Finite Group Databasebeta

← #14416632

Subgroups — #14416632

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#919C211yesmaximal, characteristic
2Dic5×#239C212yesmaximal, complemented
3#11751285C211yesmaximal, characteristic, complemented
4C3×#65473C211yesmaximal, characteristic, complemented
5#11749242C212yesmaximal, complemented
6#11749223C212yesmaximal, complemented
7#11749211C212yesmaximal, complemented
8#11747813C211yesmaximal, characteristic, complemented
9#11747775C211yesmaximal, characteristic, complemented
10#11747679C211yesmaximal, characteristic, complemented
11D3×#3947C211yesmaximal, characteristic, complemented
12#10615628—31nomaximal, Hall
13C2×C5×#239C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15Q8×Dic15C2212yes—
16C2×C5×#215C2212yes—
17C5×#919C418yescomplemented
18C2×C5×D24C2211yescharacteristic
19C2×C5×D3×C8C2211yescharacteristic
20C3×Q8×Dic5C2212yes—
21#91435—22no—
22#91435C2212yes—
23Dic5×D12—22no—
24Dic5×D12C2212yes—
25C4×D3×Dic5—22no—
26C4×D3×Dic5C2211yescharacteristic
27#91338—22no—
28#91338C2212yes—
29C2×D3×#168C2211yescharacteristic
30#91119C2212yes—
31#91101C2211yescharacteristic
32#91099C2211yescharacteristic
33C3×#3967C2212yes—
34C3×#3949C2211yescharacteristic
35C3×#3947C2211yescharacteristic
36#90990C2212yes—
37#90967C2212yes—
38#90966C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79828—51nomaximal, Hall
42C2×C5×#135—31no—
43#41×Dic5—32no—
44#65522—32no—
45#65473—31no—
46#65473D311yescharacteristic, complemented
47#65453—32no—
48#65453—32no—
49#65441—31no—
50#65441—31no—
51#65395—31no—
52C2×#3947—31no—
53C2×C3×C5×Q8C2312yes—
54C5×#239—24no—
55C5×#239C2×C418yescomplemented
56C2×C5×D12—22no—
57C2×C5×D12C2312yes—
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3C2311yescharacteristic
60C2×D3×Dic5—22no—
61C2×D3×Dic5—22no—
62C2×D3×Dic5D412yes—
63C3×C5×Q16C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C4⋊Dic15—22no—
66C4⋊Dic15C2312yes—
67C4×Dic15—22no—
68C4×Dic15C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×#215C2×C418yescomplemented
71C2×C5×C3⋊C8C2311yescharacteristic
72C5×D24C2×C414yescomplemented
73C5×D3×C8C2×C414yescomplemented
74C3×C4⋊Dic5—22no—
75C3×C4⋊Dic5C2312yes—
76C3×C4×Dic5—22no—
77C3×C4×Dic5C2311yescharacteristic
78C2×C3×#168C2311yescharacteristic
79(C2×D3)⋊Dic5—22no—
80(C2×D3)⋊Dic5—22no—
81(C2×D3)⋊Dic5—22no—
82Dic3×Dic5—22no—
83Dic3×Dic5D412yes—
84D3×#168—22no—
85C2×#919D511yescharacteristic
86C4×#239—52no—
87C3×#441—51no—
88#5184—51no—
89#5026—52no—
90#4869—51no—
91#4860—51no—
92#4817—52no—
93#4804—52no—
94#4711—51no—
95D3×#97—51no—
96C2×C5×#41—32no—
97C5×#135—38no—
98C2×C5×Q16C2×D311yescharacteristic
99C2×C5×SD16—32no—
100C2×C5×D8—31no—
