Finite Group Databasebeta

← #14323026

Subgroups — #14323026

Order 1920.

1136 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#11750767C211yesmaximal, characteristic, complemented
3C5×#4664C211yesmaximal, characteristic, complemented
4C3×#64940C211yesmaximal, characteristic, complemented
5#11748919C212yesmaximal
6#11748895C212yesmaximal, complemented
7#11748888C211yesmaximal, characteristic, complemented
8#11748810C212yesmaximal, complemented
9#11748782C211yesmaximal, characteristic, complemented
10#11748724C212yesmaximal, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605851—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×#1203C2211yescharacteristic
16C22×#1200C2212yes—
17C2×#6714C2212yes—
18C2×C4×Dic15C2212yes—
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×Dic3⋊Dic5C2212yes—
22C2×#6668C2212yes—
23C2×#6668C2211yescharacteristic
24C2×#6667C2211yescharacteristic
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×(C2×D3)⋊Dic5C2211yescharacteristic
27C4×#1203C418yescomplemented
28C3×C5×#95C2211yescharacteristic
29#91115C2211yescharacteristic
30C5×C3⋊#95C2211yescharacteristic
31C5×C3⋊#95C2212yes—
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#74295—51nomaximal, Hall
38C2×C4×C22⋊D5—31no—
39C5×#381—31no—
40#65501—31no—
41#65245—32no—
42#65233—32no—
43#64957—32no—
44#64955—31no—
45D5×#95—31no—
46#64944—32no—
47#64940D311yescharacteristic, complemented
48#64939—31no—
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×C414yescomplemented
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C2×#1203—24no—
65C2×#1203C2×C414yes—
66C2×#1200—24no—
67C2×#1200—42no—
68C2×#1200—42no—
69#6714—24no—
70C4×Dic15—42no—
71C5×(C2×D3)⋊C4—42no—
72C3×C4×Dic5C2×C414yescomplemented
73Dic3⋊Dic5—42no—
74#6668—42no—
75#6668C2×C414yescomplemented
76#6667C2×C414yes—
77(C2×D3)⋊Dic5—42no—
78(C2×D3)⋊Dic5C2×C414yescomplemented
79C2×C4×D12—51no—
80C3×#383—51no—
81#4936—51no—
82#4670—52no—
83#4668—52no—
84#4667—51no—
85#4666—51no—
86#4665—52no—
87#4664D511yescharacteristic, complemented
88D3×#95—51no—
89#4654—52no—
90C23×C4×C5—31no—
91C22×C22⋊D5—31no—
92C22×C4×D5—31no—
93C22×C4×D5—32no—
94C2×C5×C22⋊C4—32no—
95C2×C22⋊Dic5—31no—
96C2×C22⋊Dic5—32no—
97C4×C22⋊D5—38no—
98C2×#685—31no—
99C2×#685—32no—
100C2×C4⋊Dic5—32no—
101C2×#683—31no—
102C2×#683—32no—
103C2×C4×Dic5—32no—
104C2×C4×Dic5C2×D311yescharacteristic
105C5×#95—31no—
106C5×#95—32no—
107C5×#95C2×D311yescharacteristic
108#3963—31no—
109#3963—32no—
110#3963—32no—
111#3963C2×D312yes—
112#3963C2×D311yescharacteristic
113#3963C2×D312yes—
114#2318—151noSylow
115C23×C3×C5C2411yescharacteristic
116C22×D15—21no—
117C22×D15—22no—
118C22×D15—21no—
119C22×D15C22×C412yes—
120C22×D15#4114yes—
121C22×C5×D3—22no—
122C22×C5×D3—21no—
123C22×C5×D3—22no—
124C22×C5×D3—21no—
125C22×C5×D3C22×C412yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15C22×C412yes—
136C4×D15—44no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3C22×C412yes—
142C4×C5×D3—44no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C22×C412yes—
151#1203—28no—
152#1200—48no—
153C22×D12—51no—
154C22×C4×D3—51no—
155C22×C4×D3—52no—
156C22×C4×D3C2×D511yescharacteristic
157C2×C3×C42—51no—
158C2×(C2×D3)⋊C4—51no—
159C2×(C2×D3)⋊C4—51no—
160C2×(C2×D3)⋊C4—52no—
161C2×(C2×D3)⋊C4—52no—
162C2×(C2×D3)⋊C4C2×D512yes—
163C2×C4⋊Dic3—51no—
164C2×C4⋊Dic3—52no—
165C2×Dic3⋊C4—52no—
166C2×C4×Dic3—52no—
167C4×D12—58no—
168C3×#95—52no—
169C3×#95—51no—
170C3×#95—52no—
171C3×#95C2×D511yescharacteristic
172C3⋊#95—51no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95C2×D512yes—
176C3⋊#95C2×D511yescharacteristic
