Finite Group Databasebeta

← #14417709

Subgroups — #14417709

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4065C211yesmaximal, characteristic
2#11755217C212yesmaximal, complemented
3Q16×Dic15C211yesmaximal, characteristic, complemented
4C5×Dic3×Q16C211yesmaximal, characteristic, complemented
5#11749241C212yesmaximal, complemented
6#11749234C212yesmaximal, complemented
7#11749198C212yesmaximal, complemented
8#11747809C211yesmaximal, characteristic, complemented
9Dic3×D40C211yesmaximal, characteristic, complemented
10#11747645C211yesmaximal, characteristic, complemented
11D5×#818C211yesmaximal, characteristic, complemented
12#10611452—31nomaximal, Hall
13C2×C3×#713C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15Q8×Dic15C2212yes—
16C5×Q8×Dic3C2212yes—
17C2×C3×#688C2212yes—
18C3×#4065C418yescomplemented
19C2×C3×D40C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21#91434—22no—
22#91434C2212yes—
23Dic3×D20—22no—
24Dic3×D20C2212yes—
25D5×C4⋊Dic3—22no—
26D5×C4⋊Dic3C2212yes—
27#91357—22no—
28#91357C2211yescharacteristic
29C2×#6649C2211yescharacteristic
30#91119C2212yes—
31#91102C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C5×#835C2212yes—
34C5×#818C2211yescharacteristic
35C5×C8×Dic3C2211yescharacteristic
36#90988C2212yes—
37#90965C2212yes—
38#90964C2212yes—
39#90954C2211yescharacteristic
40#90953C2211yescharacteristic
41#83898—51nomaximal, Hall
42C2×#4065D311yescharacteristic
43#65908—32no—
44C4×C5×Q16—31no—
45Q16×Dic5—31no—
46#65315—32no—
47D5×#107—31no—
48#65161—31no—
49#65106—32no—
50#65092—32no—
51C4×D40—31no—
52#64978—31no—
53C2×C3×C5×Q8C2312yes—
54C3×#713—24no—
55C3×#713C2×C418yescomplemented
56C2×C3×D20—22no—
57C2×C3×D20C2312yes—
58C2×C3×C4×D5—22no—
59C2×C3×C4×D5C2311yescharacteristic
60C2×D5×Dic3—22no—
61C2×D5×Dic3—22no—
62C2×D5×Dic3—22no—
63C3×C5×Q16C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C4⋊Dic15—22no—
66C4⋊Dic15C2312yes—
67C4×Dic15—22no—
68C4×Dic15C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×C4⋊Dic3—22no—
71C5×C4⋊Dic3C2312yes—
72C4×C5×Dic3—22no—
73C4×C5×Dic3C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C3×#688C2×C418yescomplemented
76C2×C3×#168C2311yescharacteristic
77C3×D40C2×C414yescomplemented
78C3×C8×D5C2×C414yescomplemented
79#6668—22no—
80#6668D411yescharacteristic
81#6668D411yescharacteristic
82#6665—22no—
83#6665—22no—
84#6665D411yescharacteristic
85#6665D411yescharacteristic
86#6649—22no—
87C2×C3×#135—51no—
88#5827—52no—
89#5232—52no—
90Dic3×Q16—51no—
91Dic3×Q16D511yescharacteristic, complemented
92#5164—52no—
93#5164—52no—
94Dic3×D8—51no—
95Dic3×D8—51no—
96C2×#818—51no—
97#5101—51no—
98C2×#713C2×D312yes—
99C2×C5×Q16C2×D311yescharacteristic
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#688C2×D312yes—
103#4065Dic318yescomplemented
104C2×D40C2×D311yescharacteristic