101C22×C5×C8—31no—
102Q8×Dic5—32no—
103Q8×Dic5C2×D312yes—
104D4×Dic5—32no—
105D4×Dic5—32no—
106D4×Dic5—62no—
107D4×Dic5—62no—
108#4072—32no—
109#4072—62no—
110C2×C4×Dic5—31no—
111C2×C4×Dic5—62no—
112C22×#168—31no—
113#3967—32no—
114#3967C2×D312yes—
115#3964—32no—
116#3964—32no—
117#3950—32no—
118#3949—31no—
119#3949C2×D311yescharacteristic
120#3947—31no—
121#3947—31no—
122#3947—31no—
123#3947C2×D311yescharacteristic
124#2943—151noSylow
125C22×C5×D3—22no—
126C22×C5×D3C2×D411yescharacteristic
127C3×C5×Q8—22no—
128C3×C5×Q8C22×C414yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—22no—
132C2×Dic15C2×D412yes—
133C2×C5×Dic3C2×D411yescharacteristic
134C5×D12—28no—
135C5×D12—22no—
136C5×D12C22×C414yes—
137C4×C5×D3—28no—
138C4×C5×D3C22×C412yes—
139C4×C5×D3#4112yes—
140C2×C3×Dic5—22no—
141C2×C3×Dic5C2×D412yes—
142D3×Dic5—42no—
143D3×Dic5—44no—
144D3×Dic5—44no—
145C3×C5×C8C22×C412yes—
146C3⋊#168—21no—
147C3×#168—21no—
148C5×C3⋊C8C22×C412yes—
149C2×#239C2×D512yes—
150C2×C3×Q16C2×D511yescharacteristic
151C3×C4×Q8—52no—
152Q8×Dic3—52no—
153C2×#215C2×D512yes—
154#919Dic518yescomplemented
155C2×D24C2×D511yescharacteristic
156C2×D3×C8—51no—
157C2×D3×C8C2×D511yescharacteristic
158#893—52no—
159#893—102no—
160#892—52no—
161#892—102no—
162C4×D12—52no—
163C4×D12—102no—
164C42×D3—51no—
165C42×D3—102no—
166C3×#106—51no—
167C3×#103—52no—
168C3×#97—51no—
169#835—52no—
170#821—52no—
171#817—51no—
172#815—51no—
173#815—51no—
174#809—52no—
175#807—52no—
176#803—51no—
177C5×#41—38no—
178C5×#41—64no—
179C2×C5×Q8C22×D312yes—
180C2×C5×D4—32no—
181C2×C5×D4—62no—
182C22×C4×C5—31no—
183C22×C4×C5—62no—
184C22×Dic5—32no—
185C22×Dic5—62no—
186C22×Dic5—62no—
187C5×Q16C4×D314yescomplemented
188C5×SD16—38no—
189C5×D8—34no—
190C2×C5×C8—31no—
191C2×C5×C8—34no—
192C2×C5×C8C22×D311yescharacteristic
193C22⋊Dic5—62no—
194C22⋊Dic5—62no—
195C22⋊Dic5—62no—
196C4⋊Dic5—22no—
197C4⋊Dic5—32no—
198C4⋊Dic5—62no—
199C4⋊Dic5C22×D312yes—
200C4×Dic5—22no—
201C4×Dic5—31no—
202C4×Dic5—32no—
203C4×Dic5—62no—
204C4×Dic5—62no—
205C4×Dic5C22×D311yescharacteristic
206C2×#168—31no—
207C2×#168—62no—
208C2×#168C22×D311yescharacteristic
209C2×#135—31no—
210C4×#41—152no—
211#442—151no—
212#442—151no—
213#441—51no—
214#441—151no—
215#440—152no—
216#440—152no—
217#427—151no—
218#416—152no—
219C2×#97—151no—
220C22×C3×C5C22×D411yescharacteristic
221C2×C5×D3—22no—
222C2×C5×D3—24no—
223C2×C5×D3—42no—
224C2×C5×D3—42no—
225C2×C5×D3C4×D412yes—
226C3×C4×C5—24no—
227C3×C4×C5C23×C411yescharacteristic
228C3×C4×C5C2×#4111yescharacteristic
229Dic15—22no—
230Dic15—42no—
231C3×Dic5—22no—
232C3×Dic5—42no—
233C5×Dic3C4×D412yes—
234C2×C3×Q8C22×D512yes—
235#239—24no—
236#239C2×Dic518yescomplemented
