Finite Group Databasebeta

← #14306049

Subgroups — #14306049

Order 1920.

640 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
1#11754586C211yesmaximal, characteristic
2#11751033C211yesmaximal, characteristic, complemented
3C2×C5×#805C211yesmaximal, characteristic, complemented
4C2×C3×#3937C211yesmaximal, characteristic, complemented
5#11748437C211yesmaximal, characteristic, complemented
6C2×#90978C211yesmaximal, characteristic, complemented
7C2×#90976C211yesmaximal, characteristic, complemented
8#10601150—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91571—22no—
17#91463C411yescharacteristic, complemented
18C4×#1201—22no—
19#91385C411yescharacteristic, complemented
20#91370C411yescharacteristic, complemented
21#91368C411yescharacteristic, complemented
22#91115—22no—
23C5×#805—22no—
24C3×#3937—22no—
25#90983—22no—
26#90978—22no—
27#90976—22no—
28#70357—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104—31no—
31C2×#3969—31no—
32C2×#3957—31no—
33#65407—31no—
34#65221—31no—
35C2×#3937D311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D412yes—
40C2×C5×#67—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235—21no—
45C2×C5×D12C2×C411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C5×Dic6C2×C411yescharacteristic
48C2×C3×C22⋊D5—21no—
49C3×#709—21no—
50C3×#709—21no—
51C3×#709—21no—
52C3×#709—21no—
53C2×C3×D20C2×C411yescharacteristic
54C2×C3×C4×D5—21no—
55C2×C3×Dic10C2×C411yescharacteristic
56C2×#1201—22no—
57C3×C42×C5—21no—
58C3×C42×C5D412yescomplemented
59C4×Dic15—21no—
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15C2×C411yescharacteristic
62C4×Dic15D412yes—
63C4×Dic15D412yescomplemented
64C5×#208—21no—
65C5×#208—21no—
66C2×C5×C3⋊C8—21no—
67C3×#681—21no—
68C3×#681—21no—
69C2×C3×#168—21no—
70#6669—22no—
71(C2×D3)⋊Dic5—22no—
72#6665—22no—
73#5832—51no—
74C2×C3×#104—51no—
75C2×#837—51no—
76C2×#825—51no—
77#5118—51no—
78#4932—51no—
79C2×#805D511yescharacteristic, complemented
80C2×C5×#41—31no—
81C2×#709C2×D311yescharacteristic
82C2×C5×M16—31no—
83C2×C42×C5C2×D311yescharacteristic
84#4093—31no—
85#4090—31no—
86#4086—31no—
87#4085—62no—
88#4082—31no—
89C4×C22⋊D5—62no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—31no—
92C2×#681C2×D311yescharacteristic
93C5×#104—62no—
94#3969—62no—
95#3963—62no—
96#3957—62no—
97#3946—62no—
98#3937—22no—
99#1963—151noSylow
100C23×C3×C5C2×D411yescharacteristic
101C22×C5×D3—21no—
102C22×C3×D5—21no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—42no—
113C2×Dic15—42no—
114C2×Dic15C22⋊C412yes—
115C2×Dic15C22⋊C412yes—
116C5×#67—41no—
117C5×#67—41no—
118C2×C5×Dic3—21no—
119C5×D12—21no—
120C5×D12—21no—
121C4×C5×D3—41no—
122C4×C5×D3—41no—
123C5×Dic6—21no—
124C5×Dic6—21no—
125C3×C22⋊D5—41no—
126C3×C22⋊D5—41no—
127C2×C3×Dic5—21no—
128C3×D20—21no—
129C3×D20—21no—
130C3×C4×D5—41no—
131C3×C4×D5—41no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134#1201—44no—
135C3×#168—41no—
136C5×C3⋊C8—41no—
137C2×C3×#41—51no—
138C2×#235C2×D511yescharacteristic
139C2×C3×M16—51no—
140C2×C3×C42C2×D511yescharacteristic
141#947—51no—
142#944—51no—
143#940—51no—
144#939—102no—
145#936—51no—
146C4×#67—102no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3—51no—
149C2×#208C2×D511yescharacteristic
150C3×#104—102no—
151#837—102no—
152C3⋊#95—102no—
153#825—102no—
154Dic3⋊C8—102no—
155#805—22no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C2×C5×Q8—31no—
161C2×C5×D4—31no—
162C2×C5×D4—61no—
163C22×C4×C5—21no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—21no—
167C2×C22⋊D5—62no—
168C22×Dic5—32no—
169C22×Dic5—61no—
170#709—21no—
171#709—21no—
172#709—21no—
173#709—21no—
