Finite Group Databasebeta

← #14301412

Subgroups — #14301412

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
1C5×#5477C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3#11748625C211yesmaximal, characteristic, complemented
4#11748425C211yesmaximal, characteristic, complemented
5#11748424C211yesmaximal, characteristic, complemented
6#11746344C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10602610—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#930—22no—
15C5×#875C411yescharacteristic, complemented
16C5×#875C411yescharacteristic, complemented
17C5×#874C411yescharacteristic, complemented
18C4×C5×D12—22no—
19C5×#869C411yescharacteristic, complemented
20C3×#4072C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22#91288—22no—
23D3×#681—22no—
24#91286—22no—
25#90996—22no—
26#90979—22no—
27#90978—22no—
28#68777—51nomaximal, Hall
29C5×#532—31no—
30#66153—31no—
31#65529—31no—
32#65525—31no—
33#65525—31no—
34#64743—31no—
35#64743D311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C5×#67—21no—
39C2×C5×#67D412yes—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C2×C5×D12—22no—
49C2×C5×D12C2×C411yescharacteristic
50C2×C5×D12C2×C411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C4×C5×D3D412yes—
53C2×C5×Dic6C2×C411yescharacteristic
54C2×C5×Dic6C2×C411yescharacteristic
55C3×C42×C5—21no—
56C3×C42×C5C2×C411yescharacteristic
57C3×C42×C5C2×C411yescharacteristic
58#6719—21no—
59C4⋊Dic15—21no—
60C4×Dic15—21no—
61#6710—21no—
62#6710D412yescomplemented
63C2×C3⋊#168—21no—
64C5×(C2×D3)⋊C4—22no—
65C5×(C2×D3)⋊C4—22no—
66C5×C4⋊Dic3—22no—
67C3×C22⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×C4×Dic5—21no—
70C3×#681—21no—
71C3×#681D412yescomplemented
72C2×C3×#168—21no—
73#6650—24no—
74D3×#168—24no—
75#5745—51no—
76#5477D511yescharacteristic
77#5139—51no—
78#5006—51no—
79#5005—51no—
80C3×#339—51no—
81#4523—51no—
82C2×C5×#41—31no—
83C2×C5×#41—31no—
84C5×C4⋊Q8—31no—
85C5×#127—31no—
86C5×#124—31no—
87C5×#124—31no—
88C5×#121—62no—
89C4×C5×D4—62no—
90C2×C42×C5C2×D311yescharacteristic
91#4094—62no—
92#4094—62no—
93#4072—31no—
94#4072C2×D311yescharacteristic
95C2×#681—31no—
96C2×#681—62no—
97C2×#681C2×D311yescharacteristic
98#3969—62no—
99#3969—62no—
100#3966—62no—
101#1884—151noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3—21no—
104C22×C5×D3C22⋊C412yes—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×Dic15—41no—
115C5×#67—22no—
116C5×#67—22no—
117C5×#67—41no—
118C5×#67—41no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3C22⋊C412yes—
121C5×D12—21no—
122C5×D12—21no—
123C5×D12—21no—
124C5×D12—21no—
125C5×D12—44no—
126C4×C5×D3—22no—
127C4×C5×D3—22no—
128C4×C5×D3—41no—
129C4×C5×D3—41no—
130C5×Dic6—21no—
131C5×Dic6—21no—
132C5×Dic6—21no—
133C5×Dic6—21no—
134C2×C3×Dic5—41no—
135C3⋊#168—22no—
136C3×#168—22no—
137C2×#235C2×D511yescharacteristic
138C2×#235C2×D511yescharacteristic
139C2×C3×M16—51no—
140C3×#117—51no—
141C2×C3×C42C2×D511yescharacteristic
142#930—22no—
143#926—51no—
144C2×#208—51no—
145#907—102no—
146D3×M16—102no—
147#901—102no—
148#875Dic511yescharacteristic, complemented
149#875Dic511yescharacteristic, complemented
150#874Dic511yescharacteristic, complemented
151C4×D12—22no—
152#869Dic511yescharacteristic, complemented
153#825—102no—
154#806—102no—
155#805—102no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C5×#41—61no—
161C5×#41—61no—
162C5×#41—61no—
163C5×#41—61no—
164C2×C5×Q8—31no—
165C2×C5×Q8—31no—
166C2×C5×D4—32no—
167C2×C5×D4—31no—
168C2×C5×D4—31no—
169C2×C5×D4—62no—
170C2×C5×D4—61no—
171C22×C4×C5—21no—
172C22×C4×C5—32no—
173C22×C4×C5—61no—
