Finite Group Databasebeta

← #14302405

Subgroups — #14302405

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#518C211yesmaximal, characteristic, complemented
2C2×#91821C211yesmaximal, characteristic
3#11751316C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5#11751106C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7#11746352C211yesmaximal, characteristic, complemented
8#10602444—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C3×C4×C5×D4—22no—
12C3×C4×C5×D4—22no—
13C3×C5×#117C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C3×C5×C22⋊C4—22no—
16C2×#6716C412yescomplemented
17#91821—22no—
18#91821—22no—
19C2×#6715C412yescomplemented
20#91815C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23#91116—22no—
24#91090—22no—
25#91089—22no—
26#71651—51nomaximal, Hall
27C5×#518D311yescharacteristic, complemented
28C2×#4078—31no—
29#65504—31no—
30#65295—31no—
31#65294—31no—
32#64753—31no—
33#64751—31no—
34C24×C3×C5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C412yes—
39C2×C3×C5×D4D412yes—
40C2×C3×C5×D4D412yes—
41C22×C3×C4×C5—24no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×#1220—21no—
44#6817—21no—
45#6817—21no—
46#6817—21no—
47#6817—21no—
48C2×D60C2×C411yescharacteristic, complemented
49C2×C4×D15—21no—
50C2×Dic30C2×C411yescharacteristic, complemented
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4—24no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4D412yes—
56C3×C42×C5—21no—
57C3×C42×C5D412yes—
58#6719—21no—
59#6716—24no—
60#6715—24no—
61C4⋊Dic15—21no—
62C4×Dic15—21no—
63#6710—21no—
64#6710—21no—
65#6710—21no—
66#6710—21no—
67C2×C3⋊#168—21no—
68C2×C3⋊#168C2×C412yescomplemented
69C3×#518D511yescharacteristic, complemented
70C2×#932—51no—
71#5215—51no—
72#5006—51no—
73#5005—51no—
74#4533—51no—
75#4531—51no—
76C22×C5×D4C2×D311yescharacteristic
77C2×#709—31no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C5×#117C2×D311yescharacteristic
81C5×#117C2×D311yescharacteristic
82C2×C5×C22⋊C4—22no—
83C2×#687—32no—
84#4078—62no—
85#4078—62no—
86C2×#686—32no—
87#4072—31no—
88C2×#681—31no—
89C2×#681—31no—
90#3964—62no—
91#3938—62no—
92#3937—62no—
93#1904—151noSylow
94C23×C3×C5—22no—
95C23×C3×C5—22no—
96C23×C3×C5—22no—
97C23×C3×C5—82no—
98C23×C3×C5C2×D411yescharacteristic
99C22×D15—21no—
100C3×C5×D4—22no—
101C3×C5×D4—22no—
102C3×C5×D4—22no—
103C3×C5×D4C22⋊C414yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—84no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113#1220—41no—
114#1220—41no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117D60—21no—
118D60—21no—
119C4×D15—41no—
120C4×D15—41no—
121Dic30—21no—
122Dic30—21no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C22×C3×D4C2×D511yescharacteristic
126C2×#235—51no—
127C3×C4×D4—22no—
128C3×C4×D4—22no—
129C3×#117C2×D511yescharacteristic
130C3×#117C2×D511yescharacteristic
131C2×C3×C22⋊C4—22no—
132C2×#214—52no—
133#932—102no—
134#932—102no—
135C2×#213—52no—
136#926—51no—
137C2×#208—51no—
138C2×#208—51no—
139#832—102no—
140#806—102no—
141#805—102no—
142C24×C5—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4C4×D312yes—
147C2×C5×D4D1212yes—
148C2×C5×D4#6712yes—
149C22×C4×C5—24no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—61no—
152#709—61no—
153#709—61no—
154#709—61no—
155#709—61no—
156C2×D20—31no—
157C2×C4×D5—61no—
