Finite Group Databasebeta

← #14322883

Subgroups — #14322883

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic
2C2×C4⋊C4×D15C211yesmaximal, characteristic
3C2×#91761C211yesmaximal, characteristic
4C3×C5×#384C211yesmaximal, characteristic, complemented
5#11751090C214yesmaximal
6#11751078C211yesmaximal, characteristic, complemented
7#11751077C214yesmaximal, complemented
8#11751076C211yesmaximal, characteristic, complemented
9#11751037C211yesmaximal, characteristic, complemented
10#10606090—31nomaximal, Hall
11C22×C4×D15C2212yes—
12C22×C4×D15C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2214yes—
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6714C2212yes—
18C2×#6714C2212yes—
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2212yes—
22C2×#6712C2214yes—
23C2×#6712C2212yes—
24C2×C4×Dic15C2212yes—
25C2×C4×Dic15C2211yescharacteristic
26#91781—24no—
27C4⋊C4×D15—24no—
28#91761C418yescomplemented
29#91115C2214yes—
30#91115C2214yes—
31#74359—51nomaximal, Hall
32C2×#4038—31no—
33C2×D5×C4⋊C4—31no—
34C2×#4018—31no—
35C5×#384D311yescharacteristic, complemented
36#65278—34no—
37#65266—31no—
38#65265—31no—
39#65261—34no—
40#65225—31no—
41C23×D15C2311yescharacteristic
42C22×C3×C4×C5C2312yes—
43C22×C3×C4×C5C2312yes—
44C22×C3×C4×C5C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15C2312yes—
47C22×Dic15C2312yes—
48C22×Dic15C2312yes—
49C22×Dic15C2311yescharacteristic
50C2×C4×D15—24no—
51C2×C4×D15—44no—
52C2×C4×D15C2×C414yes—
53C2×C4×D15D414yes—
54C2×C4×D15Q814yes—
55C3×C5×C4⋊C4—22no—
56C3×C5×C4⋊C4—22no—
57C3×C5×C4⋊C4—44no—
58C3×C42×C5C2×C414yescomplemented
59#6714—24no—
60#6714C2×C418yes—
61C4⋊Dic15—22no—
62C4⋊Dic15—22no—
63#6712—24no—
64#6712—44no—
65#6712C2×C418yescomplemented
66C4×Dic15—24no—
67C4×Dic15C2×C414yescomplemented
68C2×#892—51no—
69C2×D3×C4⋊C4—51no—
70C2×#872—51no—
71C3×#384D511yescharacteristic, complemented
72#4989—54no—
73#4977—51no—
74#4976—54no—
75#4975—51no—
76#4936—51no—
77C22×C4×D5—31no—
78C22×C4×D5—32no—
79C2×C5×C4⋊C4C2×D311yescharacteristic
80C2×C5×C4⋊C4C2×D311yescharacteristic
81C2×C5×C4⋊C4C2×D314yes—
82C2×C42×C5C2×D311yescharacteristic
83C2×#685—32no—
84C2×#685—32no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5—31no—
87C2×#683—32no—
88C2×#683—32no—
89C2×#683—34no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—32no—
92#4038—64no—
93D5×C4⋊C4—64no—
94#4018—38no—
95#3963—34no—
96#3963—34no—
97#2317—151noSylow
98C23×C3×C5C2411yescharacteristic
99C22×D15—22no—
100C22×D15—22no—
101C22×D15C22×C412yes—
102C22×D15C2×D412yes—
103C22×D15C2×Q812yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—24no—
109C2×C3×C4×C5—24no—
110C2×C3×C4×C5C22×C414yes—
111C2×C3×C4×C5C22×C412yes—
112C2×C3×C4×C5C2×D412yes—
113C2×C3×C4×C5C2×Q812yes—
114C2×Dic15—22no—
115C2×Dic15—22no—
116C2×Dic15—22no—
117C2×Dic15—22no—
118C2×Dic15—24no—
119C2×Dic15—24no—
120C2×Dic15C22×C414yes—
121C2×Dic15C22×C412yes—
122C2×Dic15C2×D412yes—
123C2×Dic15C2×Q812yes—
124C4×D15—48no—
125C4×D15C4⋊C4116yescomplemented
126C22×C4×D3—51no—
127C22×C4×D3—52no—
128C2×C3×C4⋊C4C2×D511yescharacteristic
129C2×C3×C4⋊C4C2×D511yescharacteristic
130C2×C3×C4⋊C4C2×D514yes—
131C2×C3×C42C2×D511yescharacteristic
132C2×(C2×D3)⋊C4—52no—
133C2×(C2×D3)⋊C4—52no—
134C2×C4⋊Dic3—51no—
135C2×C4⋊Dic3—51no—
136C2×Dic3⋊C4—52no—
137C2×Dic3⋊C4—52no—
138C2×Dic3⋊C4—54no—
139C2×C4×Dic3—51no—
140C2×C4×Dic3—52no—
141#892—104no—
