Finite Group Databasebeta

← #14294800

Subgroups — #14294800

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91931C212yesmaximal
2C2×#91403C211yesmaximal, characteristic
3#11746790C211yesmaximal, characteristic, complemented
4C3×#64919C211yesmaximal, characteristic, complemented
5#11746574C212yesmaximal, complemented
6#10604192—31nomaximal, Hall
7C22×#1200C2211yescharacteristic
8C2×#6762C2212yes—
9C2×C3×#704C2212yes—
10C2×#6740—22no—
11#91931—24no—
12#91931C418yescomplemented
13C2×#6738—22no—
14C2×#6714C411yescharacteristic
15C2×C4×C5×Dic3C411yescharacteristic
16C2×C3×#683C2211yescharacteristic
17C2×#6668C2211yescharacteristic
18C2×#6667C411yescharacteristic
19C2×Dic3×Dic5C411yescharacteristic
20#91403—22no—
21#91403—22no—
22#68989—51nomaximal, Hall
23C2×D5⋊M16—32no—
24C2×#4018—31no—
25#64919—31no—
26#64919—32no—
27#64919D311yescharacteristic, complemented
28C23×D15C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×Dic15C2×C411yescharacteristic
31C22×C5×Dic3C2×C411yescharacteristic
32C22×C5×Dic3C2×C411yescharacteristic
33C22×C3×Dic5C2×C411yescharacteristic
34C22×C3×Dic5C2311yescharacteristic
35C2×#1200C2×C414yes—
36C2×#1200D412yes—
37C2×#1200D412yes—
38C2×#1200D412yes—
39C2×#1200Q812yes—
40#6762—22no—
41#6762C2×C414yes—
42C2×C3⋊#170—22no—
43C3×#704—22no—
44C3×#704C2×C414yes—
45C2×C3×#170—22no—
46#6740—28no—
47#6738—28no—
48#6714—22no—
49C4×C5×Dic3—21no—
50C4×C5×Dic3—21no—
51C3×#683—22no—
52#6668—22no—
53#6667—22no—
54Dic3×Dic5—21no—
55Dic3×Dic5—21no—
56C2×D3×M16—52no—
57C2×#892—51no—
58C3×#343—51no—
59#4554—52no—
60#4530—51no—
61C22×C4×D5—31no—
62C2×#704—32no—
63C2×#704C2×D312yes—
64D5⋊M16—38no—
65D5⋊M16—64no—
66C2×#700—62no—
67C2×D5⋊C8—62no—
68C2×C42×C5—31no—
69C2×#685—31no—
70C2×#685—31no—
71C2×#683—31no—
72C2×#683C2×D311yescharacteristic
73C2×C4×Dic5—31no—
74#4018—62no—
75#4018—62no—
76#1742—151noSylow
77C23×C3×C5C22×C411yescharacteristic
78C22×D15—41no—
79C22×D15—41no—
80C22×D15C4212yes—
81C22×D15C22⋊C412yes—
82C22×D15C4⋊C412yes—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—41no—
85C2×Dic15—21no—
86C2×Dic15—41no—
87C2×C5×Dic3—21no—
88C2×C5×Dic3—41no—
89C2×C5×Dic3C4212yes—
90C2×C5×Dic3C22⋊C411yescharacteristic
91C2×C5×Dic3C22⋊C411yescharacteristic
92C2×C5×Dic3C4⋊C412yes—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—41no—
95C2×C3×Dic5C22×C412yes—
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D412yes—
98C2×C3×Dic5C2×Q811yescharacteristic
99#1200C22⋊C414yes—
100#1200C22⋊C414yes—
101#1200C4⋊C414yes—
102#1200C4⋊C414yes—
103C3⋊#170—24no—
104C3×#170—24no—
105C22×C4×D3—51no—
106C2×C3×M16—52no—
107C2×C3×C4⋊C4—51no—
108C2×(C2×D3)⋊C4—51no—
109C2×(C2×D3)⋊C4—51no—
110C2×C4⋊Dic3—51no—
111C2×C4×Dic3—51no—
112C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
113C2×#208—52no—
114D3×M16—58no—
115D3×M16—104no—
116C2×ΓL(1,𝔽25)—102no—
117C2×D3×C8—102no—
118#892—102no—
119#892—102no—
120C23×D5—31no—
121C22×C4×C5—31no—
122C22×C4×C5—31no—
123C22×C4×C5C4×D311yescharacteristic
124C22×Dic5—31no—
125C22×Dic5C4×D311yescharacteristic
126C22×Dic5C22×D311yescharacteristic