174C2×D20C4×D311yescharacteristic
175C2×C4×D5—21no—
176C2×Dic10C4×D311yescharacteristic
177C5×M16—61no—
178C5×M16—61no—
179C2×C5×C8—61no—
180C42×C5—21no—
181C42×C5#6712yescomplemented
182C22⋊Dic5—62no—
183#685—62no—
184#683—62no—
185C4×Dic5—31no—
186C4×Dic5—31no—
187C4×Dic5—32no—
188C4×Dic5—32no—
189C4×Dic5—61no—
190#681—21no—
191#681—21no—
192C2×#168—21no—
193#532—151no—
194#423—151no—
195C2×#104—31no—
196C2×#104—51no—
197C2×#104—151no—
198C2×#104—151no—
199#376—151no—
200C22×C3×C5—22no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C22×C3×C5#12111yescharacteristic
203C22×C3×C5#12111yescharacteristic
204C2×C5×D3—41no—
205C2×C5×D3—42no—
206C2×C3×D5—41no—
207C2×C3×D5—42no—
208C3×C4×C5—42no—
209C3×C4×C5C4×D411yescharacteristic
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5#12411yescharacteristic
212C3×C4×C5#12711yescharacteristic
213Dic15—22no—
214Dic15—22no—
215Dic15—42no—
216C3×Dic5—41no—
217C5×Dic3—41no—
218C3×#41—101no—
219C3×#41—101no—
220C3×#41—101no—
221C3×#41—101no—
222C2×C3×Q8—51no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C22×C3×C4—21no—
226C22×C3×C4—101no—
227C22×C3×C4C22×D511yescharacteristic
228C2×#67—21no—
229C2×#67—102no—
230C22×Dic3—52no—
231C22×Dic3—101no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12C4×D511yescharacteristic
237C2×C4×D3—21no—
238C2×Dic6C4×D511yescharacteristic
239C3×M16—101no—
240C3×M16—101no—
241C2×C3×C8—101no—
242C3×C42—21no—
243C3×C42C22⋊D512yescomplemented
244#217—102no—
245(C2×D3)⋊C4—102no—
246Dic3⋊C4—102no—
247C4×Dic3—51no—
248C4×Dic3—51no—
249C4×Dic3—52no—
250C4×Dic3—52no—
251C4×Dic3—101no—
252#208—21no—
253#208—21no—
254C2×C3⋊C8—21no—
255C23×C5—61no—
256C23×C5D3×D411yescharacteristic
257C22×D5—21no—
258C5×Q8—61no—
259C5×Q8—61no—
260C5×D4—61no—
261C5×D4—61no—
262C5×D4—121no—
263C5×D4—121no—
264C2×C4×C5—22no—
265C2×C4×C5—42no—
266C2×C4×C5—61no—
267C2×C4×C5—121no—
268C2×C4×C5—121no—
269C2×C4×C5C2×C4×D311yescharacteristic
270C2×C4×C5#23511yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5#23711yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C22⋊D5—41no—
276C22⋊D5—41no—
277C22⋊D5—124no—
278C2×Dic5—21no—
279C2×Dic5—32no—
280C2×Dic5—32no—
281C2×Dic5—62no—
282C2×Dic5—122no—
283C2×Dic5—122no—
284D20—21no—
285D20—21no—
286C4×D5—41no—
287C4×D5—41no—
288Dic10—21no—
289Dic10—21no—
290C5×C8—121no—
291#168—41no—
292C2×#41—31no—
293C2×#41—51no—
294C2×M16—31no—
295C2×M16—51no—
296C4⋊Q8—151no—
297#127—151no—
298#124—151no—
299#124—151no—
300#121—302no—
301C4×D4—302no—
302C2×C42—151no—
303C2×C42—151no—
304C2×C42D3×D511yescharacteristic
305C4⋊C8—302no—
306#104—62no—
307#104—102no—
308#104—302no—
309#104—302no—
310#95—302no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5#39011yescharacteristic
314C2×C3×C5#42112yes—
315C3×D5—81no—
316C5×D3—81no—
317C23×C3—101no—
318C23×C3D4×D511yescharacteristic
319C22×D3—21no—
320C3×Q8—101no—
321C3×Q8—101no—
322C3×D4—101no—
323C3×D4—101no—
324C3×D4—201no—
325C3×D4—201no—
326C2×C3×C4—22no—
327C2×C3×C4—42no—
328C2×C3×C4—101no—
329C2×C3×C4—201no—
330C2×C3×C4—201no—
331C2×C3×C4C2×C4×D511yescharacteristic
332C2×C3×C4#70911yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4#71111yescharacteristic
336C2×C3×C4C2×C22⋊D511yescharacteristic
337#67—41no—
338#67—41no—
339#67—204no—
340C2×Dic3—21no—
341C2×Dic3—52no—
342C2×Dic3—52no—
343C2×Dic3—102no—
344C2×Dic3—202no—
345C2×Dic3—202no—
346D12—21no—
347D12—21no—
348C4×D3—41no—
349C4×D3—41no—
350Dic6—21no—
351Dic6—21no—
352C3×C8—201no—
353C3⋊C8—41no—
354C22×C5—22no—
355C22×C5—121no—
356C22×C5—122no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88411yescharacteristic
359C22×C5#93911yescharacteristic
