Finite Group Databasebeta

← #14301280

Subgroups — #14301280

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
1C5×#5504C211yesmaximal, characteristic
2C2×#91309C211yesmaximal, characteristic
3C3×#65263C211yesmaximal, characteristic, complemented
4C2×#90979C211yesmaximal, characteristic
5#11748399C211yesmaximal, characteristic, complemented
6#11746351C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10602459—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C4×C5×#67—22no—
15C5×#926C2211yescharacteristic
16C5×#893—21no—
17C5×#892—21no—
18C5×D3×C4⋊C4—21no—
19C5×#887—21no—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×#6661—21no—
22#91309—22no—
23#91309C414yescomplemented
24C2×#6656—21no—
25C3×#3963—22no—
26#90979—22no—
27#90970—21no—
28#90970—21no—
29#69693—51nomaximal, Hall
30C5×#520—31no—
31C2×#4097—31no—
32C2×#3969—31no—
33#65293—31no—
34#65263D311yescharacteristic, complemented
35#64752—31no—
36#64750—31no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C2×C5×#67—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235C2×C412yes—
43C5×#235D412yes—
44C2×C5×D12D411yescharacteristic
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3—22no—
47C2×C5×Dic6D411yescharacteristic
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#6710—21no—
59#6710—21no—
60#6710—21no—
61#6710C2×C412yescomplemented
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C5×#217—21no—
65C5×(C2×D3)⋊C4—22no—
66C5×C4⋊Dic3D411yescharacteristic
67C5×C4⋊Dic3D411yescharacteristic
68C5×Dic3⋊C4—22no—
69C4×C5×Dic3—22no—
70C4×C5×Dic3—21no—
71C3×C4×Dic5—21no—
72C3×C4×Dic5—21no—
73#6661—24no—
74#6656—24no—
75C2×#942—51no—
76#5504D511yescharacteristic
77C3×#391—51no—
78#5225—51no—
79C2×#805—51no—
80#4530—51no—
81#4523—51no—
82C2×C5×#41—31no—
83C22×Dic10C2×D311yescharacteristic
84C4×C5×Q8—61no—
85C4×C5×D4—61no—
86C4×C5×D4—62no—
87C5×#117—31no—
88C5×#117—61no—
89C2×C5×C4⋊C4—61no—
90C2×C5×C4⋊C4C2×D311yescharacteristic
91#4097—34no—
92#4097—62no—
93C2×#689—61no—
94C2×#687—61no—
95C2×C4×Dic5C2×D311yescharacteristic
96C2×#681—31no—
97C2×#681—31no—
98#3969—62no—
99#3963—22no—
100#3942—61no—
101#3942—61no—
102#1882—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3—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
113C5×#67—22no—
114C5×#67—22no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C5×D12—21no—
119C5×D12C22⋊C412yes—
120C4×C5×D3—22no—
121C4×C5×D3—22no—
122C4×C5×D3—82no—
123C5×Dic6—21no—
124C5×Dic6C22⋊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—
135C3⋊#168—22no—
136C3⋊#168—41no—
137C22×C3×Q8—51no—
138C2×#235C2×D511yescharacteristic
139C2×C3×C4⋊C4C2×D511yescharacteristic
140C2×C3×C42—51no—
141C2×#216—101no—
142#942—54no—
143#942—102no—
144C2×#215—101no—
145C4×#67—22no—
146#926C2×D511yescharacteristic
147C2×#208—51no—
148C2×#208—51no—
149#893—21no—
150#892—21no—
151D3×C4⋊C4—21no—
152#887—21no—
153C3×#95—102no—
154#835—101no—
155#835—101no—
156#805—102no—
157C5×#41—32no—
158C5×#41—32no—
159C5×#41—61no—
160C5×#41—61no—
161C2×C5×Q8—31no—
162C2×C5×D4—31no—
163C2×C5×D4—61no—
164C22×C4×C5—62no—
165C22×C4×C5—61no—
166C22×C4×C5#6712yes—
167C22×C4×C5C22×D311yescharacteristic
168C22×Dic5—21no—