158C2×Dic10—31no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C22⋊C4—24no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4#6712yes—
164C42×C5—21no—
165C42×C5#6712yes—
166C22⋊Dic5—61no—
167#687—64no—
168#686—64no—
169C4⋊Dic5—61no—
170C4×Dic5—61no—
171#681—61no—
172#681—61no—
173#681—61no—
174#681—61no—
175C2×#168—32no—
176C2×#168—61no—
177C2×AGL(1,ℤ/8)—151no—
178#518D1511yescharacteristic, complemented
179#421—151no—
180#418—151no—
181#410—151no—
182#344—151no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—24no—
185C22×C3×C5—41no—
186C22×C3×C5—44no—
187C22×C3×C5—82no—
188C22×C3×C5—82no—
189C22×C3×C5C4×D411yescharacteristic
190C22×C3×C5#12011yescharacteristic
191C22×C3×C5#12111yescharacteristic
192C2×D15—41no—
193C2×D15—81no—
194C3×C4×C5—42no—
195C3×C4×C5—42no—
196C3×C4×C5C2×C22⋊C411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12311yescharacteristic
200Dic15—41no—
201Dic15—81no—
202C24×C3—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4C4×D512yes—
207C2×C3×D4D2012yes—
208C2×C3×D4C22⋊D512yes—
209C22×C3×C4—24no—
210C22×C3×C4C22×D511yescharacteristic
211C2×#67—101no—
212#235—101no—
213#235—101no—
214#235—101no—
215#235—101no—
216C2×D12—51no—
217C2×C4×D3—101no—
218C2×Dic6—51no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C22⋊C4—24no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4C22⋊D512yes—
224C3×C42—21no—
225C3×C42C22⋊D512yes—
226#217—101no—
227#214—104no—
228#213—104no—
229C4⋊Dic3—101no—
230C4×Dic3—101no—
231#208—101no—
232#208—101no—
233#208—101no—
234#208—101no—
235C2×C3⋊C8—52no—
236C2×C3⋊C8—101no—
237C23×C5—22no—
238C23×C5—22no—
239C23×C5—22no—
240C23×C5—82no—
241C23×C5C2×#6711yescharacteristic
242C22×D5—61no—
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—22no—
246C5×D4(C2×D3)⋊C414yes—
247C2×C4×C5—22no—
248C2×C4×C5—22no—
249C2×C4×C5—84no—
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5C2×D1211yescharacteristic
252C2×C4×C5#23511yescharacteristic
253C2×C4×C5#23511yescharacteristic
254C2×C4×C5C2×#6711yescharacteristic
255C2×C4×C5C2×#6711yescharacteristic
256C22⋊D5—121no—
257C22⋊D5—121no—
258C2×Dic5—61no—
259C2×Dic5—121no—
260D20—61no—
261D20—61no—
262C4×D5—121no—
263C4×D5—121no—
264Dic10—61no—
265Dic10—61no—
266#168—62no—
267#168—121no—
268C2×#41—151no—
269C22×D4C2×D1511yescharacteristic
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—151no—
275C2×M16—151no—
276C4×D4—22no—
277C4×D4—22no—
278#117—151no—
279#117C2×D1511yescharacteristic
280#117C2×D1511yescharacteristic
281C2×C22⋊C4—22no—
282#104—302no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5—44no—
289C2×C3×C5#38611yescharacteristic
290D15—81no—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—82no—
295C23×C3C2×C22⋊D511yescharacteristic
296C22×D3—101no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—22no—
300C3×D4#68514yes—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—84no—
304C2×C3×C4C2×C4×D511yescharacteristic
305C2×C3×C4C2×D2011yescharacteristic
306C2×C3×C4#70911yescharacteristic
307C2×C3×C4#70911yescharacteristic
308C2×C3×C4C2×C22⋊D511yescharacteristic
309C2×C3×C4C2×C22⋊D511yescharacteristic
310#67—201no—
311#67—201no—
312C2×Dic3—101no—
313C2×Dic3—201no—
314D12—101no—
315D12—101no—
316C4×D3—201no—
317C4×D3—201no—
318Dic6—101no—
319Dic6—101no—
320C3⋊C8—102no—
321C3⋊C8—201no—
322C22×C5—24no—
323C22×C5—41no—
324C22×C5—44no—
325C22×C5—82no—
326C22×C5—82no—
327C22×C5C4×#6711yescharacteristic
328C22×C5#93011yescharacteristic
