Finite Group Databasebeta

← #14320072

Subgroups — #14320072

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Dic5C211yesmaximal, characteristic
2#11751033C211yesmaximal, characteristic, complemented
3C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×C4×#683C211yesmaximal, characteristic, complemented
5#11748880C212yesmaximal
6#11748874C212yesmaximal
7C4×#6668C211yesmaximal, characteristic, complemented
8C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic
9#11748646C212yesmaximal, complemented
10#11748642C212yesmaximal, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10605168—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2211yescharacteristic
15C22×D3×Dic5C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C3×#683C2212yes—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×#6668C2212yes—
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×Dic3×Dic5C2211yescharacteristic
27C2×Dic3×Dic5C2211yescharacteristic
28C4×D3×Dic5C418yescomplemented
29#91115C2212yes—
30#91115C2212yes—
31C5×C3⋊#95C2212yes—
32C3×#3963C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73752—51nomaximal, Hall
38C22×C4×Dic5—31no—
39C4×C5×C22⋊C4—31no—
40C4×C22⋊Dic5—31no—
41#65232—32no—
42#65231—32no—
43#65221—31no—
44#65221—31no—
45C4×#683—31no—
46C4×#683D311yescharacteristic, complemented
47#64940—32no—
48#64939—32no—
49C23×C5×D3C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×C5×Dic3C2312yes—
56C22×C5×Dic3C2311yescharacteristic
57C2×C4×C5×D3—22no—
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C2×D3×Dic5—24no—
64C2×D3×Dic5—24no—
65C2×D3×Dic5C2×C414yes—
66C2×D3×Dic5C2×C414yes—
67C3×C42×C5—22no—
68C4×Dic15—22no—
69C4×Dic15C2×C414yes—
70C5×(C2×D3)⋊C4—24no—
71C4×C5×Dic3—22no—
72C3×#683—24no—
73C3×C4×Dic5—22no—
74C3×C4×Dic5C2×C414yes—
75#6668—24no—
76(C2×D3)⋊Dic5—24no—
77Dic3×Dic5C2×C414yes—
78Dic3×Dic5C2×C414yes—
79C2×C42×D3—51no—
80C3×C4×C4⋊C4—51no—
81#4987—52no—
82#4977—52no—
83C4×(C2×D3)⋊C4—51no—
84C4×(C2×D3)⋊C4D511yescharacteristic
85C4×C4⋊Dic3—51no—
86#4932—51no—
87#4932—51no—
88#4664—52no—
89#4651—52no—
90C23×C4×C5—31no—
91C23×Dic5—31no—
92C23×Dic5—31no—
93C2×C5×C22⋊C4—32no—
94C2×C42×C5—31no—
95C2×C42×C5C2×D311yescharacteristic
96C2×C22⋊Dic5—32no—
97C2×#683—32no—
98C2×#683C2×D312yes—
99C2×C4×Dic5—31no—
100C2×C4×Dic5—31no—
101C2×C4×Dic5—31no—
102C2×C4×Dic5—38no—
103C2×C4×Dic5—31no—
104C2×C4×Dic5C2×D311yescharacteristic
105C2×C4×Dic5C2×D311yescharacteristic
106C5×#95—32no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963C2×D312yes—
114#2283—151noSylow
115C23×C3×C5C2411yescharacteristic
116C22×C5×D3—22no—
117C22×C5×D3—21no—
118C22×C5×D3—21no—
119C22×C5×D3C22×C412yes—
120C22×C5×D3#4114yes—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5C22×C412yes—
125C2×C3×C4×C5#4112yes—
126C2×C3×C4×C5#4112yes—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15C22×C412yes—
133C2×Dic15C22×C412yes—
134C2×C5×Dic3—21no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3C22×C412yes—
140C4×C5×D3—28no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C22×C412yes—
146C2×C3×Dic5C22×C412yes—
147C2×C3×Dic5#4114yes—
148D3×Dic5—28no—
149D3×Dic5—28no—
150C22×C4×D3—51no—
151C22×C4×D3—51no—
152C22×C4×D3C2×D511yescharacteristic
153C2×C3×C4⋊C4—52no—
154C2×C3×C42—51no—
155C2×C3×C42—51no—
156C2×C3×C42C2×D511yescharacteristic
157C2×(C2×D3)⋊C4—52no—
158C2×(C2×D3)⋊C4C2×D512yes—
159C2×C4⋊Dic3—52no—
160C2×C4×Dic3—51no—
161C2×C4×Dic3—51no—
162C2×C4×Dic3—51no—
163C2×C4×Dic3—51no—
164C2×C4×Dic3C2×D511yescharacteristic
165C42×D3—58no—
