Finite Group Databasebeta

← #14328022

Subgroups — #14328022

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1203C211yesmaximal, characteristic
2#11750765C211yesmaximal, characteristic, complemented
3C5×#4664C211yesmaximal, characteristic, complemented
4C3×#64938C211yesmaximal, characteristic, complemented
5#11748908C212yesmaximal
6#11748719C211yesmaximal, characteristic, complemented
7#11748718C212yesmaximal, complemented
8#11748670C211yesmaximal, characteristic, complemented
9#11748666C212yesmaximal, complemented
10#11748638C212yesmaximal, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605792—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×#1203C2211yescharacteristic
16C2×#6714C2212yes—
17C2×C5×(C2×D3)⋊C4C2212yes—
18C2×C3×#683C2212yes—
19C2×C3×C4×Dic5C2212yes—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×#6668C2212yes—
22C2×#6668C2211yescharacteristic
23C2×#6667C2212yes—
24C2×#6667C2211yescharacteristic
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×(C2×D3)⋊Dic5C2211yescharacteristic
27C2×Dic3×Dic5C2212yes—
28C2×Dic3×Dic5C2212yes—
29C4×#1203C418yescomplemented
30C3×C5×#95C2211yescharacteristic
31#91115C2212yes—
32#91115C2211yescharacteristic
33C5×C3⋊#95C2212yes—
34C5×C3⋊#95C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36#90994C2212yes—
37#73645—51nomaximal, Hall
38C2×C4×C22⋊D5—31no—
39C5×#381—31no—
40C4×C22⋊Dic5—31no—
41#65246—32no—
42#65233—32no—
43#64958—32no—
44#64955—31no—
45#64953—31no—
46#64939—31no—
47#64938—32no—
48#64938D311yescharacteristic, complemented
49C23×D15C2311yescharacteristic
50C23×C5×D3C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C2×C4×D15—42no—
56C2×C4×D15C2×C414yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C2×C4×C5×D3—42no—
60C2×C4×C5×D3C2×C414yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2312yes—
63C22×C3×Dic5C2311yescharacteristic
64C2×#1203—22no—
65C2×#1203—22no—
66C2×#1203C2×C414yes—
67#6714—42no—
68C5×(C2×D3)⋊C4—42no—
69C3×#683—24no—
70C3×C4×Dic5—24no—
71C3×C4×Dic5C2×C414yes—
72#6668—24no—
73#6668C2×C414yes—
74#6667—24no—
75#6667C2×C414yes—
76(C2×D3)⋊Dic5—24no—
77(C2×D3)⋊Dic5C2×C414yes—
78Dic3×Dic5—42no—
79Dic3×Dic5—42no—
80C2×C4×D12—51no—
81C3×C4×C4⋊C4—51no—
82#4990—52no—
83#4990—52no—
84#4939—52no—
85#4936—51no—
86C4×C4⋊Dic3—52no—
87#4666—51no—
88#4666—51no—
89#4664—51no—
90#4664D511yescharacteristic, complemented
91C23×C4×C5—31no—
92C22×C22⋊D5—31no—
93C22×C4×D5—31no—
94C2×C5×C22⋊C4—32no—
95C2×C22⋊Dic5—31no—
96C2×C22⋊Dic5—32no—
97C4×C22⋊D5—38no—
98C2×#685—31no—
99C2×#685—32no—
100C2×#685—32no—
101C2×#683—31no—
102C2×#683—32no—
103C2×#683C2×D312yes—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D312yes—
107C2×C4×Dic5C2×D311yescharacteristic
108C5×#95—32no—
109C5×#95—31no—
110C5×#95C2×D311yescharacteristic
111#3963—32no—
112#3963—31no—
113#3963—32no—
114#3963C2×D311yescharacteristic
