Finite Group Databasebeta

← #14300528

Subgroups — #14300528

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×#6710C211yesmaximal, characteristic, complemented
3C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#91089C212yesmaximal, complemented
5#11746344C212yesmaximal, complemented
6#10600246—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C42×C5C2212yes—
11#91842—21no—
12#91819C411yescharacteristic, complemented
13#91819C411yescharacteristic, complemented
14#91818—21no—
15C4×#1220—21no—
16C4×#1220—21no—
17#91815C2211yescharacteristic
18#91813C411yescharacteristic, complemented
19#91813C411yescharacteristic, complemented
20C2×#6710—21no—
21C2×#6710—24no—
22C2×#6710C2212yes—
23C22×C3⋊#168—21no—
24C3×C5×#95—21no—
25#91089—24no—
26#69453—51nomaximal, Hall
27#66125—31no—
28C22×#681—31no—
29C4×C5×C22⋊C4D311yescharacteristic, complemented
30C2×#3937—32no—
31#64743—32no—
32C24×C3×C5D411yescharacteristic
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5—22no—
35C22×C3×C4×C5—22no—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—21no—
45#6817—22no—
46#6817—22no—
47C2×D60C2×C411yescharacteristic
48C2×C4×D15—21no—
49C2×Dic30C2×C411yescharacteristic
50C3×C5×C22⋊C4—24no—
51C3×C42×C5—22no—
52C3×C42×C5—22no—
53#6719—21no—
54#6719—21no—
55#6719—21no—
56#6714—21no—
57#6714—21no—
58C4⋊Dic15C2×C411yescharacteristic
59C4⋊Dic15C2×C411yescharacteristic
60#6712—21no—
61#6712—21no—
62C4×Dic15—21no—
63#6710—24no—
64#6710—22no—
65#6710D414yescomplemented
66C2×C3⋊#168—24no—
67C2×C3⋊#168—22no—
68#5791—51no—
69C22×#208—51no—
70C3×C4×C22⋊C4D511yescharacteristic, complemented
71C2×#805—52no—
72#4523—52no—
73C23×C4×C5C2×D311yescharacteristic
74C2×#709—31no—
75C2×C5×C22⋊C4—21no—
76C2×C42×C5C2×D312yes—
77#4099—61no—
78#4076—31no—
79#4076—31no—
80#4075—61no—
81C4×C22⋊D5—61no—
82C4×C22⋊D5—61no—
83#4072—31no—
84#4070—31no—
85#4070—31no—
86C2×#681—32no—
87C2×#681—64no—
88C2×#681—61no—
89C22×#168—61no—
90C5×#95—21no—
91#3937—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×C5—24no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5—42no—
110C2×C3×C4×C5C22⋊C411yescharacteristic
111C2×C3×C4×C5C22⋊C411yescharacteristic
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D412yes—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4112yes—
116#1220—42no—
117#1220—42no—
118#1220—42no—
119C2×Dic15—21no—
120C2×Dic15—21no—
121C2×Dic15—21no—
122D60—22no—
123C4×D15—41no—
124C4×D15—41no—
125Dic30—22no—
126C3⋊#168—24no—
127C23×C3×C4C2×D511yescharacteristic
128C2×#235—51no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C42C2×D512yes—
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—52no—
141C2×#208—104no—
142C2×#208—101no—
143C22×C3⋊C8—101no—
144C3×#95—21no—
145#805—104no—
146C24×C5#6711yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5C4×D311yescharacteristic
151C22×C4×C5C4×D311yescharacteristic
152C22×C4×C5D1211yescharacteristic
153C22×C4×C5D1211yescharacteristic
154C22×C4×C5#6711yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—61no—
157C2×C22⋊D5—61no—
158C2×C22⋊D5—61no—
159#709—62no—
160#709—62no—
161C2×D20—31no—
162C2×C4×D5—61no—
163C2×Dic10—31no—
164C5×C22⋊C4—24no—
165C42×C5—22no—
166C42×C5—22no—
167C22⋊Dic5—61no—
168C22⋊Dic5—61no—
169C22⋊Dic5—61no—
170#685—61no—
171#685—61no—
172C4⋊Dic5—31no—
173C4⋊Dic5—31no—
174#683—61no—
175#683—61no—
176C4×Dic5—61no—
177#681—34no—
178#681—64no—
179#681—62no—
180C2×#168—64no—
181C2×#168—62no—
182C22×M16—151no—
183#525—151no—
184C2×#104—152no—
185C4×C22⋊C4D1511yescharacteristic, complemented
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×C5—44no—
204C3×C4×C5C4×D412yes—
205C3×C4×C5#12011yescharacteristic
206C3×C4×C5#12311yescharacteristic
207Dic15—41no—
208Dic15—41no—
209Dic15—41no—
210C24×C3C22⋊D511yescharacteristic
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4C4×D511yescharacteristic
215C22×C3×C4C4×D511yescharacteristic
216C22×C3×C4D2011yescharacteristic
217C22×C3×C4D2011yescharacteristic
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—24no—
229C3×C42—22no—
230C3×C42—22no—
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—54no—
242#208—104no—
243#208—102no—
244C2×C3⋊C8—104no—
245C2×C3⋊C8—102no—
