Finite Group Databasebeta

← #14302905

Subgroups — #14302905

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
1C3×#65855C211yesmaximal, characteristic, complemented
2#11754602C211yesmaximal, characteristic
3#11751106C211yesmaximal, characteristic, complemented
4#11748429C211yesmaximal, characteristic, complemented
5C2×#90958C211yesmaximal, characteristic, complemented
6C5×#4531C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10599498—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C3×#4039—22no—
17C3×D5×C22⋊C4—22no—
18C3×C4×D20—22no—
19#91564—22no—
20#91465—22no—
21#91458C412yescomplemented
22#91364C412yescomplemented
23#91089—22no—
24#90981—22no—
25#90958—22no—
26#71652—51nomaximal, Hall
27#65859—31no—
28#65855D311yescharacteristic, complemented
29#65428—31no—
30C2×#3955—31no—
31#65294—31no—
32C5×H(3,ℤ/4)—31no—
33#64751—31no—
34C23×C3×D5D412yes—
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×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20C2×C412yes—
49C2×C3×D20D412yes—
50C2×C3×C4×D5—24no—
51C2×#1202—24no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C42×C5D412yescomplemented
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#217—21no—
59C5×C4⋊Dic3—21no—
60C4×C5×Dic3C2×C412yescomplemented
61C5×#208—21no—
62C5×#208—21no—
63C2×C5×C3⋊C8—21no—
64C3×C22⋊Dic5—21no—
65C3×#685—24no—
66C3×C4⋊Dic5—21no—
67C3×C4×Dic5D412yescomplemented
68#6665—24no—
69C3×#518—51no—
70#5805—51no—
71C2×#833—51no—
72#5005—51no—
73#5005—51no—
74#4531—51no—
75#4531D511yescharacteristic, complemented
76C2×#709—31no—
77C22×D20C2×D311yescharacteristic
78C2×C5×M16—31no—
79C5×#117—31no—
80C5×#117C2×D311yescharacteristic
81#4072C2×D311yescharacteristic
82C2×#681—31no—
83#4041—62no—
84#4039—22no—
85#4028—62no—
86D5×C22⋊C4—22no—
87#4021—32no—
88#4020—32no—
89C4×D20—22no—
90#3957—62no—
91#3955—62no—
92#3937—62no—
93#1911—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×C3×D5—22no—
97C22×C3×D5—22no—
98C22×C3×D5—82no—
99C22×C3×D5C22⋊C414yes—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107#1220—41no—
108#1220—41no—
109C2×Dic15—21no—
110D60—21no—
111D60—21no—
112C4×D15—41no—
113C4×D15—41no—
114Dic30—21no—
115Dic30—21no—
116C2×C5×Dic3—22no—
117C2×C3×Dic5—22no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20—22no—
122C3×C4×D5—84no—
123#1202—84no—
124C3⋊#168—41no—
125C5×C3⋊C8—41no—
126C22×C3×D4—51no—
127C2×#235—51no—
128C3×C4×D4—102no—
129C3×C4×D4—102no—
130C3×#117—51no—
131C3×#117C2×D511yescharacteristic
132C2×C3×C22⋊C4—102no—
133#953—102no—
134#940—52no—
135#938—102no—
136#936—52no—
137#926C2×D511yescharacteristic
138C2×#208—51no—
139C2×#208C2×D511yescharacteristic
140#833—102no—
141#805—102no—
142#805—102no—
143C23×D5#6712yes—
144C22×C4×C5C22×D311yescharacteristic
145C2×C22⋊D5—61no—
146#709—61no—
147#709—61no—
148#709—61no—
149#709—61no—
150C2×D20—21no—
151C2×D20—21no—
152C2×D20—21no—
153C2×D20—21no—
154C2×D20—31no—
155C2×D20—64no—
156C2×D20C4×D312yes—
157C2×D20D1212yes—
158C2×C4×D5—24no—
159C2×C4×D5—61no—
160C2×Dic10—31no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—61no—
166C5×C22⋊C4—21no—
167C5×C22⋊C4—61no—
168C42×C5—32no—
169C42×C5#6712yescomplemented
170C22⋊Dic5—21no—
171#685—24no—
172#685—64no—
