Finite Group Databasebeta

← #14301395

Subgroups — #14301395

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66079C211yesmaximal, characteristic, complemented
2#11754586C211yesmaximal, characteristic
3C5×#5139C211yesmaximal, characteristic, complemented
4#11748624C211yesmaximal, characteristic, complemented
5#11748424C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10601210—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4053—22no—
17C3×D5×M16—22no—
18C3×#4047—22no—
19#91571—22no—
20#91463C411yescharacteristic, complemented
21C4×#1201—22no—
22#91385C411yescharacteristic, complemented
23#91370C411yescharacteristic, complemented
24#91368C411yescharacteristic, complemented
25C5×#825—22no—
26#90995—22no—
27#90978—22no—
28#72021—51nomaximal, Hall
29#66166—31no—
30#66079D311yescharacteristic, complemented
31C5×#421—31no—
32#65525—31no—
33#65295—31no—
34#64775—31no—
35#64752—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×C5×#67—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46C2×C3×C22⋊D5D412yes—
47C3×#709—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709—21no—
51C2×C3×D20C2×C411yescharacteristic
52C2×C3×C4×D5D412yes—
53C2×C3×Dic10C2×C411yescharacteristic
54C2×#1201—22no—
55C3×C5×M16—21no—
56C3×C5×M16D412yescomplemented
57C2×C3×C5×C8—21no—
58#6719—21no—
59C4⋊Dic15—21no—
60C4×Dic15—21no—
61C4×Dic15—21no—
62C4×Dic15C2×C411yescharacteristic
63C4×Dic15C2×C411yescharacteristic
64C5×#217—21no—
65C5×C4⋊Dic3—21no—
66C4×C5×Dic3—21no—
67C3×#681—21no—
68C3×#681D412yescomplemented
69C2×C3×#168—21no—
70C3×#676—24no—
71C3×C8×D5—24no—
72#6669—22no—
73(C2×D3)⋊Dic5—22no—
74#6665—22no—
75C3×#568—51no—
76#5832—51no—
77#5240—51no—
78#5139—51no—
79#5139D511yescharacteristic, complemented
80#4555—51no—
81#4555—51no—
82C2×C5×#41—31no—
83C2×#709C2×D311yescharacteristic
84C2×C5×M16C2×D311yescharacteristic
85C5×#117—31no—
86#4093—31no—
87#4090—31no—
88#4086—31no—
89#4085—62no—
90#4082—31no—
91C4×C22⋊D5—62no—
92#4072—31no—
93C2×C4×Dic5—31no—
94C2×#681C2×D311yescharacteristic
95#4053—22no—
96D5×M16—22no—
97#4047—22no—
98C5×#104—62no—
99#3969—62no—
100#3938—62no—
101#1884—151noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3—21no—
104C22×C3×D5C22⋊C412yes—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—21no—
112C2×Dic15—21no—
113C2×Dic15—42no—
114C2×Dic15—41no—
115C5×#67—41no—
116C5×#67—41no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—41no—
119C5×D12—21no—
120C5×D12—21no—
121C4×C5×D3—41no—
122C4×C5×D3—41no—
123C5×Dic6—21no—
124C5×Dic6—21no—
125C3×C22⋊D5—22no—
126C3×C22⋊D5—22no—
127C2×C3×Dic5C22⋊C412yes—
128C3×D20—21no—
129C3×D20—21no—
130C3×C4×D5—22no—
131C3×C4×D5—22no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134#1201—44no—
135C3×C5×C8—22no—
136C3×#168—22no—
137C2×C3×#41—51no—
138C2×#235C2×D511yescharacteristic
139C3×#131—102no—
140C3×#131—102no—
141C2×C3×M16—51no—
142C2×C3×M16—102no—
143C2×C3×M16C2×D511yescharacteristic
144#947—51no—
145#944—51no—
146#940—51no—
147#939—102no—
148#936—51no—
149C4×#67—102no—
150#926—51no—
151#926C2×D511yescharacteristic
152C2×C4×Dic3—51no—
153#834—102no—
154#825—22no—
155#825—102no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C2×C5×Q8—31no—
161C2×C5×D4—31no—
162C2×C5×D4—61no—
163C22×C4×C5—61no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—62no—
166C2×C22⋊D5D1212yes—
167C22×Dic5—61no—
168#709—21no—
169#709—21no—
170#709—21no—
171#709—21no—
172C2×D20C4×D311yescharacteristic