169C22×Dic5—21no—
170C2×Dic10—21no—
171C2×Dic10—21no—
172C2×Dic10—21no—
173C2×Dic10—21no—
174C2×Dic10—21no—
175C2×Dic10C4×D312yescomplemented
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—31no—
179C5×C4⋊C4—31no—
180C5×C4⋊C4—62no—
181C5×C22⋊C4—62no—
182C5×C22⋊C4—61no—
183C42×C5—62no—
184C42×C5—61no—
185#689—64no—
186#687—64no—
187C4×Dic5—21no—
188C4×Dic5—21no—
189#681—32no—
190#681—61no—
191#681—61no—
192#681—61no—
193C2×#168—61no—
194C2×#168—61no—
195C2×#137—151no—
196#520—31no—
197C2×#104—151no—
198#419—151no—
199#391—51no—
200#343—151no—
201#339—151no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×C5×D3—22no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C3×C4×C5—42no—
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215C3×Dic5—42no—
216C3×Dic5—42no—
217C5×Dic3—22no—
218C5×Dic3—41no—
219C5×Dic3—41no—
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×C4C22⋊D512yes—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—21no—
231#235—21no—
232#235—21no—
233#235C4×D512yes—
234#235D2012yes—
235C2×D12C22⋊D511yescharacteristic
236C2×C4×D3—21no—
237C2×C4×D3—22no—
238C2×Dic6C22⋊D511yescharacteristic
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C42—101no—
242C3×C42—101no—
243#217—21no—
244#216—104no—
245#215—104no—
246(C2×D3)⋊C4—22no—
247C4⋊Dic3C22⋊D511yescharacteristic
248C4⋊Dic3C22⋊D511yescharacteristic
249Dic3⋊C4—22no—
250C4×Dic3—22no—
251C4×Dic3—21no—
252#208—52no—
253#208—101no—
254#208—101no—
255#208—101no—
256C2×C3⋊C8—101no—
257C2×C3⋊C8—101no—
258C23×C5—61no—
259C23×C5C2×#6711yescharacteristic
260C5×Q8—32no—
261C5×Q8—61no—
262C5×D4—32no—
263C5×D4—62no—
264C5×D4—62no—
265C5×D4—61no—
266C2×C4×C5—22no—
267C2×C4×C5—42no—
268C2×C4×C5—61no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—242no—
274C2×C4×C5C2×C4×D311yescharacteristic
275C2×C4×C5#23511yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5#23711yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—41no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—41no—
286Dic10—22no—
287Dic10—22no—
288Dic10—41no—
289Dic10—41no—
290#168—62no—
291#168—121no—
292C2×#41—31no—
293C22×Q8—51no—
294#137—154no—
295#137—302no—
296C2×Q16—301no—
297C2×SD16—301no—
298C2×M16—151no—
299C2×M16—151no—
300C4×Q8—61no—
301C4×D4—61no—
302C4×D4—62no—
303#117—31no—
304#117—61no—
305C2×C4⋊C4—61no—
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
317C5×D3—42no—
318C23×C3C2×C22⋊D511yescharacteristic
319C22×D3—21no—
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×C4C2×D2011yescharacteristic
334C2×C3×C4#70911yescharacteristic
335C2×C3×C4#70911yescharacteristic
336C2×C3×C4C2×C22⋊D511yescharacteristic
337C2×C3×C4C2×C22⋊D511yescharacteristic
338#67—22no—
339#67—22no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343D12—21no—
344D12#68512yes—
345C4×D3—22no—
346C4×D3—22no—
347C4×D3—82no—
348Dic6—21no—
349Dic6#68512yes—
350C3⋊C8—102no—
351C3⋊C8—201no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—62no—
355C22×C5—121no—
356C22×C5—121no—
357C22×C5C4×#6711yescharacteristic
358C22×C5#93711yescharacteristic
359C22×C5#93811yescharacteristic
360C4×C5—42no—
361C4×C5—62no—
362C4×C5—121no—
363C4×C5—121no—
364C4×C5D3×C22⋊C411yescharacteristic
