Finite Group Databasebeta

← #14301229

Subgroups — #14301229

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#11756586C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic
3C2×C3×C5×#104C211yesmaximal, characteristic
4#11751221C211yesmaximal, characteristic, complemented
5#11751030C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10601158—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13#91840—22no—
14#91840C414yescomplemented
15Q8×Dic15—21no—
16C2×#6718—21no—
17D4×Dic15—21no—
18D4×Dic15—22no—
19C2×#6716—21no—
20#91815—21no—
21#91815C2211yescharacteristic
22C2×C4⋊Dic15—21no—
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25C3×C5×#104—22no—
26#91115—22no—
27#91100—21no—
28#91100—21no—
29#70365—51nomaximal, Hall
30#66161—31no—
31C2×#4097—31no—
32C2×C5×#104D311yescharacteristic
33#65409—31no—
34#65218—31no—
35#64774—31no—
36#64743—31no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41C2×C412yes—
40C3×C5×#41D412yes—
41C2×C3×C5×Q8D411yescharacteristic
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4D411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C22×Dic15—22no—
49C22×Dic15D412yes—
50C2×Dic30—21no—
51C2×Dic30—21no—
52C2×Dic30—21no—
53C2×Dic30—21no—
54C2×Dic30—21no—
55C2×Dic30C2×C412yescomplemented
56C3×C5×M16—21no—
57C3×C5×M16—21no—
58C2×C3×C5×C8—21no—
59C3×C42×C5—21no—
60C3×C42×C5—21no—
61#6719—22no—
62#6719—21no—
63#6718—24no—
64#6716—24no—
65C4⋊Dic15—22no—
66C4⋊Dic15—21no—
67C4⋊Dic15—21no—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15D411yescharacteristic
70C4×Dic15—22no—
71C4×Dic15—21no—
72#6710—21no—
73#6710C2×C412yescomplemented
74C2×C3⋊#168—21no—
75#5827—51no—
76C2×#951—51no—
77C2×C3×#104D511yescharacteristic
78#5120—51no—
79#4929—51no—
80#4554—51no—
81#4523—51no—
82C2×C5×#41C2×D311yescharacteristic
83C22×Dic10—31no—
84C2×C5×M16C2×D311yescharacteristic
85C2×C42×C5C2×D311yescharacteristic
86#4097—34no—
87#4097—62no—
88Q8×Dic5—61no—
89C2×#689—61no—
90D4×Dic5—62no—
91D4×Dic5—61no—
92C2×#687—61no—
93#4072—31no—
94#4072—61no—
95C2×C4⋊Dic5—31no—
96C2×C4⋊Dic5—61no—
97C2×#681—31no—
98C5×#104—22no—
99#3963—62no—
100#3948—61no—
101#3948—61no—
102#1882—151noSylow
103C23×C3×C5—21no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×Q8—21no—
106C3×C5×Q8C22⋊C412yes—
107C3×C5×D4—22no—
108C3×C5×D4—22no—
109C3×C5×D4—21no—
110C3×C5×D4C22⋊C412yes—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5#4111yescharacteristic
122C2×C3×C4×C5#4111yescharacteristic
123C2×Dic15—22no—
124C2×Dic15—21no—
125C2×Dic15—22no—
126C2×Dic15—21no—
127C2×Dic15—41no—
128C2×Dic15—41no—
129C2×Dic15—42no—
130C2×Dic15—82no—
131Dic30—22no—
132Dic30—22no—
133Dic30—41no—
134Dic30—41no—
135C3×C5×C8—41no—
136C3⋊#168—22no—
137C2×C3×#41C2×D511yescharacteristic
138C22×Dic6—51no—
139C2×C3×M16C2×D511yescharacteristic
140C2×C3×C42C2×D511yescharacteristic
141#951—54no—
142#951—102no—
143Q8×Dic3—101no—
144C2×#216—101no—
145D4×Dic3—102no—
146D4×Dic3—101no—
147C2×#214—101no—
148#926—51no—
149#926—101no—
150C2×C4⋊Dic3—51no—
151C2×C4⋊Dic3—101no—
152C2×#208—51no—
153C3×#104—22no—
154C3⋊#95—102no—
155#816—101no—
156#816—101no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41C4×D312yes—
160C5×#41#6712yes—
161C2×C5×Q8D1211yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4D1211yescharacteristic
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5C22×D311yescharacteristic
167C22×Dic5—32no—
168C22×Dic5—61no—
169C22×Dic5—62no—
170C2×Dic10—32no—
