Finite Group Databasebeta

← #14284730

Subgroups — #14284730

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#11754805C211yesmaximal, characteristic
2#11751796C212yesmaximal, complemented
3#11746796C211yesmaximal, characteristic, complemented
4C3×#64925C211yesmaximal, characteristic, complemented
5#11746511C212yesmaximal, complemented
6#10605004—31nomaximal, Hall
7C2×C5×#237C411yescharacteristic
8C2×#6765C411yescharacteristic
9#91825C411yescharacteristic
10C3×#4086C2211yescharacteristic
11#91565—22no—
12Dic3×C22⋊D5—22no—
13C4×D3×Dic5C2211yescharacteristic
14#91376C2211yescharacteristic
15#91368C411yescharacteristic
16#91233C2212yes—
17C3×#4004C2212yes—
18(C2×D3)⋊#170—22no—
19Dic3×#170—22no—
20#68382—51nomaximal, Hall
21#66166—31no—
22#65754—32no—
23#64931—32no—
24#64925—31no—
25#64925D311yescharacteristic, complemented
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C2×C5×#67—21no—
29C22×C5×Dic3—21no—
30C5×#237—42no—
31C2×C4×C5×D3C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×C22⋊D5—22no—
34C2×C3×D20C2×C411yescharacteristic
35C2×#1201—21no—
36C2×D3×Dic5D412yes—
37C2×D5×Dic3—21no—
38#6765—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41#6719—22no—
42C4×Dic15C2×C411yescharacteristic
43C3×C4×Dic5C2311yescharacteristic
44#6668—22no—
45#6665—22no—
46Dic3×Dic5D412yes—
47#5716—51no—
48#4833—52no—
49C3×#331—51no—
50#4544—51no—
51#4481—52no—
52C2×C5×#41—31no—
53C2×#709—31no—
54#4093—31no—
55#4090—31no—
56#4086C2×D311yescharacteristic
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
66C23×C3×C5—21no—
67C22×C5×D3C22⋊C411yescharacteristic
68C22×C3×D5—21no—
69C3×C5×D4—41no—
70C2×C3×C4×C5C22×C411yescharacteristic
71C2×Dic15—21no—
72C2×Dic15C22⋊C412yes—
73Dic30—41no—
74C5×#67—42no—
75C2×C5×Dic3—21no—
76C2×C5×Dic3—42no—
77C2×C5×Dic3C22⋊C411yescharacteristic
78C4×C5×D3—22no—
79C5×Dic6—41no—
80C3×C22⋊D5—42no—
81C3×C22⋊D5—42no—
82C2×C3×Dic5C2×D412yes—
83C3×D20—41no—
84#1201—42no—
85D3×Dic5—22no—
86D3×Dic5—22no—
87D5×Dic3—42no—
88C3⋊#170—42no—
89C3×#170—42no—
90C2×#237—51no—
91C2×#237AGL(1,𝔽5)11yescharacteristic
92C3×#127—51no—
93#938—102no—
94#936—51no—
95#936—51no—
96D4×Dic3—102no—
97C42×D3—51no—
98#869—51no—
99C3×C4⋊C8—52no—
100(C2×D3)⋊C8—102no—
101C8×Dic3—102no—
102C4⋊(C3⋊C8)—52no—
103C5×#41—122no—
104C2×C5×Q8—31no—
105C2×C5×D4—61no—
106C2×C5×D4C4×D311yescharacteristic
107C22×C4×C5—31no—
108C22×C4×C5—61no—
109C2×C22⋊D5—22no—
110C2×C22⋊D5—61no—
111C22×Dic5—32no—
112#709—122no—
113C2×D20C4×D311yescharacteristic
114C2×C4×D5—61no—
115C2×Dic10—31no—
116C2×#170—22no—
117C2×#170—62no—
118C22⋊Dic5—62no—
119#685—62no—
120#683—62no—
121C4×Dic5—31no—
122C4×Dic5—32no—
123C4×Dic5C22×D311yescharacteristic
124#532—151no—
125#431—152no—
126#333—152no—
127#331—51no—
128#331—151no—
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5C2×C22⋊C411yescharacteristic
132C2×C5×D3—21no—
133C2×C5×D3—22no—
134C2×C3×D5—41no—
135C2×C3×D5—42no—
136C3×C4×C5—21no—
137Dic15—22no—
138Dic15—41no—
139C3×Dic5#13512yes—
140C3×Dic5#13512yes—
141C5×Dic3—41no—
142C5×Dic3#10012yes—
143C2×C3×D4—51no—
144C2×C3×D4—102no—
145C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
146C2×#67—21no—
147C2×#67—101no—
148C22×Dic3—21no—
149C22×Dic3—101no—
150#237—42no—
151#237—202no—
152C2×C4×D3—52no—
153C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
154C2×Dic6—51no—
155C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
156C2×C3×C8—102no—
157C3×C42—51no—
158#217—102no—
159#217—102no—
160C4⋊Dic3—102no—
161C4×Dic3—51no—
162C4×Dic3—52no—
163C2×C3⋊C8—102no—
164C23×C5—21no—
165C23×C5—31no—
