Finite Group Databasebeta

← #14301281

Subgroups — #14301281

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×#91321C211yesmaximal, characteristic
3C5×#4973C211yesmaximal, characteristic, complemented
4C2×#90980C211yesmaximal, characteristic
5#11748409C211yesmaximal, characteristic, complemented
6C3×#64750C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10600486—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C4×#1220—22no—
13#91815C2211yescharacteristic
14#91782—21no—
15#91781—21no—
16C4⋊C4×D15—21no—
17#91776—21no—
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91321—22no—
22#91321C414yescomplemented
23C2×#6663—21no—
24C2×#6660—21no—
25C5×C3⋊#95—22no—
26#90980—22no—
27#90973—21no—
28#90973—21no—
29#69004—51nomaximal, Hall
30C2×#4088—31no—
31#65838—31no—
32C5×#391—31no—
33#65514—31no—
34C2×#3937—31no—
35#64750D311yescharacteristic, complemented
36#64743—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×C5×Dic3—21no—
49C22×C5×Dic3—21no—
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6—21no—
54C2×C5×Dic6—21no—
55C2×C5×Dic6C2×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—
65C4×C5×Dic3—21no—
66C4×C5×Dic3—21no—
67C3×#681—21no—
68C3×#681—21no—
69C3×#681—21no—
70C3×#681C2×C412yescomplemented
71C2×C3×#168—21no—
72C2×C3×#168—21no—
73#6663—24no—
74#6660—24no—
75C2×#909—51no—
76#5504—51no—
77C2×#825—51no—
78#5120—51no—
79#4973D511yescharacteristic, complemented
80C3×#343—51no—
81#4555—51no—
82C22×C5×Q8—31no—
83C2×#709—31no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×C42×C5—31no—
86C2×#689—61no—
87#4088—34no—
88#4088—62no—
89C2×#688—61no—
90C4×C22⋊D5—62no—
91#4072—31no—
92C2×#681C2×D311yescharacteristic
93C2×#681C2×D311yescharacteristic
94#4039—61no—
95#4038—61no—
96D5×C4⋊C4—61no—
97#4033—61no—
98C5×#95—62no—
99#3967—61no—
100#3967—61no—
101#3937—62no—
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×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3—41no—
130C2×C5×Dic3—41no—
131C5×Dic6—22no—
132C5×Dic6—22no—
133C5×Dic6—41no—
134C5×Dic6—41no—
135C3×#168—22no—
136C3×#168—41no—
137C2×#235—51no—
138C22×Dic6C2×D511yescharacteristic
139C2×C3×M16—51no—
140C2×C3×M16—51no—
141C2×C3×C4⋊C4C2×D511yescharacteristic
142C4×#67—102no—
143#926—51no—
144C2×C4×Dic3C2×D511yescharacteristic
145#909—54no—
146#909—102no—
147C2×Dic12—101no—
148C2×#204—101no—
149#893—101no—
150#892—101no—
151D3×C4⋊C4—101no—
152#887—101no—
153C3⋊#95—22no—
154#825—102no—
155#816—101no—
156#816—101no—
157C2×C5×Q8—32no—
158C2×C5×Q8—61no—
159C2×C5×Q8—61no—
160C2×C5×Q8—61no—
161C2×C5×Q8—61no—
162C2×C5×Q8—61no—
163C22×C4×C5—61no—
164C22×C4×C5—61no—
165C22×C4×C5D1212yes—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—61no—
168#709—32no—
169#709—32no—
170#709—61no—
171#709—61no—
172C2×D20—31no—
173C2×C4×D5—61no—
174C2×C4×D5—62no—
175C2×Dic10—31no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C42×C5—61no—
179C42×C5—61no—
180C22⋊Dic5—61no—
181#689—64no—
182#688—64no—
183#685—62no—
184C4⋊Dic5—31no—
185C4⋊Dic5—31no—
186#683—62no—
187C4×Dic5—62no—
188C4×Dic5—61no—
189#681—21no—
190#681—21no—
191#681—21no—
192#681C4×D312yescomplemented
193C2×#168—21no—
194C2×#168—21no—
195C2×#137—151no—
196#520—151no—
197C2×#104—151no—
198#419—151no—
199#391—31no—
200#343—51no—
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—
218C5×Dic3—42no—
219C5×Dic3—42no—
220C22×C3×C4C22⋊D512yes—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—101no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225#235—52no—
226#235—52no—
227#235—101no—
228#235—101no—
229C2×D12—51no—
230C2×C4×D3—101no—
231C2×C4×D3—102no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6—51no—
238C2×Dic6C4×D512yescomplemented
239C3×M16—52no—
240C3×M16—101no—
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—101no—
244C2×C3×C8—101no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247#217—101no—
248(C2×D3)⋊C4—102no—
249C4⋊Dic3—51no—
250C4⋊Dic3—51no—
251Dic3⋊C4—102no—
252C4×Dic3—21no—
253C4×Dic3—21no—
254C4×Dic3—102no—
255C4×Dic3—101no—
256Dic12—104no—
257#204—104no—
258C23×C5C2×D1211yescharacteristic
259C22×D5—61no—
260C5×Q8—62no—
261C5×Q8—62no—
262C5×Q8—121no—
263C5×Q8—121no—
264C2×C4×C5—22no—
265C2×C4×C5—42no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5#23911yescharacteristic
278C22⋊D5—62no—
279C22⋊D5—62no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283D20—32no—
284D20—61no—
285C4×D5—62no—
286C4×D5—62no—
287C4×D5—242no—
288Dic10—32no—
