Finite Group Databasebeta

← #14284474

Subgroups — #14284474

Order 1920.

476 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#11754814C211yesmaximal, characteristic
2#11751805C212yesmaximal, complemented
3#11746792C211yesmaximal, characteristic, complemented
4C3×#64921C211yesmaximal, characteristic, complemented
5#11746505C212yesmaximal, complemented
6#10604995—31nomaximal, Hall
7C2×C5×#237C411yescharacteristic
8C2×#6769C411yescharacteristic
9#91829C411yescharacteristic
10C3×#4082C2211yescharacteristic
11#91558—22no—
12#91556—22no—
13C4×D3×Dic5C2211yescharacteristic
14#91385C411yescharacteristic
15#91375C2211yescharacteristic
16#91231C2212yes—
17C3×#4002C2212yes—
18Dic3⋊#170—22no—
19(C2×D3)⋊#170—22no—
20#68349—51nomaximal, Hall
21#66166—31no—
22#65759—32no—
23#64927—32no—
24#64921—31no—
25#64921D311yescharacteristic, complemented
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×#1220—22no—
28C2×D60C2×C411yescharacteristic
29C2×C5×#67—21no—
30C22×C5×Dic3—21no—
31C5×#237—42no—
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C2×C3×Dic10C2×C411yescharacteristic
35C2×#1203—21no—
36C2×#1200—21no—
37C2×D3×Dic5D412yes—
38#6769—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41C4×Dic15C2×C411yescharacteristic
42C3×C22⋊Dic5—22no—
43C3×C4×Dic5C2311yescharacteristic
44#6669—22no—
45#6667—22no—
46Dic3×Dic5D412yes—
47#5668—51no—
48#4705—52no—
49C3×#329—51no—
50#4540—51no—
51#4464—52no—
52C2×C5×#41—31no—
53C2×#709—31no—
54#4093—31no—
55#4090—31no—
56#4086—31no—
57#4085—62no—
58#4082C2×D311yescharacteristic
59C4×C22⋊D5—62no—
60C2×C4×Dic5—31no—
61C22⋊#170—62no—
62#4002—32no—
63#4002C2×D312yes—
64C4⋊#170—62no—
65#1536—151noSylow
66C23×C3×C5—21no—
67C22×D15—21no—
68C22×C5×D3C22⋊C411yescharacteristic
69C3×C5×D4—41no—
70C2×C3×C4×C5C22×C411yescharacteristic
71#1220—44no—
72C2×Dic15C22⋊C412yes—
73D60—41no—
74C5×#67—42no—
75C2×C5×Dic3—21no—
76C2×C5×Dic3—42no—
77C2×C5×Dic3C22⋊C411yescharacteristic
78C4×C5×D3—22no—
79C5×Dic6—41no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5C2×D412yes—
82C3×Dic10—41no—
83#1203—42no—
84#1200—42no—
85D3×Dic5—42no—
86C3⋊#170—42no—
87C3×#170—42no—
88C2×#239—51no—
89C2×#237AGL(1,𝔽5)11yescharacteristic
90C3×#124—51no—
91#944—51no—
92#940—51no—
93#884—102no—
94#67⋊C4—102no—
95#875—51no—
96C42×D3—51no—
97C3×#97—52no—
98(C2×D3)⋊C8—102no—
99Dic3⋊C8—102no—
100#803—52no—
101C5×#41—122no—
102C2×C5×Q8—31no—
103C2×C5×D4—61no—
104C2×C5×D4C4×D311yescharacteristic
105C22×C4×C5—31no—
106C22×C4×C5—61no—
107C2×C22⋊D5—61no—
108C2×C22⋊D5—62no—
109C22×Dic5—32no—
110#709—122no—
111C2×D20—31no—
112C2×C4×D5—61no—
113C2×Dic10C4×D311yescharacteristic
114C2×#170—22no—
115C2×#170—62no—
116C22⋊Dic5—22no—
117#685—62no—
118#683—62no—
119C4×Dic5—31no—
120C4×Dic5—32no—
121C4×Dic5C22×D311yescharacteristic
122#532—151no—
123#432—152no—
124#329—51no—
125#329—152no—
126#329—151no—
127C22×C3×C5—41no—
128C22×C3×C5—42no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×D15—41no—
131C2×D15—42no—
132C2×C5×D3—21no—
133C2×C5×D3—22no—
134C3×C4×C5—21no—
135Dic15—22no—
136C3×Dic5—22no—
137C3×Dic5—41no—
138C5×Dic3—41no—
139C5×Dic3#10012yes—
140C2×C3×Q8—51no—
141C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
142C2×#67—21no—
143C2×#67—102no—
144C22×Dic3—21no—
145#239—202no—
146#237—42no—
147C2×D12—51no—
148C2×D12—101no—
149C2×C4×D3—52no—
150C2×C4×D3—101no—
151C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
152C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
153C2×C3×C8—102no—
154C3×C22⋊C4—102no—
155C3×C42—51no—
156(C2×D3)⋊C4—102no—
157Dic3⋊C4—102no—
158C4×Dic3—51no—
159C4×Dic3—52no—
