Finite Group Databasebeta

← #14301431

Subgroups — #14301431

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91836C211yesmaximal, characteristic
2#11756280C211yesmaximal, characteristic
3C3×C5×#419C211yesmaximal, characteristic, complemented
4#11751326C211yesmaximal, characteristic, complemented
5C2×#91107C211yesmaximal, characteristic
6#11746376C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10601136—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91836—22no—
14#91836C414yescomplemented
15C2×#6714—22no—
16#91815C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19#91782—22no—
20C22⋊C4×D15—22no—
21C4×D60—22no—
22C3×C5×#103—22no—
23#91119—22no—
24#91107—22no—
25#70343—51nomaximal, Hall
26C2×#4093—31no—
27#65855—31no—
28C5×#419D311yescharacteristic, complemented
29#65514—31no—
30C2×#3955—31no—
31#64775—31no—
32#64752—31no—
33C23×D15D412yes—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yescomplemented
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60C2×C412yes—
48C2×D60D412yes—
49C2×C4×D15—24no—
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4D412yes—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—21no—
56#6719—21no—
57#6714—24no—
58#6714—28no—
59C4⋊Dic15D412yes—
60C4×Dic15—21no—
61C4×Dic15—21no—
62C4×Dic15C2×C412yescomplemented
63#6710—21no—
64#6710—21no—
65C2×C3⋊#168—21no—
66C2×#947—51no—
67#5521—51no—
68C3×#419D511yescharacteristic, complemented
69#5225—51no—
70C2×#823—51no—
71#4555—51no—
72#4532—51no—
73C22×C5×Q8C2×D311yescharacteristic
74C22×D20—31no—
75C2×C5×M16C2×D311yescharacteristic
76C5×#117C2×D311yescharacteristic
77#4093—34no—
78#4093—62no—
79C2×#685—62no—
80#4072—31no—
81C2×C4×Dic5—31no—
82C2×#681—31no—
83#4039—62no—
84D5×C22⋊C4—62no—
85C4×D20—62no—
86C5×#103—22no—
87#3967—62no—
88#3955—62no—
89#1885—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×D15—22no—
92C22×D15—22no—
93C22×D15—44no—
94C22×D15C22⋊C414yes—
95C3×C5×Q8—22no—
96C3×C5×Q8—22no—
97C3×C5×Q8—41no—
98C3×C5×Q8—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—22no—
110C2×Dic15—22no—
111C2×Dic15—42no—
112D60—22no—
113D60—22no—
114D60—22no—
115D60—22no—
116C4×D15—84no—
117C3×C5×C8—41no—
118C3⋊#168—41no—
119C22×C3×Q8C2×D511yescharacteristic
120C22×D12—51no—
121C2×C3×M16C2×D511yescharacteristic
122C3×#117C2×D511yescharacteristic
123#947—54no—
124#947—102no—
125C2×(C2×D3)⋊C4—102no—
126#926—51no—
127C2×C4×Dic3—51no—
128C2×#208—51no—
129#893—102no—
130D3×C22⋊C4—102no—
131C4×D12—102no—
132C3×#103—22no—
133#835—102no—
134#823—102no—
135C23×D5—32no—
136C2×C5×Q8—21no—
137C2×C5×Q8—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8C4×D312yescomplemented
142C22×C4×C5—21no—
143C22×C4×C5C22×D311yescharacteristic
144C22×Dic5—61no—
145C2×D20—32no—
146C2×D20—32no—
147C2×D20—61no—
148C2×D20—61no—
149C2×D20—61no—
150C2×D20—61no—
151C2×C4×D5—64no—
152C5×M16—21no—
153C5×M16—21no—
154C2×C5×C8—21no—
155C5×C4⋊C4#6712yes—
156C5×C22⋊C4—21no—
157C42×C5—21no—
158C22⋊Dic5—61no—
159#685—68no—
160#685—64no—
161C4⋊Dic5—32no—