105C2×#676—31no—
106C2×C8×D5C2×D311yescharacteristic
107#4039—32no—
108#4039—62no—
109D5×C4⋊C4—32no—
110D5×C4⋊C4—62no—
111C4×D20—32no—
112C4×D20—62no—
113#4018—31no—
114#4018—62no—
115C5×#107—31no—
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—32no—
120#3950—31no—
121#3947—31no—
122C8×Dic5—31no—
123#3941—32no—
124#3939—32no—
125#3935—31no—
126#2951—151noSylow
127C22×C3×D5—22no—
128C22×C3×D5C2×D411yescharacteristic
129C3×C5×Q8—22no—
130C3×C5×Q8C22×C414yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—22no—
134C2×Dic15C2×D411yescharacteristic
135C2×Dic15C2×D411yescharacteristic
136C2×C5×Dic3—22no—
137C2×C5×Dic3C2×D411yescharacteristic
138C2×C5×Dic3C2×D411yescharacteristic
139C2×C3×Dic5C2×D411yescharacteristic
140C3×D20—28no—
141C3×D20—22no—
142C3×D20C22×C414yes—
143C3×C4×D5—28no—
144C3×C4×D5C22×C412yes—
145C3×C4×D5#4112yes—
146D5×Dic3—82no—
147D5×Dic3—82no—
148D5×Dic3—82no—
149C3×C5×C8C22×C412yes—
150C3⋊#168—21no—
151C3×#168C22×C412yes—
152C5×C3⋊C8—21no—
153C2×C3×#41—52no—
154C3×#135—58no—
155C2×C3×Q16C2×D511yescharacteristic
156C2×C3×SD16—52no—
157C2×C3×D8—51no—
158C22×C3×C8—51no—
159Q8×Dic3—52no—
160Q8×Dic3C2×D512yes—
161D4×Dic3—52no—
162D4×Dic3—52no—
163D4×Dic3—102no—
164D4×Dic3—102no—
165#926—51no—
166#926—102no—
167C2×C4⋊Dic3—52no—
168C2×C4⋊Dic3—102no—
169C2×#208—51no—
170#835—52no—
171#835C2×D512yes—
172#832—52no—
173#832—52no—
174#818—51no—
175#818—52no—
176#818C2×D511yescharacteristic
177#815—51no—
178#815—51no—
179C8×Dic3—51no—
180C8×Dic3C2×D511yescharacteristic
181C2×C5×Q8C22×D312yes—
182#713—24no—
183#713C2×Dic318yescomplemented
184C2×D20—22no—
185C2×D20C22×D312yes—
186C2×C4×D5—22no—
187C2×C4×D5—62no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×C4×D5C22×D311yescharacteristic
191C5×Q16C2×Dic314yescomplemented
192C2×C5×C8—31no—
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—32no—
195C5×C4⋊C4—62no—
196C42×C5—31no—
197C42×C5—62no—
198#688C2×Dic318yescomplemented
199#685—31no—
200#685—31no—
201#685—62no—
202#685—62no—
203C4⋊Dic5—32no—
204C4⋊Dic5—62no—
205#683—31no—
206#683—31no—
207#683—62no—
208C4×Dic5—31no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168C22×D311yescharacteristic
212D40C2×Dic314yescomplemented
213#676—62no—
214C8×D5C2×Dic314yescomplemented
215C2×#135—51no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—31no—
220C4×Q16—151no—
221C4×D8—151no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—21no—
228C2×C3×D5—21no—
229C2×C3×D5—24no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5C4×D412yes—
233C3×C4×C5—24no—
234C3×C4×C5C23×C411yescharacteristic
235C3×C4×C5C2×#4111yescharacteristic
236Dic15—21no—
237Dic15—21no—
238Dic15—42no—
239C3×Dic5C4×D412yes—
240C5×Dic3—21no—
241C5×Dic3—21no—
242C5×Dic3—42no—
243C3×#41—58no—
244C3×#41—104no—
245C2×C3×Q8C22×D512yes—
246C2×C3×D4—52no—