329C22×C5#95311yescharacteristic
330C2×D5—121no—
331C2×D5—241no—
332C4×C5—42no—
333C4×C5—42no—
334C4×C5C2×(C2×D3)⋊C411yescharacteristic
335C4×C5C4×#6711yescharacteristic
336C4×C5#92911yescharacteristic
337C4×C5#93011yescharacteristic
338Dic5—121no—
339Dic5—241no—
340C24—21no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—151no—
350C2×D4—301no—
351C2×D4C4×D1512yes—
352C2×D4D6012yes—
353C2×D4#122012yes—
354C22×C4—24no—
355C22×C4—301no—
356C22×C4C22×D1511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—301no—
360M16—301no—
361M16—301no—
362M16—301no—
363C2×C8—152no—
364C2×C8—301no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—301no—
368C22⋊C4—24no—
369C22⋊C4—21no—
370C22⋊C4—301no—
371C22⋊C4#122012yes—
372C42—21no—
373C42—301no—
374C42#122012yes—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—24no—
377C22×C3—41no—
378C22×C3—44no—
379C22×C3—82no—
380C22×C3—82no—
381C22×C3C4×C22⋊D511yescharacteristic
382C22×C3#407611yescharacteristic
383C22×C3#409911yescharacteristic
384C2×D3—201no—
385C2×D3—401no—
386C3×C4—42no—
387C3×C4—42no—
388C3×C4C2×#68511yescharacteristic
389C3×C4C4×C22⋊D511yescharacteristic
390C3×C4#407511yescharacteristic
391C3×C4#407611yescharacteristic
392Dic3—201no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—44no—
398C2×C5#521311yescharacteristic
399D5—241no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—82no—
404C23—301no—
405C23C2×#122011yescharacteristic
406Q8—301no—
407Q8—301no—
408D4—22no—
409D4—22no—
410D4—22no—
411D4—301no—
412D4—301no—
413D4—601no—
414D4—601no—
415D4#671414yes—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—84no—
419C2×C4—301no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4C2×C4×D1511yescharacteristic
424C2×C4C2×D6011yescharacteristic
425C2×C4#681711yescharacteristic
426C2×C4#681711yescharacteristic
427C2×C4C2×#122011yescharacteristic
428C2×C4C2×#122011yescharacteristic
429C8—302no—
430C8—601no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—44no—
435C2×C3#6550211yescharacteristic
436D3—401no—
437C5#7165111yescharacteristic, complemented, Sylow
438C22—24no—
439C22—41no—
440C22—44no—
441C22—82no—
442C22—82no—
443C22—601no—
444C22—1201no—
445C22C4×#122011yescharacteristic
446C22#9181911yescharacteristic
447C22#9184211yescharacteristic
448C4—42no—
449C4—42no—
450C4—601no—
451C4—1201no—
452C4C2×#671411yescharacteristic
453C4C4×#122011yescharacteristic
454C4#9181811yescharacteristic
455C4#9181911yescharacteristic
456C3#1060244411yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—44no—
461C2—1201no—
462C2#1175131411yescharacteristic
subgroupG/H
centerC2#11751314
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#518C2
socleC2×C3×C5#386
prime radicalC2×#91821C2
cosocleC22×C3×C4×C5C23
hypercenter#518D15
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C3×C5×#518C2semidirect
3. #11751316C2semidirect
4. #11751107C2semidirect
5. #11751106C2semidirect
6. #11746354C2semidirect
7. #11746352C2semidirect
16. C2×#6716C4semidirect
19. C2×#6715C4semidirect
27. C5×#518D3semidirect
48. C2×D60C2×C4semidirect
50. C2×Dic30C2×C4semidirect
68. C2×C3⋊#168C2×C4semidirect
69. C3×#518D5semidirect
178. #518D15semidirect
375. C3×C5#1904semidirect
437. C5#71651semidirect
456. C3#10602444semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
C2×#918212
#117513162
#117511072
#117511062
#117463542
#117463522
#106024443
#716515