Finite Group Databasebeta

← #14300558

Subgroups — #14300558

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×C3×#681C211yesmaximal, characteristic, complemented
3C4×C5×#217C211yesmaximal, characteristic, complemented
4C2×#90980C212yesmaximal, complemented
5#11745976C212yesmaximal, complemented
6#10600246—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×#217—21no—
19C2×C4×C5×Dic3C2212yes—
20C2×C3×#681—21no—
21C2×C3×#681—24no—
22C2×C3×#681C2212yes—
23C22×C3×#168—21no—
24C5×C3⋊#95—21no—
25#90980—24no—
26#71984—51nomaximal, Hall
27#66125—31no—
28C22×#681D311yescharacteristic, complemented
29C4×C5×C22⋊C4—31no—
30C2×#3937—32no—
31#64743—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×C5×Dic3—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×#217—24no—
61C4×C5×Dic3—22no—
62C4×C5×Dic3—22no—
63C3×#681—24no—
64C3×#681—22no—
65C3×#681D414yescomplemented
66C2×C3×#168—24no—
67C2×C3×#168—22no—
68C22×C3×M16—51no—
69#5791—51no—
70C4×#217D511yescharacteristic, complemented
71C2×#825—52no—
72#4555—52no—
73C23×C4×C5C2×D311yescharacteristic
74C2×#709—31no—
75C2×C5×C22⋊C4—61no—
76C2×C42×C5—32no—
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—21no—
87C2×#681—24no—
88C2×#681C2×D312yes—
89C22×#168—21no—
90C5×#95—61no—
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×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×C5×Dic3—24no—
124C2×C5×Dic3—42no—
125C2×C5×Dic3—42no—
126C3×#168—24no—
127C23×C3×C4C2×D511yescharacteristic
128C2×#235—51no—
129C2×C3×M16—52no—
130C2×C3×M16—104no—
131C2×C3×M16—101no—
132C22×C3×C8—101no—
133#953—101no—
134C2×#217—21no—
135#930—51no—
136#930—51no—
137#929—101no—
138C4×#67—101no—
139C4×#67—101no—
140#926—51no—
141#924—51no—
142#924—51no—
143C2×C4×Dic3C2×D512yes—
144C3⋊#95—21no—
145#825—104no—
146C24×C5D1211yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—62no—
150C22×C4×C5C4×D311yescharacteristic
151C22×C4×C5C4×D311yescharacteristic
152C22×C4×C5D1211yescharacteristic
153C22×C4×C5#6711yescharacteristic
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—64no—
165C42×C5—62no—
166C42×C5—62no—
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—24no—
178#681—22no—
179#681#6714yescomplemented
180C2×#168—24no—
181C2×#168—22no—
182C22×M16—51no—
183#525—151no—
184C2×#104—152no—
185C4×C22⋊C4—31no—
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—
209C5×Dic3—44no—
210C24×C3C22⋊D511yescharacteristic
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4C4×D511yescharacteristic
214C22×C3×C4C4×D511yescharacteristic
215C22×C3×C4D2011yescharacteristic
216C22×C3×C4D2011yescharacteristic
217C22×C3×C4C22⋊D511yescharacteristic
218C22×C3×C4C22×D511yescharacteristic
219C2×#67—101no—
220C2×#67—101no—
221C2×#67—101no—
222C22×Dic3—22no—
223#235—102no—
224#235—102no—
225C2×D12—51no—
226C2×C4×D3—101no—
227C2×Dic6—51no—
228C3×M16—54no—
229C3×M16—104no—
230C3×M16—102no—
231C2×C3×C8—104no—
232C2×C3×C8—102no—
233#217—24no—
234#217—101no—
235#217—101no—
236#217—101no—
237(C2×D3)⋊C4—101no—
238(C2×D3)⋊C4—101no—
239C4⋊Dic3—51no—
240C4⋊Dic3—51no—
241Dic3⋊C4—101no—
242Dic3⋊C4—101no—
243C4×Dic3—22no—
244C4×Dic3—22no—
245C4×Dic3—101no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—41no—
249C23×C5(C2×D3)⋊C411yescharacteristic
250C23×C5(C2×D3)⋊C411yescharacteristic
251C23×C5C2×D1211yescharacteristic
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—64no—
261C2×C4×C5—122no—
262C2×C4×C5—122no—
263C2×C4×C5(C2×D3)⋊C411yescharacteristic
264C2×C4×C5(C2×D3)⋊C411yescharacteristic
265C2×C4×C5C2×C4×D311yescharacteristic
266C2×C4×C5#23512yes—
267C2×C4×C5C2×#6711yescharacteristic
268C2×C4×C5C2×#6712yes—
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—24no—
280C2×#41—151no—
