Finite Group Databasebeta

← #14327565

Subgroups — #14327565

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2#11751312C211yesmaximal, characteristic, complemented
3C4×C5×#217C211yesmaximal, characteristic, complemented
4#11749518C212yesmaximal
5#11749485C212yesmaximal, complemented
6Dic3×#685C212yesmaximal, complemented
7D5×C3⋊#95C211yesmaximal, characteristic, complemented
8#11748738C211yesmaximal, characteristic, complemented
9#11748635C211yesmaximal, characteristic, complemented
10#11748612C211yesmaximal, characteristic, complemented
11#11748590C212yesmaximal, complemented
12#10605307—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C2×#6719C2212yes—
18C2×C5×#217C2212yes—
19C2×C4×C5×Dic3C2212yes—
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C3×C4×C22⋊D5C418yescomplemented
22C2×C3×#685C2211yescharacteristic
23C2×C3×#683C2211yescharacteristic
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×#6668C2212yes—
26C2×#6665C2212yes—
27C2×Dic3×Dic5C2212yes—
28#91115C2211yescharacteristic
29#91115C2212yes—
30#91115C2211yescharacteristic
31C5×C3⋊#95C2211yescharacteristic
32C5×C3⋊#95C2211yescharacteristic
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#82336—51nomaximal, Hall
38C2×C4×C22⋊D5D311yescharacteristic
39C4×C5×C22⋊C4—31no—
40#65500—31no—
41#65245—32no—
42#65233—32no—
43C4×#685—32no—
44#65222—32no—
45#64956—31no—
46D5×#95—31no—
47#64940—31no—
48#64937—31no—
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yescomplemented
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2312yes—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5C2×C414yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—42no—
66C2×C3×C4×D5C2×C414yes—
67C2×D5×Dic3—24no—
68C2×D5×Dic3—24no—
69C2×D5×Dic3—42no—
70#6719—42no—
71C5×#217—24no—
72C4×C5×Dic3—42no—
73C3×C22⋊Dic5C2×C414yescomplemented
74C3×#685C2×C414yes—
75C3×#683C2×C414yescomplemented
76C3×C4×Dic5C2×C414yescomplemented
77#6668—42no—
78#6665—24no—
79Dic3×Dic5—24no—
80C2×C3×C4×D4—51no—
81#5220—52no—
82#5212—51no—
83#5211—51no—
84C4×#217D511yescharacteristic, complemented
85C2×C3⋊#95—51no—
86#4980—52no—
87#4951—52no—
88Dic3×C22⋊C4—52no—
89#4937—51no—
90#4932—51no—
91C23×C4×C5C2×D311yescharacteristic
92C22×C22⋊D5C2×D311yescharacteristic
93C22×C4×D5—32no—
94C22×C4×D5C2×D311yescharacteristic
95C2×C5×C22⋊C4—32no—
96C2×C42×C5—32no—
97C2×C22⋊Dic5—32no—
98C2×C22⋊Dic5C2×D311yescharacteristic
99C4×C22⋊D5Dic318yescomplemented
100C2×#685—32no—
101C2×#685C2×D311yescharacteristic
102C2×#683—32no—
103C2×#683C2×D311yescharacteristic
104C2×C4×Dic5—32no—
105C2×C4×Dic5C2×D311yescharacteristic
106C5×#95—31no—
107C5×#95—31no—
108#3963—31no—
109#3963—31no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963—32no—
115#2353—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—22no—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5C22×C412yes—
125C22×C3×D5#4112yes—
126C22×C3×D5#4112yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—44no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3#4114yes—
144C3×C22⋊D5—28no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5C22×C412yes—
152C3×C4×D5—44no—
153D5×Dic3—48no—
154C22×C3×D4—51no—
155C23×C3×C4—51no—
156C23×C3×C4C2×D511yescharacteristic
157C23×Dic3—52no—
158C3×C4×D4—58no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C22⋊C4—51no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C42—51no—
163C2×#217—52no—
164C2×#217—52no—
165C2×#217C2×D512yes—
166C2×C4⋊Dic3—52no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3C2×D512yes—
169C3⋊#95—51no—
170C3⋊#95—51no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95C2×D511yescharacteristic
177C3⋊#95C2×D511yescharacteristic
178C24×C5C22×D311yescharacteristic
179C23×D5C22×D311yescharacteristic
180C22×C4×C5—32no—
