Finite Group Databasebeta

← #14302899

Subgroups — #14302899

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#11754602C211yesmaximal, characteristic
2#11754488C211yesmaximal, characteristic, complemented
3#11751240C211yesmaximal, characteristic, complemented
4C2×C3×#3955C211yesmaximal, characteristic, complemented
5#11748428C211yesmaximal, characteristic, complemented
6C5×#4557C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10599498—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91564—22no—
17D5×#217—22no—
18#91465—22no—
19#91458C412yescomplemented
20#91434—22no—
21Dic3×D20—22no—
22#91364C412yescomplemented
23#91109—22no—
24C3×#3955—22no—
25#90980—22no—
26#70071—51nomaximal, Hall
27#65859—31no—
28#65855—31no—
29#65428—31no—
30C2×#3955D311yescharacteristic, complemented
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×#1202—24no—
51C2×D5×Dic3—24no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C2×C3×C5×C8—21no—
55#6719—21no—
56C4⋊Dic15—21no—
57C4×Dic15D412yescomplemented
58C5×#217—21no—
59C5×#217—21no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3—21no—
62C4×C5×Dic3C2×C412yescomplemented
63C4×C5×Dic3D412yescomplemented
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168—21no—
67#6665—24no—
68#6665—24no—
69#5805—51no—
70#5798—51no—
71C2×C3×#100—51no—
72#5139—51no—
73#5139—51no—
74#4557—51no—
75#4557D511yescharacteristic, complemented
76C2×#709—31no—
77C22×D20C2×D311yescharacteristic
78C2×C5×M16C2×D311yescharacteristic
79C5×#117—31no—
80C5×#117—31no—
81#4072—31no—
82C2×#681C2×D311yescharacteristic
83#4041—62no—
84#4039—62no—
85#4028—62no—
86D5×C22⋊C4—62no—
87#4021—32no—
88#4020—32no—
89C4×D20—62no—
90#3957—62no—
91#3955—22no—
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×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—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—22no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20—22no—
122#1202—84no—
123D5×Dic3—84no—
124C3×C5×C8—41no—
125C3×#168—41no—
126C22×C3×D4—51no—
127C2×#235—51no—
128C2×C3×M16—51no—
129C2×C3×M16C2×D511yescharacteristic
130#953—102no—
131C2×#217—102no—
132#940—52no—
133#938—102no—
134#936—52no—
135D4×Dic3—102no—
136D4×Dic3—102no—
137#926—51no—
138#926C2×D511yescharacteristic
139#926C2×D511yescharacteristic
140C3×#100—102no—
141#825—102no—
142#825—102no—
143C23×D5D1212yes—
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×D20#6712yes—
158C2×C4×D5—61no—
159C2×C4×D5—64no—
160C2×Dic10—31no—
161C5×M16—21no—
162C5×M16—21no—
163C2×C5×C8—21no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—61no—
168C42×C5—32no—
169C42×C5—32no—
170C22⋊Dic5—61no—
171#685—64no—
172#685—64no—
173C4⋊Dic5—61no—
174C4×Dic5—32no—
175#681—21no—
176#681—21no—
177C2×#168—21no—
178#535—151no—
179#518—151no—
180#421—151no—
181#421—151no—
182C2×#100—51no—
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×C5C4×D411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12111yescharacteristic
199Dic15—42no—
200Dic15—41no—
201C5×Dic3—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×C4C22×D511yescharacteristic
211C2×#67—104no—
212C2×#67—101no—
213C22×Dic3—104no—
214#235—101no—
215#235—101no—
216#235—101no—
217#235—101no—
218C2×D12—51no—
219C2×C4×D3—101no—
220C2×Dic6—51no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—101no—
224C3×M16—101no—
225C2×C3×C8—21no—
226C2×C3×C8—101no—
227#217—21no—
228#217—21no—
229#217—104no—
230#217—104no—
231#217—101no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—101no—
235C4×Dic3—52no—
236C4×Dic3C4×D512yescomplemented
237C4×Dic3D2012yescomplemented
238C23×C5C2×D1211yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—61no—
242C22×D5—82no—
243C22×D5(C2×D3)⋊C414yes—
244C2×C4×C5—62no—
245C2×C4×C5—62no—
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5#23711yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C22⋊D5—121no—
253C22⋊D5—121no—
254C2×Dic5—62no—
255C2×Dic5—61no—
256D20—22no—
257D20—22no—
258D20—22no—
259D20—22no—
260D20—61no—
261D20—61no—
262D20—244no—
263C4×D5—121no—
264C4×D5—121no—
265C4×D5—244no—
266Dic10—61no—
