Finite Group Databasebeta

← #14300561

Subgroups — #14300561

Order 1920.

752 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
1C22×C5×#208C211yesmaximal, characteristic, complemented
2C3×#66125C211yesmaximal, characteristic
3C4×#6719C211yesmaximal, characteristic, complemented
4C2×#90976C212yesmaximal, complemented
5#11745973C212yesmaximal, complemented
6#10602777—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×#6719—21no—
10C2×C4×Dic15C2212yes—
11C2×C5×#208—21no—
12C2×C5×#208—24no—
13C2×C5×#208C2212yes—
14C22×C5×C3⋊C8—21no—
15C3×#4099—21no—
16C3×#4076C411yescharacteristic, complemented
17C3×#4076C411yescharacteristic, complemented
18C3×#4075—21no—
19C3×C4×C22⋊D5—21no—
20C3×C4×C22⋊D5—21no—
21C3×#4072C2211yescharacteristic
22C3×#4070C411yescharacteristic, complemented
23C3×#4070C411yescharacteristic, complemented
24#91115—21no—
25#90976—24no—
26#71713—51nomaximal, Hall
27C22×C5×M16—31no—
28#66125D311yescharacteristic
29C4×C22⋊Dic5—31no—
30C2×#3957—32no—
31#64775—32no—
32C24×C3×C5D411yescharacteristic
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5—22no—
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—22no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C3×#709—22no—
46C3×#709—22no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50#6719—24no—
51C4×Dic15—22no—
52C4×Dic15—22no—
53C5×#208—24no—
54C5×#208—22no—
55C5×#208D414yescomplemented
56C2×C5×C3⋊C8—24no—
57C2×C5×C3⋊C8—22no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×#685—21no—
62C3×#685—21no—
63C3×C4⋊Dic5C2×C411yescharacteristic
64C3×C4⋊Dic5C2×C411yescharacteristic
65C3×#683—21no—
66C3×#683—21no—
67C3×C4×Dic5—21no—
68C3×#525—51no—
69C22×#208D511yescharacteristic, complemented
70C2×#837—52no—
71C4×#217—51no—
72#4532—52no—
73C23×C4×C5C2×D311yescharacteristic
74C2×#709C2×D311yescharacteristic
75C2×C5×M16—32no—
76C2×C5×M16—64no—
77C2×C5×M16—61no—
78C22×C5×C8—61no—
79#4099—21no—
80C2×C22⋊Dic5—61no—
81#4076Dic311yescharacteristic, complemented
82#4076Dic311yescharacteristic, complemented
83#4075—21no—
84C4×C22⋊D5—21no—
85C4×C22⋊D5—21no—
86#4072C2×D311yescharacteristic
87#4070Dic311yescharacteristic, complemented
88#4070Dic311yescharacteristic, complemented
89C2×C4×Dic5—32no—
90#3963—61no—
91#3957—64no—
92#1871—151noSylow
93C23×C3×C5—22no—
94C23×C3×C5—22no—
95C23×C3×C5—41no—
96C23×C3×C5C22⋊C411yescharacteristic
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—21no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5C22⋊C411yescharacteristic
108C2×C3×C4×C5C22⋊C411yescharacteristic
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D412yes—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4112yes—
113C2×Dic15—24no—
114C2×Dic15—42no—
115C2×Dic15—42no—
116C3×C22⋊D5—42no—
117C3×C22⋊D5—42no—
118C3×C22⋊D5—42no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122C3×D20—22no—
123C3×C4×D5—41no—
124C3×C4×D5—41no—
125C3×Dic10—22no—
126C5×C3⋊C8—24no—
127C2×C3×#41—51no—
128C23×C3×C4C2×D511yescharacteristic
129C3×#123—101no—
130C3×C22⋊Q8—51no—
131C3×C22⋊Q8—51no—
132C3×#121—51no—
133C3×#121—51no—
134C3×#120—101no—
135C3×C4×D4—101no—
136C3×C4×D4—101no—
137C3×#117—51no—
138C2×#217—101no—
139C2×C4×Dic3—52no—
140C2×#208—21no—
141C2×#208—24no—
142C2×#208C2×D512yes—
143C22×C3⋊C8—21no—
144#837—104no—
145C3⋊#95—101no—
146C24×C5#6711yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5C2×Dic311yescharacteristic
150C22×C4×C5C2×Dic311yescharacteristic
151C22×C4×C5#6711yescharacteristic
152C22×C4×C5#6711yescharacteristic
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—21no—
156C2×C22⋊D5—21no—
157C2×C22⋊D5—21no—
158C22×Dic5—62no—
159#709—22no—
160#709—22no—