181C22×C4×C5—32no—
182C22×C4×C5—42no—
183C22×C4×C5C2×Dic314yescomplemented
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—22no—
187C2×C22⋊D5—22no—
188C2×C22⋊D5C2×Dic314yes—
189C22×Dic5—32no—
190C22×Dic5—32no—
191C22×Dic5C22×D311yescharacteristic
192C22×Dic5C22×D311yescharacteristic
193C22×Dic5C22×D311yescharacteristic
194C2×C4×D5—42no—
195C2×C4×D5—64no—
196C2×C4×D5—64no—
197C2×C4×D5—122no—
198C2×C4×D5C2×Dic314yes—
199C5×C22⋊C4—64no—
200C42×C5—122no—
201C22⋊Dic5—122no—
202C22⋊Dic5C2×Dic314yescomplemented
203#685—64no—
204#685C2×Dic314yes—
205#683—122no—
206#683C2×Dic314yescomplemented
207C4×Dic5—64no—
208C4×Dic5C2×Dic314yescomplemented
209C2×C4×D4—51no—
210#388—152no—
211#387—152no—
212#386—152no—
213#383—151no—
214#381—151no—
215#380—151no—
216C4×C22⋊C4—31no—
217C4×C22⋊C4—152no—
218#376—151no—
219C2×#95—151no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—22no—
223C22×C3×C5—42no—
224C22×C3×C5—42no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C2×#4112yes—
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C22×C3×C5H(5,𝔽2)12yes—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—24no—
233C2×C3×D5—24no—
234C2×C3×D5#11714yes—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237Dic15—42no—
238Dic15—42no—
239C3×Dic5—22no—
240C3×Dic5—22no—
241C3×Dic5—22no—
242C5×Dic3—24no—
243C5×Dic3—42no—
244C24×C3—51no—
245C24×C3C22×D511yescharacteristic
246C2×C3×D4—54no—
247C2×C3×D4—102no—
248C2×C3×D4—102no—
249C22×C3×C4—42no—
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—51no—
253C22×C3×C4—54no—
254C22×C3×C4—202no—
255C22×C3×C4C4×D514yescomplemented
256C22×C3×C4C22×D511yescharacteristic
257C22×C3×C4C22×D511yescharacteristic
258C22×Dic3—52no—
259C22×Dic3—52no—
260C22×Dic3—104no—
261C22×Dic3—104no—
262C22×Dic3—202no—
263C22×Dic3C22×D512yes—
264C22×Dic3C22×D512yes—
265C3×C4⋊C4—54no—
266C3×C22⋊C4—54no—
267C3×C22⋊C4—54no—
268C3×C42—54no—
269#217—24no—
270#217—104no—
271#217—202no—
272C4⋊Dic3—202no—
273C4×Dic3—42no—
274C4×Dic3—104no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—22no—
278C23×C5—22no—
279C23×C5C22×Dic312yes—
280C23×C5C23×D311yescharacteristic
281C22×D5—22no—
282C22×D5—22no—
283C22×D5#23512yes—
284C22×D5#23512yes—
285C22×D5C22×Dic312yes—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—34no—
289C2×C4×C5—44no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5C22×Dic312yes—
296C2×C4×C5C22×Dic312yes—
297C22⋊D5—28no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5C22×Dic312yes—
309C2×Dic5C22×Dic312yes—
310C2×Dic5C22×Dic312yes—
311C4×D5—44no—
312C4×D5—128no—
313C22×D4—51no—
314C23×C4—51no—
315C23×C4—152no—
316C23×C4D3×D511yescharacteristic
317C4×D4—58no—
318C2×C4⋊C4—51no—
319C2×C4⋊C4—152no—
320C2×C22⋊C4—32no—
321C2×C22⋊C4—51no—
322C2×C22⋊C4—51no—
323C2×C22⋊C4—152no—
324C2×C22⋊C4—152no—
325C2×C42—32no—
326C2×C42—51no—
327C2×C42—152no—
328#95—31no—
329#95—31no—
330#95—152no—
331#95—152no—
332#95—152no—
333#95—152no—
334#95—151no—
335#95—151no—
336#95—152no—
337C2×C3×C5—42no—
338C2×C3×C5C2×#11711yescharacteristic
339C2×C3×C5C4×#4111yescharacteristic
340C2×C3×C5#51811yescharacteristic
341C2×C3×C5#55112yes—
342C2×C3×C5#55312yes—
343C3×D5—24no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—52no—
349C23×C3—52no—
350C23×C3—52no—
351C23×C3—102no—
352C23×C3—102no—
353C23×C3C2×C4×D512yes—
354C23×C3C23×D511yescharacteristic
355C3×D4—108no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—44no—
359C2×C3×C4—52no—
360C2×C3×C4—52no—
361C2×C3×C4—52no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—101no—
365C2×C3×C4—101no—
366C2×C3×C4—204no—
367C2×C3×C4C2×C4×D512yes—
368C2×C3×C4C2×C4×D512yes—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3—102no—
380C2×Dic3—208no—
381C2×Dic3#70914yes—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5C2×#23511yescharacteristic
