Finite Group Databasebeta

← #14282760

Subgroups — #14282760

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756238C211yesmaximal, characteristic
2C3×C5×#431C211yesmaximal, characteristic, complemented
3#11751033C211yesmaximal, characteristic, complemented
4#11746291C212yesmaximal
5#11746288C212yesmaximal, complemented
6#10601581—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8#91819C2211yescharacteristic
9#91818—21no—
10C4×#1220—21no—
11#91813C2211yescharacteristic
12C2×C4×Dic15—21no—
13#91765—21no—
14#91764C411yescharacteristic, complemented
15C4×D60C411yescharacteristic, complemented
16#91761—21no—
17#91759C411yescharacteristic, complemented
18C4×Dic30C411yescharacteristic, complemented
19C3×C5×C4⋊C8—21no—
20C3×C5×C22⋊C8C2212yes—
21C3×C4×C5×C8—21no—
22#91115—21no—
23#91115C2212yes—
24#70788—51nomaximal, Hall
25#65813—31no—
26C5×#431D311yescharacteristic, complemented
27#65221—31no—
28#64690—32no—
29#64687—32no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220—21no—
34C22×Dic15—22no—
35C2×D60C2×C411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30C2×C411yescharacteristic
38C2×C3×C5×C8—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5C2×C411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C3×C42×C5D411yescharacteristic
43#6719—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C4⋊Dic15C2×C411yescharacteristic
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54C4×Dic15—24no—
55C4×Dic15—21no—
56#5479—51no—
57C3×#431D511yescharacteristic, complemented
58#4932—51no—
59#4470—52no—
60#4467—52no—
61C2×C42×C5C2×D311yescharacteristic
62#4076—31no—
63#4075—61no—
64C4×C22⋊D5—61no—
65#4070—31no—
66C2×C4×Dic5—61no—
67#4022—61no—
68#4021—31no—
69C4×D20—31no—
70#4018—61no—
71#4016—31no—
72C4×Dic10—31no—
73C5×C4⋊C8—21no—
74C5×C22⋊C8C2×D312yes—
75C4×C5×C8—21no—
76#3963—32no—
77#3963—61no—
78#1500—151noSylow
79C23×C3×C5C2×D411yescharacteristic
80C22×D15—21no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90#1220—42no—
91C2×Dic15—24no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×Dic15—42no—
96C2×Dic15—42no—
97D60—41no—
98C4×D15—42no—
99Dic30—41no—
100C3×C5×C8—42no—
101C2×C3×C42C2×D511yescharacteristic
102#930—51no—
103#929—101no—
104C4×#67—101no—
105#924—51no—
106C2×C4×Dic3—101no—
107#876—101no—
108#875—51no—
109C4×D12—51no—
110#872—101no—
111#870—51no—
112C4×Dic6—51no—
113C3×C4⋊C8—21no—
114C3×C22⋊C8C2×D512yes—
115C3×C4×C8—21no—
116C3⋊#95—52no—
117C3⋊#95—101no—
118C22×C4×C5D1211yescharacteristic
119C22×C4×C5D1211yescharacteristic
120C22×C4×C5C22×D311yescharacteristic
121C2×C22⋊D5—61no—
122C22×Dic5—62no—
123C2×D20—31no—
124C2×C4×D5—61no—
125C2×Dic10—31no—
126C2×C5×C8—22no—
127C42×C5C4×D311yescharacteristic
128C42×C5C4×D311yescharacteristic
129C42×C5#6711yescharacteristic
130C42×C5#6711yescharacteristic
131C22⋊Dic5—61no—
132#685—61no—
133#685—61no—
134#685—61no—
135#685—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—31no—
138#683—61no—
139#683—61no—
140#683—61no—
141#683—61no—
142C4×Dic5—64no—
143C4×Dic5—61no—
144#529—151no—
145#431D1511yescharacteristic, complemented
146#376—151no—
147#328—152no—
148#327—152no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C22×C3×C5#13512yes—
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5#10412yes—
162Dic15—44no—
163Dic15—41no—
164Dic15—41no—
165Dic15—41no—
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4D2011yescharacteristic
168C22×C3×C4C22×D511yescharacteristic
169C2×#67—101no—
170C22×Dic3—102no—
171C2×D12—51no—
172C2×C4×D3—101no—
173C2×Dic6—51no—
174C2×C3×C8—22no—
175C3×C42C4×D511yescharacteristic
176C3×C42C4×D511yescharacteristic
177C3×C42C22⋊D511yescharacteristic
178C3×C42C22⋊D511yescharacteristic
179#217—101no—
180(C2×D3)⋊C4—101no—
181(C2×D3)⋊C4—101no—
182(C2×D3)⋊C4—101no—
183(C2×D3)⋊C4—101no—
184C4⋊Dic3—51no—
185C4⋊Dic3—51no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189Dic3⋊C4—101no—
190C4×Dic3—104no—
191C4×Dic3—101no—
192C23×C5C2×D1211yescharacteristic
193C22×D5—61no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—41no—
197C2×C4×C5(C2×D3)⋊C411yescharacteristic
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5(C2×D3)⋊C411yescharacteristic
