Finite Group Databasebeta

← #14320102

Subgroups — #14320102

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D5C211yesmaximal, characteristic
2#11751037C211yesmaximal, characteristic, complemented
3C5×#4936C211yesmaximal, characteristic, complemented
4#11748759C212yesmaximal
5#11748737C212yesmaximal
6#11748702C212yesmaximal
7Dic5×C4⋊Dic3C212yesmaximal, complemented
8#11748635C212yesmaximal, complemented
9#11748612C212yesmaximal, complemented
10#10605878—31nomaximal, Hall
11C22×C3×C4×D5C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4⋊Dic15C2212yes—
16C2×C5×C4⋊Dic3C2212yes—
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C3×C42×D5C418yescomplemented
21C2×#6665C2214yes—
22C2×Dic3×Dic5C2214yes—
23#91115C2212yes—
24#91115C2212yes—
25C5×C3⋊#95C2212yes—
26C5×C3⋊#95C2212yes—
27#90994C2214yes—
28#90994C2214yes—
29#82060—51nomaximal, Hall
30C2×C42×D5D311yescharacteristic
31C5×#382—31no—
32#65276—32no—
33C4⋊C4×Dic5—32no—
34#65225—31no—
35#64955—32no—
36#64953—32no—
37#64940—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—22no—
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5—24no—
52C2×C3×C4×D5C2×C414yes—
53C2×C3×C4×D5C2×C414yes—
54C2×C3×C4×D5C2×C414yes—
55C3×C42×C5C2×C414yes—
56C4⋊Dic15—24no—
57C5×C4⋊Dic3—24no—
58C3×C4×Dic5C2×C414yes—
59C3×C4×Dic5C2×C414yes—
60C3×C4×Dic5C2×C414yes—
61#6665—28no—
62Dic3×Dic5—28no—
63C22×C3×C42—51no—
64#5212—52no—
65#5211—52no—
66C4×#217—52no—
67#4937—52no—
68#4936—51no—
69#4936D511yescharacteristic, complemented
70C4×C4⋊Dic3—52no—
71#4932—52no—
72C22×C4×D5C2×D311yescharacteristic
73C22×C4×D5C2×D311yescharacteristic
74C22×C4×D5C2×D311yescharacteristic
75C2×C5×C4⋊C4—32no—
76C2×C42×C5C2×D311yescharacteristic
77C2×#685—34no—
78C2×C4⋊Dic5—32no—
79C2×C4×Dic5—34no—
80C2×C4×Dic5C2×D311yescharacteristic
81C2×C4×Dic5C2×D311yescharacteristic
82C2×C4×Dic5C2×D311yescharacteristic
83C42×D5Dic318yescomplemented
84C5×#95—32no—
85C5×#95—32no—
86#3963—32no—
87#3963—32no—
88#3963—34no—
89#3963—34no—
90#2283—151noSylow
91C23×C3×C5C2411yescharacteristic
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—22no—
95C22×C3×D5C22×C412yes—
96C22×C3×D5#4114yes—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C22×C412yes—
100C2×C3×C4×C5C22×C412yes—
101C2×C3×C4×C5C22×C412yes—
102C2×C3×C4×C5#4112yes—
103C2×C3×C4×C5#4112yes—
104C2×Dic15—24no—
105C2×Dic15—24no—
106C2×Dic15—24no—
107C2×C5×Dic3—24no—
108C2×C5×Dic3—24no—
109C2×C5×Dic3—24no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5C22×C412yes—
114C2×C3×Dic5C22×C412yes—
115C2×C3×Dic5C22×C412yes—
116C2×C3×Dic5#4114yes—
117C3×C4×D5—28no—
118C3×C4×D5—28no—
119C3×C4×D5—28no—
120C23×C3×C4—51no—
121C23×C3×C4—51no—
122C23×C3×C4—51no—
123C2×C3×C42—51no—
124C2×C3×C42—51no—
125C2×C3×C42—51no—
126C2×C3×C42—58no—
127C2×C3×C42C2×D511yescharacteristic
128C2×#217—54no—
129C2×C4⋊Dic3—52no—
130C2×C4⋊Dic3C2×D512yes—
131C2×C4×Dic3—54no—
132C3⋊#95—52no—
133C3⋊#95—52no—
134C3⋊#95—54no—
135C3⋊#95—54no—
136C3⋊#95C2×D512yes—
137C3⋊#95C2×D512yes—
138C23×D5C22×D311yescharacteristic
139C22×C4×C5—34no—
140C22×C4×C5C22×D311yescharacteristic
141C22×C4×C5C22×D311yescharacteristic
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—34no—