173C2×C4×D5#6712yes—
174C2×Dic10C4×D311yescharacteristic
175C5×M16—21no—
176C5×M16#6712yescomplemented
177C2×C5×C8—21no—
178C5×C4⋊C4—61no—
179C5×C22⋊C4—61no—
180C42×C5—61no—
181C22⋊Dic5—62no—
182C22⋊Dic5—61no—
183#685—62no—
184C4⋊Dic5—61no—
185#683—62no—
186C4×Dic5—31no—
187C4×Dic5—31no—
188C4×Dic5—61no—
189C4×Dic5—61no—
190#681—21no—
191#681#6712yescomplemented
192C2×#168—21no—
193#676—24no—
194C8×D5—24no—
195#568—51no—
196#532—151no—
197#421—31no—
198#421—151no—
199#410—151no—
200#339—151no—
201#339—151no—
202C22×C3×C5—41no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×C5×D3—42no—
207C2×C5×D3—41no—
208C2×C3×D5—22no—
209C2×C3×D5—42no—
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12011yescharacteristic
213C3×C4×C5#12311yescharacteristic
214Dic15—22no—
215Dic15—41no—
216Dic15—81no—
217C3×Dic5—22no—
218C5×Dic3—41no—
219C5×Dic3—81no—
220C3×#41—101no—
221C3×#41—101no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—51no—
225C2×C3×D4—52no—
226C2×C3×D4—51no—
227C22×C3×C4—52no—
228C22×C3×C4C22×D511yescharacteristic
229C2×#67—21no—
230C2×#67—102no—
231C22×Dic3—101no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12C4×D511yescharacteristic
237C2×C4×D3—21no—
238C2×Dic6C4×D511yescharacteristic
239C3×M16—21no—
240C3×M16—52no—
241C3×M16—104no—
242C3×M16—101no—
243C3×M16C22⋊D512yescomplemented
244C2×C3×C8—21no—
245C2×C3×C8—104no—
246C2×C3×C8—101no—
247#217—21no—
248#217—102no—
249#217—101no—
250(C2×D3)⋊C4—102no—
251C4⋊Dic3—21no—
252C4⋊Dic3—101no—
253Dic3⋊C4—102no—
254C4×Dic3—21no—
255C4×Dic3—51no—
256C4×Dic3—51no—
257C4×Dic3—101no—
258C4×Dic3—101no—
259C23×C5—61no—
260C23×C5C2×D1211yescharacteristic
261C22×D5(C2×D3)⋊C412yes—
262C5×Q8—61no—
263C5×Q8—61no—
264C5×D4—61no—
265C5×D4—61no—
266C5×D4—121no—
267C5×D4—121no—
268C2×C4×C5—61no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5#23511yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—22no—
279C22⋊D5—22no—
280C22⋊D5—124no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—122no—
284C2×Dic5—121no—
285C2×Dic5(C2×D3)⋊C412yes—
286D20—21no—
287D20—21no—
288C4×D5—22no—
289C4×D5—22no—
290Dic10—21no—
291Dic10—21no—
292C5×C8—22no—
293#168—22no—
294C2×#41—31no—
295C2×#41—51no—
296#131—102no—
297#131—102no—
298C2×M16—51no—
299C2×M16—102no—
300C2×M16D3×D511yescharacteristic
301C4⋊Q8—151no—
302#127—151no—
303#124—151no—
304#124—151no—
305#121—302no—
306C4×D4—302no—
307#117—31no—
308#117—151no—
309C2×C42—151no—
310#104—62no—
311#104—302no—
312#99—302no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C3×D5—42no—
318C5×D3—81no—
319C23×C3—52no—
320C23×C3D4×D511yescharacteristic
321C22×D3—21no—
322C3×Q8—101no—
323C3×Q8—101no—
324C3×D4—102no—
325C3×D4—102no—
326C3×D4—101no—
327C3×D4—101no—
328C2×C3×C4—52no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4C2×C4×D511yescharacteristic
332C2×C3×C4#70911yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4#71111yescharacteristic
336C2×C3×C4C2×C22⋊D511yescharacteristic
337#67—41no—
338#67—41no—
339#67—204no—
340C2×Dic3—21no—
341C2×Dic3—41no—
342C2×Dic3—101no—
343C2×Dic3—101no—
344C2×Dic3—202no—
345C2×Dic3—201no—
346D12—21no—
347D12—21no—
348C4×D3—41no—
349C4×D3—41no—
350Dic6—21no—
351Dic6—21no—
352C3×C8—22no—
353C3×C8—102no—
354C22×C5—41no—
355C22×C5—122no—
356C22×C5—121no—
357C22×C5C2×(C2×D3)⋊C411yescharacteristic
358C22×C5#93011yescharacteristic
359C22×C5#93011yescharacteristic
360C2×D5—22no—
361C2×D5—42no—
362C4×C5—121no—
363C4×C5—241no—
