Finite Group Databasebeta

← #14320075

Subgroups — #14320075

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D5C211yesmaximal, characteristic
2#11751033C211yesmaximal, characteristic, complemented
3C5×#4932C211yesmaximal, characteristic, complemented
4C4×#6668C212yesmaximal, complemented
5#11748738C212yesmaximal
6#11748737C212yesmaximal
7C4×#6665C212yesmaximal
8#11748612C212yesmaximal, complemented
9#11748580C212yesmaximal, complemented
10#10605144—31nomaximal, Hall
11C22×C3×C4×D5C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4×Dic15C2212yes—
16C2×C4×C5×Dic3C2212yes—
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C3×C42×D5C418yescomplemented
21C2×#6668C2214yes—
22C2×#6665C2214yes—
23#91115C2212yes—
24#91115C2212yes—
25C5×C3⋊#95C2212yes—
26C5×C3⋊#95C2212yes—
27#90994C2214yes—
28#90994C2214yes—
29#82060—51nomaximal, Hall
30C2×C42×D5D311yescharacteristic
31C5×#376—31no—
32C4×#685—32no—
33#65221—31no—
34C4×#683—32no—
35#64956—32no—
36#64953—32no—
37#64940—32no—
38#64939—32no—
39C23×C3×D5C2311yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15C2314yes—
44C22×C5×Dic3C2314yes—
45C22×C3×Dic5C2311yescharacteristic
46C22×C3×Dic5C2311yescharacteristic
47C22×C3×Dic5C2311yescharacteristic
48C2×C3×C4×D5—24no—
49C2×C3×C4×D5—24no—
50C2×C3×C4×D5—24no—
51C2×C3×C4×D5C2×C414yes—
52C2×C3×C4×D5C2×C414yes—
53C2×C3×C4×D5C2×C414yes—
54C3×C42×C5C2×C414yes—
55C4×Dic15—24no—
56C4×C5×Dic3—24no—
57C3×C4×Dic5C2×C414yes—
58C3×C4×Dic5C2×C414yes—
59C3×C4×Dic5C2×C414yes—
60#6668—28no—
61#6665—28no—
62C22×C3×C42—51no—
63#5212—52no—
64#5211—52no—
65C4×#217—52no—
66#4937—52no—
67#4936—52no—
68C4×C4⋊Dic3—52no—
69#4932—51no—
70#4932D511yescharacteristic, complemented
71C22×C4×D5C2×D311yescharacteristic
72C22×C4×D5C2×D311yescharacteristic
73C22×C4×D5C2×D311yescharacteristic
74C2×C42×C5—32no—
75C2×C42×C5C2×D311yescharacteristic
76C2×#685—34no—
77C2×#683—34no—
78C2×C4×Dic5—32no—
79C2×C4×Dic5C2×D311yescharacteristic
80C2×C4×Dic5C2×D311yescharacteristic
81C2×C4×Dic5C2×D311yescharacteristic
82C42×D5Dic318yescomplemented
83C5×#95—32no—
84C5×#95—32no—
85#3963—32no—
86#3963—32no—
87#3963—34no—
88#3963—34no—
89#2283—151noSylow
90C23×C3×C5C2411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5C22×C412yes—
94C22×C3×D5#4114yes—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5C22×C412yes—
98C2×C3×C4×C5C22×C412yes—
99C2×C3×C4×C5C22×C412yes—
100C2×C3×C4×C5#4114yes—
101C2×Dic15—24no—
102C2×Dic15—24no—
103C2×Dic15—24no—
104C2×C5×Dic3—24no—
105C2×C5×Dic3—24no—
106C2×C5×Dic3—24no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5C22×C412yes—
110C2×C3×Dic5C22×C412yes—
111C2×C3×Dic5C22×C412yes—
112C2×C3×Dic5#4114yes—
113C3×C4×D5—28no—
114C3×C4×D5—28no—
115C3×C4×D5—28no—
116C23×C3×C4—51no—
117C23×C3×C4—51no—
118C23×C3×C4—51no—
119C2×C3×C42—51no—
120C2×C3×C42—51no—
121C2×C3×C42—51no—
122C2×C3×C42—58no—
123C2×C3×C42C2×D511yescharacteristic
124C2×#217—54no—
125C2×C4⋊Dic3—54no—
126C2×C4×Dic3—52no—
127C2×C4×Dic3C2×D512yes—
128C3⋊#95—52no—
129C3⋊#95—52no—