281C23×C4D3×D511yescharacteristic
282C2×M16—52no—
283C2×M16—104no—
284C2×M16—101no—
285C22×C8—101no—
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—61no—
296C2×C42—32no—
297#104—304no—
298#95—61no—
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#68511yescharacteristic
321C2×C3×C4#68511yescharacteristic
322C2×C3×C4C2×C4×D511yescharacteristic
323C2×C3×C4C2×D2011yescharacteristic
324C2×C3×C4D4×D512yes—
325C2×C3×C4#71112yes—
326#67—202no—
327#67—202no—
328#67—202no—
329C2×Dic3—24no—
330C2×Dic3—42no—
331C2×Dic3—42no—
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#82512yescomplemented
349C22×C5C2×(C2×D3)⋊C411yescharacteristic
350C22×C5#93012yes—
351C2×D5—121no—
352C2×D5—121no—
353C2×D5—121no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—124no—
357C4×C5C4×#6712yes—
358C4×C5#92911yescharacteristic
359C4×C5#95311yescharacteristic
360Dic5—121no—
361Dic5—121no—
362Dic5—121no—
363C24#120311yescharacteristic
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—62no—
374C22×C4—301no—
375C22×C4#120011yescharacteristic
376C22×C4#120011yescharacteristic
377C22×C4#120211yescharacteristic
378C22×C4#120211yescharacteristic
379C22×C4#120311yescharacteristic
380C22×C4C2×D3×D511yescharacteristic
381M16—54no—
382M16—104no—
383M16—102no—
384C2×C8—104no—
385C2×C8—102no—
386C4⋊C4—151no—
387C4⋊C4—151no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C22⋊C4—64no—
391C22⋊C4—301no—
392C22⋊C4—301no—
393C22⋊C4—301no—
394C22⋊C4—301no—
395C22⋊C4—301no—
396C42—62no—
397C42—62no—
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#402712yes—
417C3×C4#402811yescharacteristic
418C3×C4#403211yescharacteristic
419Dic3—44no—
420Dic3—201no—
421Dic3—201no—
422Dic3—201no—
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5C2×#82511yescharacteristic
427C2×C5#513911yescharacteristic
428C2×C5#521311yescharacteristic
429D5—241no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—301no—
434C23#666711yescharacteristic
435C23#666711yescharacteristic
436C23C2×#120311yescharacteristic
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—64no—
450C2×C4—122no—
451C2×C4—122no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—601no—
456C2×C4—601no—
457C2×C4#666711yescharacteristic
458C2×C4#666711yescharacteristic
459C2×C4#678212yes—
460C2×C4C2×#120011yescharacteristic
461C2×C4C2×#120211yescharacteristic
462C2×C4D5×#6712yes—
463C8—104no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3C2×#393711yescharacteristic
468C2×C3#6524711yescharacteristic
469C2×C3#6529411yescharacteristic
470D3—401no—
471C5#7198411yescharacteristic, 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#9098012yescomplemented
484C22C2×#666711yescharacteristic
485C22#9156612yes—
486C4—21no—
487C4—21no—
488C4—124no—
489C4—601no—
490C4—601no—
491C4—601no—
492C4#9154611yescharacteristic
493C4#9155212yes—
494C4#9156411yescharacteristic
495C3#1060024611yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—1201no—
500C2C2×#9098011yescharacteristic
501C2#1174842811yescharacteristic
502C2#1174949411yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
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×C3×#681C2semidirect
3. C4×C5×#217C2semidirect
4. C2×#90980C2semidirect
5. #11745976C2semidirect
10. #91819C4semidirect
11. #91819C4semidirect
16. #91813C4semidirect
17. #91813C4semidirect
28. C22×#681D3semidirect
65. C3×#681D4semidirect
70. C4×#217D5semidirect
179. #681#67semidirect
195. C22×C3×C5#104semidirect
348. C22×C5#825semidirect
399. C3×C5#1871semidirect
408. C22×C3#3937semidirect
471. C5#71984semidirect
483. C22#90980semidirect
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×C3×#6812
C4×C5×#2172
C2×#909802
#117459762
#106002463
#719845