Finite Group Databasebeta

← #14321130

Subgroups — #14321130

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#872C211yesmaximal, characteristic
2C2×C4×D3×Dic5C211yesmaximal, characteristic
3C2×#91371C211yesmaximal, characteristic
4C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
5C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
6#11748903C212yesmaximal
7#11748897C212yesmaximal
8C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
9C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
10#11748693C212yesmaximal, complemented
11#11748677C212yesmaximal, complemented
12#10613958—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×C4⋊Dic15C2212yes—
17C2×C4×Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2211yescharacteristic
21C2×C5×Dic3⋊C4C2211yescharacteristic
22C2×C5×Dic3⋊C4C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C5×#872C418yescomplemented
25C2×C3×C4⋊Dic5C2212yes—
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5C2212yes—
29C2×Dic3⋊Dic5C2212yes—
30C2×Dic3⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33C4×D3×Dic5—24no—
34#91371—24no—
35#91115C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73755—51nomaximal, Hall
40C2×C5×#117—31no—
41C2×#4072—31no—
42C22×C4×Dic5—31no—
43#65274—32no—
44#65274—32no—
45#65239—32no—
46#65239—32no—
47C4×C4⋊Dic5—31no—
48C4×C4⋊Dic5—31no—
49C4×C4⋊Dic5—31no—
50C4×C4⋊Dic5D311yescharacteristic, complemented
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3C2×C414yes—
61C2×C4×C5×D3D414yes—
62C2×C4×C5×D3Q814yes—
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2312yes—
65C2×D3×Dic5—24no—
66C2×D3×Dic5—24no—
67C2×D3×Dic5—24no—
68C3×C42×C5C2×C414yescomplemented
69C4⋊Dic15—24no—
70C4×Dic15—22no—
71C4×Dic15—22no—
72C5×(C2×D3)⋊C4C2×C414yes—
73C5×(C2×D3)⋊C4C2×C414yes—
74C5×Dic3⋊C4C2×C414yescomplemented
75C5×Dic3⋊C4C2×C414yescomplemented
76C4×C5×Dic3C2×C414yescomplemented
77C3×C4⋊Dic5—24no—
78C3×C4×Dic5—22no—
79C3×C4×Dic5—22no—
80Dic3⋊Dic5—24no—
81Dic3⋊Dic5—24no—
82Dic3⋊Dic5—24no—
83(C2×D3)⋊Dic5—24no—
84Dic3×Dic5—24no—
85C2×#872—51no—
86C2×#872D511yescharacteristic
87C2×C42×D3—51no—
88C3×C4×C4⋊C4—51no—
89#4989—52no—
90#4976—52no—
91C4×C4⋊Dic3—51no—
92C4×Dic3⋊C4—51no—
93C4×Dic3⋊C4—51no—
94#4668—52no—
95#4647—52no—
96C23×C4×C5—31no—
97C23×Dic5—32no—
98C5×#117—38no—
99C2×C5×C4⋊C4—31no—
100C2×C5×C4⋊C4—31no—
101C2×C5×C22⋊C4—31no—
102C2×C5×C22⋊C4—31no—
103C2×C42×C5—31no—
104C2×C42×C5C2×D311yescharacteristic
105C2×C22⋊Dic5—32no—
106#4072—64no—
107C2×C4⋊Dic5—32no—
108C2×C4⋊Dic5—32no—
109C2×C4⋊Dic5—32no—
110C2×C4⋊Dic5—32no—
111C2×C4⋊Dic5C2×D312yes—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—64no—
116C2×C4×Dic5C2×D311yescharacteristic
117C2×C4×Dic5C2×D311yescharacteristic
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#3963C2×D312yes—
122#2296—151noSylow
123C23×C3×C5C2411yescharacteristic
124C22×C5×D3—22no—
125C22×C5×D3—22no—
126C22×C5×D3C22×C412yes—
127C22×C5×D3C2×D412yes—