247C2×C3×D4—102no—
248C22×C3×C4—51no—
249C22×C3×C4—102no—
250C22×Dic3—102no—
251C22×Dic3—102no—
252C22×Dic3—102no—
253C3×Q16C4×D514yescomplemented
254C3×SD16—58no—
255C3×D8—54no—
256C2×C3×C8—51no—
257C2×C3×C8—54no—
258C2×C3×C8C22×D511yescharacteristic
259#217—51no—
260#217—51no—
261#217—102no—
262#217—102no—
263C4⋊Dic3—22no—
264C4⋊Dic3—51no—
265C4⋊Dic3—51no—
266C4⋊Dic3—52no—
267C4⋊Dic3—102no—
268C4⋊Dic3—102no—
269C4⋊Dic3C22×D512yes—
270C4×Dic3—22no—
271C4×Dic3—51no—
272C4×Dic3—102no—
273C4×Dic3C22×D511yescharacteristic
274#208—102no—
275C2×C3⋊C8—51no—
276C2×C3⋊C8C22×D511yescharacteristic
277C22×D5—22no—
278C22×D5D3×D411yescharacteristic
279C5×Q8—22no—
280C5×Q8C22×Dic314yes—
281C2×C4×C5—22no—
282C2×C4×C5—31no—
283C2×C4×C5—31no—
284C2×C4×C5—62no—
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—31no—
287C2×Dic5—31no—
288C2×Dic5—62no—
289C2×Dic5D3×D411yescharacteristic
290D20—28no—
291D20—22no—
292D20C22×Dic314yes—
293C4×D5—28no—
294C4×D5—242no—
295C4×D5—242no—
296C4×D5—242no—
297C4×D5#23712yes—
298C4×D5C22×Dic312yes—
299C5×C8—61no—
300C5×C8C22×Dic312yes—
301#168—61no—
302#168C22×Dic312yes—
303C2×#41—52no—
304#135—58no—
305C2×Q16D3×D511yescharacteristic
306C2×SD16—52no—
307C2×D8—51no—
308C2×M16—151no—
309C22×C8—51no—
310C4×Q8—32no—
311C4×Q8—152no—
312C4×D4—152no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—31no—
321#107—152no—
322#107—151no—
323#103—32no—
324#103—152no—
325#102—152no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—31no—
330C4×C8—151no—
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334C3×D5—22no—
335C3×D5—44no—
336C23×C3—51no—
337C23×C3—102no—
338C3×Q8—22no—
339C3×Q8C2×C4×D514yes—
340C3×D4—54no—
341C3×D4—108no—
342C3×D4—102no—
343C2×C3×C4—22no—
344C2×C3×C4—51no—
345C2×C3×C4—52no—
346C2×C3×C4—52no—
347C2×C3×C4—108no—
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—51no—
351C2×Dic3—51no—
352C2×Dic3—102no—
353C2×Dic3—402no—
354C2×Dic3—402no—
355C2×Dic3—402no—
356C2×Dic3D4×D511yescharacteristic
357C2×Dic3D4×D511yescharacteristic
358C3×C8—52no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—21no—
361C3⋊C8—101no—
362C22×C5C2×D3×D411yescharacteristic
363C2×D5—21no—
364C2×D5—21no—
365C2×D5—24no—
366C2×D5—42no—
367C2×D5—42no—
368C2×D5D4×Dic312yes—
369C4×C5—24no—
370C4×C5—61no—
371C4×C5—61no—
372C4×C5—122no—
373C4×C5C2×#23711yescharacteristic
374C4×C5C23×Dic311yescharacteristic
375Dic5—61no—
376Dic5—61no—
377Dic5—122no—
378Dic5D4×Dic312yes—
379#41—58no—
380#41—104no—
381C2×Q8C2×D3×D512yes—
382C2×D4—52no—
383C2×D4—102no—
384C22×C4—51no—
385C22×C4—102no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16D5×Dic314yescomplemented
390SD16—58no—
391D8—54no—
392M16—302no—
393C2×C8—31no—
394C2×C8—51no—
395C2×C8—54no—
396C2×C8—151no—
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—32no—
399C4⋊C4—62no—