162C4×Dic5—32no—
163C4×Dic5—61no—
164C4×Dic5—61no—
165#681—61no—
166#681—61no—
167C2×#168—61no—
168C2×#124—151no—
169#518—151no—
170#419—151no—
171#419D1511yescharacteristic, complemented
172C2×#100—151no—
173#339—151no—
174#339—151no—
175C22×C3×C5—22no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12011yescharacteristic
178C22×C3×C5#12311yescharacteristic
179C2×D15—24no—
180C2×D15—44no—
181C2×D15—44no—
182C2×D15—82no—
183C3×C4×C5—42no—
184C3×C4×C5—42no—
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5#12111yescharacteristic
188C3×C4×C5#12111yescharacteristic
189Dic15—42no—
190Dic15—42no—
191C23×D3—52no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8C4×D512yescomplemented
198C22×C3×C4—21no—
199C22×C3×C4C22×D511yescharacteristic
200C22×Dic3—101no—
201C2×D12—52no—
202C2×D12—52no—
203C2×D12—101no—
204C2×D12—101no—
205C2×D12—101no—
206C2×D12—101no—
207C2×C4×D3—104no—
208C3×M16—21no—
209C3×M16—21no—
210C2×C3×C8—21no—
211C3×C4⋊C4C22⋊D512yes—
212C3×C22⋊C4—21no—
213C3×C42—21no—
214#217—101no—
215(C2×D3)⋊C4—108no—
216(C2×D3)⋊C4—104no—
217C4⋊Dic3—52no—
218C4×Dic3—52no—
219C4×Dic3—101no—
220C4×Dic3—101no—
221#208—101no—
222#208—101no—
223C2×C3⋊C8—101no—
224C23×C5D3×D411yescharacteristic
225C22×D5—34no—
226C22×D5—62no—
227C22×D5—62no—
228C22×D5—124no—
229C5×Q8—22no—
230C5×Q8—22no—
231C5×Q8—41no—
232C5×Q8—41no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5#23711yescharacteristic
242C2×C4×C5C2×#6711yescharacteristic
243C2×Dic5—62no—
244C2×Dic5—62no—
245C2×Dic5—122no—
246D20—62no—
247D20—62no—
248D20—62no—
249D20—62no—
250C4×D5—244no—
251C5×C8—41no—
252#168—121no—
253C22×Q8C2×D1511yescharacteristic
254C22×D4—151no—
255C2×M16—151no—
256C2×M16C2×D1511yescharacteristic
257#124—154no—
258#124—302no—
259C4×D4—302no—
260C4×D4—302no—
261#117—151no—
262#117C2×D1511yescharacteristic
263C2×C22⋊C4—302no—
264C2×C22⋊C4—302no—
265C2×C42—151no—
266#103—22no—
267#103—302no—
268#100—302no—
269C2×C3×C5—21no—
270C2×C3×C5—21no—
271C2×C3×C5#38611yescharacteristic
272C2×C3×C5#45512yes—
273D15—44no—
274C23×C3D4×D511yescharacteristic
275C22×D3—54no—
276C22×D3—102no—
277C22×D3—102no—
278C22×D3—204no—
279C3×Q8—22no—
280C3×Q8—22no—
281C3×Q8—41no—
282C3×Q8—41no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4#70911yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293C2×Dic3—102no—
294C2×Dic3—102no—
295C2×Dic3—202no—
296D12—102no—
297D12—102no—
298D12—102no—
299D12—102no—
300C4×D3—404no—
301C3×C8—41no—
302C3⋊C8—201no—
303C22×C5—22no—
304C22×C5D3×C22⋊C411yescharacteristic
305C22×C5#88311yescharacteristic
306C22×C5#93711yescharacteristic
307C2×D5—64no—
308C2×D5—124no—
309C2×D5—124no—
310C2×D5—242no—
311C4×C5—42no—
312C4×C5—42no—
313C4×C5#67⋊C411yescharacteristic
314C4×C5#88411yescharacteristic
315C4×C5C4×#6711yescharacteristic
316C4×C5#93811yescharacteristic
317Dic5—122no—
318Dic5—122no—
319C24—152no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8C4×D1512yescomplemented
326C2×D4—152no—
327C2×D4—152no—
328C2×D4—301no—
