Finite Group Databasebeta

← #14326709

Subgroups — #14326709

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#683C211yesmaximal, characteristic
2C4×#6719C211yesmaximal, characteristic
3C5×#5212C211yesmaximal, characteristic
4#11749506C211yesmaximal, characteristic
5#11749506C211yesmaximal, characteristic
6Dic5×#217C211yesmaximal, characteristic
7Dic5×#217C211yesmaximal, characteristic
8#11748690C212yesmaximal, complemented
9#11748681C212yesmaximal, complemented
10#11748637C212yesmaximal, complemented
11#11748601C212yesmaximal, complemented
12#10605611—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19C2×C5×#217C2211yescharacteristic
20C2×C5×#217C2211yescharacteristic
21C2×C5×C4⋊Dic3C2212yes—
22C2×C3×#683C418yescomplemented
23C2×C3×#683C2211yescharacteristic
24C2×C3×#683C2211yescharacteristic
25C2×C3×#683C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×#6668C2212yes—
28C2×#6668C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31#91115C2212yes—
32C5×C3⋊#95C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#82160—51nomaximal, Hall
38C22×#683D311yescharacteristic
39C5×#380—31no—
40C4×C22⋊Dic5—31no—
41#65267—32no—
42#65261—32no—
43#65231—31no—
44#65231—31no—
45C22⋊C4×Dic5—31no—
46C22⋊C4×Dic5—31no—
47#64941—32no—
48#64938—32no—
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—42no—
51C22×C3×C4×C5C2×C414yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C3×Dic5—24no—
59C22×C3×Dic5—42no—
60C22×C3×Dic5C2×C414yes—
61C22×C3×Dic5C2×C414yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66#6719—22no—
67#6719Q814yes—
68C4×Dic15—42no—
69C5×#217—22no—
70C5×#217—22no—
71C5×C4⋊Dic3—42no—
72C3×#683C2×C414yes—
73C3×#683C2×C414yes—
74C3×#683C2×C414yes—
75C3×#683C2×C414yes—
76#6668—24no—
77#6668—42no—
78Dic3×Dic5—24no—
79Dic3×Dic5—42no—
80C22×C3×C4⋊C4—51no—
81#5212—51no—
82#5212—51no—
83#5212D511yescharacteristic
84C4×#217—51no—
85C4×#217—51no—
86C4×#217—51no—
87#4984—52no—
88#4980—52no—
89#4980—52no—
90Dic3×C4⋊C4—52no—
91C23×C4×C5C2×D311yescharacteristic
92C23×Dic5C2×D311yescharacteristic
93C23×Dic5C2×D311yescharacteristic
94C2×C5×C4⋊C4—32no—
95C2×C5×C22⋊C4—31no—
96C2×C5×C22⋊C4—31no—
97C2×C22⋊Dic5—31no—
98C2×C22⋊Dic5—31no—
99C2×#683—32no—
100C2×#683—32no—
101C2×#683Dic318yescomplemented
102C2×#683C2×D311yescharacteristic
103C2×#683C2×D311yescharacteristic
104C2×#683C2×D311yescharacteristic
105C2×#683C2×D311yescharacteristic
106C2×C4×Dic5—32no—
107C2×C4×Dic5—32no—
108C2×C4×Dic5—32no—
109C5×#95—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963—32no—
115#2345—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—22no—
118C23×C3×C5C22×C412yes—
119C23×C3×C5C2×Q812yes—
120C23×C3×C5#4112yes—
121C23×C3×C5C2411yescharacteristic
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—44no—
125C2×C3×C4×C5C22×C412yes—
126C2×C3×C4×C5C22×C412yes—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15C2×Q814yes—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—28no—
143C2×C3×Dic5—44no—
144C2×C3×Dic5C22×C412yes—
145C2×C3×Dic5C22×C412yes—
146C2×C3×Dic5C22×C412yes—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5#4114yes—
149C23×C3×C4—51no—
150C23×C3×C4—51no—
151C23×C3×C4C2×D511yescharacteristic
152C2×C3×C4⋊C4—58no—
153C2×C3×C4⋊C4—51no—
154C2×C3×C4⋊C4—51no—
155C2×C3×C4⋊C4—51no—
156C2×C3×C4⋊C4—51no—
157C2×#217—51no—
158C2×#217—51no—
159C2×#217C2×D511yescharacteristic
160C2×#217C2×D511yescharacteristic
161C2×C4⋊Dic3—52no—
162C2×C4⋊Dic3—52no—
163C2×C4⋊Dic3C2×D512yes—
164C2×C4×Dic3—52no—
165C2×C4×Dic3—52no—
166C2×C4×Dic3—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C3⋊#95—52no—
