Finite Group Databasebeta

← #14302897

Subgroups — #14302897

Order 1920.

724 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
1#11754606C211yesmaximal, characteristic
2#11754503C211yesmaximal, characteristic, complemented
3#11751240C211yesmaximal, characteristic, complemented
4C2×C5×#823C211yesmaximal, characteristic, complemented
5#11748429C211yesmaximal, characteristic, complemented
6C3×#64777C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10600864—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16#91570—22no—
17D3×C22⋊Dic5—22no—
18#91466—22no—
19#91451C412yescomplemented
20#91435—22no—
21Dic5×D12—22no—
22#91373C412yescomplemented
23#91109—22no—
24C5×#823—22no—
25#90981—22no—
26#68705—51nomaximal, Hall
27#66139—31no—
28#66132—31no—
29C2×C5×#100—31no—
30#65428—31no—
31#65428—31no—
32#64777—31no—
33#64777D311yescharacteristic, complemented
34C23×C5×D3D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60C2×C411yescharacteristic, complemented
42C2×C4×D15—21no—
43C2×Dic30C2×C411yescharacteristic, complemented
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12C2×C412yes—
49C2×C5×D12D412yes—
50C2×#1203—24no—
51C2×D3×Dic5—24no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C2×C3×C5×C8—21no—
55#6719—21no—
56C4⋊Dic15—21no—
57C4×Dic15D412yescomplemented
58C5×#208—21no—
59C5×#208—21no—
60C2×C5×C3⋊C8—21no—
61C3×C22⋊Dic5—21no—
62C3×C22⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5—21no—
65C3×C4×Dic5C2×C412yescomplemented
66C3×C4×Dic5D412yescomplemented
67(C2×D3)⋊Dic5—24no—
68(C2×D3)⋊Dic5—24no—
69#5525—51no—
70#5521—51no—
71#5139—51no—
72C2×#823D511yescharacteristic, complemented
73#5005—51no—
74C3×H(3,ℤ/4)—51no—
75#4531—51no—
76C22×C5×D4—31no—
77C2×#709—31no—
78C2×C5×M16—31no—
79C2×C5×M16C2×D311yescharacteristic
80#4099—62no—
81C2×C22⋊Dic5—62no—
82#4086—32no—
83#4084—62no—
84#4082—32no—
85D4×Dic5—62no—
86D4×Dic5—62no—
87#4072—31no—
88#4072C2×D311yescharacteristic
89#4072C2×D311yescharacteristic
90C5×#100—62no—
91#3957—62no—
92#3957—62no—
93#1911—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×C5×D3—22no—
97C22×C5×D3—22no—
98C22×C5×D3—82no—
99C22×C5×D3C22⋊C414yes—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106#1220—41no—
107#1220—41no—
108C2×Dic15—21no—
109C2×Dic15—22no—
110D60—21no—
111D60—21no—
112C4×D15—41no—
113C4×D15—41no—
114Dic30—21no—
115Dic30—21no—
116C5×D12—22no—
117C5×D12—22no—
118C5×D12—22no—
119C5×D12—22no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—22no—
122#1203—84no—
123D3×Dic5—84no—
124C3×C5×C8—41no—
125C5×C3⋊C8—41no—
126C2×#235—51no—
127C22×D12C2×D511yescharacteristic
128C2×C3×M16C2×D511yescharacteristic
129C3×#117—51no—
130C3×#117—51no—
131#926—51no—
132C2×#208C2×D511yescharacteristic
133#895—102no—
134#893—102no—
135#882—102no—
136D3×C22⋊C4—102no—
137#875—52no—
138#874—52no—
139C4×D12—102no—
140#825—102no—
141#823—22no—
142#805—102no—
143C24×C5—32no—
144C2×C5×D4—32no—
145C2×C5×D4—32no—
146C2×C5×D4—61no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—64no—
152C2×C22⋊D5—61no—
153C22×Dic5—64no—
154#709—61no—
155#709—61no—
156#709—61no—
157#709—61no—
158C2×D20—31no—
159C2×C4×D5—61no—
160C2×Dic10—31no—
161C5×M16—21no—
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—61no—
