Finite Group Databasebeta

← #14471925

Subgroups — #14471925

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
1#11756477C211yesmaximal, characteristic
2#11752473C211yesmaximal, characteristic, complemented
3C5×#5070C211yesmaximal, characteristic, complemented
4C3×#65364C211yesmaximal, characteristic, complemented
5#11749116C212yesmaximal, complemented
6#11749017C212yesmaximal, complemented
7#11749008C212yesmaximal, complemented
8#11748943C212yesmaximal, complemented
9C4×#6658C211yesmaximal, characteristic, complemented
10#11746885C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10613319—31nomaximal, Hall
13C2×#6819—21no—
14C3×C5×#127C2211yescharacteristic
15#91829C2212yes—
16#91828—22no—
17#91827—21no—
18D4×Dic15C2212yes—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C2×C3×#687C2212yes—
23C3×C4×Dic10C2211yescharacteristic
24#91470C2212yes—
25#91468—21no—
26#91333—21no—
27#91331C2212yes—
28#91329—22no—
29C2×#6658C2211yescharacteristic
30C5×#832C2212yes—
31C5×#832C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3964C2212yes—
34C3×C4⋊#168C2211yescharacteristic
35#90987C2211yescharacteristic
36#90985C2212yes—
37#90983C2212yes—
38#90971C2211yescharacteristic
39#90969C2212yes—
40#90968C2211yescharacteristic
41#90951C2212yes—
42#80369—51nomaximal, Hall
43#66056—31no—
44#66052—31no—
45C5×#486—31no—
46#65373—31no—
47#65364D311yescharacteristic, complemented
48#65051—32no—
49#65050—32no—
50#65049—32no—
51#65047—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C2×#1220—22no—
58C2×#1220—22no—
59C22×Dic15—22no—
60#6819—44no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30D411yescharacteristic
64C2×C5×Dic6—21no—
65C2×C3×Dic10C2311yescharacteristic
66C2×#1204—22no—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6714—21no—
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712D412yes—
73C4×Dic15C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×#687—24no—
79C3×C4⋊Dic5C2311yescharacteristic
80C3×#683—21no—
81C3×C4×Dic5—21no—
82C2×C3×#168C2312yes—
83#6669—22no—
84#6668—22no—
85Dic3×Dic5—22no—
86#6658—22no—
87#5718—51no—
88Q8×Dic6—51no—
89C3×#460—51no—
90#5163—52no—
91Dic3×SD16—52no—
92#5070D511yescharacteristic, complemented
93C4×#215—51no—
94#4842—51no—
95#4830—51no—
96#4761—52no—
97#4760—52no—
98C2×#711—61no—
99C5×C4⋊Q8—31no—
100C5×#127C2×D311yescharacteristic
101#4090—62no—
102#4086—32no—
103#4085—62no—
104#4084—61no—
105D4×Dic5—32no—
106C2×#687C2×D312yes—
107C2×#677—31no—
108#4034—32no—
109#4034—61no—
110#4033—32no—
111#4033—61no—
112C4×D20—31no—
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#102—32no—
116C5×#102—32no—
117C4×C5×C8—31no—
118#3964C2×D312yes—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168C2×D311yescharacteristic
127#3362—151noSylow
128C23×C3×C5—22no—
129C22×D15—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
137#1220—44no—
138#1220—82no—
139C2×Dic15—21no—
140C2×Dic15—44no—
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143D60—21no—
144D60—21no—
145C4×D15—42no—
146Dic30SD1614yescomplemented
147C2×C5×Dic3—22no—
148C5×Dic6—81no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C3×Dic10—21no—
152C3×Dic10#4112yescomplemented
153#1204—82no—
154C3×#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#237—101no—
158C2×C3×SD16—52no—
159C3×#127C2×D511yescharacteristic
160C3×C4×Q8—51no—
161Q8×Dic3—52no—
162C2×#215—51no—
163#940—52no—
164#939—102no—
165#938—101no—
166D4×Dic3—52no—
167#888—52no—
168#888—102no—
169C4×D12—51no—
170#869—101no—
171#869C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×C4⋊C8—51no—
175C3×#102—52no—
176#835—51no—
177#832C2×D512yes—
178#832C2×D512yes—
179#821—52no—
180#817—52no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—51no—
184#808—51no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—61no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4C22×D312yes—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20—31no—
195C2×C4×D5—61no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—31no—
200C2×C5×C8—31no—
201C5×C4⋊C4—32no—
202C5×C4⋊C4—61no—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205#687—24no—
206#685—61no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209C4⋊Dic5C22×D311yescharacteristic
210#683—21no—
211#683—32no—
212#683—62no—
213#683—62no—
214C4×Dic5—21no—
215C4×Dic5—32no—
216C4×Dic5—62no—
217C2×#168C22×D312yes—
218#677—62no—
219Q82—151no—
220#550—151no—
221#486—31no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—51no—
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×D15—41no—
235C2×D15—41no—
236C2×D15—41no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15—41no—
243Dic15C2×SD1614yes—
244C3×Dic5—22no—