127C2×C4×D5—34no—
128C2×C4×D5—32no—
129C2×C4×D5—32no—
130C2×C4×D5—32no—
131C2×C4×D5—32no—
132#704—22no—
133#704—34no—
134#704—62no—
135#704C4×D314yes—
136C2×#170—22no—
137C2×#170—62no—
138#700—68no—
139D5⋊C8—68no—
140C42×C5—61no—
141C42×C5—61no—
142#685—62no—
143#685—62no—
144#683—22no—
145#683—62no—
146C4×Dic5—61no—
147C4×Dic5—61no—
148C22×M16—152no—
149C2×#117—151no—
150#343—51no—
151#343—151no—
152#343—152no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5C2×C4211yescharacteristic
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C2×C4⋊C411yescharacteristic
158C2×D15—22no—
159C2×D15—22no—
160C2×D15—42no—
161C2×D15—42no—
162C2×D15#9514yes—
163C3×C4×C5—41no—
164Dic15—41no—
165C3×Dic5—41no—
166C3×Dic5C2×C22⋊C412yes—
167C3×Dic5C2×C4⋊C412yes—
168C5×Dic3—41no—
169C5×Dic3#9512yes—
170C5×Dic3#9512yes—
171C23×D3—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
175C22×Dic3—51no—
176C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
177C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
178C2×C4×D3—54no—
179C2×C4×D3—52no—
180C2×C4×D3—52no—
181C2×C4×D3—52no—
182C2×C4×D3—52no—
183C3×M16—54no—
184C3×M16—102no—
185C2×C3×C8—102no—
186C3×C4⋊C4—102no—
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—102no—
189C4⋊Dic3—102no—
190C4×Dic3—21no—
191C4×Dic3—21no—
192C4×Dic3—101no—
193C4×Dic3—101no—
194#208—54no—
195#208—102no—
196C2×C3⋊C8—102no—
197ΓL(1,𝔽25)—108no—
198D3×C8—108no—
199C23×C5C2×C4×D311yescharacteristic
200C22×D5—32no—
201C22×D5—32no—
202C22×D5—32no—
203C22×D5—121no—
204C22×D5—121no—
205C2×C4×C5—21no—
206C2×C4×C5—32no—
207C2×C4×C5—31no—
208C2×C4×C5—31no—
209C2×C4×C5—32no—
210C2×C4×C5—41no—
211C2×C4×C5—61no—
212C2×C4×C5—121no—
213C2×Dic5—21no—
214C2×Dic5—41no—
215C2×Dic5—61no—
216C2×Dic5—121no—
217C2×Dic5C2×C4×D312yes—
218C2×Dic5D3×D411yescharacteristic
219C2×Dic5D3×D412yes—
220C2×Dic5D3×Q811yescharacteristic
221C4×D5—34no—
222C4×D5—34no—
223C4×D5—34no—
224C4×D5—34no—
225#170—24no—
226#170—64no—
227C23×C4—151no—
228C2×M16—52no—
229C2×M16—158no—
230C2×M16—152no—
231C2×M16—302no—
232C2×M16—304no—
233C22×C8—302no—
234#117—302no—
235#117—302no—
236C2×C4⋊C4—51no—
237C2×C4⋊C4—151no—
238C2×C22⋊C4—151no—
239C2×C22⋊C4—151no—
240C2×C42—31no—
241C2×C42—151no—
242C2×C3×C5—21no—
243C2×C3×C5—21no—
244C2×C3×C5C2×#9511yescharacteristic
245C2×C3×C5#41311yescharacteristic
246C2×C3×C5#41311yescharacteristic
247D15—24no—
248C23×C3C22×AGL(1,𝔽5)11yescharacteristic
249C22×D3—52no—
250C22×D3—52no—
251C22×D3—52no—
252C22×D3—201no—
253C22×D3—201no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—52no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—52no—
260C2×C3×C4—101no—
261C2×C3×C4—201no—
262C2×Dic3—21no—
263C2×Dic3—41no—
264C2×Dic3—101no—
265C2×Dic3—201no—
266C2×Dic3C4×AGL(1,𝔽5)12yes—
267C2×Dic3C4⋊AGL(1,𝔽5)12yes—
268C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
269C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
270C4×D3—54no—
271C4×D3—54no—
272C4×D3—54no—
273C4×D3—54no—
274C3×C8—104no—
275C3⋊C8—104no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5C42×D311yescharacteristic
