Finite Group Databasebeta

← #14283112

Subgroups — #14283112

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91819C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3#11751308C211yesmaximal, characteristic, complemented
4#11746272C214yesmaximal, complemented
5#10600237—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×#1220—21no—
8C22×D60C411yescharacteristic, complemented
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C42×C5—21no—
11#91819—21no—
12#91819—21no—
13#91819C412yescomplemented
14#91819C2212yes—
15C2×#6714—21no—
16C2×C4⋊Dic15C411yescharacteristic, complemented
17C2×#6710—21no—
18C3×C5×#95C2212yescomplemented
19#91114—21no—
20#91114C2212yescomplemented
21#69444—51nomaximal, Hall
22C2×#4076—31no—
23C4×C5×C22⋊C4D311yescharacteristic, 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—24no—
44C3×C42×C5—42no—
45#6714—22no—
46#6714—22no—
47C4⋊Dic15—21no—
48C4⋊Dic15C2×C412yes—
49#6710—42no—
50C2×C3⋊#168—22no—
51C2×#930—51no—
52C3×C4×C22⋊C4D511yescharacteristic, complemented
53#5207—51no—
54#4451—54no—
55C23×C4×C5C2×D311yescharacteristic
56C22×C22⋊D5—61no—
57C22×D20—31no—
58C2×C5×C22⋊C4—21no—
59C2×C42×C5—21no—
60#4076—32no—
61#4076—32no—
62#4076—61no—
63#4076—61no—
64C2×#685—61no—
65C2×C4⋊Dic5—31no—
66C2×#681—61no—
67C5×#95C2×D312yescomplemented
68C22⋊#168—32no—
69C22⋊#168—61no—
70#1507—151noSylow
71C23×C3×C5—22no—
72C23×C3×C5—22no—
73C23×C3×C5—41no—
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22⋊C411yescharacteristic
76C23×C3×C5C2×D411yescharacteristic
77C22×D15—22no—
78C22×D15—42no—
79C22×D15—42no—
80C22×D15—42no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—24no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—42no—
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—44no—
95#1220—44no—
96C2×Dic15—22no—
97C2×Dic15—42no—
98D60—42no—
99D60—42no—
100C3⋊#168—42no—
101C23×C3×C4C2×D511yescharacteristic
102C22×#67—101no—
103C22×D12—51no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C42—21no—
106#930—52no—
107#930—52no—
108#930—101no—
109#930—101no—
110C2×(C2×D3)⋊C4—101no—
111C2×C4⋊Dic3—51no—
112C2×#208—101no—
113C3×#95C2×D512yescomplemented
114#830—52no—
115#830—101no—
116C24×C5#6711yescharacteristic
117C23×D5—61no—
118C22×C4×C5—22no—
119C22×C4×C5—42no—
120C22×C4×C5C4×D311yescharacteristic
121C22×C4×C5C4×D311yescharacteristic
122C22×C4×C5D1211yescharacteristic
123C22×C4×C5D1211yescharacteristic
124C22×C4×C5#6711yescharacteristic
125C22×C4×C5C22×D311yescharacteristic
126C2×C22⋊D5—62no—
127C2×C22⋊D5—62no—
128C2×C22⋊D5—124no—
129C22×Dic5—61no—
130C2×D20—32no—
131C2×D20—61no—
132C2×D20—122no—
133C5×C22⋊C4—24no—
134C42×C5—42no—
135#685—62no—
136#685—62no—
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139#681—122no—
140C2×#168—62no—
141C2×#121—151no—
142#407—151no—
143C4×C22⋊C4D1511yescharacteristic, complemented
144#327—154no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—44no—
153C22×C3×C5#10412yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C22×C3×C5AGL(1,ℤ/8)12yes—
156C2×D15—42no—
157C2×D15—42no—
158C2×D15—42no—
159C2×D15—84no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—44no—
164C3×C4×C5#9912yes—
165Dic15—42no—
166C24×C3C22⋊D511yescharacteristic
167C23×D3—101no—
168C22×C3×C4—22no—
169C22×C3×C4—42no—
170C22×C3×C4C4×D511yescharacteristic
171C22×C3×C4C4×D511yescharacteristic
172C22×C3×C4D2011yescharacteristic
173C22×C3×C4D2011yescharacteristic
174C22×C3×C4C22⋊D511yescharacteristic
175C22×C3×C4C22×D511yescharacteristic
176C2×#67—102no—
177C2×#67—102no—
178C2×#67—204no—
179C22×Dic3—101no—
180C2×D12—52no—
181C2×D12—101no—
182C2×D12—202no—
183C3×C22⋊C4—24no—
184C3×C42—42no—
185(C2×D3)⋊C4—102no—
186(C2×D3)⋊C4—102no—
187C4⋊Dic3—52no—
188C4⋊Dic3—101no—
189#208—202no—
190C2×C3⋊C8—102no—
191C23×C5—22no—
192C23×C5—22no—
193C23×C5—41no—
194C23×C5(C2×D3)⋊C411yescharacteristic
195C23×C5(C2×D3)⋊C411yescharacteristic
196C23×C5C2×#6711yescharacteristic
197C22×D5—62no—
198C22×D5—122no—
199C22×D5—122no—
200C22×D5—122no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—24no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—42no—
209C2×C4×C5—42no—
210C2×C4×C5(C2×D3)⋊C411yescharacteristic
211C2×C4×C5(C2×D3)⋊C411yescharacteristic
212C2×C4×C5C2×C4×D311yescharacteristic
213C2×C4×C5C2×D1211yescharacteristic
214C22⋊D5—124no—
215C22⋊D5—124no—
216C2×Dic5—62no—
217C2×Dic5—122no—
218D20—122no—
219D20—122no—