161C2×D20C2×Dic311yescharacteristic
162C2×C4×D5—21no—
163C2×Dic10C2×Dic311yescharacteristic
164C5×M16—34no—
165C5×M16—64no—
166C5×M16—62no—
167C2×C5×C8—64no—
168C2×C5×C8—62no—
169C22⋊Dic5—21no—
170C22⋊Dic5—21no—
171C22⋊Dic5—21no—
172C22⋊Dic5—64no—
173#685—21no—
174#685—21no—
175C4⋊Dic5C2×Dic311yescharacteristic
176C4⋊Dic5C2×Dic311yescharacteristic
177#683—21no—
178#683—21no—
179C4×Dic5—21no—
180C4×Dic5—62no—
181C4×Dic5—62no—
182C22×M16—31no—
183#525—51no—
184C2×#104—152no—
185C4×C22⋊C4—151no—
186#339—152no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—21no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—44no—
195C22×C3×C5#10412yescomplemented
196C22×C3×C5C2×C22⋊C411yescharacteristic
197C22×C3×C5#12112yes—
198C2×C3×D5—41no—
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5C4×D412yes—
204C3×C4×C5#12011yescharacteristic
205C3×C4×C5#12311yescharacteristic
206Dic15—44no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C3×Dic5—41no—
210C24×C3D2011yescharacteristic
211C3×#41—102no—
212C3×#41—102no—
213C2×C3×Q8—51no—
214C2×C3×D4—51no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—101no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—101no—
221C22×C3×C4C4×D511yescharacteristic
222C22×C3×C4C4×D511yescharacteristic
223C22×C3×C4D2011yescharacteristic
224C22×C3×C4C22⋊D511yescharacteristic
225C22×C3×C4C22⋊D511yescharacteristic
226C22×C3×C4C22×D511yescharacteristic
227C22×Dic3—102no—
228C3×C4⋊C4—51no—
229C3×C4⋊C4—51no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—101no—
232C3×C22⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—101no—
235C3×C22⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C42—101no—
238#217—104no—
239C4×Dic3—102no—
240C4×Dic3—102no—
241#208—24no—
242#208—22no—
243#208C22⋊D514yescomplemented
244C2×C3⋊C8—24no—
245C2×C3⋊C8—22no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—41no—
249C23×C5#21711yescharacteristic
250C23×C5#21711yescharacteristic
251C23×C5C2×#6711yescharacteristic
252C22×D5—21no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5#21711yescharacteristic
261C2×C4×C5#21711yescharacteristic
262C2×C4×C5D3×D412yes—
263C2×C4×C5#23712yes—
264C2×C4×C5C22×Dic311yescharacteristic
265C2×C4×C5C2×#6711yescharacteristic
266C22⋊D5—42no—
267C22⋊D5—42no—
268C22⋊D5—42no—
269C2×Dic5—21no—
270C2×Dic5—21no—
271C2×Dic5—21no—
272C2×Dic5—64no—
273C2×Dic5—122no—
274C2×Dic5—122no—
275D20—22no—
276C4×D5—41no—
277C4×D5—41no—
278Dic10—22no—
279C5×C8—64no—
280C2×#41—51no—
281C23×C4D3×D511yescharacteristic
282C2×M16—32no—
283C2×M16—64no—
284C2×M16—61no—
285C22×C8—61no—
286#123—101no—
287C22⋊Q8—51no—
288C22⋊Q8—51no—
289#121—51no—
290#121—51no—
291#120—101no—
292C4×D4—101no—
293C4×D4—101no—
294#117—51no—
295C2×C22⋊C4—301no—
296C2×C42—152no—
297#104—304no—
298#95—301no—
299C2×C3×C5—22no—
300C2×C3×C5—22no—
301C2×C3×C5—41no—
302C2×C3×C5#38611yescharacteristic
303C2×C3×C5C2×#10411yescharacteristic
304C2×C3×C5#42111yescharacteristic
305C3×D5—81no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—41no—
309C23×C3—101no—
310C23×C3#68511yescharacteristic
311C23×C3#68511yescharacteristic
312C23×C3C2×D2011yescharacteristic
313C3×Q8—102no—
314C3×D4—102no—
315C3×D4—202no—
316C3×D4—202no—
317C3×D4—202no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—101no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4#68511yescharacteristic
331C2×C3×C4#68511yescharacteristic
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4#70912yes—
334C2×C3×C4C2×C22⋊D511yescharacteristic
335C2×C3×C4C2×C22⋊D512yes—
336C2×Dic3—104no—
337C2×Dic3—202no—
338C2×Dic3—202no—
339C3⋊C8—24no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—44no—
