Finite Group Databasebeta

← #14300559

Subgroups — #14300559

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×#6710C211yesmaximal, characteristic, complemented
2C3×#66125C211yesmaximal, characteristic
3C4×C5×#217C211yesmaximal, characteristic, complemented
4C2×#90977C212yesmaximal, complemented
5#11745974C212yesmaximal, complemented
6#10600246—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×#6710—21no—
10C2×#6710—24no—
11C2×#6710C2212yes—
12C22×C3⋊#168—21no—
13C2×C5×#217—21no—
14C2×C4×C5×Dic3C2212yes—
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
24C5×C3⋊#95—21no—
25#90977—24no—
26#71713—51nomaximal, Hall
27#66125D311yescharacteristic
28C22×#681—31no—
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
41C22×C5×Dic3—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#6710—24no—
51#6710—22no—
52#6710D414yescomplemented
53C2×C3⋊#168—24no—
54C2×C3⋊#168—22no—
55C5×#217—24no—
56C4×C5×Dic3—22no—
57C4×C5×Dic3—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×#208—51no—
70C2×#837—52no—
71C4×#217D511yescharacteristic, complemented
72#4532—52no—
73C23×C4×C5C2×D311yescharacteristic
74C2×#709C2×D311yescharacteristic
75C2×C5×C22⋊C4—61no—
76C2×C42×C5—32no—
77#4099—21no—
78#4076Dic311yescharacteristic, complemented
79#4076Dic311yescharacteristic, complemented
80#4075—21no—
81C4×C22⋊D5—21no—
82C4×C22⋊D5—21no—
83#4072C2×D311yescharacteristic
84#4070Dic311yescharacteristic, complemented
85#4070Dic311yescharacteristic, complemented
86C2×#681—32no—
87C2×#681—64no—
88C2×#681—61no—
89C22×#168—61no—
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×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×C5×Dic3—24no—
114C2×C5×Dic3—42no—
115C2×C5×Dic3—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—
126C3⋊#168—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—21no—
139C2×C4×Dic3C2×D512yes—
140C2×#208—52no—
141C2×#208—104no—
142C2×#208—101no—
143C22×C3⋊C8—101no—
144#837—104no—
145C3⋊#95—21no—
146C24×C5#6711yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—62no—
150C22×C4×C5C2×Dic311yescharacteristic
151C22×C4×C5C2×Dic311yescharacteristic
152C22×C4×C5#6711yescharacteristic
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5#6711yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—21no—
157C2×C22⋊D5—21no—
158C2×C22⋊D5—21no—
159#709—22no—
160#709—22no—
161C2×D20C2×Dic311yescharacteristic
162C2×C4×D5—21no—
163C2×Dic10C2×Dic311yescharacteristic
164C5×C22⋊C4—64no—
165C42×C5—62no—
166C42×C5—62no—
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5—21no—
170#685—21no—
171#685—21no—
172C4⋊Dic5C2×Dic311yescharacteristic
173C4⋊Dic5C2×Dic311yescharacteristic
174#683—21no—
175#683—21no—
176C4×Dic5—21no—
177#681—34no—
178#681—64no—
179#681—62no—
180C2×#168—64no—
181C2×#168—62no—
182C22×M16—151no—
183#525—51no—
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×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
206C3×Dic5—41no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C5×Dic3—44no—
210C24×C3C22⋊D511yescharacteristic
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×C4D2011yescharacteristic
225C22×C3×C4C22⋊D511yescharacteristic
226C22×C3×C4C22×D511yescharacteristic
227C22×Dic3—22no—
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—24no—
239C4×Dic3—22no—
240C4×Dic3—22no—
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#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—64no—
261C2×C4×C5—122no—
262C2×C4×C5—122no—
263C2×C4×C5#21711yescharacteristic
264C2×C4×C5#21711yescharacteristic
265C2×C4×C5D3×D412yes—
266C2×C4×C5#23712yes—
267C2×C4×C5C22×Dic311yescharacteristic
268C2×C4×C5C2×#6711yescharacteristic
269C22⋊D5—42no—
270C22⋊D5—42no—
271C22⋊D5—42no—
272C2×Dic5—21no—
273C2×Dic5—21no—
274C2×Dic5—21no—
275D20—22no—
276C4×D5—41no—
277C4×D5—41no—
278Dic10—22no—
279#168—64no—
280C2×#41—51no—
281C23×C4D3×D511yescharacteristic
