Finite Group Databasebeta

← #14285444

Subgroups — #14285444

Order 1920.

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

normal subgroups only

This group has 508 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#11751920C212yesmaximal, complemented
3#11746802C211yesmaximal, characteristic, complemented
4C3×#64931C211yesmaximal, characteristic, complemented
5#11746508C212yesmaximal, complemented
6#10605006—31nomaximal, Hall
7C2×C5×#239C411yescharacteristic
8C2×#6769C411yescharacteristic
9C2×#6739—22no—
10#91836C411yescharacteristic
11C3×#4090C2211yescharacteristic
12#91451C2211yescharacteristic
13#91446—22no—
14#91416—22no—
15C4×D3×Dic5C2211yescharacteristic
16#91370C411yescharacteristic
17#91233C2212yes—
18C3×#4004C2212yes—
19Dic3⋊#170—22no—
20#68489—51nomaximal, Hall
21#66166—31no—
22#65758—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#6739—44no—
42#6714—22no—
43C4×Dic15C2×C411yescharacteristic
44C3×#683—22no—
45C3×C4×Dic5C2311yescharacteristic
46(C2×D3)⋊Dic5—22no—
47Dic3×Dic5D412yes—
48#5725—51no—
49#4837—52no—
50C3×#333—51no—
51#4546—51no—
52#4485—52no—
53C2×C5×#41—31no—
54C2×#709—31no—
55C2×#704—62no—
56#4093—31no—
57#4090C2×D311yescharacteristic
58#4086—31no—
59#4085—62no—
60#4082—31no—
61C4×C22⋊D5—62no—
62C2×C4×Dic5—31no—
63#4004—32no—
64#4004C2×D312yes—
65C4⋊#170—62no—
66#1560—151noSylow
67C22×D15—21no—
68C22×C5×D3—21no—
69C22×C5×D3C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×Dic15C22⋊C412yes—
74D60—41no—
75C2×C5×Dic3C22⋊C411yescharacteristic
76C5×D12—41no—
77C5×D12—42no—
78C4×C5×D3—22no—
79C4×C5×D3—42no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5C2×D412yes—
82C3×Dic10—41no—
83#1203—42no—
84#1203—42no—
85#1203—42no—
86#1200—42no—
87D3×Dic5—22no—
88D3×Dic5—22no—
89C3⋊#170—42no—
90C3×#170—42no—
91C2×#239—51no—
92C2×#239AGL(1,𝔽5)11yescharacteristic
93C3×C4⋊Q8—51no—
94#947—51no—
95#947—51no—
96C2×ΓL(1,𝔽25)—102no—
97#895—102no—
98#893—102no—
99#874—51no—
100C42×D3—51no—
101C3×C4⋊C8—52no—
102Dic3⋊C8—102no—
103C4⋊(C3⋊C8)—52no—
104C5×#41—122no—
105C2×C5×Q8C4×D311yescharacteristic
106C2×C5×D4—31no—
107C2×C5×D4—61no—
108C22×C4×C5—31no—
109C22×C4×C5—61no—
110C2×C22⋊D5—61no—
111C2×C22⋊D5—62no—
112C22×Dic5—32no—
113#709—122no—
114C2×D20—31no—
115C2×C4×D5—61no—
116C2×Dic10C4×D311yescharacteristic
117#704—124no—
118C2×#170—22no—
119C2×#170—62no—
120C22⋊Dic5—62no—
121#685—62no—
122#683—22no—
123C4×Dic5—31no—
124C4×Dic5—32no—
125C4×Dic5C22×D311yescharacteristic
126#532—151no—
127#423—152no—
128#333—51no—
129#333—151no—
130#331—152no—
131C22×C3×C5C2×C22⋊C411yescharacteristic
132C2×D15—41no—
133C2×D15—42no—
134C2×C5×D3—21no—
135C2×C5×D3—22no—
136C2×C5×D3—41no—
137C2×C5×D3—42no—
138C3×C4×C5—21no—
139C3×C4×C5—41no—
140Dic15—22no—
141C3×Dic5—41no—
142C3×Dic5AGL(1,ℤ/8)12yes—
143C3×Dic5#13712yes—
144C5×Dic3#10012yes—
145C2×C3×Q8—51no—
146C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
147#239—42no—
148#239—202no—
149C2×D12—21no—
150C2×D12—51no—
151C2×D12—102no—
152C2×D12—101no—
153C2×D12C2×AGL(1,𝔽5)11yescharacteristic
154C2×C4×D3—21no—
155C2×C4×D3—52no—
156C2×C4×D3—101no—
157C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
158C2×C3×C8—102no—
159C3×C4⋊C4—102no—
160C3×C42—51no—
161(C2×D3)⋊C4—102no—
162(C2×D3)⋊C4—102no—
163C4×Dic3—51no—
164C4×Dic3—52no—
165C2×C3⋊C8—102no—
166ΓL(1,𝔽25)—204no—
167C23×C5—31no—
168C23×C5—61no—
169C22×D5—61no—
170C5×Q8—41no—
171C5×D4—121no—
172C5×D4—122no—
173C2×C4×C5—21no—
174C2×C4×C5—31no—
175C2×C4×C5—62no—
176C2×C4×C5—122no—
