Finite Group Databasebeta

← #14313415

Subgroups — #14313415

Order 1920.

516 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C3×#66166C211yesmaximal, characteristic
2#11752404C212yesmaximal, complemented
3#11746799C212yesmaximal, complemented
4#11746793C212yesmaximal, complemented
5#10604996—31nomaximal, Hall
6C2×C3×C5×#41C411yescharacteristic, complemented
7C2×C3×#709C2211yescharacteristic
8#91989—22no—
9C3×#4093C2211yescharacteristic
10C3×#4090C411yescharacteristic, complemented
11C3×#4086C2211yescharacteristic
12C3×#4085—22no—
13C3×#4082C411yescharacteristic, complemented
14C3×C4×C22⋊D5—22no—
15C2×C3×C4×Dic5C411yescharacteristic, complemented
16#91240—22no—
17#91228C2214yes—
18#71819—51nomaximal, Hall
19#66166D311yescharacteristic
20#65745—32no—
21#64928—32no—
22#64922—32no—
23C3×C5×#41—41no—
24C3×C5×#41—41no—
25C2×C3×C5×Q8C2×C411yescharacteristic
26C2×C3×C5×D4—21no—
27C2×C3×C5×D4C2×C411yescharacteristic
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C2×C3×C22⋊D5—22no—
31C2×C3×C22⋊D5D412yes—
32C22×C3×Dic5—21no—
33C3×#709—41no—
34C3×#709—41no—
35C2×C3×D20C2311yescharacteristic
36C2×C3×C4×D5D412yes—
37C2×C3×Dic10C2×C411yescharacteristic
38#6763—24no—
39C4⋊ΓL(1,𝔽16)—42no—
40C4×ΓL(1,𝔽16)—42no—
41C3×C22⋊Dic5—22no—
42C3×#685—22no—
43C3×#683—22no—
44C3×C4×Dic5—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×C4×Dic5C2×C411yescharacteristic
47C3×#532—51no—
48#5240—52no—
49#4545—52no—
50#4541—52no—
51C2×C5×#41Dic311yescharacteristic, complemented
52C2×#709C2×D311yescharacteristic
53#4130—62no—
54#4093C2×D311yescharacteristic
55#4090Dic311yescharacteristic, complemented
56#4086C2×D311yescharacteristic
57#4085—22no—
58#4082Dic311yescharacteristic, complemented
59C4×C22⋊D5—22no—
60C2×C4×Dic5Dic311yescharacteristic, complemented
61#4011—62no—
62#3999—34no—
63#2126—151noSylow
64C23×C3×C5—21no—
65C23×C3×C5C22⋊C411yescharacteristic
66C22×C3×D5C2×D412yes—
67C2×ΓL(1,𝔽16)—44no—
68C3×C5×Q8—41no—
69C3×C5×D4—41no—
70C3×C5×D4—42no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22×C411yescharacteristic
78C3×C22⋊D5—42no—
79C3×C22⋊D5—44no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5—42no—
83C2×C3×Dic5C22⋊C412yes—
84C3×D20—41no—
85C3×C4×D5—22no—
86C3×C4×D5—22no—
87C3×Dic10—41no—
88C2×C3×#41—51no—
89C2×C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
90C3×C4⋊Q8—51no—
91C3×#127—51no—
92C3×#124—51no—
93C3×#124—51no—
94C3×#121—102no—
95C3×C4×D4—102no—
96C2×C3×C42—51no—
97#926—102no—
98#834—54no—
99#834—102no—
100C5×#41—41no—
101C5×#41—41no—
102C2×C5×Q8C2×Dic311yescharacteristic
103C2×C5×D4—21no—
104C2×C5×D4C2×Dic311yescharacteristic
105C22×C4×C5—21no—
106C22×C4×C5C2×Dic311yescharacteristic
107C2×C22⋊D5—22no—
108C2×C22⋊D5#6712yes—
109C22×Dic5—21no—
110#709—41no—
111#709—41no—
112C2×D20C22×D311yescharacteristic
113C2×C4×D5#6712yes—
114C2×Dic10C2×Dic311yescharacteristic
115C22⋊AGL(1,𝔽5)—64no—
116C4⋊AGL(1,𝔽5)—122no—
117C4×AGL(1,𝔽5)—122no—
118C22⋊Dic5—22no—
119#685—22no—
120#683—22no—
121C4×Dic5—21no—
122C4×Dic5C2×Dic311yescharacteristic
123C4×Dic5C2×Dic311yescharacteristic
124#532—51no—
125#410—152no—
126#354—152no—
127#353—152no—
128C22×C3×C5—21no—
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×C3×D5—22no—
134C2×C3×D5—42no—
135ΓL(1,𝔽16)—84no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138C3×C4×C5#9911yescharacteristic
139C3×C4×C5#9911yescharacteristic
140C3×Dic5—22no—
141C3×Dic5—22no—
142C3×Dic5—41no—
143C3×#41—41no—
144C3×#41—41no—
145C3×#41—201no—
146C3×#41—201no—
147C2×C3×Q8—51no—
148C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
149C2×C3×D4—21no—
150C2×C3×D4—52no—
151C2×C3×D4—51no—
152C2×C3×D4—102no—
153C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—52no—
156C22×C3×C4—101no—
157C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
158C3×C4⋊C4—102no—
159C3×C22⋊C4—102no—
160C3×C22⋊C4—102no—
161C3×C42—51no—
162C3×C42—51no—
163C3×C42—101no—
164#217—104no—
165C4⋊Dic3—202no—
166C4×Dic3—202no—
167C23×C5—21no—
168C23×C5#21711yescharacteristic
169C22×D5C2×#6712yes—
170C2×AGL(1,𝔽5)—124no—
171C5×Q8—41no—
172C5×D4—41no—