142D3×C4⋊C4—104no—
143#872—58no—
144C3⋊#95—54no—
145C3⋊#95—54no—
146C23×D5—31no—
147C22×C4×C5C22×D312yes—
148C22×C4×C5C22×D312yes—
149C22×C4×C5C22×D312yes—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—31no—
152C22×Dic5—32no—
153C22×Dic5—32no—
154C22×Dic5—32no—
155C2×C4×D5—34no—
156C2×C4×D5—34no—
157C2×C4×D5—34no—
158C2×C4×D5—64no—
159C2×C4×D5—124no—
160C5×C4⋊C4—22no—
161C5×C4⋊C4—22no—
162C5×C4⋊C4—44no—
163C42×C5C4×D314yescomplemented
164#685—38no—
165#685—64no—
166C4⋊Dic5—62no—
167C4⋊Dic5—62no—
168#683—38no—
169#683—64no—
170#683—124no—
171C4×Dic5—34no—
172C4×Dic5—64no—
173C2×#117—151no—
174C2×#117—151no—
175C22×C4⋊C4—151no—
176#389—154no—
177#385—154no—
178#384—151no—
179#384D1511yescharacteristic, complemented
180#382—151no—
181#382—151no—
182C22×C3×C5C23×C411yescharacteristic
183C22×C3×C5C22×D411yescharacteristic
184C22×C3×C5C22×Q811yescharacteristic
185C22×C3×C5H(5,𝔽2)12yes—
186C22×C3×C52−1+412yes—
187C2×D15—24no—
188C2×D15—22no—
189C2×D15—22no—
190C2×D15—24no—
191C2×D15C2×C4⋊C414yes—
192C3×C4×C5—24no—
193C3×C4×C5—42no—
194C3×C4×C5—42no—
195C3×C4×C5C2×C4⋊C414yes—
196Dic15—24no—
197Dic15—42no—
198Dic15—42no—
199Dic15C2×C4⋊C414yes—
200C23×D3—51no—
201C22×C3×C4C22×D512yes—
202C22×C3×C4C22×D512yes—
203C22×C3×C4C22×D512yes—
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—51no—
206C22×Dic3—52no—
207C22×Dic3—52no—
208C22×Dic3—52no—
209C2×C4×D3—54no—
210C2×C4×D3—54no—
211C2×C4×D3—54no—
212C2×C4×D3—104no—
213C2×C4×D3—204no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—44no—
217C3×C42C4×D514yescomplemented
218(C2×D3)⋊C4—58no—
219(C2×D3)⋊C4—104no—
220C4⋊Dic3—102no—
221C4⋊Dic3—102no—
222Dic3⋊C4—58no—
223Dic3⋊C4—104no—
224Dic3⋊C4—204no—
225C4×Dic3—54no—
226C4×Dic3—104no—
227C23×C5C23×D311yescharacteristic
228C22×D5—32no—
229C22×D5—32no—
230C22×D5—32no—
231C22×D5—62no—
232C22×D5—62no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—24no—
238C2×C4×C5—24no—
239C2×C4×C5C2×C4×D314yes—
240C2×C4×C5C2×C4×D312yes—
241C2×C4×C5D3×D412yes—
242C2×C4×C5D3×Q812yes—
243C2×Dic5—32no—
244C2×Dic5—32no—
245C2×Dic5—32no—
246C2×Dic5—34no—
247C2×Dic5—62no—
248C2×Dic5—62no—
249C2×Dic5—62no—
250C2×Dic5—62no—
251C2×Dic5—64no—
252C2×Dic5—64no—
253C4×D5—316no—
254C4×D5—128no—
255C23×C4—151no—
256C23×C4—152no—
257#117—158no—
258#117—304no—
259C2×C4⋊C4—152no—
260C2×C4⋊C4—151no—
261C2×C4⋊C4—152no—
262C2×C4⋊C4—151no—
263C2×C4⋊C4—154no—
264C2×C4⋊C4—304no—
265C2×C4⋊C4C2×D1511yescharacteristic
266C2×C4⋊C4C2×D1511yescharacteristic
267C2×C4⋊C4C2×D1514yes—
268C2×C22⋊C4—152no—
269C2×C22⋊C4—152no—
270C2×C42—151no—
271C2×C42—152no—
272C2×C42C2×D1511yescharacteristic
273#95—154no—
274#95—154no—
275C2×C3×C5C22×C4⋊C411yescharacteristic
276C2×C3×C5#52012yes—
277C2×C3×C5#53511yescharacteristic
278C2×C3×C5#53611yescharacteristic
279C2×C3×C5#54412yes—
280D15—24no—
281C23×C3C23×D511yescharacteristic
282C22×D3—52no—
283C22×D3—52no—
284C22×D3—52no—
285C22×D3—102no—
286C22×D3—102no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—24no—
292C2×C3×C4—24no—
293C2×C3×C4C2×C4×D514yes—
294C2×C3×C4C2×C4×D512yes—
295C2×C3×C4D4×D512yes—
296C2×C3×C4Q8×D512yes—
297C2×Dic3—52no—
298C2×Dic3—52no—
299C2×Dic3—52no—
300C2×Dic3—54no—
301C2×Dic3—102no—
302C2×Dic3—102no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3—104no—
306C2×Dic3—104no—
307C4×D3—516no—
308C4×D3—208no—
309C22×C5C22×C4×D311yescharacteristic
310C22×C5C2×D3×D411yescharacteristic
