Finite Group Databasebeta

← #14301736

Subgroups — #14301736

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×#66125C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11751308C211yesmaximal, characteristic, complemented
4C5×#5207C211yesmaximal, characteristic, complemented
5#11748353C211yesmaximal, characteristic, complemented
6#11745993C211yesmaximal, characteristic, complemented
7#11745992C211yesmaximal, characteristic, complemented
8#10600785—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4099C412yes—
16C3×#4076—21no—
17C3×#4075C412yes—
18C3×C4×C22⋊D5—22no—
19C3×#4072C2211yescharacteristic
20C3×#4070—21no—
21#91284—22no—
22#91283—22no—
23D5×#208—22no—
24#91114—22no—
25C5×#830—22no—
26#90961—21no—
27#90958—21no—
28#71714—51nomaximal, Hall
29#66125D311yescharacteristic
30#66079—31no—
31C5×#407—31no—
32#65496—31no—
33#65421—31no—
34#64779—31no—
35#64776—31no—
36C24×C3×C5C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2×C411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C22⋊D5—22no—
46C2×C3×C22⋊D5C2×C412yes—
47C3×#709—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709—21no—
51C2×C3×D20D411yescharacteristic
52C2×C3×C4×D5D412yes—
53C2×C3×Dic10D411yescharacteristic
54#6710—21no—
55#6710—21no—
56#6710—21no—
57#6710—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168D412yescomplemented
60C5×#208—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8D412yescomplemented
66C3×C22⋊Dic5—22no—
67C3×C22⋊Dic5C2×C412yes—
68C3×#685—22no—
69C3×C4⋊Dic5—21no—
70C3×#683—22no—
71C3×C4×Dic5—21no—
72#6649—24no—
73D5×C3⋊C8—24no—
74C3×#525—51no—
75#5819—51no—
76#5237—51no—
77#5207—51no—
78#5207D511yescharacteristic, complemented
79#4533—51no—
80#4533—51no—
81C23×C4×C5C2×D311yescharacteristic
82C2×#709C2×D311yescharacteristic
83C2×C5×M16—31no—
84C2×C5×M16—31no—
85#4099Dic312yes—
86#4076—21no—
87#4075Dic312yes—
88C4×C22⋊D5—22no—
89#4072C2×D311yescharacteristic
90#4070—21no—
91C2×#681—31no—
92C2×#681—31no—
93#4053—62no—
94D5×M16—62no—
95#4047—62no—
96C5×C22⋊C8—62no—
97C22⋊#168—62no—
98#3956—61no—
99#3955—61no—
100#1891—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5—21no—
103C23×C3×C5—21no—
104C23×C3×C5—42no—
105C23×C3×C5C22×C411yescharacteristic
106C22×C3×D5C22⋊C412yes—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C3×C22⋊D5—22no—
121C3×C22⋊D5—22no—
122C3×C22⋊D5—44no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5C22⋊C412yes—
125C3×D20—21no—
126C3×D20—21no—
127C3×C4×D5—22no—
128C3×C4×D5—22no—
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×C4C2×D511yescharacteristic
137C3×#123—52no—
138C3×C22⋊Q8—101no—
139C3×#121—101no—
140C3×#120—52no—
141C3×C4×D4—102no—
142C3×#117—51no—
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—22no—
153#830—102no—
154C24×C5C2×Dic311yescharacteristic
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5C2×Dic311yescharacteristic
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—22no—
164C2×C22⋊D5C2×Dic312yes—
165#709—21no—
166#709—21no—
167#709—21no—
168#709—21no—
169C2×D20#6711yescharacteristic
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—
178C22⋊Dic5—22no—
179C22⋊Dic5C2×Dic312yes—
180#685—22no—
181C4⋊Dic5—21no—
182#683—22no—
183C4×Dic5—21no—
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—31no—
196#407—151no—
197#344—151no—
198#344—151no—
199C22×C3×C5—22no—
200C22×C3×C5—22no—
201C22×C3×C5—22no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5—41no—
205C22×C3×C5—41no—
206C22×C3×C5—41no—
207C22×C3×C5C2×C22⋊C411yescharacteristic
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5C4×D411yescharacteristic
210C2×C3×D5—22no—
211C2×C3×D5—42no—
212C3×C4×C5—41no—
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217C3×Dic5—22no—
218C3×Dic5—42no—
219C24×C3C4×D511yescharacteristic
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—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—52no—
235C22×C3×C4C4×D511yescharacteristic
236C22×C3×C4C22×D511yescharacteristic
237C3×C4⋊C4—102no—
238C3×C4⋊C4—101no—
239C3×C22⋊C4—52no—
240C3×C22⋊C4—102no—
241C3×C22⋊C4—102no—
242C3×C42—101no—
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⋊C8C22⋊D512yescomplemented
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—42no—
261C23×C5C22×Dic311yescharacteristic