144C22×Dic5C22×D311yescharacteristic
145C22×Dic5C22×D311yescharacteristic
146C22×Dic5C22×D311yescharacteristic
147C2×C4×D5—24no—
148C2×C4×D5—22no—
149C2×C4×D5—22no—
150C2×C4×D5—24no—
151C2×C4×D5C2×Dic314yes—
152C2×C4×D5C2×Dic314yes—
153C2×C4×D5C2×Dic314yes—
154C5×C4⋊C4—64no—
155C42×C5C2×Dic314yes—
156#685—68no—
157C4⋊Dic5—64no—
158C4×Dic5—68no—
159C4×Dic5C2×Dic314yes—
160C4×Dic5C2×Dic314yes—
161C4×Dic5C2×Dic314yes—
162C22×C42—51no—
163#383—152no—
164#382—31no—
165#382—151no—
166#381—152no—
167#380—152no—
168C4×C4⋊C4—152no—
169C4×C22⋊C4—152no—
170#376—152no—
171C22×C3×C5C23×C411yescharacteristic
172C22×C3×C5C2×#4111yescharacteristic
173C22×C3×C5C2×#4111yescharacteristic
174C22×C3×C5C2×#4112yes—
175C22×C3×C5C2×#4112yes—
176C2×C3×D5—22no—
177C2×C3×D5—22no—
178C2×C3×D5—24no—
179C2×C3×D5—24no—
180C2×C3×D5#11714yes—
181C3×C4×C5—22no—
182C3×C4×C5—22no—
183C3×C4×C5#11714yes—
184Dic15—44no—
185C3×Dic5—22no—
186C3×Dic5—22no—
187C3×Dic5#11714yes—
188C5×Dic3—44no—
189C24×C3—51no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—54no—
194C22×C3×C4—54no—
195C22×C3×C4—54no—
196C22×C3×C4—104no—
197C22×C3×C4—104no—
198C22×C3×C4—102no—
199C22×C3×C4—102no—
200C22×C3×C4C22×D511yescharacteristic
201C22×C3×C4C22×D511yescharacteristic
202C22×C3×C4C22×D511yescharacteristic
203C22×Dic3—54no—
204C22×Dic3C22×D514yes—
205C3×C42—54no—
206C3×C42—54no—
207C3×C42—54no—
208C3×C42C4×D514yes—
209#217—108no—
210C4⋊Dic3—24no—
211C4⋊Dic3—104no—
212C4×Dic3—108no—
213C23×C5C23×D311yescharacteristic
214C22×D5—21no—
215C22×D5—21no—
216C22×D5—22no—
217C22×D5#23514yes—
218C22×D5C22×Dic312yes—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—64no—
222C2×C4×C5—64no—
223C2×C4×C5—64no—
224C2×C4×C5#23512yes—
225C2×C4×C5#23512yes—
226C2×C4×C5C22×Dic312yes—
227C2×C4×C5C22×Dic312yes—
228C2×C4×C5C22×Dic312yes—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—22no—
232C2×Dic5—64no—
233C2×Dic5—64no—
234C2×Dic5—64no—
235C2×Dic5#23514yes—
236C2×Dic5C22×Dic312yes—
237C2×Dic5C22×Dic312yes—
238C2×Dic5C22×Dic312yes—
239C4×D5—28no—
240C4×D5—28no—
241C4×D5—28no—
242C23×C4—51no—
243C23×C4—51no—
244C23×C4—51no—
245C2×C4⋊C4—32no—
246C2×C4⋊C4—152no—
247C2×C22⋊C4—154no—
248C2×C42—51no—
249C2×C42—51no—
250C2×C42—51no—
251C2×C42—58no—
252C2×C42—154no—
253C2×C42D3×D511yescharacteristic
254#95—32no—
255#95—32no—
256#95—154no—
257#95—154no—
258#95—152no—
259#95—152no—
260C2×C3×C5C2×#11711yescharacteristic
261C2×C3×C5C2×#11711yescharacteristic
262C2×C3×C5C2×#11711yescharacteristic
263C2×C3×C5#52912yes—
264C2×C3×C5#52912yes—
265C3×D5—24no—
266C23×C3—52no—
267C23×C3—54no—
268C23×C3—101no—
269C23×C3—101no—
270C23×C3—102no—
271C23×C3C23×D511yescharacteristic
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—52no—
275C2×C3×C4—54no—
276C2×C3×C4—52no—
277C2×C3×C4—52no—
278C2×C3×C4—108no—
279C2×C3×C4—108no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—102no—
283C2×C3×C4—108no—
284C2×C3×C4C2×C4×D512yes—
285C2×C3×C4C2×C4×D512yes—
286C2×C3×C4C2×C4×D512yes—
287C2×C3×C4#71112yes—
288C2×C3×C4#71312yes—
289C2×Dic3—24no—
290C2×Dic3—24no—
291C2×Dic3—24no—
292C2×Dic3—104no—
293C2×Dic3—104no—
294C2×Dic3—104no—
