Finite Group Databasebeta

← #14301739

Subgroups — #14301739

Order 1920.

684 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×#65858C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11748353C211yesmaximal, characteristic, complemented
4#11748341C211yesmaximal, characteristic, complemented
5#11748341C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7C5×#4533C211yesmaximal, characteristic, complemented
8#10599829—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4043—21no—
17C3×#4041—21no—
18C3×#4032C412yes—
19C3×#4028C412yes—
20C3×C4×D20—22no—
21#91284—22no—
22#91283—22no—
23D5×#208—22no—
24#90961—21no—
25#90958—21no—
26#90955—22no—
27#90955—22no—
28#71714—51nomaximal, Hall
29#66079—31no—
30#65858D311yescharacteristic
31#65421—31no—
32#65415—31no—
33#65415—31no—
34C5×#344—31no—
35#64753—31no—
36C23×C3×D5C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C2×C3×C22⋊D5C2×C412yes—
39C22×C3×Dic5C2×C411yescharacteristic
40C3×#709—21no—
41C3×#709—21no—
42C3×#709—21no—
43C3×#709—21no—
44C2×C3×D20—22no—
45C2×C3×D20D411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5D412yes—
53C2×C3×Dic10D411yescharacteristic
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4C2×C412yes—
56C3×C42×C5—21no—
57#6710—21no—
58#6710—21no—
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168D412yescomplemented
63C5×#208—21no—
64C5×#208—21no—
65C5×#208—21no—
66C5×#208—21no—
67C2×C5×C3⋊C8—21no—
68C2×C5×C3⋊C8D412yescomplemented
69C3×#685—22no—
70C3×#685—22no—
71C3×C4⋊Dic5—22no—
72#6649—24no—
73D5×C3⋊C8—24no—
74C3×#525—51no—
75#5819—51no—
76#5237—51no—
77#5207—51no—
78#5207—51no—
79#4533—51no—
80#4533D511yescharacteristic, complemented
81C2×#709C2×D311yescharacteristic
82C22×C4×D5C2×D311yescharacteristic
83C2×C5×M16—31no—
84C2×C5×M16—31no—
85C5×#117C2×D311yescharacteristic
86C2×#681—31no—
87C2×#681—31no—
88#4053—62no—
89D5×M16—62no—
90#4047—62no—
91#4043—21no—
92#4041—21no—
93#4032Dic312yes—
94#4028Dic312yes—
95C4×D20—22no—
96#3956—61no—
97#3955—61no—
98#3952—62no—
99#3952—62no—
100#1891—151noSylow
101C23×C3×C5C22×C411yescharacteristic
102C22×C3×D5—21no—
103C22×C3×D5—21no—
104C22×C3×D5—21no—
105C22×C3×D5—42no—
106C22×C3×D5C22⋊C412yes—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5C2×D411yescharacteristic
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
114C3×C22⋊D5—22no—
115C3×C22⋊D5—22no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5C22⋊C412yes—
120C3×D20—21no—
121C3×D20—21no—
122C3×D20—44no—
123C3×C4×D5—22no—
124C3×C4×D5—22no—
125C3×C4×D5—41no—
126C3×C4×D5—41no—
127C3×C4×D5—41no—
128C3×C4×D5—41no—
129C3×Dic10—21no—
130C3×Dic10—21no—
131C3⋊#168—22no—
132C3⋊#168—41no—
133C5×C3⋊C8—22no—
134C5×C3⋊C8—41no—
135C2×C3×#41—51no—
136C23×C3×C4—51no—
137C3×#123—52no—
138C3×C22⋊Q8—101no—
139C3×#121—101no—
140C3×#120—52no—
141C3×C4×D4—102no—
142C3×#117C2×D511yescharacteristic
143#948—102no—
144#948—102no—
145C2×#208—51no—
146C2×#208—51no—
147C2×#208—102no—
148C2×#208C2×D511yescharacteristic
149C2×#208C2×D511yescharacteristic
150#836—101no—
151#833—101no—
152#830—102no—
153#830—102no—
154C23×D5C2×Dic311yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5C2×Dic312yes—
157C22×Dic5C2×Dic311yescharacteristic
158#709—21no—
159#709—21no—
160#709—21no—
161#709—21no—
162C2×D20—22no—
163C2×D20#6711yescharacteristic
164C2×C4×D5—21no—
165C2×C4×D5—21no—
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5#6712yes—
171C2×Dic10#6711yescharacteristic
172C5×M16—61no—