279C22×C5D3×C22⋊C411yescharacteristic
280C22×C5D3×C4⋊C411yescharacteristic
281C2×D5—34no—
282C2×D5—62no—
283C2×D5—62no—
284C2×D5—122no—
285C2×D5—122no—
286C4×C5—32no—
287C4×C5—32no—
288C4×C5—41no—
289C4×C5—121no—
290Dic5—41no—
291Dic5—121no—
292Dic5D3×C22⋊C412yes—
293Dic5D3×C4⋊C412yes—
294C24—151no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—152no—
300C22×C4—152no—
301C22×C4—154no—
302C22×C4—152no—
303C22×C4—152no—
304C22×C4—151no—
305C22×C4D3×AGL(1,𝔽5)11yescharacteristic
306M16—54no—
307M16—102no—
308M16—154no—
309M16—308no—
310M16—302no—
311C2×C8—102no—
312C2×C8—308no—
313C2×C8—302no—
314C4⋊C4—102no—
315C4⋊C4—302no—
316C22⋊C4—302no—
317C22⋊C4—302no—
318C42—61no—
319C42—61no—
320C42—301no—
321C42—301no—
322C3×C5#174211yescharacteristic, complemented, Hall
323C22×C3—21no—
324C22×C3—21no—
325C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
326C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
327C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
328C2×D3—54no—
329C2×D3—102no—
330C2×D3—102no—
331C2×D3—202no—
332C2×D3—202no—
333C3×C4—41no—
334C3×C4—52no—
335C3×C4—52no—
336C3×C4—201no—
337Dic3—41no—
338Dic3—201no—
339Dic3(C2×AGL(1,𝔽5))⋊C412yes—
340Dic3(C2×AGL(1,𝔽5))⋊C412yes—
341C2×C5—21no—
342C2×C5—21no—
343C2×C5D3×#9511yescharacteristic
344C2×C5#474511yescharacteristic
345C2×C5#475111yescharacteristic
346D5—64no—
347C23—152no—
348C23—152no—
349C23—152no—
350C23—601no—
351C23—601no—
352C23C2×D3×AGL(1,𝔽5)11yescharacteristic
353C2×C4—21no—
354C2×C4—32no—
355C2×C4—32no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—41no—
359C2×C4—52no—
360C2×C4—51no—
361C2×C4—51no—
362C2×C4—52no—
363C2×C4—61no—
364C2×C4—101no—
365C2×C4—121no—
366C2×C4—154no—
367C2×C4—154no—
368C2×C4—154no—
369C2×C4—154no—
370C2×C4—201no—
371C2×C4—301no—
372C2×C4—601no—
373C8—104no—
374C8—304no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3#6576111yescharacteristic
378C2×C3#6576111yescharacteristic
379C2×C3C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
380D3—104no—
381C5#6898911yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—154no—
385C22—302no—
386C22—302no—
387C22—602no—
388C22—602no—
389C22C4×D3×AGL(1,𝔽5)11yescharacteristic
390C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
391C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
392C4—32no—
393C4—32no—
394C4—41no—
395C4—52no—
396C4—52no—
397C4—121no—
398C4—201no—
399C4—601no—
400C3#1060419211yescharacteristic, complemented, Sylow
401C2—21no—
402C2—21no—
403C2—304no—
404C2#1175191711yescharacteristic
405C2D3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
406C2#1175204911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1742
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
4. C3×#64919C2semidirect
5. #11746574C2semidirect
12. #91931C4semidirect
27. #64919D3semidirect
322. C3×C5#1742semidirect
381. C5#68989semidirect
400. C3#10604192semidirect

Maximal subgroups

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

subgroupindex
C2×#919312
C2×#914032
#117467902
C3×#649192
#117465742
#106041923
#689895