Finite Group Databasebeta

← #14301278

Subgroups — #14301278

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756263C211yesmaximal, characteristic
2C2×#91315C211yesmaximal, characteristic
3C3×#65263C211yesmaximal, characteristic, complemented
4C2×#90981C211yesmaximal, characteristic
5#11748400C211yesmaximal, characteristic, complemented
6C5×#4530C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10599797—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C4×#1220—22no—
13#91815C2211yescharacteristic
14#91782—21no—
15#91781—21no—
16C4⋊C4×D15—21no—
17#91776—21no—
18C2×C5×#208C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×#6662—21no—
22#91315—22no—
23#91315C414yescomplemented
24C2×#6658—21no—
25C3×#3963—22no—
26#90981—22no—
27#90971—21no—
28#90971—21no—
29#69693—51nomaximal, Hall
30C2×#4055—31no—
31#65838—31no—
32C2×#3957—31no—
33#65409—31no—
34#65263D311yescharacteristic, complemented
35C5×#343—31no—
36#64775—31no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40#6817—21no—
41#6817—21no—
42#6817C2×C412yes—
43#6817D412yes—
44C2×D60D411yescharacteristic
45C2×C4×D15—21no—
46C2×C4×D15—22no—
47C2×Dic30D411yescharacteristic
48C22×C3×Dic5—21no—
49C22×C3×Dic5—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10—21no—
54C2×C3×Dic10—21no—
55C2×C3×Dic10C2×C412yescomplemented
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6719—21no—
59#6714—22no—
60C4⋊Dic15D411yescharacteristic
61C4⋊Dic15D411yescharacteristic
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15—21no—
65C5×#208—21no—
66C5×#208—21no—
67C5×#208—21no—
68C5×#208C2×C412yescomplemented
69C2×C5×C3⋊C8—21no—
70C2×C5×C3⋊C8—21no—
71C3×C4×Dic5—21no—
72C3×C4×Dic5—21no—
73#6662—24no—
74#6658—24no—
75C2×#942—51no—
76#5504—51no—
77C3×#391—51no—
78#5225—51no—
79C2×#805—51no—
80#4530D511yescharacteristic, complemented
81#4523—51no—
82C2×#709—31no—
83C22×Dic10C2×D311yescharacteristic
84C2×C5×M16—31no—
85C2×C5×M16—31no—
86C2×C5×C4⋊C4C2×D311yescharacteristic
87C4×C22⋊D5—62no—
88#4072—31no—
89C2×C4×Dic5C2×D311yescharacteristic
90#4055—34no—
91#4055—62no—
92C2×Dic20—61no—
93C2×#677—61no—
94#4039—61no—
95#4038—61no—
96D5×C4⋊C4—61no—
97#4033—61no—
98#3963—22no—
99#3957—62no—
100#3948—61no—
101#3948—61no—
102#1882—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×D15—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113#1220—22no—
114#1220—22no—
115C2×Dic15—21no—
116C2×Dic15—21no—
117C2×Dic15—21no—
118D60—21no—
119D60C22⋊C412yes—
120C4×D15—22no—
121C4×D15—22no—
122C4×D15—82no—
123Dic30—21no—
124Dic30C22⋊C412yes—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130C2×C3×Dic5—41no—
131C3×Dic10—22no—
132C3×Dic10—22no—
133C3×Dic10—41no—
134C3×Dic10—41no—
135C5×C3⋊C8—22no—
136C5×C3⋊C8—41no—
137C22×C3×Q8—51no—
138C2×#235—51no—
139C2×C3×C4⋊C4C2×D511yescharacteristic
140C2×C3×C42—51no—
141C2×#216—101no—
142#942—54no—
143#942—102no—
144C2×#215—101no—
145C4×#67—102no—
146#926—51no—
147C2×#208C2×D511yescharacteristic
148C2×#208C2×D511yescharacteristic
149#893—101no—
150#892—101no—
151D3×C4⋊C4—101no—
152#887—101no—
153C3×#95—102no—
154#835—101no—
155#835—101no—
156#805—102no—
157C22×C4×C5#6712yes—
158C22×C4×C5C22×D311yescharacteristic
159C2×C22⋊D5—61no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162#709—32no—
163#709—32no—
164#709—61no—
165#709—61no—
166C2×D20—31no—
167C2×C4×D5—61no—
168C2×C4×D5—62no—
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10—21no—
