Finite Group Databasebeta

← #14307502

Subgroups — #14307502

Order 1920.

648 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×C5×#924C211yesmaximal, characteristic
2C4×#6719C211yesmaximal, characteristic
3C3×#65501C211yesmaximal, characteristic
4#11746018C214yesmaximal
5#10602494—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C5×Dic6C411yescharacteristic, complemented
8C2×#6719C2212yes—
9C2×C4×Dic15—21no—
10C2×C5×#217C2212yes—
11C2×C5×C4⋊Dic3C411yescharacteristic, complemented
12C5×#924—21no—
13C5×#924—21no—
14C5×#924—21no—
15C5×#924—21no—
16C2×C5×Dic3⋊C4C412yescomplemented
17C2×C3×C22⋊Dic5C2212yes—
18C2×C3×C4⋊Dic5—21no—
19#91115—21no—
20C3×#3963—21no—
21#69529—51nomaximal, Hall
22C2×C5×C22⋊Q8—31no—
23#65501D311yescharacteristic
24C4×C22⋊Dic5—31no—
25#64746—34no—
26C24×C3×C5C2311yescharacteristic
27C22×C3×C4×C5—42no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×Dic15—22no—
35C22×C5×Dic3C2×C412yes—
36C22×C5×Dic3C2×C412yes—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6—42no—
40C22×C3×Dic5—22no—
41#6719—22no—
42#6719Q814yescomplemented
43C4×Dic15—42no—
44C5×#217—22no—
45C5×#217—22no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C5×Dic3⋊C4—22no—
49C5×Dic3⋊C4—22no—
50C3×C22⋊Dic5—24no—
51C3×C4⋊Dic5—42no—
52C2×#924D511yescharacteristic
53C3×#380—51no—
54C4×#217—51no—
55#4527—54no—
56C22×C5×Q8—31no—
57C23×C4×C5C2×D311yescharacteristic
58C5×C22⋊Q8—61no—
59C5×C22⋊Q8—61no—
60C5×C22⋊Q8—61no—
61C5×C22⋊Q8—61no—
62C2×C5×C4⋊C4—32no—
63C2×C5×C4⋊C4—31no—
64C2×C5×C22⋊C4—32no—
65C2×C22⋊Dic5—32no—
66C2×C22⋊Dic5C2×D312yes—
67C2×C4⋊Dic5—21no—
68C2×C4×Dic5—61no—
69#3963—21no—
70#3963—61no—
71#1996—151noSylow
72C23×C3×C5—41no—
73C23×C3×C5—41no—
74C23×C3×C5C22×C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C23×C3×C5C2×D411yescharacteristic
77C23×C3×C5C2×Q812yes—
78C23×C3×C5#4112yes—
79C2×C3×C4×C5—22no—
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×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×Dic15—24no—
90C2×Dic15—42no—
91C2×Dic15—42no—
92C2×C5×Dic3—22no—
93C2×C5×Dic3—22no—
94C2×C5×Dic3—42no—
95C2×C5×Dic3—42no—
96C5×Dic6—42no—
97C5×Dic6—42no—
98C2×C3×Dic5—42no—
99C2×C3×Dic5—42no—
100C2×C3×Dic5—42no—
101C23×C3×C4C2×D511yescharacteristic
102C22×Dic6Dic511yescharacteristic, complemented
103C2×C3×C4⋊C4—101no—
104C2×C3×C22⋊C4—52no—
105C2×#217—52no—
106C2×#217C2×D512yes—
107C2×C4⋊Dic3Dic511yescharacteristic, complemented
108#924—21no—
109#924—21no—
110#924—21no—
111#924—21no—
112C2×Dic3⋊C4Dic512yescomplemented
113C2×C4×Dic3—101no—
114C3×#95—101no—
115C3⋊#95—101no—
116C24×C5C22×D311yescharacteristic
117C2×C5×Q8—61no—
118C2×C5×Q8—61no—
119C2×C5×Q8—122no—
120C22×C4×C5—32no—
121C22×C4×C5—32no—
122C22×C4×C5—42no—
123C22×C4×C5C4×D311yescharacteristic
124C22×C4×C5C4×D311yescharacteristic
125C22×C4×C5D1211yescharacteristic
126C22×C4×C5D1211yescharacteristic
127C22×C4×C5#6711yescharacteristic
128C22×C4×C5#6711yescharacteristic
129C22×Dic5—22no—
130C22×Dic5—62no—
131C5×C4⋊C4—62no—
132C5×C4⋊C4—62no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4—61no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—62no—