365C4×C5#67⋊C411yescharacteristic
366C4×C5#88311yescharacteristic
367C4×C5#88411yescharacteristic
368Dic5—42no—
369Dic5—42no—
370#41—32no—
371#41—32no—
372#41—61no—
373#41—61no—
374C2×Q8—31no—
375C2×Q8—52no—
376C2×Q8—101no—
377C2×Q8—101no—
378C2×Q8—101no—
379C2×Q8—101no—
380C2×Q8—101no—
381C2×D4—31no—
382C2×D4—61no—
383C22×C4—62no—
384C22×C4—61no—
385C22×C4—101no—
386C22×C4—101no—
387C22×C4#120112yes—
388C22×C4C2×D3×D511yescharacteristic
389Q16—304no—
390SD16—304no—
391M16—152no—
392M16—301no—
393M16—301no—
394M16—301no—
395C2×C8—301no—
396C2×C8—301no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C22⋊C4—62no—
403C22⋊C4—61no—
404C42—62no—
405C42—61no—
406C42—101no—
407C42—101no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3C4×C22⋊D511yescharacteristic
412C22×C3#407611yescharacteristic
413C22×C3#409911yescharacteristic
414C2×D3—22no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—42no—
418C3×C4—202no—
419C3×C4—202no—
420C3×C4C2×#68511yescharacteristic
421C3×C4C4×C22⋊D511yescharacteristic
422C3×C4#407511yescharacteristic
423C3×C4#407611yescharacteristic
424Dic3—22no—
425Dic3—41no—
426Dic3—41no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5—122no—
430C2×C5#495611yescharacteristic
431C2×C5#506111yescharacteristic
432C2×C5#509511yescharacteristic
433C23—61no—
434C23C2×#120111yescharacteristic
435Q8—32no—
436Q8—61no—
437Q8—102no—
438Q8—102no—
439Q8—201no—
440Q8—201no—
441D4—32no—
442D4—62no—
443D4—62no—
444D4—61no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—102no—
453C2×C4—102no—
454C2×C4—201no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—242no—
459C2×C4#676511yescharacteristic
460C2×C4#677111yescharacteristic
461C2×C4C4×D3×D511yescharacteristic
462C2×C4D3×D2011yescharacteristic
463C2×C4D3×C22⋊D511yescharacteristic
464C2×C4D3×C22⋊D511yescharacteristic
465C8—302no—
466C8—601no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#6550211yescharacteristic
470C2×C3#6553111yescharacteristic
471C2×C3#6553511yescharacteristic
472D3—42no—
473C5#6969311yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—62no—
477C22—121no—
478C22—121no—
479C22C4×#120111yescharacteristic
480C22#9145611yescharacteristic
481C22#9156811yescharacteristic
482C4—42no—
483C4—62no—
484C4—121no—
485C4—121no—
486C4—202no—
487C4—202no—
488C4#9144111yescharacteristic
489C4#9145211yescharacteristic
490C4#9145411yescharacteristic
491C4D3×#68511yescharacteristic
492C3#1060245911yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—122no—
496C2#1174891011yescharacteristic
497C2#1174914711yescharacteristic
498C2#1174939311yescharacteristic
subgroupG/H
centerC22#91568
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×C5×#235C22
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. #11748399C2semidirect
6. #11746351C2semidirect
7. #11745977C2semidirect
23. #91309C4semidirect
34. #65263D3semidirect
55. C2×C3×Dic10C2×C4semidirect
61. #6710C2×C4semidirect
175. C2×Dic10C4×D3semidirect
408. C3×C5#1882semidirect
473. C5#69693semidirect
492. C3#10602459semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
C2×#913092
C3×#652632
C2×#909792
#117483992
#117463512
#117459772
#106024593
#696935