171C2×Dic10—61no—
172C2×Dic10—61no—
173C2×Dic10—61no—
174C2×Dic10—61no—
175C2×Dic10—61no—
176C5×M16—21no—
177C5×M16—21no—
178C2×C5×C8—21no—
179C42×C5—21no—
180C42×C5—21no—
181C22⋊Dic5—62no—
182C22⋊Dic5—61no—
183#689—64no—
184#687—64no—
185C4⋊Dic5—31no—
186C4⋊Dic5—31no—
187C4⋊Dic5—62no—
188C4⋊Dic5—61no—
189C4⋊Dic5—61no—
190C4×Dic5—62no—
191C4×Dic5—61no—
192#681—32no—
193#681—61no—
194C2×#168—61no—
195C2×#137—151no—
196#520—151no—
197C2×#104D1511yescharacteristic
198#419—151no—
199#391—151no—
200#343—151no—
201#339—151no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5—22no—
205C22×C3×C5—41no—
206C22×C3×C5—41no—
207C22×C3×C5C4×D411yescharacteristic
208C22×C3×C5#12011yescharacteristic
209C22×C3×C5#12111yescharacteristic
210C3×C4×C5—22no—
211C3×C4×C5—42no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—42no—
217Dic15—42no—
218Dic15—41no—
219Dic15—41no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41C4×D512yes—
223C3×#41C22⋊D512yes—
224C2×C3×Q8D2011yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4D2011yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C22×D511yescharacteristic
230C22×Dic3—52no—
231C22×Dic3—101no—
232C22×Dic3—102no—
233C2×Dic6—52no—
234C2×Dic6—101no—
235C2×Dic6—101no—
236C2×Dic6—101no—
237C2×Dic6—101no—
238C2×Dic6—101no—
239C3×M16—21no—
240C3×M16—21no—
241C2×C3×C8—21no—
242C3×C42—21no—
243C3×C42—21no—
244#217—102no—
245#217—101no—
246#216—104no—
247#214—104no—
248C4⋊Dic3—51no—
249C4⋊Dic3—51no—
250C4⋊Dic3—102no—
251C4⋊Dic3—101no—
252C4⋊Dic3—101no—
253C4×Dic3—102no—
254C4×Dic3—101no—
255#208—52no—
256#208—101no—
257C2×C3⋊C8—101no—
258C23×C5—21no—
259C23×C5D3×D411yescharacteristic
260C5×Q8—21no—
261C5×Q8(C2×D3)⋊C412yes—
262C5×D4—22no—
263C5×D4—22no—
264C5×D4—21no—
265C5×D4(C2×D3)⋊C412yes—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5C2×D1211yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23711yescharacteristic
276C2×C4×C5#23711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C2×Dic5—62no—
279C2×Dic5—61no—
280C2×Dic5—61no—
281C2×Dic5—62no—
282C2×Dic5—121no—
283C2×Dic5—121no—
284C2×Dic5—122no—
285C2×Dic5—242no—
286Dic10—62no—
287Dic10—62no—
288Dic10—121no—
289Dic10—121no—
290C5×C8—41no—
291#168—62no—
292C2×#41C2×D1511yescharacteristic
293C22×Q8—151no—
294#137—154no—
295#137—302no—
296C2×Q16—301no—
297C2×SD16—301no—
298C2×M16—151no—
299C2×M16C2×D1511yescharacteristic
300C4×Q8—301no—
301C4×D4—302no—
302C4×D4—301no—
303#117—151no—
304#117—301no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—301no—
307C2×C42C2×D1511yescharacteristic
308#104—22no—
309#103—301no—
310#103—301no—
311#95—302no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5—42no—
315C2×C3×C5#38611yescharacteristic
316C2×C3×C5#45511yescharacteristic
317C2×C3×C5#45611yescharacteristic
318C23×C3—21no—
319C23×C3D4×D511yescharacteristic
320C3×Q8—21no—
321C3×Q8#68512yes—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—21no—
325C3×D4#68512yes—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4C2×D2011yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4#71111yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4C2×C22⋊D511yescharacteristic
338C2×Dic3—102no—
339C2×Dic3—101no—
340C2×Dic3—101no—
341C2×Dic3—102no—
342C2×Dic3—201no—
343C2×Dic3—201no—
344C2×Dic3—202no—
345C2×Dic3—402no—
346Dic6—102no—
347Dic6—102no—
348Dic6—201no—
349Dic6—201no—
350C3×C8—41no—