115#2357—151noSylow
116C23×C3×C5C2411yescharacteristic
117C22×D15—22no—
118C22×D15—21no—
119C22×D15—21no—
120C22×D15—22no—
121C22×D15C22×C412yes—
122C22×C5×D3—22no—
123C22×C5×D3—21no—
124C22×C5×D3—21no—
125C22×C5×D3—22no—
126C22×C5×D3C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C412yes—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15C22×C412yes—
137C4×D15—44no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3C22×C412yes—
143C4×C5×D3—44no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5#4114yes—
150C2×C3×Dic5#4112yes—
151C2×C3×Dic5#4112yes—
152#1203—28no—
153C22×D12—51no—
154C22×C4×D3—51no—
155C22×C4×D3C2×D511yescharacteristic
156C2×C3×C4⋊C4—52no—
157C2×C3×C42—51no—
158C2×C3×C42—52no—
159C2×(C2×D3)⋊C4—51no—
160C2×(C2×D3)⋊C4—51no—
161C2×(C2×D3)⋊C4—52no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4—52no—
164C2×(C2×D3)⋊C4C2×D512yes—
165C2×C4⋊Dic3—51no—
166C2×C4⋊Dic3—52no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—52no—
169C4×D12—58no—
170C3×#95—51no—
171C3×#95C2×D511yescharacteristic
172C3⋊#95—51no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95C2×D511yescharacteristic
176C3⋊#95C2×D512yes—
177C24×C5—31no—
178C23×D5—31no—
179C22×C4×C5—31no—
180C22×C4×C5—34no—
181C22×C4×C5—32no—
182C22×C4×C5—122no—
183C22×C4×C5C22×D312yes—
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—34no—
186C2×C22⋊D5—62no—
187C2×C22⋊D5—62no—
188C22×Dic5—31no—
189C22×Dic5—32no—
190C22×Dic5C22×D311yescharacteristic
191C22×Dic5C22×D312yes—
192C22×Dic5C22×D311yescharacteristic
193C2×C4×D5—34no—
194C2×C4×D5—122no—
195C5×C22⋊C4—122no—
196C22⋊Dic5—34no—
197C22⋊Dic5—64no—
198#685—34no—
199#685—64no—
200#685—122no—
201#683—24no—
202#683—34no—
203#683—64no—
204C4×Dic5—24no—
205C4×Dic5—122no—
206C4×Dic5—122no—
207C4×Dic5C4×D314yes—
208C2×C4×D4—151no—
209#390—152no—
210#388—152no—
211#388—152no—
212#382—151no—
213#381—31no—
214#381—151no—
215C4×C4⋊C4—51no—
216C4×C4⋊C4—152no—
217C4×C22⋊C4—151no—
218C4×C22⋊C4—151no—
219C22×C3×C5C23×C411yescharacteristic
220C22×C3×C5C2×#4112yes—
221C22×C3×C5C2×#4111yescharacteristic
222C22×C3×C5C2×#4111yescharacteristic
223C22×C3×C5H(5,𝔽2)12yes—
224C2×D15—22no—
225C2×D15—22no—
226C2×D15—22no—
227C2×D15—42no—
228C2×D15—42no—
229C2×C5×D3—22no—
230C2×C5×D3—22no—
231C2×C5×D3—22no—
232C2×C5×D3—42no—
233C2×C5×D3—42no—
234C3×C4×C5—22no—
235C3×C4×C5—42no—
236Dic15—22no—
237Dic15—42no—
238C3×Dic5—22no—
239C3×Dic5—24no—
240C3×Dic5#11714yes—
241C5×Dic3—22no—
242C5×Dic3—42no—
243C23×D3—51no—
244C23×D3C22×D511yescharacteristic
245C22×C3×C4—51no—
246C22×C3×C4—51no—
247C22×C3×C4—52no—
248C22×C3×C4C22×D512yes—
249C22×C3×C4C22×D511yescharacteristic
250C22×Dic3—51no—
251C22×Dic3—52no—
252C22×Dic3C22×D512yes—
253C22×Dic3C22×D511yescharacteristic
254C2×D12—54no—
255C2×D12—102no—
256C2×D12—102no—
257C2×C4×D3—42no—
258C2×C4×D3—54no—
