Finite Group Databasebeta

← #14471936

Subgroups — #14471936

Order 1920.

784 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
1C5×#5553C211yesmaximal, characteristic
2#11752472C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic, complemented
5#11749013C212yesmaximal, complemented
6#11748941C212yesmaximal, complemented
7#11747419C212yesmaximal, complemented
8#11747277C212yesmaximal, complemented
9#11747086C211yesmaximal, characteristic, complemented
10#11746901C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615317—31nomaximal, Hall
13C2×C5×#235—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C2×#6716C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×#940C2212yes—
18C5×#930—21no—
19C5×#893C2212yes—
20C5×#884—22no—
21C5×#874C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91470—21no—
25#91469C2212yes—
26#91344—21no—
27#91340C2212yes—
28#91327—22no—
29C2×#6659C2212yes—
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3964C2212yes—
35C3×#3940C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90967C2212yes—
39#90966C2212yes—
40#90966C2212yes—
41Dic3×#168C2212yes—
42#81090—51nomaximal, Hall
43C5×#550—31no—
44Q8×Dic10—31no—
45#65364—32no—
46#65364—31no—
47#65359—31no—
48#65359—32no—
49Q8×#168—31no—
50C4×#687—32no—
51C4×#687—31no—
52#65297—32no—
53#65297D311yescharacteristic, complemented
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×#67—22no—
58C2×C5×#67—22no—
59C5×#235—44no—
60C2×C5×D12—21no—
61C2×C5×D12—21no—
62C2×C5×D12C2312yes—
63C2×C4×C5×D3—22no—
64C2×C5×Dic6D411yescharacteristic
65C2×C3×Dic10—21no—
66C2×#1204—22no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6716—22no—
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73C4×Dic15—21no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×(C2×D3)⋊C4—22no—
77C5×C4⋊Dic3D411yescharacteristic
78C5×Dic3⋊C4D412yes—
79C4×C5×Dic3C2312yes—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82C2×C3×#168C2312yes—
83Dic3⋊Dic5—22no—
84#6669—22no—
85Dic3×Dic5—22no—
86#6659—24no—
87#5722—51no—
88#5553D511yescharacteristic
89C3×#476—51no—
90#5088—51no—
91C4×#214—51no—
92#4870—52no—
93#4852—52no—
94#4848—51no—
95#4830—51no—
96#4762—52no—
97#4760—52no—
98C2×C5×#41—61no—
99C5×#127—32no—
100C5×#127—31no—
101C5×#121—62no—
102C5×#121—61no—
103C4×C5×Q8—31no—
104C4×C5×D4—32no—
105C4×C5×D4C2×D311yescharacteristic
106Q8×Dic5—61no—
107C2×#687—31no—
108C2×#687—32no—
109#4034—61no—
110#4034—62no—
111#4015—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—32no—
115#3964—31no—
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3964C2×D312yes—
120#3942—31no—
121#3940—31no—
122#3940C2×D312yes—
123C4⋊#168—32no—
124C4⋊#168C2×D311yescharacteristic
125C4×#168—31no—
126C4×#168—32no—
127#3362—151noSylow
128C23×C3×C5—21no—
129C22×C5×D3—22no—
130C3×C5×D4—21no—
131C3×C5×D4—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—42no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139Dic30—21no—
140Dic30#4112yescomplemented
141C5×#67—44no—
142C5×#67—82no—
143C2×C5×Dic3C2×D412yes—
144C2×C5×Dic3C2×D412yes—
145C5×D12—22no—
146C5×D12—22no—
147C5×D12—42no—
148C5×D12—81no—
149C4×C5×D3—44no—
150C5×Dic6SD1614yescomplemented
151C2×C3×Dic5—22no—
152C3×Dic10—81no—
153#1204—82no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C3×#168—22no—
157C2×#235—21no—
158C3×C4⋊Q8—51no—
159C3×C4×D4C2×D511yescharacteristic
160#944—102no—
161#940C2×D512yes—
162C2×#214—51no—