174C22×C4×C5C22×D311yescharacteristic
175C5×C4⋊C4—62no—
176C5×C22⋊C4—62no—
177C5×C22⋊C4—62no—
178C42×C5—21no—
179C42×C5C4×D311yescharacteristic
180C42×C5C4×D311yescharacteristic
181C22⋊Dic5—21no—
182C22⋊Dic5—61no—
183C4⋊Dic5—21no—
184C4⋊Dic5—61no—
185C4×Dic5—21no—
186C4×Dic5—61no—
187#681—21no—
188#681—32no—
189#681—64no—
190#681—61no—
191#681D1212yescomplemented
192C2×#168—21no—
193C2×#168—64no—
194C2×#168—61no—
195#568—151no—
196#532—31no—
197#421—151no—
198#421—151no—
199#410—151no—
200#339—51no—
201#339—151no—
202C22×C3×C5—41no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×C5×D3—22no—
207C2×C5×D3—42no—
208C2×C5×D3—42no—
209C2×C5×D3—41no—
210C3×C4×C5—22no—
211C3×C4×C5—41no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12011yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—81no—
217C3×Dic5—81no—
218C5×Dic3—22no—
219C5×Dic3—41no—
220C22×C3×C4—21no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—21no—
223C2×#67C22⋊D512yes—
224#235—21no—
225#235—21no—
226#235—21no—
227#235—21no—
228#235—21no—
229#235—21no—
230#235—21no—
231#235—21no—
232C2×D12—22no—
233C2×D12C2×Dic511yescharacteristic
234C2×D12C2×Dic511yescharacteristic
235C2×C4×D3—21no—
236C2×C4×D3C22⋊D512yes—
237C2×Dic6C2×Dic511yescharacteristic
238C2×Dic6C2×Dic511yescharacteristic
239C3×M16—52no—
240C3×M16—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—101no—
243C3×C22⋊C4—101no—
244C3×C42—21no—
245C3×C42—101no—
246C3×C42C2×Dic511yescharacteristic
247C3×C42C2×Dic511yescharacteristic
248#217—101no—
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—22no—
251C4⋊Dic3—22no—
252C4⋊Dic3—101no—
253C4×Dic3—101no—
254#208—52no—
255#208—101no—
256C2×C3⋊C8—101no—
257ΓL(1,𝔽25)—104no—
258D3×C8—104no—
259C23×C5—32no—
260C23×C5—61no—
261C23×C5D3×D411yescharacteristic
262C5×Q8—61no—
263C5×Q8—61no—
264C5×Q8—61no—
265C5×Q8—61no—
266C5×D4—62no—
267C5×D4—62no—
268C5×D4—61no—
269C5×D4—61no—
270C5×D4—61no—
271C5×D4—61no—
272C5×D4—124no—
273C5×D4—121no—
274C5×D4—121no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—32no—
278C2×C4×C5—42no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—61no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5C2×C4×D311yescharacteristic
285C2×C4×C5C2×D1211yescharacteristic
286C2×C4×C5#23511yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5#23911yescharacteristic
290C2×Dic5—41no—
291C2×Dic5—121no—
292#168—22no—
293#168—62no—
294C2×#41—31no—
295C2×#41—31no—
296#131—302no—
297#131—302no—
298C2×M16—51no—
299C2×M16—151no—
300C2×M16—302no—
301C4⋊Q8—31no—
302#127—31no—
303#124—31no—
304#124—31no—
305#121—62no—
306C4×D4—62no—
307#117—51no—
308#117—151no—
309C2×C42D3×D511yescharacteristic
310#104—302no—
311#104—302no—
312#99—302no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C5×D3—42no—
318C5×D3—81no—
319C23×C3C2×C22⋊D511yescharacteristic
320C22×D3—21no—
321C22×D3C22⋊Dic512yes—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—42no—
325C2×C3×C4—201no—
326C2×C3×C4D4×D511yescharacteristic
327C2×C3×C4D4×D511yescharacteristic
328C2×C3×C4#71111yescharacteristic
329C2×C3×C4#71111yescharacteristic
330C2×C3×C4C22×Dic511yescharacteristic
331C2×C3×C4C2×C22⋊D511yescharacteristic
332#67—22no—
333#67—22no—
334#67—41no—
335#67—41no—
336C2×Dic3—21no—
337C2×Dic3—201no—
338C2×Dic3C22⋊Dic512yes—
339D12—21no—
340D12—21no—
341D12—21no—
342D12—21no—
343D12—44no—
344C4×D3—22no—
345C4×D3—22no—
346C4×D3—41no—
347C4×D3—41no—
348Dic6—21no—
349Dic6—21no—
350Dic6—21no—
351Dic6—21no—
352C3×C8—102no—
353C3⋊C8—102no—
354C22×C5—41no—
355C22×C5—62no—
356C22×C5—122no—
357C22×C5—122no—
358C22×C5—121no—
359C22×C5D3×C22⋊C411yescharacteristic