173C4⋊Dic5—21no—
174C4×Dic5#6712yescomplemented
175#681—61no—
176#681—61no—
177C2×#168—61no—
178#535—151no—
179#518—51no—
180#421—151no—
181#421—151no—
182C2×#100—151no—
183H(3,ℤ/4)—31no—
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×C3×D5—24no—
192C2×C3×D5—44no—
193C2×C3×D5—44no—
194C2×C3×D5—82no—
195C3×C4×C5—42no—
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200Dic15—41no—
201C3×Dic5—42no—
202C5×Dic3—42no—
203C24×C3—52no—
204C2×C3×D4—52no—
205C2×C3×D4—52no—
206C2×C3×D4—101no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C22×C3×C4—104no—
211C22×C3×C4C22×D511yescharacteristic
212C2×#67—104no—
213C2×#67—101no—
214#235—101no—
215#235—101no—
216#235—101no—
217#235—101no—
218C2×D12—51no—
219C2×C4×D3—101no—
220C2×Dic6—51no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—101no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—104no—
225C3×C22⋊C4—101no—
226C3×C42—52no—
227C3×C42D2012yescomplemented
228#217—21no—
229#217—104no—
230C4⋊Dic3—21no—
231C4×Dic3C4×D512yescomplemented
232#208—21no—
233#208—21no—
234#208—101no—
235#208—101no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—101no—
238C23×C5C2×#6711yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—61no—
242C22×D5—82no—
243C22×D5(C2×D3)⋊C414yes—
244C2×C4×C5—22no—
245C2×C4×C5—62no—
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5C2×D1211yescharacteristic
248C2×C4×C5#23511yescharacteristic
249C2×C4×C5#23511yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C22⋊D5—121no—
253C22⋊D5—121no—
254C2×Dic5—22no—
255C2×Dic5—61no—
256D20—22no—
257D20—22no—
258D20—22no—
259D20—22no—
260D20—61no—
261D20—61no—
262D20—244no—
263C4×D5—84no—
264C4×D5—121no—
265C4×D5—121no—
266Dic10—61no—
267Dic10—61no—
268C5×C8—121no—
269#168—121no—
270C2×#41—151no—
271C22×D4—51no—
272C2×M16—31no—
273C2×M16—151no—
274#127—152no—
275#124—152no—
276#121—302no—
277#120—302no—
278C4×D4—102no—
279C4×D4—102no—
280#117—31no—
281#117—51no—
282#117D3×D511yescharacteristic
283C2×C22⋊C4—102no—
284#104—302no—
285#104—302no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—81no—
292C3×D5—44no—
293C23×C3—54no—
294C23×C3—102no—
295C23×C3—102no—
296C23×C3—402no—
297C23×C3D4×D511yescharacteristic
298C22×D3—101no—
299C3×D4—102no—
300C3×D4—102no—
301C3×D4—102no—
302C3×D4—102no—
303C2×C3×C4—22no—
304C2×C3×C4—102no—
305C2×C3×C4—404no—
306C2×C3×C4C2×C4×D511yescharacteristic
307C2×C3×C4C2×D2011yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4#71311yescharacteristic
312#67—201no—
313#67—201no—
314#67—404no—
315C2×Dic3—22no—
316C2×Dic3—101no—
317D12—101no—
318D12—101no—
319C4×D3—201no—
320C4×D3—201no—
321Dic6—101no—
322Dic6—101no—
323C3⋊C8—41no—
324C3⋊C8—201no—
325C22×C5—41no—
326C22×C5C2×(C2×D3)⋊C411yescharacteristic
327C22×C5#92911yescharacteristic
328C22×C5#95311yescharacteristic
329C2×D5—24no—
330C2×D5—44no—
331C2×D5—44no—
332C2×D5—82no—
333C2×D5—122no—
334C2×D5—121no—
335C4×C5—42no—
336C4×C5—122no—
337C4×C5C4×#6711yescharacteristic
338C4×C5C4×#6711yescharacteristic
339C4×C5#93011yescharacteristic
340C4×C5#93011yescharacteristic
341Dic5—42no—
342Dic5—121no—
343C24—52no—
344#41—301no—
345#41—301no—
346#41—301no—
347#41—301no—
348C2×Q8—151no—
349C2×D4—52no—