128C22×C5×D3C2×Q812yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×Q812yes—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15#4114yes—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C412yes—
146C2×C5×Dic3C22×C412yes—
147C2×C5×Dic3C2×D412yes—
148C2×C5×Dic3C2×Q812yes—
149C4×C5×D3C4⋊C4116yescomplemented
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5#4114yes—
156D3×Dic5—216no—
157C22×C4×D3—52no—
158C22×C4×D3C2×D511yescharacteristic
159C2×C3×C4⋊C4—52no—
160C2×C3×C42—51no—
161C2×C3×C42—51no—
162C2×C3×C42C2×D511yescharacteristic
163C2×(C2×D3)⋊C4—52no—
164C2×(C2×D3)⋊C4C2×D511yescharacteristic
165C2×(C2×D3)⋊C4C2×D511yescharacteristic
166C2×C4⋊Dic3—52no—
167C2×Dic3⋊C4—52no—
168C2×Dic3⋊C4—52no—
169C2×Dic3⋊C4—52no—
170C2×Dic3⋊C4C2×D511yescharacteristic
171C2×Dic3⋊C4C2×D511yescharacteristic
172C2×C4×Dic3—51no—
173C2×C4×Dic3—51no—
174C2×C4×Dic3—52no—
175C2×C4×Dic3C2×D511yescharacteristic
176#872—104no—
177#872Dic518yescomplemented
178C42×D3—104no—
179C3×#95—52no—
180C3⋊#95—52no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C24×C5—31no—
184C22×C4×C5—31no—
185C22×C4×C5—34no—
186C22×C4×C5—34no—
187C22×C4×C5—34no—
188C22×C4×C5—31no—
189C22×C4×C5—31no—
190C22×C4×C5C22×D311yescharacteristic
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—32no—
194C22×Dic5—32no—
195C22×Dic5—64no—
196C22×Dic5—64no—
197C22×Dic5—64no—
198C22×Dic5C22×D312yes—
199C22×Dic5C22×D312yes—
200C5×C4⋊C4—34no—
201C5×C4⋊C4—34no—
202C5×C22⋊C4—34no—
203C5×C22⋊C4—34no—
204C42×C5—34no—
205C42×C5C4×D314yescomplemented
206C22⋊Dic5—64no—
207C4⋊Dic5—24no—
208C4⋊Dic5—64no—
209C4⋊Dic5—64no—
210C4⋊Dic5—64no—
211C4⋊Dic5—64no—
212C4×Dic5—22no—
213C4×Dic5—22no—
214C4×Dic5—64no—
215C4×Dic5—62no—
216C4×Dic5—62no—
217C2×#117—31no—
218C2×#117—151no—
219C22×C42—151no—
220#389—152no—
221#389—152no—
222#385—152no—
223#385—152no—
224C4×C4⋊C4—51no—
225C4×C4⋊C4—151no—
226C4×C4⋊C4—151no—
227C4×C4⋊C4—151no—
228C22×C3×C5C23×C411yescharacteristic
229C22×C3×C5C22×D411yescharacteristic
230C22×C3×C5C22×Q811yescharacteristic
231C22×C3×C5C2×#4112yes—
232C22×C3×C5C2×#4112yes—
233C2×C5×D3—22no—
234C2×C5×D3—22no—
235C2×C5×D3—24no—
236C2×C5×D3—24no—
237C2×C5×D3C2×C4⋊C414yes—
238C3×C4×C5—22no—
239C3×C4×C5—22no—
240C3×C4×C5C2×C4⋊C414yes—
241Dic15—24no—
242Dic15—42no—
243C3×Dic5—24no—
244C3×Dic5—42no—
245C5×Dic3—22no—
246C5×Dic3—22no—
247C5×Dic3C2×C4⋊C414yes—
248C23×D3C22×D511yescharacteristic
249C22×C3×C4—52no—
250C22×C3×C4—52no—
251C22×C3×C4C22×D511yescharacteristic
252C22×C3×C4C22×D511yescharacteristic
253C22×C3×C4C22×D511yescharacteristic
254C22×Dic3—52no—
255C22×Dic3—52no—
256C22×Dic3C22×D511yescharacteristic
257C22×Dic3C22×D511yescharacteristic
258C22×Dic3C22×D511yescharacteristic
259C2×C4×D3—104no—
260C2×C4×D3—104no—
261C2×C4×D3—104no—
262C2×C4×D3Dic1014yes—
263C2×C4×D3D2014yes—
264C2×C4×D3C2×Dic514yes—
265C3×C4⋊C4—104no—
266C3×C42—102no—
267C3×C42—102no—
268C3×C42C2×Dic514yescomplemented
269(C2×D3)⋊C4—104no—
270(C2×D3)⋊C4C2×Dic514yes—
271(C2×D3)⋊C4C2×Dic514yes—
272C4⋊Dic3—104no—
273Dic3⋊C4—104no—
274Dic3⋊C4—104no—
275Dic3⋊C4—104no—
276Dic3⋊C4C2×Dic514yescomplemented
