Finite Group Databasebeta

← #14301738

Subgroups — #14301738

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
1C5×#5791C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3#11751308C211yesmaximal, characteristic, complemented
4C3×#65496C211yesmaximal, characteristic, complemented
5#11748355C211yesmaximal, characteristic, complemented
6#11745989C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10602507—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#953C412yes—
14C5×#930—21no—
15C5×#929C412yes—
16C4×C5×#67—22no—
17C5×#926C2211yescharacteristic
18C5×#924—21no—
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91288—22no—
22D3×#681—22no—
23#91286—22no—
24#91114—22no—
25C3×C22⋊#168—22no—
26#90962—21no—
27#90959—21no—
28#69992—51nomaximal, Hall
29C5×#525—31no—
30#66153—31no—
31#65526—31no—
32#65496—31no—
33#65496D311yescharacteristic, complemented
34#64753—31no—
35#64753—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×C5×#67—22no—
46C2×C5×#67C2×C412yes—
47C5×#235—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C2×C5×D12D411yescharacteristic
52C2×C4×C5×D3D412yes—
53C2×C5×Dic6D411yescharacteristic
54#6710—21no—
55#6710—21no—
56#6710—21no—
57#6710—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168D412yescomplemented
60C5×#217—22no—
61C5×#217C2×C412yes—
62C5×(C2×D3)⋊C4—22no—
63C5×C4⋊Dic3—21no—
64C5×Dic3⋊C4—22no—
65C4×C5×Dic3—21no—
66C3×#681—21no—
67C3×#681—21no—
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71C2×C3×#168D412yescomplemented
72#6650—24no—
73D3×#168—24no—
74#5791D511yescharacteristic
75#5745—51no—
76C3×#407—51no—
77#5207—51no—
78#5132—51no—
79#4559—51no—
80#4556—51no—
81C2×C5×#41—31no—
82C23×C4×C5C2×D311yescharacteristic
83C5×#123—32no—
84C5×C22⋊Q8—61no—
85C5×#121—61no—
86C5×#120—32no—
87C4×C5×D4—62no—
88C5×#117—31no—
89#4094—62no—
90#4094—62no—
91C2×#681—31no—
92C2×#681—31no—
93C2×#681—62no—
94C2×#681C2×D311yescharacteristic
95C2×#681C2×D311yescharacteristic
96#3968—61no—
97#3965—61no—
98C22⋊#168—22no—
99C22⋊#168—62no—
100#1891—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5—21no—
103C23×C3×C5—21no—
104C23×C3×C5—42no—
105C23×C3×C5C22×C411yescharacteristic
106C22×C5×D3C22⋊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
120C5×#67—22no—
121C5×#67—22no—
122C5×#67—44no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3C22⋊C412yes—
125C5×D12—21no—
126C5×D12—21no—
127C4×C5×D3—22no—
128C4×C5×D3—22no—
129C5×Dic6—21no—
130C5×Dic6—21no—
131C3⋊#168—22no—
132C3⋊#168—41no—
133C3×#168—22no—
134C3×#168—41no—
135C23×C3×C4C2×D511yescharacteristic
136C2×#235C2×D511yescharacteristic
137C2×C3×M16—51no—
138C2×C3×M16—51no—
139#953Dic512yes—
140#930—21no—
141#929Dic512yes—
142C4×#67—22no—
143#926C2×D511yescharacteristic
144#924—21no—
145C2×#208—51no—
146C2×#208—51no—
147#907—102no—
148D3×M16—102no—
149#901—102no—
150C3×C22⋊C8—102no—
151#830—102no—
152#824—101no—
153#823—101no—
154C24×C5C4×D311yescharacteristic
155C5×#41—61no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C2×C5×Q8—31no—
160C2×C5×D4—32no—
161C2×C5×D4—31no—
162C2×C5×D4—62no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—32no—
170C22×C4×C5C4×D311yescharacteristic
171C22×C4×C5C22×D311yescharacteristic
172C5×C4⋊C4—62no—
173C5×C4⋊C4—61no—
174C5×C22⋊C4—32no—
175C5×C22⋊C4—62no—
176C5×C22⋊C4—62no—
177C42×C5—61no—
178#681—21no—
179#681—21no—
180#681—21no—
181#681—21no—
182#681—64no—
183#681—61no—
184#681—61no—
185#681—61no—
186#681—61no—
187C2×#168—21no—
188C2×#168—32no—
189C2×#168—64no—
190C2×#168—61no—
191C2×#168#6712yescomplemented
192#568—151no—
193#525—31no—
194#413—151no—
195#407—51no—
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×C5×D3—22no—
211C2×C5×D3—42no—
212C3×C4×C5—41no—
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217C5×Dic3—22no—
218C5×Dic3—42no—
219C24×C3C2×Dic511yescharacteristic
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×C4C2×Dic511yescharacteristic
227C22×C3×C4C22×D511yescharacteristic
228C2×#67—22no—
229C2×#67C2×Dic512yes—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234C2×D12C22⋊D511yescharacteristic
235C2×C4×D3C22⋊D512yes—
236C2×Dic6C22⋊D511yescharacteristic
237C3×M16—101no—
238C3×M16—101no—
239C3×M16—101no—
240C3×M16—101no—
241C2×C3×C8—52no—
242C2×C3×C8—101no—
243#217—22no—
244#217C2×Dic512yes—
245(C2×D3)⋊C4—22no—
246C4⋊Dic3—21no—
247Dic3⋊C4—22no—
248C4×Dic3—21no—
249#208—101no—
250#208—101no—
251#208—101no—
252#208—101no—
253C2×C3⋊C8—52no—
254C2×C3⋊C8—101no—
255ΓL(1,𝔽25)—104no—
256D3×C8—104no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—32no—
261C23×C5—42no—
262C23×C5C2×C4×D311yescharacteristic
263C5×Q8—61no—
264C5×Q8—61no—
265C5×D4—62no—
