Finite Group Databasebeta

← #14302900

Subgroups — #14302900

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#11754600C211yesmaximal, characteristic
3C5×#5005C211yesmaximal, characteristic, complemented
4#11748425C211yesmaximal, characteristic, complemented
5C2×#90958C211yesmaximal, characteristic, complemented
6#11746352C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10601201—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C3×#4039—22no—
17C3×D5×C22⋊C4—22no—
18C3×C4×D20—22no—
19#91563—22no—
20#91463C412yescomplemented
21#91456—22no—
22#91368C412yescomplemented
23C5×#805—22no—
24#90979—22no—
25#90958—22no—
26#71652—51nomaximal, Hall
27#66164—31no—
28#65855D311yescharacteristic, complemented
29C5×#421—31no—
30#65525—31no—
31C2×#3955—31no—
32#64777—31no—
33#64751—31no—
34C23×C3×D5D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C5×#67—21no—
37C5×#235—21no—
38C5×#235—21no—
39C5×#235—21no—
40C5×#235—21no—
41C2×C5×D12C2×C411yescharacteristic, complemented
42C2×C4×C5×D3—21no—
43C2×C5×Dic6C2×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×#1201—24no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C42×C5D412yescomplemented
55#6719—21no—
56C4⋊Dic15—21no—
57C4×Dic15C2×C412yescomplemented
58#6710—21no—
59#6710—21no—
60C2×C3⋊#168—21no—
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#5005D511yescharacteristic, complemented
74#4531—51no—
75#4531—51no—
76C2×C5×#41—31no—
77C22×D20C2×D311yescharacteristic
78C2×C5×M16—31no—
79C5×#117C2×D311yescharacteristic
80#4093—32no—
81#4086—32no—
82#4083—62no—
83#4076—62no—
84#4072—31no—
85#4072C2×D311yescharacteristic
86C2×#681—31no—
87#4039—22no—
88D5×C22⋊C4—22no—
89C4×D20—22no—
90C5×#104—62no—
91#3969—62no—
92#3955—62no—
93#1911—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—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
107C2×Dic15—22no—
108C5×#67—41no—
109C5×#67—41no—
110C2×C5×Dic3—21no—
111C5×D12—21no—
112C5×D12—21no—
113C4×C5×D3—41no—
114C4×C5×D3—41no—
115C5×Dic6—21no—
116C5×Dic6—21no—
117C2×C3×Dic5—22no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20—22no—
122C3×C4×D5—84no—
123#1201—84no—
124C3⋊#168—41no—
125C5×C3⋊C8—41no—
126C22×C3×D4—51no—
127C2×#235C2×D511yescharacteristic
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#926—51no—
138C2×#208—51no—
139C2×#208C2×D511yescharacteristic
140#833—102no—
141#805—22no—
142#805—102no—
143C23×D5#6712yes—
144C5×#41—61no—
145C5×#41—61no—
146C5×#41—61no—
147C5×#41—61no—
148C2×C5×Q8—31no—
149C2×C5×D4—31no—
150C2×C5×D4—61no—
151C22×C4×C5—61no—
152C22×C4×C5C22×D311yescharacteristic
153C2×C22⋊D5—64no—
154C2×D20—21no—
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20C4×D312yes—
159C2×D20D1212yes—
160C2×C4×D5—24no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C5×C4⋊C4—21no—
165C5×C22⋊C4—21no—
166C42×C5#6712yescomplemented
167C22⋊Dic5—21no—
168C22⋊Dic5—61no—
169#685—24no—
170#685—64no—
171C4⋊Dic5—21no—
172C4⋊Dic5—61no—
173C4×Dic5—32no—
174C4×Dic5#6712yescomplemented
175#681—61no—
176#681—61no—
177C2×#168—61no—
178#535—151no—
179#518—51no—
180#421—31no—
181#421—151no—
182C2×#100—151no—
183H(3,ℤ/4)—151no—
184H(3,ℤ/4)—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5#12311yescharacteristic
189C2×C5×D3—42no—
190C2×C5×D3—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—42no—
201C3×Dic5—42no—
202C5×Dic3—41no—
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—21no—
213C2×#67—104no—
214#235—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218C2×D12C4×D511yescharacteristic, complemented
219C2×C4×D3—21no—
220C2×Dic6C4×D511yescharacteristic, complemented
221C3×C4⋊C4—21no—
222C3×C4⋊C4—101no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—104no—
225C3×C22⋊C4—101no—
226C3×C42—52no—
227C3×C42C22⋊D512yescomplemented
228#217—104no—
229#217—101no—
230C4⋊Dic3—101no—
231C4×Dic3—52no—
232#208—21no—
233#208—21no—
234#208—101no—
235#208—101no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—101no—
238C23×C5—61no—
239C23×C5C2×#6711yescharacteristic
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—82no—
243C22×D5(C2×D3)⋊C414yes—
244C5×Q8—61no—
245C5×Q8—61no—
246C5×D4—61no—
247C5×D4—61no—
248C5×D4—121no—
249C5×D4—121no—
250C2×C4×C5—22no—
251C2×C4×C5—61no—
252C2×C4×C5—121no—
253C2×C4×C5—121no—
254C2×C4×C5C2×C4×D311yescharacteristic
255C2×C4×C5C2×D1211yescharacteristic
256C2×C4×C5#23511yescharacteristic
257C2×C4×C5#23511yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C2×C4×C5C2×#6711yescharacteristic
260C22⋊D5—244no—