277Dic3⋊C4C2×Dic514yescomplemented
278C4×Dic3—102no—
279C4×Dic3—102no—
280C4×Dic3—104no—
281C4×Dic3C2×Dic514yescomplemented
282C23×C5—32no—
283C23×C5—32no—
284C23×C5—32no—
285C23×C5—62no—
286C23×C5—62no—
287C23×C5C23×D311yescharacteristic
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—32no—
291C2×C4×C5—32no—
292C2×C4×C5—32no—
293C2×C4×C5—316no—
294C2×C4×C5—32no—
295C2×C4×C5—32no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5C2×C4×D312yes—
299C2×C4×C5C2×C4×D312yes—
300C2×C4×C5C2×C4×D312yes—
301C2×C4×C5D3×D412yes—
302C2×C4×C5D3×Q812yes—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—34no—
309C2×Dic5—616no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5—62no—
314C2×Dic5—62no—
315C2×Dic5#23514yes—
316C23×C4—31no—
317C23×C4—152no—
318#117—38no—
319#117—304no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—52no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4—152no—
325C2×C4⋊C4—152no—
326C2×C4⋊C4—152no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—152no—
330C2×C42—31no—
331C2×C42—51no—
332C2×C42—51no—
333C2×C42—152no—
334C2×C42—151no—
335C2×C42—151no—
336C2×C42—304no—
337C2×C42D3×D511yescharacteristic
338#95—52no—
339#95—152no—
340#95—152no—
341#95—152no—
342C2×C3×C5C22×C4⋊C411yescharacteristic
343C2×C3×C5C4×#4111yescharacteristic
344C2×C3×C5C4×#4111yescharacteristic
345C2×C3×C5#52512yes—
346C2×C3×C5#53312yes—
347C5×D3—24no—
348C23×C3C23×D511yescharacteristic
349C22×D3—22no—
350C22×D3—22no—
351C22×D3C2×Dic1012yes—
352C22×D3C2×D2012yes—
353C22×D3C22×Dic512yes—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—54no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4C2×Dic1012yes—
363C2×C3×C4C2×D2012yes—
364C2×C3×C4C22×Dic512yes—
365C2×C3×C4C22×Dic512yes—
366C2×C3×C4C22×Dic512yes—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—54no—
370C2×Dic3—102no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3C2×Dic1012yes—
376C2×Dic3C2×D2012yes—
377C2×Dic3C22×Dic512yes—
378C2×Dic3C22×Dic512yes—
379C2×Dic3C22×Dic512yes—
380C4×D3—1016no—
381C4×D3C4⋊Dic5116yescomplemented
382C22×C5—34no—
383C22×C5—62no—
384C22×C5—62no—
385C22×C5—64no—
386C22×C5—64no—
387C22×C5C22×C4×D311yescharacteristic
388C22×C5C2×#23512yes—
389C22×C5C2×D3×D411yescharacteristic
390C22×C5C2×D3×Q811yescharacteristic
391C22×C5D3×#4112yes—
392C4×C5—22no—
393C4×C5—22no—
394C4×C5—34no—
395C4×C5—62no—
396C4×C5—62no—
397C4×C5D3×C4⋊C414yes—
398Dic5—24no—
399Dic5—42no—
400Dic5—64no—
401Dic5—122no—
402C24—31no—
403C22×C4—31no—
404C22×C4—34no—
405C22×C4—34no—
406C22×C4—34no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—52no—
410C22×C4—52no—
411C22×C4—152no—
412C22×C4—152no—
413C22×C4—304no—
414C22×C4—304no—
415C22×C4—304no—
416C22×C4C2×D3×D511yescharacteristic
417C22×C4C2×D3×D511yescharacteristic
418C22×C4C2×D3×D511yescharacteristic
419C4⋊C4—34no—
420C4⋊C4—34no—
421C4⋊C4—104no—
422C4⋊C4—304no—
423C4⋊C4—304no—
424C4⋊C4—304no—
425C4⋊C4—304no—
426C22⋊C4—34no—
427C22⋊C4—34no—
428C22⋊C4—304no—
429C42—34no—
430C42—102no—