329C2×D4—301no—
330C2×D4—301no—
331C2×D4—301no—
332C22×C4—21no—
333C22×C4—304no—
334C22×C4—301no—
335C22×C4C22×D1511yescharacteristic
336M16—21no—
337M16—21no—
338M16—301no—
339M16—301no—
340C2×C8—21no—
341C2×C8—301no—
342C4⋊C4—152no—
343C4⋊C4#122012yes—
344C22⋊C4—21no—
345C22⋊C4—308no—
346C22⋊C4—304no—
347C22⋊C4—301no—
348C42—21no—
349C42—152no—
350C42—301no—
351C42—301no—
352C3×C5#188511yescharacteristic, complemented, Hall
353C22×C3—22no—
354C22×C3D5×C22⋊C411yescharacteristic
355C22×C3#402911yescharacteristic
356C22×C3#408311yescharacteristic
357C2×D3—104no—
358C2×D3—204no—
359C2×D3—204no—
360C2×D3—402no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4#402711yescharacteristic
364C3×C4#403011yescharacteristic
365C3×C4C4×C22⋊D511yescharacteristic
366C3×C4#408411yescharacteristic
367Dic3—202no—
368Dic3—202no—
369C2×C5—21no—
370C2×C5—21no—
371C2×C5#495611yescharacteristic
372C2×C5#520212yes—
373D5—124no—
374C23—154no—
375C23—302no—
376C23—302no—
377C23—604no—
378C23D4×D1511yescharacteristic
379Q8—22no—
380Q8—22no—
381Q8—41no—
382Q8—41no—
383D4—302no—
384D4—302no—
385D4—302no—
386D4—302no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—302no—
392C2×C4—302no—
393C2×C4—602no—
394C2×C4—1204no—
395C2×C4C2×C4×D1511yescharacteristic
396C2×C4#681711yescharacteristic
397C2×C4D4×D1511yescharacteristic
398C2×C4D4×D1511yescharacteristic
399C2×C4#681911yescharacteristic
400C2×C4C2×#122011yescharacteristic
401C8—41no—
402C8—601no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3#6524511yescharacteristic
406C2×C3#6549112yes—
407D3—204no—
408C5#7034311yescharacteristic, complemented, Sylow
409C22—22no—
410C22—304no—
411C22—604no—
412C22—604no—
413C22—1202no—
414C22C22⋊C4×D1511yescharacteristic
415C22#9177211yescharacteristic
416C22#9182611yescharacteristic
417C4—42no—
418C4—42no—
419C4—602no—
420C4—602no—
421C4#9177011yescharacteristic
422C4#9177311yescharacteristic
423C4C4×#122011yescharacteristic
424C4#9182711yescharacteristic
425C3#1060113611yescharacteristic, complemented, Sylow
426C2—21no—
427C2—21no—
428C2—604no—
429C2#1175105711yescharacteristic
430C2#1175130312yes—
subgroupG/H
centerC22#91826
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#419C2
socleC22×C3×C5#120
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenter#419D15
hypocenterC3×C5#1885
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C3×C5×#419C2semidirect
4. #11751326C2semidirect
6. #11746376C2semidirect
7. #11746353C2semidirect
14. #91836C4semidirect
28. C5×#419D3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
62. C4×Dic15C2×C4semidirect
68. C3×#419D5semidirect
141. C2×C5×Q8C4×D3semidirect
171. #419D15semidirect
197. C2×C3×Q8C4×D5semidirect
325. C2×Q8C4×D15semidirect
352. C3×C5#1885semidirect
408. C5#70343semidirect
425. C3#10601136semidirect

Maximal subgroups

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

subgroupindex
C2×#918362
#117562802
C3×C5×#4192
#117513262
C2×#911072
#117463762
#117463532
#106011363
#703435