166C3×#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C3⋊#95—52no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95C2×D512yes—
174C24×C5—31no—
175C22×C4×C5—31no—
176C22×C4×C5—34no—
177C22×C4×C5—32no—
178C22×C4×C5—62no—
179C22×C4×C5—62no—
180C22×C4×C5C22×D312yes—
181C22×C4×C5C22×D311yescharacteristic
182C22×Dic5—31no—
183C22×Dic5—31no—
184C22×Dic5—34no—
185C22×Dic5—34no—
186C22×Dic5—32no—
187C22×Dic5—64no—
188C22×Dic5—64no—
189C22×Dic5C22×D312yes—
190C22×Dic5C22×D311yescharacteristic
191C22×Dic5C22×D311yescharacteristic
192C5×C22⋊C4—64no—
193C42×C5—22no—
194C42×C5—62no—
195C22⋊Dic5—64no—
196#683—24no—
197#683—64no—
198C4×Dic5—22no—
199C4×Dic5—34no—
200C4×Dic5—34no—
201C4×Dic5—34no—
202C4×Dic5—62no—
203C4×Dic5C4×D314yes—
204C22×C42—151no—
205#383—152no—
206#382—152no—
207#381—152no—
208#380—152no—
209C4×C4⋊C4—51no—
210C4×C4⋊C4—151no—
211C4×C22⋊C4—31no—
212C4×C22⋊C4—151no—
213#376—151no—
214#376—151no—
215C22×C3×C5C23×C411yescharacteristic
216C22×C3×C5C2×#4112yes—
217C22×C3×C5C2×#4111yescharacteristic
218C22×C3×C5C2×#4111yescharacteristic
219C22×C3×C5C2×#4112yes—
220C2×C5×D3—22no—
221C2×C5×D3—22no—
222C2×C5×D3—24no—
223C2×C5×D3—24no—
224C2×C5×D3#11714yes—
225C3×C4×C5—42no—
226C3×C4×C5#11714yes—
227Dic15—22no—
228Dic15—22no—
229Dic15—42no—
230C3×Dic5—22no—
231C3×Dic5—42no—
232C3×Dic5#11714yes—
233C5×Dic3—22no—
234C5×Dic3—42no—
235C23×D3C22×D511yescharacteristic
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C22×C3×C4—52no—
239C22×C3×C4C22×D512yes—
240C22×C3×C4C22×D511yescharacteristic
241C22×Dic3—51no—
242C22×Dic3—51no—
243C22×Dic3—52no—
244C22×Dic3C22×D512yes—
245C22×Dic3C22×D511yescharacteristic
246C2×C4×D3—22no—
247C2×C4×D3—22no—
248C2×C4×D3—54no—
249C2×C4×D3—54no—
250C2×C4×D3—104no—
251C2×C4×D3—104no—
252C2×C4×D3C4×D514yes—
253C3×C4⋊C4—104no—
254C3×C42—22no—
255C3×C42—54no—
256C3×C42—102no—
257(C2×D3)⋊C4—24no—
258(C2×D3)⋊C4—104no—
259C4⋊Dic3—104no—
260C4×Dic3—22no—
261C4×Dic3—54no—
262C4×Dic3—54no—
263C4×Dic3—54no—
264C4×Dic3—102no—
265C23×C5—32no—
266C23×C5—34no—
267C23×C5—62no—
268C23×C5—61no—
269C23×C5—61no—
270C23×C5C23×D311yescharacteristic
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—32no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5—68no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5C2×C4×D312yes—
282C2×C4×C5#23712yes—
283C2×C4×C5#23912yes—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—68no—
291C2×Dic5—62no—
292C2×Dic5—62no—
293C2×Dic5—68no—
294C2×Dic5—62no—
295C2×Dic5—62no—
296C2×Dic5—62no—
297C2×Dic5C2×C4×D312yes—
298C2×Dic5C2×C4×D312yes—
299C2×Dic5#23514yes—
300C23×C4—31no—
301C23×C4—151no—
302C23×C4—151no—
303C2×C4⋊C4—52no—
304C2×C4⋊C4—152no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—152no—
307C2×C42—31no—
308C2×C42—51no—
309C2×C42—51no—
310C2×C42—158no—
311C2×C42—151no—
312C2×C42—151no—
313C2×C42—151no—
314C2×C42—151no—
315C2×C42D3×D511yescharacteristic
316#95—32no—
317#95—52no—
318#95—152no—
319#95—152no—
320#95—152no—
321#95—152no—
322#95—152no—
323#95—152no—
324C2×C3×C5C2×#11711yescharacteristic
325C2×C3×C5C2×#11711yescharacteristic
326C2×C3×C5C2×#11711yescharacteristic
327C2×C3×C5#52912yes—
328C2×C3×C5#52912yes—
329C5×D3—24no—
330C23×C3C23×D511yescharacteristic
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—22no—
334C22×D3C2×C4×D512yes—
335C22×D3#70914yes—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—52no—
340C2×C3×C4—54no—
341C2×C3×C4—52no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4C2×C4×D512yes—
347C2×C3×C4#71112yes—
348C2×C3×C4#71112yes—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—52no—