137C22⋊Dic5—24no—
138C22⋊Dic5—34no—
139C22⋊Dic5—62no—
140C4⋊Dic5—42no—
141C4×Dic5—122no—
142C2×C22⋊Q8—31no—
143#380—51no—
144C4×C22⋊C4—151no—
145#342—154no—
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—42no—
153C22×C3×C5—42no—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C22×C3×C5C4×Q812yes—
156C22×C3×C5C22⋊Q812yes—
157C22×C3×C5#12411yescharacteristic
158C22×C3×C5C4⋊Q811yescharacteristic
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5#9912yes—
163Dic15—44no—
164C3×Dic5—82no—
165C5×Dic3—42no—
166C5×Dic3—42no—
167C24×C3C22×D511yescharacteristic
168C22×C3×C4—42no—
169C22×C3×C4—102no—
170C22×C3×C4C2×Dic511yescharacteristic
171C22×C3×C4C2×Dic511yescharacteristic
172C22×C3×C4C22⋊D511yescharacteristic
173C22×C3×C4C22⋊D511yescharacteristic
174C22×C3×C4C22⋊D511yescharacteristic
175C22×C3×C4C22⋊D511yescharacteristic
176C22×Dic3—102no—
177C22×Dic3C2×Dic512yes—
178C22×Dic3C2×Dic512yes—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6—42no—
182C3×C4⋊C4—202no—
183C3×C22⋊C4—104no—
184#217—22no—
185#217—22no—
186#217—54no—
187#217—102no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190Dic3⋊C4—22no—
191Dic3⋊C4—22no—
192C4×Dic3—202no—
193C23×C5—41no—
194C23×C5—41no—
195C23×C5C2×C4×D311yescharacteristic
196C23×C5C2×D1211yescharacteristic
197C23×C5#23712yes—
198C23×C5D3×Q812yes—
199C23×C5C2×#6711yescharacteristic
200C5×Q8—122no—
201C5×Q8—122no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—62no—
209C2×C4×C5—62no—
210C2×C4×C5—122no—
211C2×C4×C5—122no—
212C2×C4×C5(C2×D3)⋊C411yescharacteristic
213C2×C4×C5(C2×D3)⋊C411yescharacteristic
214C2×C4×C5(C2×D3)⋊C411yescharacteristic
215C2×C4×C5(C2×D3)⋊C411yescharacteristic
216C2×Dic5—42no—
217C2×Dic5—42no—
218C2×Dic5—42no—
219C2×Dic5—64no—
220C2×Dic5—122no—
221C2×Dic5—122no—
222C22×Q8—31no—
223C23×C4D3×D511yescharacteristic
224C22⋊Q8—61no—
225C22⋊Q8—61no—
226C22⋊Q8—61no—
227C22⋊Q8—61no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—31no—
230C2×C4⋊C4—101no—
231C2×C22⋊C4—32no—
232C2×C22⋊C4—52no—
233C2×C22⋊C4—152no—
234C2×C42—301no—
235#95—101no—
236#95—301no—
237C2×C3×C5—21no—
238C2×C3×C5—22no—
239C2×C3×C5—22no—
240C2×C3×C5—21no—
241C2×C3×C5#39111yescharacteristic
242C2×C3×C5C2×#9911yescharacteristic
243C2×C3×C5#41011yescharacteristic
244C23×C3—41no—
245C23×C3—41no—
246C23×C3Q8×D512yes—
247C23×C3#71312yes—
248C23×C3C22×Dic511yescharacteristic
249C23×C3C2×C22⋊D511yescharacteristic
250C23×C3C2×C22⋊D511yescharacteristic
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—202no—
258C2×C3×C4—202no—
259C2×C3×C4—202no—
260C2×C3×C4C22⋊Dic511yescharacteristic
261C2×C3×C4C22⋊Dic511yescharacteristic
262C2×C3×C4C22⋊Dic511yescharacteristic
263C2×C3×C4C22⋊Dic511yescharacteristic
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—42no—
267C2×Dic3—42no—
268C2×Dic3—104no—
269C2×Dic3—202no—
270C2×Dic3—202no—
271Dic6—42no—
272Dic6—42no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—42no—
280C22×C5—42no—
281C22×C5#88712yes—
282C22×C5#89712yes—
283C22×C5C2×(C2×D3)⋊C411yescharacteristic
