Finite Group Databasebeta

← #14471921

Subgroups — #14471921

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
1C3×#66052C211yesmaximal, characteristic
2Dic6×Dic10C211yesmaximal, characteristic, complemented
3#11751171C211yesmaximal, characteristic, complemented
4C5×#5075C211yesmaximal, characteristic, complemented
5#11749104C212yesmaximal, complemented
6#11749102C212yesmaximal, complemented
7#11748999C212yesmaximal, complemented
8Dic5×#214C212yesmaximal, complemented
9C4×#6655C211yesmaximal, characteristic, complemented
10#11746881C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612100—31nomaximal, Hall
13C2×C3×#711—21no—
14C3×C5×#127C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×#214C2212yes—
17C4×C5×Dic6C2211yescharacteristic
18C3×#4086C2212yes—
19C3×#4085—22no—
20C3×#4084—21no—
21C3×D4×Dic5C2212yes—
22C3×C4×D20C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91469—21no—
25#91468C2212yes—
26Dic5×Dic6C2212yes—
27Dic3×Dic10—21no—
28#91328—22no—
29C2×#6655C2211yescharacteristic
30#91116C2212yes—
31#91116C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C5×#832C2212yes—
34C5×C4⋊(C3⋊C8)C2211yescharacteristic
35#90987C2212yes—
36#90986C2211yescharacteristic
37#90982C2212yes—
38#90972C2211yescharacteristic
39#90965C2212yes—
40#90964C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83586—51nomaximal, Hall
43#66052D311yescharacteristic
44Q8×Dic10—31no—
45C5×#460—31no—
46#65452—32no—
47SD16×Dic5—32no—
48#65359—31no—
49C4×#688—31no—
50#65131—31no—
51#65119—31no—
52#65050—32no—
53#65049—32no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C2×Dic30—21no—
58C2×C5×Dic6C2311yescharacteristic
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C22×C3×Dic5—22no—
62C3×#711—44no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×C3×Dic10D411yescharacteristic
66C2×#1204—22no—
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C5×#214—24no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C4×C5×Dic3—21no—
76C2×C5×C3⋊C8C2312yes—
77C3×C22⋊Dic5—22no—
78C3×#685—21no—
79C3×C4⋊Dic5D411yescharacteristic
80C3×C4⋊Dic5C2311yescharacteristic
81C3×#683D412yes—
82C3×C4×Dic5C2312yes—
83Dic3⋊Dic5—22no—
84#6668—22no—
85Dic3×Dic5—22no—
86#6655—22no—
87C3×#550—51no—
88Q8×Dic6—51no—
89#5075—52no—
90#5075D511yescharacteristic, complemented
91#5070—51no—
92#5070—52no—
93Q8×C3⋊C8—51no—
94C4×#214—52no—
95C4×#214—51no—
96#5008—52no—
97#5008—51no—
98C2×#711—21no—
99C2×C5×SD16—32no—
100C5×#127C2×D311yescharacteristic
101C4×C5×Q8—31no—
102Q8×Dic5—32no—
103C2×#688—31no—
104#4086C2×D312yes—
105#4085—22no—
106#4084—21no—
107D4×Dic5C2×D312yes—
108#4034—32no—
109#4034—62no—
110C4×D20C2×D311yescharacteristic
111#4015—31no—
112#4015—61no—
113C4×Dic10—61no—
114C4×Dic10C2×D311yescharacteristic
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3967—31no—
118#3964—32no—
119#3964—32no—
120#3953—32no—
121#3949—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—31no—
125#3940—31no—
126C4×#168—31no—
127#3362—151noSylow
128C23×C3×C5—22no—
129C22×C3×D5—21no—
130C3×C5×D4—22no—
131C3×C5×D4—22no—
132C3×C5×D4—42no—
133C3×C5×D4—81no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—22no—
138Dic30—81no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C5×Dic6—21no—
142C5×Dic6#4112yescomplemented
143C3×C22⋊D5—44no—
144C3×C22⋊D5—82no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—44no—
147C2×C3×Dic5C2×D412yes—
148C2×C3×Dic5C2×D412yes—
149C3×D20—21no—
150C3×D20—21no—