163#930—21no—
164C2×#204—52no—
165#893C2×D512yes—
166#888—52no—
167#888—101no—
168#887—52no—
169#887—101no—
170#884—22no—
171#874C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#106—52no—
175C3×C4⋊C8—51no—
176C3×#102—52no—
177#832—51no—
178#821—52no—
179Dic3⋊C8—52no—
180C8×Dic3—52no—
181#810—51no—
182#809—52no—
183#809—52no—
184#808—51no—
185C4×C3⋊C8—51no—
186C5×#41—124no—
187C2×C5×Q8—31no—
188C2×C5×D4—32no—
189C2×C5×D4—62no—
190C2×C5×D4—62no—
191C2×C5×D4—61no—
192C2×C5×D4—61no—
193C2×C5×D4C22×D311yescharacteristic
194C22×C4×C5—21no—
195C22×C4×C5—62no—
196C2×Dic10—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C5×C4⋊C4—32no—
200C5×C4⋊C4—31no—
201C5×C4⋊C4C22×D311yescharacteristic
202C5×C22⋊C4—21no—
203C5×C22⋊C4—62no—
204C42×C5—32no—
205C42×C5C22×D311yescharacteristic
206#687—64no—
207#687—62no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—62no—
211C4⋊Dic5C22×D312yes—
212#683—62no—
213#683—61no—
214C4×Dic5—62no—
215C4×Dic5—61no—
216C2×#168—31no—
217C2×#168—31no—
218C2×#168C22×D312yes—
219Q82—151no—
220#550—31no—
221#486—152no—
222#486—151no—
223#476—51no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5C22×D411yescharacteristic
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—42no—
237C3×C4×C5—21no—
238C3×C4×C5—41no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—22no—
243Dic15—41no—
244C3×Dic5—42no—
245C5×Dic3—22no—
246C5×Dic3C2×SD1614yes—
247C2×C3×Q8—101no—
248C2×C3×D4C22×D511yescharacteristic
249C22×C3×C4—21no—
250C2×#67—22no—
251C2×#67—22no—
252#235—44no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12C22×D512yes—
256C2×C4×D3—22no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6C22⋊D511yescharacteristic
260C2×C3×C8—52no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4C22×D511yescharacteristic
264C3×C22⋊C4—21no—
265C3×C42C22×D511yescharacteristic
266#214—102no—
267(C2×D3)⋊C4—22no—
268C4⋊Dic3—51no—
269C4⋊Dic3C22⋊D511yescharacteristic
270Dic3⋊C4—101no—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4C22⋊D512yes—
274C4×Dic3—101no—
275C4×Dic3—102no—
276C4×Dic3C22×D512yes—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279#204—104no—
280C23×C5—21no—
281C23×C5—62no—
282C5×Q8—34no—
283C5×D4—21no—
284C5×D4—21no—
285C5×D4—62no—
286C5×D4—62no—
287C5×D4—124no—
288C5×D4—122no—
289C5×D4—241no—
290C5×D4—242no—
291C2×C4×C5—21no—
292C2×C4×C5—32no—
293C2×C4×C5—32no—
294C2×C4×C5—42no—
295C2×C4×C5—124no—
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—22no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302Dic10—32no—
303Dic10—61no—
304Dic10—81no—
305Dic10—242no—
306#168—22no—
307#168—61no—
308#168—61no—
309C2×#41—61no—
310C2×SD16—152no—
311C2×SD16—151no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—32no—
317#127—31no—
318#121—62no—
319#121—61no—
320C4×Q8—31no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—32no—
325C4×D4D3×D511yescharacteristic
326#106—52no—
327#106—151no—
328C4⋊C8—51no—
329C4⋊C8—152no—
330#103—151no—
331#102—52no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—151no—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5—81no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342C5×D3—82no—
343C23×C3—21no—
344C22×D3—22no—
345C3×Q8—401no—
346C3×D4—21no—
347C3×D4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—42no—
350C2×C3×C4—102no—
351C2×C3×C4C2×C22⋊D511yescharacteristic
352C2×C3×C4C2×C22⋊D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—44no—
