Finite Group Databasebeta

← #14320100

Subgroups — #14320100

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1200C211yesmaximal, characteristic
2#11750767C211yesmaximal, characteristic
3C5×#4651C211yesmaximal, characteristic, complemented
4C3×#64939C211yesmaximal, characteristic, complemented
5#11748889C212yesmaximal
6#11748876C212yesmaximal
7#11748670C211yesmaximal, characteristic
8#11748653C212yesmaximal, complemented
9#11748637C212yesmaximal, complemented
10#11748618C211yesmaximal, characteristic, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605989—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×#1200C2211yescharacteristic
15C22×#1200C2211yescharacteristic
16C2×#6714C2212yes—
17C2×C4×Dic15C2212yes—
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C3×#683C2212yes—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×#6668C2212yes—
22C2×#6667C2212yes—
23C2×Dic3×Dic5C2212yes—
24C2×Dic3×Dic5C2211yescharacteristic
25C2×Dic3×Dic5C2211yescharacteristic
26C4×#1200C418yescomplemented
27C3×C5×#95C2211yescharacteristic
28#91115C2211yescharacteristic
29C5×C3⋊#95C2212yes—
30C5×C3⋊#95C2212yes—
31C5×C3⋊#95C2211yescharacteristic
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#74147—51nomaximal, Hall
38C2×C42×D5—31no—
39C5×#383—31no—
40#65226—31no—
41#64956—32no—
42#64955—31no—
43#64955—31no—
44#64953—32no—
45#64939—31no—
46#64939D311yescharacteristic, complemented
47#64938—32no—
48#64937—32no—
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C2×C4×D15—24no—
55C2×C4×D15C2×C414yes—
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C2×#1200—24no—
63C2×#1200—22no—
64C2×#1200—22no—
65C2×#1200C2×C414yes—
66C2×#1200C2×C414yes—
67#6714—24no—
68C4×Dic15—24no—
69C4×C5×Dic3C2×C414yes—
70C3×#683—24no—
71C3×C4×Dic5C2×C414yes—
72#6668—24no—
73#6667—24no—
74Dic3×Dic5—24no—
75Dic3×Dic5C2×C414yes—
76Dic3×Dic5C2×C414yes—
77C2×C42×D3—51no—
78C3×#382—51no—
79#4987—52no—
80Dic3×C4⋊C4—52no—
81#4936—51no—
82#4666—51no—
83#4666—51no—
84#4664—52no—
85#4651—51no—
86#4651D511yescharacteristic, complemented
87#4648—52no—
88C22×C4×D5—31no—
89C22×C4×D5—31no—
90C22×C4×D5—31no—
91C2×C42×C5—31no—
92C2×#685—32no—
93C2×#685—32no—
94C2×#683—32no—
95C2×#683C2×D312yes—
96C2×C4×Dic5—31no—
97C2×C4×Dic5—31no—
98C2×C4×Dic5—32no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5C2×D311yescharacteristic
101C42×D5—38no—
102C5×#95—32no—
103C5×#95—32no—
104C5×#95—31no—
105C5×#95C2×D311yescharacteristic
106#3963—31no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#3963C2×D312yes—
111#3963C2×D311yescharacteristic
112#2283—151noSylow
113C23×C3×C5C2411yescharacteristic
114C22×D15—21no—
115C22×D15—21no—
116C22×D15—22no—
117C22×D15C22×C412yes—
118C22×D15#4114yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5C22×C412yes—
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15C22×C412yes—
128C2×Dic15#4114yes—
129C4×D15—28no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3—21no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3C22×C412yes—
137C2×C5×Dic3C22×C412yes—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5C22×C412yes—
143C2×C3×Dic5C22×C412yes—
144C2×C3×Dic5#4112yes—
145C2×C3×Dic5#4112yes—
146#1200—28no—
147#1200—28no—
148C22×C4×D3—51no—
149C22×C4×D3—51no—
150C22×C4×D3—51no—
151C2×C3×C4⋊C4—52no—
152C2×C3×C42—51no—
153C2×(C2×D3)⋊C4—52no—
154C2×(C2×D3)⋊C4—52no—
155C2×C4⋊Dic3—52no—
156C2×C4×Dic3—51no—
157C2×C4×Dic3—51no—
158C2×C4×Dic3—52no—
159C2×C4×Dic3—52no—
160C2×C4×Dic3C2×D511yescharacteristic
