Finite Group Databasebeta

← #14328039

Subgroups — #14328039

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×#1202C211yesmaximal, characteristic
2#11750767C211yesmaximal, characteristic, complemented
3C5×#4649C211yesmaximal, characteristic, complemented
4C3×#64955C211yesmaximal, characteristic, complemented
5#11748912C212yesmaximal
6C4×Dic3⋊Dic5C212yesmaximal, complemented
7#11748737C211yesmaximal, characteristic, complemented
8#11748727C212yesmaximal, complemented
9#11748709C212yesmaximal, complemented
10#11748606C211yesmaximal, characteristic, complemented
11#11748600C211yesmaximal, characteristic, complemented
12#10605376—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1202C2211yescharacteristic
16C2×#6714C2212yes—
17C2×C4×Dic15C2212yes—
18C2×C5×Dic3⋊C4C2212yes—
19C2×C4×C5×Dic3C2212yes—
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C3×#685C2212yes—
22C2×C3×C4×Dic5C2212yes—
23C2×Dic3⋊Dic5C2212yes—
24C2×Dic3⋊Dic5C2211yescharacteristic
25C2×#6667C2212yes—
26C2×#6667C2211yescharacteristic
27C2×#6665C2212yes—
28C2×#6665C2211yescharacteristic
29C4×#1202C418yescomplemented
30C3×C5×#95C2211yescharacteristic
31#91115C2211yescharacteristic
32C5×C3⋊#95C2211yescharacteristic
33C3×#3963C2211yescharacteristic
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73463—51nomaximal, Hall
38C2×C4×D20—31no—
39C4×C5×C4⋊C4—31no—
40#65279—32no—
41#65279—32no—
42#65228—32no—
43#65225—31no—
44C4×C4⋊Dic5—32no—
45#64955—31no—
46#64955D311yescharacteristic, complemented
47#64953—31no—
48#64953—31no—
49C23×D15C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C2×C4×D15—42no—
56C2×C4×D15C2×C414yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5—42no—
63C2×C3×C4×D5C2×C414yes—
64C2×#1202—22no—
65C2×#1202—22no—
66C2×#1202C2×C414yes—
67#6714—24no—
68C4×Dic15—42no—
69C5×Dic3⋊C4—24no—
70C4×C5×Dic3—24no—
71C4×C5×Dic3C2×C414yes—
72C3×#685—24no—
73C3×C4×Dic5—42no—
74Dic3⋊Dic5—24no—
75Dic3⋊Dic5C2×C414yes—
76#6667—42no—
77#6667C2×C414yes—
78#6665—42no—
79#6665C2×C414yes—
80C2×C4×#67—51no—
81C3×C4×C22⋊C4—51no—
82#5211—51no—
83#4957—52no—
84#4945—52no—
85#4940—52no—
86C4×Dic3⋊C4—52no—
87#4666—51no—
88#4664—51no—
89#4650—51no—
90#4649D511yescharacteristic, complemented
91C22×D20—31no—
92C22×C4×D5—31no—
93C22×C4×D5C2×D311yescharacteristic
94C2×C5×C4⋊C4—32no—
95C2×C42×C5—31no—
96C2×C42×C5—32no—
97C2×#685—31no—
98C2×#685—31no—
99C2×#685—32no—
100C2×#685—32no—
101C2×#685—32no—
102C2×#685C2×D312yes—
103C2×C4⋊Dic5—31no—
104C2×C4⋊Dic5—32no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D312yes—
107C4×D20—38no—
108C5×#95—31no—
109C5×#95C2×D311yescharacteristic
110#3963—31no—
111#3963—32no—
112#3963—32no—
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×C3×D5—22no—
123C22×C3×D5—21no—
124C22×C3×D5—21no—
125C22×C3×D5—22no—
126C22×C3×D5C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5#4114yes—
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—
143C2×C5×Dic3C22×C412yes—
144C2×C5×Dic3#4112yes—
145C2×C5×Dic3#4112yes—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5C22×C412yes—
151C3×C4×D5—44no—
152#1202—28no—
153C23×C3×C4—51no—
154C22×#67—51no—
155C22×C4×D3—51no—
156C2×C3×C22⋊C4—52no—
157C2×C3×C42—52no—
158C2×#217—51no—
159C2×#217—52no—
160C4×#67—58no—
161C2×(C2×D3)⋊C4—51no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4—52no—
164C2×Dic3⋊C4—51no—
165C2×Dic3⋊C4—52no—
166C2×Dic3⋊C4C2×D512yes—
167C2×C4×Dic3—52no—
168C2×C4×Dic3C2×D512yes—
169C2×C4×Dic3C2×D511yescharacteristic
170C3×#95—51no—
