Finite Group Databasebeta

← #14322863

Subgroups — #14322863

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#877C211yesmaximal, characteristic
2C22×Dic3⋊Dic5C211yesmaximal, characteristic
3C2×#91529C211yesmaximal, characteristic
4#11751043C211yesmaximal, characteristic
5C3×#65231C211yesmaximal, characteristic
6#11749516C211yesmaximal, characteristic
7#11749506C211yesmaximal, characteristic
8#11748820C212yesmaximal, complemented
9#11748803C212yesmaximal, complemented
10#11748664C212yesmaximal, complemented
11#11748630C212yesmaximal, complemented
12#10613963—31nomaximal, Hall
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18C2×#6712C2212yes—
19C2×C5×#217C2211yescharacteristic
20C2×C5×Dic3⋊C4C2212yes—
21C2×C4×C5×Dic3C2212yes—
22C5×#877—24no—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×Dic3⋊Dic5C418yescomplemented
26C2×Dic3⋊Dic5C2212yes—
27C2×Dic3⋊Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5C2211yescharacteristic
29C2×Dic3⋊Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×#6669C2212yes—
32C2×#6668C2212yes—
33#91529—24no—
34C2×Dic3×Dic5C2212yes—
35#91115C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73869—51nomaximal, Hall
40C2×C5×#117—31no—
41C2×#4072—31no—
42C22×C4⋊Dic5—31no—
43#65262—32no—
44#65262—32no—
45#65231—31no—
46#65231—31no—
47#65231—31no—
48#65231D311yescharacteristic
49#65217—32no—
50#65217—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×Dic15—42no—
54C22×Dic15C2×C414yes—
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2×C414yes—
59C22×C5×Dic3D414yes—
60C22×C5×Dic3Q814yes—
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C22×C3×Dic5—42no—
65C22×C3×Dic5C2×C414yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2311yescharacteristic
69C3×C5×C22⋊C4—22no—
70#6719—22no—
71#6712—42no—
72C5×#217—22no—
73C5×Dic3⋊C4—24no—
74C4×C5×Dic3—24no—
75C3×C22⋊Dic5—22no—
76C3×#683—42no—
77Dic3⋊Dic5—24no—
78Dic3⋊Dic5C2×C414yes—
79Dic3⋊Dic5C2×C414yes—
80Dic3⋊Dic5C2×C414yes—
81Dic3⋊Dic5C2×C414yes—
82#6669—42no—
83#6668—42no—
84Dic3×Dic5—24no—
85C22×Dic3⋊C4—51no—
86C2×#877—51no—
87C2×#877D511yescharacteristic
88C3×#380—51no—
89#5212—51no—
90#4976—52no—
91#4976—52no—
92#4942—51no—
93#4942—51no—
94#4647—52no—
95#4647—52no—
96C23×C4×C5—31no—
97C23×Dic5—31no—
98C23×Dic5C2×D311yescharacteristic
99C5×#117—64no—
100C2×C5×C4⋊C4—32no—
101C2×C5×C22⋊C4—31no—
102C2×C5×C22⋊C4C2×D311yescharacteristic
103C2×C42×C5—32no—
104C2×C22⋊Dic5—31no—
105C2×C22⋊Dic5C2×D311yescharacteristic
106#4072—64no—
107C2×C4⋊Dic5—38no—
108C2×C4⋊Dic5—31no—
109C2×C4⋊Dic5—31no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5—32no—
113C2×#683—32no—
114C2×#683—32no—
115C2×#683—32no—
116C2×#683C2×D312yes—
117C2×C4×Dic5—32no—
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#3963C2×D312yes—
122#2316—151noSylow
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5C22×C412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×Q812yes—
128C23×C3×C5C2411yescharacteristic
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—44no—
138C2×Dic15C22×C412yes—
139C2×Dic15C22×C412yes—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3C4⋊C4116yescomplemented
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C412yes—
146C2×C5×Dic3C2×D412yes—
147C2×C5×Dic3C2×D412yes—
148C2×C5×Dic3C2×Q812yes—
149C2×C5×Dic3C2×Q812yes—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—44no—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C22×C412yes—
158C23×C3×C4—51no—
159C23×Dic3—51no—
160C23×Dic3C2×D511yescharacteristic
161C2×C3×C4⋊C4—52no—
162C2×C3×C22⋊C4—51no—
163C2×C3×C22⋊C4C2×D511yescharacteristic
164C2×#217—51no—
165C2×#217C2×D511yescharacteristic
166C2×C4⋊Dic3—52no—
167C2×Dic3⋊C4—58no—
168C2×Dic3⋊C4—51no—
169C2×Dic3⋊C4—51no—
170C2×Dic3⋊C4—51no—
