Finite Group Databasebeta

← #14417599

Subgroups — #14417599

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#11753397C212yesmaximal
3#11750974C211yesmaximal, characteristic, complemented
4C5×#4873C211yesmaximal, characteristic, complemented
5C3×#65169C211yesmaximal, characteristic
6#11747886C211yesmaximal, characteristic, complemented
7#11747873C211yesmaximal, characteristic, complemented
8#11747645C211yesmaximal, characteristic
9#11747487C212yesmaximal
10#11747281C212yesmaximal, complemented
11#11747276C212yesmaximal, complemented
12#10611451—31nomaximal, Hall
13C2×D5×Dic6C2212yes—
14C2×Dic60C2211yescharacteristic
15#91776C2212yes—
16C2×C5×Dic12C2211yescharacteristic
17C5×#887C2212yes—
18C2×C3×C8×D5C2211yescharacteristic
19C3×#4038C2212yes—
20C4×#1204—22no—
21#91394—22no—
22#91393—22no—
23#91357C2211yescharacteristic
24#91344C2212yes—
25#91340C2212yes—
26#91323—22no—
27C2×#6663C2212yes—
28C2×#6649C2211yescharacteristic
29D5×Dic12C418yescomplemented
30C3×C5×#107C2211yescharacteristic
31C8×Dic15C2211yescharacteristic
32#91094C2212yes—
33C5×C8×Dic3C2211yescharacteristic
34C5×#810C2212yes—
35C3×#3950C2211yescharacteristic
36C3×#3940C2212yes—
37#90974C2212yes—
38#90972C2212yes—
39#90954C2211yescharacteristic
40#90953C2211yescharacteristic
41#79169—51nomaximal, Hall
42C2×D5×Q16—31no—
43#65906—32no—
44C4×C5×Q16—31no—
45Q16×Dic5—31no—
46#65319—32no—
47#65169D311yescharacteristic
48#65162—31no—
49#65091—32no—
50#65078—32no—
51C4×Dic20—31no—
52#64978—31no—
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
61C3×C5×C4⋊C4C2312yes—
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15C2311yescharacteristic
65C2×C3⋊#168C2311yescharacteristic
66Dic60C2×C414yes—
67C5×Dic3⋊C4—22no—
68C4×C5×Dic3—22no—
69C4×C5×Dic3C2311yescharacteristic
70C2×C5×C3⋊C8C2311yescharacteristic
71C5×Dic12C2×C414yes—
72C3×#685—22no—
73C3×C4⋊Dic5C2312yes—
74C3×C4×Dic5—22no—
75C2×C3×#168C2311yescharacteristic
76C3×C8×D5C2×C414yes—
77Dic3⋊Dic5—22no—
78#6669—22no—
79#6668D411yescharacteristic
80#6668D411yescharacteristic
81#6665D411yescharacteristic
82#6665D411yescharacteristic
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6663C2×C418yes—
86#6649—22no—
87C22×Dic12—51no—
88#5516—52no—
89C3×#427—51no—
90#5101—51no—
91#5004—52no—
92#4873—51no—
93#4873—51no—
94#4873—51no—
95#4873D511yescharacteristic, complemented
96#4853—52no—
97#4853—52no—
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×#676—31no—
106C2×C8×D5C2×D311yescharacteristic
107#4038—62no—
108#4038C2×D312yes—
109#4033—32no—
110#4033—62no—
111#4018—31no—
112#4018—62no—
113C4×Dic10—32no—
114C4×Dic10—62no—
115C5×#107C2×D311yescharacteristic
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967—32no—
119#3950C2×D311yescharacteristic
120#3948—32no—
121#3947—31no—
122C8×Dic5—31no—
123#3942—32no—
124#3940C2×D312yes—
125#3935—31no—
126#2950—151noSylow
127C22×C3×D5C2×D411yescharacteristic
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—22no—
131C2×Dic15C2×D411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133Dic30—22no—
134Dic30C22×C414yes—
135C2×C5×Dic3—22no—
136C2×C5×Dic3C2×D411yescharacteristic
137C2×C5×Dic3C2×D411yescharacteristic
138C5×Dic6—22no—
139C5×Dic6C22×C414yes—
140C2×C3×Dic5—22no—