259C2×C4×D3—202no—
260C2×C4×D3C4×D514yes—
261C3×C4⋊C4—104no—
262C3×C42—54no—
263C3×C42—104no—
264(C2×D3)⋊C4—42no—
265(C2×D3)⋊C4—54no—
266(C2×D3)⋊C4—54no—
267(C2×D3)⋊C4—104no—
268(C2×D3)⋊C4—104no—
269(C2×D3)⋊C4—202no—
270C4⋊Dic3—54no—
271C4⋊Dic3—104no—
272C4×Dic3—202no—
273C4×Dic3—202no—
274C23×C5—32no—
275C23×C5—62no—
276C23×C5—61no—
277C23×C5—61no—
278C23×C5—62no—
279C23×C5C23×D311yescharacteristic
280C22×D5—32no—
281C22×D5—62no—
282C22×D5—61no—
283C22×D5—61no—
284C22×D5—62no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—32no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—124no—
295C2×C4×C5C2×C4×D312yes—
296C22⋊D5—68no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—32no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5C2×C4×D312yes—
306C2×Dic5C2×C4×D312yes—
307C2×Dic5#23514yes—
308C2×Dic5#23712yes—
309C2×Dic5#23912yes—
310C4×D5—124no—
311C22×D4—151no—
312C23×C4—31no—
313C23×C4—151no—
314C4×D4—158no—
315C2×C4⋊C4—52no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—151no—
320C2×C22⋊C4—151no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C22⋊C4—152no—
324C2×C42—51no—
325C2×C42—52no—
326C2×C42—152no—
327C2×C42—152no—
328#95—31no—
329#95—32no—
330#95—51no—
331#95—152no—
332#95—151no—
333#95—152no—
334#95D3×D511yescharacteristic
335C2×C3×C5C2×#11711yescharacteristic
336C2×C3×C5C4×#4111yescharacteristic
337C2×C3×C5#51811yescharacteristic
338C2×C3×C5#55312yes—
339C2×C3×C5#55912yes—
340D15—42no—
341C5×D3—42no—
342C23×C3C23×D511yescharacteristic
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3—52no—
348C22×D3—102no—
349C22×D3—102no—
350C22×D3—101no—
351C22×D3—101no—
352C22×D3C2×C4×D512yes—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—52no—
358C2×C3×C4—52no—
359C2×C3×C4—52no—
360C2×C3×C4—52no—
361C2×C3×C4—54no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4C2×C4×D512yes—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—52no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3C2×C4×D512yes—
376D12—108no—
377C4×D3—44no—
378C4×D3—204no—
379C22×C5—62no—
380C22×C5—62no—
381C22×C5—62no—
382C22×C5—122no—
383C22×C5—122no—
384C22×C5C22×C4×D311yescharacteristic
385C22×C5C2×#23512yes—
386C22×C5C2×#23711yescharacteristic
387C22×C5C2×#23911yescharacteristic
388C22×C5#100912yes—
389C2×D5—62no—
390C2×D5—62no—
391C2×D5—62no—
392C2×D5—122no—
393C2×D5—122no—
394C4×C5—22no—
395C4×C5—42no—
396C4×C5—62no—
397C4×C5—122no—
398Dic5—22no—
399Dic5—24no—
400Dic5—62no—
401Dic5—122no—
402Dic5#89214yes—
403C24—31no—
404C24—151no—
405C2×D4—154no—
406C2×D4—302no—
407C2×D4—302no—
408C22×C4—31no—
409C22×C4—34no—
410C22×C4—32no—
411C22×C4—51no—
412C22×C4—52no—
413C22×C4—51no—
414C22×C4—122no—
415C22×C4—151no—
416C22×C4—154no—
417C22×C4—152no—
418C22×C4—602no—
419C22×C4C2×D3×D512yes—
420C22×C4C2×D3×D511yescharacteristic
421C4⋊C4—104no—
422C4⋊C4—154no—
423C4⋊C4—304no—
