Finite Group Databasebeta

← #14320105

Subgroups — #14320105

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D5C211yesmaximal, characteristic
2#11751038C211yesmaximal, characteristic, complemented
3C5×#4937C211yesmaximal, characteristic, complemented
4#11748738C212yesmaximal
5#11748737C212yesmaximal
6#11748702C212yesmaximal
7#11748638C212yesmaximal, complemented
8#11748635C212yesmaximal, complemented
9#11748580C212yesmaximal, complemented
10#10605989—31nomaximal, Hall
11C22×C3×C4×D5C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17C2×C3×C4×Dic5C2211yescharacteristic
18C3×C42×D5C418yescomplemented
19C2×#6668C2214yes—
20C2×#6665C2214yes—
21C2×Dic3×Dic5C2214yes—
22#91115C2212yes—
23#91115C2212yes—
24#91115C2212yes—
25C5×C3⋊#95C2212yes—
26C5×C3⋊#95C2212yes—
27C5×C3⋊#95C2212yes—
28#90994C2214yes—
29#82060—51nomaximal, Hall
30C2×C42×D5D311yescharacteristic
31C5×#383—31no—
32#65226—31no—
33#64956—32no—
34#64955—32no—
35#64953—32no—
36#64939—32no—
37#64938—32no—
38#64937—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—
55C3×C4×Dic5C2×C414yes—
56C3×C4×Dic5C2×C414yes—
57C3×C4×Dic5C2×C414yes—
58#6668—28no—
59#6665—28no—
60Dic3×Dic5—28no—
61C22×C3×C42—51no—
62#5212—52no—
63#5211—52no—
64C4×#217—52no—
65#4937—51no—
66#4937D511yescharacteristic, complemented
67#4936—52no—
68C4×C4⋊Dic3—52no—
69#4932—52no—
70C22×C4×D5C2×D311yescharacteristic
71C22×C4×D5C2×D311yescharacteristic
72C22×C4×D5C2×D311yescharacteristic
73C2×C42×C5C2×D311yescharacteristic
74C2×#685—34no—
75C2×#683—34no—
76C2×C4×Dic5—34no—
77C2×C4×Dic5C2×D311yescharacteristic
78C2×C4×Dic5C2×D311yescharacteristic
79C2×C4×Dic5C2×D311yescharacteristic
80C42×D5Dic318yescomplemented
81C5×#95—32no—
82C5×#95—32no—
83C5×#95—32no—
84#3963—32no—
85#3963—32no—
86#3963—32no—
87#3963—34no—
88#2283—151noSylow
89C23×C3×C5C2411yescharacteristic
90C22×C3×D5—22no—
91C22×C3×D5—22no—
92C22×C3×D5C22×C412yes—
93C22×C3×D5#4114yes—
94C2×C3×C4×C5—22no—
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×Dic15—24no—
101C2×Dic15—24no—
102C2×Dic15—24no—
103C2×C5×Dic3—24no—
104C2×C5×Dic3—24no—
105C2×C5×Dic3—24no—
106C2×C3×Dic5—22no—
107C2×C3×Dic5C22×C412yes—
108C2×C3×Dic5C22×C412yes—
109C2×C3×Dic5C22×C412yes—
110C2×C3×Dic5#4114yes—
111C2×C3×Dic5#4114yes—
112C3×C4×D5—28no—
113C3×C4×D5—28no—
114C3×C4×D5—28no—
115C23×C3×C4—51no—
116C23×C3×C4—51no—
117C23×C3×C4—51no—
118C2×C3×C42—51no—
119C2×C3×C42—51no—
120C2×C3×C42—51no—
121C2×C3×C42—58no—
122C2×C3×C42C2×D511yescharacteristic
123C2×#217—54no—
124C2×C4⋊Dic3—54no—
125C2×C4×Dic3—54no—
126C3⋊#95—52no—
127C3⋊#95—52no—
128C3⋊#95—52no—
129C3⋊#95—54no—
130C3⋊#95C2×D512yes—
131C3⋊#95C2×D512yes—
132C3⋊#95C2×D512yes—
133C23×D5C22×D311yescharacteristic
134C22×C4×C5—34no—
135C22×C4×C5C22×D311yescharacteristic
136C22×C4×C5C22×D311yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C22×Dic5—34no—
