Finite Group Databasebeta

← #14295126

Subgroups — #14295126

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91398C211yesmaximal, characteristic
2C2×(C2×D3)⋊#170C211yesmaximal, characteristic
3C2×(C2×D3)⋊#170C211yesmaximal, characteristic
4C2×#91169C211yesmaximal, characteristic, complemented
5C2×Dic3×#170C211yesmaximal, characteristic, complemented
6#11746789C211yesmaximal, characteristic, complemented
7C3×#64918C211yesmaximal, characteristic, complemented
8#10604224—31nomaximal, Hall
9C22×D3×Dic5C2211yescharacteristic
10C22×C3⋊#170C2211yescharacteristic
11C22×C3⋊#170C2211yescharacteristic
12C22×C3×#170C2211yescharacteristic
13C22×C3×#170C2211yescharacteristic
14C2×#6712C411yescharacteristic
15C2×C5×(C2×D3)⋊C4C411yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17C2×#6669C411yescharacteristic
18C2×(C2×D3)⋊Dic5C411yescharacteristic
19C2×Dic3×Dic5C2211yescharacteristic
20#91398—22no—
21#91398—22no—
22(C2×D3)⋊#170C414yescomplemented
23(C2×D3)⋊#170C414yescomplemented
24#91169—22no—
25Dic3×#170—22no—
26#68601—51nomaximal, Hall
27C2×#4023—31no—
28C2×C22⋊#170—31no—
29C2×C22⋊#170—31no—
30C2×#4002—31no—
31C2×C4×#170—31no—
32#64918—31no—
33#64918D311yescharacteristic, complemented
34C23×C5×D3C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×Dic15C2×C411yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C22×C5×Dic3C2×C411yescharacteristic
39C22×C3×Dic5C2×C411yescharacteristic
40C22×C3×Dic5C2311yescharacteristic
41C2×D3×Dic5—21no—
42C2×D3×Dic5—21no—
43C2×D3×Dic5—21no—
44C2×D3×Dic5—21no—
45C2×D3×Dic5C2×C412yes—
46C2×D3×Dic5C2×C412yes—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3⋊#170—21no—
50C2×C3⋊#170—21no—
51C2×C3⋊#170C2×C412yes—
52C2×C3⋊#170C2×C412yes—
53C2×C3×#170—21no—
54C2×C3×#170—21no—
55C2×C3×#170—21no—
56C2×C3×#170—21no—
57C2×C3×#170C2×C412yes—
58C2×C3×#170C2×C412yes—
59#6712—22no—
60C5×(C2×D3)⋊C4—22no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5—21no—
63#6669—22no—
64(C2×D3)⋊Dic5—22no—
65Dic3×Dic5D412yes—
66Dic3×Dic5D412yes—
67C2×#872—51no—
68C2×(C2×D3)⋊C8—51no—
69C2×(C2×D3)⋊C8—51no—
70C2×#815—51no—
71C2×C8×Dic3—51no—
72C3×#336—51no—
73#4524—51no—
74C23×Dic5—31no—
75C22×#170—31no—
76C22×#170—31no—
77C22×#170C2×D311yescharacteristic
78C22×#170C2×D311yescharacteristic
79C2×C5×C22⋊C4—31no—
80C2×C22⋊Dic5—31no—
81C2×#683—31no—
82C2×#683—31no—
83C2×C4×Dic5—31no—
84C2×C4×Dic5C2×D311yescharacteristic
85#4023—62no—
86#4023—62no—
87C22⋊#170—34no—
88C22⋊#170—34no—
89#4002—62no—
90C4×#170—62no—
91#1750—151noSylow
92C23×C3×C5C22×C411yescharacteristic
93C22×C5×D3—21no—
94C22×C5×D3—21no—
95C22×C5×D3—21no—
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3C4212yes—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15C4212yes—
108C2×Dic15C22⋊C412yes—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3C22⋊C412yes—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5C22×C411yescharacteristic
