Finite Group Databasebeta

← #14417356

Subgroups — #14417356

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×D8C211yesmaximal, characteristic
2#11754910C212yesmaximal, complemented
3#11751253C211yesmaximal, characteristic, complemented
4C5×#5152C211yesmaximal, characteristic, complemented
5#11748993C212yesmaximal, complemented
6Dic3×#686C212yesmaximal, complemented
7#11748962C212yesmaximal, complemented
8#11747815C211yesmaximal, characteristic, complemented
9#11747799C211yesmaximal, characteristic, complemented
10#11747671C211yesmaximal, characteristic, complemented
11#11747646C211yesmaximal, characteristic, complemented
12#10611598—31nomaximal, Hall
13C2×C3×D4×D5C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15D4×Dic15C2212yescomplemented
16C5×D4×Dic3C2212yescomplemented
17C2×C3×#686C2212yes—
18C3×D5×D8C418yescomplemented
19C2×C3×D40C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21#91559—22no—
22Dic3×C22⋊D5—22no—
23D5×#217—22no—
24C2×#6665—22no—
25#91434C2212yescomplemented
26Dic3×D20C2212yescomplemented
27#91358C2212yes—
28#91357C2211yescharacteristic
29C2×#6649C2211yescharacteristic
30#91116C2212yescomplemented
31#91101C2211yescharacteristic, complemented
32#91099C2211yescharacteristic, complemented
33C5×#832C2212yescomplemented
34C5×#817C2211yescharacteristic, complemented
35C5×#815C2211yescharacteristic, complemented
36#90988C2212yescomplemented
37#90965C2212yescomplemented
38#90964C2212yescomplemented
39#90951C2211yescharacteristic, complemented
40Dic3×#168C2211yescharacteristic, complemented
41#83823—51nomaximal, Hall
42C2×D5×D8D311yescharacteristic
43#65879—32no—
44C5×#442—31no—
45#65441—31no—
46C4×#686—32no—
47#65158—31no—
48#65149—31no—
49#65059—32no—
50#65045—32no—
51#65000—31no—
52#64997—31no—
53C23×C3×D5—22no—
54C2×C3×C5×D4C2312yes—
55C22×Dic15—22no—
56C22×C5×Dic3—22no—
57C2×C3×C22⋊D5—22no—
58C3×D4×D5—24no—
59C3×D4×D5C2×C418yescomplemented
60C2×C3×D20C2312yes—
61C2×C3×C4×D5C2311yescharacteristic
62C2×D5×Dic3—22no—
63C2×D5×Dic3—22no—
64C3×C5×D8C2×C414yescomplemented
65C2×C3×C5×C8C2311yescharacteristic
66#6719—22no—
67C4⋊Dic15C2312yes—
68C4×Dic15C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×#217—22no—
71C5×C4⋊Dic3C2312yes—
72C4×C5×Dic3C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×#686C2×C418yescomplemented
75C2×C3×#168C2311yescharacteristic
76C3×D40C2×C414yescomplemented
77C3×C8×D5C2×C414yescomplemented
78#6668D412yes—
79#6665—22no—
80#6665—22no—
81#6665—22no—
82#6665D412yes—
83Dic3×Dic5—22no—
84#6649—22no—
85C22×C3×D8—51no—
86#5798—52no—
87#5215—52no—
88#5152—51no—
89#5152—51no—
90#5152—51no—
91#5152D511yescharacteristic, complemented
92Dic3×D8—52no—
93Dic3×D8—52no—
94#5106—51no—
95#5101—51no—
96C2×D4×D5C2×D312yes—
97C2×C5×D8C2×D311yescharacteristic
98C4×C5×D4—32no—
99D4×Dic5—32no—
100C2×#686C2×D312yes—
101C4×C22⋊D5—62no—
102C2×#685—62no—
103D5×D8Dic318yescomplemented
104C2×D40C2×D311yescharacteristic
105C2×#676—31no—
106C2×C8×D5C2×D311yescharacteristic