424C22⋊C4—122no—
425C22⋊C4—154no—
426C22⋊C4—154no—
427C22⋊C4—304no—
428C22⋊C4—304no—
429C22⋊C4—602no—
430C42—54no—
431C42—104no—
432C42—602no—
433C42—602no—
434C3×C5#235711yescharacteristic, complemented, Hall
435C22×C3C22×C4×D511yescharacteristic
436C22×C3#414412yes—
437C22×C3D5×#4112yes—
438C22×C3D5×#4111yescharacteristic
439C22×C3D5×#4111yescharacteristic
440C2×D3—22no—
441C2×D3—22no—
442C2×D3—22no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—102no—
446C2×D3—102no—
447C2×D3—102no—
448C2×D3—202no—
449C2×D3—202no—
450C3×C4—22no—
451C3×C4—42no—
452C3×C4—54no—
453C3×C4—102no—
454C3×C4—104no—
455Dic3—22no—
456Dic3—42no—
457Dic3—102no—
458Dic3—202no—
459C2×C5—122no—
460C2×C5C4×#23511yescharacteristic
461C2×C5C2×#89211yescharacteristic
462C2×C5#552111yescharacteristic
463C2×C5#556512yes—
464C2×C5#558512yes—
465D5—122no—
466C23—32no—
467C23—62no—
468C23—61no—
469C23—62no—
470C23—61no—
471C23—152no—
472C23—302no—
473C23—301no—
474C23—302no—
475C23—301no—
476C23C22×D3×D511yescharacteristic
477D4—308no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—32no—
483C2×C4—52no—
484C2×C4—52no—
485C2×C4—52no—
486C2×C4—52no—
487C2×C4—54no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—124no—
496C2×C4—152no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—604no—
502C2×C4C4×D3×D512yes—
503C2×C3#6582011yescharacteristic
504C2×C3D5×#11711yescharacteristic
505C2×C3#6585611yescharacteristic
506C2×C3#6599512yes—
507C2×C3#6599812yes—
508D3—42no—
509D3—202no—
510C5#7364511yescharacteristic, complemented, Sylow
511C22—62no—
512C22—62no—
513C22—62no—
514C22—122no—
515C22—122no—
516C22—302no—
517C22—302no—
518C22—302no—
519C22—602no—
520C22—602no—
521C22C2×C4×D3×D511yescharacteristic
522C22D5×#23512yes—
523C22D5×#23711yescharacteristic
524C22#9202712yes—
525C22D5×#23911yescharacteristic
526C4—22no—
527C4—42no—
528C4—54no—
529C4—62no—
530C4—104no—
531C4—102no—
532C4—122no—
533C4—302no—
534C4—602no—
535C3#1060579211yescharacteristic, complemented, Sylow
536C2—122no—
537C2—602no—
538C2#1175266511yescharacteristic
539C2#1175306711yescharacteristic
540C2#1175308812yes—
541C2#1175373012yes—
542C2D5×#89211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenter#95D3×D5
hypocenterC3×C5#2357
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750765C2semidirect
3. C5×#4664C2semidirect
4. C3×#64938C2semidirect
6. #11748719C2semidirect
7. #11748718C2semidirect
8. #11748670C2semidirect
9. #11748666C2semidirect
10. #11748638C2semidirect
11. #11748580C2semidirect
29. C4×#1203C4semidirect
48. #64938D3semidirect
90. #4664D5semidirect
434. C3×C5#2357semidirect
510. C5#73645semidirect
535. C3#10605792semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12032
#117507652
C5×#46642
C3×#649382
#117489082
#117487192
#117487182
#117486702
#117486662
#117486382
#117485802
#106057923
#736455