355C2×Dic3—52no—
356C2×Dic3—102no—
357C2×Dic3—102no—
358C2×Dic3—102no—
359C2×Dic3—102no—
360C2×Dic3—102no—
361C2×Dic3C2×C4×D512yes—
362C4×D3—28no—
363C4×D3—108no—
364C4×D3—108no—
365C22×C5—34no—
366C22×C5—62no—
367C22×C5—62no—
368C22×C5—64no—
369C22×C5—64no—
370C22×C5C22×C4×D311yescharacteristic
371C22×C5C2×#23512yes—
372C22×C5C2×#23711yescharacteristic
373C22×C5C2×#23911yescharacteristic
374C22×C5D3×#4112yes—
375C4×C5—42no—
376C4×C5—62no—
377C4×C5—122no—
378C4×C5#89214yes—
379Dic5—22no—
380Dic5—42no—
381Dic5—62no—
382Dic5—62no—
383Dic5—122no—
384Dic5#87214yes—
385C24—31no—
386C22×C4—31no—
387C22×C4—34no—
388C22×C4—32no—
389C22×C4—51no—
390C22×C4—51no—
391C22×C4—52no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—154no—
395C22×C4—154no—
396C22×C4—151no—
397C22×C4—151no—
398C22×C4—152no—
399C22×C4—304no—
400C22×C4—304no—
401C22×C4C2×D3×D512yes—
402C22×C4C2×D3×D511yescharacteristic
403C4⋊C4—104no—
404C4⋊C4—304no—
405C22⋊C4—64no—
406C22⋊C4—304no—
407C42—22no—
408C42—54no—
409C42—62no—
410C42—102no—
411C42—154no—
412C42—154no—
413C42—154no—
414C42—302no—
415C3×C5#228311yescharacteristic, complemented, Hall
416C22×C3C22×C4×D511yescharacteristic
417C22×C3C2×#70912yes—
418C22×C3C2×#71111yescharacteristic
419C22×C3C2×#71111yescharacteristic
420C22×C3D5×#4112yes—
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—24no—
424C2×D3—24no—
425C2×D3#401814yes—
426C3×C4—42no—
427C3×C4—54no—
428C3×C4—102no—
429C3×C4—202no—
430C3×C4#402314yes—
431Dic3—22no—
432Dic3—42no—
433Dic3—102no—
434Dic3—102no—
435Dic3—202no—
436C2×C5—64no—
437C2×C5C2×#87211yescharacteristic
438C2×C5C2×#89211yescharacteristic
439C2×C5D3×#11711yescharacteristic
440C2×C5#555712yes—
441C2×C5#558012yes—
442C23—32no—
443C23—34no—
444C23—61no—
445C23—62no—
446C23—61no—
447C23C22×D3×D511yescharacteristic
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—32no—
452C2×C4—52no—
453C2×C4—54no—
454C2×C4—52no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—68no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—152no—
466C2×C4—152no—
467C2×C4—308no—
468C2×C4—308no—
469C2×C4—302no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4#676812yes—
475C2×C4C4×D3×D512yes—
476C2×C4#678012yes—
477C2×C3C2×#401811yescharacteristic
478C2×C3C2×#402311yescharacteristic
479C2×C3D5×#11711yescharacteristic
480C2×C3#6587212yes—
481C2×C3#6587212yes—
482D3—24no—
483C5#7375211yescharacteristic, complemented, Sylow
484C22—34no—
485C22—62no—
486C22—62no—
487C22—64no—
488C22—64no—
489C22C2×#676811yescharacteristic
490C22C2×C4×D3×D511yescharacteristic
491C22D5×#23512yes—
492C22D3×#70912yes—
493C22C2×#678011yescharacteristic
494C4—42no—
495C4—54no—
496C4—62no—
497C4—102no—
498C4—122no—
499C4—202no—
500C4—302no—
501C4—302no—
502C4—602no—
503C4#9140014yes—
504C3#1060516811yescharacteristic, complemented, Sylow
505C2—64no—
506C2#1175257912yes—
507C2D5×#87211yescharacteristic
508C2D3×#401811yescharacteristic
509C2C2×#9140011yescharacteristic
510C2#1175456512yes—
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#2283
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
2. #11751033C2semidirect
4. C3×C4×#683C2semidirect
7. C4×#6668C2semidirect
9. #11748646C2semidirect
10. #11748642C2semidirect
11. #11748611C2semidirect
28. C4×D3×Dic5C4semidirect
46. C4×#683D3semidirect
415. C3×C5#2283semidirect
483. C5#73752semidirect
504. C3#10605168semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Dic52
#117510332
C4×C5×(C2×D3)⋊C42
C3×C4×#6832
#117488802
#117488742
C4×#66682
C4×(C2×D3)⋊Dic52
#117486462
#117486422
#117486112
#106051683
#737525