171C3×#95C2×D511yescharacteristic
172C3⋊#95—51no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95C2×D511yescharacteristic
177C23×D5—31no—
178C23×D5C22×D311yescharacteristic
179C22×C4×C5—31no—
180C22×C4×C5—31no—
181C22×C4×C5—32no—
182C22×C4×C5C22×D311yescharacteristic
183C22×C4×C5C22×D312yes—
184C22×Dic5—31no—
185C22×Dic5—32no—
186C22×Dic5C22×D312yes—
187C22×Dic5C22×D311yescharacteristic
188C2×D20—34no—
189C2×D20—62no—
190C2×D20—62no—
191C2×C4×D5—34no—
192C2×C4×D5—42no—
193C2×C4×D5—122no—
194C2×C4×D5C4×D314yes—
195C5×C4⋊C4—64no—
196C42×C5—34no—
197C42×C5—64no—
198#685—24no—
199#685—34no—
200#685—34no—
201#685—64no—
202#685—122no—
203#685—122no—
204C4⋊Dic5—34no—
205C4⋊Dic5—64no—
206C4×Dic5—42no—
207C4×Dic5—122no—
208C2×C4×D4—151no—
209#390—152no—
210#388—152no—
211#388—152no—
212#382—151no—
213#381—151no—
214#381—151no—
215C4×C4⋊C4—31no—
216C4×C4⋊C4—152no—
217C4×C22⋊C4—51no—
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×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—42no—
233C2×C3×D5—42no—
234C3×C4×C5—22no—
235C3×C4×C5—24no—
236Dic15—22no—
237Dic15—42no—
238C3×Dic5—22no—
239C3×Dic5—42no—
240C5×Dic3—22no—
241C5×Dic3—42no—
242C5×Dic3#11714yes—
243C24×C3—51no—
244C23×D3—51no—
245C22×C3×C4—51no—
246C22×C3×C4—54no—
247C22×C3×C4—52no—
248C22×C3×C4—202no—
249C22×C3×C4C22×D511yescharacteristic
250C22×C3×C4C22×D512yes—
251C2×#67—54no—
252C2×#67—102no—
253C2×#67—102no—
254C22×Dic3—51no—
255C22×Dic3—52no—
256C22×Dic3C22×D512yes—
257C22×Dic3C22×D511yescharacteristic
258C22×Dic3C22×D511yescharacteristic
259C2×C4×D3—54no—
260C2×C4×D3—202no—
261C3×C22⋊C4—104no—
262C3×C42—202no—
263#217—54no—
264#217—202no—
265(C2×D3)⋊C4—54no—
266(C2×D3)⋊C4—104no—
267(C2×D3)⋊C4—202no—
268Dic3⋊C4—24no—
269Dic3⋊C4—54no—
270Dic3⋊C4—104no—
271C4×Dic3—24no—
272C4×Dic3—202no—
273C4×Dic3C4×D514yes—
274C23×C5C23×D311yescharacteristic
275C22×D5—22no—
276C22×D5—22no—
277C22×D5—21no—
278C22×D5—21no—
279C22×D5—32no—
280C22×D5—62no—
281C22×D5—62no—
282C22×D5—61no—
283C22×D5—61no—
284C22×D5C2×C4×D312yes—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—32no—
289C2×C4×C5—32no—
290C2×C4×C5—32no—
291C2×C4×C5—32no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5C2×C4×D312yes—
297C2×C4×C5#23514yes—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—32no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5C2×C4×D312yes—
308D20—68no—
309C4×D5—44no—
310C4×D5—124no—
311C22×D4—151no—
312C23×C4—51no—
313C23×C4—151no—
314C4×D4—158no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—52no—
319C2×C22⋊C4—151no—
320C2×C22⋊C4—151no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C22⋊C4—152no—
324C2×C42—31no—
325C2×C42—32no—
326C2×C42—52no—
327C2×C42—152no—
328#95—31no—
329#95—51no—
330#95—152no—
331#95—152no—
332#95—152no—
333#95—151no—
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—
341C3×D5—42no—
342C23×C3—52no—
343C23×C3—102no—
344C23×C3—101no—
345C23×C3—101no—
346C23×C3—102no—
347C23×C3C23×D511yescharacteristic
348C22×D3—52no—
349C22×D3—102no—
350C22×D3—101no—
351C22×D3—101no—
352C22×D3—102no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—52no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—204no—
362C2×C3×C4C2×C4×D512yes—
363C2×C3×C4#70914yes—
364#67—108no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—52no—
370C2×Dic3—102no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3C2×C4×D512yes—
375C2×Dic3C2×C4×D512yes—
376C2×Dic3#71112yes—
377C2×Dic3#71312yes—
378C4×D3—204no—
379C22×C5C22×C4×D311yescharacteristic