350C2×D4—52no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—101no—
354C2×D4—101no—
355C2×D4—151no—
356C2×D4—304no—
357C2×D4—301no—
358C22×C4—104no—
359C22×C4—301no—
360C22×C4C2×D3×D511yescharacteristic
361M16—61no—
362M16—61no—
363M16—301no—
364M16—301no—
365C2×C8—61no—
366C2×C8—301no—
367C4⋊C4—21no—
368C4⋊C4—61no—
369C4⋊C4—101no—
370C22⋊C4—21no—
371C22⋊C4—61no—
372C22⋊C4—104no—
373C22⋊C4—101no—
374C22⋊C4—304no—
375C42—32no—
376C42—52no—
377C42#120212yescomplemented
378C3×C5#191111yescharacteristic, complemented, Hall
379C22×C3—41no—
380C22×C3—104no—
381C22×C3—204no—
382C22×C3—204no—
383C22×C3—402no—
384C22×C3D5×C22⋊C411yescharacteristic
385C22×C3#402811yescharacteristic
386C22×C3#404011yescharacteristic
387C2×D3—202no—
388C2×D3—201no—
389C3×C4—42no—
390C3×C4—202no—
391C3×C4C4×D2011yescharacteristic
392C3×C4#403011yescharacteristic
393C3×C4#403911yescharacteristic
394C3×C4#404111yescharacteristic
395Dic3—42no—
396Dic3—201no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5#521311yescharacteristic
401D5—44no—
402D5—241no—
403C23—54no—
404C23—102no—
405C23—102no—
406C23—301no—
407C23—402no—
408C23D5×#6711yescharacteristic
409Q8—301no—
410Q8—301no—
411D4—102no—
412D4—102no—
413D4—102no—
414D4—102no—
415D4—301no—
416D4—301no—
417D4—601no—
418D4—601no—
419D4—1204no—
420C2×C4—22no—
421C2×C4—62no—
422C2×C4—102no—
423C2×C4—301no—
424C2×C4—404no—
425C2×C4—601no—
426C2×C4—601no—
427C2×C4#677111yescharacteristic
428C2×C4#677311yescharacteristic
429C2×C4C4×D3×D511yescharacteristic
430C2×C4D5×D1211yescharacteristic
431C2×C4C2×#120211yescharacteristic
432C2×C4D5×#6711yescharacteristic
433C8—121no—
434C8—601no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—204no—
439C2×C3#6495411yescharacteristic
440D3—401no—
441C5#7165211yescharacteristic, complemented, Sylow
442C22—41no—
443C22—104no—
444C22—204no—
445C22—204no—
446C22—402no—
447C22—602no—
448C22—601no—
449C22#9134811yescharacteristic
450C22D5×(C2×D3)⋊C411yescharacteristic
451C22#9156411yescharacteristic
452C4—42no—
453C4—122no—
454C4—202no—
455C4—601no—
456C4C4×#120211yescharacteristic
457C4#9144411yescharacteristic
458C4#9144811yescharacteristic
459C4#9145011yescharacteristic
460C3#1059949811yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—204no—
465C2—1201no—
466C2#1174890711yescharacteristic
subgroupG/H
centerC2#11748907
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11754602C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#65855C2semidirect
3. #11751106C2semidirect
4. #11748429C2semidirect
5. C2×#90958C2semidirect
6. C5×#4531C2semidirect
7. #11745969C2semidirect
21. #91458C4semidirect
22. #91364C4semidirect
28. #65855D3semidirect
41. C2×D60C2×C4semidirect
43. C2×Dic30C2×C4semidirect
54. C3×C42×C5D4semidirect
60. C4×C5×Dic3C2×C4semidirect
67. C3×C4×Dic5D4semidirect
75. #4531D5semidirect
169. C42×C5#67semidirect
174. C4×Dic5#67semidirect
227. C3×C42D20semidirect
231. C4×Dic3C4×D5semidirect
377. C42#1202semidirect
378. C3×C5#1911semidirect
441. C5#71652semidirect
460. C3#10599498semidirect

Maximal subgroups

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

subgroupindex
C3×#658552
#117546022
#117511062
#117484292
C2×#909582
C5×#45312
#117459692
#105994983
#716525