284C22×C5#93611yescharacteristic
285C22×C5#94411yescharacteristic
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—122no—
290C4×C5—122no—
291C4×C5#80612yes—
292Dic5—82no—
293Dic5—124no—
294C24C2×D3×D511yescharacteristic
295C2×Q8—61no—
296C2×Q8—61no—
297C2×Q8—122no—
298C22×C4—32no—
299C22×C4—32no—
300C22×C4—42no—
301C22×C4—102no—
302C22×C4—302no—
303C22×C4D3×Dic511yescharacteristic
304C22×C4D3×Dic511yescharacteristic
305C22×C4#120111yescharacteristic
306C22×C4#120111yescharacteristic
307C22×C4#120311yescharacteristic
308C22×C4#120311yescharacteristic
309C4⋊C4—62no—
310C4⋊C4—62no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—202no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—104no—
317C22⋊C4—154no—
318C22⋊C4—302no—
319C42—602no—
320C3×C5#199611yescharacteristic, complemented, Hall
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3#409011yescharacteristic
330C22×C3Q8×Dic512yes—
331C22×C3#409212yes—
332C22×C3#409311yescharacteristic
333C22×C3C2×C22⋊Dic511yescharacteristic
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—402no—
338C3×C4#396612yes—
339Dic3—42no—
340Dic3—42no—
341Dic3—204no—
342C2×C5—21no—
343C2×C5—22no—
344C2×C5—22no—
345C2×C5—21no—
346C2×C5C2×#80611yescharacteristic
347C2×C5#497311yescharacteristic
348C2×C5#500611yescharacteristic
349C23—41no—
350C23—41no—
351C23#676612yes—
352C23D15⋊Q812yes—
353C23C2×D3×Dic511yescharacteristic
354C23C2×#120111yescharacteristic
355C23C2×#120311yescharacteristic
356Q8—122no—
357Q8—122no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—122no—
367C2×C4—122no—
368C2×C4—202no—
369C2×C4—202no—
370C2×C4—202no—
371C2×C4—304no—
372C2×C4—602no—
373C2×C4—602no—
374C2×C4(C2×D3)⋊Dic511yescharacteristic
375C2×C4(C2×D3)⋊Dic511yescharacteristic
376C2×C4(C2×D3)⋊Dic511yescharacteristic
377C2×C4(C2×D3)⋊Dic511yescharacteristic
378C2×C3—22no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—22no—
382C2×C3C2×#396611yescharacteristic
383C2×C3#6551911yescharacteristic
384C2×C3#6552911yescharacteristic
385C5#6952911yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22#9134412yes—
395C22#9136811yescharacteristic
396C22#9138312yes—
397C22#9138511yescharacteristic
398C22C2×(C2×D3)⋊Dic511yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—122no—
403C4—122no—
404C4—402no—
405C4—604no—
406C4#9099612yes—
407C3#1060249411yescharacteristic, complemented, Sylow
408C2—21no—
409C2—22no—
410C2—22no—
411C2—21no—
412C2#1174860711yescharacteristic
413C2#1174862511yescharacteristic
414C2C2×#9099611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical, cosocleC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1996
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
7. C22×C5×Dic6C4semidirect
11. C2×C5×C4⋊Dic3C4semidirect
16. C2×C5×Dic3⋊C4C4semidirect
42. #6719Q8semidirect
102. C22×Dic6Dic5semidirect
107. C2×C4⋊Dic3Dic5semidirect
112. C2×Dic3⋊C4Dic5semidirect
320. C3×C5#1996semidirect
385. C5#69529semidirect
407. C3#10602494semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9242
C4×#67192
C3×#655012
#117460182
#106024943
#695295