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C22⋊D5—122no—
204C2×Dic5—64no—
205C2×Dic5—61no—
206C2×Dic5—61no—
207C2×Dic5—61no—
208C2×Dic5—122no—
209C2×Dic5—122no—
210D20—121no—
211C4×D5—122no—
212Dic10—121no—
213C5×C8—42no—
214#126—301no—
215#125—151no—
216#124—151no—
217#123—301no—
218C22⋊Q8—151no—
219#121—151no—
220C4×Q8—151no—
221C4×D4—151no—
222C4×D4—301no—
223#117—301no—
224C2×C42—301no—
225C2×C42C2×D1511yescharacteristic
226C4⋊C8—21no—
227C22⋊C8C2×D1512yes—
228C4×C8—21no—
229#95—152no—
230#95—301no—
231C2×C3×C5—22no—
232C2×C3×C5#41011yescharacteristic
233C2×C3×C5#41611yescharacteristic
234C2×C3×C5C2×#10411yescharacteristic
235D15—81no—
236C23×C3C2×D2011yescharacteristic
237C22×D3—101no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—41no—
241C2×C3×C4#68511yescharacteristic
242C2×C3×C4#68511yescharacteristic
243C2×C3×C4#68511yescharacteristic
244C2×C3×C4#68511yescharacteristic
245C2×C3×C4C2×C4×D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247#67—202no—
248C2×Dic3—104no—
249C2×Dic3—101no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252C2×Dic3—202no—
253C2×Dic3—202no—
254D12—201no—
255C4×D3—202no—
256Dic6—201no—
257C3×C8—42no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5#90412yes—
261C22×C5C2×(C2×D3)⋊C411yescharacteristic
262C2×D5—121no—
263C2×D5—121no—
264C2×D5—121no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5#82512yes—
271Dic5—124no—
272Dic5—121no—
273Dic5—121no—
274Dic5—121no—
275C2×Q8—151no—
276C2×D4—151no—
277C2×D4—301no—
278C22×C4—302no—
279C22×C4—301no—
280C22×C4D6011yescharacteristic
281C22×C4D6011yescharacteristic
282C22×C4C22×D1511yescharacteristic
283C2×C8—22no—
284C4⋊C4—151no—
285C4⋊C4—151no—
286C4⋊C4—301no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C22⋊C4—301no—
291C22⋊C4—301no—
292C22⋊C4—301no—
293C22⋊C4—301no—
294C22⋊C4—301no—
295C42—304no—
296C42—301no—
297C42C4×D1511yescharacteristic
298C42C4×D1511yescharacteristic
299C42#122011yescharacteristic
300C42#122011yescharacteristic
301C3×C5#150011yescharacteristic, complemented, Hall
302C22×C3—21no—
303C22×C3—21no—
304C22×C3#405012yes—
305C22×C3C2×#68511yescharacteristic
306C2×D3—201no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4#395712yes—
315Dic3—204no—
316Dic3—201no—
317Dic3—201no—
318Dic3—201no—
319C2×C5—22no—
320C2×C5#500611yescharacteristic
321C2×C5#511311yescharacteristic
322C2×C5C2×#82511yescharacteristic
323D5—241no—
324C23—301no—
325C23C2×D6011yescharacteristic
326Q8—601no—
327D4—601no—
328D4—602no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—304no—
333C2×C4—301no—
334C2×C4—301no—
335C2×C4—301no—
336C2×C4—602no—
337C2×C4—602no—
338C2×C4—602no—
339C2×C4#671411yescharacteristic
340C2×C4#671411yescharacteristic
341C2×C4#671411yescharacteristic
342C2×C4#671411yescharacteristic
343C2×C4C2×C4×D1511yescharacteristic
344C2×C4C2×#122011yescharacteristic
345C8—42no—
346C2×C3—22no—
347C2×C3#6529511yescharacteristic
348C2×C3#6540211yescharacteristic
349C2×C3C2×#395711yescharacteristic
350D3—401no—
351C5#7078811yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—601no—
355C22—601no—
356C22—601no—
357C22#9179312yes—
358C22C2×#671411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—604no—
365C4—601no—
366C4—601no—
367C4—601no—
368C4#9110912yes—
369C3#1060158111yescharacteristic, complemented, Sylow
370C2—22no—
371C2—1201no—
372C2#1175110711yescharacteristic
373C2#1175121411yescharacteristic
374C2C2×#9110911yescharacteristic
subgroupG/H
centerC2×C4#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#431C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenter#431D15
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C3×C5×#431C2semidirect
3. #11751033C2semidirect
5. #11746288C2semidirect
14. #91764C4semidirect
15. C4×D60C4semidirect
17. #91759C4semidirect
18. C4×Dic30C4semidirect
26. C5×#431D3semidirect
57. C3×#431D5semidirect
145. #431D15semidirect
301. C3×C5#1500semidirect
351. C5#70788semidirect
369. C3#10601581semidirect

Maximal subgroups

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

subgroupindex
#117562382
C3×C5×#4312
#117510332
#117462912
#117462882
#106015813
#707885