Finite Group Databasebeta

← #14438031

Subgroups — #14438031

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#11756591C211yesmaximal, characteristic
2#11754617C211yesmaximal, characteristic, complemented
3C5×#5233C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5#11749363C212yesmaximal, complemented
6#11749336C212yesmaximal, complemented
7#11749117C212yesmaximal, complemented
8#11749090C212yesmaximal, complemented
9#11748411C211yesmaximal, characteristic, complemented
10#11748393C211yesmaximal, characteristic, complemented
11C2×#90954C211yesmaximal, characteristic, complemented
12#10610557—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15#91836C2211yescharacteristic
16#91833C2211yescharacteristic
17#91829C2211yescharacteristic
18#91828—22no—
19#91825C2211yescharacteristic
20C4×#1220—22no—
21C2×C4×Dic15C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26#91576—22no—
27#91470C2212yes—
28C4×#1204—22no—
29#91384C2212yes—
30C5×#835C2212yes—
31C5×#832C2212yes—
32C3×#3967C2212yes—
33C3×#3964C2212yes—
34#90975C2212yes—
35#90974C2212yes—
36#90969C2212yes—
37#90968C2212yes—
38#90954C2212yes—
39#90954C2212yes—
40#78826—51nomaximal, Hall
41#66166—31no—
42#65851—31no—
43C5×#416—31no—
44#65522D311yescharacteristic, complemented
45#65402—31no—
46C2×#3947—31no—
47#65291—31no—
48#65086—32no—
49#65084—32no—
50#65054—32no—
51#65053—32no—
52C3×C5×#41—22no—
53C3×C5×#41—22no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C2×#1220—22no—
61C22×Dic15D412yes—
62#6817—22no—
63#6817—22no—
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×Dic30C2311yescharacteristic
67C2×#1204—22no—
68#6719—22no—
69#6714—22no—
70#6712—22no—
71C4×Dic15D412yes—
72C4×Dic15C2311yescharacteristic
73C4×Dic15C2311yescharacteristic
74C5×#217—21no—
75C5×C4⋊Dic3C2312yes—
76C4×C5×Dic3—21no—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yes—
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C3×C4×Dic5—21no—
82C2×C3×#168—22no—
83C2×C3×#168C2312yes—
84Dic3⋊Dic5—22no—
85#6669—22no—
86#6668—22no—
87#5832—51no—
88#5517—51no—
89C3×#416—51no—
90#5233D511yescharacteristic, complemented
91#5113—51no—
92C2×#815—51no—
93#5002—51no—
94#4797—52no—
95#4794—52no—
96#4765—52no—
97#4764—52no—
98C2×C5×#41C2×D311yescharacteristic
99C2×#709—31no—
100C22×C5×C8—31no—
101C5×#117—31no—
102#4093—31no—
103#4090—31no—
104#4086—31no—
105#4085—62no—
106#4082—31no—
107C4×C22⋊D5—62no—
108#4072C2×D311yescharacteristic
109C2×C4×Dic5—31no—
110C22×#168C2×D311yescharacteristic
111#4036—32no—
112#4034—32no—
113#4024—62no—
114C4×Dic10—62no—
115C5×#103—32no—
116C5×#102—32no—
117#3967C2×D312yes—
118#3964C2×D312yes—
119#3953—32no—
120#3948—32no—
121#3947—32no—
122#3947—32no—
123#3942—32no—
124#3941—32no—
125#3135—151noSylow
126C23×C3×C5—21no—
127C23×C3×C5C2×D411yescharacteristic
128C22×D15—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C3×C5×D4—21no—
132C3×C5×D4—21no—
133C3×C5×D4—42no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5#4112yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140#1220—44no—
141#1220—42no—
142C2×Dic15—21no—
143C2×Dic15—42no—
144C2×Dic15C2×D412yes—
145C2×Dic15C2×D412yes—
146D60—21no—
147D60—21no—
148C4×D15—42no—
149Dic30—21no—
150Dic30—21no—
151C2×C5×Dic3—22no—
152C2×C3×Dic5—22no—
153#1204—44no—
154C3×#168—22no—
155C5×C3⋊C8—22no—
156C2×C3×#41C2×D511yescharacteristic
157C2×#235—51no—
158C22×C3×C8—51no—
159C3×#117—51no—
160#947—51no—
161#944—51no—
162#940—51no—
163#939—102no—
164#936—51no—
165C4×#67—102no—