237C2×D12—22no—
238C2×D12C22×D512yes—
239C2×C4×D3—22no—
240C2×C4×D3—52no—
241C2×C4×D3—102no—
242C2×C4×D3—102no—
243C2×C4×D3C22×D511yescharacteristic
244C3×Q16C2×Dic514yescomplemented
245C2×C3×C8—51no—
246C2×C3×C8C22×D511yescharacteristic
247C3×C4⋊C4—52no—
248C3×C4⋊C4—102no—
249C3×C42—51no—
250C3×C42—102no—
251#215C2×Dic518yescomplemented
252(C2×D3)⋊C4—102no—
253(C2×D3)⋊C4—102no—
254(C2×D3)⋊C4—102no—
255C4⋊Dic3—52no—
256C4⋊Dic3—102no—
257C4×Dic3—51no—
258C4×Dic3—52no—
259C4×Dic3—102no—
260C4×Dic3—102no—
261C2×C3⋊C8—51no—
262C2×C3⋊C8C22×D511yescharacteristic
263D24C2×Dic514yescomplemented
264D3×C8—102no—
265D3×C8C2×Dic514yescomplemented
266C23×C5—31no—
267C23×C5—62no—
268C5×Q8—22no—
269C5×Q8C2×C4×D314yes—
270C5×D4—34no—
271C5×D4—68no—
272C5×D4—62no—
273C2×C4×C5—22no—
274C2×C4×C5—31no—
275C2×C4×C5—32no—
276C2×C4×C5—32no—
277C2×C4×C5—68no—
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—22no—
280C2×Dic5—32no—
281C2×Dic5—62no—
282C2×Dic5—122no—
283C2×Dic5—124no—
284C2×Dic5—124no—
285C2×Dic5D3×D412yes—
286C5×C8—32no—
287C5×C8C2×C4×D312yes—
288#168—21no—
289#168—61no—
290C2×#41—32no—
291#135—38no—
292C2×Q16D3×D511yescharacteristic
293C2×SD16—32no—
294C2×D8—31no—
295C22×C8—31no—
296C22×C8—151no—
297C4×Q8—52no—
298C4×Q8—152no—
299C4×D4—152no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—152no—
304#117—302no—
305C2×C42—151no—
306C2×C42—302no—
307#107—152no—
308#106—51no—
309#106—151no—
310#103—52no—
311#103—152no—
312#102—152no—
313#102—152no—
314#97—51no—
315#97—151no—
316#97—151no—
317#97—151no—
318C2×C3×C5C2×C4×D411yescharacteristic
319C2×C3×C5#57512yes—
320C5×D3—22no—
321C5×D3—44no—
322C22×D3—22no—
323C22×D3D4×D511yescharacteristic
324C3×Q8—22no—
325C3×Q8C22×Dic514yes—
326C2×C3×C4—22no—
327C2×C3×C4—52no—
328C2×C3×C4—102no—
329C2×C3×C4C23×D511yescharacteristic
330C2×Dic3—52no—
331C2×Dic3—102no—
332C2×Dic3D4×D511yescharacteristic
333D12—28no—
334D12—22no—
335D12C22×Dic514yes—
336C4×D3—28no—
337C4×D3—202no—
338C4×D3—204no—
339C4×D3—204no—
340C4×D3#71112yes—
341C4×D3C22×Dic512yes—
342C3×C8—101no—
343C3×C8C22×Dic512yes—
344C3⋊C8—101no—
345C3⋊C8C22×Dic512yes—
346C22×C5—32no—
347C22×C5—62no—
348C22×C5—64no—
349C22×C5—122no—
350C22×C5—122no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—24no—
353C4×C5—32no—
354C4×C5C22×C4×D311yescharacteristic
355C4×C5D3×#4111yescharacteristic
356Dic5—22no—
357Dic5—42no—
358Dic5—62no—
359Dic5—122no—
360#41—38no—
361#41—64no—
362C2×Q8C2×D3×D512yes—
363C2×D4—32no—
364C2×D4—62no—
365C22×C4—31no—
366C22×C4—62no—
367C22×C4—152no—
368C22×C4—302no—
369C22×C4—302no—
370Q16D3×Dic514yescomplemented
371SD16—38no—
372D8—34no—
373C2×C8—31no—
374C2×C8—34no—
375C2×C8—51no—
376C2×C8—151no—
377C2×C8—302no—
