Finite Group Databasebeta

← #14284475

Subgroups — #14284475

Order 1920.

476 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 78 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#11754828C211yesmaximal, characteristic
2#11751828C212yesmaximal, complemented
3#11746792C211yesmaximal, characteristic, complemented
4C3×#64921C211yesmaximal, characteristic, complemented
5#11746504C212yesmaximal, complemented
6#10604599—31nomaximal, Hall
7C2×#6819C411yescharacteristic
8C2×#6768C411yescharacteristic
9C5×#940C411yescharacteristic
10C3×#4082C2211yescharacteristic
11#67⋊Dic5—22no—
12#91557—22no—
13C4×#1200C2211yescharacteristic
14#91389C411yescharacteristic
15#91373C2211yescharacteristic
16#91231C2212yes—
17C3×#4002C2212yes—
18#91177—22no—
19#91171—22no—
20#68349—51nomaximal, Hall
21#66050—31no—
22#65684—32no—
23#64921—31no—
24#64921—32no—
25#64921D311yescharacteristic, complemented
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×#1220—21no—
28C22×Dic15—21no—
29#6819—42no—
30C2×C4×D15C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×#67—22no—
33C2×C5×D12C2×C411yescharacteristic
34C2×C3×Dic10C2×C411yescharacteristic
35C2×#1203—21no—
36C2×#1200D412yes—
37C2×D3×Dic5—21no—
38#6768—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41C4×C5×Dic3C2×C411yescharacteristic
42C3×C22⋊Dic5—22no—
43C3×C4×Dic5C2311yescharacteristic
44Dic3⋊Dic5—22no—
45(C2×D3)⋊Dic5—22no—
46Dic3×Dic5D412yes—
47#5668—51no—
48#4705—52no—
49C3×#329—51no—
50#4540—51no—
51#4464—52no—
52C2×#711—31no—
53C2×#711—31no—
54C5×#127—31no—
55#4084—62no—
56#4082—31no—
57#4082C2×D311yescharacteristic
58D4×Dic5—62no—
59C42×D5—31no—
60#4015—31no—
61#4004—62no—
62#4003—62no—
63#4002—32no—
64#4002C2×D312yes—
65#1536—151noSylow
66C23×C3×C5—21no—
67C22×D15C22⋊C411yescharacteristic
68C22×C5×D3—21no—
69C3×C5×D4—41no—
70C2×C3×C4×C5C22×C411yescharacteristic
71#1220—42no—
72C2×Dic15—21no—
73C2×Dic15—42no—
74C2×Dic15C22⋊C411yescharacteristic
75C4×D15—22no—
76Dic30—41no—
77C5×#67—44no—
78C2×C5×Dic3C22⋊C412yes—
79C5×D12—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×#237—51no—
90C3×#124—51no—
91#944—51no—
92#940AGL(1,𝔽5)11yescharacteristic
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—
101C2×C5×D4—31no—
102C2×C5×D4—62no—
103C2×C5×D4C4×D311yescharacteristic
104C2×C22⋊D5—61no—
105C2×C22⋊D5—61no—
106C22×Dic5—61no—
107C22×Dic5—61no—
108#711—122no—
109#711—122no—
110C2×C4×D5—31no—
111C2×C4×D5—32no—
112C2×Dic10—31no—
113C2×Dic10C4×D311yescharacteristic
114C2×#170—22no—
115C2×#170—62no—
116C42×C5—31no—
117C22⋊Dic5—22no—
118C22⋊Dic5—62no—
119C4⋊Dic5—62no—
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—21no—
131C2×D15—22no—
132C2×C5×D3—41no—
133C2×C5×D3—42no—
134C3×C4×C5—21no—
135Dic15—41no—
136Dic15#10012yes—
137C3×Dic5—22no—
138C3×Dic5—41no—
139C5×Dic3—22no—
140C2×C3×Q8—51no—
141C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
142C2×#67—22no—
143C2×#67—101no—
144C22×Dic3—101no—
145#239—202no—
146#237—202no—
147C2×D12—101no—
148C2×D12C2×AGL(1,𝔽5)11yescharacteristic
149C2×C4×D3—51no—
150C2×C4×D3—52no—
151C2×C4×D3—101no—
152C2×Dic6—51no—
153C2×C3×C8—102no—
154C3×C22⋊C4—102no—
155C3×C42—51no—
156(C2×D3)⋊C4—102no—
157Dic3⋊C4—102no—
158C4×Dic3—52no—
159C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
160C2×C3⋊C8—102no—