166#926C2×D511yescharacteristic
167C2×C4×Dic3—51no—
168C22×C3⋊C8C2×D511yescharacteristic
169#890—52no—
170#888—52no—
171#878—102no—
172C4×Dic6—102no—
173C3×#103—52no—
174C3×#102—52no—
175#835C2×D512yes—
176#832C2×D512yes—
177#821—52no—
178#816—52no—
179#815—52no—
180#815—52no—
181#810—52no—
182#809—52no—
183C5×#41—22no—
184C5×#41—22no—
185C2×C5×Q8C22×D311yescharacteristic
186C2×C5×D4—21no—
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—62no—
191C2×C22⋊D5—61no—
192C22×Dic5—32no—
193#709—62no—
194#709—62no—
195C2×D20—31no—
196C2×C4×D5—61no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8—32no—
200C2×C5×C8—62no—
201C5×C4⋊C4—32no—
202C5×C22⋊C4—61no—
203C42×C5—61no—
204C22⋊Dic5—21no—
205C22⋊Dic5—62no—
206#685—62no—
207C4⋊Dic5—62no—
208C4⋊Dic5C22×D312yes—
209#683—62no—
210#683—62no—
211#683—62no—
212C4×Dic5—21no—
213C4×Dic5—32no—
214C4×Dic5—31no—
215C4×Dic5—31no—
216C2×#168—22no—
217C2×#168C22×D312yes—
218#533—151no—
219#532—151no—
220#491—152no—
221#490—152no—
222#489—152no—
223#489—152no—
224#416—31no—
225#416—51no—
226#416—151no—
227#416—151no—
228C2×#97—151no—
229C22×C3×C5—22no—
230C22×C3×C5—41no—
231C22×C3×C5—42no—
232C22×C3×C5#12412yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—41no—
235C2×D15—42no—
236C3×C4×C5—41no—
237C3×C4×C5#12412yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—22no—
241Dic15—22no—
242Dic15—41no—
243C3×Dic5—42no—
244C5×Dic3—42no—
245C3×#41—22no—
246C3×#41—22no—
247C2×C3×Q8C22×D511yescharacteristic
248C2×C3×D4—21no—
249C2×C3×D4C22×D511yescharacteristic
250C22×C3×C4—21no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—102no—
253C2×#67—101no—
254C22×Dic3—52no—
255#235—102no—
256#235—102no—
257C2×D12—51no—
258C2×C4×D3—101no—
259C2×Dic6—51no—
260C2×Dic6—102no—
261C2×C3×C8—52no—
262C2×C3×C8—102no—
263C3×C4⋊C4—52no—
264C3×C22⋊C4—101no—
265C3×C42—101no—
266#217—21no—
267#217—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22×D512yes—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—21no—
275C4×Dic3—52no—
276C4×Dic3—51no—
277C4×Dic3—51no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—21no—
281C23×C5D3×D411yescharacteristic
282C22×D5—61no—
283C5×Q8—21no—
284C5×Q8—21no—
285C5×D4—21no—
286C5×D4—21no—
287C5×D4—42no—
288C2×C4×C5—21no—
289C2×C4×C5—42no—
290C2×C4×C5—62no—
291C2×C4×C5#23512yes—
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5#23712yes—
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—124no—
296C22⋊D5—122no—
297C2×Dic5—22no—
298C2×Dic5—32no—
299C2×Dic5—32no—
300C2×Dic5—61no—
301C2×Dic5—122no—
302D20—61no—
303D20—61no—
304C4×D5—122no—
305Dic10—61no—
306Dic10—61no—
307Dic10—124no—
308C5×C8—62no—
309#168—22no—
310C2×#41—151no—
311C2×#41D3×D511yescharacteristic
312C22×C8—31no—
313C22×C8—51no—
314C4⋊Q8—152no—
315C4⋊Q8—151no—
316#127—151no—
317#125—152no—
318#124—151no—
319#124—151no—
320C22⋊Q8—302no—
321#121—302no—
322C4×Q8—302no—
323C4×D4—302no—
324#117—31no—
325#117—51no—
326C2×C42—151no—
327#103—32no—
328#103—52no—
329#103—152no—
330#103—152no—
331#102—32no—
332#102—52no—
333#102—152no—
334#102—152no—
335#97—152no—
336#97—152no—
337C2×C3×C5—22no—
338C2×C3×C5—81no—
339C2×C3×C5C2×#12411yescharacteristic
340C2×C3×C5#57512yes—
341D15—81no—
342C23×C3—21no—
343C23×C3D4×D511yescharacteristic
344C22×D3—101no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—42no—
350C2×C3×C4—21no—
351C2×C3×C4—42no—
352C2×C3×C4—102no—
353C2×C3×C4#70912yes—
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4#71112yes—
356C2×C3×C4C23×D511yescharacteristic