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—52no—
380C4⋊C4—102no—
381C4⋊C4—152no—
382C4⋊C4—302no—
383C22⋊C4—302no—
384C22⋊C4—302no—
385C22⋊C4—302no—
386C42—51no—
387C42—102no—
388C42—152no—
389C42—151no—
390C42—302no—
391C42—302no—
392C3×C5#294311yescharacteristic, complemented, Hall
393C22×C3C2×D4×D511yescharacteristic
394C2×D3—22no—
395C2×D3—24no—
396C2×D3—42no—
397C2×D3—42no—
398C2×D3D4×Dic512yes—
399C3×C4—24no—
400C3×C4—102no—
401C3×C4—202no—
402C3×C4C2×#71111yescharacteristic
403C3×C4C23×Dic511yescharacteristic
404Dic3—102no—
405Dic3—202no—
406Dic3D4×Dic512yes—
407C2×C5—62no—
408C2×C5—124no—
409C2×C5C4×D3×D411yescharacteristic
410C2×C5#577712yes—
411C23—31no—
412C23—62no—
413Q8—22no—
414Q8C2×D3×Dic514yes—
415D4—34no—
416D4—68no—
417D4—62no—
418C2×C4—22no—
419C2×C4—31no—
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—52no—
423C2×C4—68no—
424C2×C4—102no—
425C2×C4—152no—
426C2×C4—302no—
427C2×C4—602no—
428C2×C4—604no—
429C2×C4—604no—
430C2×C4C22×D3×D511yescharacteristic
431C8—32no—
432C8—101no—
433C8—301no—
434C8C2×D3×Dic512yes—
435C2×C3#6610212yes—
436C2×C3C2×D4×Dic511yescharacteristic
437D3—22no—
438D3—44no—
439C5#7982811yescharacteristic, complemented, Sylow
440C22—32no—
441C22—62no—
442C22—64no—
443C22—122no—
444C22—122no—
445C22D3×D4×D511yescharacteristic
446C4—24no—
447C4—32no—
448C4—102no—
449C4—202no—
450C4—302no—
451C4—602no—
452C4D3×#71111yescharacteristic
453C4C22×D3×Dic511yescharacteristic
454C3#1061562811yescharacteristic, complemented, Sylow
455C2—62no—
456C2—124no—
457C2#1175410212yes—
458C2D3×D4×Dic511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#919C2
cosocleC2×C3×C4×C5C24
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2943
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. Dic5×#239C2semidirect
3. #11751285C2semidirect
4. C3×#65473C2semidirect
5. #11749242C2semidirect
6. #11749223C2semidirect
7. #11749211C2semidirect
8. #11747813C2semidirect
9. #11747775C2semidirect
10. #11747679C2semidirect
11. D3×#3947C2semidirect
17. C5×#919C4semidirect
46. #65473D3semidirect
55. C5×#239C2×C4semidirect
63. C3×C5×Q16C2×C4semidirect
70. C5×#215C2×C4semidirect
72. C5×D24C2×C4semidirect
73. C5×D3×C8C2×C4semidirect
154. #919Dic5semidirect
187. C5×Q16C4×D3semidirect
236. #239C2×Dic5semidirect
244. C3×Q16C2×Dic5semidirect
251. #215C2×Dic5semidirect
263. D24C2×Dic5semidirect
265. D3×C8C2×Dic5semidirect
370. Q16D3×Dic5semidirect
392. C3×C5#2943semidirect
439. C5#79828semidirect
454. C3#10615628semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9192
Dic5×#2392
#117512852
C3×#654732
#117492422
#117492232
#117492112
#117478132
#117477752
#117476792
D3×#39472
#106156283
#798285