Finite Group Databasebeta

← #14322944

Subgroups — #14322944

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×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic
3C2×#91357C211yesmaximal, characteristic
4#11751076C211yesmaximal, characteristic, complemented
5C5×#4977C211yesmaximal, characteristic, complemented
6#11748861C211yesmaximal, characteristic, complemented
7#11748704C214yesmaximal
8#11748627C214yesmaximal, complemented
9#11748623C211yesmaximal, characteristic, complemented
10#10605956—31nomaximal, Hall
11C22×C3×C4×D5C2212yes—
12C22×C3×C4×D5C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×#6712C2214yes—
16C2×C4×Dic15C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#683C2212yes—
21C3×D5×C4⋊C4—24no—
22C2×Dic3⋊Dic5C2214yes—
23C2×#6668C2212yes—
24C2×#6665C2212yes—
25C2×#6665C2212yes—
26C2×Dic3×Dic5C2212yes—
27#91358—24no—
28#91357C418yescomplemented
29C5×C3⋊#95C2214yes—
30#90994C2214yes—
31#82157—51nomaximal, Hall
32C2×#4038—31no—
33C2×D5×C4⋊C4D311yescharacteristic
34C2×#4018—31no—
35C5×#382—31no—
36#65266—31no—
37#65265—31no—
38#65224—31no—
39#64957—34no—
40#64936—34no—
41C23×C3×D5C2311yescharacteristic
42C22×C3×C4×C5C2312yes—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15C2312yes—
45C22×Dic15C2312yes—
46C22×C5×Dic3C2312yes—
47C22×C5×Dic3C2312yes—
48C22×C3×Dic5C2312yes—
49C22×C3×Dic5C2311yescharacteristic
50C2×C3×C4×D5—24no—
51C2×C3×C4×D5—44no—
52C2×C3×C4×D5C2×C414yes—
53C2×C3×C4×D5D414yes—
54C2×C3×C4×D5Q814yes—
55C3×C5×C4⋊C4—22no—
56C4⋊Dic15—22no—
57#6712—44no—
58C4×Dic15C2×C414yescomplemented
59C5×C4⋊Dic3—22no—
60C4×C5×Dic3C2×C414yescomplemented
61C3×C4⋊Dic5—22no—
62C3×#683—24no—
63Dic3⋊Dic5—44no—
64#6668C2×C418yescomplemented
65#6665—24no—
66#6665C2×C418yes—
67Dic3×Dic5—24no—
68C22×C3×C4⋊C4—51no—
69C2×#926—51no—
70C2×#926—51no—
71#5210—54no—
72#4977—51no—
73#4977D511yescharacteristic, complemented
74#4975—51no—
75#4975—51no—
76#4972—54no—
77C22×C4×D5C2×D312yes—
78C22×C4×D5C2×D311yescharacteristic
79C2×C5×C4⋊C4—31no—
80C2×C5×C4⋊C4C2×D311yescharacteristic
81C2×C42×C5—31no—
82C2×#685—32no—
83C2×#685—32no—
84C2×C4⋊Dic5—31no—
85C2×C4⋊Dic5—34no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87C2×#683—32no—
88C2×#683—34no—
89C2×#683C2×D312yes—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—32no—
92#4038—64no—
93D5×C4⋊C4—24no—
94#4018—38no—
95C5×#95—34no—
96#3963—34no—
97#2317—151noSylow
98C23×C3×C5C2411yescharacteristic
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5C22×C412yes—
102C22×C3×D5C2×D412yes—
103C22×C3×D5C2×Q812yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—24no—
106C2×C3×C4×C5C22×C412yes—
107C2×C3×C4×C5C2×D412yes—
108C2×C3×C4×C5C2×Q812yes—
109C2×Dic15—22no—
110C2×Dic15—22no—
111C2×Dic15—22no—
112C2×Dic15—24no—
113C2×Dic15C22×C414yes—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—24no—
118C2×C5×Dic3C22×C414yes—
119C2×C3×Dic5—22no—
120C2×C3×Dic5—24no—
121C2×C3×Dic5C22×C412yes—
122C2×C3×Dic5C2×D412yes—
123C2×C3×Dic5C2×Q812yes—
124C3×C4×D5—48no—
125C3×C4×D5C4⋊C4116yescomplemented
126C23×C3×C4—51no—
127C23×C3×C4—52no—
128C2×C3×C4⋊C4—52no—
129C2×C3×C4⋊C4—51no—
130C2×C3×C4⋊C4—104no—
131C2×C3×C4⋊C4C2×D511yescharacteristic
132C2×#217—52no—
133C2×#217—52no—
134#926—58no—
135#926—104no—
136C2×C4⋊Dic3—52no—
137C2×C4⋊Dic3—51no—
138C2×C4⋊Dic3C2×D511yescharacteristic
139C2×Dic3⋊C4—54no—
140C2×Dic3⋊C4—54no—