130C3⋊#95—54no—
131C3⋊#95—54no—
132C3⋊#95C2×D512yes—
133C3⋊#95C2×D512yes—
134C23×D5C22×D311yescharacteristic
135C22×C4×C5—34no—
136C22×C4×C5C22×D311yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C22×C4×C5C22×D311yescharacteristic
139C22×Dic5—34no—
140C22×Dic5C22×D311yescharacteristic
141C22×Dic5C22×D311yescharacteristic
142C22×Dic5C22×D311yescharacteristic
143C2×C4×D5—24no—
144C2×C4×D5—24no—
145C2×C4×D5—24no—
146C2×C4×D5C2×Dic314yes—
147C2×C4×D5C2×Dic314yes—
148C2×C4×D5C2×Dic314yes—
149C42×C5—64no—
150C42×C5C2×Dic314yes—
151#685—68no—
152#683—68no—
153C4×Dic5—64no—
154C4×Dic5C2×Dic314yes—
155C4×Dic5C2×Dic314yes—
156C4×Dic5C2×Dic314yes—
157C22×C42—51no—
158#383—152no—
159#382—152no—
160#381—152no—
161#380—152no—
162C4×C4⋊C4—152no—
163C4×C22⋊C4—152no—
164#376—31no—
165#376—151no—
166C22×C3×C5C23×C411yescharacteristic
167C22×C3×C5C2×#4112yes—
168C22×C3×C5C2×#4112yes—
169C22×C3×C5C2×#4112yes—
170C2×C3×D5—22no—
171C2×C3×D5—22no—
172C2×C3×D5—28no—
173C2×C3×D5#11714yes—
174C3×C4×C5—22no—
175C3×C4×C5—22no—
176C3×C4×C5#11714yes—
177Dic15—44no—
178C3×Dic5—22no—
179C3×Dic5—22no—
180C3×Dic5#11714yes—
181C5×Dic3—44no—
182C24×C3—51no—
183C22×C3×C4—51no—
184C22×C3×C4—51no—
185C22×C3×C4—51no—
186C22×C3×C4—54no—
187C22×C3×C4—54no—
188C22×C3×C4—54no—
189C22×C3×C4—104no—
190C22×C3×C4—104no—
191C22×C3×C4—104no—
192C22×C3×C4C22×D511yescharacteristic
193C22×C3×C4C22×D511yescharacteristic
194C22×C3×C4C22×D511yescharacteristic
195C22×Dic3—54no—
196C22×Dic3C22×D514yes—
197C3×C42—54no—
198C3×C42—54no—
199C3×C42—54no—
200C3×C42C4×D514yes—
201#217—108no—
202C4⋊Dic3—108no—
203C4×Dic3—24no—
204C4×Dic3—104no—
205C23×C5C23×D311yescharacteristic
206C22×D5—22no—
207C22×D5—22no—
208C22×D5#23514yes—
209C22×D5C22×Dic312yes—
210C2×C4×C5—22no—
211C2×C4×C5—22no—
212C2×C4×C5—64no—
213C2×C4×C5—64no—
214C2×C4×C5—64no—
215C2×C4×C5#23514yes—
216C2×C4×C5C22×Dic312yes—
217C2×C4×C5C22×Dic312yes—
218C2×C4×C5C22×Dic312yes—
219C2×Dic5—22no—
220C2×Dic5—22no—
221C2×Dic5—64no—
222C2×Dic5—64no—
223C2×Dic5—64no—
224C2×Dic5#23514yes—
225C2×Dic5C22×Dic312yes—
226C2×Dic5C22×Dic312yes—
227C2×Dic5C22×Dic312yes—
228C4×D5—28no—
229C4×D5—28no—
230C4×D5—28no—
231C23×C4—51no—
232C23×C4—51no—
233C23×C4—51no—
234C2×C4⋊C4—154no—
235C2×C22⋊C4—154no—
236C2×C42—32no—
237C2×C42—51no—
238C2×C42—51no—
239C2×C42—51no—
240C2×C42—58no—
241C2×C42—152no—
242C2×C42D3×D511yescharacteristic
243#95—32no—
244#95—32no—
245#95—154no—
246#95—154no—
247#95—152no—
248#95—152no—
249C2×C3×C5C2×#11711yescharacteristic
250C2×C3×C5C2×#11711yescharacteristic
251C2×C3×C5C2×#11711yescharacteristic
252C2×C3×C5#52914yes—
253C3×D5—24no—
254C23×C3—52no—
255C23×C3—54no—
256C23×C3—102no—
257C23×C3—102no—
258C23×C3C23×D511yescharacteristic
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—52no—
262C2×C3×C4—54no—
263C2×C3×C4—52no—
264C2×C3×C4—52no—
265C2×C3×C4—108no—
266C2×C3×C4—108no—
267C2×C3×C4—102no—
268C2×C3×C4—102no—
269C2×C3×C4—108no—
270C2×C3×C4C2×C4×D512yes—
271C2×C3×C4C2×C4×D512yes—
272C2×C3×C4C2×C4×D512yes—