245C3×Dic5—41no—
246C5×Dic3—42no—
247C2×C3×Q8—51no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4C22×D512yes—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12—51no—
256C2×C4×D3—101no—
257C2×Dic6—21no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C3×SD16—104no—
261C2×C3×C8—52no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—101no—
264C3×C42—101no—
265C3×C42C22×D511yescharacteristic
266#217—102no—
267#215—102no—
268(C2×D3)⋊C4—101no—
269C4⋊Dic3—21no—
270C4⋊Dic3—51no—
271C4⋊Dic3—51no—
272C4⋊Dic3—102no—
273C4⋊Dic3C22×D512yes—
274Dic3⋊C4—52no—
275Dic3⋊C4—102no—
276C4×Dic3—52no—
277C4×Dic3—102no—
278C2×C3⋊C8C22×D511yescharacteristic
279C2×C3⋊C8C22×D511yescharacteristic
280C23×C5—22no—
281C22×D5—61no—
282C5×Q8—241no—
283C5×D4—22no—
284C5×D4—22no—
285C5×D4—42no—
286C5×D4—81no—
287C2×C4×C5—62no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—61no—
298C2×Dic5—124no—
299D20—61no—
300D20—61no—
301C4×D5—122no—
302Dic10—21no—
303Dic10—34no—
304Dic10—242no—
305Dic10#23712yescomplemented
306C5×C8—61no—
307C5×C8—61no—
308#168—22no—
309C2×#41—301no—
310C2×SD16—52no—
311C2×SD16—151no—
312C4⋊Q8—31no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127D3×D511yescharacteristic
318#121—301no—
319#121—302no—
320C4×Q8—51no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4—151no—
326#106—152no—
327#106—151no—
328C4⋊C8—51no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—32no—
333#102—52no—
334#102—152no—
335#102—151no—
336C4×C8—31no—
337C4×C8—152no—
338C2×C3×C5—82no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342D15—81no—
343C23×C3—22no—
344C22×D3—101no—
345C3×Q8—52no—
346C3×Q8—101no—
347C3×D4—22no—
348C3×D4—22no—
349C3×D4—42no—
350C3×D4—81no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—22no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361C2×Dic3—101no—
362C2×Dic3—204no—
363D12—101no—
364D12—101no—
365C4×D3—202no—
366Dic6—54no—
367Dic6—81no—
368Dic6—402no—
369C3×C8—102no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—122no—
381C4×C5D3×SD1612yes—
382C4×C5C2×#23711yescharacteristic
383C4×C5#101011yescharacteristic
384Dic5—22no—
385Dic5—34no—
386Dic5—41no—
387Dic5—62no—
388Dic5—121no—
389#41—604no—
390C2×Q8—51no—
391C2×Q8—61no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—151no—
397C2×D4—302no—
398C2×D4—302no—
399C2×D4C2×D3×D512yes—
400C22×C4—302no—
401C22×C4—301no—
402SD16—104no—
403SD16—302no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—52no—
407C4⋊C4—32no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—101no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—101no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—102no—
432C3×C4—201no—
433C3×C4D5×SD1612yes—
434C3×C4D5×#4111yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—42no—
437Dic3—54no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—82no—
441C2×C5#559811yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—241no—
445C23—22no—
446C23—301no—
447Q8—52no—
448Q8—101no—
449Q8—154no—
450Q8—241no—
451Q8—1202no—
452D4—22no—
453D4—22no—
454D4—42no—
455D4—81no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—1202no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—152no—
464C2×C4—152no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—102no—
474C2×C3—82no—
475C2×C3#6601111yescharacteristic
476C2×C3#6609111yescharacteristic
477C2×C3C2×D5×SD1611yescharacteristic
478D3—401no—
479C5#8036911yescharacteristic, complemented, Sylow
480C22—42no—
481C22—42no—
482C22—42no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—102no—
489C4—122no—
490C4—154no—
491C4—201no—
492C4—302no—
493C4—601no—
494C4#9148712yes—
495C4#9202011yescharacteristic
496C4D5×#23711yescharacteristic
497C3#1061331911yescharacteristic, complemented, Sylow
498C2—82no—
499C2—1201no—
500C2#1175470411yescharacteristic
501C2C2×#9148711yescharacteristic
502C2#1175481611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radical#11756477C2
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. #11752473C2semidirect
3. C5×#5070C2semidirect
4. C3×#65364C2semidirect
5. #11749116C2semidirect
6. #11749017C2semidirect
7. #11749008C2semidirect
8. #11748943C2semidirect
9. C4×#6658C2semidirect
10. #11746885C2semidirect
11. #11746855C2semidirect
47. #65364D3semidirect
92. #5070D5semidirect
146. Dic30SD16semidirect
152. C3×Dic10#41semidirect
305. Dic10#237semidirect
422. C3×C5#3362semidirect
479. C5#80369semidirect
497. C3#10613319semidirect

Maximal subgroups

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

subgroupindex
#117564772
#117524732
C5×#50702
C3×#653642
#117491162
#117490172
#117490082
#117489432
C4×#66582
#117468852
#117468552
#106133193
#803695