Finite Group Databasebeta

← #14283261

Subgroups — #14283261

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91819C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic, complemented
3#11751308C211yesmaximal, characteristic, complemented
4#11746272C214yesmaximal, complemented
5#10600324—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×#1220—21no—
8C22×D60C411yescharacteristic, complemented
9C2×C3×C5×C22⋊C4—21no—
10#91819—21no—
11#91819—21no—
12#91819C412yescomplemented
13#91819C2212yes—
14C2×#6714—21no—
15C2×C4⋊Dic15C411yescharacteristic, complemented
16C2×#6710—21no—
17C3×C5×#95—21no—
18C3×C5×#95C2212yescomplemented
19#91114—21no—
20#91114C2212yescomplemented
21#69531—51nomaximal, Hall
22C2×#4076—31no—
23C5×#381D311yescharacteristic, complemented
24#65496—31no—
25#64671—34no—
26C24×C3×C5D411yescharacteristic
27C23×D15—21no—
28C22×C3×C4×C5—22no—
29C22×C3×C4×C5—42no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—22no—
37C2×#1220—22no—
38C2×#1220—44no—
39C22×Dic15—21no—
40C2×D60—21no—
41C2×D60—42no—
42C2×D60C2×C412yes—
43C3×C5×C22⋊C4—42no—
44#6714—22no—
45#6714—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15C2×C412yes—
48#6710—42no—
49C2×C3⋊#168—22no—
50C2×#930—51no—
51C3×#381D511yescharacteristic, complemented
52#5207—51no—
53#4451—54no—
54C23×C4×C5C2×D311yescharacteristic
55C22×C22⋊D5—61no—
56C22×D20—31no—
57C2×C5×C22⋊C4—21no—
58#4076—32no—
59#4076—32no—
60#4076—61no—
61#4076—61no—
62C2×#685—61no—
63C2×C4⋊Dic5—31no—
64C2×#681—61no—
65C5×#95—21no—
66C5×#95C2×D312yescomplemented
67C22⋊#168—32no—
68C22⋊#168—61no—
69#1510—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×D15—22no—
77C22×D15—42no—
78C22×D15—42no—
79C22×D15—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—42no—
87C2×C3×C4×C5—42no—
88C2×C3×C4×C5—42no—
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93#1220—44no—
94#1220—44no—
95C2×Dic15—22no—
96C2×Dic15—42no—
97D60—42no—
98D60—42no—
99C3⋊#168—42no—
100C23×C3×C4C2×D511yescharacteristic
101C22×#67—101no—
102C22×D12—51no—
103C2×C3×C22⋊C4—21no—
104#930—52no—
105#930—52no—
106#930—101no—
107#930—101no—
108C2×(C2×D3)⋊C4—101no—
109C2×C4⋊Dic3—51no—
110C2×#208—101no—
111C3×#95—21no—
112C3×#95C2×D512yescomplemented
113#830—52no—
114#830—101no—
115C24×C5#6711yescharacteristic
116C23×D5—61no—
117C22×C4×C5—22no—
118C22×C4×C5—42no—
119C22×C4×C5C4×D311yescharacteristic
120C22×C4×C5C4×D311yescharacteristic
121C22×C4×C5D1211yescharacteristic
122C22×C4×C5D1211yescharacteristic
123C22×C4×C5#6711yescharacteristic
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—62no—
126C2×C22⋊D5—62no—
127C2×C22⋊D5—124no—
128C22×Dic5—61no—
129C2×D20—32no—
130C2×D20—61no—
131C2×D20—122no—
132C5×C22⋊C4—42no—
133#685—62no—
134#685—62no—
135C4⋊Dic5—32no—
136C4⋊Dic5—61no—
137#681—122no—
138C2×#168—62no—
139C2×#121—151no—
140#407—151no—
141#381D1511yescharacteristic, complemented
142#327—154no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—44no—
151C22×C3×C5#9912yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5AGL(1,ℤ/8)12yes—
154C2×D15—42no—
155C2×D15—42no—
156C2×D15—42no—
157C2×D15—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—82no—
163Dic15—42no—
164C24×C3C22⋊D511yescharacteristic
165C23×D3—101no—
166C22×C3×C4—22no—
167C22×C3×C4—42no—
168C22×C3×C4C4×D511yescharacteristic
169C22×C3×C4C4×D511yescharacteristic
170C22×C3×C4D2011yescharacteristic
171C22×C3×C4D2011yescharacteristic
172C22×C3×C4C22⋊D511yescharacteristic
173C22×C3×C4C22×D511yescharacteristic
174C2×#67—102no—
175C2×#67—102no—
176C2×#67—204no—
177C22×Dic3—101no—
178C2×D12—52no—
179C2×D12—101no—
180C2×D12—202no—
181C3×C22⋊C4—42no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184C4⋊Dic3—52no—
185C4⋊Dic3—101no—
186#208—202no—
187C2×C3⋊C8—102no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—41no—
191C23×C5(C2×D3)⋊C411yescharacteristic
192C23×C5(C2×D3)⋊C411yescharacteristic
193C23×C5C2×#6711yescharacteristic
194C22×D5—62no—
195C22×D5—122no—
196C22×D5—122no—
197C22×D5—122no—
198C2×C4×C5—22no—
199C2×C4×C5—22no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—42no—
207C2×C4×C5(C2×D3)⋊C411yescharacteristic
208C2×C4×C5(C2×D3)⋊C411yescharacteristic
209C2×C4×C5C2×C4×D311yescharacteristic