161C42×D3—58no—
162C3×#95—52no—
163C3×#95—51no—
164C3×#95C2×D511yescharacteristic
165C3⋊#95—51no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95C2×D512yes—
170C3⋊#95C2×D512yes—
171C3⋊#95C2×D511yescharacteristic
172C23×D5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—31no—
175C22×C4×C5—32no—
176C22×C4×C5C22×D312yes—
177C22×C4×C5C22×D311yescharacteristic
178C22×Dic5—31no—
179C22×Dic5—32no—
180C22×Dic5C22×D312yes—
181C22×Dic5C22×D311yescharacteristic
182C22×Dic5C22×D311yescharacteristic
183C2×C4×D5—34no—
184C2×C4×D5—34no—
185C2×C4×D5—34no—
186C2×C4×D5—64no—
187C2×C4×D5—64no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C42×C5—34no—
191#685—64no—
192#685—64no—
193#683—24no—
194#683—64no—
195C4×Dic5—34no—
196C4×Dic5—34no—
197C4×Dic5—64no—
198C4×Dic5—64no—
199C4×Dic5C4×D314yes—
200C22×C42—151no—
201#383—31no—
202#383—151no—
203#382—51no—
204#382—151no—
205#381—152no—
206#380—152no—
207C4×C4⋊C4—152no—
208C4×C22⋊C4—151no—
209C4×C22⋊C4—151no—
210#376—152no—
211C22×C3×C5C23×C411yescharacteristic
212C22×C3×C5C2×#4111yescharacteristic
213C22×C3×C5C2×#4111yescharacteristic
214C22×C3×C5C2×#4112yes—
215C22×C3×C5C2×#4112yes—
216C2×D15—22no—
217C2×D15—22no—
218C2×D15—24no—
219C2×D15—24no—
220C2×D15#11714yes—
221C3×C4×C5—22no—
222C3×C4×C5—42no—
223Dic15—42no—
224Dic15#11714yes—
225C3×Dic5—22no—
226C3×Dic5—42no—
227C3×Dic5#11714yes—
228C5×Dic3—22no—
229C5×Dic3—22no—
230C5×Dic3—42no—
231C23×D3—51no—
232C22×C3×C4—51no—
233C22×C3×C4—51no—
234C22×C3×C4—52no—
235C22×C3×C4C22×D512yes—
236C22×C3×C4C22×D511yescharacteristic
237C22×Dic3—51no—
238C22×Dic3—52no—
239C22×Dic3C22×D512yes—
240C22×Dic3C22×D511yescharacteristic
241C22×Dic3C22×D511yescharacteristic
242C2×C4×D3—54no—
243C2×C4×D3—54no—
244C2×C4×D3—54no—
245C2×C4×D3—102no—
246C2×C4×D3—102no—
247C2×C4×D3—104no—
248C2×C4×D3—104no—
249C3×C4⋊C4—104no—
250C3×C42—54no—
251(C2×D3)⋊C4—104no—
252(C2×D3)⋊C4—104no—
253C4⋊Dic3—104no—
254C4×Dic3—54no—
255C4×Dic3—54no—
256C4×Dic3—104no—
257C4×Dic3—104no—
258C4×Dic3C4×D514yes—
259C23×C5C23×D311yescharacteristic
260C22×D5—32no—
261C22×D5—34no—
262C22×D5—61no—
263C22×D5—61no—
264C22×D5—62no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—32no—
270C2×C4×C5—32no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5C2×C4×D312yes—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—32no—
283C2×Dic5—34no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5C2×C4×D312yes—
288C2×Dic5C2×C4×D312yes—
289C2×Dic5#23712yes—
290C2×Dic5#23912yes—
291C4×D5—68no—
292C4×D5—68no—
293C4×D5—68no—
294C23×C4—151no—
295C23×C4—151no—
296C23×C4—151no—
297C2×C4⋊C4—52no—
298C2×C4⋊C4—152no—
299C2×C22⋊C4—152no—
300C2×C22⋊C4—152no—
301C2×C42—31no—
302C2×C42—51no—
303C2×C42—158no—
304C2×C42—151no—
305C2×C42—151no—
306C2×C42—152no—
307C2×C42—152no—
308#95—32no—
309#95—31no—
310#95—32no—
311#95—52no—
312#95—51no—
313#95—152no—
314#95—152no—
315#95—152no—
316#95—151no—
317#95D3×D511yescharacteristic
318C2×C3×C5C2×#11711yescharacteristic
319C2×C3×C5C2×#11711yescharacteristic
320C2×C3×C5C2×#11711yescharacteristic
321C2×C3×C5#52912yes—
322C2×C3×C5#52912yes—
323D15—24no—
324C23×C3C23×D511yescharacteristic
325C22×D3—52no—
326C22×D3—54no—
327C22×D3—101no—
328C22×D3—102no—
329C22×D3—101no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—52no—
335C2×C3×C4—52no—
336C2×C3×C4—52no—
337C2×C3×C4—52no—
338C2×C3×C4—102no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4C2×C4×D512yes—
343C2×Dic3—22no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—52no—
