Finite Group Databasebeta

← #14300563

Subgroups — #14300563

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
1C5×#5791C211yesmaximal, characteristic
2C22×C3×#681C211yesmaximal, characteristic, complemented
3C4×#6719C211yesmaximal, characteristic, complemented
4C2×#90978C212yesmaximal, complemented
5#11745975C212yesmaximal, complemented
6#10602506—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C5×#235C2211yescharacteristic
9C2×#6719—21no—
10C2×C4×Dic15C2212yes—
11C5×#953—21no—
12C5×#930C411yescharacteristic, complemented
13C5×#930C411yescharacteristic, complemented
14C5×#929—21no—
15C4×C5×#67—21no—
16C4×C5×#67—21no—
17C5×#926C2211yescharacteristic
18C5×#924C411yescharacteristic, complemented
19C5×#924C411yescharacteristic, complemented
20C2×C3×#681—21no—
21C2×C3×#681—24no—
22C2×C3×#681C2212yes—
23C22×C3×#168—21no—
24#91115—21no—
25#90978—24no—
26#71984—51nomaximal, Hall
27C5×#525—31no—
28C22×#681D311yescharacteristic, complemented
29C2×#3969—32no—
30C4×C22⋊Dic5—31no—
31#64752—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×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C5×#235—22no—
46C5×#235—22no—
47C2×C5×D12C2×C411yescharacteristic
48C2×C4×C5×D3—21no—
49C2×C5×Dic6C2×C411yescharacteristic
50#6719—24no—
51C4×Dic15—22no—
52C4×Dic15—22no—
53C5×#217—21no—
54C5×#217—21no—
55C5×#217—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3C2×C411yescharacteristic
59C5×C4⋊Dic3C2×C411yescharacteristic
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C4×C5×Dic3—21no—
63C3×#681—24no—
64C3×#681—22no—
65C3×#681D414yescomplemented
66C2×C3×#168—24no—
67C2×C3×#168—22no—
68C22×C3×M16—51no—
69#5791D511yescharacteristic
70C4×#217—51no—
71C2×#825—52no—
72#4555—52no—
73C2×C5×#41—31no—
74C23×C4×C5C2×D311yescharacteristic
75C5×#123—61no—
76C5×C22⋊Q8—31no—
77C5×C22⋊Q8—31no—
78C5×#121—31no—
79C5×#121—31no—
80C5×#120—61no—
81C4×C5×D4—61no—
82C4×C5×D4—61no—
83C5×#117—31no—
84C2×C22⋊Dic5—61no—
85C2×C4×Dic5—32no—
86C2×#681—21no—
87C2×#681—24no—
88C2×#681C2×D312yes—
89C22×#168—21no—
90#3969—64no—
91#3963—61no—
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×C5×D3—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—
116C5×#67—42no—
117C5×#67—42no—
118C5×#67—42no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C5×D12—22no—
123C4×C5×D3—41no—
124C4×C5×D3—41no—
125C5×Dic6—22no—
126C3×#168—24no—
127C23×C3×C4C2×D511yescharacteristic
128C2×#235C2×D511yescharacteristic
129C2×C3×M16—52no—
130C2×C3×M16—104no—
131C2×C3×M16—101no—
132C22×C3×C8—101no—
133#953—21no—
134C2×#217—101no—
135#930Dic511yescharacteristic, complemented
136#930Dic511yescharacteristic, complemented
137#929—21no—
138C4×#67—21no—
139C4×#67—21no—
140#926C2×D511yescharacteristic
141#924Dic511yescharacteristic, complemented
142#924Dic511yescharacteristic, complemented
143C2×C4×Dic3—52no—
144C3⋊#95—101no—
145#825—104no—
146C24×C5D1211yescharacteristic
147C5×#41—62no—
148C5×#41—62no—
149C2×C5×Q8—31no—
150C2×C5×D4—31no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—61no—
157C22×C4×C5C4×D311yescharacteristic
158C22×C4×C5C4×D311yescharacteristic
159C22×C4×C5D1211yescharacteristic
160C22×C4×C5#6711yescharacteristic
161C22×C4×C5#6711yescharacteristic
162C22×C4×C5C22×D311yescharacteristic
163C22×Dic5—62no—
164C5×C4⋊C4—31no—