357#67—204no—
358#67—202no—
359C2×Dic3—22no—
360C2×Dic3—52no—
361C2×Dic3—52no—
362C2×Dic3—101no—
363C2×Dic3—202no—
364D12—101no—
365D12—101no—
366C4×D3—202no—
367Dic6—101no—
368Dic6—101no—
369Dic6—204no—
370C3×C8—102no—
371C3⋊C8—22no—
372C22×C5—22no—
373C22×C5—41no—
374C22×C5—42no—
375C22×C5#88512yes—
376C22×C5C2×D3×D411yescharacteristic
377C2×D5—121no—
378C2×D5—122no—
379C4×C5—41no—
380C4×C5—122no—
381C4×C5#88512yes—
382C4×C5C2×#23511yescharacteristic
383C4×C5C2×#23711yescharacteristic
384Dic5—42no—
385Dic5—62no—
386Dic5—62no—
387Dic5—121no—
388#41—22no—
389#41—22no—
390#41—302no—
391#41—302no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×Q8C2×D3×D511yescharacteristic
395C2×D4—21no—
396C2×D4—151no—
397C2×D4—302no—
398C2×D4—301no—
399C2×D4C2×D3×D511yescharacteristic
400C22×C4—21no—
401C22×C4—152no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404C2×C8—32no—
405C2×C8—52no—
406C2×C8—62no—
407C2×C8—102no—
408C4⋊C4—32no—
409C4⋊C4—52no—
410C4⋊C4—302no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C22⋊C4—61no—
415C22⋊C4—101no—
416C22⋊C4—302no—
417C22⋊C4—302no—
418C42—61no—
419C42—101no—
420C42—152no—
421C42—151no—
422C42—151no—
423C3×C5#313511yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3—41no—
426C22×C3—42no—
427C22×C3#403112yes—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—201no—
430C2×D3—202no—
431C3×C4—41no—
432C3×C4—202no—
433C3×C4#403112yes—
434C3×C4C2×#70911yescharacteristic
435C3×C4C2×#71111yescharacteristic
436Dic3—42no—
437Dic3—102no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—22no—
441C2×C5—81no—
442C2×C5C2×#88511yescharacteristic
443C2×C5#576812yes—
444D5—241no—
445C23—21no—
446C23—301no—
447C23#679011yescharacteristic
448Q8—21no—
449Q8—21no—
450Q8—301no—
451Q8—301no—
452Q8—604no—
453D4—21no—
454D4—21no—
455D4—42no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—602no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—62no—
463C2×C4—102no—
464C2×C4—152no—
465C2×C4—152no—
466C2×C4—301no—
467C2×C4—602no—
468C2×C4—602no—
469C2×C4#677912yes—
470C2×C4#678212yes—
471C2×C4#679011yescharacteristic
472C2×C4C22×D3×D511yescharacteristic
473C8—62no—
474C8—102no—
475C2×C3—22no—
476C2×C3—81no—
477C2×C3C2×#403111yescharacteristic
478C2×C3#6610212yes—
479D3—401no—
480C5#7882611yescharacteristic, complemented, Sylow
481C22—22no—
482C22—42no—
483C22—41no—
484C22—602no—
485C22—601no—
486C22#9152612yes—
487C22C2×#679011yescharacteristic
488C4—41no—
489C4—122no—
490C4—202no—
491C4—302no—
492C4—302no—
493C4—601no—
494C4#9152612yes—
495C4C2×#677911yescharacteristic
496C4C2×#678211yescharacteristic
497C3#1061055711yescharacteristic, complemented, Sylow
498C2—22no—
499C2—81no—
500C2—1201no—
501C2#1175532912yes—
502C2C2×#9152611yescharacteristic
subgroupG/H
centerC2×C4#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radical#11756591C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754617C2semidirect
3. C5×#5233C2semidirect
4. C3×#65522C2semidirect
5. #11749363C2semidirect
6. #11749336C2semidirect
7. #11749117C2semidirect
8. #11749090C2semidirect
9. #11748411C2semidirect
10. #11748393C2semidirect
11. C2×#90954C2semidirect
44. #65522D3semidirect
90. #5233D5semidirect
423. C3×C5#3135semidirect
480. C5#78826semidirect
497. C3#10610557semidirect

Maximal subgroups

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

subgroupindex
#117565912
#117546172
C5×#52332
C3×#655222
#117493632
#117493362
#117491172
#117490902
#117484112
#117483932
C2×#909542
#106105573
#788265