161C23×C5—21no—
162C23×C5—61no—
163C22×D5—31no—
164C5×D4—41no—
165C5×D4—121no—
166C5×D4—124no—
167C2×C4×C5—32no—
168C2×C4×C5C2×C4×D311yescharacteristic
169C22⋊D5—122no—
170C22⋊D5—122no—
171C2×Dic5—21no—
172C2×Dic5—31no—
173C2×Dic5—61no—
174C2×Dic5—122no—
175C2×Dic5—122no—
176C2×Dic5D3×D412yes—
177C4×D5—62no—
178C4×D5—122no—
179Dic10—41no—
180Dic10—121no—
181#170—42no—
182#170—122no—
183C2×#41—151no—
184C2×#41—151no—
185C4⋊Q8—151no—
186#127—31no—
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—41no—
200C5×D3—81no—
201C23×C3—21no—
202C22×D3—21no—
203C22×D3—51no—
204C3×Q8—201no—
205C3×D4—41no—
206C2×C3×C4—52no—
207C2×C3×C4—101no—
208C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
209#67—44no—
210#67—202no—
211C2×Dic3—51no—
212C2×Dic3—101no—
213C2×Dic3—202no—
214C2×Dic3C22⋊AGL(1,𝔽5)12yes—
215D12—41no—
216D12—202no—
217C4×D3—102no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—201no—
221C3×C8—202no—
222C3⋊C8—202no—
223C22×C5—41no—
224C22×C5—42no—
225C22×C5—121no—
226C22×C5—122no—
227C22×C5D3×C22⋊C411yescharacteristic
228C2×D5—61no—
229C2×D5—62no—
230C4×C5—21no—
231C4×C5—62no—
232Dic5—22no—
233Dic5—32no—
234Dic5—41no—
235Dic5—121no—
236#41—602no—
237#41—602no—
238C2×Q8—51no—
239C2×Q8—151no—
240C2×D4—31no—
241C2×D4—62no—
242C2×D4—301no—
243C2×D4—301no—
244C2×D4D3×AGL(1,𝔽5)11yescharacteristic
245C22×C4—152no—
246C22×C4—151no—
247C22×C4—301no—
248C22×C4—301no—
249C2×C8—102no—
250C2×C8—302no—
251C4⋊C4—302no—
252C22⋊C4—102no—
253C22⋊C4—302no—
254C42—31no—
255C42—51no—
256C42—152no—
257C3×C5#153611yescharacteristic, complemented, Hall
258C22×C3—42no—
259C22×C3—41no—
260C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
261C2×D3—42no—
262C2×D3—41no—
263C2×D3—102no—
264C2×D3—101no—
265C3×C4—21no—
266C3×C4—102no—
267C3×C4—201no—
268Dic3—22no—
269Dic3—52no—
270Dic3—201no—
271C2×C5—81no—
272C2×C5—241no—
273C2×C5D3×#10011yescharacteristic
274C2×C5#482112yes—
275D5—121no—
276C23—21no—
277C23—61no—
278C23—151no—
279Q8—201no—
280Q8—601no—
281D4—41no—
282D4—121no—
283D4—124no—
284D4—602no—
285D4—602no—
286C2×C4—32no—
287C2×C4—52no—
288C2×C4—101no—
289C2×C4—151no—
290C2×C4—302no—
291C2×C4—301no—
292C2×C4—602no—
293C2×C4—602no—
294C2×C4—602no—
295C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
296C8—202no—
297C8—602no—
298C2×C3—81no—
299C2×C3#6576912yes—
300C2×C3D5⋊#10011yescharacteristic
301D3—81no—
302D3—201no—
303C5#6834911yescharacteristic, complemented, Sylow
304C22—42no—
305C22—41no—
306C22—122no—
307C22—121no—
308C22—302no—
309C22—301no—
310C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
311C4—21no—
312C4—62no—
313C4—102no—
314C4—152no—
315C4—201no—
316C4—601no—
317C3#1060459911yescharacteristic, complemented, Sylow
318C2—81no—
319C2—241no—
320C2—601no—
321C2#1175195012yes—
322C2#1175205011yescharacteristic
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#11754828C2
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. #11751828C2semidirect
3. #11746792C2semidirect
4. C3×#64921C2semidirect
5. #11746504C2semidirect
25. #64921D3semidirect
257. C3×C5#1536semidirect
303. C5#68349semidirect
317. C3#10604599semidirect

Maximal subgroups

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

subgroupindex
#117548282
#117518282
#117467922
C3×#649212
#117465042
#106045993
#683495