107#4039—32no—
108#4038—32no—
109#4027—62no—
110D5×C22⋊C4—62no—
111C4×D20—32no—
112#4018—31no—
113C5×#106—31no—
114C5×#102—32no—
115C5×#97—31no—
116#3964—32no—
117#3953—32no—
118#3949—31no—
119#3947—31no—
120C8×Dic5—31no—
121#3941—32no—
122#3939—32no—
123C4×#168—31no—
124#2948—151noSylow
125C23×C3×C5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—28no—
128C22×C3×D5—82no—
129C22×C3×D5—82no—
130C22×C3×D5C2×D411yescharacteristic
131C3×C5×D4—22no—
132C3×C5×D4C22×C414yes—
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—22no—
135C2×Dic15—82no—
136C2×Dic15C2×D412yes—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—82no—
139C2×C5×Dic3C2×D412yes—
140C3×C22⋊D5—28no—
141C2×C3×Dic5C2×D411yescharacteristic
142C3×D20—22no—
143C3×D20C22×C414yes—
144C3×C4×D5C22×C412yes—
145C3×C4×D5#4112yes—
146D5×Dic3—82no—
147D5×Dic3—82no—
148C3×C5×C8C22×C412yes—
149C3⋊#168—21no—
150C3×#168C22×C412yes—
151C5×C3⋊C8—21no—
152C22×C3×D4—52no—
153C2×C3×D8—52no—
154C2×C3×D8—58no—
155C2×C3×D8—51no—
156C2×C3×D8C2×D511yescharacteristic
157C22×C3×C8—51no—
158C2×#217—102no—
159C2×#217—102no—
160D4×Dic3—52no—
161D4×Dic3—52no—
162D4×Dic3—52no—
163D4×Dic3—102no—
164D4×Dic3—102no—
165D4×Dic3C2×D512yescomplemented
166#926—51no—
167#926—52no—
168C2×#208—51no—
169#832—52no—
170#832—52no—
171#832—52no—
172#832C2×D512yescomplemented
173#818—52no—
174#817—51no—
175#817C2×D511yescharacteristic, complemented
176#815—51no—
177#815C2×D511yescharacteristic, complemented
178C8×Dic3—51no—
179C8×Dic3—51no—
180C23×D5—22no—
181C2×C5×D4C22×D312yes—
182C22×C4×C5—62no—
183C2×C22⋊D5—22no—
184C22×Dic5—62no—
185D4×D5—24no—
186D4×D5C2×Dic318yescomplemented
187C2×D20C22×D312yes—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×C4×D5C22×D311yescharacteristic
191C5×D8C2×Dic314yescomplemented
192C2×C5×C8—31no—
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—32no—
195C5×C22⋊C4—62no—
196C42×C5—31no—
197C22⋊Dic5—62no—
198#686C2×Dic318yescomplemented
199#685—32no—
200#685—62no—
201#685—62no—
202#685—62no—
203C4⋊Dic5—32no—
204#683—32no—
205C4×Dic5—31no—
206C4×Dic5—62no—
207C2×#168—31no—
208C2×#168C22×D311yescharacteristic
209D40C2×Dic314yescomplemented
210#676—62no—
211C8×D5C2×Dic314yescomplemented
212C22×D8—51no—
213#518—152no—
214#442—31no—
215#442—151no—
216#442—151no—
217#442—151no—
218C4×D8—152no—
219C4×D8—152no—
220#427—151no—
221#418—152no—
222#405—151no—
223C22×C3×C5—24no—
224C22×C3×C5—42no—
225C22×C3×C5—42no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—24no—
229C2×C3×D5—42no—
230C2×C3×D5—42no—
231C2×C3×D5—88no—
232C2×C3×D5C4×D412yes—
233C3×C4×C5C23×C411yescharacteristic
234C3×C4×C5C2×#4111yescharacteristic
235Dic15—22no—
236Dic15—42no—
237C3×Dic5C4×D412yes—
238C5×Dic3—22no—
239C5×Dic3—42no—
240C24×C3—102no—
241C2×C3×D4—58no—
242C2×C3×D4—52no—
243C2×C3×D4—104no—
244C2×C3×D4—102no—
245C2×C3×D4C22×D512yes—
246C22×C3×C4—51no—
247C22×Dic3—22no—
248C22×Dic3—102no—
249C22×Dic3—102no—
250C22×Dic3—102no—
251C3×D8—58no—