380C22×C5C2×#23512yes—
381C22×C5#100412yes—
382C22×C5D3×#4111yescharacteristic
383C22×C5D3×#4111yescharacteristic
384C2×D5—22no—
385C2×D5—22no—
386C2×D5—22no—
387C2×D5—42no—
388C2×D5—42no—
389C2×D5—62no—
390C2×D5—62no—
391C2×D5—62no—
392C2×D5—122no—
393C2×D5—122no—
394C4×C5—22no—
395C4×C5—24no—
396C4×C5—34no—
397C4×C5—62no—
398C4×C5—122no—
399Dic5—22no—
400Dic5—42no—
401Dic5—62no—
402Dic5—122no—
403C24—51no—
404C24—151no—
405C2×D4—154no—
406C2×D4—302no—
407C2×D4—302no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—32no—
411C22×C4—51no—
412C22×C4—54no—
413C22×C4—52no—
414C22×C4—151no—
415C22×C4—154no—
416C22×C4—152no—
417C22×C4—202no—
418C22×C4—602no—
419C22×C4C2×D3×D512yes—
420C22×C4C2×D3×D511yescharacteristic
421C4⋊C4—64no—
422C4⋊C4—154no—
423C4⋊C4—304no—
424C22⋊C4—104no—
425C22⋊C4—154no—
426C22⋊C4—154no—
427C22⋊C4—304no—
428C22⋊C4—602no—
429C22⋊C4—602no—
430C42—34no—
431C42—64no—
432C42—202no—
433C42—602no—
434C3×C5#235711yescharacteristic, complemented, Hall
435C22×C3—102no—
436C22×C3—102no—
437C22×C3—102no—
438C22×C3—202no—
439C22×C3—202no—
440C22×C3C22×C4×D511yescharacteristic
441C22×C3C2×#70912yes—
442C22×C3C2×#71111yescharacteristic
443C22×C3C2×#71311yescharacteristic
444C22×C3#414912yes—
445C2×D3—102no—
446C2×D3—102no—
447C2×D3—102no—
448C2×D3—202no—
449C2×D3—202no—
450C3×C4—22no—
451C3×C4—24no—
452C3×C4—102no—
453C3×C4—202no—
454Dic3—22no—
455Dic3—42no—
456Dic3—102no—
457Dic3—202no—
458Dic3#403814yes—
459C2×C5C4×#23511yescharacteristic
460C2×C5#548611yescharacteristic
461C2×C5D3×#11711yescharacteristic
462C2×C5#554012yes—
463C2×C5#555912yes—
464D5—42no—
465D5—122no—
466C23—52no—
467C23—102no—
468C23—101no—
469C23—102no—
470C23—101no—
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—32no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—52no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—152no—
495C2×C4—204no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—604no—
501C2×C4#677114yes—
502C2×C4C4×D3×D512yes—
503C2×C3—202no—
504C2×C3C4×#70911yescharacteristic
505C2×C3C2×#403811yescharacteristic
506C2×C3#6585511yescharacteristic
507C2×C3#6589912yes—
508C2×C3#6591912yes—
509D3—202no—
510C5#7346311yescharacteristic, complemented, Sylow
511C22—102no—
512C22—102no—
513C22—102no—
514C22—202no—
515C22—202no—
516C22—302no—
517C22—302no—
518C22—302no—
519C22—602no—
520C22—602no—
521C22C2×#677112yes—
522C22C2×C4×D3×D511yescharacteristic
523C22D3×#71111yescharacteristic
524C22#9202612yes—
525C22D3×#71311yescharacteristic
526C4—22no—
527C4—24no—
528C4—34no—
529C4—62no—
530C4—102no—
531C4—122no—
532C4—202no—
533C4—302no—
534C4—602no—
535C3#1060537611yescharacteristic, complemented, Sylow
536C2—202no—
537C2—602no—
538C2C4×#677111yescharacteristic
539C2#1175306611yescharacteristic
540C2#1175314012yes—
541C2#1175378112yes—
542C2D3×#403811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
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. #11750767C2semidirect
3. C5×#4649C2semidirect
4. C3×#64955C2semidirect
6. C4×Dic3⋊Dic5C2semidirect
7. #11748737C2semidirect
8. #11748727C2semidirect
9. #11748709C2semidirect
10. #11748606C2semidirect
11. #11748600C2semidirect
29. C4×#1202C4semidirect
46. #64955D3semidirect
90. #4649D5semidirect
434. C3×C5#2357semidirect
510. C5#73463semidirect
535. C3#10605376semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12022
#117507672
C5×#46492
C3×#649552
#117489122
C4×Dic3⋊Dic52
#117487372
#117487272
#117487092
#117486062
#117486002
#106053763
#734635