165C5×C4⋊C4—31no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4—61no—
168C5×C22⋊C4—61no—
169C5×C22⋊C4—61no—
170C5×C22⋊C4—61no—
171C5×C22⋊C4—61no—
172C5×C22⋊C4—61no—
173C42×C5—61no—
174C22⋊Dic5—64no—
175C4×Dic5—62no—
176C4×Dic5—62no—
177#681—24no—
178#681—22no—
179#681#6714yescomplemented
180C2×#168—24no—
181C2×#168—22no—
182C22×M16—51no—
183#525—31no—
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×C5×D3—41no—
199C2×C5×D3—41no—
200C2×C5×D3—41no—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5C4×D412yes—
204C3×C4×C5#12011yescharacteristic
205C3×C4×C5#12311yescharacteristic
206Dic15—44no—
207C5×Dic3—41no—
208C5×Dic3—41no—
209C5×Dic3—41no—
210C24×C3C22⋊D511yescharacteristic
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4C2×Dic511yescharacteristic
214C22×C3×C4C2×Dic511yescharacteristic
215C22×C3×C4C22⋊D511yescharacteristic
216C22×C3×C4C22⋊D511yescharacteristic
217C22×C3×C4C22⋊D511yescharacteristic
218C22×C3×C4C22×D511yescharacteristic
219C2×#67—21no—
220C2×#67—21no—
221C2×#67—21no—
222C22×Dic3—102no—
223#235—22no—
224#235—22no—
225C2×D12C2×Dic511yescharacteristic
226C2×C4×D3—21no—
227C2×Dic6C2×Dic511yescharacteristic
228C3×M16—54no—
229C3×M16—104no—
230C3×M16—102no—
231C2×C3×C8—104no—
232C2×C3×C8—102no—
233#217—21no—
234#217—21no—
235#217—21no—
236#217—104no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—21no—
239C4⋊Dic3C2×Dic511yescharacteristic
240C4⋊Dic3C2×Dic511yescharacteristic
241Dic3⋊C4—21no—
242Dic3⋊C4—21no—
243C4×Dic3—21no—
244C4×Dic3—102no—
245C4×Dic3—102no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—41no—
249C23×C5—61no—
250C23×C5(C2×D3)⋊C411yescharacteristic
251C23×C5(C2×D3)⋊C411yescharacteristic
252C23×C5C2×D1211yescharacteristic
253C5×Q8—62no—
254C5×D4—62no—
255C5×D4—122no—
256C5×D4—122no—
257C5×D4—122no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—61no—
266C2×C4×C5—61no—
267C2×C4×C5—61no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5(C2×D3)⋊C411yescharacteristic
271C2×C4×C5(C2×D3)⋊C411yescharacteristic
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5#23512yes—
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C2×#6712yes—
276C2×Dic5—64no—
277C2×Dic5—122no—
278C2×Dic5—122no—
279#168—24no—
280C2×#41—31no—
281C23×C4D3×D511yescharacteristic
282C2×M16—52no—
283C2×M16—104no—
284C2×M16—101no—
285C22×C8—101no—
286#123—61no—
287C22⋊Q8—31no—
288C22⋊Q8—31no—
289#121—31no—
290#121—31no—
291#120—61no—
292C4×D4—61no—
293C4×D4—61no—
294#117—31no—
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
305C5×D3—81no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—41no—
309C23×C3C22⋊Dic511yescharacteristic
310C23×C3C22⋊Dic511yescharacteristic
311C23×C3C2×C22⋊D511yescharacteristic
312C22×D3—21no—
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×C4C22⋊Dic511yescharacteristic
321C2×C3×C4C22⋊Dic511yescharacteristic
322C2×C3×C4D4×D512yes—
323C2×C3×C4#71112yes—
324C2×C3×C4C22×Dic511yescharacteristic
325C2×C3×C4C2×C22⋊D511yescharacteristic
326#67—42no—
327#67—42no—
328#67—42no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—104no—
333C2×Dic3—202no—
334C2×Dic3—202no—
335D12—22no—
336C4×D3—41no—
337C4×D3—41no—
338Dic6—22no—
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—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5#82512yescomplemented