165C2×C5×C8—21no—
166C2×C5×C8—61no—
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5—64no—
170C22⋊Dic5—64no—
171C22⋊Dic5—61no—
172C4⋊Dic5—21no—
173C4⋊Dic5—21no—
174C4⋊Dic5—61no—
175C4×Dic5—32no—
176C4×Dic5C4×D312yescomplemented
177C4×Dic5D1212yescomplemented
178#535—151no—
179#518—151no—
180#421—151no—
181#421—151no—
182C2×#100—31no—
183H(3,ℤ/4)—51no—
184H(3,ℤ/4)—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5#12311yescharacteristic
189C2×D15—42no—
190C2×D15—41no—
191C2×C5×D3—24no—
192C2×C5×D3—44no—
193C2×C5×D3—44no—
194C2×C5×D3—82no—
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12111yescharacteristic
199Dic15—42no—
200Dic15—41no—
201C3×Dic5—42no—
202C3×Dic5—42no—
203C23×D3D2012yes—
204C22×C3×C4C22×D511yescharacteristic
205C2×#67—101no—
206#235—101no—
207#235—101no—
208#235—101no—
209#235—101no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—51no—
215C2×D12—104no—
216C2×D12C4×D512yes—
217C2×D12C22⋊D512yes—
218C2×C4×D3—101no—
219C2×C4×D3—104no—
220C2×Dic6—51no—
221C3×M16—21no—
222C3×M16—21no—
223C2×C3×C8—21no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C22⋊C4—101no—
227C3×C22⋊C4—101no—
228C3×C42—52no—
229C3×C42—52no—
230#217—101no—
231(C2×D3)⋊C4—104no—
232(C2×D3)⋊C4—104no—
233C4⋊Dic3—101no—
234C4×Dic3—52no—
235#208—21no—
236#208—21no—
237C2×C3⋊C8—21no—
238C23×C5—34no—
239C23×C5—62no—
240C23×C5—62no—
241C23×C5—242no—
242C23×C5D3×D411yescharacteristic
243C22×D5—61no—
244C5×D4—62no—
245C5×D4—62no—
246C5×D4—62no—
247C5×D4—62no—
248C2×C4×C5C2×C4×D311yescharacteristic
249C2×C4×C5C2×D1211yescharacteristic
250C2×C4×C5#23511yescharacteristic
251C2×C4×C5D3×D411yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23911yescharacteristic
254C22⋊D5—121no—
255C22⋊D5—121no—
256C22⋊D5—244no—
257C2×Dic5—22no—
258C2×Dic5—22no—
259C2×Dic5—61no—
260C2×Dic5—62no—
261C2×Dic5—244no—
262D20—61no—
263D20—61no—
264C4×D5—121no—
265C4×D5—121no—
266Dic10—61no—
267Dic10—61no—
268C5×C8—41no—
269C5×C8—121no—
270C2×#41—151no—
271C22×D4—31no—
272C2×M16—31no—
273C2×M16D3×D511yescharacteristic
274#127—152no—
275#124—152no—
276#121—302no—
277#120—302no—
278C4×D4—302no—
279C4×D4—302no—
280#117—51no—
281#117—51no—
282#117—151no—
283C2×C22⋊C4—302no—
284#104—302no—
285#104—302no—
286#100—62no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—81no—
292C5×D3—44no—
293C23×C3C2×D2011yescharacteristic
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—82no—
297C22×D3—101no—
298C22×D3#68514yes—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×C3×C4C2×C22⋊D511yescharacteristic
307#67—201no—
308#67—201no—
309C2×Dic3—102no—
310C2×Dic3—101no—
311D12—22no—
312D12—22no—
313D12—22no—
314D12—22no—
315D12—101no—
316D12—101no—
317D12—404no—
318C4×D3—201no—
319C4×D3—201no—
320C4×D3—404no—
321Dic6—101no—
322Dic6—101no—
323C3×C8—41no—
324C3⋊C8—41no—
325C22×C5—41no—
326C22×C5—64no—
327C22×C5—124no—
328C22×C5—124no—
329C22×C5—242no—
330C22×C5D3×C22⋊C411yescharacteristic
331C22×C5#88211yescharacteristic
332C22×C5#89411yescharacteristic
333C2×D5—122no—
334C2×D5—121no—
335C4×C5C4×D1211yescharacteristic
336C4×C5#88411yescharacteristic
337C4×C5#89311yescharacteristic
338C4×C5#89511yescharacteristic
339Dic5—42no—
340Dic5—42no—
341Dic5—122no—