116C2×C3×Dic5C22×C411yescharacteristic
117C2×C3×Dic5C2×D411yescharacteristic
118C2×C3×Dic5C2×D411yescharacteristic
119C2×C3×Dic5#4111yescharacteristic
120C2×C3×Dic5#4111yescharacteristic
121D3×Dic5—22no—
122D3×Dic5—22no—
123D3×Dic5—22no—
124D3×Dic5—22no—
125C3⋊#170—22no—
126C3⋊#170—22no—
127C3×#170—22no—
128C3×#170—22no—
129C22×C4×D3—51no—
130C22×C3×C8—51no—
131C22×C3×C8—51no—
132C2×C3×C42—51no—
133C2×(C2×D3)⋊C4—51no—
134C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic
135C2×Dic3⋊C4—51no—
136C2×Dic3⋊C4—51no—
137C2×C4×Dic3—51no—
138C22×C3⋊C8—51no—
139C22×C3⋊C8—51no—
140#872—102no—
141#872—102no—
142(C2×D3)⋊C8—54no—
143(C2×D3)⋊C8—54no—
144#815—102no—
145C8×Dic3—102no—
146C24×C5—31no—
147C22×C4×C5—31no—
148C22×C4×C5C4×D311yescharacteristic
149C22×Dic5—31no—
150C22×Dic5—31no—
151C22×Dic5—32no—
152C22×Dic5—32no—
153C22×Dic5—61no—
154C22×Dic5—61no—
155C22×Dic5—61no—
156C22×Dic5—61no—
157C22×Dic5C4×D311yescharacteristic
158C22×Dic5C22×D311yescharacteristic
159C2×#170—21no—
160C2×#170—21no—
161C2×#170—21no—
162C2×#170—21no—
163C2×#170—32no—
164C2×#170—32no—
165C2×#170—61no—
166C2×#170—61no—
167C2×#170—61no—
168C2×#170—61no—
169C2×#170C4×D312yes—
170C2×#170C4×D312yes—
171C5×C22⋊C4—62no—
172C22⋊Dic5—62no—
173#683—62no—
174#683—62no—
175C4×Dic5—21no—
176C4×Dic5—21no—
177C4×Dic5—32no—
178C4×Dic5—32no—
179C2×#117—151no—
180C2×C22⋊C8—151no—
181C2×C22⋊C8—151no—
182C2×#97—151no—
183C2×C4×C8—151no—
184#336—51no—
185#336—151no—
186C22×C3×C5C2×C4211yescharacteristic
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5#11711yescharacteristic
189C22×C3×C5#13111yescharacteristic
190C22×C3×C5#13111yescharacteristic
191C22×C3×C5#13111yescharacteristic
192C22×C3×C5#13111yescharacteristic
193C2×C5×D3—22no—
194C2×C5×D3—22no—
195C2×C5×D3—22no—
196C2×C5×D3—41no—
197C2×C5×D3—41no—
198C2×C5×D3—41no—
199C2×C5×D3—41no—
200C3×C4×C5—41no—
201Dic15—22no—
202Dic15—22no—
203C3×Dic5—41no—
204C3×Dic5C4×D411yescharacteristic
205C3×Dic5C4×D411yescharacteristic
206C3×Dic5C4×D411yescharacteristic
207C3×Dic5C4×D411yescharacteristic
208C5×Dic3—22no—
209C23×D3C2×AGL(1,𝔽5)11yescharacteristic
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
213C22×Dic3—51no—
214C22×Dic3—51no—
215C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
216C2×C4×D3—52no—
217C2×C4×D3—52no—
218C2×C4×D3—101no—
219C2×C4×D3—101no—
220C2×C4×D3—101no—
221C2×C4×D3—101no—
222C2×C3×C8—52no—
223C2×C3×C8—52no—
224C2×C3×C8—101no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227C2×C3×C8—101no—
228C3×C42—101no—
229C3×C42—101no—
230(C2×D3)⋊C4—22no—
231(C2×D3)⋊C4—102no—
232Dic3⋊C4—102no—
233Dic3⋊C4—102no—
234C4×Dic3—52no—
235C4×Dic3—52no—
236C2×C3⋊C8—52no—
237C2×C3⋊C8—52no—
238C2×C3⋊C8—101no—
239C2×C3⋊C8—101no—
240C2×C3⋊C8—101no—
241C2×C3⋊C8—101no—
242C23×C5—32no—
243C23×C5—61no—
244C23×C5—61no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—61no—
248C23×C5—61no—
249C23×C5C2×C4×D311yescharacteristic