267Dic10—61no—
268C5×C8—41no—
269#168—41no—
270C2×#41—151no—
271C22×D4—51no—
272C2×M16—51no—
273C2×M16D3×D511yescharacteristic
274#127—152no—
275#124—152no—
276#121—302no—
277#120—302no—
278C4×D4—302no—
279C4×D4—302no—
280#117—31no—
281#117—31no—
282#117—151no—
283C2×C22⋊C4—302no—
284#104—302no—
285#104—302no—
286#100—102no—
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×C4C2×C4×D511yescharacteristic
304C2×C3×C4C2×D2011yescharacteristic
305C2×C3×C4#70911yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4#71311yescharacteristic
309#67—201no—
310#67—201no—
311#67—404no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—101no—
315C2×Dic3—102no—
316C2×Dic3—404no—
317D12—101no—
318D12—101no—
319C4×D3—201no—
320C4×D3—201no—
321Dic6—101no—
322Dic6—101no—
323C3×C8—41no—
324C3×C8—201no—
325C22×C5—41no—
326C22×C5#88211yescharacteristic
327C22×C5#88611yescharacteristic
328C22×C5C2×(C2×D3)⋊C411yescharacteristic
329C2×D5—24no—
330C2×D5—44no—
331C2×D5—44no—
332C2×D5—82no—
333C2×D5—122no—
334C2×D5—121no—
335C4×C5—122no—
336C4×C5—122no—
337C4×C5#67⋊C411yescharacteristic
338C4×C5#67⋊C411yescharacteristic
339C4×C5#93911yescharacteristic
340C4×C5#93911yescharacteristic
341Dic5—122no—
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—304no—
359C22×C4—301no—
360C22×C4C2×D3×D511yescharacteristic
361M16—21no—
362M16—21no—
363M16—101no—
364M16—101no—
365C2×C8—21no—
366C2×C8—101no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—301no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—304no—
373C22⋊C4—304no—
374C22⋊C4—301no—
375C42—32no—
376C42—32no—
377C42—152no—
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×C4C4×D2011yescharacteristic
390C3×C4#403011yescharacteristic
391C3×C4#403911yescharacteristic
392C3×C4#404111yescharacteristic
393Dic3—42no—
394Dic3—42no—
395Dic3—202no—
396Dic3—201no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5#495811yescharacteristic
401D5—44no—
402D5—241no—
403C23—54no—
404C23—102no—
405C23—102no—
406C23—301no—
407C23—402no—
408C23D5×D1211yescharacteristic
409Q8—301no—
410Q8—301no—
411D4—102no—
412D4—102no—
413D4—102no—
414D4—102no—
415D4—301no—
416D4—301no—
417D4—601no—
418D4—601no—
419D4—1204no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—301no—
423C2×C4—302no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4—1204no—
427C2×C4#676611yescharacteristic
428C2×C4C4×D3×D511yescharacteristic
429C2×C4D3×D2011yescharacteristic
430C2×C4#677911yescharacteristic
431C2×C4D5×#6711yescharacteristic
432C2×C4#679011yescharacteristic
433C8—41no—
434C8—201no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—204no—
439C2×C3#6495411yescharacteristic
440D3—401no—
441C5#7007111yescharacteristic, complemented, Sylow
442C22—41no—
443C22—104no—
444C22—204no—
445C22—204no—
446C22—402no—
447C22—602no—
448C22—601no—
449C22#9141311yescharacteristic
450C22D5×(C2×D3)⋊C411yescharacteristic
451C22#9147611yescharacteristic
452C4—122no—
453C4—122no—
454C4—602no—
455C4—601no—
456C4#9139511yescharacteristic
457C4#9139611yescharacteristic
458C4#9140911yescharacteristic
459C4#9155011yescharacteristic
460C3#1059949811yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—204no—
465C2—1201no—
466C2#1174887211yescharacteristic
subgroupG/H
centerC2#11748872
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754602C2
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. #11754488C2semidirect
3. #11751240C2semidirect
4. C2×C3×#3955C2semidirect
5. #11748428C2semidirect
6. C5×#4557C2semidirect
7. #11745971C2semidirect
19. #91458C4semidirect
22. #91364C4semidirect
30. C2×#3955D3semidirect
41. C2×D60C2×C4semidirect
43. C2×Dic30C2×C4semidirect
57. C4×Dic15D4semidirect
62. C4×C5×Dic3C2×C4semidirect
63. C4×C5×Dic3D4semidirect
75. #4557D5semidirect
236. C4×Dic3C4×D5semidirect
237. C4×Dic3D20semidirect
378. C3×C5#1911semidirect
441. C5#70071semidirect
460. C3#10599498semidirect

Maximal subgroups

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

subgroupindex
#117546022
#117544882
#117512402
C2×C3×#39552
#117484282
C5×#45572
#117459712
#105994983
#700715