266C5×D4—62no—
267C5×D4—61no—
268C5×D4—61no—
269C5×D4—124no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—32no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5#23511yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5#23711yescharacteristic
286C2×C4×C5C2×#6711yescharacteristic
287#168—22no—
288#168—41no—
289#168—62no—
290#168—121no—
291C2×#41—31no—
292C23×C4D3×D511yescharacteristic
293#131—302no—
294#131—302no—
295C2×M16—51no—
296C2×M16—51no—
297C2×M16—151no—
298C2×M16—151no—
299C2×M16—302no—
300#123—32no—
301C22⋊Q8—61no—
302#121—61no—
303#120—32no—
304C4×D4—62no—
305#117—31no—
306#101—301no—
307#100—301no—
308C22⋊C8—102no—
309C22⋊C8—302no—
310C2×C3×C5—21no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5—42no—
314C2×C3×C5#38611yescharacteristic
315C5×D3—42no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—42no—
320C23×C3C22×Dic511yescharacteristic
321C22×D3C22⋊Dic512yes—
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×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4#71111yescharacteristic
332C2×C3×C4#71111yescharacteristic
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×C3×C4C2×C22⋊D511yescharacteristic
335#67—22no—
336#67—22no—
337#67—44no—
338C2×Dic3—22no—
339C2×Dic3C22⋊Dic512yes—
340D12—21no—
341D12—21no—
342C4×D3—22no—
343C4×D3—22no—
344Dic6—21no—
345Dic6—21no—
346C3×C8—102no—
347C3×C8—201no—
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×C5—62no—
359C22×C5—122no—
360C22×C5D3×C22⋊C411yescharacteristic
361C22×C5#67⋊C411yescharacteristic
362C22×C5C4×#6711yescharacteristic
363C4×C5—41no—
364C4×C5—62no—
365C4×C5—122no—
366C4×C5#88311yescharacteristic
367C4×C5#88411yescharacteristic
368C4×C5#93711yescharacteristic
369C4×C5#93811yescharacteristic
370C24D3×Dic511yescharacteristic
371#41—61no—
372#41—61no—
373#41—61no—
374#41—61no—
375C2×Q8—31no—
376C2×D4—32no—
377C2×D4—31no—
378C2×D4—62no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—32no—
386C22×C4D3×Dic511yescharacteristic
387C22×C4C2×D3×D511yescharacteristic
388M16—101no—
389M16—101no—
390M16—101no—
391M16—101no—
392M16—304no—
393M16—301no—
394M16—301no—
395M16—301no—
396M16—301no—
397C2×C8—52no—
398C2×C8—101no—
399C2×C8—152no—
400C2×C8—304no—
401C2×C8—301no—
402C4⋊C4—62no—
403C4⋊C4—61no—
404C22⋊C4—32no—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C42—61no—
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×C3D4×Dic511yescharacteristic
418C22×C3D4×Dic511yescharacteristic
419C22×C3C2×C22⋊Dic511yescharacteristic
420C2×D3—22no—
421C2×D3—42no—
422C3×C4—41no—
423C3×C4#408111yescharacteristic
424C3×C4#408311yescharacteristic
425C3×C4#408511yescharacteristic
426C3×C4#408511yescharacteristic
427Dic3—22no—
428Dic3—42no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—42no—
433C2×C5—122no—
434C2×C5#495611yescharacteristic
435C23—21no—
436C23—21no—
437C23—21no—
438C23—32no—
439C23—42no—
440C23C2×D3×Dic511yescharacteristic
441Q8—61no—
442Q8—61no—
443D4—62no—
444D4—62no—
445D4—61no—
446D4—61no—
447D4—124no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—32no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4#678011yescharacteristic
460C2×C4#678211yescharacteristic
461C2×C4D5×#6711yescharacteristic
462C2×C4D3×C22⋊D511yescharacteristic
463C2×C4D3×C22⋊D511yescharacteristic
464C2×C4#679011yescharacteristic
465C8—102no—
466C8—201no—
467C8—302no—
468C8—601no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—42no—
473C2×C3#6550911yescharacteristic
474D3—42no—
475C5#6999211yescharacteristic, complemented, Sylow
476C22—22no—
477C22—22no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—62no—
485C22—122no—
486C22Dic5×#6711yescharacteristic
487C22D3×C22⋊Dic511yescharacteristic
488C22#67⋊Dic511yescharacteristic
489C4—41no—
490C4—62no—
491C4—122no—
492C4#9155511yescharacteristic
493C4#9155811yescharacteristic
494C4#9156511yescharacteristic
495C4#9157711yescharacteristic
496C3#1060250711yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—42no—
501C2—122no—
502C2#1174951911yescharacteristic
subgroupG/H
centerC4#91577
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC2×C3×C5#386
prime radicalC5×#5791C2
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. #11754125C2semidirect
3. #11751308C2semidirect
4. C3×#65496C2semidirect
5. #11748355C2semidirect
6. #11745989C2semidirect
7. #11745988C2semidirect
33. #65496D3semidirect
59. C2×C3⋊#168D4semidirect
71. C2×C3×#168D4semidirect
191. C2×#168#67semidirect
408. C3×C5#1891semidirect
475. C5#69992semidirect
496. C3#10602507semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
#117541252
#117513082
C3×#654962
#117483552
#117459892
#117459882
#106025073
#699925