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—32no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—32no—
260C2×Dic5—32no—
261C2×Dic5—61no—
262C2×Dic5—61no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5—62no—
266C2×Dic5—62no—
267C2×Dic5—62no—
268C2×Dic5—62no—
269C2×Dic5C2×C4×D311yescharacteristic
270C2×Dic5C2×C4×D311yescharacteristic
271C2×Dic5D3×D411yescharacteristic
272C2×Dic5D3×D411yescharacteristic
273C2×Dic5#23711yescharacteristic
274C2×Dic5#23911yescharacteristic
275#170—22no—
276#170—22no—
277#170—62no—
278#170—62no—
279C23×C4—151no—
280C22×C8—51no—
281C22×C8—51no—
282C22×C8—151no—
283C22×C8—151no—
284#117—302no—
285#117—302no—
286C2×C4⋊C4—151no—
287C2×C4⋊C4—151no—
288C2×C22⋊C4—31no—
289C2×C22⋊C4—151no—
290C2×C42—51no—
291C2×C42—151no—
292C22⋊C8—154no—
293C22⋊C8—154no—
294#97—302no—
295C4×C8—302no—
296C2×C3×C5C4×C22⋊C411yescharacteristic
297C2×C3×C5#40511yescharacteristic
298C2×C3×C5#40511yescharacteristic
299C2×C3×C5#40811yescharacteristic
300C2×C3×C5#40811yescharacteristic
301C2×C3×C5#43311yescharacteristic
302C2×C3×C5#43311yescharacteristic
303C5×D3—42no—
304C23×C3C22×AGL(1,𝔽5)11yescharacteristic
305C22×D3—21no—
306C22×D3—21no—
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—21no—
311C22×D3C4×AGL(1,𝔽5)12yes—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—51no—
320C2×C3×C4—51no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—52no—
327C2×Dic3—52no—
328C2×Dic3—101no—
329C2×Dic3—101no—
330C2×Dic3—101no—
331C2×Dic3—101no—
332C2×Dic3C22⋊AGL(1,𝔽5)12yes—
333C4×D3—102no—
334C4×D3—102no—
335C4×D3—102no—
336C4×D3—102no—
337C3×C8—102no—
338C3×C8—102no—
339C3⋊C8—102no—
340C3⋊C8—102no—
341C22×C5—62no—
342C22×C5—62no—
343C22×C5—62no—
344C22×C5—121no—
345C22×C5—121no—
346C22×C5—121no—
347C22×C5—121no—
348C22×C5C42×D311yescharacteristic
349C22×C5D3×C22⋊C411yescharacteristic
350C22×C5#89211yescharacteristic
351C22×C5#90111yescharacteristic
352C22×C5#90111yescharacteristic
353C22×C5#90711yescharacteristic
354C22×C5#90711yescharacteristic
355C4×C5—41no—
356C4×C5—62no—
357Dic5—41no—
358Dic5—62no—
359Dic5—62no—
360Dic5#67⋊C411yescharacteristic
361Dic5#67⋊C411yescharacteristic
362Dic5#89311yescharacteristic
363Dic5#89311yescharacteristic
364C24—31no—
365C22×C4—31no—
366C22×C4—51no—
367C22×C4—51no—
368C22×C4—152no—
369C22×C4—152no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—301no—
373C22×C4—301no—
374C22×C4—301no—
375C22×C4—301no—
376C22×C4D3×AGL(1,𝔽5)11yescharacteristic
377C2×C8—52no—
378C2×C8—52no—
379C2×C8—101no—
380C2×C8—101no—
381C2×C8—101no—
382C2×C8—101no—
383C2×C8—152no—
384C2×C8—152no—
385C2×C8—301no—
386C2×C8—301no—
387C2×C8—301no—
388C2×C8—301no—
389C4⋊C4—302no—
390C4⋊C4—302no—
391C22⋊C4—62no—
392C22⋊C4—302no—
393C42—101no—
394C42—101no—
395C42—152no—
396C42—152no—
397C3×C5#175011yescharacteristic, complemented, Hall
398C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
399C22×C3#413011yescharacteristic