141C2×C4×Dic3—51no—
142C2×C4×Dic3—52no—
143C2×C4×Dic3C2×D511yescharacteristic
144C3⋊#95—54no—
145C3⋊#95C2×D514yes—
146C23×D5C22×D311yescharacteristic
147C22×C4×C5—32no—
148C22×C4×C5—32no—
149C22×C4×C5C22×D312yes—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—32no—
152C22×Dic5—32no—
153C22×Dic5C22×D312yes—
154C22×Dic5C22×D311yescharacteristic
155C2×C4×D5—24no—
156C2×C4×D5—44no—
157C2×C4×D5Dic614yes—
158C2×C4×D5C4×D314yes—
159C2×C4×D5#6714yes—
160C5×C4⋊C4—22no—
161C5×C4⋊C4—62no—
162C42×C5—34no—
163#685—38no—
164#685—64no—
165C4⋊Dic5—22no—
166C4⋊Dic5—62no—
167C4⋊Dic5—124no—
168#683—24no—
169#683—38no—
170#683—124no—
171C4×Dic5—34no—
172C4×Dic5—64no—
173C2×#117—151no—
174C2×#117—151no—
175C22×C4⋊C4—51no—
176#389—154no—
177#385—154no—
178#384—151no—
179#384—151no—
180#382—31no—
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×C3×D5—24no—
188C2×C3×D5—22no—
189C2×C3×D5—22no—
190C2×C3×D5—24no—
191C2×C3×D5C2×C4⋊C414yes—
192C3×C4×C5—42no—
193C3×C4×C5C2×C4⋊C414yes—
194Dic15—24no—
195Dic15—42no—
196C3×Dic5—42no—
197C3×Dic5C2×C4⋊C414yes—
198C5×Dic3—24no—
199C5×Dic3—42no—
200C24×C3—51no—
201C22×C3×C4—51no—
202C22×C3×C4—54no—
203C22×C3×C4—54no—
204C22×C3×C4—54no—
205C22×C3×C4—52no—
206C22×C3×C4—104no—
207C22×C3×C4—204no—
208C22×C3×C4C22×D512yes—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—52no—
211C22×Dic3—52no—
212C22×Dic3C22×D512yes—
213C22×Dic3C22×D512yes—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—104no—
216C3×C4⋊C4—102no—
217#217—58no—
218#217—104no—
219C4⋊Dic3—22no—
220C4⋊Dic3—58no—
221C4⋊Dic3—102no—
222Dic3⋊C4—204no—
223Dic3⋊C4—204no—
224C4×Dic3—54no—
225C4×Dic3—104no—
226C4×Dic3C4×D514yescomplemented
227C23×C5C23×D311yescharacteristic
228C22×D5—22no—
229C22×D5—22no—
230C22×D5C2×Dic612yes—
231C22×D5C2×C4×D312yes—
232C22×D5C2×#6712yes—
233C2×C4×C5—24no—
234C2×C4×C5—22no—
235C2×C4×C5—34no—
236C2×C4×C5—62no—
237C2×C4×C5—62no—
238C2×C4×C5—64no—
239C2×C4×C5—62no—
240C2×C4×C5C2×Dic612yes—
241C2×C4×C5C2×C4×D312yes—
242C2×C4×C5C2×#6712yes—
243C2×Dic5—24no—
244C2×Dic5—22no—
245C2×Dic5—34no—
246C2×Dic5—62no—
247C2×Dic5—62no—
248C2×Dic5—64no—
249C2×Dic5—62no—
250C2×Dic5C2×Dic612yes—
251C2×Dic5C2×C4×D312yes—
252C2×Dic5C2×#6712yes—
253C4×D5—48no—
254C4×D5Dic3⋊C4116yescomplemented
255C23×C4—51no—
256C23×C4—52no—
257#117—158no—
258#117—304no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—51no—
261C2×C4⋊C4—52no—
262C2×C4⋊C4—104no—
263C2×C4⋊C4—152no—
264C2×C4⋊C4—151no—
265C2×C4⋊C4—154no—
266C2×C4⋊C4—154no—
267C2×C4⋊C4D3×D511yescharacteristic
268C2×C22⋊C4—152no—
269C2×C22⋊C4—152no—
270C2×C42—31no—
271C2×C42—151no—
272C2×C42—152no—
273#95—34no—
274#95—154no—
275C2×C3×C5C22×C4⋊C411yescharacteristic
276C2×C3×C5#52012yes—
277C2×C3×C5#53511yescharacteristic
278C2×C3×C5#53611yescharacteristic
279C2×C3×C5#54412yes—
280C3×D5—24no—
281C23×C3—52no—
282C23×C3—52no—
283C23×C3—52no—
284C23×C3—102no—
285C23×C3—102no—
286C23×C3C23×D511yescharacteristic
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—52no—
290C2×C3×C4—52no—
291C2×C3×C4—52no—
292C2×C3×C4—516no—
293C2×C3×C4—102no—
294C2×C3×C4—104no—
295C2×C3×C4—208no—
296C2×C3×C4C2×C4×D512yes—
297C2×C3×C4D4×D512yes—
298C2×C3×C4Q8×D512yes—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—24no—
303C2×Dic3—54no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306C2×Dic3—102no—
307C2×Dic3—104no—
308C2×Dic3C2×C4×D514yes—