173C5×M16—61no—
174C5×M16—61no—
175C5×M16—61no—
176C2×C5×C8—32no—
177C2×C5×C8—61no—
178C5×C4⋊C4—21no—
179C5×C22⋊C4C2×Dic312yes—
180C42×C5—21no—
181#685—22no—
182#685—22no—
183C4⋊Dic5—22no—
184#681—61no—
185#681—61no—
186#681—61no—
187#681—61no—
188C2×#168—32no—
189C2×#168—61no—
190#676—64no—
191C8×D5—64no—
192#568—151no—
193#525—51no—
194#413—151no—
195#407—151no—
196#407—151no—
197#344—31no—
198#344—151no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C22×C3×C5C4×D411yescharacteristic
202C22×C3×C5C4×D411yescharacteristic
203C2×C3×D5—22no—
204C2×C3×D5—22no—
205C2×C3×D5—22no—
206C2×C3×D5—22no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C2×C3×D5—41no—
211C2×C3×D5—42no—
212C3×C4×C5—42no—
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217C3×Dic5—22no—
218C3×Dic5—41no—
219C24×C3—51no—
220C3×#41—101no—
221C3×#41—101no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—51no—
225C2×C3×D4—52no—
226C2×C3×D4—51no—
227C2×C3×D4—102no—
228C22×C3×C4—52no—
229C22×C3×C4—51no—
230C22×C3×C4—101no—
231C22×C3×C4—101no—
232C22×C3×C4—101no—
233C22×C3×C4—101no—
234C22×C3×C4—101no—
235C22×C3×C4—101no—
236C22×C3×C4C22×D511yescharacteristic
237C3×C4⋊C4—21no—
238C3×C4⋊C4—102no—
239C3×C22⋊C4—102no—
240C3×C22⋊C4—102no—
241C3×C22⋊C4C4×D512yes—
242C3×C42—21no—
243#208—21no—
244#208—21no—
245#208—21no—
246#208—21no—
247#208—104no—
248#208—101no—
249#208—101no—
250#208—101no—
251#208—101no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—52no—
254C2×C3⋊C8—104no—
255C2×C3⋊C8—101no—
256C2×C3⋊C8D2012yescomplemented
257C23×C5C22×Dic311yescharacteristic
258C22×D5—21no—
259C22×D5—21no—
260C22×D5—21no—
261C22×D5—42no—
262C22×D5#21712yes—
263C2×C4×C5—22no—
264C2×C4×C5D3×D411yescharacteristic
265C2×C4×C5D3×D411yescharacteristic
266C2×C4×C5#23711yescharacteristic
267C2×C4×C5#23711yescharacteristic
268C2×C4×C5C2×#6711yescharacteristic
269C2×C4×C5C2×#6711yescharacteristic
270C22⋊D5—22no—
271C22⋊D5—22no—
272C2×Dic5—21no—
273C2×Dic5—21no—
274C2×Dic5—21no—
275C2×Dic5#21712yes—
276D20—21no—
277D20—21no—
278D20—44no—
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—41no—
282C4×D5—41no—
283C4×D5—41no—
284C4×D5—41no—
285Dic10—21no—
286Dic10—21no—
287C5×C8—62no—
288C5×C8—121no—
289#168—62no—
290#168—121no—
291C2×#41—51no—
292C23×C4—51no—
293#131—302no—
294#131—302no—
295C2×M16—31no—
296C2×M16—31no—
297C2×M16—151no—
298C2×M16—151no—
299C2×M16—302no—
300#123—52no—
301C22⋊Q8—101no—
302#121—101no—
303#120—52no—
304C4×D4—102no—
305#117D3×D511yescharacteristic
306#101—301no—
307#100—301no—
308C22⋊C8—302no—
309C22⋊C8—302no—
310C2×C3×C5—21no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5#38611yescharacteristic
314C3×D5—42no—
315C3×D5—42no—
316C23×C3—52no—
317C23×C3—101no—
318C23×C3—101no—
319C23×C3—101no—
320C23×C3—202no—
321C23×C3C2×C4×D511yescharacteristic
322C3×Q8—101no—
323C3×Q8—101no—
324C3×D4—102no—
325C3×D4—102no—
326C3×D4—101no—
327C3×D4—101no—
328C3×D4—204no—
329C2×C3×C4—22no—
330C2×C3×C4—52no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—101no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4—201no—
339C2×C3×C4—201no—
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4#70911yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4#71311yescharacteristic
346C3⋊C8—22no—
347C3⋊C8—41no—
348C3⋊C8—102no—
349C3⋊C8—201no—
350C22×C5—41no—
351C22×C5D4×Dic311yescharacteristic
352C22×C5D4×Dic311yescharacteristic
353C22×C5C2×#21711yescharacteristic
354C2×D5—22no—
