Finite Group Databasebeta

← #14302854

Subgroups — #14302854

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66079C211yesmaximal, characteristic, complemented
2#11754609C211yesmaximal, characteristic
3#11751232C211yesmaximal, characteristic, complemented
4#11748624C211yesmaximal, characteristic, complemented
5#11748396C211yesmaximal, characteristic, complemented
6C5×#4557C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10599506—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4053—22no—
17C3×D5×M16—22no—
18C3×#4047—22no—
19#91572—22no—
20#91458C412yescomplemented
21#91450—22no—
22#91374C412yescomplemented
23#91105—22no—
24#90995—22no—
25#90969—22no—
26#72025—51nomaximal, Hall
27#66079D311yescharacteristic, complemented
28#65859—31no—
29#65420—31no—
30#65295—31no—
31#65290—31no—
32C5×H(3,ℤ/4)—31no—
33#64751—31no—
34C23×D15—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60C2×C412yes—
42C2×C3×C22⋊D5D412yes—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5D412yes—
49C2×C3×Dic10C2×C411yescharacteristic
50C2×#1202—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8D412yescomplemented
54#6719—21no—
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57C5×#217—21no—
58C5×#217—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3—21no—
62C4×C5×Dic3C2×C412yes—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168D412yescomplemented
66C3×#676—24no—
67C3×C8×D5—24no—
68#6667—24no—
69C3×#568—51no—
70#5830—51no—
71#5240—51no—
72#5131—51no—
73#5131—51no—
74#4557—51no—
75#4557D511yescharacteristic, complemented
76C2×#709C2×D311yescharacteristic
77C22×D20—31no—
78C2×C5×M16C2×D311yescharacteristic
79C5×#117—31no—
80C5×#117—31no—
81#4072—31no—
82C2×#681C2×D311yescharacteristic
83#4053—22no—
84D5×M16—22no—
85#4047—22no—
86#4041—62no—
87#4028—62no—
88#4021—32no—
89#4020—32no—
90#3953—62no—
91#3941—62no—
92#3938—62no—
93#1910—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—41no—
97C22×D15—41no—
98C22×D15—82no—
99C22×C3×D5C22⋊C412yes—
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
106C2×Dic15—41no—
107D60—22no—
108D60—22no—
109D60—41no—
110D60—41no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—41no—
113C3×C22⋊D5—22no—
114C3×C22⋊D5—22no—
115C2×C3×Dic5C22⋊C412yes—
116C3×D20—21no—
117C3×D20—21no—
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3×Dic10—21no—
121C3×Dic10—21no—
122#1202—84no—
123C3×C5×C8—22no—
124C3×#168—22no—
125C2×C3×#41—51no—
126C22×D12—51no—
127C3×#131—102no—
128C3×#131—102no—
129C2×C3×M16—51no—
130C2×C3×M16—102no—
131C2×C3×M16C2×D511yescharacteristic
132#947—52no—
133#940—52no—
134#937—102no—
135#930—102no—
136#926—51no—
137#926C2×D511yescharacteristic
138#926C2×D511yescharacteristic
139#834—102no—
140#821—102no—
141#821—102no—
142C23×D5—61no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5D1212yes—
145#709—21no—
146#709—21no—
147#709—21no—
148#709—21no—
149C2×D20—32no—
150C2×D20—61no—
151C2×D20—61no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—64no—
156C2×D20C4×D311yescharacteristic
157C2×C4×D5#6712yes—
158C2×Dic10C4×D311yescharacteristic
159C5×M16—21no—
160C5×M16—21no—
161C2×C5×C8#6712yescomplemented
162C5×C4⋊C4—61no—
163C5×C4⋊C4—61no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—61no—
166C42×C5—32no—
167C42×C5—61no—
168C22⋊Dic5—61no—
169#685—64no—
170C4⋊Dic5—61no—
171C4×Dic5—61no—
172#681—21no—
173#681—21no—
174C2×#168#6712yescomplemented
175#676—24no—
176C8×D5—24no—
177#568—51no—
178#535—151no—
179#418—151no—
180#418—151no—
181#410—151no—
182H(3,ℤ/4)—31no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5#12111yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×D15—44no—
189C2×D15—42no—
190C2×D15—82no—
191C2×D15—82no—
192C2×C3×D5—22no—
193C2×C3×D5—42no—
194C3×C4×C5C4×D411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5#12011yescharacteristic
197C3×C4×C5#12311yescharacteristic
198Dic15—81no—
199C3×Dic5—22no—
200C5×Dic3—42no—
201C5×Dic3—81no—
202C23×D3—101no—
203C3×#41—101no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C2×C3×Q8—51no—
208C2×C3×D4—52no—
209C2×C3×D4—51no—
210C22×C3×C4—52no—
211C22×C3×C4C22×D511yescharacteristic
212C2×#67—104no—
213C2×D12—52no—
214C2×D12—101no—
215C2×D12—101no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12—101no—
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—104no—
222C3×M16—101no—
223C3×M16—101no—
224C2×C3×C8—52no—
225C2×C3×C8—104no—
226C2×C3×C8D2012yescomplemented
227#217—21no—
228#217—21no—
229#217—101no—
230(C2×D3)⋊C4—104no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3—101no—
234C4×Dic3—21no—
235C4×Dic3—101no—
236C4×Dic3C4×D512yes—
237C23×C5C2×D1211yescharacteristic
238C22×D5—62no—
239C22×D5—121no—
240C22×D5—121no—
241C22×D5—242no—
242C22×D5(C2×D3)⋊C412yes—
243C2×C4×C5—62no—
244C2×C4×C5—121no—
