Finite Group Databasebeta

← #14284733

Subgroups — #14284733

Order 1920.

492 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 88 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#11755164C211yesmaximal, characteristic
2#11751796C212yesmaximal, complemented
3#11746802C211yesmaximal, characteristic, complemented
4C3×#64931C211yesmaximal, characteristic, complemented
5#11746508C212yesmaximal, complemented
6#10605004—31nomaximal, Hall
7C2×C5×#239C411yescharacteristic
8C2×#6769C411yescharacteristic
9#91836C411yescharacteristic
10C3×#4090C2211yescharacteristic
11#91451C2211yescharacteristic
12#91446—22no—
13#91416—22no—
14C4×D3×Dic5C2211yescharacteristic
15#91370C411yescharacteristic
16#91233C2212yes—
17C3×#4004C2212yes—
18(C2×D3)⋊#170—22no—
19Dic3×#170—22no—
20#68482—51nomaximal, Hall
21#66166—31no—
22#65754—32no—
23#64931—31no—
24#64931D311yescharacteristic, complemented
25#64925—32no—
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×D60C2×C411yescharacteristic
28C5×#239—42no—
29C2×C5×D12—21no—
30C2×C5×D12C2×C411yescharacteristic
31C2×C4×C5×D3—21no—
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C3×Dic10C2×C411yescharacteristic
34C2×#1203—21no—
35C2×#1203—22no—
36C2×#1200—21no—
37C2×D3×Dic5D412yes—
38#6769—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41#6714—22no—
42C4×Dic15C2×C411yescharacteristic
43C3×#683—22no—
44C3×C4×Dic5C2311yescharacteristic
45(C2×D3)⋊Dic5—22no—
46Dic3×Dic5D412yes—
47#5725—51no—
48#4833—52no—
49C3×#333—51no—
50#4546—51no—
51#4485—52no—
52C2×C5×#41—31no—
53C2×#709—31no—
54#4093—31no—
55#4090C2×D311yescharacteristic
56#4086—31no—
57#4085—62no—
58#4082—31no—
59C4×C22⋊D5—62no—
60C2×C4×Dic5—31no—
61C22⋊#170—62no—
62#4004—32no—
63#4004C2×D312yes—
64C4×#170—62no—
65#1543—151noSylow
66C22×D15—21no—
67C22×C5×D3—21no—
68C22×C5×D3C22⋊C411yescharacteristic
69C3×C5×Q8—41no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×Dic15C22⋊C412yes—
73D60—41no—
74C2×C5×Dic3C22⋊C411yescharacteristic
75C5×D12—41no—
76C5×D12—42no—
77C4×C5×D3—22no—
78C4×C5×D3—42no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5C2×D412yes—
81C3×Dic10—41no—
82#1203—42no—
83#1203—42no—
84#1203—42no—
85#1200—42no—
86D3×Dic5—22no—
87D3×Dic5—22no—
88C3⋊#170—42no—
89C3×#170—42no—
90C2×#239—51no—
91C2×#239AGL(1,𝔽5)11yescharacteristic
92C3×C4⋊Q8—51no—
93#947—51no—
94#947—51no—
95#895—102no—
96#893—102no—
97#874—51no—
98C42×D3—51no—
99C3×C4⋊C8—52no—
100(C2×D3)⋊C8—102no—
101C8×Dic3—102no—
102C4⋊(C3⋊C8)—52no—
103C5×#41—122no—
104C2×C5×Q8C4×D311yescharacteristic
105C2×C5×D4—31no—
106C2×C5×D4—61no—
107C22×C4×C5—31no—
108C22×C4×C5—61no—
109C2×C22⋊D5—61no—
110C2×C22⋊D5—62no—
111C22×Dic5—32no—
112#709—122no—
113C2×D20—31no—
114C2×C4×D5—61no—
115C2×Dic10C4×D311yescharacteristic
116C2×#170—22no—
117C2×#170—62no—
118C22⋊Dic5—62no—
119#685—62no—
120#683—22no—
121C4×Dic5—31no—
122C4×Dic5—32no—
123C4×Dic5C22×D311yescharacteristic
124#532—151no—
125#431—152no—
126#333—51no—
127#333—151no—
128#331—152no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×D15—41no—
131C2×D15—42no—
132C2×C5×D3—21no—
133C2×C5×D3—22no—
134C2×C5×D3—41no—
135C2×C5×D3—42no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138Dic15—22no—
139C3×Dic5—41no—
140C3×Dic5#13512yes—
141C3×Dic5#13512yes—
142C5×Dic3#10012yes—
143C2×C3×Q8—51no—
144C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
145#239—42no—
146#239—202no—
147C2×D12—21no—
148C2×D12—51no—
149C2×D12—102no—
150C2×D12—101no—
151C2×D12C2×AGL(1,𝔽5)11yescharacteristic
152C2×C4×D3—21no—
153C2×C4×D3—52no—
154C2×C4×D3—101no—
155C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
156C2×C3×C8—102no—
157C3×C4⋊C4—102no—
158C3×C42—51no—
159(C2×D3)⋊C4—102no—
160(C2×D3)⋊C4—102no—
161C4×Dic3—51no—
