Finite Group Databasebeta

← #14326817

Subgroups — #14326817

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4018C211yesmaximal, characteristic
2#11751033C211yesmaximal, characteristic, complemented
3C5×#4936C211yesmaximal, characteristic, complemented
4#11748791C212yesmaximal
5#11748771C212yesmaximal
6#11748738C211yesmaximal, characteristic
7#11748702C211yesmaximal, characteristic
8#11748681C212yesmaximal, complemented
9#11748637C212yesmaximal, complemented
10#11748635C211yesmaximal, characteristic, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605887—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4×Dic15C2212yes—
16C2×C5×C4⋊Dic3C2212yes—
17C2×C3×#685C2211yescharacteristic
18C2×C3×#685C2211yescharacteristic
19C2×C3×#683C2211yescharacteristic
20C2×C3×#683C2211yescharacteristic
21C2×C3×C4×Dic5C2211yescharacteristic
22C3×#4018C418yescomplemented
23C2×#6668C2212yes—
24C2×#6668C2212yes—
25C2×#6665C2212yes—
26C2×#6665C2212yes—
27C2×Dic3×Dic5C2212yes—
28C2×Dic3×Dic5C2212yes—
29#91115C2211yescharacteristic
30#91115C2212yes—
31#91115C2211yescharacteristic
32C5×C3⋊#95C2211yescharacteristic
33C5×C3⋊#95C2212yes—
34C5×C3⋊#95C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#82239—51nomaximal, Hall
38C2×#4018D311yescharacteristic
39C5×#382—31no—
40#65279—32no—
41#65261—32no—
42#65221—31no—
43#64958—32no—
44#64956—31no—
45#64955—31no—
46#64939—31no—
47#64938—32no—
48#64937—31no—
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2312yes—
55C22×C5×Dic3C2312yes—
56C22×C5×Dic3C2312yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×C4×D5—24no—
61C2×C3×C4×D5C2×C414yes—
62C3×C42×C5C2×C414yes—
63C4×Dic15—24no—
64C5×C4⋊Dic3—42no—
65C3×#685C2×C414yes—
66C3×#685C2×C414yes—
67C3×#683C2×C414yes—
68C3×#683C2×C414yes—
69C3×C4×Dic5C2×C414yes—
70#6668—24no—
71#6668—42no—
72#6665—24no—
73#6665—42no—
74Dic3×Dic5—24no—
75Dic3×Dic5—24no—
76C2×C3×#117—51no—
77#5212—51no—
78C4×#217—51no—
79#4984—52no—
80Dic3×C4⋊C4—52no—
81#4951—52no—
82#4951—52no—
83#4936—51no—
84#4936D511yescharacteristic, complemented
85#4932—51no—
86#4932—51no—
87C22×C4×D5C2×D311yescharacteristic
88C2×C5×C4⋊C4—32no—
89C2×C42×C5C2×D311yescharacteristic
90C2×#685—32no—
91C2×#685—32no—
92C2×#685C2×D311yescharacteristic
93C2×#685C2×D311yescharacteristic
94C2×#683—32no—
95C2×#683—32no—
96C2×#683C2×D311yescharacteristic
97C2×#683C2×D311yescharacteristic
98C2×C4×Dic5—32no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5—32no—
101C2×C4×Dic5C2×D311yescharacteristic
102#4018Dic318yescomplemented
103C5×#95—31no—
104C5×#95—32no—
105C5×#95—31no—
106#3963—31no—
107#3963—31no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#2346—151noSylow
112C23×C3×C5C2411yescharacteristic
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5C22×C412yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5C22×C412yes—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C22×C412yes—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—22no—
130C2×Dic15#4114yes—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—22no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5C22×C412yes—
141C2×C3×Dic5C22×C412yes—
142C2×C3×Dic5C22×C412yes—
143C2×C3×Dic5#4114yes—
144C3×C4×D5—28no—
145C23×C3×C4—51no—
146C3×#117—58no—
147C2×C3×C4⋊C4—51no—
148C2×C3×C4⋊C4—51no—
149C2×C3×C22⋊C4—51no—
150C2×C3×C22⋊C4—51no—
151C2×C3×C42—51no—
152C2×C3×C42C2×D511yescharacteristic
153C2×#217—52no—
154C2×#217—52no—
155C2×C4⋊Dic3—52no—
156C2×C4⋊Dic3—52no—
157C2×C4⋊Dic3C2×D512yes—
158C2×C4×Dic3—52no—
159C2×C4×Dic3—52no—