351C3⋊C8—102no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—22no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5#67⋊C411yescharacteristic
358C22×C5#88211yescharacteristic
359C22×C5#93911yescharacteristic
360C4×C5—22no—
361C4×C5—42no—
362C4×C5#67⋊C411yescharacteristic
363C4×C5#88611yescharacteristic
364C4×C5C2×(C2×D3)⋊C411yescharacteristic
365C4×C5#93911yescharacteristic
366Dic5—122no—
367Dic5—122no—
368Dic5—121no—
369Dic5—121no—
370#41—21no—
371#41—21no—
372#41C4×D1512yes—
373#41#122012yes—
374C2×Q8—152no—
375C2×Q8—301no—
376C2×Q8—301no—
377C2×Q8—301no—
378C2×Q8—301no—
379C2×Q8—301no—
380C2×Q8D6011yescharacteristic
381C2×D4—21no—
382C2×D4D6011yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—152no—
386C22×C4—301no—
387C22×C4—302no—
388C22×C4C22×D1511yescharacteristic
389Q16—304no—
390SD16—304no—
391M16—21no—
392M16—21no—
393M16—152no—
394M16—301no—
395C2×C8—21no—
396C2×C8—301no—
397C4⋊C4—151no—
398C4⋊C4—151no—
399C4⋊C4—302no—
400C4⋊C4—301no—
401C4⋊C4—301no—
402C22⋊C4—302no—
403C22⋊C4—301no—
404C42—21no—
405C42—21no—
406C42—302no—
407C42—301no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3#402711yescharacteristic
415C22×C3#402811yescharacteristic
416C22×C3#408511yescharacteristic
417C3×C4—22no—
418C3×C4—42no—
419C3×C4#402711yescharacteristic
420C3×C4#403211yescharacteristic
421C3×C4C2×#68511yescharacteristic
422C3×C4#408511yescharacteristic
423Dic3—202no—
424Dic3—201no—
425Dic3—201no—
426Dic3—202no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5—42no—
430C2×C5#482511yescharacteristic
431C2×C5#482611yescharacteristic
432C2×C5#495811yescharacteristic
433C23—21no—
434C23D4×D1511yescharacteristic
435Q8—21no—
436Q8—302no—
437Q8—302no—
438Q8—601no—
439Q8—601no—
440Q8#671412yes—
441D4—22no—
442D4—22no—
443D4—21no—
444D4#671412yes—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—302no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—302no—
455C2×C4—601no—
456C2×C4—601no—
457C2×C4—602no—
458C2×C4—1202no—
459C2×C4C2×C4×D1511yescharacteristic
460C2×C4C2×D6011yescharacteristic
461C2×C4D4×D1511yescharacteristic
462C2×C4#681911yescharacteristic
463C2×C4#681911yescharacteristic
464C2×C4C2×#122011yescharacteristic
465C8—41no—
466C8—302no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—42no—
470C2×C3#6511411yescharacteristic
471C2×C3#6511511yescharacteristic
472C2×C3#6524711yescharacteristic
473C5#7036511yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22#9177011yescharacteristic
480C22#9177111yescharacteristic
481C22#9182811yescharacteristic
482C4—22no—
483C4—42no—
484C4—602no—
485C4—601no—
486C4—601no—
487C4—602no—
488C4#9177011yescharacteristic
489C4#9177511yescharacteristic
490C4C2×#671411yescharacteristic
491C4#9182811yescharacteristic
492C3#1060115811yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—42no—
496C2#1175092611yescharacteristic
497C2#1175092711yescharacteristic
498C2#1175105911yescharacteristic
subgroupG/H
centerC22#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5#1882
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
4. #11751221C2semidirect
5. #11751030C2semidirect
6. #11746375C2semidirect
7. #11746344C2semidirect
14. #91840C4semidirect
55. C2×Dic30C2×C4semidirect
73. #6710C2×C4semidirect
408. C3×C5#1882semidirect
473. C5#70365semidirect
492. C3#10601158semidirect

Maximal subgroups

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

subgroupindex
#117565862
C2×#918402
C2×C3×C5×#1042
#117512212
#117510302
#117463752
#117463442
#106011583
#703655