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5#23511yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C22⋊D5—22no—
252C22⋊D5—22no—
253C2×Dic5—121no—
254C2×Dic5(C2×D3)⋊C412yes—
255D20—21no—
256D20—21no—
257D20—62no—
258D20—62no—
259D20—121no—
260D20—121no—
261D20—244no—
262C4×D5—22no—
263C4×D5—22no—
264Dic10—21no—
265Dic10—21no—
266C5×C8—22no—
267#168—22no—
268C2×#41—51no—
269C22×D4—151no—
270#131—102no—
271#131—102no—
272C2×M16—51no—
273C2×M16—102no—
274C2×M16D3×D511yescharacteristic
275#127—152no—
276#124—152no—
277#121—302no—
278#120—302no—
279#117—31no—
280#117—31no—
281#117—151no—
282#102—302no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289D15—82no—
290C3×D5—42no—
291C23×C3—52no—
292C23×C3D4×D511yescharacteristic
293C22×D3—102no—
294C22×D3—201no—
295C22×D3—201no—
296C22×D3—402no—
297C3×Q8—101no—
298C3×Q8—101no—
299C3×D4—102no—
300C3×D4—102no—
301C3×D4—101no—
302C3×D4—101no—
303C2×C3×C4—52no—
304C2×C3×C4—102no—
305C2×C3×C4—102no—
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—404no—
313C2×Dic3—22no—
314C2×Dic3—41no—
315C2×Dic3—201no—
316D12—102no—
317D12—102no—
318D12—201no—
319D12—201no—
320C3×C8—22no—
321C3×C8—102no—
322C22×C5—41no—
323C22×C5C2×(C2×D3)⋊C411yescharacteristic
324C22×C5#93011yescharacteristic
325C22×C5#93011yescharacteristic
326C2×D5—22no—
327C2×D5—42no—
328C2×D5—124no—
329C2×D5—122no—
330C2×D5—242no—
331C2×D5—242no—
332C4×C5—122no—
333C4×C5—241no—
334C4×C5C4×#6711yescharacteristic
335C4×C5C4×#6711yescharacteristic
336C4×C5#92911yescharacteristic
337C4×C5#95311yescharacteristic
338Dic5—22no—
339Dic5—241no—
340C24—301no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—52no—
347C2×D4—51no—
348C2×D4—152no—
349C2×D4—304no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—301no—
355C22×C4—52no—
356C22×C4C2×D3×D511yescharacteristic
357M16—21no—
358M16—21no—
359M16—104no—
360M16—101no—
361M16—101no—
362C2×C8—52no—
363C2×C8—104no—
364C2×C8#120212yescomplemented
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—301no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—304no—
371C22⋊C4—301no—
372C42—32no—
373C42—61no—
374C42—301no—
375C3×C5#191011yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—102no—
378C22×C3—202no—
379C22×C3D5×C22⋊C411yescharacteristic
380C22×C3#403011yescharacteristic
381C22×C3#404111yescharacteristic
382C2×D3—204no—
383C2×D3—202no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—102no—
387C3×C4C4×D2011yescharacteristic
388C3×C4#402811yescharacteristic
389C3×C4#403911yescharacteristic
390C3×C4#404011yescharacteristic
391Dic3—42no—
392Dic3—81no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5#521311yescharacteristic
398D5—42no—
399D5—242no—
400C23—52no—
401C23—302no—
402C23—601no—
403C23—601no—
404C23—1202no—
405C23D5×D1211yescharacteristic
406Q8—101no—
407Q8—101no—
408D4—102no—
409D4—102no—
410D4—101no—
411D4—101no—
412D4—302no—
413D4—302no—
414D4—601no—
415D4—601no—
416D4—1204no—
417C2×C4—52no—
418C2×C4—62no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—121no—
422C2×C4—601no—
423C2×C4#677111yescharacteristic
424C2×C4#677311yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4C2×#120211yescharacteristic
427C2×C4D5×#6711yescharacteristic
428C2×C4D5×#6711yescharacteristic
429C8—22no—
430C8—102no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—202no—
435C2×C3#6495411yescharacteristic
436D3—402no—
437C5#7202511yescharacteristic, complemented, Sylow
438C22—41no—
439C22—102no—
440C22—202no—
441C22—604no—
442C22—602no—
443C22—1202no—
444C22—1202no—
445C22#9144811yescharacteristic
446C22#9145011yescharacteristic
447C22D5×(C2×D3)⋊C411yescharacteristic
448C4—102no—
449C4—122no—
450C4—241no—
451C4—1201no—
452C4#9134811yescharacteristic
453C4C4×#120211yescharacteristic
454C4#9144411yescharacteristic
455C4#9156411yescharacteristic
456C3#1059950611yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—202no—
461C2—1202no—
462C2#1174890711yescharacteristic
subgroupG/H
centerC2#11748907
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754609C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1910
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
1. C3×#66079C2semidirect
3. #11751232C2semidirect
4. #11748624C2semidirect
5. #11748396C2semidirect
6. C5×#4557C2semidirect
7. #11745971C2semidirect
20. #91458C4semidirect
22. #91374C4semidirect
27. #66079D3semidirect
53. C2×C3×C5×C8D4semidirect
65. C2×C3×#168D4semidirect
75. #4557D5semidirect
161. C2×C5×C8#67semidirect
174. C2×#168#67semidirect
226. C2×C3×C8D20semidirect
364. C2×C8#1202semidirect
375. C3×C5#1910semidirect
437. C5#72025semidirect
456. C3#10599506semidirect

Maximal subgroups

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

subgroupindex
C3×#660792
#117546092
#117512322
#117486242
#117483962
C5×#45572
#117459712
#105995063
#720255