177C2×C4×C5C2×C4×D311yescharacteristic
178C22⋊D5—122no—
179C22⋊D5—122no—
180C22⋊D5—122no—
181C2×Dic5—21no—
182C2×Dic5—32no—
183C2×Dic5—62no—
184C2×Dic5—62no—
185C2×Dic5D3×D412yes—
186D20—121no—
187C4×D5—122no—
188Dic10—41no—
189#170—42no—
190#170—122no—
191C2×#41—31no—
192C2×#41—151no—
193C2×M16—302no—
194C4⋊Q8—51no—
195#127—151no—
196#124—151no—
197#124—151no—
198#121—302no—
199C4×D4—302no—
200C2×C42—151no—
201C4⋊C8—52no—
202C4⋊C8—152no—
203C4⋊C8—302no—
204C2×C3×C5C2×#10011yescharacteristic
205C2×C3×C5#41712yes—
206D15—81no—
207C5×D3—41no—
208C5×D3—81no—
209C22×D3—21no—
210C22×D3—101no—
211C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
212C3×Q8—41no—
213C3×Q8—201no—
214C2×C3×C4—21no—
215C2×C3×C4—52no—
216C2×C3×C4—101no—
217C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
218C2×Dic3—52no—
219C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
220D12—41no—
221D12—42no—
222D12—201no—
223D12—202no—
224D12—202no—
225D12—202no—
226C4×D3—22no—
227C4×D3—42no—
228C4×D3—102no—
229C4×D3—102no—
230C4×D3—202no—
231C3×C8—202no—
232C3⋊C8—202no—
233C22×C5—61no—
234C22×C5—62no—
235C22×C5—121no—
236C22×C5—122no—
237C22×C5D3×C22⋊C411yescharacteristic
238C2×D5—121no—
239C2×D5—122no—
240C4×C5—21no—
241C4×C5—32no—
242C4×C5—41no—
243Dic5—41no—
244Dic5—62no—
245Dic5#91412yes—
246Dic5#91812yes—
247#41—122no—
248#41—602no—
249C2×Q8—51no—
250C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
251C2×D4—31no—
252C2×D4—61no—
253C2×D4—151no—
254C2×D4—302no—
255C2×D4—301no—
256C22×C4—31no—
257C22×C4—61no—
258C22×C4—152no—
259C22×C4—301no—
260M16—604no—
261C2×C8—102no—
262C2×C8—302no—
263C4⋊C4—102no—
264C22⋊C4—302no—
265C22⋊C4—302no—
266C42—51no—
267C42—152no—
268C42—151no—
269C3×C5#156011yescharacteristic, complemented, Hall
270C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
271C2×D3—22no—
272C2×D3—21no—
273C2×D3—42no—
274C2×D3—41no—
275C2×D3—202no—
276C2×D3—201no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—52no—
280C3×C4—52no—
281C3×C4—201no—
282Dic3—102no—
283Dic3#401312yes—
284C2×C5—121no—
285C2×C5—241no—
286C2×C5D3×#10011yescharacteristic
287C2×C5#480312yes—
288D5—241no—
289C23—31no—
290C23—61no—
291C23—301no—
292Q8—41no—
293Q8—201no—
294D4—121no—
295D4—122no—
296D4—601no—
297D4—602no—
298D4—602no—
299D4—602no—
300C2×C4—21no—
301C2×C4—31no—
302C2×C4—52no—
303C2×C4—62no—
304C2×C4—101no—
305C2×C4—122no—
306C2×C4—152no—
307C2×C4—302no—
308C2×C4—302no—
309C2×C4—602no—
310C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
311C8—202no—
312C8—602no—
313C2×C3#6579312yes—
314C2×C3C2×#401311yescharacteristic
315D3—41no—
316D3—81no—
317D3—401no—
318C5#6848911yescharacteristic, complemented, Sylow
319C22—62no—
320C22—61no—
321C22—122no—
322C22—121no—
323C22—602no—
324C22—601no—
325C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
326C4—21no—
327C4—32no—
328C4—41no—
329C4—52no—
330C4—52no—
331C4—201no—
332C4—302no—
333C3#1060500611yescharacteristic, complemented, Sylow
334C2—121no—
335C2—241no—
336C2—1201no—
337C2#1175196112yes—
338C2D3×#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#1560
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. #11751920C2semidirect
3. #11746802C2semidirect
4. C3×#64931C2semidirect
5. #11746508C2semidirect
24. #64931D3semidirect
269. C3×C5#1560semidirect
318. C5#68489semidirect
333. C3#10605006semidirect

Maximal subgroups

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

subgroupindex
#117551642
#117519202
#117468022
C3×#649312
#117465082
#106050063
#684895