166C22×D5—21no—
167C5×Q8—121no—
168C5×D4—41no—
169C5×D4—122no—
170C2×C4×C5—31no—
171C2×C4×C5—62no—
172C2×C4×C5—61no—
173C2×C4×C5—122no—
174C2×C4×C5C2×C4×D311yescharacteristic
175C22⋊D5—42no—
176C22⋊D5—42no—
177C22⋊D5—122no—
178C2×Dic5—32no—
179C2×Dic5—62no—
180C2×Dic5—62no—
181C2×Dic5—61no—
182C2×Dic5D3×D412yes—
183D20—41no—
184C4×D5—122no—
185Dic10—121no—
186#170—42no—
187#170—122no—
188C2×#41—31no—
189C2×#41—151no—
190C4⋊Q8—151no—
191#127—51no—
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×C5—81no—
202C2×C3×C5C2×#10011yescharacteristic
203C2×C3×C5#41612yes—
204C3×D5—81no—
205C5×D3—41no—
206C23×C3—21no—
207C23×C3—101no—
208C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
209C3×D4—41no—
210C3×D4—201no—
211C3×D4—202no—
212C3×D4—202no—
213C2×C3×C4—52no—
214C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
215#67—42no—
216#67—202no—
217C2×Dic3—21no—
218C2×Dic3—42no—
219C2×Dic3—52no—
220C2×Dic3—101no—
221C2×Dic3—202no—
222C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
223C4×D3—22no—
224C4×D3—102no—
225C4×D3—102no—
226Dic6—41no—
227Dic6—201no—
228C3×C8—202no—
229C3⋊C8—202no—
230C22×C5—41no—
231C22×C5—42no—
232C22×C5—61no—
233C22×C5—62no—
234C22×C5D3×C22⋊C411yescharacteristic
235C2×D5—41no—
236C2×D5—42no—
237C4×C5—21no—
238C4×C5—32no—
239C4×C5—121no—
240Dic5—62no—
241Dic5—121no—
242Dic5#91212yes—
243Dic5#91612yes—
244#41—122no—
245#41—602no—
246C2×Q8—31no—
247C2×Q8—151no—
248C2×D4—51no—
249C2×D4—61no—
250C2×D4—102no—
251C2×D4—301no—
252C2×D4D3×AGL(1,𝔽5)11yescharacteristic
253C22×C4—31no—
254C22×C4—61no—
255C22×C4—152no—
256C22×C4—301no—
257C2×C8—102no—
258C2×C8—302no—
259C4⋊C4—302no—
260C22⋊C4—302no—
261C22⋊C4—302no—
262C42—51no—
263C42—152no—
264C42—151no—
265C3×C5#154311yescharacteristic, complemented, Hall
266C22×C3—42no—
267C22×C3—41no—
268C22×C3—202no—
269C22×C3—201no—
270C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
271C2×D3—22no—
272C2×D3—21no—
273C3×C4—21no—
274C3×C4—52no—
275C3×C4—52no—
276Dic3—41no—
277Dic3—102no—
278Dic3—201no—
279Dic3#401312yes—
280C2×C5—81no—
281C2×C5—121no—
282C2×C5D3×#10011yescharacteristic
283C2×C5#477212yes—
284D5—81no—
285C23—21no—
286C23—31no—
287C23—101no—
288Q8—121no—
289Q8—601no—
290D4—41no—
291D4—122no—
292D4—201no—
293D4—202no—
294D4—202no—
295D4—602no—
296C2×C4—31no—
297C2×C4—52no—
298C2×C4—62no—
299C2×C4—61no—
300C2×C4—122no—
301C2×C4—152no—
302C2×C4—302no—
303C2×C4—302no—
304C2×C4—301no—
305C2×C4—602no—
306C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
307C8—202no—
308C8—602no—
309C2×C3—81no—
310C2×C3—401no—
311C2×C3#6579412yes—
312C2×C3C2×#401311yescharacteristic
313D3—41no—
314C5#6838211yescharacteristic, complemented, Sylow
315C22—42no—
316C22—41no—
317C22—62no—
318C22—61no—
319C22—202no—
320C22—201no—
321C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
322C4—21no—
323C4—32no—
324C4—52no—
325C4—52no—
326C4—121no—
327C4—302no—
328C4—601no—
329C3#1060500411yescharacteristic, complemented, Sylow
330C2—81no—
331C2—121no—
332C2—401no—
333C2#1175194712yes—
334C2D3×#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#11754805C2
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1543
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. #11751796C2semidirect
3. #11746796C2semidirect
4. C3×#64925C2semidirect
5. #11746511C2semidirect
25. #64925D3semidirect
265. C3×C5#1543semidirect
314. C5#68382semidirect
329. C3#10605004semidirect

Maximal subgroups

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

subgroupindex
#117548052
#117517962
#117467962
C3×#649252
#117465112
#106050043
#683825