342Dic5—121no—
343C24—32no—
344#41—301no—
345#41—301no—
346#41—301no—
347#41—301no—
348C2×Q8—151no—
349C2×D4—32no—
350C2×D4—32no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—151no—
356C2×D4—304no—
357C2×D4—301no—
358C22×C4—304no—
359C22×C4—301no—
360C22×C4C2×D3×D511yescharacteristic
361M16—21no—
362M16—21no—
363M16—61no—
364M16—61no—
365C2×C8—21no—
366C2×C8—61no—
367C4⋊C4—101no—
368C4⋊C4—101no—
369C4⋊C4—301no—
370C22⋊C4—101no—
371C22⋊C4—101no—
372C22⋊C4—304no—
373C22⋊C4—304no—
374C22⋊C4—301no—
375C42—52no—
376C42—52no—
377C42—152no—
378C3×C5#191111yescharacteristic, complemented, Hall
379C22×C3—41no—
380C22×C3#402811yescharacteristic
381C22×C3#403211yescharacteristic
382C22×C3C2×#68511yescharacteristic
383C2×D3—24no—
384C2×D3—44no—
385C2×D3—44no—
386C2×D3—82no—
387C2×D3—202no—
388C2×D3—201no—
389C3×C4—202no—
390C3×C4—202no—
391C3×C4#402711yescharacteristic
392C3×C4#402711yescharacteristic
393C3×C4#408511yescharacteristic
394C3×C4#408511yescharacteristic
395Dic3—202no—
396Dic3—201no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5—124no—
401C2×C5#466511yescharacteristic
402D5—241no—
403C23—34no—
404C23—62no—
405C23—62no—
406C23—242no—
407C23—301no—
408C23D3×D2011yescharacteristic
409Q8—301no—
410Q8—301no—
411D4—62no—
412D4—62no—
413D4—62no—
414D4—62no—
415D4—301no—
416D4—301no—
417D4—601no—
418D4—601no—
419D4—1204no—
420C2×C4—102no—
421C2×C4—102no—
422C2×C4—301no—
423C2×C4—302no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4—1204no—
427C2×C4#676811yescharacteristic
428C2×C4C4×D3×D511yescharacteristic
429C2×C4D5×D1211yescharacteristic
430C2×C4#678211yescharacteristic
431C2×C4D3×C22⋊D511yescharacteristic
432C2×C4#679011yescharacteristic
433C8—41no—
434C8—121no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3#6524711yescharacteristic
439D3—44no—
440D3—401no—
441C5#6870511yescharacteristic, complemented, Sylow
442C22—41no—
443C22—64no—
444C22—124no—
445C22—124no—
446C22—242no—
447C22—602no—
448C22—601no—
449C22#9142711yescharacteristic
450C22D3×#68511yescharacteristic
451C22#9147611yescharacteristic
452C4—202no—
453C4—202no—
454C4—602no—
455C4—601no—
456C4#9140511yescharacteristic
457C4#9140611yescharacteristic
458C4#9141611yescharacteristic
459C4#9155811yescharacteristic
460C3#1060086411yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—124no—
465C2—1201no—
466C2#1174888311yescharacteristic
subgroupG/H
centerC2#11748883
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754606C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754503C2semidirect
3. #11751240C2semidirect
4. C2×C5×#823C2semidirect
5. #11748429C2semidirect
6. C3×#64777C2semidirect
7. #11745970C2semidirect
19. #91451C4semidirect
22. #91373C4semidirect
33. #64777D3semidirect
41. C2×D60C2×C4semidirect
43. C2×Dic30C2×C4semidirect
57. C4×Dic15D4semidirect
65. C3×C4×Dic5C2×C4semidirect
66. C3×C4×Dic5D4semidirect
72. C2×#823D5semidirect
176. C4×Dic5C4×D3semidirect
177. C4×Dic5D12semidirect
378. C3×C5#1911semidirect
441. C5#68705semidirect
460. C3#10600864semidirect

Maximal subgroups

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

subgroupindex
#117546062
#117545032
#117512402
C2×C5×#8232
#117484292
C3×#647772
#117459702
#106008643
#687055