162C4×Dic3—52no—
163C2×C3⋊C8—102no—
164C23×C5—31no—
165C23×C5—61no—
166C22×D5—61no—
167C5×Q8—41no—
168C5×D4—121no—
169C5×D4—122no—
170C2×C4×C5—21no—
171C2×C4×C5—31no—
172C2×C4×C5—62no—
173C2×C4×C5—122no—
174C2×C4×C5C2×C4×D311yescharacteristic
175C22⋊D5—122no—
176C22⋊D5—122no—
177C22⋊D5—122no—
178C2×Dic5—21no—
179C2×Dic5—32no—
180C2×Dic5—62no—
181C2×Dic5—62no—
182C2×Dic5D3×D412yes—
183D20—121no—
184C4×D5—122no—
185Dic10—41no—
186#170—42no—
187#170—122no—
188C2×#41—31no—
189C2×#41—151no—
190C4⋊Q8—51no—
191#127—151no—
192#124—151no—
193#124—151no—
194#121—302no—
195C4×D4—302no—
196C2×C42—151no—
197C4⋊C8—52no—
198C4⋊C8—152no—
199C22⋊C8—302no—
200C4×C8—302no—
201C2×C3×C5C2×#10011yescharacteristic
202C2×C3×C5#41612yes—
203D15—81no—
204C5×D3—41no—
205C5×D3—81no—
206C22×D3—21no—
207C22×D3—101no—
208C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
209C3×Q8—41no—
210C3×Q8—201no—
211C2×C3×C4—21no—
212C2×C3×C4—52no—
213C2×C3×C4—101no—
214C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
215C2×Dic3—52no—
216C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
217D12—41no—
218D12—42no—
219D12—201no—
220D12—202no—
221D12—202no—
222D12—202no—
223C4×D3—22no—
224C4×D3—42no—
225C4×D3—102no—
226C4×D3—102no—
227C4×D3—202no—
228C3×C8—202no—
229C3⋊C8—202no—
230C22×C5—61no—
231C22×C5—62no—
232C22×C5—121no—
233C22×C5—122no—
234C22×C5D3×C22⋊C411yescharacteristic
235C2×D5—121no—
236C2×D5—122no—
237C4×C5—21no—
238C4×C5—32no—
239C4×C5—41no—
240Dic5—41no—
241Dic5—62no—
242Dic5#91612yes—
243Dic5#91912yes—
244#41—122no—
245#41—602no—
246C2×Q8—51no—
247C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
248C2×D4—31no—
249C2×D4—61no—
250C2×D4—151no—
251C2×D4—302no—
252C2×D4—301no—
253C22×C4—31no—
254C22×C4—61no—
255C22×C4—152no—
256C22×C4—301no—
257C2×C8—102no—
258C2×C8—302no—
259C4⋊C4—102no—
260C22⋊C4—302no—
261C22⋊C4—302no—
262C42—51no—
263C42—152no—
264C42—151no—
265C3×C5#154311yescharacteristic, complemented, Hall
266C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×D3—22no—
268C2×D3—21no—
269C2×D3—42no—
270C2×D3—41no—
271C2×D3—202no—
272C2×D3—201no—
273C3×C4—21no—
274C3×C4—41no—
275C3×C4—52no—
276C3×C4—52no—
277C3×C4—201no—
278Dic3—102no—
279Dic3#401312yes—
280C2×C5—121no—
281C2×C5—241no—
282C2×C5D3×#10011yescharacteristic
283C2×C5#480412yes—
284D5—241no—
285C23—31no—
286C23—61no—
287C23—301no—
288Q8—41no—
289Q8—201no—
290D4—121no—
291D4—122no—
292D4—601no—
293D4—602no—
294D4—602no—
295D4—602no—
296C2×C4—21no—
297C2×C4—31no—
298C2×C4—52no—
299C2×C4—62no—
300C2×C4—101no—
301C2×C4—122no—
302C2×C4—152no—
303C2×C4—302no—
304C2×C4—302no—
305C2×C4—602no—
306C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
307C8—202no—
308C8—602no—
309C2×C3#6579412yes—
310C2×C3C2×#401311yescharacteristic
311D3—41no—
312D3—81no—
313D3—401no—
314C5#6848211yescharacteristic, complemented, Sylow
315C22—62no—
316C22—61no—
317C22—122no—
318C22—121no—
319C22—602no—
320C22—601no—
321C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
322C4—21no—
323C4—32no—
324C4—41no—
325C4—52no—
326C4—52no—
327C4—201no—
328C4—302no—
329C3#1060500411yescharacteristic, complemented, Sylow
330C2—121no—
331C2—241no—
332C2—1201no—
333C2#1175197112yes—
334C2D3×#401311yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11755164C2
cosocleC3×C4×Dic5C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11751796C2semidirect
3. #11746802C2semidirect
4. C3×#64931C2semidirect
5. #11746508C2semidirect
24. #64931D3semidirect
265. C3×C5#1543semidirect
314. C5#68482semidirect
329. C3#10605004semidirect

Maximal subgroups

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

subgroupindex
#117551642
#117517962
#117468022
C3×#649312
#117465082
#106050043
#684825