220#168—122no—
221C22×D4—151no—
222C22×D4—301no—
223C23×C4C2×D1511yescharacteristic
224C2×M16—301no—
225#121—152no—
226#121—152no—
227#121—301no—
228#121—301no—
229C2×C4⋊C4—151no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—301no—
232C2×C42—21no—
233C22⋊C8—152no—
234C22⋊C8—301no—
235#95C2×D1512yescomplemented
236C2×C3×C5—22no—
237C2×C3×C5—22no—
238C2×C3×C5—41no—
239C2×C3×C5C2×#9911yescharacteristic
240C2×C3×C5#41811yescharacteristic
241C2×C3×C5C2×#10411yescharacteristic
242D15—82no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—41no—
246C23×C3#68511yescharacteristic
247C23×C3#68511yescharacteristic
248C23×C3C2×C22⋊D511yescharacteristic
249C22×D3—102no—
250C22×D3—202no—
251C22×D3—202no—
252C22×D3—202no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—24no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4#68511yescharacteristic
263C2×C3×C4#68511yescharacteristic
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4C2×D2011yescharacteristic
266#67—204no—
267#67—204no—
268C2×Dic3—102no—
269C2×Dic3—202no—
270D12—202no—
271D12—202no—
272C3⋊C8—202no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—44no—
281C22×C5#80512yes—
282C22×C5C2×(C2×D3)⋊C411yescharacteristic
283C22×C5#94912yes—
284C2×D5—122no—
285C2×D5—122no—
286C2×D5—122no—
287C2×D5—244no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—44no—
292C4×C5#80612yes—
293Dic5—122no—
294C24—301no—
295C24#122011yescharacteristic
296C2×D4—152no—
297C2×D4—302no—
298C2×D4—302no—
299C2×D4—301no—
300C2×D4—602no—
301C2×D4—604no—
302C22×C4—22no—
303C22×C4—42no—
304C22×C4—301no—
305C22×C4C4×D1511yescharacteristic
306C22×C4C4×D1511yescharacteristic
307C22×C4D6011yescharacteristic
308C22×C4D6011yescharacteristic
309C22×C4#122011yescharacteristic
310C22×C4C22×D1511yescharacteristic
311M16—602no—
312C2×C8—302no—
313C4⋊C4—152no—
314C4⋊C4—301no—
315C22⋊C4—24no—
316C22⋊C4—302no—
317C22⋊C4—302no—
318C42—42no—
319C3×C5#150711yescharacteristic, complemented, Hall
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—44no—
328C22×C3#393712yes—
329C22×C3C2×#68511yescharacteristic
330C22×C3#409512yes—
331C2×D3—202no—
332C2×D3—202no—
333C2×D3—202no—
334C2×D3—404no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—44no—
339C3×C4#393812yes—
340Dic3—202no—
341C2×C5—22no—
342C2×C5—22no—
343C2×C5—41no—
344C2×C5C2×#80511yescharacteristic
345C2×C5C2×#80611yescharacteristic
346C2×C5#500111yescharacteristic
347D5—242no—
348C23—22no—
349C23—22no—
350C23—41no—
351C23—302no—
352C23—602no—
353C23—602no—
354C23—602no—
355C23#671411yescharacteristic
356C23#671411yescharacteristic
357C23C2×#122011yescharacteristic
358D4—602no—
359D4—604no—
360D4—604no—
361D4—602no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—302no—
372C2×C4—602no—
373C2×C4#671411yescharacteristic
374C2×C4#671411yescharacteristic
375C2×C4C2×C4×D1511yescharacteristic
376C2×C4C2×D6011yescharacteristic
377C8—602no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—41no—
381C2×C3C2×#393711yescharacteristic
382C2×C3C2×#393811yescharacteristic
383C2×C3#6529011yescharacteristic
384D3—402no—
385C5#6944411yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—602no—
395C22—602no—
396C22—602no—
397C22—1204no—
398C22#9108912yes—
399C22C2×#671411yescharacteristic
400C22#9183812yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—44no—
405C4—602no—
406C4#9109012yes—
407C3#1060023711yescharacteristic, complemented, Sylow
408C2—22no—
409C2—22no—
410C2—41no—
411C2—1202no—
412C2C2×#9108911yescharacteristic
413C2C2×#9109011yescharacteristic
414C2#1175110211yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C4×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91819C2
cosocleC22×C3×C4×C5C23
hypercenterC4×C22⋊C4D15
hypocenterC3×C5#1507
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C22⋊C4C2semidirect
3. #11751308C2semidirect
4. #11746272C2semidirect
8. C22×D60C4semidirect
13. #91819C4semidirect
16. C2×C4⋊Dic15C4semidirect
18. C3×C5×#95C22semidirect
20. #91114C22semidirect
23. C4×C5×C22⋊C4D3semidirect
52. C3×C4×C22⋊C4D5semidirect
67. C5×#95C2×D3semidirect
113. C3×#95C2×D5semidirect
143. C4×C22⋊C4D15semidirect
235. #95C2×D15semidirect
319. C3×C5#1507semidirect
385. C5#69444semidirect
407. C3#10600237semidirect

Maximal subgroups

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

subgroupindex
C2×#918192
C3×C4×C5×C22⋊C42
#117513082
#117462722
#106002373
#694445