Finite Group Databasebeta

← #14460051

Subgroups — #14460051

Order 1920.

772 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#11752676C211yesmaximal, characteristic
2#11752508C211yesmaximal, characteristic, complemented
3#11750950C211yesmaximal, characteristic, complemented
4C5×#4846C211yesmaximal, characteristic, complemented
5C3×#65123C211yesmaximal, characteristic, complemented
6#11748164C212yesmaximal, complemented
7#11748135C212yesmaximal, complemented
8#11747943C212yesmaximal, complemented
9#11747673C212yesmaximal, complemented
10C4×#6659C211yesmaximal, characteristic, complemented
11#11746930C211yesmaximal, characteristic, complemented
12#10612712—31nomaximal, Hall
13C2×#6772C2212yes—
14C2×Dic60C2212yes—
15#91758C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C2×C3×C8×D5C2212yes—
20C3×C4×D20C2211yescharacteristic
21#91457—22no—
22#91456—21no—
23D3×C4⋊Dic5—21no—
24#91368—21no—
25#91361—22no—
26#91360C2212yes—
27#91360C2212yes—
28#91358C2212yes—
29#91344—21no—
30C2×#6659C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32#91100C2212yes—
33C5×#821C2212yes—
34C5×#818C2212yes—
35C3×#3952C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90985C2211yescharacteristic
38#90975C2212yes—
39#90975C2212yes—
40#90975C2211yescharacteristic
41#90967C2211yescharacteristic
42#79442—51nomaximal, Hall
43#66066—31no—
44#65889—31no—
45C5×#474—31no—
46#65382—31no—
47C4×#687—31no—
48#65177—32no—
49#65176—32no—
50#65138—31no—
51#65123D311yescharacteristic, complemented
52#65072—32no—
53#65061—32no—
54C2×Dic30C2312yes—
55C2×Dic30C2311yescharacteristic
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6—21no—
59C2×C3×D20D411yescharacteristic
60C2×C3×C4×D5C2312yes—
61C2×#1201—22no—
62C2×D3×Dic5—22no—
63#6772—24no—
64#6772—42no—
65C2×C3×C5×C8C2312yes—
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71C4×Dic15—21no—
72Dic60—42no—
73C5×(C2×D3)⋊C4—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C5×C4⋊Dic3C2311yescharacteristic
77C3×#685D412yes—
78C3×C4⋊Dic5D411yescharacteristic
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81C3×C8×D5—42no—
82Dic3⋊Dic5—22no—
83Dic3⋊Dic5—22no—
84#6665—22no—
85#6665—22no—
86#6665—22no—
87Dic3×Dic5—22no—
88#6659—22no—
89#5551—51no—
90#5542—51no—
91C3×C8×D4—51no—
92#5116—52no—
93#5113—52no—
94#4849—51no—
95#4846D511yescharacteristic, complemented
96#4733—52no—
97#4723—52no—
98C4×#204—51no—
99#4681—51no—
100C2×#711—32no—
101C5×C4⋊Q8—31no—
102C4×C5×D4—31no—
103#4093—61no—
104Q8×Dic5—61no—
105C2×#687—31no—
106#4076—61no—
107C2×C4⋊Dic5—61no—
108C2×Dic20—32no—
109C2×C8×D5C2×D312yes—
110#4044—62no—
111#4043—32no—
112#4043—32no—
113#4038—32no—
114#4032—62no—
115C4×D20C2×D311yescharacteristic
116#4015—31no—
117C4×Dic10—31no—
118C5×#107—32no—
119C5×C4⋊C8C2×D311yescharacteristic
120C5×#102—32no—
121#3964—31no—
122#3952C2×D312yes—
123#3948—32no—
124#3942—31no—
125#3942—32no—
126#3942—32no—
127#3940—31no—
128C4×#168C2×D311yescharacteristic
129#3302—151noSylow
130C22×C5×D3—21no—
131C22×C3×D5C2×D412yes—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138Dic30—21no—
139Dic30—22no—
140Dic30—21no—
141Dic30—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—21no—
144C5×D12—21no—
145C5×D12#4112yes—
146C4×C5×D3—42no—
147C5×Dic6—42no—
148C2×C3×Dic5C2×D412yes—
149C3×D20—22no—
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152#1201—44no—
153D3×Dic5—44no—
154C3×C5×C8—22no—