360C22×C5#88411yescharacteristic
361C22×C5#89511yescharacteristic
362C4×C5—22no—
363C4×C5—41no—
364C4×C5—62no—
365C4×C5—121no—
366C4×C5C4×D1211yescharacteristic
367C4×C5#88211yescharacteristic
368C4×C5#89311yescharacteristic
369C4×C5#89411yescharacteristic
370Dic5—81no—
371Dic5—241no—
372#41—61no—
373#41—61no—
374#41—61no—
375#41—61no—
376#41—61no—
377#41—61no—
378#41—61no—
379#41—61no—
380C2×Q8—31no—
381C2×Q8—31no—
382C2×D4—32no—
383C2×D4—31no—
384C2×D4—31no—
385C2×D4—62no—
386C2×D4—61no—
387C22×C4—21no—
388C22×C4—32no—
389C22×C4—61no—
390C22×C4C2×D3×D511yescharacteristic
391M16—52no—
392M16—101no—
393M16—152no—
394M16—304no—
395M16—301no—
396C2×C8—101no—
397C2×C8—304no—
398C2×C8—301no—
399C4⋊C4—62no—
400C4⋊C4—101no—
401C4⋊C4—301no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C22⋊C4—101no—
405C22⋊C4—301no—
406C42—21no—
407C42—101no—
408C42—301no—
409C42D3×Dic511yescharacteristic
410C42D3×Dic511yescharacteristic
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3#408511yescharacteristic
414C22×C3#408511yescharacteristic
415C22×C3C2×C22⋊Dic511yescharacteristic
416C2×D3—22no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—41no—
420C3×C4—22no—
421C3×C4—41no—
422C3×C4—401no—
423C3×C4D4×Dic511yescharacteristic
424C3×C4D4×Dic511yescharacteristic
425C3×C4#408111yescharacteristic
426C3×C4#408311yescharacteristic
427Dic3—22no—
428Dic3—41no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—122no—
434C2×C5—241no—
435C2×C5#466511yescharacteristic
436C23—32no—
437C23—61no—
438C23D3×C22⋊D511yescharacteristic
439Q8—61no—
440Q8—61no—
441Q8—61no—
442Q8—61no—
443D4—62no—
444D4—62no—
445D4—61no—
446D4—61no—
447D4—61no—
448D4—61no—
449D4—124no—
450D4—121no—
451D4—121no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—32no—
455C2×C4—42no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—201no—
462C2×C4—601no—
463C2×C4#676811yescharacteristic
464C2×C4#677211yescharacteristic
465C2×C4D5×D1211yescharacteristic
466C2×C4#677711yescharacteristic
467C2×C4C2×D3×Dic511yescharacteristic
468C2×C4D3×C22⋊D511yescharacteristic
469C8—102no—
470C8—302no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3#6550911yescharacteristic
475D3—42no—
476D3—81no—
477C5#6877711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—62no—
480C22—122no—
481C22—122no—
482C22—121no—
483C22#9141611yescharacteristic
484C22#9145311yescharacteristic
485C22D3×C22⋊Dic511yescharacteristic
486C4—22no—
487C4—41no—
488C4—62no—
489C4—121no—
490C4—401no—
491C4—1201no—
492C4Dic5×D1211yescharacteristic
493C4#9142311yescharacteristic
494C4#9143511yescharacteristic
495C4#9147511yescharacteristic
496C3#1060261011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—122no—
501C2—241no—
502C2#1174890111yescharacteristic
subgroupG/H
centerC4#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#386
prime radicalC5×#5477C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11754125C2semidirect
3. #11748625C2semidirect
4. #11748425C2semidirect
5. #11748424C2semidirect
6. #11746344C2semidirect
7. C3×#64743C2semidirect
15. C5×#875C4semidirect
16. C5×#875C4semidirect
17. C5×#874C4semidirect
19. C5×#869C4semidirect
35. #64743D3semidirect
62. #6710D4semidirect
71. C3×#681D4semidirect
148. #875Dic5semidirect
149. #875Dic5semidirect
150. #874Dic5semidirect
152. #869Dic5semidirect
191. #681D12semidirect
411. C3×C5#1884semidirect
477. C5#68777semidirect
496. C3#10602610semidirect

Maximal subgroups

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

subgroupindex
C5×#54772
#117541252
#117486252
#117484252
#117484242
#117463442
C3×#647432
#106026103
#687775