Finite Group Databasebeta

← #14306048

Subgroups — #14306048

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#11754572C211yesmaximal, characteristic
2C2×#91089C211yesmaximal, characteristic, complemented
3C2×C5×#805C211yesmaximal, characteristic, complemented
4C3×#65221C211yesmaximal, characteristic, complemented
5#11748431C211yesmaximal, characteristic, complemented
6C2×#90981C211yesmaximal, characteristic, complemented
7C2×#90979C211yesmaximal, characteristic, complemented
8#10601150—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16#91566—22no—
17#91451C411yescharacteristic, complemented
18C4×#1203—22no—
19#91376C411yescharacteristic, complemented
20#91375C411yescharacteristic, complemented
21#91373C411yescharacteristic, complemented
22#91089—22no—
23C5×#805—22no—
24C3×#3963—22no—
25#90982—22no—
26#90981—22no—
27#90979—22no—
28#69440—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104—31no—
31C2×#3969—31no—
32C2×#3957—31no—
33#65407—31no—
34#65221D311yescharacteristic, complemented
35C2×#3937—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39#6817—21no—
40#6817—21no—
41#6817—21no—
42#6817—21no—
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×Dic30C2×C411yescharacteristic
46C2×C5×#67—21no—
47C5×#235—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C2×C5×D12C2×C411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C5×Dic6C2×C411yescharacteristic
54C22×C3×Dic5—21no—
55C22×C3×Dic5D412yes—
56C2×#1203—22no—
57C3×C42×C5—21no—
58C3×C42×C5D412yescomplemented
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×C4×Dic5—21no—
66C3×C4×Dic5C2×C411yescharacteristic
67C3×C4×Dic5C2×C411yescharacteristic
68C3×C4×Dic5D412yes—
69C3×C4×Dic5D412yescomplemented
70#6668—22no—
71#6667—22no—
72(C2×D3)⋊Dic5—22no—
73#5477—51no—
74C3×#376—51no—
75C2×#805—51no—
76C2×#805—51no—
77C2×#805—51no—
78C2×#805D511yescharacteristic, complemented
79#4924—51no—
80C2×C5×#41—31no—
81C2×#709—31no—
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×Dic5C2×D311yescharacteristic
91C2×C4×Dic5C2×D311yescharacteristic
92C2×#681—31no—
93C5×#104—62no—
94#3969—62no—
95#3963—22no—
96#3957—62no—
97#3946—62no—
98#3937—62no—
99#1963—151noSylow
100C23×C3×C5C2×D411yescharacteristic
101C22×D15—21no—
102C22×C5×D3—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
111#1220—41no—
112#1220—41no—
113C2×Dic15—21no—
114D60—21no—
115D60—21no—
116C4×D15—41no—
117C4×D15—41no—
118Dic30—21no—
119Dic30—21no—
120C5×#67—41no—
121C5×#67—41no—
122C2×C5×Dic3—21no—
123C5×D12—21no—
124C5×D12—21no—
125C4×C5×D3—41no—
126C4×C5×D3—41no—
127C5×Dic6—21no—
128C5×Dic6—21no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—42no—
131C2×C3×Dic5—42no—
132C2×C3×Dic5C22⋊C412yes—
133C2×C3×Dic5C22⋊C412yes—
134#1203—44no—
135C3⋊#168—41no—
136C5×C3⋊C8—41no—
137C2×#235—51no—
138C2×#235C2×D511yescharacteristic
139C2×C3×C42—51no—
140C2×C3×C42—51no—
141C2×C3×C42C2×D511yescharacteristic
142#930—102no—
143C2×#208—51no—
144C2×#208C2×D511yescharacteristic
145#875—51no—
146#875—51no—
147#874—51no—
148C4×D12—102no—
149#869—51no—
150C3×#95—102no—
151#805—22no—
152#805—102no—
153#805—102no—
154#805—102no—
155C4⋊(C3⋊C8)—102no—
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—61no—
167C2×C22⋊D5—62no—
168C22×Dic5—21no—
169C22×Dic5#6712yes—
170#709—61no—
171#709—61no—
172#709—61no—
173#709—61no—
174C2×D20—31no—
175C2×C4×D5—61no—
176C2×Dic10—31no—
177C5×M16—61no—
178C5×M16—61no—
179C2×C5×C8—61no—
180C42×C5—21no—
181C42×C5D1212yescomplemented
182C22⋊Dic5—62no—
183#685—62no—