252C3×D8—54no—
253C3×D8C4×D514yescomplemented
254C2×C3×C8—51no—
255C2×C3×C8—54no—
256C2×C3×C8C22×D511yescharacteristic
257#217—22no—
258#217—52no—
259#217—102no—
260#217—102no—
261#217—102no—
262#217—102no—
263C4⋊Dic3—52no—
264C4⋊Dic3—52no—
265C4⋊Dic3C22×D512yes—
266C4×Dic3—51no—
267C4×Dic3—102no—
268C4×Dic3C22×D511yescharacteristic
269#208—102no—
270C2×C3⋊C8—51no—
271C2×C3⋊C8C22×D511yescharacteristic
272C23×C5—22no—
273C22×D5—22no—
274C22×D5—28no—
275C22×D5—82no—
276C22×D5—82no—
277C22×D5D3×D411yescharacteristic
278C5×D4—22no—
279C5×D4C22×Dic314yes—
280C2×C4×C5—32no—
281C2×C4×C5—62no—
282C2×C4×C5—242no—
283C2×C4×C5C23×D311yescharacteristic
284C22⋊D5—28no—
285C2×Dic5—32no—
286C2×Dic5—62no—
287C2×Dic5—242no—
288C2×Dic5D3×D411yescharacteristic
289D20—22no—
290D20C22×Dic314yes—
291C4×D5—242no—
292C4×D5—242no—
293C4×D5#23712yes—
294C4×D5C22×Dic312yes—
295C5×C8—61no—
296C5×C8C22×Dic312yes—
297#168—61no—
298#168C22×Dic312yes—
299C22×D4—52no—
300C2×D8—52no—
301C2×D8—58no—
302C2×D8—51no—
303C2×D8D3×D511yescharacteristic
304C2×M16—151no—
305C22×C8—51no—
306C4×D4—32no—
307C4×D4—152no—
308C4×D4—152no—
309C4×D4—152no—
310C4×D4—302no—
311C4×D4—302no—
312#117—151no—
313#117—152no—
314C2×C22⋊C4—302no—
315C2×C22⋊C4—302no—
316#107—152no—
317#106—31no—
318#106—151no—
319#102—32no—
320#102—152no—
321#102—152no—
322#102—152no—
323#97—31no—
324#97—151no—
325C4×C8—151no—
326C4×C8—151no—
327C2×C3×C5—44no—
328C2×C3×C5C2×C4×D411yescharacteristic
329C2×C3×C5#57612yes—
330C3×D5—22no—
331C3×D5—44no—
332C23×C3—22no—
333C23×C3—51no—
334C23×C3—108no—
335C23×C3—102no—
336C23×C3—402no—
337C23×C3—402no—
338C3×D4—22no—
339C3×D4—54no—
340C3×D4—108no—
341C3×D4—102no—
342C3×D4C2×C4×D514yes—
343C2×C3×C4—51no—
344C2×C3×C4—52no—
345C2×C3×C4—52no—
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—52no—
349C2×Dic3—82no—
350C2×Dic3—102no—
351C2×Dic3—402no—
352C2×Dic3—402no—
353C2×Dic3—402no—
354C2×Dic3D4×D512yes—
355C3×C8—52no—
356C3×C8C2×C4×D512yes—
357C3⋊C8—21no—
358C3⋊C8—101no—
359C22×C5—24no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5C2×D3×D411yescharacteristic
363C2×D5—22no—
364C2×D5—24no—
365C2×D5—42no—
366C2×D5—42no—
367C2×D5—88no—
368C2×D5D4×Dic312yes—
369C4×C5—62no—
370C4×C5—122no—
371C4×C5C2×#23711yescharacteristic
372C4×C5C23×Dic311yescharacteristic
373Dic5—62no—
374Dic5—122no—
375Dic5D4×Dic312yes—
376C24—102no—
377C2×D4—58no—
378C2×D4—52no—
379C2×D4—104no—
380C2×D4—102no—
381C2×D4C2×D3×D512yes—
382C22×C4—51no—
383C22×C4—62no—
384C22×C4—302no—
385C22×C4—302no—
386C22×C4—302no—
387D8—58no—
388D8—54no—
389D8D5×Dic314yescomplemented
390M16—302no—
391C2×C8—31no—
392C2×C8—51no—
393C2×C8—54no—
394C2×C8—151no—
395C2×C8C2×D3×D511yescharacteristic
396C4⋊C4—32no—
397C4⋊C4—152no—
398C4⋊C4—152no—
399C22⋊C4—62no—
400C22⋊C4—152no—
401C22⋊C4—302no—
402C22⋊C4—302no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C42—31no—
406C42—151no—
407C42—302no—
408C3×C5#294811yescharacteristic, complemented, Hall