400C4⋊C4—151no—
401C4⋊C4—151no—
402C4⋊C4—152no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—151no—
406C22⋊C4—151no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—31no—
410C42—62no—
411C42—151no—
412C42—302no—
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3—52no—
415C22×C3—101no—
416C22×C3—101no—
417C22×C3—104no—
418C22×C3—202no—
419C22×C3—202no—
420C22×C3C2×D4×D511yescharacteristic
421C3×C4—24no—
422C3×C4—52no—
423C3×C4C22×C4×D511yescharacteristic
424C3×C4D5×#4111yescharacteristic
425Dic3—21no—
426Dic3—21no—
427Dic3—42no—
428Dic3—101no—
429Dic3—101no—
430Dic3—202no—
431C2×C5#576911yescharacteristic
432C2×C5#577111yescharacteristic
433C2×C5C2×D4×Dic311yescharacteristic
434D5—22no—
435D5—44no—
436C23—51no—
437C23—102no—
438Q8—22no—
439Q8C2×D5×Dic314yes—
440D4—54no—
441D4—108no—
442D4—102no—
443C2×C4—22no—
444C2×C4—31no—
445C2×C4—31no—
446C2×C4—51no—
447C2×C4—52no—
448C2×C4—52no—
449C2×C4—62no—
450C2×C4—108no—
451C2×C4—151no—
452C2×C4—151no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4—1202no—
457C2×C4C22×D3×D511yescharacteristic
458C8—52no—
459C8—61no—
460C8—301no—
461C8C2×D5×Dic312yes—
462C2×C3—102no—
463C2×C3—204no—
464C2×C3C4×D4×D511yescharacteristic
465C2×C3#6610011yescharacteristic
466C2×C3#6610311yescharacteristic
467C5#8389811yescharacteristic, complemented, Sylow
468C22—52no—
469C22—101no—
470C22—101no—
471C22—104no—
472C22—202no—
473C22—202no—
474C22D3×D4×D511yescharacteristic
475C4—24no—
476C4—52no—
477C4—61no—
478C4—61no—
479C4—122no—
480C4—301no—
481C4—301no—
482C4—602no—
483C4D5×#23711yescharacteristic
484C4C22×D5×Dic311yescharacteristic
485C3#1061145211yescharacteristic, complemented, Sylow
486C2—102no—
487C2—204no—
488C2#1175411311yescharacteristic
489C2#1175411511yescharacteristic
490C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4065C2
cosocleC2×C3×C4×C5C24
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #11755217C2semidirect
3. Q16×Dic15C2semidirect
4. C5×Dic3×Q16C2semidirect
5. #11749241C2semidirect
6. #11749234C2semidirect
7. #11749198C2semidirect
8. #11747809C2semidirect
9. Dic3×D40C2semidirect
10. #11747645C2semidirect
11. D5×#818C2semidirect
18. C3×#4065C4semidirect
55. C3×#713C2×C4semidirect
63. C3×C5×Q16C2×C4semidirect
75. C3×#688C2×C4semidirect
77. C3×D40C2×C4semidirect
78. C3×C8×D5C2×C4semidirect
91. Dic3×Q16D5semidirect
103. #4065Dic3semidirect
183. #713C2×Dic3semidirect
191. C5×Q16C2×Dic3semidirect
198. #688C2×Dic3semidirect
212. D40C2×Dic3semidirect
214. C8×D5C2×Dic3semidirect
253. C3×Q16C4×D5semidirect
389. Q16D5×Dic3semidirect
413. C3×C5#2951semidirect
467. C5#83898semidirect
485. C3#10611452semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40652
#117552172
Q16×Dic152
C5×Dic3×Q162
#117492412
#117492342
#117491982
#117478092
Dic3×D402
#117476452
D5×#8182
#106114523
#838985