309C22×C5C22×Dic611yescharacteristic
310C22×C5C22×C4×D311yescharacteristic
311C22×C5#100412yes—
312C22×C5#100712yes—
313C22×C5C22×#6711yescharacteristic
314C2×D5—24no—
315C2×D5—24no—
316C2×D5—22no—
317C2×D5—22no—
318C2×D5C2×Dic3⋊C414yes—
319C4×C5—42no—
320C4×C5—64no—
321C4×C5—122no—
322C4×C5C2×Dic3⋊C414yes—
323Dic5—42no—
324Dic5—64no—
325Dic5—122no—
326Dic5C2×Dic3⋊C414yes—
327C24—51no—
328C22×C4—32no—
329C22×C4—32no—
330C22×C4—51no—
331C22×C4—54no—
332C22×C4—54no—
333C22×C4—54no—
334C22×C4—52no—
335C22×C4—104no—
336C22×C4—152no—
337C22×C4—152no—
338C22×C4—204no—
339C22×C4C2×D3×D512yes—
340C22×C4C2×D3×D511yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—62no—
343C4⋊C4—104no—
344C4⋊C4—102no—
345C4⋊C4—158no—
346C4⋊C4—302no—
347C4⋊C4—604no—
348C4⋊C4—604no—
349C22⋊C4—158no—
350C22⋊C4—304no—
351C42—34no—
352C42—154no—
353C42—304no—
354C3×C5#231711yescharacteristic, complemented, Hall
355C22×C3—54no—
356C22×C3—104no—
357C22×C3—102no—
358C22×C3—102no—
359C22×C3—104no—
360C22×C3C22×C4×D511yescharacteristic
361C22×C3C2×D4×D511yescharacteristic
362C22×C3C2×Q8×D511yescharacteristic
363C22×C3#414912yes—
364C22×C3#415012yes—
365C3×C4—42no—
366C3×C4—54no—
367C3×C4—202no—
368C3×C4D5×C4⋊C414yes—
369Dic3—24no—
370Dic3—42no—
371Dic3—104no—
372Dic3—202no—
373C2×C5#550012yes—
374C2×C5#550412yes—
375C2×C5C22×Dic3⋊C411yescharacteristic
376C2×C5#580511yescharacteristic
377C2×C5#581611yescharacteristic
378D5—24no—
379C23—52no—
380C23—52no—
381C23—52no—
382C23—102no—
383C23—102no—
384C23C22×D3×D511yescharacteristic
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—34no—
388C2×C4—52no—
389C2×C4—52no—
390C2×C4—52no—
391C2×C4—516no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—64no—
395C2×C4—62no—
396C2×C4—104no—
397C2×C4—102no—
398C2×C4—154no—
399C2×C4—208no—
400C2×C4—302no—
401C2×C4—302no—
402C2×C4—304no—
403C2×C4—302no—
404C2×C4D5×Dic612yes—
405C2×C4C4×D3×D512yes—
406C2×C4D5×#6712yes—
407C2×C3—104no—
408C2×C3C2×D5×C4⋊C411yescharacteristic
409C2×C3#6585712yes—
410C2×C3#6600811yescharacteristic
411C2×C3#6600911yescharacteristic
412C2×C3#6602312yes—
413C5#8215711yescharacteristic, complemented, Sylow
414C22—54no—
415C22—104no—
416C22—102no—
417C22—104no—
418C22—102no—
419C22C2×D5×Dic611yescharacteristic
420C22C2×C4×D3×D511yescharacteristic
421C22#9202612yes—
422C22#9203012yes—
423C22C2×D5×#6711yescharacteristic
424C4—42no—
425C4—54no—
426C4—64no—
427C4—122no—
428C4—202no—
429C4—304no—
430C4—602no—
431C4D5×Dic3⋊C414yes—
432C3#1060595611yescharacteristic, complemented, Sylow
433C2—104no—
434C2#1175336912yes—
435C2#1175366812yes—
436C2C2×D5×Dic3⋊C411yescharacteristic
437C2#1175493711yescharacteristic
438C2#1175522411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2317
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751076C2semidirect
5. C5×#4977C2semidirect
6. #11748861C2semidirect
8. #11748627C2semidirect
9. #11748623C2semidirect
28. #91357C4semidirect
58. C4×Dic15C2×C4semidirect
60. C4×C5×Dic3C2×C4semidirect
64. #6668C2×C4semidirect
73. #4977D5semidirect
125. C3×C4×D5C4⋊C4semidirect
226. C4×Dic3C4×D5semidirect
254. C4×D5Dic3⋊C4semidirect
354. C3×C5#2317semidirect
413. C5#82157semidirect
432. C3#10605956semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×#913582
C2×#913572
#117510762
C5×#49772
#117488612
#117487042
#117486272
#117486232
#106059563
#821575