141C2×C3×Dic5C2×D411yescharacteristic
142C3×C4×D5C22×C412yes—
143C3×C4×D5#4112yes—
144#1204—28no—
145D5×Dic3—28no—
146C3×C5×C8C22×C412yes—
147C3⋊#168—21no—
148C3×#168C22×C412yes—
149C5×C3⋊C8—21no—
150C22×Dic6—52no—
151C22×C3×C8—51no—
152C3×#117—52no—
153#926—51no—
154C2×#208—51no—
155C2×Dic12—52no—
156C2×Dic12—51no—
157C2×Dic12—58no—
158C2×Dic12C2×D511yescharacteristic
159#887—52no—
160#887—52no—
161#887—52no—
162#887C2×D512yes—
163#877—102no—
164#877—102no—
165C4×Dic6—102no—
166C4×Dic6—102no—
167C3×#107—51no—
168C3×#107C2×D511yescharacteristic
169C3×#106—52no—
170#815—51no—
171#815—51no—
172C8×Dic3—51no—
173C8×Dic3C2×D511yescharacteristic
174#810—52no—
175#810—52no—
176#810—52no—
177#810C2×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×C8—31no—
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—62no—
189C5×C4⋊C4C22×D312yes—
190C42×C5—31no—
191C42×C5—62no—
192#689—38no—
193#685—22no—
194#685—31no—
195#685—31no—
196C4⋊Dic5—62no—
197C4⋊Dic5C22×D312yes—
198#683—31no—
199#683—31no—
200#683—62no—
201#683—62no—
202C4×Dic5—22no—
203C4×Dic5—31no—
204C4×Dic5—62no—
205C4×Dic5—62no—
206C4×Dic5—62no—
207C2×#168—31no—
208C2×#168C22×D311yescharacteristic
209Dic20—34no—
210#676—62no—
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—51no—
221#419—152no—
222#405—151no—
223C22×C3×C5C22×D411yescharacteristic
224C2×C3×D5—21no—
225C2×C3×D5—21no—
226C2×C3×D5C4×D412yes—
227C3×C4×C5—42no—
228C3×C4×C5C23×C411yescharacteristic
229C3×C4×C5C2×#4111yescharacteristic
230Dic15—24no—
231Dic15—21no—
232Dic15—21no—
233C3×Dic5—42no—
234C3×Dic5C4×D412yes—
235C5×Dic3—24no—
236C5×Dic3—21no—
237C5×Dic3—21no—
238C22×C3×C4—51no—
239C22×Dic3—102no—
240C2×Dic6—52no—
241C2×Dic6—58no—
242C2×Dic6—104no—
243C2×Dic6—102no—
244C2×Dic6C22×D512yes—
245C2×C3×C8—51no—
246C2×C3×C8—54no—
247C2×C3×C8C22×D511yescharacteristic
248C3×C4⋊C4—52no—
249C3×C4⋊C4C22×D512yes—
250C3×C22⋊C4—102no—
251C3×C42—102no—
252#217—51no—
253#217—51no—
254C4⋊Dic3—51no—
255C4⋊Dic3—51no—
256Dic3⋊C4—22no—
257Dic3⋊C4—102no—
258Dic3⋊C4—102no—
259Dic3⋊C4—102no—
260C4×Dic3—22no—
261C4×Dic3—51no—
262C4×Dic3—102no—
263C4×Dic3—102no—
264C4×Dic3—102no—
265C4×Dic3C22×D511yescharacteristic
266#208—102no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8C22×D511yescharacteristic
269Dic12—58no—
270Dic12—54no—
271Dic12C4×D514yes—
272C22×D5D3×D411yescharacteristic
273C5×Q8—34no—
274C5×Q8—62no—
275C2×C4×C5—22no—
276C2×C4×C5—31no—
277C2×C4×C5—31no—
278C2×C4×C5—62no—
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—31no—
282C2×Dic5—31no—
283C2×Dic5—62no—
284C2×Dic5D3×D411yescharacteristic
285C4×D5—68no—
286C4×D5C2×C4×D312yes—
287C4×D5#23912yes—
288Dic10—34no—
289Dic10—62no—
290Dic10—68no—
291C5×C8—61no—
292C5×C8C2×C4×D312yes—
293#168—61no—
294#168C2×C4×D312yes—
295C22×Q8—152no—
296C2×Q16—31no—
297C2×Q16—158no—
298C2×Q16—152no—
299C2×Q16—151no—
300C2×M16—151no—
301C22×C8—51no—
302C4×Q8—32no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—302no—
307C4×Q8—302no—
308#117—52no—
309#117—151no—
310#117—302no—
311#117—302no—
312#107—51no—
313#107D3×D511yescharacteristic
314#106—52no—
315#103—32no—
316#103—152no—
317#103—152no—
318#103—152no—
319#97—151no—
320#97—151no—
321C4×C8—31no—
322C4×C8—151no—