171C2×Dic3⋊C4—51no—
172C2×Dic3⋊C4—52no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4C2×D512yes—
176C2×C4×Dic3—52no—
177C2×C4×Dic3C2×D512yes—
178#877—24no—
179#877—104no—
180C3×#95—52no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C24×C5C22×D311yescharacteristic
185C22×C4×C5—34no—
186C22×C4×C5—34no—
187C22×C4×C5—34no—
188C22×C4×C5—31no—
189C22×C4×C5—31no—
190C22×C4×C5—32no—
191C22×C4×C5C22×D312yes—
192C22×Dic5—31no—
193C22×Dic5—31no—
194C22×Dic5—34no—
195C22×Dic5—32no—
196C22×Dic5—42no—
197C22×Dic5—122no—
198C22×Dic5C4×D314yes—
199C22×Dic5C22×D312yes—
200C22×Dic5C22×D311yescharacteristic
201C22×Dic5C22×D311yescharacteristic
202C5×C4⋊C4—64no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—62no—
205C42×C5—64no—
206C22⋊Dic5—22no—
207C22⋊Dic5—62no—
208C4⋊Dic5—34no—
209C4⋊Dic5—34no—
210C4⋊Dic5—34no—
211C4⋊Dic5—34no—
212C4⋊Dic5—64no—
213#683—42no—
214#683—122no—
215#683—122no—
216#683—122no—
217C4×Dic5—64no—
218C2×#117—31no—
219C2×#117—151no—
220C22×C4⋊C4—151no—
221#389—152no—
222#389—152no—
223#389—152no—
224#389—152no—
225#380—51no—
226#380—151no—
227#380—151no—
228#380—151no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5C2×C4⋊C414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C22×Q811yescharacteristic
237C22×C3×C5H(5,𝔽2)12yes—
238C22×C3×C52−1+412yes—
239C3×C4×C5—42no—
240Dic15—22no—
241Dic15—22no—
242Dic15—42no—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C3×Dic5—42no—
246C5×Dic3—42no—
247C5×Dic3C2×C4⋊C414yes—
248C5×Dic3C2×C4⋊C414yes—
249C24×C3C22×D511yescharacteristic
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—54no—
253C22×C3×C4—52no—
254C22×C3×C4—202no—
255C22×C3×C4C22×D512yes—
256C22×Dic3—51no—
257C22×Dic3—51no—
258C22×Dic3—54no—
259C22×Dic3—52no—
260C22×Dic3—202no—
261C22×Dic3Dic1014yes—
262C22×Dic3C4×D514yes—
263C22×Dic3C22⋊D514yes—
264C22×Dic3C22×D512yes—
265C22×Dic3C22×D511yescharacteristic
266C22×Dic3C22×D511yescharacteristic
267C3×C4⋊C4—202no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—102no—
270#217—22no—
271#217—102no—
272C4⋊Dic3—202no—
273Dic3⋊C4—24no—
274Dic3⋊C4—54no—
275Dic3⋊C4—54no—
276Dic3⋊C4—54no—
277Dic3⋊C4—54no—
278Dic3⋊C4—104no—
279Dic3⋊C4—202no—
280Dic3⋊C4—202no—
281C4×Dic3—24no—
282C4×Dic3—104no—
283C23×C5—22no—
284C23×C5—22no—
285C23×C5C2×C4×D312yes—
286C23×C5D3×D412yes—
287C23×C5D3×Q812yes—
288C23×C5C23×D311yescharacteristic
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—316no—
293C2×C4×C5—32no—
294C2×C4×C5—32no—
295C2×C4×C5—32no—
296C2×C4×C5—32no—
297C2×C4×C5—32no—
298C2×C4×C5—32no—
299C2×C4×C5—62no—
300C2×C4×C5—62no—
301C2×C4×C5—62no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—32no—
308C2×Dic5—32no—
309C2×Dic5—44no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5—62no—
314C2×Dic5—62no—
315C2×Dic5—124no—
316C2×Dic5C2×C4×D312yes—
317C2×Dic5C2×C4×D312yes—
318C23×C4—31no—
319C23×C4—51no—
320C23×C4—151no—
321#117—64no—
322#117—304no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4—151no—
326C2×C4⋊C4—151no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4—151no—
329C2×C4⋊C4—158no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—152no—
333C2×C4⋊C4—152no—
334C2×C22⋊C4—31no—
335C2×C22⋊C4—51no—
336C2×C22⋊C4—151no—
337C2×C22⋊C4D3×D511yescharacteristic
338C2×C42—32no—
339C2×C42—152no—
340#95—52no—
341#95—152no—
342#95—152no—
343#95—152no—
344C2×C3×C5—24no—
345C2×C3×C5C22×C4⋊C411yescharacteristic
346C2×C3×C5#51811yescharacteristic
347C2×C3×C5#51911yescharacteristic
348C2×C3×C5#53712yes—
349C2×C3×C5#54412yes—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3C2×Dic1012yes—
353C23×C3C2×C4×D512yes—
354C23×C3C2×C22⋊D512yes—
355C23×C3C23×D511yescharacteristic
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—52no—
