Finite Group Databasebeta

← #14300560

Subgroups — #14300560

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
1#11756550C211yesmaximal, characteristic
2C22×C5×#208C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×#90981C212yesmaximal, complemented
5#11745978C212yesmaximal, complemented
6#10602777—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9#91842—21no—
10#91819C411yescharacteristic, complemented
11#91819C411yescharacteristic, complemented
12#91818—21no—
13C4×#1220—21no—
14C4×#1220—21no—
15#91815C2211yescharacteristic
16#91813C411yescharacteristic, complemented
17#91813C411yescharacteristic, complemented
18C2×C5×#208—21no—
19C2×C5×#208—24no—
20C2×C5×#208C2212yes—
21C22×C5×C3⋊C8—21no—
22C2×C3×C22⋊Dic5—21no—
23C2×C3×C4×Dic5C2212yes—
24C3×#3963—21no—
25#90981—24no—
26#69453—51nomaximal, Hall
27C22×C5×M16—31no—
28#66125—31no—
29C4×C22⋊Dic5D311yescharacteristic, complemented
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
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44#6817—22no—
45#6817—22no—
46C2×D60C2×C411yescharacteristic
47C2×C4×D15—21no—
48C2×Dic30C2×C411yescharacteristic
49C22×C3×Dic5—22no—
50#6719—21no—
51#6719—21no—
52#6719—21no—
53#6714—21no—
54#6714—21no—
55C4⋊Dic15C2×C411yescharacteristic
56C4⋊Dic15C2×C411yescharacteristic
57#6712—21no—
58#6712—21no—
59C4×Dic15—21no—
60C5×#208—24no—
61C5×#208—22no—
62C5×#208D414yescomplemented
63C2×C5×C3⋊C8—24no—
64C2×C5×C3⋊C8—22no—
65C3×C22⋊Dic5—24no—
66C3×C4×Dic5—22no—
67C3×C4×Dic5—22no—
68#5791—51no—
69C22×#208D511yescharacteristic, complemented
70C3×C4×C22⋊C4—51no—
71C2×#805—52no—
72#4523—52no—
73C23×C4×C5C2×D311yescharacteristic
74C2×#709—31no—
75C2×C5×M16—32no—
76C2×C5×M16—64no—
77C2×C5×M16—61no—
78C22×C5×C8—61no—
79#4099—61no—
80C2×C22⋊Dic5—21no—
81#4076—31no—
82#4076—31no—
83#4075—61no—
84C4×C22⋊D5—61no—
85C4×C22⋊D5—61no—
86#4072—31no—
87#4070—31no—
88#4070—31no—
89C2×C4×Dic5C2×D312yes—
90#3963—21no—
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×D15—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—
113#1220—42no—
114#1220—42no—
115#1220—42no—
116C2×Dic15—21no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119D60—22no—
120C4×D15—41no—
121C4×D15—41no—
122Dic30—22no—
123C2×C3×Dic5—24no—
124C2×C3×Dic5—42no—
125C2×C3×Dic5—42no—
126C5×C3⋊C8—24no—
127C23×C3×C4C2×D511yescharacteristic
128C2×#235—51no—
129C2×C3×C22⋊C4—101no—
130C2×C3×C42—52no—
131#953—101no—
132#930—51no—
133#930—51no—
134#929—101no—
135C4×#67—101no—
136C4×#67—101no—
137#926—51no—
138#924—51no—
139#924—51no—
140C2×#208—21no—
141C2×#208—24no—
142C2×#208C2×D512yes—
143C22×C3⋊C8—21no—
144C3×#95—101no—
145#805—104no—
146C24×C5#6711yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5C4×D311yescharacteristic
150C22×C4×C5C4×D311yescharacteristic
151C22×C4×C5D1211yescharacteristic
152C22×C4×C5D1211yescharacteristic
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—61no—
156C2×C22⋊D5—61no—
157C2×C22⋊D5—61no—
158C22×Dic5—22no—
159#709—62no—
160#709—62no—
161C2×D20—31no—
162C2×C4×D5—61no—
163C2×Dic10—31no—
164C5×M16—34no—
165C5×M16—64no—
166C5×M16—62no—
167C2×C5×C8—64no—
168C2×C5×C8—62no—
169C22⋊Dic5—24no—
170C22⋊Dic5—61no—
171C22⋊Dic5—61no—
172C22⋊Dic5—61no—
173#685—61no—
174#685—61no—
175C4⋊Dic5—31no—
176C4⋊Dic5—31no—
177#683—61no—
178#683—61no—