172C2×Dic10—21no—
173C2×Dic10—21no—
174C2×Dic10—31no—
175C2×Dic10C4×D312yescomplemented
176C5×M16—32no—
177C5×M16—61no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C2×C5×C8—61no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C22⋊Dic5—61no—
185#685—62no—
186C4⋊Dic5—31no—
187C4⋊Dic5—31no—
188#683—62no—
189C4×Dic5—21no—
190C4×Dic5—21no—
191C4×Dic5—62no—
192C4×Dic5—61no—
193Dic20—64no—
194#677—64no—
195C2×#137—151no—
196#520—151no—
197C2×#104—151no—
198#419—151no—
199#391—51no—
200#343—31no—
201#339—151no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×D15—22no—
208C2×D15—41no—
209C2×D15—41no—
210C3×C4×C5—42no—
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—22no—
216Dic15—41no—
217Dic15—41no—
218C3×Dic5—42no—
219C3×Dic5—42no—
220C2×C3×Q8—52no—
221C2×C3×Q8—101no—
222C2×C3×Q8—101no—
223C2×C3×Q8—101no—
224C2×C3×Q8—101no—
225C2×C3×Q8—101no—
226C22×C3×C4—101no—
227C22×C3×C4—101no—
228C22×C3×C4D2012yes—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—101no—
231#235—52no—
232#235—52no—
233#235—101no—
234#235—101no—
235C2×D12—51no—
236C2×C4×D3—101no—
237C2×C4×D3—102no—
238C2×Dic6—51no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C42—101no—
242C3×C42—101no—
243#217—101no—
244#216—104no—
245#215—104no—
246(C2×D3)⋊C4—102no—
247C4⋊Dic3—51no—
248C4⋊Dic3—51no—
249Dic3⋊C4—102no—
250C4×Dic3—102no—
251C4×Dic3—101no—
252#208—21no—
253#208—21no—
254#208—21no—
255#208C4×D512yescomplemented
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C23×C5C2×#6711yescharacteristic
259C22×D5—61no—
260C2×C4×C5—22no—
261C2×C4×C5—42no—
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×C4×C5#23511yescharacteristic
264C2×C4×C5D3×D411yescharacteristic
265C2×C4×C5D3×D411yescharacteristic
266C2×C4×C5D3×D411yescharacteristic
267C2×C4×C5#23711yescharacteristic
268C22⋊D5—62no—
269C22⋊D5—62no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—41no—
273C2×Dic5—41no—
274C2×Dic5—41no—
275C2×Dic5—41no—
276C2×Dic5—61no—
277C2×Dic5—61no—
278C2×Dic5—61no—
279D20—32no—
280D20—61no—
281C4×D5—62no—
282C4×D5—62no—
283C4×D5—242no—
284Dic10—22no—
285Dic10—22no—
286Dic10—32no—
287Dic10—41no—
288Dic10—41no—
289Dic10—61no—
290C5×C8—62no—
291C5×C8—121no—
292C2×#41—151no—
293C22×Q8—51no—
294#137—154no—
295#137—302no—
296C2×Q16—301no—
297C2×SD16—301no—
298C2×M16—31no—
299C2×M16—31no—
300C4×Q8—301no—
301C4×D4—301no—
302C4×D4—302no—
303#117—151no—
304#117—301no—
305C2×C4⋊C4—301no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C42—51no—
308#104—302no—
309#103—301no—
310#103—301no—
311#95—102no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317D15—42no—
318C23×C3C2×D2011yescharacteristic
319C22×D3—101no—
320C3×Q8—102no—
321C3×Q8—102no—
322C3×Q8—201no—
323C3×Q8—201no—
324C2×C3×C4—22no—
325C2×C3×C4—42no—
326C2×C3×C4—102no—
327C2×C3×C4—102no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4—201no—
331C2×C3×C4—201no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4#70911yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4#71311yescharacteristic
338#67—102no—
339#67—102no—
340C2×Dic3—101no—
341C2×Dic3—101no—
342C2×Dic3—101no—
343D12—52no—
344D12—101no—
345C4×D3—102no—
346C4×D3—102no—
347C4×D3—402no—
348Dic6—52no—
349Dic6—101no—
350C3⋊C8—22no—
351C3⋊C8—41no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5C4×#6711yescharacteristic
355C22×C5#93711yescharacteristic
356C22×C5#93811yescharacteristic
357C2×D5—62no—
358C2×D5—121no—