431C42—102no—
432C42—304no—
433C42—302no—
434C42—302no—
435C42D3×Dic514yescomplemented
436C3×C5#229611yescharacteristic, complemented, Hall
437C22×C3C22×Dic1011yescharacteristic
438C22×C3C22×D2011yescharacteristic
439C22×C3D5×#4112yes—
440C22×C3D5×#4112yes—
441C22×C3C23×Dic511yescharacteristic
442C2×D3—24no—
443C2×D3—24no—
444C2×D3—22no—
445C2×D3—22no—
446C2×D3C2×C4⋊Dic514yes—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—104no—
450C3×C4—202no—
451C3×C4C2×C4⋊Dic514yes—
452Dic3—22no—
453Dic3—22no—
454Dic3—104no—
455Dic3—202no—
456Dic3C2×C4⋊Dic514yes—
457C2×C5—64no—
458C2×C5C4×#23511yescharacteristic
459C2×C5C2×D3×C4⋊C411yescharacteristic
460C2×C5#552211yescharacteristic
461C2×C5#554712yes—
462C2×C5#557812yes—
463C23—32no—
464C23—32no—
465C23—32no—
466C23—62no—
467C23—62no—
468C23C22×D3×D511yescharacteristic
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—316no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—54no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—102no—
481C2×C4—102no—
482C2×C4—102no—
483C2×C4—102no—
484C2×C4—102no—
485C2×C4—154no—
486C2×C4—3016no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4—302no—
492C2×C4D3×Dic1012yes—
493C2×C4D3×D2012yes—
494C2×C4C2×D3×Dic512yes—
495C2×C4C2×D3×Dic512yes—
496C2×C4C2×D3×Dic512yes—
497C2×C3#6585112yes—
498C2×C3#6585812yes—
499C2×C3C22×C4⋊Dic511yescharacteristic
500C2×C3#41×Dic511yescharacteristic
501C2×C3#41×Dic511yescharacteristic
502D3—24no—
503C5#7375511yescharacteristic, complemented, Sylow
504C22—34no—
505C22—64no—
506C22—64no—
507C22—62no—
508C22—62no—
509C22C2×D3×Dic1011yescharacteristic
510C22C2×D3×D2011yescharacteristic
511C22D5×#23512yes—
512C22#9201612yes—
513C22C22×D3×Dic511yescharacteristic
514C4—22no—
515C4—22no—
516C4—34no—
517C4—62no—
518C4—62no—
519C4—104no—
520C4—202no—
521C4—304no—
522C4—602no—
523C4D3×C4⋊Dic514yes—
524C3#1061395811yescharacteristic, complemented, Sylow
525C2—64no—
526C2#1175257812yes—
527C2#1175273912yes—
528C2C2×D3×C4⋊Dic511yescharacteristic
529C2Dic5×#23511yescharacteristic
530C2#1175445511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2296
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C4×C4⋊Dic15C2semidirect
5. C3×C4×C4⋊Dic5C2semidirect
8. C4×Dic3⋊Dic5C2semidirect
9. C4×Dic3⋊Dic5C2semidirect
10. #11748693C2semidirect
11. #11748677C2semidirect
24. C5×#872C4semidirect
50. C4×C4⋊Dic5D3semidirect
68. C3×C42×C5C2×C4semidirect
74. C5×Dic3⋊C4C2×C4semidirect
75. C5×Dic3⋊C4C2×C4semidirect
76. C4×C5×Dic3C2×C4semidirect
149. C4×C5×D3C4⋊C4semidirect
177. #872Dic5semidirect
205. C42×C5C4×D3semidirect
268. C3×C42C2×Dic5semidirect
276. Dic3⋊C4C2×Dic5semidirect
277. Dic3⋊C4C2×Dic5semidirect
281. C4×Dic3C2×Dic5semidirect
381. C4×D3C4⋊Dic5semidirect
435. C42D3×Dic5semidirect
436. C3×C5#2296semidirect
503. C5#73755semidirect
524. C3#10613958semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
C2×C4×D3×Dic52
C2×#913712
C4×C4⋊Dic152
C3×C4×C4⋊Dic52
#117489032
#117488972
C4×Dic3⋊Dic52
#117486932
#117486772
#106139583
#737555