179C4×Dic5—22no—
180C4×Dic5—22no—
181C4×Dic5—61no—
182C22×M16—31no—
183#525—151no—
184C2×#104—152no—
185C4×C22⋊C4—51no—
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×D15—41no—
199C2×D15—41no—
200C2×D15—41no—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5C4×D412yes—
204C3×C4×C5#12011yescharacteristic
205C3×C4×C5#12311yescharacteristic
206Dic15—41no—
207Dic15—41no—
208Dic15—41no—
209C3×Dic5—44no—
210C24×C3D2011yescharacteristic
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—102no—
214C22×C3×C4C4×D511yescharacteristic
215C22×C3×C4C4×D511yescharacteristic
216C22×C3×C4D2011yescharacteristic
217C22×C3×C4C22⋊D511yescharacteristic
218C22×C3×C4C22⋊D511yescharacteristic
219C22×C3×C4C22×D511yescharacteristic
220C2×#67—101no—
221C2×#67—101no—
222C2×#67—101no—
223#235—102no—
224#235—102no—
225C2×D12—51no—
226C2×C4×D3—101no—
227C2×Dic6—51no—
228C3×C22⋊C4—104no—
229C3×C42—102no—
230C3×C42—102no—
231#217—101no—
232#217—101no—
233#217—101no—
234(C2×D3)⋊C4—101no—
235(C2×D3)⋊C4—101no—
236C4⋊Dic3—51no—
237C4⋊Dic3—51no—
238Dic3⋊C4—101no—
239Dic3⋊C4—101no—
240C4×Dic3—101no—
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(C2×D3)⋊C411yescharacteristic
250C23×C5(C2×D3)⋊C411yescharacteristic
251C23×C5C2×#6711yescharacteristic
252C22×D5—61no—
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(C2×D3)⋊C411yescharacteristic
261C2×C4×C5(C2×D3)⋊C411yescharacteristic
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×C4×C5C2×D1211yescharacteristic
264C2×C4×C5D3×D412yes—
265C2×C4×C5#23712yes—
266C22⋊D5—122no—
267C22⋊D5—122no—
268C22⋊D5—122no—
269C2×Dic5—24no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—61no—
273C2×Dic5—61no—
274C2×Dic5—61no—
275D20—62no—
276C4×D5—121no—
277C4×D5—121no—
278Dic10—62no—
279C5×C8—64no—
280C2×#41—151no—
281C23×C4D3×D511yescharacteristic
282C2×M16—32no—
283C2×M16—64no—
284C2×M16—61no—
285C22×C8—61no—
286#123—301no—
287C22⋊Q8—151no—
288C22⋊Q8—151no—
289#121—151no—
290#121—151no—
291#120—301no—
292C4×D4—301no—
293C4×D4—301no—
294#117—151no—
295C2×C22⋊C4—101no—
296C2×C42—52no—
297#104—304no—
298#95—101no—
299C2×C3×C5—22no—
300C2×C3×C5—22no—
301C2×C3×C5—41no—
302C2×C3×C5#38611yescharacteristic
303C2×C3×C5C2×#10411yescharacteristic
304C2×C3×C5#42111yescharacteristic
305D15—81no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—41no—
309C23×C3#68511yescharacteristic
310C23×C3#68511yescharacteristic
311C23×C3C2×D2011yescharacteristic
312C22×D3—101no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—104no—
321C2×C3×C4—202no—
322C2×C3×C4—202no—
323C2×C3×C4#68511yescharacteristic
324C2×C3×C4#68511yescharacteristic
325C2×C3×C4C2×C4×D511yescharacteristic
326C2×C3×C4#70912yes—
327C2×C3×C4C2×C22⋊D511yescharacteristic
328C2×C3×C4C2×C22⋊D512yes—
329#67—202no—
330#67—202no—
331#67—202no—
332C2×Dic3—101no—
333C2×Dic3—101no—
334C2×Dic3—101no—
335D12—102no—
336C4×D3—201no—
337C4×D3—201no—
338Dic6—102no—
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#80512yescomplemented
349C22×C5C2×(C2×D3)⋊C411yescharacteristic
350C22×C5#93912yes—
351C2×D5—121no—
352C2×D5—121no—
353C2×D5—121no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5#67⋊C412yes—
357C4×C5#88211yescharacteristic
358C4×C5#88611yescharacteristic
359Dic5—44no—
360Dic5—121no—
361Dic5—121no—
362Dic5—121no—