359C2×D5—121no—
360C4×C5—42no—
361C4×C5D3×C22⋊C411yescharacteristic
362C4×C5#67⋊C411yescharacteristic
363C4×C5#88311yescharacteristic
364C4×C5#88411yescharacteristic
365Dic5—42no—
366Dic5—42no—
367Dic5—62no—
368Dic5—121no—
369Dic5—121no—
370#41—152no—
371#41—152no—
372#41—301no—
373#41—301no—
374C2×Q8—52no—
375C2×Q8—101no—
376C2×Q8—101no—
377C2×Q8—101no—
378C2×Q8—101no—
379C2×Q8—101no—
380C2×Q8—151no—
381C2×D4—151no—
382C2×D4—301no—
383C22×C4—101no—
384C22×C4—101no—
385C22×C4—302no—
386C22×C4—301no—
387C22×C4#120212yes—
388C22×C4C2×D3×D511yescharacteristic
389Q16—304no—
390SD16—304no—
391M16—32no—
392M16—61no—
393M16—61no—
394M16—61no—
395C2×C8—61no—
396C2×C8—61no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C22⋊C4—302no—
403C22⋊C4—301no—
404C42—101no—
405C42—101no—
406C42—302no—
407C42—301no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3C4×D2011yescharacteristic
412C22×C3#402811yescharacteristic
413C22×C3#404111yescharacteristic
414C2×D3—102no—
415C2×D3—201no—
416C2×D3—201no—
417C3×C4—42no—
418C3×C4—202no—
419C3×C4—202no—
420C3×C4D5×C22⋊C411yescharacteristic
421C3×C4#403011yescharacteristic
422C3×C4#403911yescharacteristic
423C3×C4#404011yescharacteristic
424Dic3—102no—
425Dic3—201no—
426Dic3—201no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5#495611yescharacteristic
430C2×C5#506111yescharacteristic
431C2×C5#509511yescharacteristic
432D5—122no—
433C23—301no—
434C23C2×#120211yescharacteristic
435Q8—102no—
436Q8—102no—
437Q8—152no—
438Q8—201no—
439Q8—201no—
440Q8—301no—
441D4—152no—
442D4—302no—
443D4—302no—
444D4—301no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—201no—
450C2×C4—201no—
451C2×C4—201no—
452C2×C4—201no—
453C2×C4—301no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4—301no—
457C2×C4—301no—
458C2×C4—1202no—
459C2×C4#676611yescharacteristic
460C2×C4#677111yescharacteristic
461C2×C4C4×D3×D511yescharacteristic
462C2×C4#677711yescharacteristic
463C2×C4#679011yescharacteristic
464C2×C4#679011yescharacteristic
465C8—62no—
466C8—121no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#6495411yescharacteristic
470C2×C3#6503511yescharacteristic
471C2×C3#6504111yescharacteristic
472D3—202no—
473C5#6969311yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—302no—
477C22—601no—
478C22—601no—
479C22C4×#120211yescharacteristic
480C22#9146511yescharacteristic
481C22#9157211yescharacteristic
482C4—42no—
483C4—202no—
484C4—202no—
485C4—302no—
486C4—601no—
487C4—601no—
488C4#9135411yescharacteristic
489C4#9139611yescharacteristic
490C4#9146111yescharacteristic
491C4#9147311yescharacteristic
492C3#1059979711yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—602no—
496C2#1174891711yescharacteristic
497C2#1174914911yescharacteristic
498C2#1174939511yescharacteristic
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1882
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#65263C2semidirect
5. #11748400C2semidirect
6. C5×#4530C2semidirect
7. #11745978C2semidirect
23. #91315C4semidirect
34. #65263D3semidirect
55. C2×C3×Dic10C2×C4semidirect
68. C5×#208C2×C4semidirect
80. #4530D5semidirect
175. C2×Dic10C4×D3semidirect
255. #208C4×D5semidirect
408. C3×C5#1882semidirect
473. C5#69693semidirect
492. C3#10599797semidirect

Maximal subgroups

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

subgroupindex
#117562632
C2×#913152
C3×#652632
C2×#909812
#117484002
C5×#45302
#117459782
#105997973
#696935