350C2×Dic3—54no—
351C2×Dic3—102no—
352C2×Dic3—102no—
353C2×Dic3—102no—
354C2×Dic3C2×C4×D512yes—
355C2×Dic3C2×C4×D512yes—
356C4×D3—108no—
357C4×D3—108no—
358C4×D3—108no—
359C22×C5C22×C4×D311yescharacteristic
360C22×C5C2×#23711yescharacteristic
361C22×C5C2×#23911yescharacteristic
362C22×C5D3×#4112yes—
363C22×C5D3×#4112yes—
364C2×D5—34no—
365C2×D5—64no—
366C2×D5—64no—
367C2×D5—62no—
368C2×D5—62no—
369C4×C5—22no—
370C4×C5—42no—
371C4×C5—62no—
372C4×C5—62no—
373C4×C5—122no—
374Dic5—22no—
375Dic5—34no—
376Dic5—42no—
377Dic5—122no—
378Dic5#89214yes—
379C24—151no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—32no—
383C22×C4—51no—
384C22×C4—51no—
385C22×C4—52no—
386C22×C4—154no—
387C22×C4—154no—
388C22×C4—151no—
389C22×C4—154no—
390C22×C4—152no—
391C22×C4—304no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4—304no—
395C22×C4C2×D3×D512yes—
396C22×C4C2×D3×D511yescharacteristic
397C4⋊C4—104no—
398C4⋊C4—304no—
399C22⋊C4—304no—
400C22⋊C4—304no—
401C42—34no—
402C42—54no—
403C42—154no—
404C42—154no—
405C42—304no—
406C42—304no—
407C3×C5#228311yescharacteristic, complemented, Hall
408C22×C3C22×C4×D511yescharacteristic
409C22×C3D5×#4112yes—
410C22×C3D5×#4111yescharacteristic
411C22×C3D5×#4112yes—
412C22×C3D5×#4111yescharacteristic
413C2×D3—54no—
414C2×D3—102no—
415C2×D3—102no—
416C2×D3—104no—
417C2×D3—104no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—54no—
421C3×C4—102no—
422C3×C4—202no—
423Dic3—22no—
424Dic3—22no—
425Dic3—42no—
426Dic3—54no—
427Dic3—202no—
428C2×C5C2×#89211yescharacteristic
429C2×C5D3×#11711yescharacteristic
430C2×C5D3×#11711yescharacteristic
431C2×C5#568012yes—
432C2×C5#569112yes—
433D5—64no—
434C23—152no—
435C23—154no—
436C23—301no—
437C23—302no—
438C23—301no—
439C23C22×D3×D511yescharacteristic
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—52no—
447C2×C4—52no—
448C2×C4—52no—
449C2×C4—52no—
450C2×C4—62no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—102no—
457C2×C4—102no—
458C2×C4—102no—
459C2×C4—102no—
460C2×C4—152no—
461C2×C4—154no—
462C2×C4—308no—
463C2×C4—308no—
464C2×C4—308no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4C4×D3×D512yes—
469C2×C3D5×#11711yescharacteristic
470C2×C3D5×#11711yescharacteristic
471C2×C3D5×#11711yescharacteristic
472C2×C3#6604012yes—
473C2×C3#6604012yes—
474D3—104no—
475C5#7414711yescharacteristic, complemented, Sylow
476C22—154no—
477C22—304no—
478C22—302no—
479C22—302no—
480C22—304no—
481C22C2×C4×D3×D511yescharacteristic
482C22#9201612yes—
483C22D5×#23711yescharacteristic
484C22#9202412yes—
485C22D5×#23911yescharacteristic
486C4—22no—
487C4—42no—
488C4—54no—
489C4—62no—
490C4—62no—
491C4—102no—
492C4—122no—
493C4—154no—
494C4—202no—
495C4—602no—
496C3#1060598911yescharacteristic, complemented, Sylow
497C2—304no—
498C2#1175272311yescharacteristic
499C2#1175282511yescharacteristic
500C2#1175294612yes—
501C2#1175355012yes—
502C2D5×#89211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#95D3×D5
hypocenterC3×C5#2283
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C5×#4651C2semidirect
4. C3×#64939C2semidirect
8. #11748653C2semidirect
9. #11748637C2semidirect
10. #11748618C2semidirect
11. #11748580C2semidirect
26. C4×#1200C4semidirect
46. #64939D3semidirect
86. #4651D5semidirect
407. C3×C5#2283semidirect
475. C5#74147semidirect
496. C3#10605989semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12002
#117507672
C5×#46512
C3×#649392
#117488892
#117488762
#117486702
#117486532
#117486372
#117486182
#117485802
#106059893
#741475