Finite Group Databasebeta

← #14301737

Subgroups — #14301737

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
1#11756550C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic, complemented
3C5×#5207C211yesmaximal, characteristic, complemented
4C3×#65496C211yesmaximal, characteristic, complemented
5#11748357C211yesmaximal, characteristic, complemented
6#11745991C211yesmaximal, characteristic, complemented
7#11745990C211yesmaximal, characteristic, complemented
8#10600785—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11#91842C412yes—
12#91819—21no—
13#91818C412yes—
14C4×#1220—22no—
15#91815C2211yescharacteristic
16#91813—21no—
17C2×C5×#208C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91292—22no—
22#91291—22no—
23#91290—22no—
24C5×#830—22no—
25C3×C22⋊#168—22no—
26#90963—21no—
27#90960—21no—
28#69992—51nomaximal, Hall
29#66125—31no—
30#66079—31no—
31C5×#407—31no—
32#65496D311yescharacteristic, complemented
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×#1220—22no—
46C2×#1220C2×C412yes—
47#6817—21no—
48#6817—21no—
49#6817—21no—
50#6817—21no—
51C2×D60D411yescharacteristic
52C2×C4×D15D412yes—
53C2×Dic30D411yescharacteristic
54#6719—22no—
55#6719C2×C412yes—
56#6714—22no—
57C4⋊Dic15—21no—
58#6712—22no—
59C4×Dic15—21no—
60C5×#208—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8D412yescomplemented
66C3×#681—21no—
67C3×#681—21no—
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71C2×C3×#168D412yescomplemented
72#6651—24no—
73#6648—24no—
74#5791—51no—
75#5745—51no—
76C3×#407—51no—
77#5207D511yescharacteristic, complemented
78#5132—51no—
79#4559—51no—
80#4556—51no—
81C23×C4×C5C2×D311yescharacteristic
82C2×#709—31no—
83C2×C5×M16—31no—
84C2×C5×M16—31no—
85#4099—32no—
86#4076—61no—
87#4075—32no—
88C4×C22⋊D5—62no—
89#4072—31no—
90#4070—61no—
91C2×#681C2×D311yescharacteristic
92C2×#681C2×D311yescharacteristic
93#4053—62no—
94D5×M16—62no—
95#4047—62no—
96C5×C22⋊C8—62no—
97C22⋊#168—22no—
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×D15C22⋊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
120#1220—22no—
121#1220—22no—
122#1220—44no—
123C2×Dic15—22no—
124C2×Dic15C22⋊C412yes—
125D60—21no—
126D60—21no—
127C4×D15—22no—
128C4×D15—22no—
129Dic30—21no—
130Dic30—21no—
131C3×#168—22no—
132C3×#168—41no—
133C5×C3⋊C8—22no—
134C5×C3⋊C8—41no—
135C23×C3×C4C2×D511yescharacteristic
136C2×#235—51no—
137C2×C3×M16—51no—
138C2×C3×M16—51no—
139#953—52no—
140#930—101no—
141#929—52no—
142C4×#67—102no—
143#926—51no—
144#924—101no—
145C2×#208C2×D511yescharacteristic
146C2×#208C2×D511yescharacteristic
147#907—102no—
148D3×M16—102no—
149#901—102no—
150C3×C22⋊C8—102no—
151#830—22no—
152#824—101no—
153#823—101no—
154C24×C5C4×D311yescharacteristic
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×C5C4×D311yescharacteristic
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—32no—
164C2×C22⋊D5—62no—
165#709—61no—
166#709—61no—
167#709—61no—
168#709—61no—
169C2×D20—31no—
170C2×C4×D5—32no—
171C2×Dic10—31no—
172C5×M16—61no—
173C5×M16—61no—
174C5×M16—61no—
175C5×M16—61no—
176C2×C5×C8—32no—
177C2×C5×C8—61no—
178C22⋊Dic5—32no—
179C22⋊Dic5—62no—
180#685—62no—
181C4⋊Dic5—61no—
182#683—62no—
183C4×Dic5—61no—
184#681—21no—
185#681—21no—
186#681—21no—
187#681—21no—
188C2×#168—21no—
189C2×#168#6712yescomplemented
190#676—64no—
191C8×D5—64no—
192#568—151no—
193#525—151no—
194#413—151no—
195#407—31no—
196#407—51no—
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×D15—22no—
211C2×D15—42no—
212C3×C4×C5—41no—
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217Dic15—22no—
218Dic15—42no—
219C24×C3C4×D511yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4C4×D511yescharacteristic
227C22×C3×C4C22×D511yescharacteristic
228C2×#67—52no—
229C2×#67—102no—
230#235—101no—
231#235—101no—
232#235—101no—
233#235—101no—
234C2×D12—51no—
235C2×C4×D3—52no—
236C2×Dic6—51no—
237C3×M16—101no—
238C3×M16—101no—
239C3×M16—101no—
240C3×M16—101no—
241C2×C3×C8—52no—
242C2×C3×C8—101no—
243#217—52no—
244#217—102no—
245(C2×D3)⋊C4—102no—
246C4⋊Dic3—101no—
247Dic3⋊C4—102no—
248C4×Dic3—101no—
249#208—21no—
250#208—21no—
251#208—21no—
252#208—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8C22⋊D512yescomplemented
255ΓL(1,𝔽25)—104no—
256D3×C8—104no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—42no—
261C23×C5C2×C4×D311yescharacteristic
262C22×D5—32no—
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×C5#23511yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5#23711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C22⋊D5—62no—
277C22⋊D5—62no—