210C2×C4×C5C2×D1211yescharacteristic
211C22⋊D5—124no—
212C22⋊D5—124no—
213C2×Dic5—62no—
214C2×Dic5—122no—
215D20—122no—
216D20—122no—
217#168—122no—
218C22×D4—151no—
219C22×D4—301no—
220C23×C4C2×D1511yescharacteristic
221C2×M16—301no—
222#121—152no—
223#121—152no—
224#121—301no—
225#121—301no—
226C2×C4⋊C4—151no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—301no—
229C22⋊C8—152no—
230C22⋊C8—301no—
231#95—21no—
232#95C2×D1512yescomplemented
233C2×C3×C5—22no—
234C2×C3×C5—22no—
235C2×C3×C5—41no—
236C2×C3×C5C2×#9911yescharacteristic
237C2×C3×C5#41811yescharacteristic
238C2×C3×C5#42111yescharacteristic
239D15—82no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3#68511yescharacteristic
244C23×C3#68511yescharacteristic
245C23×C3C2×C22⋊D511yescharacteristic
246C22×D3—102no—
247C22×D3—202no—
248C22×D3—202no—
249C22×D3—202no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4#68511yescharacteristic
260C2×C3×C4#68511yescharacteristic
261C2×C3×C4C2×C4×D511yescharacteristic
262C2×C3×C4C2×D2011yescharacteristic
263#67—204no—
264#67—204no—
265C2×Dic3—102no—
266C2×Dic3—202no—
267D12—202no—
268D12—202no—
269C3⋊C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—44no—
278C22×C5#80612yes—
279C22×C5C2×(C2×D3)⋊C411yescharacteristic
280C22×C5#94912yes—
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C2×D5—244no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—82no—
290Dic5—122no—
291C24—301no—
292C24#122011yescharacteristic
293C2×D4—152no—
294C2×D4—302no—
295C2×D4—302no—
296C2×D4—301no—
297C2×D4—602no—
298C2×D4—604no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—301no—
302C22×C4C4×D1511yescharacteristic
303C22×C4C4×D1511yescharacteristic
304C22×C4D6011yescharacteristic
305C22×C4D6011yescharacteristic
306C22×C4#122011yescharacteristic
307C22×C4C22×D1511yescharacteristic
308M16—602no—
309C2×C8—302no—
310C4⋊C4—152no—
311C4⋊C4—301no—
312C22⋊C4—42no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3#393812yes—
325C22×C3C2×#68511yescharacteristic
326C22×C3#409512yes—
327C2×D3—202no—
328C2×D3—202no—
329C2×D3—202no—
330C2×D3—404no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—82no—
336Dic3—202no—
337C2×C5—22no—
338C2×C5—22no—
339C2×C5—41no—
340C2×C5C2×#80611yescharacteristic
341C2×C5#500111yescharacteristic
342C2×C5#500511yescharacteristic
343D5—242no—
344C23—22no—
345C23—22no—
346C23—41no—
347C23—302no—
348C23—602no—
349C23—602no—
350C23—602no—
351C23#671411yescharacteristic
352C23#671411yescharacteristic
353C23C2×#122011yescharacteristic
354D4—602no—
355D4—602no—
356D4—604no—
357D4—604no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—302no—
368C2×C4—602no—
369C2×C4#671411yescharacteristic
370C2×C4#671411yescharacteristic
371C2×C4C2×C4×D1511yescharacteristic
372C2×C4C2×D6011yescharacteristic
373C8—602no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3C2×#393811yescharacteristic
378C2×C3#6529011yescharacteristic
379C2×C3#6529411yescharacteristic
380D3—402no—
381C5#6953111yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—44no—
390C22—602no—
391C22—602no—
392C22—602no—
393C22—1204no—
394C22#9109012yes—
395C22C2×#671411yescharacteristic
396C22#9183812yes—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—82no—
402C4—602no—
403C3#1060032411yescharacteristic, complemented, Sylow
404C2—22no—
405C2—22no—
406C2—41no—
407C2—1202no—
408C2C2×#9109011yescharacteristic
409C2#1175110211yescharacteristic
410C2#1175110611yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#381C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91819C2
cosocleC22×C3×C4×C5C23
hypercenter#381D15
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C3×C5×#381C2semidirect
3. #11751308C2semidirect
4. #11746272C2semidirect
8. C22×D60C4semidirect
12. #91819C4semidirect
15. C2×C4⋊Dic15C4semidirect
18. C3×C5×#95C22semidirect
20. #91114C22semidirect
23. C5×#381D3semidirect
51. C3×#381D5semidirect
66. C5×#95C2×D3semidirect
112. C3×#95C2×D5semidirect
141. #381D15semidirect
232. #95C2×D15semidirect
315. C3×C5#1510semidirect
381. C5#69531semidirect
403. C3#10600324semidirect

Maximal subgroups

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

subgroupindex
C2×#918192
C3×C5×#3812
#117513082
#117462722
#106003243
#695315