171C3⋊#95—52no—
172C3⋊#95C2×D512yes—
173C24×C5C22×D311yescharacteristic
174C22×C4×C5—32no—
175C22×C4×C5—32no—
176C22×C4×C5—42no—
177C22×C4×C5C2×Dic314yes—
178C22×C4×C5C22×D311yescharacteristic
179C22×C4×C5C22×D311yescharacteristic
180C22×Dic5—24no—
181C22×Dic5—32no—
182C22×Dic5—32no—
183C22×Dic5—42no—
184C22×Dic5C2×Dic314yes—
185C22×Dic5C2×Dic314yes—
186C22×Dic5C22×D311yescharacteristic
187C22×Dic5C22×D311yescharacteristic
188C22×Dic5C22×D311yescharacteristic
189C22×Dic5C22×D311yescharacteristic
190C5×C4⋊C4—122no—
191C5×C22⋊C4—62no—
192C5×C22⋊C4—62no—
193C22⋊Dic5—34no—
194C22⋊Dic5—62no—
195#683—64no—
196#683—122no—
197#683C2×Dic314yes—
198#683C2×Dic314yes—
199#683C2×Dic314yes—
200#683C2×Dic314yes—
201C4×Dic5—64no—
202C4×Dic5—122no—
203C4×Dic5—122no—
204C22×C4⋊C4—51no—
205#389—152no—
206#387—152no—
207#387—152no—
208#380—31no—
209#380—151no—
210#380—151no—
211C4×C4⋊C4—152no—
212C4×C22⋊C4—151no—
213C4×C22⋊C4—151no—
214C4×C22⋊C4—151no—
215C22×C3×C5—22no—
216C22×C3×C5—22no—
217C22×C3×C5—24no—
218C22×C3×C5—24no—
219C22×C3×C5C4×Q814yes—
220C22×C3×C5C23×C411yescharacteristic
221C22×C3×C5C22×Q811yescharacteristic
222C22×C3×C5C2×#4111yescharacteristic
223C22×C3×C5C2×#4112yes—
224C22×C3×C5H(5,𝔽2)12yes—
225C3×C4×C5—22no—
226C3×C4×C5—22no—
227Dic15—24no—
228Dic15—42no—
229C3×Dic5—22no—
230C3×Dic5—22no—
231C3×Dic5—22no—
232C3×Dic5#11714yes—
233C5×Dic3—42no—
234C5×Dic3—42no—
235C24×C3C22×D511yescharacteristic
236C22×C3×C4—42no—
237C22×C3×C4—51no—
238C22×C3×C4—54no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—51no—
242C22×C3×C4—54no—
243C22×C3×C4—104no—
244C22×C3×C4—202no—
245C22×C3×C4C4×D514yes—
246C22×C3×C4C22×D511yescharacteristic
247C22×C3×C4C22×D511yescharacteristic
248C22×Dic3—52no—
249C22×Dic3—52no—
250C22×Dic3C22×D512yes—
251C22×Dic3C22×D512yes—
252C3×C4⋊C4—54no—
253C3×C4⋊C4—54no—
254C3×C4⋊C4—54no—
255C3×C4⋊C4—54no—
256#217—22no—
257#217—22no—
258#217—54no—
259#217—102no—
260C4⋊Dic3—42no—
261C4⋊Dic3—104no—
262C4⋊Dic3—202no—
263C4×Dic3—104no—
264C4×Dic3—202no—
265C4×Dic3—202no—
266C23×C5—22no—
267C23×C5—22no—
268C23×C5D3×Q812yes—
269C23×C5#23912yes—
270C23×C5C22×Dic312yes—
271C23×C5C23×D311yescharacteristic
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—44no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5C22×Dic312yes—
282C2×C4×C5C22×Dic312yes—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—28no—
287C2×Dic5—34no—
288C2×Dic5—44no—
289C2×Dic5—62no—
290C2×Dic5—62no—
291C2×Dic5—62no—
292C2×Dic5—62no—
293C2×Dic5—62no—
294C2×Dic5#23514yes—
295C2×Dic5C22×Dic312yes—
296C2×Dic5C22×Dic312yes—
297C2×Dic5C22×Dic312yes—
298C2×Dic5C22×Dic312yes—
299C23×C4—51no—
300C23×C4—51no—
301C23×C4D3×D511yescharacteristic
302C2×C4⋊C4—32no—
303C2×C4⋊C4—58no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—51no—
306C2×C4⋊C4—51no—
307C2×C4⋊C4—51no—
308C2×C4⋊C4—152no—
309C2×C4⋊C4—152no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—151no—
313C2×C22⋊C4—151no—
314C2×C42—152no—
315C2×C42—152no—
316C2×C42—152no—
317#95—32no—
318#95—152no—
319#95—152no—
320#95—152no—
321#95—152no—
322#95—152no—
323C2×C3×C5—24no—
324C2×C3×C5C2×#11711yescharacteristic
325C2×C3×C5C2×C4×Q811yescharacteristic
326C2×C3×C5#51811yescharacteristic
327C2×C3×C5#55312yes—
328C2×C3×C5#55412yes—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3C2×C4×D512yes—
332C23×C3#71112yes—
333C23×C3Q8×D512yes—
334C23×C3C23×D511yescharacteristic
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—44no—
338C2×C3×C4—52no—
339C2×C3×C4—54no—
340C2×C3×C4—52no—
341C2×C3×C4—52no—
342C2×C3×C4—52no—