262C22×D5#21712yes—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5D3×D411yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5#23711yescharacteristic
273C2×C4×C5#23711yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C22⋊D5—22no—
277C22⋊D5—22no—
278C22⋊D5—44no—
279C2×Dic5—22no—
280C2×Dic5#21712yes—
281D20—21no—
282D20—21no—
283C4×D5—22no—
284C4×D5—22no—
285Dic10—21no—
286Dic10—21no—
287C5×C8—62no—
288C5×C8—121no—
289#168—62no—
290#168—121no—
291C2×#41—51no—
292C23×C4D3×D511yescharacteristic
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#117—51no—
306#101—301no—
307#100—301no—
308C22⋊C8—62no—
309C22⋊C8—302no—
310C2×C3×C5—21no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5—42no—
314C2×C3×C5#38611yescharacteristic
315C3×D5—42no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—42no—
320C23×C3—52no—
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—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—52no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4—102no—
340C2×C3×C4#70911yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4#71111yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C3⋊C8—22no—
347C3⋊C8—41no—
348C3⋊C8—102no—
349C3⋊C8—201no—
350C22×C5—22no—
351C22×C5—22no—
352C22×C5—22no—
353C22×C5—41no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5D4×Dic311yescharacteristic
359C22×C5D4×Dic311yescharacteristic
360C22×C5C2×#21711yescharacteristic
361C2×D5—22no—
362C2×D5—42no—
363C4×C5—41no—
364C4×C5#93511yescharacteristic
365C4×C5#93711yescharacteristic
366C4×C5#93911yescharacteristic
367C4×C5#93911yescharacteristic
368Dic5—22no—
369Dic5—42no—
370C24D5×Dic311yescharacteristic
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—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—52no—
386C22×C4D5×Dic311yescharacteristic
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—102no—
403C4⋊C4—101no—
404C22⋊C4—52no—
405C22⋊C4—102no—
406C22⋊C4—102no—
407C42—101no—
408C3×C5#189111yescharacteristic, complemented, Hall
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—102no—
418C22×C3—202no—
419C22×C3D5×C22⋊C411yescharacteristic
420C22×C3#402711yescharacteristic
421C22×C3C4×C22⋊D511yescharacteristic
422C3×C4—41no—
423C3×C4—102no—
424C3×C4—202no—
425C3×C4#402911yescharacteristic
426C3×C4#403011yescharacteristic
427C3×C4#408311yescharacteristic
428C3×C4#408411yescharacteristic
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—42no—
433C2×C5#522011yescharacteristic
434D5—42no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—42no—
439C23—52no—
440C23C2×D5×Dic311yescharacteristic
441Q8—101no—
442Q8—101no—
443D4—102no—
444D4—102no—
445D4—101no—
446D4—101no—
447D4—204no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—52no—
456C2×C4—102no—
457C2×C4—102no—
458C2×C4—102no—
459C2×C4#677911yescharacteristic
460C2×C4#678011yescharacteristic
461C2×C4D5×#6711yescharacteristic
462C2×C4D5×#6711yescharacteristic
463C2×C4D3×C22⋊D511yescharacteristic
464C2×C4#679011yescharacteristic
465C8—62no—
466C8—121no—
467C8—302no—
468C8—601no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—42no—
473C2×C3—202no—
474C2×C3#6524511yescharacteristic
475C5#7171411yescharacteristic, complemented, Sylow
476C22—22no—
477C22—22no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—102no—
485C22—202no—
486C22D5×#21711yescharacteristic
487C22Dic3×C22⋊D511yescharacteristic
488C22#9155911yescharacteristic
489C4—41no—
490C4—102no—
491C4—202no—
492C4#9154811yescharacteristic
493C4#9154911yescharacteristic
494C4#9155011yescharacteristic
495C4#9157711yescharacteristic
496C3#1060078511yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—42no—
501C2—202no—
502C2#1174951811yescharacteristic
subgroupG/H
centerC4#91577
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC2×C3×C5#386
prime radicalC3×#66125C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11754120C2semidirect
3. #11751308C2semidirect
4. C5×#5207C2semidirect
5. #11748353C2semidirect
6. #11745993C2semidirect
7. #11745992C2semidirect
59. C2×C3⋊#168D4semidirect
65. C2×C5×C3⋊C8D4semidirect
78. #5207D5semidirect
256. C2×C3⋊C8C22⋊D5semidirect
408. C3×C5#1891semidirect
475. C5#71714semidirect
496. C3#10600785semidirect

Maximal subgroups

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

subgroupindex
C3×#661252
#117541202
#117513082
C5×#52072
#117483532
#117459932
#117459922
#106007853
#717145