388C22×C5C2×#23511yescharacteristic
389C22×C5#100412yes—
390C22×C5D3×#4112yes—
391C22×C5C23×Dic311yescharacteristic
392C2×D5—24no—
393C2×D5—22no—
394C2×D5—24no—
395C2×D5—22no—
396C2×D5#92614yes—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—64no—
400C4×C5—122no—
401Dic5—22no—
402Dic5—22no—
403Dic5—22no—
404Dic5—122no—
405Dic5—122no—
406C24—51no—
407C24C2×D3×D511yescharacteristic
408C2×D4—54no—
409C2×D4—102no—
410C2×D4—102no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—42no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—54no—
418C22×C4—152no—
419C22×C4—152no—
420C22×C4—202no—
421C22×C4—304no—
422C22×C4—304no—
423C22×C4—602no—
424C22×C4D5×Dic314yescomplemented
425C22×C4C2×D3×D511yescharacteristic
426C22×C4C2×D3×D511yescharacteristic
427C4⋊C4—54no—
428C4⋊C4—602no—
429C22⋊C4—54no—
430C22⋊C4—54no—
431C22⋊C4—64no—
432C22⋊C4—304no—
433C22⋊C4—602no—
434C42—54no—
435C42—122no—
436C42—304no—
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—54no—
444C22×C3—102no—
445C22×C3—102no—
446C22×C3—104no—
447C22×C3—104no—
448C22×C3C22×C4×D511yescharacteristic
449C22×C3C2×#70912yes—
450C22×C3#414412yes—
451C22×C3D5×#4111yescharacteristic
452C22×C3D5×#4111yescharacteristic
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—102no—
456C3×C4—102no—
457C3×C4—102no—
458Dic3—24no—
459Dic3—42no—
460Dic3—202no—
461Dic3—202no—
462C2×C5—42no—
463C2×C5#554012yes—
464C2×C5#555612yes—
465C2×C5C2×#92611yescharacteristic
466C2×C5#579811yescharacteristic
467C2×C5Dic3×#4111yescharacteristic
468D5—24no—
469C23—21no—
470C23—21no—
471C23—22no—
472C23—22no—
473C23—52no—
474C23—52no—
475C23—52no—
476C23—102no—
477C23—102no—
478C23C2×D5×Dic312yes—
479C23C22×D3×D511yescharacteristic
480D4—108no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—34no—
484C2×C4—44no—
485C2×C4—52no—
486C2×C4—52no—
487C2×C4—52no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—204no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—608no—
505C2×C4C2×D5×Dic312yes—
506C2×C4C2×D5×Dic312yes—
507C2×C3—42no—
508C2×C3—104no—
509C2×C3C4×#70911yescharacteristic
510C2×C3#6582011yescharacteristic
511C2×C3D5×#11711yescharacteristic
512C2×C3#6589012yes—
513C2×C3#6589212yes—
514C5#8233611yescharacteristic, complemented, Sylow
515C22—22no—
516C22—22no—
517C22—22no—
518C22—42no—
519C22—42no—
520C22—54no—
521C22—102no—
522C22—104no—
523C22—102no—
524C22—104no—
525C22D5×#23511yescharacteristic
526C22D5×#23511yescharacteristic
527C22D3×#70912yes—
528C22C22×D5×Dic311yescharacteristic
529C22#9204912yes—
530C4—22no—
531C4—22no—
532C4—64no—
533C4—102no—
534C4—102no—
535C4—102no—
536C4—122no—
537C4—602no—
538C4—602no—
539C3#1060530711yescharacteristic, complemented, Sylow
540C2—42no—
541C2—104no—
542C2D5×#92611yescharacteristic
543C2#1175440412yes—
544C2Dic3×#70911yescharacteristic
545C2#1175467712yes—
546C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751312C2semidirect
3. C4×C5×#217C2semidirect
5. #11749485C2semidirect
6. Dic3×#685C2semidirect
7. D5×C3⋊#95C2semidirect
8. #11748738C2semidirect
9. #11748635C2semidirect
10. #11748612C2semidirect
11. #11748590C2semidirect
21. C3×C4×C22⋊D5C4semidirect
52. C22×C3×C4×C5C2×C4semidirect
73. C3×C22⋊Dic5C2×C4semidirect
75. C3×#683C2×C4semidirect
76. C3×C4×Dic5C2×C4semidirect
84. C4×#217D5semidirect
99. C4×C22⋊D5Dic3semidirect
183. C22×C4×C5C2×Dic3semidirect
202. C22⋊Dic5C2×Dic3semidirect
206. #683C2×Dic3semidirect
208. C4×Dic5C2×Dic3semidirect
255. C22×C3×C4C4×D5semidirect
424. C22×C4D5×Dic3semidirect
437. C3×C5#2353semidirect
514. C5#82336semidirect
539. C3#10605307semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
#117513122
C4×C5×#2172
#117495182
#117494852
Dic3×#6852
D5×C3⋊#952
#117487382
#117486352
#117486122
#117485902
#106053073
#823365