289Dic10—61no—
290#168—22no—
291#168—41no—
292C2×#41—151no—
293C22×Q8—31no—
294#137—154no—
295#137—302no—
296C2×Q16—301no—
297C2×SD16—301no—
298C2×M16—51no—
299C2×M16—51no—
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—31no—
308#104—302no—
309#103—301no—
310#103—301no—
311#95—62no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317D15—42no—
318C23×C3C2×C22⋊D511yescharacteristic
319C22×D3—101no—
320C2×C3×C4—22no—
321C2×C3×C4—42no—
322C2×C3×C4C2×C4×D511yescharacteristic
323C2×C3×C4#70911yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327C2×C3×C4#71111yescharacteristic
328#67—102no—
329#67—102no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—101no—
337C2×Dic3—101no—
338C2×Dic3—101no—
339D12—52no—
340D12—101no—
341C4×D3—102no—
342C4×D3—102no—
343C4×D3—402no—
344Dic6—22no—
345Dic6—22no—
346Dic6—41no—
347Dic6—41no—
348Dic6—52no—
349Dic6—101no—
350C3×C8—102no—
351C3×C8—201no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5C4×D1211yescharacteristic
355C22×C5#88211yescharacteristic
356C22×C5#89511yescharacteristic
357C2×D5—62no—
358C2×D5—121no—
359C2×D5—121no—
360C4×C5—42no—
361C4×C5—122no—
362C4×C5—122no—
363C4×C5D3×C22⋊C411yescharacteristic
364C4×C5#88411yescharacteristic
365C4×C5#89311yescharacteristic
366C4×C5#89411yescharacteristic
367Dic5—62no—
368Dic5—121no—
369Dic5—121no—
370#41—152no—
371#41—152no—
372#41—301no—
373#41—301no—
374C2×Q8—32no—
375C2×Q8—61no—
376C2×Q8—61no—
377C2×Q8—61no—
378C2×Q8—61no—
379C2×Q8—61no—
380C2×Q8—151no—
381C2×D4—151no—
382C2×D4—301no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—302no—
386C22×C4—301no—
387C22×C4#120312yes—
388C22×C4C2×D3×D511yescharacteristic
389Q16—304no—
390SD16—304no—
391M16—52no—
392M16—101no—
393M16—101no—
394M16—101no—
395C2×C8—101no—
396C2×C8—101no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C22⋊C4—302no—
403C22⋊C4—301no—
404C42—61no—
405C42—61no—
406C42—302no—
407C42—301no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3C4×C22⋊D511yescharacteristic
412C22×C3#408311yescharacteristic
413C22×C3#408411yescharacteristic
414C2×D3—102no—
415C2×D3—201no—
416C2×D3—201no—
417C3×C4—42no—
418C3×C4D5×C22⋊C411yescharacteristic
419C3×C4#402711yescharacteristic
420C3×C4#402911yescharacteristic
421C3×C4#403011yescharacteristic
422Dic3—42no—
423Dic3—42no—
424Dic3—102no—
425Dic3—201no—
426Dic3—201no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5#466511yescharacteristic
430C2×C5#474611yescharacteristic
431C2×C5#475211yescharacteristic
432D5—122no—
433C23—301no—
434C23C2×#120311yescharacteristic
435Q8—62no—
436Q8—62no—
437Q8—121no—
438Q8—121no—
439Q8—152no—
440Q8—301no—
441D4—152no—
442D4—302no—
443D4—302no—
444D4—301no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—301no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4—301no—
457C2×C4—301no—
458C2×C4—1202no—
459C2×C4#676811yescharacteristic
460C2×C4#677111yescharacteristic
461C2×C4C4×D3×D511yescharacteristic
462C2×C4#677711yescharacteristic
463C2×C4#679011yescharacteristic
464C2×C4#679011yescharacteristic
465C8—102no—
466C8—201no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#6524511yescharacteristic
470C2×C3#6535011yescharacteristic
471C2×C3#6538411yescharacteristic
472D3—202no—
473C5#6900411yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—302no—
477C22—601no—
478C22—601no—
479C22C4×#120311yescharacteristic
480C22#9146611yescharacteristic
481C22#9157311yescharacteristic
482C4—42no—
483C4—122no—
484C4—122no—
485C4—302no—
486C4—601no—
487C4—601no—
488C4#9135511yescharacteristic
489C4#9140611yescharacteristic
490C4#9146111yescharacteristic
491C4#9147311yescharacteristic
492C3#1060048611yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—602no—
496C2#1174891811yescharacteristic
497C2#1174915011yescharacteristic
498C2#1174939611yescharacteristic
subgroupG/H
centerC22#91573
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. C5×#4973C2semidirect
5. #11748409C2semidirect
6. C3×#64750C2semidirect
7. #11745976C2semidirect
22. #91321C4semidirect
35. #64750D3semidirect
55. C2×C5×Dic6C2×C4semidirect
70. C3×#681C2×C4semidirect
79. #4973D5semidirect
192. #681C4×D3semidirect
238. C2×Dic6C4×D5semidirect
408. C3×C5#1882semidirect
473. C5#69004semidirect
492. C3#10600486semidirect

Maximal subgroups

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

subgroupindex
#117562632
C2×#913212
C5×#49732
C2×#909802
#117484092
C3×#647502
#117459762
#106004863
#690045