278C22⋊D5—124no—
279C2×Dic5—32no—
280C2×Dic5—62no—
281D20—61no—
282D20—61no—
283C4×D5—62no—
284C4×D5—62no—
285Dic10—61no—
286Dic10—61no—
287C5×C8—62no—
288C5×C8—121no—
289#168—22no—
290#168—41no—
291C2×#41—151no—
292C23×C4D3×D511yescharacteristic
293#131—302no—
294#131—302no—
295C2×M16—31no—
296C2×M16—31no—
297C2×M16—51no—
298C2×M16—51no—
299C2×M16—302no—
300#123—152no—
301C22⋊Q8—301no—
302#121—301no—
303#120—152no—
304C4×D4—302no—
305#117—151no—
306#101—301no—
307#100—301no—
308C22⋊C8—62no—
309C22⋊C8—102no—
310C2×C3×C5—21no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5—42no—
314C2×C3×C5#38611yescharacteristic
315D15—42no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—42no—
320C23×C3C2×C4×D511yescharacteristic
321C22×D3—52no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4#70911yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4#71111yescharacteristic
334C2×C3×C4C2×C22⋊D511yescharacteristic
335#67—102no—
336#67—102no—
337#67—204no—
338C2×Dic3—52no—
339C2×Dic3—102no—
340D12—101no—
341D12—101no—
342C4×D3—102no—
343C4×D3—102no—
344Dic6—101no—
345Dic6—101no—
346C3×C8—102no—
347C3×C8—201no—
348C3⋊C8—22no—
349C3⋊C8—41no—
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×C5D3×C22⋊C411yescharacteristic
359C22×C5#67⋊C411yescharacteristic
360C22×C5C4×#6711yescharacteristic
361C2×D5—62no—
362C2×D5—122no—
363C4×C5—41no—
364C4×C5#88311yescharacteristic
365C4×C5#88411yescharacteristic
366C4×C5#93711yescharacteristic
367C4×C5#93811yescharacteristic
368Dic5—62no—
369Dic5—122no—
370C24#120011yescharacteristic
371#41—301no—
372#41—301no—
373#41—301no—
374#41—301no—
375C2×Q8—151no—
376C2×D4—152no—
377C2×D4—151no—
378C2×D4—302no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—152no—
386C22×C4#120011yescharacteristic
387C22×C4C2×D3×D511yescharacteristic
388M16—61no—
389M16—61no—
390M16—61no—
391M16—61no—
392M16—101no—
393M16—101no—
394M16—101no—
395M16—101no—
396M16—304no—
397C2×C8—32no—
398C2×C8—52no—
399C2×C8—61no—
400C2×C8—101no—
401C2×C8—304no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—152no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C42—301no—
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×C3D5×C22⋊C411yescharacteristic
418C22×C3#402711yescharacteristic
419C22×C3C4×C22⋊D511yescharacteristic
420C2×D3—102no—
421C2×D3—202no—
422C3×C4—41no—
423C3×C4#402911yescharacteristic
424C3×C4#403011yescharacteristic
425C3×C4#408311yescharacteristic
426C3×C4#408411yescharacteristic
427Dic3—102no—
428Dic3—202no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—42no—
433C2×C5#495611yescharacteristic
434D5—122no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—42no—
439C23—152no—
440C23C2×#120011yescharacteristic
441Q8—301no—
442Q8—301no—
443D4—302no—
444D4—302no—
445D4—301no—
446D4—301no—
447D4—604no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—152no—
456C2×C4—302no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4#677911yescharacteristic
460C2×C4#678211yescharacteristic
461C2×C4D5×#6711yescharacteristic
462C2×C4D3×C22⋊D511yescharacteristic
463C2×C4#679011yescharacteristic
464C2×C4#679011yescharacteristic
465C8—62no—
466C8—102no—
467C8—121no—
468C8—201no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—42no—
473C2×C3#6524511yescharacteristic
474D3—202no—
475C5#6999211yescharacteristic, complemented, Sylow
476C22—22no—
477C22—22no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—302no—
485C22—602no—
486C22#9155211yescharacteristic
487C22#9155611yescharacteristic
488C22#9156111yescharacteristic
489C4—41no—
490C4—302no—
491C4—602no—
492C4#9153311yescharacteristic
493C4#9155711yescharacteristic
494C4#9156211yescharacteristic
495C4#9157711yescharacteristic
496C3#1060078511yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—42no—
501C2—602no—
502C2#1174952011yescharacteristic
subgroupG/H
centerC4#91577
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC2×C3×C5#386
prime radical#11756550C2
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. #11754130C2semidirect
3. C5×#5207C2semidirect
4. C3×#65496C2semidirect
5. #11748357C2semidirect
6. #11745991C2semidirect
7. #11745990C2semidirect
32. #65496D3semidirect
65. C2×C5×C3⋊C8D4semidirect
71. C2×C3×#168D4semidirect
77. #5207D5semidirect
189. C2×#168#67semidirect
254. C2×C3⋊C8C22⋊D5semidirect
408. C3×C5#1891semidirect
475. C5#69992semidirect
496. C3#10600785semidirect

Maximal subgroups

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

subgroupindex
#117565502
#117541302
C5×#52072
C3×#654962
#117483572
#117459912
#117459902
#106007853
#699925