311C22×C5#100412yes—
312C22×C5C2×D3×Q811yescharacteristic
313C22×C5#100712yes—
314C2×D5—34no—
315C2×D5—62no—
316C2×D5—62no—
317C2×D5—64no—
318C2×D5—64no—
319C4×C5—24no—
320C4×C5—42no—
321C4×C5—42no—
322C4×C5D3×C4⋊C414yes—
323Dic5—34no—
324Dic5—64no—
325Dic5—122no—
326Dic5—122no—
327C24—151no—
328C22×C4—151no—
329C22×C4—154no—
330C22×C4—154no—
331C22×C4—154no—
332C22×C4—152no—
333C22×C4—152no—
334C22×C4—152no—
335C22×C4—304no—
336C22×C4—604no—
337C22×C4C22×D1512yes—
338C22×C4C22×D1512yes—
339C22×C4C22×D1512yes—
340C22×C4C22×D1511yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—44no—
344C4⋊C4—158no—
345C4⋊C4—304no—
346C4⋊C4—302no—
347C4⋊C4—302no—
348C4⋊C4—604no—
349C22⋊C4—158no—
350C22⋊C4—304no—
351C42—154no—
352C42—304no—
353C42C4×D1514yescomplemented
354C3×C5#231711yescharacteristic, complemented, Hall
355C22×C3C22×C4×D511yescharacteristic
356C22×C3C2×D4×D511yescharacteristic
357C22×C3#414412yes—
358C22×C3C2×Q8×D511yescharacteristic
359C22×C3#414712yes—
360C2×D3—54no—
361C2×D3—102no—
362C2×D3—102no—
363C2×D3—104no—
364C2×D3—104no—
365C3×C4—24no—
366C3×C4—42no—
367C3×C4—42no—
368C3×C4D5×C4⋊C414yes—
369Dic3—54no—
370Dic3—104no—
371Dic3—202no—
372Dic3—202no—
373C2×C5C2×D3×C4⋊C411yescharacteristic
374C2×C5#550412yes—
375C2×C5#571511yescharacteristic
376C2×C5#572411yescharacteristic
377C2×C5#572912yes—
378D5—64no—
379C23—152no—
380C23—152no—
381C23—152no—
382C23—302no—
383C23—302no—
384C23C23×D1511yescharacteristic
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—152no—
392C2×C4—152no—
393C2×C4—152no—
394C2×C4—1516no—
395C2×C4—154no—
396C2×C4—302no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4—304no—
401C2×C4—304no—
402C2×C4—608no—
403C2×C4C2×C4×D1514yes—
404C2×C4C2×C4×D1512yes—
405C2×C4D4×D1512yes—
406C2×C4Q8×D1512yes—
407C2×C3C2×D5×C4⋊C411yescharacteristic
408C2×C3#6583812yes—
409C2×C3#6604911yescharacteristic
410C2×C3#6605811yescharacteristic
411C2×C3#6606312yes—
412D3—104no—
413C5#7435911yescharacteristic, complemented, Sylow
414C22—154no—
415C22—302no—
416C22—302no—
417C22—304no—
418C22—304no—
419C22C22×C4×D1511yescharacteristic
420C22C2×D4×D1511yescharacteristic
421C22#9209512yes—
422C22C2×Q8×D1511yescharacteristic
423C22#9209812yes—
424C4—24no—
425C4—42no—
426C4—42no—
427C4—154no—
428C4—304no—
429C4—602no—
430C4—602no—
431C4C4⋊C4×D1514yes—
432C3#1060609011yescharacteristic, complemented, Sylow
433C2—304no—
434C2C2×C4⋊C4×D1511yescharacteristic
435C2#1175626312yes—
436C2#1175647411yescharacteristic
437C2#1175648311yescharacteristic
438C2#1175648812yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#384C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#384D15
hypocenterC3×C5#2317
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
4. C3×C5×#384C2semidirect
6. #11751078C2semidirect
7. #11751077C2semidirect
8. #11751076C2semidirect
9. #11751037C2semidirect
28. #91761C4semidirect
35. C5×#384D3semidirect
58. C3×C42×C5C2×C4semidirect
65. #6712C2×C4semidirect
67. C4×Dic15C2×C4semidirect
71. C3×#384D5semidirect
125. C4×D15C4⋊C4semidirect
163. C42×C5C4×D3semidirect
179. #384D15semidirect
217. C3×C42C4×D5semidirect
353. C42C4×D15semidirect
354. C3×C5#2317semidirect
413. C5#74359semidirect
432. C3#10606090semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×C4⋊C4×D152
C2×#917612
C3×C5×#3842
#117510902
#117510782
#117510772
#117510762
#117510372
#106060903
#743595