364C4×C5C4×#6711yescharacteristic
365C4×C5C4×#6711yescharacteristic
366C4×C5#92911yescharacteristic
367C4×C5#95311yescharacteristic
368Dic5—22no—
369Dic5—62no—
370Dic5—121no—
371Dic5—241no—
372#41—61no—
373#41—61no—
374#41—61no—
375#41—61no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×D4—31no—
383C2×D4—52no—
384C2×D4—51no—
385C2×D4—61no—
386C2×D4—302no—
387C22×C4—52no—
388C22×C4—61no—
389C22×C4—301no—
390C22×C4C2×D3×D511yescharacteristic
391M16—21no—
392M16—52no—
393M16—104no—
394M16—101no—
395M16#120112yescomplemented
396C2×C8—21no—
397C2×C8—104no—
398C2×C8—101no—
399C4⋊C4—61no—
400C4⋊C4—302no—
401C4⋊C4—301no—
402C22⋊C4—61no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C22⋊C4—301no—
406C42—61no—
407C42—151no—
408C42—151no—
409C42—301no—
410C42—301no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—102no—
414C22×C3—202no—
415C22×C3D5×C22⋊C411yescharacteristic
416C22×C3#403011yescharacteristic
417C22×C3#408411yescharacteristic
418C2×D3—42no—
419C2×D3—41no—
420C3×C4—102no—
421C3×C4#402711yescharacteristic
422C3×C4#402911yescharacteristic
423C3×C4C4×C22⋊D511yescharacteristic
424C3×C4#408311yescharacteristic
425Dic3—41no—
426Dic3—81no—
427Dic3—102no—
428Dic3—201no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—241no—
434C2×C5#521311yescharacteristic
435D5—42no—
436C23—52no—
437C23—61no—
438C23D5×D1211yescharacteristic
439Q8—61no—
440Q8—61no—
441Q8—101no—
442Q8—101no—
443D4—61no—
444D4—61no—
445D4—102no—
446D4—102no—
447D4—101no—
448D4—101no—
449D4—121no—
450D4—121no—
451D4—604no—
452C2×C4—52no—
453C2×C4—61no—
454C2×C4—102no—
455C2×C4—102no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—301no—
460C2×C4—301no—
461C2×C4—602no—
462C2×C4—601no—
463C2×C4#677111yescharacteristic
464C2×C4#677211yescharacteristic
465C2×C4C4×D3×D511yescharacteristic
466C2×C4C2×#120111yescharacteristic
467C2×C4D5×#6711yescharacteristic
468C2×C4D5×#6711yescharacteristic
469C8—22no—
470C8—102no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—202no—
475C2×C3#6524511yescharacteristic
476D3—81no—
477C5#7202111yescharacteristic, complemented, Sylow
478C22—41no—
479C22—102no—
480C22—122no—
481C22—121no—
482C22—202no—
483C22#9144811yescharacteristic
484C22#9144911yescharacteristic
485C22D5×(C2×D3)⋊C411yescharacteristic
486C4—102no—
487C4—121no—
488C4—241no—
489C4—302no—
490C4—601no—
491C4—1201no—
492C4C4×#120111yescharacteristic
493C4#9144011yescharacteristic
494C4#9144711yescharacteristic
495C4#9156311yescharacteristic
496C3#1060121011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—202no—
501C2—241no—
502C2#1174890511yescharacteristic
subgroupG/H
centerC4#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754586C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#66079C2semidirect
3. C5×#5139C2semidirect
4. #11748624C2semidirect
5. #11748424C2semidirect
6. #11746376C2semidirect
7. #11745975C2semidirect
20. #91463C4semidirect
22. #91385C4semidirect
23. #91370C4semidirect
24. #91368C4semidirect
30. #66079D3semidirect
56. C3×C5×M16D4semidirect
68. C3×#681D4semidirect
79. #5139D5semidirect
176. C5×M16#67semidirect
191. #681#67semidirect
243. C3×M16C22⋊D5semidirect
395. M16#1201semidirect
411. C3×C5#1884semidirect
477. C5#72021semidirect
496. C3#10601210semidirect

Maximal subgroups

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

subgroupindex
C3×#660792
#117545862
C5×#51392
#117486242
#117484242
#117463762
#117459752
#106012103
#720215