155C3×#168—21no—
156C3×#168—21no—
157C2×#235—52no—
158C22×C3×C8—52no—
159C3×C4×D4—51no—
160#938—101no—
161#936—101no—
162#926—52no—
163#924—52no—
164#924—52no—
165C2×Dic12—52no—
166C2×#204—51no—
167D3×C4⋊C4—101no—
168#887—101no—
169#883—102no—
170#879—102no—
171C4×D12C2×D511yescharacteristic
172#869—51no—
173#869C2×D511yescharacteristic
174C4×Dic6—51no—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×C22⋊C8—52no—
177C3×C4×C8—51no—
178#821—51no—
179#821C2×D512yes—
180#818C2×D512yes—
181#817—51no—
182#816—52no—
183#816—52no—
184#816—52no—
185#816—51no—
186C2×C5×Q8—61no—
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C22×Dic5—62no—
191#711—64no—
192#711—122no—
193C2×D20D1211yescharacteristic
194C2×C4×D5C22×D312yes—
195C2×Dic10—32no—
196C2×Dic10—31no—
197C2×C5×C8C22×D312yes—
198C5×C4⋊C4—31no—
199C5×C4⋊C4—32no—
200C5×C4⋊C4—61no—
201C5×C22⋊C4—61no—
202C42×C5C22×D311yescharacteristic
203#687—62no—
204#685—62no—
205#685—62no—
206#685—62no—
207#685D1212yes—
208C4⋊Dic5—31no—
209C4⋊Dic5—61no—
210C4⋊Dic5—61no—
211C4⋊Dic5—62no—
212C4⋊Dic5—62no—
213C4⋊Dic5D1211yescharacteristic
214#683—61no—
215C4×Dic5—61no—
216C4×Dic5—62no—
217C2×#168C22×D311yescharacteristic
218C2×#168C22×D311yescharacteristic
219Dic20—122no—
220C8×D5—42no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—31no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—51no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—22no—
234C2×C5×D3—41no—
235C2×C5×D3—41no—
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5—22no—
239C3×C4×C5—21no—
240C3×C4×C5#13512yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C5H(5,𝔽2)11yescharacteristic
243Dic15—42no—
244Dic15—41no—
245Dic15—41no—
246C3×Dic5—22no—
247C5×Dic3—42no—
248C5×Dic3—41no—
249C2×C3×D4—51no—
250C22×C3×C4—52no—
251C2×#67—102no—
252#235—104no—
253#235—202no—
254C2×D12C22×D511yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—102no—
257C2×Dic6—21no—
258C2×Dic6—52no—
259C2×Dic6—51no—
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C2×C3×C8—202no—
263C2×C3×C8C22×D512yes—
264C3×C4⋊C4—51no—
265C3×C22⋊C4—52no—
266C3×C42C22×D511yescharacteristic
267#217—102no—
268#217—102no—
269#217—102no—
270(C2×D3)⋊C4—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—51no—
273C4⋊Dic3—101no—
274C4⋊Dic3—101no—
275C4⋊Dic3C22×D512yes—
276C4⋊Dic3C22×D511yescharacteristic
277Dic3⋊C4—102no—
278Dic3⋊C4—102no—
279Dic3⋊C4—101no—
280C4×Dic3—102no—
281C4×Dic3—101no—
282Dic12—202no—
283#204—102no—
284C23×C5—61no—
285C22×D5C2×D1212yes—
286C5×Q8—122no—
287C5×D4—32no—
288C5×D4—61no—
289C2×C4×C5—62no—
290C2×C4×C5—61no—
291C2×C4×C5—122no—
292C2×C4×C5C2×D1211yescharacteristic
293C2×C4×C5C2×D1211yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—124no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—62no—
299C2×Dic5—124no—
300C2×Dic5C2×D1212yes—
301D20—22no—
302C4×D5—22no—
303C4×D5—22no—
304Dic10—61no—
305Dic10—62no—
306Dic10—61no—
307Dic10—62no—
308C5×C8—22no—
309#168—21no—
310#168—21no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—52no—
315C4⋊Q8—31no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—151no—
324C4×Q8—301no—
325C4×D4—31no—
326C4×D4—51no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—32no—
330#106—151no—
331C4⋊C8D3×D511yescharacteristic
332#103—152no—
333#103—151no—
334#103—152no—
335#103—152no—
336#102—32no—
337#102—151no—
338C22⋊C8—52no—
339C4×C8—51no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343C3×D5—42no—