360C2×C3×C4—52no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4—102no—
366C2×C3×C4—204no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—52no—
371C2×Dic3—52no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3—204no—
378C2×Dic3#683116yescomplemented
379C2×Dic3C2×Dic1012yes—
380C2×Dic3C2×Dic1012yes—
381C2×Dic3C2×C4×D512yes—
382C2×Dic3C2×C4×D512yes—
383C2×Dic3C2×C22⋊D512yes—
384C2×Dic3C2×C22⋊D512yes—
385C22×C5—22no—
386C22×C5—22no—
387C22×C5—24no—
388C22×C5—24no—
389C22×C5D3×C4⋊C414yes—
390C22×C5C22×C4×D311yescharacteristic
391C22×C5C2×D3×D411yescharacteristic
392C22×C5#100412yes—
393C22×C5C2×D3×Q811yescharacteristic
394C22×C5#101012yes—
395C4×C5—34no—
396C4×C5—34no—
397C4×C5—42no—
398C4×C5—122no—
399Dic5—22no—
400Dic5—22no—
401Dic5—42no—
402Dic5—62no—
403Dic5—62no—
404Dic5—122no—
405C24C2×D3×D511yescharacteristic
406C22×C4—34no—
407C22×C4—34no—
408C22×C4—34no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—32no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—54no—
415C22×C4—52no—
416C22×C4—151no—
417C22×C4—151no—
418C22×C4—154no—
419C22×C4—152no—
420C22×C4—202no—
421C22×C4—602no—
422C22×C4C2×D3×D512yes—
423C4⋊C4—64no—
424C4⋊C4—154no—
425C4⋊C4—154no—
426C4⋊C4—154no—
427C4⋊C4—154no—
428C4⋊C4—202no—
429C4⋊C4—304no—
430C4⋊C4—602no—
431C4⋊C4—602no—
432C4⋊C4—602no—
433C22⋊C4—22no—
434C22⋊C4—62no—
435C22⋊C4—102no—
436C22⋊C4—302no—
437C42—64no—
438C42—304no—
439C3×C5#231611yescharacteristic, complemented, Hall
440C22×C3—22no—
441C22×C3—24no—
442C22×C3—22no—
443C22×C3—24no—
444C22×C3C2×#68314yes—
445C22×C3C22×Dic1011yescharacteristic
446C22×C3C22×C4×D511yescharacteristic
447C22×C3#414912yes—
448C22×C3#415012yes—
449C22×C3C22×C22⋊D511yescharacteristic
450C3×C4—42no—
451C3×C4—102no—
452C3×C4—102no—
453C3×C4—202no—
454Dic3—42no—
455Dic3—102no—
456Dic3—102no—
457Dic3—202no—
458Dic3C2×#68314yes—
459Dic3C2×#68314yes—
460C2×C5—24no—
461C2×C5#548611yescharacteristic
462C2×C5C2×D3×C4⋊C411yescharacteristic
463C2×C5#551611yescharacteristic
464C2×C5#559712yes—
465C2×C5#562312yes—
466C23—22no—
467C23—22no—
468C23D3×Dic1012yes—
469C23C4×D3×D512yes—
470C23D3×C22⋊D512yes—
471C23C22×D3×D511yescharacteristic
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—316no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—52no—
483C2×C4—52no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—152no—
493C2×C4—152no—
494C2×C4—204no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—604no—
501C2×C3—24no—
502C2×C3#6585011yescharacteristic
503C2×C3#6585312yes—
504C2×C3#6585511yescharacteristic
505C2×C3C22×#68311yescharacteristic
506C2×C3#6616712yes—
507C5#7386911yescharacteristic, complemented, Sylow
508C22—24no—
509C22—24no—
510C22—22no—
511C22—22no—
512C22D3×#68314yes—
513C22C2×D3×Dic1011yescharacteristic
514C22C2×C4×D3×D511yescharacteristic
515C22#9202012yes—
516C22#9202612yes—
517C22C2×D3×C22⋊D511yescharacteristic
518C4—34no—
519C4—34no—
520C4—42no—
521C4—102no—
522C4—102no—
523C4—122no—
524C4—202no—
525C4—302no—
526C4—302no—
527C4—602no—
528C3#1061396311yescharacteristic, complemented, Sylow
529C2—24no—
530C2#1175279712yes—
531C2#1175306611yescharacteristic
532C2#1175318711yescharacteristic
533C2C2×D3×#68311yescharacteristic
534C2#1175480412yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2316
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #11748820C2semidirect
9. #11748803C2semidirect
10. #11748664C2semidirect
11. #11748630C2semidirect
25. C2×Dic3⋊Dic5C4semidirect
143. C2×C5×Dic3C4⋊C4semidirect
378. C2×Dic3#683semidirect
439. C3×C5#2316semidirect
507. C5#73869semidirect
528. C3#10613963semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8772
C22×Dic3⋊Dic52
C2×#915292
#117510432
C3×#652312
#117495162
#117495062
#117488202
#117488032
#117486642
#117486302
#106139633
#738695