261C2×Dic5—22no—
262C2×Dic5—62no—
263D20—22no—
264D20—22no—
265D20—22no—
266D20—22no—
267C4×D5—84no—
268C5×C8—121no—
269#168—121no—
270C2×#41—31no—
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—51no—
281#117—151no—
282#117D3×D511yescharacteristic
283C2×C22⋊C4—102no—
284#104—62no—
285#104—302no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291C3×D5—44no—
292C5×D3—81no—
293C23×C3—54no—
294C23×C3—102no—
295C23×C3—102no—
296C23×C3—402no—
297C23×C3D4×D511yescharacteristic
298C22×D3—21no—
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×C4#70911yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4#71111yescharacteristic
311C2×C3×C4C2×C22⋊D511yescharacteristic
312#67—41no—
313#67—41no—
314#67—404no—
315C2×Dic3—21no—
316C2×Dic3—102no—
317D12—21no—
318D12—21no—
319C4×D3—41no—
320C4×D3—41no—
321Dic6—21no—
322Dic6—21no—
323C3⋊C8—41no—
324C3⋊C8—201no—
325C22×C5—41no—
326C22×C5—122no—
327C22×C5—121no—
328C22×C5C2×(C2×D3)⋊C411yescharacteristic
329C22×C5#92911yescharacteristic
330C22×C5#95311yescharacteristic
331C2×D5—24no—
332C2×D5—44no—
333C2×D5—44no—
334C2×D5—82no—
335C4×C5—42no—
336C4×C5—121no—
337C4×C5C4×#6711yescharacteristic
338C4×C5C4×#6711yescharacteristic
339C4×C5#93011yescharacteristic
340C4×C5#93011yescharacteristic
341Dic5—42no—
342Dic5—122no—
343C24—52no—
344#41—61no—
345#41—61no—
346#41—61no—
347#41—61no—
348C2×Q8—31no—
349C2×D4—31no—
350C2×D4—52no—
351C2×D4—52no—
352C2×D4—61no—
353C2×D4—101no—
354C2×D4—101no—
355C2×D4—101no—
356C2×D4—101no—
357C2×D4—304no—
358C22×C4—61no—
359C22×C4—104no—
360C22×C4C2×D3×D511yescharacteristic
361M16—61no—
362M16—61no—
363M16—301no—
364M16—301no—
365C2×C8—61no—
366C2×C8—301no—
367C4⋊C4—21no—
368C4⋊C4—101no—
369C4⋊C4—301no—
370C22⋊C4—21no—
371C22⋊C4—104no—
372C22⋊C4—101no—
373C22⋊C4—304no—
374C22⋊C4—301no—
375C42—52no—
376C42—152no—
377C42#120112yescomplemented
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#402911yescharacteristic
386C22×C3#408311yescharacteristic
387C2×D3—42no—
388C2×D3—41no—
389C3×C4—42no—
390C3×C4—202no—
391C3×C4#402711yescharacteristic
392C3×C4#403011yescharacteristic
393C3×C4C4×C22⋊D511yescharacteristic
394C3×C4#408411yescharacteristic
395Dic3—41no—
396Dic3—202no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5—241no—
401C2×C5#521311yescharacteristic
402D5—44no—
403C23—54no—
404C23—61no—
405C23—102no—
406C23—102no—
407C23—402no—
408C23D5×#6711yescharacteristic
409Q8—61no—
410Q8—61no—
411D4—61no—
412D4—61no—
413D4—102no—
414D4—102no—
415D4—102no—
416D4—102no—
417D4—121no—
418D4—121no—
419D4—1204no—
420C2×C4—22no—
421C2×C4—61no—
422C2×C4—102no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—302no—
426C2×C4—404no—
427C2×C4#677111yescharacteristic
428C2×C4#677211yescharacteristic
429C2×C4C4×D3×D511yescharacteristic
430C2×C4D5×D1211yescharacteristic
431C2×C4C2×#120111yescharacteristic
432C2×C4D5×#6711yescharacteristic
433C8—121no—
434C8—601no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—204no—
439C2×C3#6524511yescharacteristic
440D3—81no—
441C5#7165211yescharacteristic, complemented, Sylow
442C22—41no—
443C22—104no—
444C22—122no—
445C22—121no—
446C22—204no—
447C22—204no—
448C22—402no—
449C22#9144711yescharacteristic
450C22D5×(C2×D3)⋊C411yescharacteristic
451C22#9156311yescharacteristic
452C4—42no—
453C4—121no—
454C4—202no—
455C4—602no—
456C4C4×#120111yescharacteristic
457C4#9144011yescharacteristic
458C4#9144811yescharacteristic
459C4#9144911yescharacteristic
460C3#1060120111yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—204no—
465C2—241no—
466C2#1174890511yescharacteristic
subgroupG/H
centerC2#11748905
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11754600C2
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. C5×#5005C2semidirect
4. #11748425C2semidirect
5. C2×#90958C2semidirect
6. #11746352C2semidirect
7. #11745970C2semidirect
20. #91463C4semidirect
22. #91368C4semidirect
28. #65855D3semidirect
41. C2×C5×D12C2×C4semidirect
43. C2×C5×Dic6C2×C4semidirect
54. C3×C42×C5D4semidirect
57. C4×Dic15C2×C4semidirect
67. C3×C4×Dic5D4semidirect
73. #5005D5semidirect
166. C42×C5#67semidirect
174. C4×Dic5#67semidirect
218. C2×D12C4×D5semidirect
220. C2×Dic6C4×D5semidirect
227. C3×C42C22⋊D5semidirect
377. C42#1201semidirect
378. C3×C5#1911semidirect
441. C5#71652semidirect
460. C3#10601201semidirect

Maximal subgroups

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

subgroupindex
C3×#658552
#117546002
C5×#50052
#117484252
C2×#909582
#117463522
#117459702
#106012013
#716525