160C2×C3⋊C8—102no—
161C23×C5—21no—
162C23×C5—31no—
163C22×D5—61no—
164C5×Q8—121no—
165C5×D4—41no—
166C5×D4—122no—
167C2×C4×C5—31no—
168C2×C4×C5—62no—
169C2×C4×C5—61no—
170C2×C4×C5—122no—
171C2×C4×C5C2×C4×D311yescharacteristic
172C22⋊D5—122no—
173C22⋊D5—124no—
174C2×Dic5—21no—
175C2×Dic5—32no—
176C2×Dic5—122no—
177C2×Dic5D3×D412yes—
178D20—121no—
179C4×D5—122no—
180Dic10—41no—
181#170—42no—
182#170—122no—
183C2×#41—31no—
184C2×#41—151no—
185C4⋊Q8—151no—
186#127—151no—
187#124—51no—
188#124—151no—
189#121—302no—
190C4×D4—302no—
191C2×C42—151no—
192C4⋊C8—302no—
193C22⋊C8—302no—
194#97—52no—
195#97—152no—
196C2×C3×C5—81no—
197C2×C3×C5C2×#10011yescharacteristic
198C2×C3×C5#42112yes—
199D15—81no—
200C5×D3—41no—
201C23×C3—21no—
202C22×D3—101no—
203C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
204C3×Q8—201no—
205C3×D4—41no—
206C2×C3×C4—52no—
207C2×C3×C4—101no—
208C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
209#67—42no—
210#67—204no—
211C2×Dic3—21no—
212C2×Dic3—42no—
213C2×Dic3—52no—
214C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
215D12—201no—
216D12—202no—
217C4×D3—22no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—41no—
221C3×C8—202no—
222C3⋊C8—202no—
223C22×C5—41no—
224C22×C5—42no—
225C22×C5—61no—
226C22×C5—62no—
227C22×C5D3×C22⋊C411yescharacteristic
228C2×D5—121no—
229C2×D5—122no—
230C4×C5—21no—
231C4×C5—32no—
232C4×C5—121no—
233Dic5—22no—
234Dic5—41no—
235Dic5—62no—
236#41—122no—
237#41—602no—
238C2×Q8—31no—
239C2×Q8—51no—
240C2×D4—61no—
241C2×D4—151no—
242C2×D4—301no—
243C2×D4—302no—
244C2×D4D3×AGL(1,𝔽5)11yescharacteristic
245C22×C4—31no—
246C22×C4—61no—
247C22×C4—152no—
248C22×C4—301no—
249C2×C8—102no—
250C2×C8—302no—
251C4⋊C4—302no—
252C22⋊C4—102no—
253C22⋊C4—302no—
254C42—51no—
255C42—152no—
256C42—151no—
257C3×C5#153611yescharacteristic, complemented, Hall
258C22×C3—42no—
259C22×C3—41no—
260C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
261C2×D3—22no—
262C2×D3—21no—
263C2×D3—202no—
264C2×D3—201no—
265C3×C4—21no—
266C3×C4—102no—
267C3×C4—201no—
268Dic3—41no—
269Dic3—102no—
270Dic3#401312yes—
271C2×C5—81no—
272C2×C5—121no—
273C2×C5D3×#10011yescharacteristic
274C2×C5#482112yes—
275D5—241no—
276C23—21no—
277C23—31no—
278C23—301no—
279Q8—121no—
280Q8—201no—
281D4—41no—
282D4—122no—
283D4—601no—
284D4—602no—
285D4—604no—
286C2×C4—31no—
287C2×C4—52no—
288C2×C4—62no—
289C2×C4—61no—
290C2×C4—101no—
291C2×C4—122no—
292C2×C4—152no—
293C2×C4—602no—
294C2×C4—602no—
295C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
296C8—202no—
297C8—602no—
298C2×C3—81no—
299C2×C3#6579512yes—
300C2×C3C2×#401311yescharacteristic
301D3—41no—
302D3—401no—
303C5#6834911yescharacteristic, complemented, Sylow
304C22—42no—
305C22—41no—
306C22—62no—
307C22—61no—
308C22—602no—
309C22—601no—
310C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
311C4—21no—
312C4—32no—
313C4—102no—
314C4—121no—
315C4—201no—
316C4—302no—
317C3#1060499511yescharacteristic, complemented, Sylow
318C2—81no—
319C2—121no—
320C2—1201no—
321C2#1175194912yes—
322C2D3×#401311yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11754814C2
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1536
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751805C2semidirect
3. #11746792C2semidirect
4. C3×#64921C2semidirect
5. #11746505C2semidirect
25. #64921D3semidirect
257. C3×C5#1536semidirect
303. C5#68349semidirect
317. C3#10604995semidirect

Maximal subgroups

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

subgroupindex
#117548142
#117518052
#117467922
C3×#649212
#117465052
#106049953
#683495