160C2×C4×Dic3—52no—
161C3⋊#95—51no—
162C3⋊#95—51no—
163C3⋊#95—52no—
164C3⋊#95—52no—
165C3⋊#95—52no—
166C3⋊#95C2×D511yescharacteristic
167C3⋊#95C2×D511yescharacteristic
168C3⋊#95C2×D512yes—
169C23×D5C22×D311yescharacteristic
170C22×C4×C5—32no—
171C22×C4×C5—32no—
172C22×C4×C5C22×D311yescharacteristic
173C22×C4×C5C22×D311yescharacteristic
174C22×C4×C5C22×D311yescharacteristic
175C22×Dic5—32no—
176C22×Dic5—32no—
177C22×Dic5C22×D311yescharacteristic
178C22×Dic5C22×D311yescharacteristic
179C22×Dic5C22×D311yescharacteristic
180C2×C4×D5—24no—
181C2×C4×D5C2×Dic314yes—
182C5×C4⋊C4—122no—
183C42×C5C2×Dic314yes—
184#685—64no—
185#685—122no—
186#685C2×Dic314yes—
187#685C2×Dic314yes—
188#683—64no—
189#683—122no—
190#683C2×Dic314yes—
191#683C2×Dic314yes—
192C4×Dic5—64no—
193C4×Dic5—64no—
194C4×Dic5—64no—
195C4×Dic5C2×Dic314yes—
196C2×#117—51no—
197#389—152no—
198#388—152no—
199#388—152no—
200#382—31no—
201#382—151no—
202#380—151no—
203C4×C4⋊C4—152no—
204C4×C22⋊C4—151no—
205#376—151no—
206#376—151no—
207C22×C3×C5C23×C411yescharacteristic
208C22×C3×C5C2×#4112yes—
209C22×C3×C5C2×#4112yes—
210C22×C3×C5H(5,𝔽2)11yescharacteristic
211C22×C3×C52−1+411yescharacteristic
212C2×C3×D5—22no—
213C2×C3×D5—22no—
214C2×C3×D5—22no—
215C2×C3×D5—42no—
216C2×C3×D5—42no—
217C3×C4×C5—22no—
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220Dic15—24no—
221Dic15—42no—
222C3×Dic5—22no—
223C3×Dic5—22no—
224C3×Dic5#11714yes—
225C5×Dic3—42no—
226C5×Dic3—42no—
227C24×C3—51no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—54no—
232C22×C3×C4—104no—
233C22×C3×C4C22×D511yescharacteristic
234C22×C3×C4C22×D511yescharacteristic
235C22×C3×C4C22×D511yescharacteristic
236C22×Dic3—52no—
237C22×Dic3—52no—
238C22×Dic3C22×D512yes—
239C22×Dic3C22×D512yes—
240C3×C4⋊C4—54no—
241C3×C4⋊C4—54no—
242C3×C22⋊C4—54no—
243C3×C22⋊C4—54no—
244C3×C42—54no—
245C3×C42C4×D514yes—
246#217—104no—
247#217—202no—
248C4⋊Dic3—42no—
249C4⋊Dic3—104no—
250C4⋊Dic3—202no—
251C4×Dic3—104no—
252C4×Dic3—104no—
253C4×Dic3—104no—
254C23×C5C23×D311yescharacteristic
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—21no—
258C22×D5—21no—
259C22×D5C22×Dic312yes—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—62no—
265C2×C4×C5—62no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5C22×Dic312yes—
271C2×C4×C5C22×Dic312yes—
272C2×C4×C5C22×Dic312yes—
273C2×Dic5—22no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—34no—
277C2×Dic5—62no—
278C2×Dic5—62no—
279C2×Dic5—62no—
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5#23514yes—
283C2×Dic5C22×Dic312yes—
284C2×Dic5C22×Dic312yes—
285C2×Dic5C22×Dic312yes—
286C4×D5—28no—
287C23×C4—51no—
288#117—58no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—51no—
291C2×C4⋊C4—51no—
292C2×C4⋊C4—152no—
293C2×C4⋊C4—152no—
294C2×C22⋊C4—51no—
295C2×C22⋊C4—51no—
296C2×C22⋊C4—152no—
297C2×C22⋊C4—152no—
298C2×C42—51no—
299C2×C42—152no—
300C2×C42—152no—
301C2×C42—152no—
302C2×C42D3×D511yescharacteristic
303#95—31no—
304#95—31no—
305#95—32no—
306#95—152no—
307#95—152no—
308#95—151no—
309#95—151no—
310#95—152no—
311C2×C3×C5C2×#11711yescharacteristic
312C2×C3×C5C4×#4111yescharacteristic
313C2×C3×C5#52011yescharacteristic
314C2×C3×C5#55212yes—
315C2×C3×C5#55512yes—
316C3×D5—42no—
317C23×C3—52no—
318C23×C3—101no—
319C23×C3—101no—
320C23×C3—102no—
321C23×C3—102no—
322C23×C3C23×D511yescharacteristic
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—52no—
328C2×C3×C4—54no—
329C2×C3×C4—52no—
330C2×C3×C4—52no—
331C2×C3×C4—108no—
332C2×C3×C4—101no—