400C22×C3#413111yescharacteristic
401C22×C3#413111yescharacteristic
402C22×C3#413111yescharacteristic
403C22×C3#413111yescharacteristic
404C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
405C2×D3—22no—
406C2×D3—22no—
407C2×D3—22no—
408C2×D3—41no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C3×C4—41no—
413C3×C4—51no—
414C3×C4—51no—
415C3×C4—51no—
416C3×C4—51no—
417C3×C4—201no—
418Dic3—22no—
419Dic3—102no—
420Dic3—102no—
421C2×C5—122no—
422C2×C5#466611yescharacteristic
423C2×C5#468911yescharacteristic
424C2×C5#470811yescharacteristic
425C2×C5#472711yescharacteristic
426C2×C5#472711yescharacteristic
427C2×C5#484011yescharacteristic
428C2×C5#484011yescharacteristic
429C23—32no—
430C23—61no—
431C23—61no—
432C23—61no—
433C23—61no—
434C23—61no—
435C23—61no—
436C23C2×D3×AGL(1,𝔽5)11yescharacteristic
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—32no—
441C2×C4—51no—
442C2×C4—51no—
443C2×C4—51no—
444C2×C4—51no—
445C2×C4—51no—
446C2×C4—51no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—152no—
453C2×C4—152no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4—302no—
457C2×C4—302no—
458C2×C4—301no—
459C2×C4—301no—
460C2×C4—301no—
461C2×C4—301no—
462C8—102no—
463C8—102no—
464C8—302no—
465C8—302no—
466C2×C3#6569111yescharacteristic
467C2×C3#6569111yescharacteristic
468C2×C3#6569711yescharacteristic
469C2×C3#6569711yescharacteristic
470C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
471C2×C3#6577511yescharacteristic
472C2×C3#6577611yescharacteristic
473D3—42no—
474C5#6860111yescharacteristic, complemented, Sylow
475C22—62no—
476C22—62no—
477C22—62no—
478C22—121no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22#9190711yescharacteristic
483C22#9191111yescharacteristic
484C22#9191311yescharacteristic
485C22C4×D3×AGL(1,𝔽5)11yescharacteristic
486C22#9192711yescharacteristic
487C22#9192911yescharacteristic
488C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
489C4—41no—
490C4—51no—
491C4—51no—
492C4—51no—
493C4—51no—
494C4—62no—
495C4—201no—
496C4—302no—
497C4—302no—
498C3#1060422411yescharacteristic, complemented, Sylow
499C2—122no—
500C2#1175177211yescharacteristic
501C2#1175179911yescharacteristic
502C2#1175184811yescharacteristic
503C2#1175186811yescharacteristic
504C2#1175187011yescharacteristic
505C2#1175189611yescharacteristic
506C2#1175204011yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1750
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#91169C2semidirect
5. C2×Dic3×#170C2semidirect
6. #11746789C2semidirect
7. C3×#64918C2semidirect
22. (C2×D3)⋊#170C4semidirect
23. (C2×D3)⋊#170C4semidirect
33. #64918D3semidirect
397. C3×C5#1750semidirect
474. C5#68601semidirect
498. C3#10604224semidirect

Maximal subgroups

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

subgroupindex
C2×#913982
C2×(C2×D3)⋊#1702
C2×#911692
C2×Dic3×#1702
#117467892
C3×#649182
#106042243
#686015