139C22×Dic5C22×D311yescharacteristic
140C22×Dic5C22×D311yescharacteristic
141C22×Dic5C22×D311yescharacteristic
142C2×C4×D5—24no—
143C2×C4×D5—24no—
144C2×C4×D5—24no—
145C2×C4×D5C2×Dic314yes—
146C2×C4×D5C2×Dic314yes—
147C2×C4×D5C2×Dic314yes—
148C42×C5C2×Dic314yes—
149#685—68no—
150#683—68no—
151C4×Dic5—68no—
152C4×Dic5C2×Dic314yes—
153C4×Dic5C2×Dic314yes—
154C4×Dic5C2×Dic314yes—
155C22×C42—51no—
156#383—31no—
157#383—151no—
158#382—152no—
159#381—152no—
160#380—152no—
161C4×C4⋊C4—152no—
162C4×C22⋊C4—152no—
163#376—152no—
164C22×C3×C5C23×C411yescharacteristic
165C22×C3×C5C2×#4112yes—
166C22×C3×C5C2×#4112yes—
167C22×C3×C5C2×#4112yes—
168C2×C3×D5—22no—
169C2×C3×D5—22no—
170C2×C3×D5—28no—
171C2×C3×D5#11714yes—
172C3×C4×C5—22no—
173C3×C4×C5—22no—
174C3×C4×C5—22no—
175Dic15—44no—
176C3×Dic5—22no—
177C3×Dic5#11714yes—
178C3×Dic5#11714yes—
179C5×Dic3—44no—
180C24×C3—51no—
181C22×C3×C4—51no—
182C22×C3×C4—51no—
183C22×C3×C4—51no—
184C22×C3×C4—54no—
185C22×C3×C4—54no—
186C22×C3×C4—54no—
187C22×C3×C4—104no—
188C22×C3×C4—104no—
189C22×C3×C4—104no—
190C22×C3×C4C22×D511yescharacteristic
191C22×C3×C4C22×D511yescharacteristic
192C22×C3×C4C22×D511yescharacteristic
193C22×Dic3—54no—
194C22×Dic3C22×D514yes—
195C3×C42—54no—
196C3×C42—54no—
197C3×C42—54no—
198C3×C42C4×D514yes—
199#217—108no—
200C4⋊Dic3—108no—
201C4×Dic3—108no—
202C23×C5C23×D311yescharacteristic
203C22×D5—22no—
204C22×D5—22no—
205C22×D5#23514yes—
206C22×D5C22×Dic312yes—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—22no—
210C2×C4×C5—64no—
211C2×C4×C5—64no—
212C2×C4×C5—64no—
213C2×C4×C5C22×Dic312yes—
214C2×C4×C5C22×Dic312yes—
215C2×C4×C5C22×Dic312yes—
216C2×Dic5—22no—
217C2×Dic5—64no—
218C2×Dic5—64no—
219C2×Dic5—64no—
220C2×Dic5#23514yes—
221C2×Dic5#23514yes—
222C2×Dic5C22×Dic312yes—
223C2×Dic5C22×Dic312yes—
224C2×Dic5C22×Dic312yes—
225C4×D5—28no—
226C4×D5—28no—
227C4×D5—28no—
228C23×C4—51no—
229C23×C4—51no—
230C23×C4—51no—
231C2×C4⋊C4—154no—
232C2×C22⋊C4—154no—
233C2×C42—51no—
234C2×C42—51no—
235C2×C42—51no—
236C2×C42—58no—
237C2×C42—154no—
238C2×C42D3×D511yescharacteristic
239#95—32no—
240#95—32no—
241#95—32no—
242#95—154no—
243#95—152no—
244#95—152no—
245#95—152no—
246C2×C3×C5C2×#11711yescharacteristic
247C2×C3×C5C2×#11711yescharacteristic
248C2×C3×C5C2×#11711yescharacteristic
249C2×C3×C5#52914yes—
250C3×D5—24no—
251C23×C3—52no—
252C23×C3—54no—
253C23×C3—102no—
254C23×C3—102no—
255C23×C3C23×D511yescharacteristic
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—52no—
260C2×C3×C4—52no—
261C2×C3×C4—54no—
262C2×C3×C4—54no—
263C2×C3×C4—52no—
264C2×C3×C4—108no—
265C2×C3×C4—108no—
266C2×C3×C4—108no—
267C2×C3×C4—102no—
268C2×C3×C4C2×C4×D512yes—
269C2×C3×C4C2×C4×D512yes—
270C2×C3×C4C2×C4×D512yes—
271C2×Dic3—24no—
272C2×Dic3—24no—
273C2×Dic3—24no—
274C2×Dic3—104no—
275C2×Dic3—104no—