352C22×C5C2×(C2×D3)⋊C411yescharacteristic
353C22×C5#93012yes—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—121no—
357C4×C5—121no—
358C4×C5—121no—
359C4×C5C4×#6712yes—
360C4×C5#92911yescharacteristic
361C4×C5#95311yescharacteristic
362Dic5—124no—
363C24#120311yescharacteristic
364#41—62no—
365#41—62no—
366C2×Q8—31no—
367C2×D4—31no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—61no—
374C22×C4—302no—
375C22×C4D3×Dic511yescharacteristic
376C22×C4D3×Dic511yescharacteristic
377C22×C4#120111yescharacteristic
378C22×C4#120111yescharacteristic
379C22×C4#120311yescharacteristic
380C22×C4C2×D3×D511yescharacteristic
381M16—54no—
382M16—104no—
383M16—102no—
384C2×C8—104no—
385C2×C8—102no—
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—304no—
396C42—61no—
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#396912yescomplemented
409C22×C3#408512yes—
410C22×C3C2×C22⋊Dic511yescharacteristic
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4D4×Dic512yes—
417C3×C4#408111yescharacteristic
418C3×C4#408311yescharacteristic
419Dic3—41no—
420Dic3—41no—
421Dic3—41no—
422Dic3—204no—
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5—241no—
427C2×C5C2×#82511yescharacteristic
428C2×C5#513911yescharacteristic
429C2×C5#521311yescharacteristic
430C23—22no—
431C23—22no—
432C23—41no—
433C23—61no—
434C23(C2×D3)⋊Dic511yescharacteristic
435C23(C2×D3)⋊Dic511yescharacteristic
436C23C2×#120311yescharacteristic
437Q8—62no—
438D4—62no—
439D4—122no—
440D4—122no—
441D4—122no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—121no—
453C2×C4—121no—
454C2×C4—304no—
455C2×C4—602no—
456C2×C4—602no—
457C2×C4(C2×D3)⋊Dic511yescharacteristic
458C2×C4(C2×D3)⋊Dic511yescharacteristic
459C2×C4C2×D3×Dic511yescharacteristic
460C2×C4#678212yes—
461C2×C4C2×#120111yescharacteristic
462C2×C4D5×#6712yes—
463C8—104no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3#6550911yescharacteristic
468C2×C3C2×#396911yescharacteristic
469C2×C3#6552511yescharacteristic
470D3—81no—
471C5#7198411yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22#9097812yescomplemented
484C22C2×(C2×D3)⋊Dic511yescharacteristic
485C22#9156612yes—
486C4—21no—
487C4—21no—
488C4—121no—
489C4—121no—
490C4—121no—
491C4—604no—
492C4#9153911yescharacteristic
493C4Dic5×#6712yes—
494C4#9156311yescharacteristic
495C3#1060250611yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—241no—
500C2C2×#9097811yescharacteristic
501C2#1174842411yescharacteristic
502C2#1174949211yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5791C2
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×#6719C2semidirect
4. C2×#90978C2semidirect
5. #11745975C2semidirect
12. C5×#930C4semidirect
13. C5×#930C4semidirect
18. C5×#924C4semidirect
19. C5×#924C4semidirect
28. C22×#681D3semidirect
65. C3×#681D4semidirect
135. #930Dic5semidirect
136. #930Dic5semidirect
141. #924Dic5semidirect
142. #924Dic5semidirect
179. #681#67semidirect
195. C22×C3×C5#104semidirect
351. C22×C5#825semidirect
399. C3×C5#1871semidirect
408. C22×C3#3969semidirect
471. C5#71984semidirect
483. C22#90978semidirect
495. C3#10602506semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
C22×C3×#6812
C4×#67192
C2×#909782
#117459752
#106025063
#719845