333C2×C3×C4—101no—
334C2×C3×C4—102no—
335C2×C3×C4C2×C4×D512yes—
336C2×C3×C4C2×C4×D512yes—
337C2×C3×C4C2×C4×D512yes—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—54no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3—102no—
350C22×C5C2×#23512yes—
351C22×C5D3×#4112yes—
352C22×C5#100911yescharacteristic
353C22×C5#101011yescharacteristic
354C22×C5C23×Dic311yescharacteristic
355C2×D5—22no—
356C2×D5—22no—
357C2×D5—22no—
358C2×D5—42no—
359C2×D5—42no—
360C4×C5—22no—
361C4×C5—22no—
362C4×C5—22no—
363C4×C5—122no—
364C4×C5—122no—
365Dic5—22no—
366Dic5—22no—
367Dic5—64no—
368Dic5—122no—
369Dic5#92614yes—
370C24—51no—
371C22×C4—32no—
372C22×C4—32no—
373C22×C4—51no—
374C22×C4—51no—
375C22×C4—51no—
376C22×C4—54no—
377C22×C4—104no—
378C22×C4—152no—
379C22×C4—152no—
380C22×C4C2×D3×D511yescharacteristic
381C22×C4C2×D3×D511yescharacteristic
382C22×C4C2×D3×D511yescharacteristic
383C4⋊C4—54no—
384C4⋊C4—54no—
385C4⋊C4—122no—
386C4⋊C4—304no—
387C4⋊C4—602no—
388C22⋊C4—54no—
389C22⋊C4—54no—
390C22⋊C4—304no—
391C22⋊C4—602no—
392C42—54no—
393C42—304no—
394C42—304no—
395C42—304no—
396C42D5×Dic314yes—
397C3×C5#234611yescharacteristic, complemented, Hall
398C22×C3—102no—
399C22×C3—102no—
400C22×C3—102no—
401C22×C3—202no—
402C22×C3—202no—
403C22×C3C22×C4×D511yescharacteristic
404C22×C3#414411yescharacteristic
405C22×C3#414711yescharacteristic
406C22×C3D5×#4112yes—
407C22×C3D5×#4112yes—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—54no—
412C3×C4—102no—
413C3×C4—102no—
414Dic3—42no—
415Dic3—42no—
416Dic3—104no—
417Dic3—202no—
418C2×C5#552912yes—
419C2×C5#553212yes—
420C2×C5C2×#92611yescharacteristic
421C2×C5Dic3×#4111yescharacteristic
422C2×C5#582711yescharacteristic
423D5—42no—
424C23—52no—
425C23—101no—
426C23—102no—
427C23—102no—
428C23—101no—
429C23C22×D3×D511yescharacteristic
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—54no—
435C2×C4—52no—
436C2×C4—52no—
437C2×C4—52no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—108no—
445C2×C4—101no—
446C2×C4—102no—
447C2×C4—101no—
448C2×C4—154no—
449C2×C4—302no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4C2×D5×Dic312yes—
455C2×C4C2×D5×Dic312yes—
456C2×C4C2×D5×Dic312yes—
457C2×C3—202no—
458C2×C3#6583811yescharacteristic
459C2×C3D5×#11711yescharacteristic
460C2×C3#6585611yescharacteristic
461C2×C3#6600412yes—
462C2×C3#6602712yes—
463C5#8223911yescharacteristic, complemented, Sylow
464C22—102no—
465C22—102no—
466C22—102no—
467C22—202no—
468C22—202no—
469C22#9200011yescharacteristic
470C22D5×#23512yes—
471C22#9201612yes—
472C22#9201811yescharacteristic
473C22C22×D5×Dic311yescharacteristic
474C4—22no—
475C4—22no—
476C4—22no—
477C4—54no—
478C4—102no—
479C4—102no—
480C4—122no—
481C4—122no—
482C4—304no—
483C4—602no—
484C3#1060588711yescharacteristic, complemented, Sylow
485C2—202no—
486C2#1175249612yes—
487C2#1175268812yes—
488C2D5×#92611yescharacteristic
489C2#1175444411yescharacteristic
490C2#1175449911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2346
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751033C2semidirect
3. C5×#4936C2semidirect
8. #11748681C2semidirect
9. #11748637C2semidirect
10. #11748635C2semidirect
11. #11748580C2semidirect
22. C3×#4018C4semidirect
84. #4936D5semidirect
102. #4018Dic3semidirect
397. C3×C5#2346semidirect
463. C5#82239semidirect
484. C3#10605887semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
#117510332
C5×#49362
#117487912
#117487712
#117487382
#117487022
#117486812
#117486372
#117486352
#117485802
#106058873
#822395