184#683—62no—
185C4×Dic5—21no—
186C4×Dic5C4×D311yescharacteristic
187C4×Dic5C4×D311yescharacteristic
188C4×Dic5D1212yes—
189C4×Dic5D1212yescomplemented
190#681—61no—
191#681—61no—
192C2×#168—61no—
193#532—151no—
194#423—151no—
195C2×#104—31no—
196C2×#104—151no—
197C2×#104—151no—
198C2×#104—151no—
199#376—51no—
200C22×C3×C5—22no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C22×C3×C5#12111yescharacteristic
203C22×C3×C5#12111yescharacteristic
204C2×D15—41no—
205C2×D15—42no—
206C2×C5×D3—41no—
207C2×C5×D3—42no—
208C3×C4×C5—42no—
209C3×C4×C5C4×D411yescharacteristic
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5#12411yescharacteristic
212C3×C4×C5#12711yescharacteristic
213Dic15—41no—
214C3×Dic5—22no—
215C3×Dic5—22no—
216C3×Dic5—42no—
217C5×Dic3—41no—
218C22×C3×C4—21no—
219C22×C3×C4—52no—
220C22×C3×C4—101no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—21no—
223C2×#67—101no—
224#235—21no—
225#235—21no—
226#235—21no—
227#235—21no—
228#235—101no—
229#235—101no—
230#235—101no—
231#235—101no—
232C2×D12—51no—
233C2×D12—102no—
234C2×D12C4×D511yescharacteristic
235C2×C4×D3—21no—
236C2×C4×D3—101no—
237C2×Dic6—51no—
238C2×Dic6C4×D511yescharacteristic
239C3×C42—21no—
240C3×C42—51no—
241C3×C42—51no—
242C3×C42—52no—
243C3×C42—52no—
244C3×C42—101no—
245C3×C42C22⋊D512yescomplemented
246(C2×D3)⋊C4—102no—
247(C2×D3)⋊C4—102no—
248C4⋊Dic3—102no—
249#208—21no—
250#208—21no—
251#208—101no—
252#208—101no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—101no—
255C23×C5—61no—
256C23×C5C2×#6711yescharacteristic
257C22×D5—61no—
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×C5C2×D1211yescharacteristic
271C2×C4×C5C2×D1211yescharacteristic
272C2×C4×C5C2×D1211yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5#23511yescharacteristic
275C22⋊D5—124no—
276C22⋊D5—121no—
277C22⋊D5—121no—
278C2×Dic5—22no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—61no—
282C2×Dic5(C2×D3)⋊C412yes—
283C2×Dic5(C2×D3)⋊C412yes—
284D20—61no—
285D20—61no—
286C4×D5—121no—
287C4×D5—121no—
288Dic10—61no—
289Dic10—61no—
290C5×C8—121no—
291#168—121no—
292C2×#41—31no—
293C2×#41—151no—
294C2×M16—31no—
295C2×M16—151no—
296C4⋊Q8—151no—
297#127—151no—
298#124—151no—
299#124—151no—
300#121—302no—
301C4×D4—302no—
302C2×C42—51no—
303C2×C42—51no—
304C2×C42D3×D511yescharacteristic
305C4⋊C8—302no—
306#104—62no—
307#104—302no—
308#104—302no—
309#104—302no—
310#95—102no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5#39011yescharacteristic
314C2×C3×C5#42112yes—
315D15—81no—
316C5×D3—81no—
317C23×C3D4×D511yescharacteristic
318C22×D3—21no—
319C22×D3—101no—
320C2×C3×C4—22no—
321C2×C3×C4—42no—
322C2×C3×C4—52no—
323C2×C3×C4—52no—
324C2×C3×C4—102no—
325C2×C3×C4—202no—
326C2×C3×C4—202no—
327C2×C3×C4C2×C4×D511yescharacteristic
328C2×C3×C4#70911yescharacteristic
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4#71111yescharacteristic
332C2×C3×C4C2×C22⋊D511yescharacteristic
333#67—41no—
334#67—41no—
335#67—201no—
336#67—201no—
337C2×Dic3—21no—
338C2×Dic3—101no—
339D12—21no—
340D12—21no—
341D12—101no—
342D12—101no—
343D12—204no—
344C4×D3—41no—
345C4×D3—41no—
346C4×D3—201no—
347C4×D3—201no—
348Dic6—21no—
349Dic6—21no—
350Dic6—101no—
351Dic6—101no—
352C3⋊C8—41no—
353C3⋊C8—201no—
354C22×C5—22no—
355C22×C5—121no—
356C22×C5—122no—
357C22×C5C2×(C2×D3)⋊C411yescharacteristic
358C22×C5#93011yescharacteristic
359C22×C5#93011yescharacteristic
360C2×D5—121no—
361C2×D5—122no—
362C4×C5—42no—
363C4×C5—121no—
364C4×C5C4×D1211yescharacteristic
365C4×C5C4×D1211yescharacteristic