348C22×C5#83712yescomplemented
349C22×C5#93912yes—
350C22×C5C2×#21711yescharacteristic
351C2×D5—41no—
352C2×D5—41no—
353C2×D5—41no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5D4×Dic312yes—
357C4×C5#93511yescharacteristic
358C4×C5#93711yescharacteristic
359Dic5—41no—
360Dic5—41no—
361Dic5—41no—
362Dic5—124no—
363C24#120211yescharacteristic
364#41—102no—
365#41—102no—
366C2×Q8—51no—
367C2×D4—51no—
368C2×D4—101no—
369C2×D4—101no—
370C2×D4—101no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—101no—
374C22×C4—302no—
375C22×C4D5×Dic311yescharacteristic
376C22×C4D5×Dic311yescharacteristic
377C22×C4#120111yescharacteristic
378C22×C4#120111yescharacteristic
379C22×C4#120211yescharacteristic
380C22×C4C2×D3×D511yescharacteristic
381M16—34no—
382M16—64no—
383M16—62no—
384C2×C8—64no—
385C2×C8—62no—
386C4⋊C4—51no—
387C4⋊C4—51no—
388C4⋊C4—101no—
389C4⋊C4—101no—
390C22⋊C4—101no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—101no—
394C22⋊C4—101no—
395C22⋊C4—304no—
396C42—101no—
397C42—302no—
398C42—302no—
399C3×C5#187111yescharacteristic, complemented, Hall
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—44no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3—201no—
411C22×C3#395712yescomplemented
412C22×C3C2×#68511yescharacteristic
413C22×C3#407612yes—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—201no—
417C3×C4—201no—
418C3×C4—201no—
419C3×C4C4×C22⋊D512yes—
420C3×C4#407511yescharacteristic
421C3×C4#409911yescharacteristic
422Dic3—204no—
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5#522011yescharacteristic
427C2×C5C2×#83711yescharacteristic
428C2×C5#523611yescharacteristic
429D5—81no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—101no—
434C23#666511yescharacteristic
435C23#666511yescharacteristic
436C23C2×#120211yescharacteristic
437Q8—102no—
438D4—102no—
439D4—202no—
440D4—202no—
441D4—202no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—201no—
453C2×C4—201no—
454C2×C4—304no—
455C2×C4—602no—
456C2×C4—602no—
457C2×C4#666511yescharacteristic
458C2×C4#666511yescharacteristic
459C2×C4C2×D5×Dic311yescharacteristic
460C2×C4#677912yes—
461C2×C4C2×#120111yescharacteristic
462C2×C4D3×C22⋊D512yes—
463C8—64no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3—401no—
468C2×C3C2×#395711yescharacteristic
469C2×C3#6542811yescharacteristic
470C2×C3#6550211yescharacteristic
471C5#7171311yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—201no—
481C22—201no—
482C22—201no—
483C22#9097612yescomplemented
484C22C2×#666511yescharacteristic
485C22#9156912yes—
486C4—21no—
487C4—21no—
488C4—201no—
489C4—201no—
490C4—201no—
491C4—604no—
492C4#9153611yescharacteristic
493C4Dic3×C22⋊D512yes—
494C4#9156811yescharacteristic
495C3#1060277711yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—401no—
500C2C2×#9097611yescharacteristic
501C2#1174842011yescharacteristic
502C2#1174949511yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#208C2semidirect
3. C4×#6719C2semidirect
4. C2×#90976C2semidirect
5. #11745973C2semidirect
16. C3×#4076C4semidirect
17. C3×#4076C4semidirect
22. C3×#4070C4semidirect
23. C3×#4070C4semidirect
55. C5×#208D4semidirect
69. C22×#208D5semidirect
81. #4076Dic3semidirect
82. #4076Dic3semidirect
87. #4070Dic3semidirect
88. #4070Dic3semidirect
195. C22×C3×C5#104semidirect
243. #208C22⋊D5semidirect
348. C22×C5#837semidirect
399. C3×C5#1871semidirect
411. C22×C3#3957semidirect
471. C5#71713semidirect
483. C22#90976semidirect
495. C3#10602777semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2082
C3×#661252
C4×#67192
C2×#909762
#117459732
#106027773
#717135