295C22×C5C2×#23511yescharacteristic
296C22×C5C2×#23511yescharacteristic
297C22×C5C2×#23512yes—
298C22×C5C2×#23512yes—
299C22×C5C23×Dic311yescharacteristic
300C2×D5—24no—
301C2×D5—24no—
302C2×D5—22no—
303C2×D5—22no—
304C2×D5#92614yes—
305C4×C5—22no—
306C4×C5—22no—
307C4×C5—124no—
308C4×C5#92614yes—
309Dic5—22no—
310Dic5—22no—
311Dic5—124no—
312Dic5#92614yes—
313C24—51no—
314C22×C4—34no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—51no—
318C22×C4—54no—
319C22×C4—54no—
320C22×C4—54no—
321C22×C4—104no—
322C22×C4—104no—
323C22×C4—102no—
324C22×C4—102no—
325C22×C4—154no—
326C22×C4C2×D3×D511yescharacteristic
327C22×C4C2×D3×D511yescharacteristic
328C22×C4C2×D3×D511yescharacteristic
329C4⋊C4—64no—
330C4⋊C4—304no—
331C22⋊C4—308no—
332C42—54no—
333C42—54no—
334C42—54no—
335C42—308no—
336C42D5×Dic314yes—
337C3×C5#228311yescharacteristic, complemented, Hall
338C22×C3—54no—
339C22×C3—102no—
340C22×C3—102no—
341C22×C3—104no—
342C22×C3—104no—
343C22×C3C22×C4×D511yescharacteristic
344C22×C3C2×#71111yescharacteristic
345C22×C3C2×#71311yescharacteristic
346C22×C3D5×#4112yes—
347C22×C3D5×#4112yes—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4—54no—
351C3×C4—102no—
352C3×C4—102no—
353C3×C4#403814yes—
354Dic3—44no—
355Dic3—204no—
356C2×C5#547912yes—
357C2×C5#547912yes—
358C2×C5C2×#92611yescharacteristic
359C2×C5C2×#92611yescharacteristic
360C2×C5C2×#92611yescharacteristic
361D5—24no—
362C23—54no—
363C23—52no—
364C23—101no—
365C23—101no—
366C23—102no—
367C23C22×D3×D511yescharacteristic
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—54no—
371C2×C4—52no—
372C2×C4—52no—
373C2×C4—52no—
374C2×C4—64no—
375C2×C4—64no—
376C2×C4—64no—
377C2×C4—108no—
378C2×C4—108no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—102no—
382C2×C4—108no—
383C2×C4—304no—
384C2×C4—304no—
385C2×C4—304no—
386C2×C4#677212yes—
387C2×C4#677312yes—
388C2×C4C2×D5×Dic312yes—
389C2×C4C2×D5×Dic312yes—
390C2×C4C2×D5×Dic312yes—
391C2×C3—104no—
392C2×C3C2×#403811yescharacteristic
393C2×C3D5×#11711yescharacteristic
394C2×C3D5×#11711yescharacteristic
395C2×C3#6601412yes—
396C2×C3#6602512yes—
397C5#8206011yescharacteristic, complemented, Sylow
398C22—54no—
399C22—102no—
400C22—104no—
401C22—104no—
402C22—102no—
403C22C2×#677211yescharacteristic
404C22C2×#677311yescharacteristic
405C22D5×#23512yes—
406C22D5×#23512yes—
407C22C22×D5×Dic311yescharacteristic
408C4—22no—
409C4—22no—
410C4—54no—
411C4—102no—
412C4—102no—
413C4—124no—
414C4—604no—
415C4#9135814yes—
416C3#1060587811yescharacteristic, complemented, Sylow
417C2—104no—
418C2#1175268312yes—
419C2#1175268512yes—
420C2C2×#9135811yescharacteristic
421C2D5×#92611yescharacteristic
422C2D5×#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. #11751037C2semidirect
3. C5×#4936C2semidirect
7. Dic5×C4⋊Dic3C2semidirect
8. #11748635C2semidirect
9. #11748612C2semidirect
20. C3×C42×D5C4semidirect
69. #4936D5semidirect
83. C42×D5Dic3semidirect
337. C3×C5#2283semidirect
397. C5#82060semidirect
416. C3#10605878semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D52
#117510372
C5×#49362
#117487592
#117487372
#117487022
Dic5×C4⋊Dic32
#117486352
#117486122
#106058783
#820605