151C3×C4×D5—42no—
152C3×Dic10SD1614yescomplemented
153#1204—82no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C5×C3⋊C8—22no—
157C2×C3×#41—101no—
158C3×#127—52no—
159C3×#127C2×D511yescharacteristic
160C3×#121—101no—
161C3×#121—102no—
162C3×C4×Q8—51no—
163C3×C4×D4—52no—
164C3×C4×D4—51no—
165Q8×Dic3—101no—
166C2×#214—51no—
167C2×#214C2×D512yes—
168#888—101no—
169#888—102no—
170#869—51no—
171#869—52no—
172C4×Dic6—52no—
173C4×Dic6C2×D511yescharacteristic
174#832—52no—
175#832—52no—
176#832—51no—
177#832—52no—
178#832C2×D512yes—
179#810—51no—
180#808—51no—
181#808—52no—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)C2×D511yescharacteristic
184C4×C3⋊C8—51no—
185C4×C3⋊C8—52no—
186C2×C5×Q8—31no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4C22×D312yes—
190C2×C22⋊D5—22no—
191C2×C22⋊D5—22no—
192C22×Dic5—22no—
193#711—44no—
194C2×D20C22×D311yescharacteristic
195C2×C4×D5—21no—
196C2×Dic10—61no—
197C2×Dic10—62no—
198C2×Dic10#6711yescharacteristic
199C5×SD16—64no—
200C2×C5×C8—32no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—61no—
203C42×C5—61no—
204C42×C5C22×D311yescharacteristic
205C22⋊Dic5—22no—
206#688—62no—
207#685—21no—
208C4⋊Dic5—32no—
209C4⋊Dic5—61no—
210C4⋊Dic5—62no—
211C4⋊Dic5#6711yescharacteristic
212C4⋊Dic5C22×D311yescharacteristic
213#683—62no—
214#683#6712yes—
215C4×Dic5—62no—
216C4×Dic5C22×D312yes—
217C2×#168—31no—
218C2×#168—31no—
219Q82—151no—
220#550—51no—
221#486—152no—
222#486—151no—
223#476—152no—
224#476—151no—
225#460—31no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5C22×D411yescharacteristic
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C2×C3×D5—41no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—42no—
242C3×Dic5—22no—
243C3×Dic5—41no—
244C3×Dic5C2×SD1614yes—
245C5×Dic3—22no—
246C5×Dic3—41no—
247C3×#41—204no—
248C2×C3×Q8—51no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—51no—
252C2×C3×D4—102no—
253C2×C3×D4—102no—
254C2×C3×D4C22×D512yes—
255C22×C3×C4—102no—
256C22×C3×C4—101no—
257C2×Dic6—102no—
258C2×Dic6—101no—
259C2×Dic6C22×D511yescharacteristic
260C3×C4⋊C4—52no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4—51no—
263C3×C22⋊C4—102no—
264C3×C22⋊C4—101no—
265C3×C42—52no—
266C3×C42C22×D511yescharacteristic
267#214—24no—
268#214—102no—
269C4⋊Dic3—52no—
270C4⋊Dic3—102no—
271C4⋊Dic3—101no—
272C4⋊Dic3C22×D511yescharacteristic
273Dic3⋊C4—21no—
274Dic3⋊C4—102no—
275C4×Dic3—21no—
276C4×Dic3—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—22no—
281C22×D5—21no—
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—22no—
285C5×D4—22no—
286C5×D4—42no—
287C5×D4—81no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—44no—
294C22⋊D5—82no—
295C2×Dic5—21no—
296C2×Dic5—44no—
297C2×Dic5—62no—
298C2×Dic5C2×#6712yes—
299C2×Dic5C2×#6712yes—
300D20—21no—
301D20—21no—
302C4×D5—42no—
303Dic10—242no—
304Dic10—241no—
305Dic10#21414yescomplemented
306C5×C8—62no—
307#168—61no—
308#168—61no—
309C2×#41—101no—
310C2×SD16—32no—
311C2×SD16—151no—
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—52no—
317#127D3×D511yescharacteristic
318#121—101no—
319#121—102no—
320C4×Q8—31no—
321C4×Q8—51no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—52no—
325C4×D4—51no—
326#106—151no—
327#106—152no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—151no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5—82no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342C3×D5—81no—
343C23×C3—22no—
344C23×C3—101no—