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—64no—
187C22×Dic5—31no—
188C22×Dic5—32no—
189C22×Dic5C22×D312yes—
190C22×Dic5C22×D311yescharacteristic
191C22×Dic5C22×D311yescharacteristic
192C2×C4×D5—34no—
193C2×C4×D5—64no—
194C2×C4×D5—122no—
195C2×C4×D5—122no—
196C2×C4×D5—122no—
197C5×C22⋊C4—122no—
198C22⋊Dic5—34no—
199C22⋊Dic5—122no—
200#685—34no—
201#685—64no—
202C4⋊Dic5—122no—
203#683—34no—
204#683—122no—
205C4×Dic5—122no—
206C4×Dic5C4×D314yescomplemented
207C2×C4×D4—151no—
208#388—152no—
209#387—152no—
210#386—152no—
211#385—152no—
212#383—51no—
213#382—151no—
214#381—31no—
215#380—151no—
216C4×C22⋊C4—151no—
217C2×#95—151no—
218C22×C3×C5C23×C411yescharacteristic
219C22×C3×C5C2×#4112yes—
220C22×C3×C5H(5,𝔽2)12yes—
221C22×C3×C5H(5,𝔽2)11yescharacteristic
222C22×C3×C52−1+411yescharacteristic
223C2×D15—22no—
224C2×D15—22no—
225C2×D15—24no—
226C2×D15—24no—
227C2×D15#11714yes—
228C2×C5×D3—22no—
229C2×C5×D3—22no—
230C2×C5×D3—22no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—22no—
234C3×C4×C5—42no—
235Dic15—22no—
236Dic15—42no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C3×Dic5—42no—
240C5×Dic3—22no—
241C5×Dic3—42no—
242C23×D3—51no—
243C23×D3C22×D511yescharacteristic
244C22×C3×C4—51no—
245C22×C3×C4—51no—
246C22×C3×C4—52no—
247C22×C3×C4C22×D512yes—
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—51no—
250C22×Dic3—52no—
251C22×Dic3C22×D512yes—
252C22×Dic3C22×D511yescharacteristic
253C2×D12—54no—
254C2×D12—104no—
255C2×C4×D3—42no—
256C2×C4×D3—54no—
257C2×C4×D3—104no—
258C2×C4×D3—202no—
259C2×C4×D3—202no—
260C2×C4×D3—202no—
261C2×C4×D3C4×D514yescomplemented
262C3×C42—54no—
263(C2×D3)⋊C4—42no—
264(C2×D3)⋊C4—54no—
265(C2×D3)⋊C4—54no—
266(C2×D3)⋊C4—104no—
267(C2×D3)⋊C4—202no—
268C4⋊Dic3—54no—
269C4⋊Dic3—202no—
270Dic3⋊C4—202no—
271C4×Dic3—202no—
272C23×C5—32no—
273C23×C5—62no—
274C23×C5—61no—
275C23×C5—62no—
276C23×C5—61no—
277C23×C5C23×D311yescharacteristic
278C22×D5—32no—
279C22×D5—34no—
280C22×D5—62no—
281C22×D5—61no—
282C22×D5—61no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—32no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—124no—
293C2×C4×C5C2×C4×D312yes—
294C22⋊D5—68no—
295C2×Dic5—22no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—32no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5C2×C4×D312yes—
307C2×Dic5C2×C4×D312yes—
308C4×D5—128no—
309C4×D5—124no—
310C22×D4—151no—
311C23×C4—31no—
312C23×C4—152no—
313C23×C4—151no—
314C4×D4—158no—
315C2×C4⋊C4—151no—
316C2×C4⋊C4—152no—
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×C42—51no—
324C2×C42—152no—
325#95—31no—
326#95—32no—
327#95—51no—
328#95—52no—
329#95—52no—
330#95—152no—
331#95—152no—
332#95—151no—
333#95D3×D511yescharacteristic
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#51811yescharacteristic
336C2×C3×C5#52011yescharacteristic
337C2×C3×C5#53812yes—
338C2×C3×C5#53912yes—
339D15—24no—
340C5×D3—42no—
341C23×C3C23×D511yescharacteristic
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—52no—
347C22×D3—54no—
348C22×D3—102no—
349C22×D3—101no—
350C22×D3—101no—
351C22×D3C2×C4×D512yes—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—52no—
357C2×C3×C4—52no—
358C2×C3×C4—102no—
359C2×C3×C4—101no—
360C2×C3×C4—101no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4C2×C4×D512yes—
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—
375D12—108no—
376C4×D3—44no—
377C4×D3—208no—
378C4×D3—204no—
379C22×C5—62no—
380C22×C5—62no—
381C22×C5—62no—
382C22×C5—122no—
383C22×C5—122no—
384C22×C5C22×C4×D311yescharacteristic
385C22×C5D3×#4112yes—
386C22×C5#100912yes—
387C22×C5#100911yescharacteristic
388C22×C5#101011yescharacteristic