273C2×C3×C4#70914yes—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—24no—
277C2×Dic3—104no—
278C2×Dic3—104no—
279C2×Dic3—104no—
280C22×C5C2×#23512yes—
281C22×C5C2×#23512yes—
282C22×C5C2×#23512yes—
283C22×C5C23×Dic311yescharacteristic
284C2×D5—28no—
285C2×D5—22no—
286C2×D5—22no—
287C2×D5#92614yes—
288C4×C5—22no—
289C4×C5—22no—
290C4×C5—124no—
291C4×C5#92614yes—
292Dic5—22no—
293Dic5—22no—
294Dic5—124no—
295Dic5#92614yes—
296C24—51no—
297C22×C4—34no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—54no—
302C22×C4—54no—
303C22×C4—54no—
304C22×C4—104no—
305C22×C4—104no—
306C22×C4—104no—
307C22×C4—154no—
308C22×C4C2×D3×D511yescharacteristic
309C22×C4C2×D3×D511yescharacteristic
310C22×C4C2×D3×D511yescharacteristic
311C4⋊C4—308no—
312C22⋊C4—308no—
313C42—54no—
314C42—54no—
315C42—54no—
316C42—64no—
317C42—304no—
318C42D5×Dic314yes—
319C3×C5#228311yescharacteristic, complemented, Hall
320C22×C3—54no—
321C22×C3—102no—
322C22×C3—102no—
323C22×C3—108no—
324C22×C3C22×C4×D511yescharacteristic
325C22×C3C2×#70912yes—
326C22×C3D5×#4112yes—
327C22×C3D5×#4112yes—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—54no—
331C3×C4—102no—
332C3×C4—102no—
333C3×C4#401814yes—
334Dic3—44no—
335Dic3—204no—
336C2×C5#547914yes—
337C2×C5C2×#92611yescharacteristic
338C2×C5C2×#92611yescharacteristic
339C2×C5C2×#92611yescharacteristic
340D5—24no—
341C23—54no—
342C23—52no—
343C23—102no—
344C23—102no—
345C23C22×D3×D511yescharacteristic
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—54no—
349C2×C4—52no—
350C2×C4—52no—
351C2×C4—52no—
352C2×C4—64no—
353C2×C4—64no—
354C2×C4—64no—
355C2×C4—108no—
356C2×C4—108no—
357C2×C4—102no—
358C2×C4—102no—
359C2×C4—108no—
360C2×C4—304no—
361C2×C4—304no—
362C2×C4—304no—
363C2×C4#677114yes—
364C2×C4C2×D5×Dic312yes—
365C2×C4C2×D5×Dic312yes—
366C2×C4C2×D5×Dic312yes—
367C2×C3—104no—
368C2×C3C2×#401811yescharacteristic
369C2×C3D5×#11711yescharacteristic
370C2×C3D5×#11711yescharacteristic
371C2×C3#6586214yes—
372C5#8206011yescharacteristic, complemented, Sylow
373C22—54no—
374C22—102no—
375C22—108no—
376C22—102no—
377C22C2×#677112yes—
378C22D5×#23512yes—
379C22D5×#23512yes—
380C22C22×D5×Dic311yescharacteristic
381C4—22no—
382C4—22no—
383C4—54no—
384C4—102no—
385C4—102no—
386C4—124no—
387C4—604no—
388C4#9135714yes—
389C3#1060514411yescharacteristic, complemented, Sylow
390C2—104no—
391C2#1175268114yes—
392C2C2×#9135711yescharacteristic
393C2D5×#92611yescharacteristic
394C2D5×#92611yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2283
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751033C2semidirect
3. C5×#4932C2semidirect
4. C4×#6668C2semidirect
8. #11748612C2semidirect
9. #11748580C2semidirect
20. C3×C42×D5C4semidirect
70. #4932D5semidirect
82. C42×D5Dic3semidirect
319. C3×C5#2283semidirect
372. C5#82060semidirect
389. C3#10605144semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D52
#117510332
C5×#49322
C4×#66682
#117487382
#117487372
C4×#66652
#117486122
#117485802
#106051443
#820605