366C4×C5#87411yescharacteristic
367C4×C5#87511yescharacteristic
368Dic5—22no—
369Dic5—22no—
370Dic5—42no—
371Dic5—121no—
372#41—61no—
373#41—61no—
374#41—61no—
375#41—61no—
376#41—301no—
377#41—301no—
378#41—301no—
379#41—301no—
380C2×Q8—31no—
381C2×Q8—151no—
382C2×D4—31no—
383C2×D4—61no—
384C2×D4—151no—
385C2×D4—302no—
386C2×D4—301no—
387C22×C4—21no—
388C22×C4—52no—
389C22×C4—61no—
390C22×C4—101no—
391C22×C4—301no—
392C22×C4C2×D3×D511yescharacteristic
393M16—61no—
394M16—61no—
395M16—301no—
396M16—301no—
397C2×C8—61no—
398C2×C8—301no—
399C4⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C42—21no—
403C42—51no—
404C42—51no—
405C42—52no—
406C42—52no—
407C42—101no—
408C42#120312yescomplemented
409C3×C5#196311yescharacteristic, complemented, Hall
410C22×C3—22no—
411C22×C3D5×C22⋊C411yescharacteristic
412C22×C3#403011yescharacteristic
413C22×C3#408511yescharacteristic
414C2×D3—42no—
415C2×D3—41no—
416C2×D3—202no—
417C2×D3—201no—
418C3×C4—42no—
419C3×C4—102no—
420C3×C4—102no—
421C3×C4—202no—
422C3×C4#402711yescharacteristic
423C3×C4#403111yescharacteristic
424C3×C4C4×C22⋊D511yescharacteristic
425C3×C4#408611yescharacteristic
426Dic3—41no—
427Dic3—201no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—241no—
431C2×C5#493911yescharacteristic
432C2×C5#500512yes—
433D5—241no—
434C23—61no—
435C23—301no—
436C23D5×#6711yescharacteristic
437Q8—61no—
438Q8—61no—
439Q8—301no—
440Q8—301no—
441D4—61no—
442D4—61no—
443D4—121no—
444D4—121no—
445D4—301no—
446D4—301no—
447D4—604no—
448D4—601no—
449D4—601no—
450C2×C4—22no—
451C2×C4—42no—
452C2×C4—52no—
453C2×C4—52no—
454C2×C4—61no—
455C2×C4—102no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—202no—
459C2×C4—202no—
460C2×C4—301no—
461C2×C4—601no—
462C2×C4—601no—
463C2×C4#677111yescharacteristic
464C2×C4C4×D3×D511yescharacteristic
465C2×C4D5×D1211yescharacteristic
466C2×C4D5×D1211yescharacteristic
467C2×C4#678211yescharacteristic
468C2×C4C2×#120311yescharacteristic
469C8—121no—
470C8—601no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3#6511012yes—
474C2×C3#6524611yescharacteristic
475D3—81no—
476D3—401no—
477C5#6944011yescharacteristic, complemented, Sylow
478C22—22no—
479C22—122no—
480C22—121no—
481C22—602no—
482C22—601no—
483C22#9144811yescharacteristic
484C22D5×(C2×D3)⋊C411yescharacteristic
485C22#9156611yescharacteristic
486C4—42no—
487C4—102no—
488C4—102no—
489C4—121no—
490C4—202no—
491C4—601no—
492C4#9135011yescharacteristic
493C4#9140511yescharacteristic
494C4C4×#120311yescharacteristic
495C4#9145111yescharacteristic
496C3#1060115011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—241no—
500C2—1201no—
501C2#1174710912yes—
502C2#1174890811yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754572C2
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. C2×#91089C2semidirect
3. C2×C5×#805C2semidirect
4. C3×#65221C2semidirect
5. #11748431C2semidirect
6. C2×#90981C2semidirect
7. C2×#90979C2semidirect
17. #91451C4semidirect
19. #91376C4semidirect
20. #91375C4semidirect
21. #91373C4semidirect
34. #65221D3semidirect
58. C3×C42×C5D4semidirect
69. C3×C4×Dic5D4semidirect
78. C2×#805D5semidirect
181. C42×C5D12semidirect
189. C4×Dic5D12semidirect
245. C3×C42C22⋊D5semidirect
408. C42#1203semidirect
409. C3×C5#1963semidirect
477. C5#69440semidirect
496. C3#10601150semidirect

Maximal subgroups

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

subgroupindex
#117545722
C2×#910892
C2×C5×#8052
C3×#652212
#117484312
C2×#909812
C2×#909792
#106011503
#694405