276C2×Dic3—104no—
277C22×C5C2×#23512yes—
278C22×C5C2×#23512yes—
279C22×C5C2×#23512yes—
280C22×C5C23×Dic311yescharacteristic
281C2×D5—28no—
282C2×D5—22no—
283C2×D5—22no—
284C2×D5#92614yes—
285C4×C5—22no—
286C4×C5—22no—
287C4×C5—22no—
288C4×C5—124no—
289Dic5—22no—
290Dic5—124no—
291Dic5#92614yes—
292Dic5#92614yes—
293C24—51no—
294C22×C4—34no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—54no—
299C22×C4—54no—
300C22×C4—54no—
301C22×C4—104no—
302C22×C4—104no—
303C22×C4—104no—
304C22×C4—154no—
305C22×C4C2×D3×D511yescharacteristic
306C22×C4C2×D3×D511yescharacteristic
307C22×C4C2×D3×D511yescharacteristic
308C4⋊C4—308no—
309C22⋊C4—308no—
310C42—54no—
311C42—54no—
312C42—54no—
313C42—308no—
314C42D5×Dic314yes—
315C3×C5#228311yescharacteristic, complemented, Hall
316C22×C3—54no—
317C22×C3—102no—
318C22×C3—102no—
319C22×C3—108no—
320C22×C3C22×C4×D511yescharacteristic
321C22×C3D5×#4112yes—
322C22×C3D5×#4112yes—
323C22×C3D5×#4112yes—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—54no—
328C3×C4—54no—
329C3×C4—102no—
330Dic3—44no—
331Dic3—204no—
332C2×C5#547914yes—
333C2×C5C2×#92611yescharacteristic
334C2×C5C2×#92611yescharacteristic
335C2×C5C2×#92611yescharacteristic
336D5—24no—
337C23—54no—
338C23—52no—
339C23—102no—
340C23—102no—
341C23C22×D3×D511yescharacteristic
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—54no—
346C2×C4—54no—
347C2×C4—52no—
348C2×C4—52no—
349C2×C4—52no—
350C2×C4—64no—
351C2×C4—64no—
352C2×C4—64no—
353C2×C4—108no—
354C2×C4—108no—
355C2×C4—108no—
356C2×C4—102no—
357C2×C4—304no—
358C2×C4—304no—
359C2×C4—304no—
360C2×C4C2×D5×Dic312yes—
361C2×C4C2×D5×Dic312yes—
362C2×C4C2×D5×Dic312yes—
363C2×C3—104no—
364C2×C3D5×#11711yescharacteristic
365C2×C3D5×#11711yescharacteristic
366C2×C3D5×#11711yescharacteristic
367C2×C3#6604014yes—
368C5#8206011yescharacteristic, complemented, Sylow
369C22—54no—
370C22—102no—
371C22—102no—
372C22—108no—
373C22D5×#23512yes—
374C22D5×#23512yes—
375C22D5×#23512yes—
376C22C22×D5×Dic311yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—54no—
381C4—54no—
382C4—102no—
383C4—124no—
384C4—604no—
385C3#1060598911yescharacteristic, complemented, Sylow
386C2—104no—
387C2#1175268414yes—
388C2D5×#92611yescharacteristic
389C2D5×#92611yescharacteristic
390C2D5×#92611yescharacteristic
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#2283
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. #11751038C2semidirect
3. C5×#4937C2semidirect
7. #11748638C2semidirect
8. #11748635C2semidirect
9. #11748580C2semidirect
18. C3×C42×D5C4semidirect
66. #4937D5semidirect
80. C42×D5Dic3semidirect
315. C3×C5#2283semidirect
368. C5#82060semidirect
385. C3#10605989semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D52
#117510382
C5×#49372
#117487382
#117487372
#117487022
#117486382
#117486352
#117485802
#106059893
#820605