Finite Group Databasebeta

← #14297621

Subgroups — #14297621

Order 1920.

544 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91324C211yesmaximal, characteristic
2#11752012C212yesmaximal
3C2×#91175C212yesmaximal
4#11746790C211yesmaximal, characteristic
5C3×#64919C211yesmaximal, characteristic
6#10604194—31nomaximal, Hall
7C22×#1204C2211yescharacteristic
8C2×#6762C2212yes—
9C2×C3×#704C2212yes—
10C2×#6712C411yescharacteristic
11C2×C4×C5×Dic3C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×Dic3⋊Dic5C411yescharacteristic
14C2×Dic3×Dic5C411yescharacteristic
15C2×Dic3×Dic5C2211yescharacteristic
16#91324—22no—
17#91324—22no—
18#91177—22no—
19Dic3⋊#170—22no—
20#91175—24no—
21#68997—51nomaximal, Hall
22C2×C4×Dic10—31no—
23C2×#4005—32no—
24#65758—32no—
25#64919—31no—
26#64919D311yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C22×C5×Dic3C2×C411yescharacteristic
31C22×C5×Dic3C2×C411yescharacteristic
32C22×C3×Dic5C2×C411yescharacteristic
33C22×C3×Dic5C2311yescharacteristic
34C2×#1204—22no—
35C2×#1204—22no—
36C2×#1204D412yes—
37C2×#1204Q812yes—
38#6762—22no—
39#6762—22no—
40C2×C3⋊#170—22no—
41C3×#704—22no—
42C3×#704—22no—
43C2×C3×#170—22no—
44#6712—22no—
45C4×C5×Dic3—21no—
46C4×C5×Dic3—21no—
47C3×#683—22no—
48Dic3⋊Dic5—22no—
49Dic3×Dic5—21no—
50Dic3×Dic5—21no—
51Dic3×Dic5D412yes—
52Dic3×Dic5D412yes—
53C2×#887—51no—
54C2×#824—52no—
55#5118—52no—
56C3×#343—51no—
57#4530—51no—
58C22×Dic10—31no—
59C2×#704—32no—
60C2×#704C2×D312yes—
61C2×C42×C5—31no—
62C2×C4⋊Dic5—31no—
63C2×#683—31no—
64C2×#683C2×D311yescharacteristic
65C2×C4×Dic5—31no—
66C2×C4×Dic5—31no—
67C4×Dic10—62no—
68C4×Dic10—62no—
69#4005—64no—
70#4004—62no—
71C4⋊#170—62no—
72#1801—151noSylow
73C23×C3×C5C22×C411yescharacteristic
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—41no—
76C2×Dic15—21no—
77C2×Dic15—21no—
78C2×Dic15—41no—
79C2×Dic15C22⋊C412yes—
80C2×Dic15C4⋊C412yes—
81C2×C5×Dic3—21no—
82C2×C5×Dic3—21no—
83C2×C5×Dic3—22no—
84C2×C5×Dic3C22⋊C411yescharacteristic
85C2×C5×Dic3C22⋊C411yescharacteristic
86C2×C5×Dic3C4⋊C412yes—
87C2×C3×Dic5—21no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5C2×D411yescharacteristic
90C2×C3×Dic5C2×D412yes—
91C2×C3×Dic5C2×Q811yescharacteristic
92C2×C3×Dic5#4112yes—
93#1204—24no—
94#1204—24no—
95C3⋊#170—42no—
96C3×#170—42no—
97C22×Dic6—51no—
98C2×C3×M16—52no—
99C2×C3×C4⋊C4—51no—
100C2×Dic3⋊C4—51no—
101C2×Dic3⋊C4—51no—
102C2×C4×Dic3—51no—
103C2×C4×Dic3—51no—
104C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
105C2×#208—52no—
106#887—102no—
107#887—102no—
108#824—104no—
109Dic3⋊C8—102no—
110Dic3⋊C8—102no—
111C22×C4×C5—31no—
112C22×C4×C5—31no—
113C22×C4×C5C4×D311yescharacteristic
114C22×Dic5—31no—
115C22×Dic5—31no—
116C22×Dic5C4×D311yescharacteristic
117C22×Dic5C22×D311yescharacteristic
118C2×Dic10—32no—
119C2×Dic10—32no—
120C2×Dic10—62no—
121C2×Dic10—62no—
122#704—22no—
123#704—22no—
124#704—62no—
125#704—62no—
126C2×#170—22no—
127C2×#170—62no—
128C42×C5—61no—
129C42×C5—61no—
130C4⋊Dic5—62no—
131#683—22no—
132#683—62no—
133C4×Dic5—32no—
134C4×Dic5—32no—
135C4×Dic5—61no—
136C4×Dic5—61no—
137C2×C4×Q8—151no—
138#423—152no—
139C2×#101—152no—
140#343—51no—
141#343—151no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5C2×C22⋊C411yescharacteristic
145C22×C3×C5C2×C4⋊C411yescharacteristic
146C22×C3×C5#11711yescharacteristic
147C3×C4×C5—41no—
148Dic15—22no—
149Dic15—22no—
150C3×Dic5—41no—
151C3×Dic5#12112yes—
152C3×Dic5C22⋊Q812yes—
153C5×Dic3—22no—
154C5×Dic3—21no—
155C5×Dic3#10112yescomplemented
156C22×C3×C4—51no—
157C22×C3×C4—51no—
158C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
159C22×Dic3—51no—
160C22×Dic3—51no—
161C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
162C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
163C2×Dic6—52no—
164C2×Dic6—52no—
165C2×Dic6—102no—
166C2×Dic6—102no—
167C3×M16—102no—
168C3×M16—102no—
169C2×C3×C8—102no—
170C3×C4⋊C4—102no—
171Dic3⋊C4—102no—
172Dic3⋊C4—102no—
173C4×Dic3—21no—
174C4×Dic3—21no—
175C4×Dic3—52no—
176C4×Dic3—52no—
177C4×Dic3—101no—
178C4×Dic3—101no—
179#208—102no—
180#208—102no—
181C2×C3⋊C8—102no—