363C24#120211yescharacteristic
364#41—302no—
365#41—302no—
366C2×Q8—151no—
367C2×D4—151no—
368C2×D4—301no—
369C2×D4—301no—
370C2×D4—301no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—102no—
374C22×C4—301no—
375C22×C4#120011yescharacteristic
376C22×C4#120011yescharacteristic
377C22×C4#120211yescharacteristic
378C22×C4#120311yescharacteristic
379C22×C4#120311yescharacteristic
380C22×C4C2×D3×D511yescharacteristic
381M16—34no—
382M16—64no—
383M16—62no—
384C2×C8—64no—
385C2×C8—62no—
386C4⋊C4—151no—
387C4⋊C4—151no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C22⋊C4—104no—
391C22⋊C4—301no—
392C22⋊C4—301no—
393C22⋊C4—301no—
394C22⋊C4—301no—
395C22⋊C4—301no—
396C42—102no—
397C42—102no—
398C42—301no—
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#395712yescomplemented
409C22×C3C2×#68511yescharacteristic
410C22×C3#407612yes—
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—204no—
417C3×C4C4×C22⋊D512yes—
418C3×C4#407511yescharacteristic
419C3×C4#409911yescharacteristic
420Dic3—201no—
421Dic3—201no—
422Dic3—201no—
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5C2×#80511yescharacteristic
427C2×C5#495811yescharacteristic
428C2×C5#500511yescharacteristic
429D5—241no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—301no—
434C23#666711yescharacteristic
435C23#666711yescharacteristic
436C23C2×#120211yescharacteristic
437Q8—302no—
438D4—302no—
439D4—602no—
440D4—602no—
441D4—602no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—104no—
450C2×C4—202no—
451C2×C4—202no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—601no—
456C2×C4—601no—
457C2×C4#666711yescharacteristic
458C2×C4#666711yescharacteristic
459C2×C4#677912yes—
460C2×C4C2×#120011yescharacteristic
461C2×C4C2×#120311yescharacteristic
462C2×C4D3×C22⋊D512yes—
463C8—64no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3C2×#395711yescharacteristic
468C2×C3#6542811yescharacteristic
469C2×C3#6550211yescharacteristic
470D3—401no—
471C5#6945311yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—601no—
481C22—601no—
482C22—601no—
483C22#9098112yescomplemented
484C22C2×#666711yescharacteristic
485C22#9156912yes—
486C4—21no—
487C4—21no—
488C4—204no—
489C4—601no—
490C4—601no—
491C4—601no—
492C4#9154211yescharacteristic
493C4#9155612yes—
494C4#9157011yescharacteristic
495C3#1060277711yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—1201no—
500C2C2×#9098111yescharacteristic
501C2#1174842911yescharacteristic
502C2#1174949811yescharacteristic
subgroupG/H
centerC2×C4C2×#1203
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
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
2. C22×C5×#208C2semidirect
3. C3×C4×C22⋊Dic5C2semidirect
4. C2×#90981C2semidirect
5. #11745978C2semidirect
10. #91819C4semidirect
11. #91819C4semidirect
16. #91813C4semidirect
17. #91813C4semidirect
29. C4×C22⋊Dic5D3semidirect
62. C5×#208D4semidirect
69. C22×#208D5semidirect
195. C22×C3×C5#104semidirect
243. #208C22⋊D5semidirect
348. C22×C5#805semidirect
399. C3×C5#1871semidirect
408. C22×C3#3957semidirect
471. C5#69453semidirect
483. C22#90981semidirect
495. C3#10602777semidirect

Maximal subgroups

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

subgroupindex
#117565502
C22×C5×#2082
C3×C4×C22⋊Dic52
C2×#909812
#117459782
#106027773
#694535