173C5×D4—42no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5#21711yescharacteristic
180C2×C4×C5C22×Dic311yescharacteristic
181C22⋊D5—42no—
182C22⋊D5—44no—
183C2×Dic5—21no—
184C2×Dic5—21no—
185C2×Dic5—42no—
186C2×Dic5#21712yes—
187D20—41no—
188C4×D5—22no—
189C4×D5—22no—
190Dic10—41no—
191C2×#41—51no—
192C2×#41ΓL(1,𝔽16)11yescharacteristic, complemented
193C4⋊Q8—51no—
194#127—51no—
195#124—51no—
196#124—51no—
197#121—102no—
198C4×D4—102no—
199#117—302no—
200C2×C42—51no—
201#99—154no—
202#99—302no—
203C2×C3×C5—21no—
204C2×C3×C5—41no—
205C2×C3×C5—81no—
206C2×C3×C5C2×#9911yescharacteristic
207C3×D5—42no—
208C23×C3—21no—
209C23×C3—52no—
210C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
211C3×Q8—41no—
212C3×Q8—201no—
213C3×D4—41no—
214C3×D4—42no—
215C3×D4—201no—
216C3×D4—202no—
217C3×D4—204no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—52no—
224C2×C3×C4—101no—
225C2×C3×C4—102no—
226C2×C3×C4—102no—
227C2×C3×C4—101no—
228C2×C3×C4—202no—
229C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
230C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
231C2×Dic3—204no—
232C22×C5—21no—
233C22×C5—41no—
234C22×C5—42no—
235C22×C5—41no—
236C22×C5C2×#21711yescharacteristic
237C2×D5—22no—
238C2×D5—42no—
239AGL(1,𝔽5)—244no—
240C4×C5—21no—
241C4×C5—41no—
242C4×C5#83411yescharacteristic
243C4×C5#83411yescharacteristic
244Dic5—22no—
245Dic5—22no—
246Dic5—41no—
247#41—41no—
248#41—41no—
249#41—201no—
250#41—201no—
251C2×Q8—51no—
252C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
253C2×D4—21no—
254C2×D4—52no—
255C2×D4—51no—
256C2×D4—102no—
257C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
258C22×C4—21no—
259C22×C4—52no—
260C22×C4—101no—
261C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
262C4⋊C4—102no—
263C4⋊C4—602no—
264C22⋊C4—102no—
265C22⋊C4—102no—
266C22⋊C4—304no—
267C42—51no—
268C42—51no—
269C42—101no—
270C42—602no—
271C3×C5#212611yescharacteristic, complemented, Hall
272C22×C3—21no—
273C22×C3—41no—
274C22×C3—42no—
275C22×C3—41no—
276C22×C3—102no—
277C22×C3—202no—
278C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—102no—
282C3×C4—102no—
283C3×C4—201no—
284C3×C4#401111yescharacteristic
285C3×C4#401111yescharacteristic
286Dic3—404no—
287C2×C5—21no—
288C2×C5—41no—
289C2×C5—81no—
290C2×C5C2×#83411yescharacteristic
291D5—42no—
292C23—21no—
293C23—52no—
294C23#676311yescharacteristic
295Q8—41no—
296Q8—201no—
297D4—41no—
298D4—42no—
299D4—201no—
300D4—202no—
301D4—204no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—52no—
308C2×C4—101no—
309C2×C4—102no—
310C2×C4—102no—
311C2×C4—101no—
312C2×C4—202no—
313C2×C4—604no—
314C2×C4#676311yescharacteristic
315C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
316C2×C3—21no—
317C2×C3—41no—
318C2×C3—81no—
319C2×C3—202no—
320C2×C3C2×#401111yescharacteristic
321C5#7181911yescharacteristic, complemented, Sylow
322C22—21no—
323C22—41no—
324C22—42no—
325C22—41no—
326C22—102no—
327C22—202no—
328C22C2×#676311yescharacteristic
329C4—21no—
330C4—41no—
331C4—102no—
332C4—102no—
333C4—201no—
334C4—1204no—
335C4#9124011yescharacteristic
336C4#9124011yescharacteristic
337C3#1060499611yescharacteristic, complemented, Sylow
338C2—21no—
339C2—41no—
340C2—81no—
341C2—202no—
342C2C2×#9124011yescharacteristic
subgroupG/H
centerC4#91240
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC2×C3×C5×#41C4
socleC2×C3×C5C2×#99
prime radicalC3×#66166C2
cosocleC2×C3×D20C23
hypercenterC2×#41ΓL(1,𝔽16)
hypocenterC3×C5#2126
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11752404C2semidirect
3. #11746799C2semidirect
4. #11746793C2semidirect
6. C2×C3×C5×#41C4semidirect
10. C3×#4090C4semidirect
13. C3×#4082C4semidirect
15. C2×C3×C4×Dic5C4semidirect
51. C2×C5×#41Dic3semidirect
55. #4090Dic3semidirect
58. #4082Dic3semidirect
60. C2×C4×Dic5Dic3semidirect
89. C2×C3×#41AGL(1,𝔽5)semidirect
192. C2×#41ΓL(1,𝔽16)semidirect
271. C3×C5#2126semidirect
321. C5#71819semidirect
337. C3#10604996semidirect

Maximal subgroups

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

subgroupindex
C3×#661662
#117524042
#117467992
#117467932
#106049963
#718195