355C2×D5—22no—
356C2×D5—22no—
357C2×D5—22no—
358C2×D5—41no—
359C2×D5—41no—
360C2×D5—41no—
361C2×D5—41no—
362C2×D5—42no—
363C4×C5—42no—
364C4×C5#93511yescharacteristic
365C4×C5#93711yescharacteristic
366C4×C5#93911yescharacteristic
367C4×C5#93911yescharacteristic
368Dic5—22no—
369Dic5—41no—
370C24—51no—
371#41—101no—
372#41—101no—
373#41—101no—
374#41—101no—
375C2×Q8—51no—
376C2×D4—52no—
377C2×D4—51no—
378C2×D4—102no—
379C22×C4—52no—
380C22×C4—51no—
381C22×C4—101no—
382C22×C4—101no—
383C22×C4—101no—
384C22×C4—101no—
385C22×C4—101no—
386C22×C4—101no—
387C22×C4C2×D3×D511yescharacteristic
388M16—61no—
389M16—61no—
390M16—61no—
391M16—61no—
392M16—304no—
393M16—301no—
394M16—301no—
395M16—301no—
396M16—301no—
397C2×C8—32no—
398C2×C8—61no—
399C2×C8—152no—
400C2×C8—304no—
401C2×C8—301no—
402C4⋊C4—21no—
403C4⋊C4—102no—
404C22⋊C4—102no—
405C22⋊C4—102no—
406C22⋊C4D5×Dic312yes—
407C42—21no—
408C3×C5#189111yescharacteristic, complemented, Hall
409C22×C3—41no—
410C22×C3—102no—
411C22×C3—102no—
412C22×C3—102no—
413C22×C3—102no—
414C22×C3—202no—
415C22×C3—201no—
416C22×C3—201no—
417C22×C3—201no—
418C22×C3—201no—
419C22×C3C4×D2011yescharacteristic
420C22×C3D5×C22⋊C411yescharacteristic
421C22×C3#403911yescharacteristic
422C3×C4—42no—
423C3×C4—102no—
424C3×C4—201no—
425C3×C4#402811yescharacteristic
426C3×C4#403011yescharacteristic
427C3×C4#404011yescharacteristic
428C3×C4#404111yescharacteristic
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5#522011yescharacteristic
433D5—42no—
434D5—42no—
435C23—52no—
436C23—101no—
437C23—101no—
438C23—101no—
439C23—202no—
440C23C2×D5×Dic311yescharacteristic
441Q8—101no—
442Q8—101no—
443D4—102no—
444D4—102no—
445D4—101no—
446D4—101no—
447D4—204no—
448C2×C4—22no—
449C2×C4—52no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—101no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—201no—
459C2×C4#676511yescharacteristic
460C2×C4#676611yescharacteristic
461C2×C4D3×D2011yescharacteristic
462C2×C4#677711yescharacteristic
463C2×C4D5×#6711yescharacteristic
464C2×C4D5×#6711yescharacteristic
465C8—62no—
466C8—121no—
467C8—302no—
468C8—601no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—202no—
473C2×C3—202no—
474C2×C3#6495411yescharacteristic
475C5#7171411yescharacteristic, complemented, Sylow
476C22—41no—
477C22—102no—
478C22—102no—
479C22—102no—
480C22—102no—
481C22—202no—
482C22—201no—
483C22—201no—
484C22—201no—
485C22—201no—
486C22Dic3×D2011yescharacteristic
487C22#9143411yescharacteristic
488C22D5×#21711yescharacteristic
489C4—42no—
490C4—102no—
491C4—201no—
492C4#9140711yescharacteristic
493C4#9140811yescharacteristic
494C4#9140911yescharacteristic
495C4#9147411yescharacteristic
496C3#1059982911yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—202no—
501C2—202no—
502C2#1174889611yescharacteristic
subgroupG/H
centerC4#91474
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC3×#65858C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754120C2semidirect
3. #11748353C2semidirect
4. #11748341C2semidirect
5. #11748341C2semidirect
6. #11746354C2semidirect
7. C5×#4533C2semidirect
62. C2×C3⋊#168D4semidirect
68. C2×C5×C3⋊C8D4semidirect
80. #4533D5semidirect
256. C2×C3⋊C8D20semidirect
408. C3×C5#1891semidirect
475. C5#71714semidirect
496. C3#10599829semidirect

Maximal subgroups

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

subgroupindex
C3×#658582
#117541202
#117483532
#117483412
#117463542
C5×#45332
#105998293
#717145