343C2×C3×C4—108no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—204no—
348C2×C3×C4C2×C4×D512yes—
349C2×C3×C4C2×C4×D512yes—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—54no—
357C2×Dic3—102no—
358C2×Dic3—102no—
359C2×Dic3—102no—
360C2×Dic3—102no—
361C2×Dic3—102no—
362C22×C5—24no—
363C22×C5—24no—
364C22×C5—22no—
365C22×C5—22no—
366C22×C5Q8×Dic314yes—
367C22×C5C2×#23512yes—
368C22×C5#100412yes—
369C22×C5C2×D3×Q811yescharacteristic
370C22×C5C2×#23911yescharacteristic
371C22×C5C23×Dic311yescharacteristic
372C4×C5—22no—
373C4×C5—22no—
374C4×C5—122no—
375C4×C5—122no—
376Dic5—22no—
377Dic5—22no—
378Dic5—22no—
379Dic5—64no—
380Dic5—122no—
381Dic5#92614yes—
382C24C2×D3×D511yescharacteristic
383C22×C4—32no—
384C22×C4—32no—
385C22×C4—42no—
386C22×C4—51no—
387C22×C4—54no—
388C22×C4—51no—
389C22×C4—51no—
390C22×C4—51no—
391C22×C4—54no—
392C22×C4—104no—
393C22×C4—152no—
394C22×C4—152no—
395C22×C4—202no—
396C22×C4D5×Dic314yes—
397C22×C4C2×D3×D511yescharacteristic
398C22×C4C2×D3×D511yescharacteristic
399C4⋊C4—54no—
400C4⋊C4—54no—
401C4⋊C4—54no—
402C4⋊C4—54no—
403C4⋊C4—122no—
404C4⋊C4—304no—
405C4⋊C4—602no—
406C22⋊C4—62no—
407C22⋊C4—62no—
408C22⋊C4—154no—
409C22⋊C4—302no—
410C42—304no—
411C42—602no—
412C42—602no—
413C3×C5#234511yescharacteristic, complemented, Hall
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3#403314yes—
419C22×C3C22×C4×D511yescharacteristic
420C22×C3C2×#71111yescharacteristic
421C22×C3#414412yes—
422C22×C3C2×Q8×D511yescharacteristic
423C22×C3D5×#4112yes—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—54no—
427C3×C4—102no—
428C3×C4—102no—
429C3×C4—102no—
430Dic3—42no—
431Dic3—42no—
432Dic3—104no—
433Dic3—202no—
434C2×C5—24no—
435C2×C5#551112yes—
436C2×C5#551412yes—
437C2×C5C2×#92611yescharacteristic
438C2×C5#579811yescharacteristic
439C2×C5C2×Q8×Dic311yescharacteristic
440C23—22no—
441C23—22no—
442C23#676812yes—
443C23D15⋊Q812yes—
444C23C2×D5×Dic312yes—
445C23C22×D3×D511yescharacteristic
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—44no—
449C2×C4—54no—
450C2×C4—52no—
451C2×C4—52no—
452C2×C4—52no—
453C2×C4—52no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—108no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—154no—
465C2×C4—204no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4—302no—
469C2×C4—302no—
470C2×C4—302no—
471C2×C4C2×D5×Dic312yes—
472C2×C4C2×D5×Dic312yes—
473C2×C3—24no—
474C2×C3#6582011yescharacteristic
475C2×C3C2×#403311yescharacteristic
476C2×C3D5×#11711yescharacteristic
477C2×C3#6593512yes—
478C2×C3#6597012yes—
479C5#8216011yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—24no—
483C22—24no—
484C22#9133114yes—
485C22C2×#676811yescharacteristic
486C22C2×D15⋊Q811yescharacteristic
487C22D5×#23512yes—
488C22C22×D5×Dic311yescharacteristic
489C22#9204912yes—
490C4—22no—
491C4—22no—
492C4—54no—
493C4—102no—
494C4—102no—
495C4—102no—
496C4—122no—
497C4—122no—
498C4—304no—
499C4—602no—
500C3#1060561111yescharacteristic, complemented, Sylow
501C2—24no—
502C2C2×#9133111yescharacteristic
503C2D5×#92611yescharacteristic
504C2#1175441312yes—
505C2#1175441712yes—
506C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#2345
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #11748690C2semidirect
9. #11748681C2semidirect
10. #11748637C2semidirect
11. #11748601C2semidirect
22. C2×C3×#683C4semidirect
101. C2×#683Dic3semidirect
413. C3×C5#2345semidirect
479. C5#82160semidirect
500. C3#10605611semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6832
C4×#67192
C5×#52122
#117495062
Dic5×#2172
#117486902
#117486812
#117486372
#117486012
#106056113
#821605