409C22×C3—24no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—52no—
413C22×C3—102no—
414C22×C3—104no—
415C22×C3—202no—
416C22×C3—202no—
417C22×C3—408no—
418C22×C3C2×D4×D511yescharacteristic
419C3×C4—52no—
420C3×C4C22×C4×D511yescharacteristic
421C3×C4D5×#4111yescharacteristic
422Dic3—22no—
423Dic3—42no—
424Dic3—102no—
425Dic3—202no—
426C2×C5—44no—
427C2×C5#575712yes—
428C2×C5C2×D4×Dic311yescharacteristic
429D5—22no—
430D5—44no—
431C23—22no—
432C23—51no—
433C23—108no—
434C23—102no—
435C23—402no—
436C23—402no—
437D4—22no—
438D4—54no—
439D4—108no—
440D4—102no—
441D4C2×D5×Dic314yes—
442C2×C4—32no—
443C2×C4—51no—
444C2×C4—52no—
445C2×C4—52no—
446C2×C4—62no—
447C2×C4—152no—
448C2×C4—242no—
449C2×C4—302no—
450C2×C4—1202no—
451C2×C4—1202no—
452C2×C4—1202no—
453C2×C4C22×D3×D511yescharacteristic
454C8—52no—
455C8—61no—
456C8—301no—
457C8C2×D5×Dic312yes—
458C2×C3—44no—
459C2×C3—102no—
460C2×C3—204no—
461C2×C3C4×D4×D511yescharacteristic
462C2×C3#6610812yes—
463C5#8382311yescharacteristic, complemented, Sylow
464C22—24no—
465C22—42no—
466C22—42no—
467C22—52no—
468C22—102no—
469C22—104no—
470C22—202no—
471C22—202no—
472C22—408no—
473C22D3×D4×D511yescharacteristic
474C4—52no—
475C4—62no—
476C4—122no—
477C4—302no—
478C4—602no—
479C4D5×#23711yescharacteristic
480C4C22×D5×Dic311yescharacteristic
481C3#1061159811yescharacteristic, complemented, Sylow
482C2—44no—
483C2—102no—
484C2—204no—
485C2#1175405512yes—
486C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D5×D8C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5#2948
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11754910C2semidirect
3. #11751253C2semidirect
4. C5×#5152C2semidirect
5. #11748993C2semidirect
6. Dic3×#686C2semidirect
7. #11748962C2semidirect
8. #11747815C2semidirect
9. #11747799C2semidirect
10. #11747671C2semidirect
11. #11747646C2semidirect
15. D4×Dic15C22semidirect
16. C5×D4×Dic3C22semidirect
18. C3×D5×D8C4semidirect
25. #91434C22semidirect
26. Dic3×D20C22semidirect
30. #91116C22semidirect
31. #91101C22semidirect
32. #91099C22semidirect
33. C5×#832C22semidirect
34. C5×#817C22semidirect
35. C5×#815C22semidirect
36. #90988C22semidirect
37. #90965C22semidirect
38. #90964C22semidirect
39. #90951C22semidirect
40. Dic3×#168C22semidirect
59. C3×D4×D5C2×C4semidirect
64. C3×C5×D8C2×C4semidirect
74. C3×#686C2×C4semidirect
76. C3×D40C2×C4semidirect
77. C3×C8×D5C2×C4semidirect
91. #5152D5semidirect
103. D5×D8Dic3semidirect
165. D4×Dic3C2×D5semidirect
172. #832C2×D5semidirect
175. #817C2×D5semidirect
177. #815C2×D5semidirect
186. D4×D5C2×Dic3semidirect
191. C5×D8C2×Dic3semidirect
198. #686C2×Dic3semidirect
209. D40C2×Dic3semidirect
211. C8×D5C2×Dic3semidirect
253. C3×D8C4×D5semidirect
389. D8D5×Dic3semidirect
408. C3×C5#2948semidirect
463. C5#83823semidirect
481. C3#10611598semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×D82
#117549102
#117512532
C5×#51522
#117489932
Dic3×#6862
#117489622
#117478152
#117477992
#117476712
#117476462
#106115983
#838235