282C2×M16—152no—
283C2×M16—304no—
284C2×M16—301no—
285C22×C8—301no—
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—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
305C3×D5—81no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—41no—
309C23×C3—101no—
310C23×C3#68511yescharacteristic
311C23×C3#68511yescharacteristic
312C23×C3C2×C22⋊D511yescharacteristic
313C3×Q8—102no—
314C3×D4—102no—
315C3×D4—202no—
316C3×D4—202no—
317C3×D4—202no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
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×C4C2×D2011yescharacteristic
334C2×C3×C4D4×D512yes—
335C2×C3×C4#71112yes—
336C2×Dic3—24no—
337C2×Dic3—42no—
338C2×Dic3—42no—
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#83712yescomplemented
349C22×C5#93912yes—
350C22×C5C2×#21711yescharacteristic
351C2×D5—41no—
352C2×D5—41no—
353C2×D5—41no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—124no—
357C4×C5D4×Dic312yes—
358C4×C5#93511yescharacteristic
359C4×C5#93711yescharacteristic
360Dic5—41no—
361Dic5—41no—
362Dic5—41no—
363C24#120111yescharacteristic
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—62no—
374C22×C4—101no—
375C22×C4D5×Dic311yescharacteristic
376C22×C4D5×Dic311yescharacteristic
377C22×C4#120111yescharacteristic
378C22×C4#120211yescharacteristic
379C22×C4#120211yescharacteristic
380C22×C4C2×D3×D511yescharacteristic
381M16—154no—
382M16—304no—
383M16—302no—
384C2×C8—304no—
385C2×C8—302no—
386C4⋊C4—51no—
387C4⋊C4—51no—
388C4⋊C4—101no—
389C4⋊C4—101no—
390C22⋊C4—64no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—101no—
394C22⋊C4—101no—
395C22⋊C4—101no—
396C42—62no—
397C42—62no—
398C42—101no—
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#393712yescomplemented
412C22×C3C2×#68511yescharacteristic
413C22×C3#408512yes—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—201no—
417C3×C4—201no—
418C3×C4—201no—
419C3×C4#402712yes—
420C3×C4#402811yescharacteristic
421C3×C4#403211yescharacteristic
422Dic3—44no—
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×#120111yescharacteristic
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—64no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—101no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4#666511yescharacteristic
458C2×C4#666511yescharacteristic
459C2×C4C2×D5×Dic311yescharacteristic
460C2×C4#678012yes—
461C2×C4C2×#120211yescharacteristic
462C2×C4#679012yes—
463C8—304no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3—401no—
468C2×C3C2×#393711yescharacteristic
469C2×C3#6524711yescharacteristic
470C2×C3#6529411yescharacteristic
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#9097712yescomplemented
484C22C2×#666511yescharacteristic
485C22#9157112yes—
486C4—21no—
487C4—21no—
488C4—124no—
489C4—201no—
490C4—201no—
491C4—201no—
492C4#9153711yescharacteristic
493C4#9155912yes—
494C4#9157211yescharacteristic
495C3#1060024611yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—401no—
500C2C2×#9097711yescharacteristic
501C2#1174842111yescharacteristic
502C2#1174950011yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
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×#6710C2semidirect
3. C4×C5×#217C2semidirect
4. C2×#90977C2semidirect
5. #11745974C2semidirect
16. C3×#4076C4semidirect
17. C3×#4076C4semidirect
22. C3×#4070C4semidirect
23. C3×#4070C4semidirect
52. #6710D4semidirect
71. C4×#217D5semidirect
78. #4076Dic3semidirect
79. #4076Dic3semidirect
84. #4070Dic3semidirect
85. #4070Dic3semidirect
195. C22×C3×C5#104semidirect
348. C22×C5#837semidirect
399. C3×C5#1871semidirect
411. C22×C3#3937semidirect
471. C5#71713semidirect
483. C22#90977semidirect
495. C3#10600246semidirect

Maximal subgroups

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

subgroupindex
C22×#67102
C3×#661252
C4×C5×#2172
C2×#909772
#117459742
#106002463
#717135