323C2×C3×C5C2×C4×D411yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C2×C3×C5#57811yescharacteristic
326C3×D5—22no—
327C23×C3—51no—
328C2×C3×C4—22no—
329C2×C3×C4—51no—
330C2×C3×C4—52no—
331C2×C3×C4—52no—
332C2×C3×C4—102no—
333C2×C3×C4C23×D511yescharacteristic
334C2×Dic3—22no—
335C2×Dic3—51no—
336C2×Dic3—51no—
337C2×Dic3—108no—
338C2×Dic3—102no—
339C2×Dic3D4×D511yescharacteristic
340C2×Dic3D4×D511yescharacteristic
341Dic6—22no—
342Dic6—54no—
343Dic6—108no—
344Dic6—102no—
345Dic6C2×C4×D514yes—
346C3×C8—52no—
347C3×C8C2×C4×D512yes—
348C3⋊C8—21no—
349C3⋊C8—101no—
350C22×C5C2×D3×D411yescharacteristic
351C2×D5—21no—
352C2×D5—21no—
353C2×D5#89312yes—
354C4×C5—42no—
355C4×C5—64no—
356C4×C5—61no—
357C4×C5—61no—
358C4×C5C22×C4×D311yescharacteristic
359C4×C5C2×#23911yescharacteristic
360Dic5—42no—
361Dic5—64no—
362Dic5—61no—
363Dic5—61no—
364Dic5#89312yes—
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—302no—
376C2×C8—31no—
377C2×C8—51no—
378C2×C8—54no—
379C2×C8—151no—
380C2×C8C2×D3×D511yescharacteristic
381C4⋊C4—52no—
382C4⋊C4—62no—
383C4⋊C4—151no—
384C4⋊C4—151no—
385C4⋊C4—302no—
386C4⋊C4—302no—
387C4⋊C4—302no—
388C4⋊C4C2×D3×D512yes—
389C22⋊C4—102no—
390C22⋊C4—151no—
391C22⋊C4—151no—
392C42—31no—
393C42—62no—
394C42—102no—
395C42—151no—
396C42—302no—
397C42—302no—
398C42—302no—
399C3×C5#295011yescharacteristic, complemented, Hall
400C22×C3—52no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3C2×D4×D511yescharacteristic
404C3×C4—42no—
405C3×C4—52no—
406C3×C4—202no—
407C3×C4C22×C4×D511yescharacteristic
408C3×C4D5×#4111yescharacteristic
409Dic3—21no—
410Dic3—21no—
411Dic3—24no—
412Dic3—101no—
413Dic3—101no—
414Dic3—104no—
415C2×C5C2×#89311yescharacteristic
416C2×C5#577111yescharacteristic
417C2×C5#577111yescharacteristic
418D5—22no—
419C23—51no—
420Q8—34no—
421Q8—62no—
422Q8—154no—
423Q8—308no—
424Q8—302no—
425C2×C4—22no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—51no—
429C2×C4—52no—
430C2×C4—52no—
431C2×C4—62no—
432C2×C4—102no—
433C2×C4—151no—
434C2×C4—151no—
435C2×C4—308no—
436C2×C4—302no—
437C2×C4C22×D3×D511yescharacteristic
438C8—52no—
439C8—61no—
440C8—301no—
441C8C4×D3×D512yes—
442C2×C3—102no—
443C2×C3C4×D4×D511yescharacteristic
444C2×C3#6610011yescharacteristic
445C2×C3#6610511yescharacteristic
446C5#7916911yescharacteristic, complemented, Sylow
447C22—52no—
448C22—101no—
449C22—101no—
450C22D3×D4×D511yescharacteristic
451C4—42no—
452C4—52no—
453C4—61no—
454C4—64no—
455C4—61no—
456C4—202no—
457C4—301no—
458C4—304no—
459C4—301no—
460C4C2×C4×D3×D511yescharacteristic
461C4D5×#23911yescharacteristic
462C3#1061145111yescharacteristic, complemented, Sylow
463C2—102no—
464C2D5×#89311yescharacteristic
465C2#1175406311yescharacteristic
466C2#1175411311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #11750974C2semidirect
4. C5×#4873C2semidirect
6. #11747886C2semidirect
7. #11747873C2semidirect
10. #11747281C2semidirect
11. #11747276C2semidirect
29. D5×Dic12C4semidirect
95. #4873D5semidirect
399. C3×C5#2950semidirect
446. C5#79169semidirect
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
#117533972
#117509742
C5×#48732
C3×#651692
#117478862
#117478732
#117476452
#117474872
#117472812
#117472762
#106114513
#791695