52no—
448C22—101no—
449C22—101no—
450C22C2×D5×D1211yescharacteristic
451C4—21no—
452C4—21no—
453C4—52no—
454C4—64no—
455C4—101no—
456C4—101no—
457C4—122no—
458C4—304no—
459C4—602no—
460C4C2×C4×D3×D511yescharacteristic
461C4D5×#23511yescharacteristic
462C3#1061145111yescharacteristic, complemented, Sylow
463C2—102no—
464C2C4×D5×D1211yescharacteristic
465C2#1175398711yescharacteristic
466C2#1175398811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C4×Dic60C2semidirect
4. C4×C5×Dic12C2semidirect
7. #11747851C2semidirect
8. Dic5×Dic12C2semidirect
9. #11747835C2semidirect
11. #11747093C2semidirect
29. D5×Dic12C4semidirect
97. C4×Dic12D5semidirect
399. C3×C5#2950semidirect
446. C5#78573semidirect
462. C3#10611451semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic122
#117525162
C4×Dic602
C4×C5×Dic122
C3×#649782
#117481222
#117478512
Dic5×Dic122
#117478352
#117476722
#117470932
#106114513
#785735