355#67—82no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358C2×Dic3C2×C22⋊D512yes—
359C2×Dic3C2×C22⋊D512yes—
360D12—22no—
361D12—22no—
362D12—42no—
363D12—81no—
364C4×D3—44no—
365Dic6—52no—
366Dic6—101no—
367Dic6—402no—
368Dic6#68714yescomplemented
369C3×C8—102no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5—122no—
376C22×C5—122no—
377C22×C5—122no—
378C22×C5C2×D3×D411yescharacteristic
379C4×C5—21no—
380C4×C5—34no—
381C4×C5—41no—
382C4×C5—62no—
383C4×C5D3×SD1612yes—
384C4×C5#100711yescharacteristic
385C4×C5D3×#4111yescharacteristic
386Dic5—42no—
387Dic5—62no—
388Dic5—121no—
389#41—124no—
390C2×Q8—31no—
391C2×Q8—101no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—32no—
395C2×D4—62no—
396C2×D4—62no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4C2×D3×D511yescharacteristic
400C22×C4—21no—
401C22×C4—62no—
402SD16—304no—
403SD16—302no—
404C2×C8—52no—
405C2×C8—151no—
406C2×C8—151no—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—101no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—62no—
418C42—32no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3C22×C22⋊D511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—21no—
431C3×C4—41no—
432C3×C4—202no—
433C3×C4C2×#68712yes—
434C3×C4D5×#4111yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—22no—
437Dic3—102no—
438Dic3—201no—
439Dic3C2×#68714yes—
440C2×C5—81no—
441C2×C5—242no—
442C2×C5#563311yescharacteristic
443C2×C5C2×D3×SD1611yescharacteristic
444C2×C5#577411yescharacteristic
445C23—21no—
446C23—62no—
447Q8—34no—
448Q8—152no—
449Q8—301no—
450Q8—401no—
451Q8—1202no—
452D4—21no—
453D4—21no—
454D4—62no—
455D4—62no—
456D4—124no—
457D4—122no—
458D4—241no—
459D4—242no—
460C2×C4—21no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—42no—
464C2×C4—102no—
465C2×C4—124no—
466C2×C4—301no—
467C2×C4—301no—
468C2×C4D3×C22⋊D511yescharacteristic
469C2×C4D3×C22⋊D511yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—102no—
472C8—301no—
473C8—301no—
474C2×C3—81no—
475C2×C3C22×#68711yescharacteristic
476C2×C3#6616511yescharacteristic
477C2×C3#6616911yescharacteristic
478D3—82no—
479C5#8109011yescharacteristic, complemented, Sylow
480C22—41no—
481C22—41no—
482C22—41no—
483C22—122no—
484C22—122no—
485C22—122no—
486C22C2×D3×C22⋊D511yescharacteristic
487C4—21no—
488C4—34no—
489C4—41no—
490C4—62no—
491C4—202no—
492C4—302no—
493C4—601no—
494C4D3×#68712yes—
495C4#9200411yescharacteristic
496C4#9201611yescharacteristic
497C3#1061531711yescharacteristic, complemented, Sylow
498C2—81no—
499C2—242no—
500C2#1175454611yescharacteristic
501C2C2×D3×#68711yescharacteristic
502C2#1175532311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5553C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752472C2semidirect
3. C4×#6716C2semidirect
4. C3×#65297C2semidirect
5. #11749013C2semidirect
6. #11748941C2semidirect
7. #11747419C2semidirect
8. #11747277C2semidirect
9. #11747086C2semidirect
10. #11746901C2semidirect
11. #11746857C2semidirect
53. #65297D3semidirect
140. Dic30#41semidirect
150. C5×Dic6SD16semidirect
368. Dic6#687semidirect
422. C3×C5#3362semidirect
479. C5#81090semidirect
497. C3#10615317semidirect

Maximal subgroups

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

subgroupindex
C5×#55532
#117524722
C4×#67162
C3×#652972
#117490132
#117489412
#117474192
#117472772
#117470862
#117469012
#117468572
#106153173
#810905