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—24no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5(C2×D3)⋊C411yescharacteristic
264C2×C4×C5(C2×D3)⋊C411yescharacteristic
265C2×C4×C5C2×C4×D311yescharacteristic
266C2×C4×C5C2×D1211yescharacteristic
267C2×C4×C5D3×D412yes—
268C2×C4×C5#23712yes—
269C22⋊D5—122no—
270C22⋊D5—122no—
271C22⋊D5—122no—
272C2×Dic5—61no—
273C2×Dic5—61no—
274C2×Dic5—61no—
275D20—62no—
276C4×D5—121no—
277C4×D5—121no—
278Dic10—62no—
279#168—64no—
280C2×#41—151no—
281C23×C4C2×D1511yescharacteristic
282C2×M16—152no—
283C2×M16—304no—
284C2×M16—301no—
285C22×C8—301no—
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—21no—
296C2×C42C2×D1512yes—
297#104—304no—
298#95—21no—
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×C22⋊D511yescharacteristic
312C22×D3—101no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—24no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4#68511yescharacteristic
324C2×C3×C4#68511yescharacteristic
325C2×C3×C4C2×C4×D511yescharacteristic
326C2×C3×C4C2×D2011yescharacteristic
327C2×C3×C4D4×D512yes—
328C2×C3×C4#71112yes—
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—104no—
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—44no—
357C4×C5#67⋊C412yes—
358C4×C5#88211yescharacteristic
359C4×C5#88611yescharacteristic
360Dic5—121no—
361Dic5—121no—
362Dic5—121no—
363C24#122011yescharacteristic
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—22no—
374C22×C4—301no—
375C22×C4C4×D1511yescharacteristic
376C22×C4C4×D1511yescharacteristic
377C22×C4D6011yescharacteristic
378C22×C4D6011yescharacteristic
379C22×C4#122011yescharacteristic
380C22×C4C22×D1511yescharacteristic
381M16—154no—
382M16—304no—
383M16—302no—
384C2×C8—304no—
385C2×C8—302no—
386C4⋊C4—151no—
387C4⋊C4—151no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C22⋊C4—24no—
391C22⋊C4—301no—
392C22⋊C4—301no—
393C22⋊C4—301no—
394C22⋊C4—301no—
395C22⋊C4—301no—
396C42—22no—
397C42—22no—
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#393712yescomplemented
409C22×C3C2×#68511yescharacteristic
410C22×C3#408512yes—
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—44no—
417C3×C4#402712yes—
418C3×C4#402811yescharacteristic
419C3×C4#403211yescharacteristic
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#671411yescharacteristic
435C23#671411yescharacteristic
436C23C2×#122011yescharacteristic
437Q8—302no—
438D4—302no—
439D4—602no—
440D4—602no—
441D4—602no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—601no—
456C2×C4—601no—
457C2×C4#671411yescharacteristic
458C2×C4#671411yescharacteristic
459C2×C4C2×C4×D1511yescharacteristic
460C2×C4C2×D6011yescharacteristic
461C2×C4D4×D1512yes—
462C2×C4#681912yes—
463C8—304no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3C2×#393711yescharacteristic
468C2×C3#6524711yescharacteristic
469C2×C3#6529411yescharacteristic
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#9108912yescomplemented
484C22C2×#671411yescharacteristic
485C22#9182812yes—
486C4—21no—
487C4—21no—
488C4—44no—
489C4—601no—
490C4—601no—
491C4—601no—
492C4#9177012yes—
493C4#9177111yescharacteristic
494C4#9177511yescharacteristic
495C3#1060024611yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—1201no—
500C2C2×#9108911yescharacteristic
501C2#1175105911yescharacteristic
502C2#1175110611yescharacteristic
subgroupG/H
centerC2×C4C2×D60
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C4×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
cosocleC22×C3×C4×C5C23
hypercenterC4×C22⋊C4D15
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6710C2semidirect
3. C3×C4×C5×C22⋊C4C2semidirect
4. C2×#91089C2semidirect
5. #11746344C2semidirect
12. #91819C4semidirect
13. #91819C4semidirect
18. #91813C4semidirect
19. #91813C4semidirect
29. C4×C5×C22⋊C4D3semidirect
65. #6710D4semidirect
70. C3×C4×C22⋊C4D5semidirect
185. C4×C22⋊C4D15semidirect
195. C22×C3×C5#104semidirect
348. C22×C5#805semidirect
399. C3×C5#1871semidirect
408. C22×C3#3937semidirect
471. C5#69453semidirect
483. C22#91089semidirect
495. C3#10600246semidirect

Maximal subgroups

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

subgroupindex
#117565502
C22×#67102
C3×C4×C5×C22⋊C42
C2×#910892
#117463442
#106002463
#694535