360C2×D5—41no—
361C2×D5—42no—
362C4×C5—42no—
363C4×C5—121no—
364C4×C5#67⋊C411yescharacteristic
365C4×C5#88511yescharacteristic
366C4×C5C4×#6711yescharacteristic
367C4×C5#94011yescharacteristic
368Dic5—41no—
369Dic5—62no—
370Dic5—62no—
371Dic5—122no—
372#41—61no—
373#41—61no—
374#41—61no—
375#41—61no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×D4—31no—
383C2×D4—51no—
384C2×D4—61no—
385C2×D4—101no—
386C2×D4—302no—
387C22×C4—21no—
388C22×C4—61no—
389C22×C4—101no—
390C22×C4—152no—
391C22×C4—301no—
392C22×C4C2×D3×D511yescharacteristic
393M16—61no—
394M16—61no—
395M16—101no—
396M16—101no—
397C2×C8—61no—
398C2×C8—101no—
399C4⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C42—21no—
403C42—151no—
404C42—151no—
405C42—152no—
406C42—152no—
407C42—301no—
408C42#120112yescomplemented
409C3×C5#196311yescharacteristic, complemented, Hall
410C22×C3—22no—
411C22×C3—202no—
412C22×C3—201no—
413C22×C3D5×C22⋊C411yescharacteristic
414C22×C3#403011yescharacteristic
415C22×C3#408511yescharacteristic
416C2×D3—42no—
417C2×D3—41no—
418C3×C4—42no—
419C3×C4—201no—
420C3×C4#402711yescharacteristic
421C3×C4#403111yescharacteristic
422C3×C4C4×C22⋊D511yescharacteristic
423C3×C4#408611yescharacteristic
424Dic3—41no—
425Dic3—102no—
426Dic3—102no—
427Dic3—202no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—241no—
431C2×C5#482112yes—
432C2×C5#495711yescharacteristic
433D5—81no—
434C23—61no—
435C23—101no—
436C23#679011yescharacteristic
437Q8—61no—
438Q8—61no—
439Q8—101no—
440Q8—101no—
441D4—61no—
442D4—61no—
443D4—101no—
444D4—101no—
445D4—121no—
446D4—121no—
447D4—201no—
448D4—201no—
449D4—604no—
450C2×C4—22no—
451C2×C4—42no—
452C2×C4—61no—
453C2×C4—101no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—152no—
457C2×C4—152no—
458C2×C4—201no—
459C2×C4—201no—
460C2×C4—302no—
461C2×C4—602no—
462C2×C4—602no—
463C2×C4#677111yescharacteristic
464C2×C4C4×D3×D511yescharacteristic
465C2×C4#677711yescharacteristic
466C2×C4#677711yescharacteristic
467C2×C4#678011yescharacteristic
468C2×C4C2×#120111yescharacteristic
469C8—121no—
470C8—201no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—401no—
474C2×C3#6511012yes—
475C2×C3#6524611yescharacteristic
476D3—81no—
477C5#7035711yescharacteristic, complemented, Sylow
478C22—22no—
479C22—122no—
480C22—121no—
481C22—202no—
482C22—201no—
483C22#9146111yescharacteristic
484C22#9147311yescharacteristic
485C22#9157111yescharacteristic
486C4—42no—
487C4—121no—
488C4—201no—
489C4—302no—
490C4—302no—
491C4—602no—
492C4C4×#120111yescharacteristic
493C4#9144211yescharacteristic
494C4#9146311yescharacteristic
495C4#9146411yescharacteristic
496C3#1060115011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—241no—
500C2—401no—
501C2#1174711312yes—
502C2#1174891511yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754586C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1963
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751033C2semidirect
3. C2×C5×#805C2semidirect
4. C2×C3×#3937C2semidirect
5. #11748437C2semidirect
6. C2×#90978C2semidirect
7. C2×#90976C2semidirect
17. #91463C4semidirect
19. #91385C4semidirect
20. #91370C4semidirect
21. #91368C4semidirect
35. C2×#3937D3semidirect
58. C3×C42×C5D4semidirect
63. C4×Dic15D4semidirect
79. C2×#805D5semidirect
181. C42×C5#67semidirect
243. C3×C42C22⋊D5semidirect
408. C42#1201semidirect
409. C3×C5#1963semidirect
477. C5#70357semidirect
496. C3#10601150semidirect

Maximal subgroups

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

subgroupindex
#117545862
#117510332
C2×C5×#8052
C2×C3×#39372
#117484372
C2×#909782
C2×#909762
#106011503
#703575