389C2×D5—34no—
390C2×D5—64no—
391C2×D5—64no—
392C2×D5—62no—
393C2×D5—62no—
394C4×C5—22no—
395C4×C5—42no—
396C4×C5—62no—
397C4×C5—122no—
398Dic5—22no—
399Dic5—22no—
400Dic5—42no—
401Dic5—62no—
402Dic5—122no—
403C24—31no—
404C24—151no—
405C2×D4—154no—
406C2×D4—304no—
407C22×C4—31no—
408C22×C4—34no—
409C22×C4—32no—
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—52no—
413C22×C4—122no—
414C22×C4—151no—
415C22×C4—154no—
416C22×C4—152no—
417C22×C4—304no—
418C22×C4—602no—
419C22×C4—602no—
420C22×C4—602no—
421C22×C4C2×D3×D512yes—
422C22×C4C2×D3×D511yescharacteristic
423C4⋊C4—154no—
424C4⋊C4—602no—
425C4⋊C4—602no—
426C22⋊C4—122no—
427C22⋊C4—154no—
428C22⋊C4—154no—
429C22⋊C4—304no—
430C22⋊C4—602no—
431C42—54no—
432C42—602no—
433C3×C5#231811yescharacteristic, complemented, Hall
434C22×C3C22×C4×D511yescharacteristic
435C22×C3#414412yes—
436C22×C3D5×#4112yes—
437C22×C3#414911yescharacteristic
438C22×C3#415011yescharacteristic
439C2×D3—22no—
440C2×D3—22no—
441C2×D3—22no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—54no—
445C2×D3—102no—
446C2×D3—102no—
447C2×D3—104no—
448C2×D3—104no—
449C3×C4—22no—
450C3×C4—42no—
451C3×C4—102no—
452C3×C4—102no—
453C3×C4—202no—
454Dic3—22no—
455Dic3—42no—
456Dic3—102no—
457Dic3—202no—
458C2×C5—122no—
459C2×C5D3×#11711yescharacteristic
460C2×C5#552111yescharacteristic
461C2×C5#552311yescharacteristic
462C2×C5#570412yes—
463C2×C5#570712yes—
464D5—64no—
465C23—32no—
466C23—62no—
467C23—61no—
468C23—62no—
469C23—61no—
470C23—152no—
471C23—154no—
472C23—301no—
473C23—302no—
474C23—301no—
475C23C22×D3×D511yescharacteristic
476D4—308no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—52no—
483C2×C4—52no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—102no—
489C2×C4—101no—
490C2×C4—101no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—124no—
495C2×C4—152no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—604no—
501C2×C4—608no—
502C2×C4C4×D3×D512yes—
503C2×C3#6582011yescharacteristic
504C2×C3D5×#11711yescharacteristic
505C2×C3#6585711yescharacteristic
506C2×C3#6599112yes—
507C2×C3#6599412yes—
508D3—42no—
509D3—104no—
510C5#7429511yescharacteristic, complemented, Sylow
511C22—62no—
512C22—62no—
513C22—62no—
514C22—122no—
515C22—122no—
516C22—154no—
517C22—304no—
518C22—302no—
519C22—302no—
520C22—304no—
521C22C2×C4×D3×D511yescharacteristic
522C22#9201612yes—
523C22#9202011yescharacteristic
524C22#9202712yes—
525C22#9203511yescharacteristic
526C4—22no—
527C4—42no—
528C4—62no—
529C4—102no—
530C4—102no—
531C4—122no—
532C4—202no—
533C4—302no—
534C4—602no—
535C3#1060585111yescharacteristic, complemented, Sylow
536C2—122no—
537C2—304no—
538C2#1175272311yescharacteristic
539C2#1175302012yes—
540C2#1175306711yescharacteristic
541C2#1175367011yescharacteristic
542C2#1175393212yes—
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#2318
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×#4664C2semidirect
4. C3×#64940C2semidirect
6. #11748895C2semidirect
7. #11748888C2semidirect
8. #11748810C2semidirect
9. #11748782C2semidirect
10. #11748724C2semidirect
11. #11748580C2semidirect
27. C4×#1203C4semidirect
47. #64940D3semidirect
60. C2×C4×C5×D3C2×C4semidirect
72. C3×C4×Dic5C2×C4semidirect
75. #6668C2×C4semidirect
78. (C2×D3)⋊Dic5C2×C4semidirect
87. #4664D5semidirect
206. C4×Dic5C4×D3semidirect
261. C2×C4×D3C4×D5semidirect
433. C3×C5#2318semidirect
510. C5#74295semidirect
535. C3#10605851semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12032
#117507672
C5×#46642
C3×#649402
#117489192
#117488952
#117488882
#117488102
#117487822
#117487242
#117485802
#106058513
#742955