182C23×C5C2×C4×D311yescharacteristic
183C2×C4×C5—21no—
184C2×C4×C5—31no—
185C2×C4×C5—31no—
186C2×C4×C5—32no—
187C2×C4×C5—41no—
188C2×C4×C5—62no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×Dic5—21no—
192C2×Dic5—32no—
193C2×Dic5—32no—
194C2×Dic5—41no—
195C2×Dic5—61no—
196C2×Dic5—61no—
197C2×Dic5—121no—
198C2×Dic5#23512yes—
199C2×Dic5D3×D411yescharacteristic
200C2×Dic5D3×D412yes—
201C2×Dic5D3×Q811yescharacteristic
202Dic10—64no—
203Dic10—64no—
204#170—42no—
205#170—122no—
206C22×Q8—151no—
207C2×M16—52no—
208C2×M16—152no—
209C4×Q8—302no—
210C4×Q8—302no—
211C2×C4⋊C4—51no—
212C2×C4⋊C4—151no—
213C2×C4⋊C4—151no—
214C2×C42—31no—
215C2×C42—151no—
216C2×C42—151no—
217C4⋊C8—302no—
218C4⋊C8—302no—
219#101—304no—
220C2×C3×C5—21no—
221C2×C3×C5—21no—
222C2×C3×C5#38011yescharacteristic
223C2×C3×C5C2×#10111yescharacteristic
224C2×C3×C5#41311yescharacteristic
225C23×C3C22×AGL(1,𝔽5)11yescharacteristic
226C2×C3×C4—21no—
227C2×C3×C4—41no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—52no—
231C2×C3×C4—52no—
232C2×C3×C4—101no—
233C2×C3×C4—201no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—22no—
237C2×Dic3—52no—
238C2×Dic3—52no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241C2×Dic3—201no—
242C2×Dic3C4⋊AGL(1,𝔽5)12yes—
243C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
244C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
245Dic6—104no—
246Dic6—104no—
247C3×C8—202no—
248C3⋊C8—202no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5#87211yescharacteristic
252C22×C5D3×C22⋊C411yescharacteristic
253C22×C5D3×C4⋊C411yescharacteristic
254C4×C5—32no—
255C4×C5—41no—
256C4×C5—62no—
257C4×C5—61no—
258Dic5—41no—
259Dic5—62no—
260Dic5—62no—
261Dic5#88412yes—
262Dic5#89612yes—
263C2×Q8—152no—
264C2×Q8—152no—
265C2×Q8—302no—
266C2×Q8—302no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—51no—
270C22×C4—51no—
271C22×C4—151no—
272C22×C4—151no—
273C22×C4D3×AGL(1,𝔽5)11yescharacteristic
274M16—102no—
275M16—102no—
276M16—302no—
277M16—302no—
278C2×C8—102no—
279C2×C8—302no—
280C4⋊C4—102no—
281C4⋊C4—302no—
282C4⋊C4—302no—
283C42—61no—
284C42—61no—
285C42—152no—
286C42—152no—
287C42—301no—
288C42—301no—
289C3×C5#180111yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
293C22×C3#413011yescharacteristic
294C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
295C3×C4—41no—
296C3×C4—52no—
297C3×C4—52no—
298C3×C4—201no—
299Dic3—21no—
300Dic3—22no—
301Dic3—102no—
302Dic3—102no—
303Dic3#400512yescomplemented
304C2×C5—21no—
305C2×C5—21no—
306C2×C5#466711yescharacteristic
307C2×C5#474511yescharacteristic
308C2×C5D3×#10111yescharacteristic
309C23C2×D3×AGL(1,𝔽5)11yescharacteristic
310Q8—304no—
311Q8—304no—
312C2×C4—21no—
313C2×C4—31no—
314C2×C4—32no—
315C2×C4—31no—
316C2×C4—41no—
317C2×C4—52no—
318C2×C4—51no—
319C2×C4—51no—
320C2×C4—52no—
321C2×C4—62no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—101no—
325C2×C4—152no—
326C2×C4—152no—
327C2×C4—201no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—601no—
331C8—202no—
332C8—602no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3C2×#400511yescharacteristic
336C2×C3#6576111yescharacteristic
337C2×C3#6576511yescharacteristic
338C5#6899711yescharacteristic, complemented, Sylow
339C22—21no—
340C22—21no—
341C22#9190911yescharacteristic
342C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
343C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
344C4—32no—
345C4—41no—
346C4—52no—
347C4—52no—
348C4—62no—
349C4—61no—
350C4—201no—
351C4—302no—
352C4—302no—
353C3#1060419411yescharacteristic, complemented, Sylow
354C2—21no—
355C2—21no—
356C2#1175185411yescharacteristic
357C2D3×#400511yescharacteristic
358C2#1175204911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1801
LCSG ▷ C23×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
155. C5×Dic3#101semidirect
289. C3×C5#1801semidirect
303. Dic3#4005semidirect
338. C5#68997semidirect
353. C3#10604194semidirect

Maximal subgroups

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

subgroupindex
C2×#913242
#117520122
C2×#911752
#117467902
C3×#649192
#106041943
#689975