345C3×Q8—54no—
346C3×D4—22no—
347C3×D4—22no—
348C3×D4—42no—
349C3×D4—81no—
350C3×D4—101no—
351C3×D4—101no—
352C3×D4—204no—
353C3×D4—402no—
354C2×C3×C4—52no—
355C2×C3×C4—52no—
356C2×C3×C4—101no—
357C2×C3×C4—204no—
358C2×C3×C4—202no—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—102no—
365Dic6—21no—
366Dic6—402no—
367Dic6—401no—
368Dic6#71112yescomplemented
369C3⋊C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—41no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—62no—
381C4×C5—121no—
382C4×C5C2×#21412yes—
383C4×C5D3×#4111yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—22no—
386Dic5—41no—
387Dic5—122no—
388Dic5C2×#21414yes—
389#41—204no—
390C2×Q8—31no—
391C2×Q8—51no—
392C2×Q8—302no—
393C2×Q8—301no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—51no—
397C2×D4—102no—
398C2×D4—102no—
399C2×D4C2×D3×D512yes—
400C22×C4—102no—
401C22×C4—101no—
402SD16—64no—
403SD16—302no—
404C2×C8—32no—
405C2×C8—151no—
406C2×C8—151no—
407C4⋊C4—31no—
408C4⋊C4—52no—
409C4⋊C4—51no—
410C4⋊C4—51no—
411C4⋊C4—61no—
412C4⋊C4—152no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—102no—
417C22⋊C4—101no—
418C42—52no—
419C42—61no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3—201no—
429C22×C3C2×D4×D511yescharacteristic
430C3×C4—21no—
431C3×C4—54no—
432C3×C4—102no—
433C3×C4—201no—
434C3×C4D5×SD1612yes—
435C3×C4C2×#71111yescharacteristic
436C3×C4#415011yescharacteristic
437Dic3—22no—
438Dic3—41no—
439Dic3—202no—
440C2×C5—82no—
441C2×C5C22×#21411yescharacteristic
442C2×C5#583111yescharacteristic
443C2×C5#583511yescharacteristic
444D5—81no—
445C23—22no—
446C23—101no—
447Q8—32no—
448Q8—54no—
449Q8—61no—
450Q8—1201no—
451Q8—1202no—
452D4—22no—
453D4—22no—
454D4—42no—
455D4—81no—
456D4—101no—
457D4—101no—
458D4—204no—
459D4—402no—
460C2×C4—52no—
461C2×C4—52no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—101no—
465C2×C4—204no—
466C2×C4—202no—
467C2×C4—302no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—301no—
473C8—301no—
474C2×C3—82no—
475C2×C3—401no—
476C2×C3#6593211yescharacteristic
477C2×C3C2×D5×SD1611yescharacteristic
478C2×C3#6610811yescharacteristic
479C5#8358611yescharacteristic, complemented, Sylow
480C22—42no—
481C22—42no—
482C22—42no—
483C22—201no—
484C22—201no—
485C22—201no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—54no—
489C4—62no—
490C4—102no—
491C4—121no—
492C4—201no—
493C4—602no—
494C4D5×#21412yes—
495C4#9202011yescharacteristic
496C4D3×#71111yescharacteristic
497C3#1061210011yescharacteristic, complemented, Sylow
498C2—82no—
499C2—401no—
500C2#1175469211yescharacteristic
501C2C2×D5×#21411yescharacteristic
502C2#1175479811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC3×#66052C2
hypercenter#127D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. Dic6×Dic10C2semidirect
3. #11751171C2semidirect
4. C5×#5075C2semidirect
5. #11749104C2semidirect
6. #11749102C2semidirect
7. #11748999C2semidirect
8. Dic5×#214C2semidirect
9. C4×#6655C2semidirect
10. #11746881C2semidirect
11. #11746846C2semidirect
90. #5075D5semidirect
142. C5×Dic6#41semidirect
152. C3×Dic10SD16semidirect
305. Dic10#214semidirect
368. Dic6#711semidirect
422. C3×C5#3362semidirect
479. C5#83586semidirect
497. C3#10612100semidirect

Maximal subgroups

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

subgroupindex
C3×#660522
Dic6×Dic102
#117511712
C5×#50752
#117491042
#117491022
#117489992
Dic5×#2142
C4×#66552
#117468812
#117468462
#106121003
#835865