344C5×D3—42no—
345C23×C3—52no—
346C22×D3—21no—
347C3×D4—102no—
348C2×C3×C4—52no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—101no—
358C2×Dic3—101no—
359C2×Dic3—102no—
360D12—21no—
361D12#71312yes—
362C4×D3—42no—
363C4×D3—204no—
364Dic6—42no—
365Dic6—101no—
366Dic6—102no—
367Dic6—101no—
368Dic6—102no—
369C3×C8—22no—
370C3×C8—101no—
371C3×C8—101no—
372C22×C5—62no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C22×D1211yescharacteristic
376C2×D5—22no—
377C2×D5—22no—
378C2×D5—22no—
379C4×C5—21no—
380C4×C5—121no—
381C4×C5—122no—
382C4×C5#90412yes—
383C4×C5#100411yescharacteristic
384C4×C5D3×#4111yescharacteristic
385Dic5—22no—
386Dic5—121no—
387Dic5—121no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—61no—
392C2×Q8—152no—
393C2×Q8—151no—
394C2×D4—31no—
395C2×D4—51no—
396C2×D4—302no—
397C22×C4—52no—
398C22×C4—61no—
399C22×C4—302no—
400Q16—602no—
401SD16—302no—
402C2×C8—51no—
403C2×C8—51no—
404C2×C8—202no—
405C2×C8C2×D3×D512yes—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—151no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C4⋊C4—301no—
416C22⋊C4—52no—
417C22⋊C4—61no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C42—302no—
422C42—301no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—102no—
427C22×C3—102no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C3×C4—21no—
433C3×C4—102no—
434C3×C4#405812yes—
435C3×C4C2×#71311yescharacteristic
436C3×C4#414911yescharacteristic
437Dic3—42no—
438Dic3—41no—
439Dic3—201no—
440Dic3—202no—
441Dic3—201no—
442C2×C5—122no—
443C2×C5#555411yescharacteristic
444C2×C5C2×#90411yescharacteristic
445C2×C5#575311yescharacteristic
446D5—42no—
447C23—52no—
448C23—61no—
449Q8—122no—
450Q8—301no—
451Q8—302no—
452Q8—301no—
453Q8—302no—
454D4—32no—
455D4—61no—
456D4—102no—
457D4—604no—
458C2×C4—52no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—122no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4D5×D1211yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—101no—
473C8—101no—
474C2×C3—202no—
475C2×C3#6596411yescharacteristic
476C2×C3C2×#405811yescharacteristic
477C2×C3#6611311yescharacteristic
478D3—42no—
479C5#7944211yescharacteristic, complemented, Sylow
480C22—62no—
481C22—102no—
482C22—102no—
483C22—102no—
484C22—121no—
485C22—121no—
486C22C2×D5×D1211yescharacteristic
487C4—21no—
488C4—102no—
489C4—121no—
490C4—122no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4#9127012yes—
495C4#9202611yescharacteristic
496C4D3×#71311yescharacteristic
497C3#1061271211yescharacteristic, complemented, Sylow
498C2—122no—
499C2—202no—
500C2#1175387611yescharacteristic
501C2C2×#9127011yescharacteristic
502C2#1175404011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752676C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752508C2semidirect
3. #11750950C2semidirect
4. C5×#4846C2semidirect
5. C3×#65123C2semidirect
6. #11748164C2semidirect
7. #11748135C2semidirect
8. #11747943C2semidirect
9. #11747673C2semidirect
10. C4×#6659C2semidirect
11. #11746930C2semidirect
51. #65123D3semidirect
95. #4846D5semidirect
424. C3×C5#3302semidirect
479. C5#79442semidirect
497. C3#10612712semidirect

Maximal subgroups

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

subgroupindex
#117526762
#117525082
#117509502
C5×#48462
C3×#651232
#117481642
#117481352
#117479432
#117476732
C4×#66592
#117469302
#106127123
#794425