Finite Group Databasebeta

← #14284349

Subgroups — #14284349

Order 1920.

496 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C5×D3×#124C211yesmaximal, characteristic
2#11746878C212yesmaximal, complemented
3#11746361C211yesmaximal, characteristic, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5#11745847C212yesmaximal, complemented
6#10602512—31nomaximal, Hall
7C2×C5×D3×Q8C411yescharacteristic
8C2×C5×D3×D4C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C5×#947C411yescharacteristic
11C5×#936C411yescharacteristic
12C5×#885—22no—
13C5×D3×C22⋊C4—22no—
14C5×#875C2211yescharacteristic
15C42×C5×D3C2211yescharacteristic
16#91087C2212yescomplemented
17C3×#3935C2212yescomplemented
18Dic3⋊#168—22no—
19(C2×D3)⋊#168—22no—
20#68347—51nomaximal, Hall
21C2×C5×#124—31no—
22#65215—32no—
23#64760—32no—
24#64760—31no—
25#64760D311yescharacteristic, complemented
26C23×C5×D3—21no—
27C2×C3×C5×Q8C2×C411yescharacteristic
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C5×#67—21no—
30C5×D3×Q8—42no—
31C5×D3×D4—42no—
32C2×C5×D12C2×C411yescharacteristic
33C2×C4×C5×D3—21no—
34C2×C4×C5×D3C2×C411yescharacteristic
35C2×C4×C5×D3D412yes—
36C2×C5×Dic6—21no—
37C2×C5×Dic6C2×C411yescharacteristic
38C3×C5×C22⋊C4—22no—
39C3×C42×C5C2311yescharacteristic
40C2×C3⋊#168—22no—
41C5×#217—22no—
42C5×(C2×D3)⋊C4—22no—
43C5×(C2×D3)⋊C4—22no—
44C4×C5×Dic3C2×C411yescharacteristic
45C4×C5×Dic3D412yes—
46C2×C3×#168—22no—
47D3×#124D511yescharacteristic
48#4705—52no—
49C3×#329—51no—
50#4540—51no—
51#4464—52no—
52C22×C5×Q8—31no—
53C22×C5×D4—31no—
54C5×#124—31no—
55C5×#124—31no—
56C5×#124—31no—
57C5×#124—62no—
58C5×#124C2×D311yescharacteristic
59C2×C5×C22⋊C4—62no—
60C2×C42×C5—31no—
61C22⋊#168—62no—
62C4⋊#168—62no—
63#3935—32no—
64#3935C2×D312yescomplemented
65#1533—151noSylow
66C23×C3×C5—21no—
67C22×C5×D3—21no—
68C22×C5×D3—44no—
69C22×C5×D3—42no—
70C22×C5×D3C22⋊C411yescharacteristic
71C3×C5×Q8—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5C22×C411yescharacteristic
75C2×C3×C4×C5C2×D412yes—
76C5×#67—42no—
77C2×C5×Dic3—21no—
78C2×C5×Dic3C22⋊C412yes—
79C2×C5×Dic3C22⋊C411yescharacteristic
80C5×D12—41no—
81C4×C5×D3—22no—
82C4×C5×D3—42no—
83C4×C5×D3—42no—
84C5×Dic6—42no—
85C5×Dic6—41no—
86C3⋊#168—42no—
87C3×#168—42no—
88C2×D3×Q8Dic511yescharacteristic
89C2×D3×D4Dic511yescharacteristic
90C3×#124C2×D511yescharacteristic
91#947Dic511yescharacteristic
92#936Dic511yescharacteristic
93#885—22no—
94D3×C22⋊C4—22no—
95#875C2×D511yescharacteristic
96C42×D3C2×D511yescharacteristic
97C3×#97—52no—
98(C2×D3)⋊C8—102no—
99Dic3⋊C8—102no—
100#803—52no—
101C24×C5—61no—
102C2×C5×Q8—31no—
103C2×C5×Q8—61no—
104C2×C5×Q8—122no—
105C2×C5×Q8C4×D311yescharacteristic
106C2×C5×D4—31no—
107C2×C5×D4—61no—
108C2×C5×D4—122no—
109C2×C5×D4C4×D311yescharacteristic
110C22×C4×C5—31no—
111C22×C4×C5—32no—
112C22×C4×C5—61no—
113C5×C22⋊C4—22no—
114C5×C22⋊C4—62no—
115C5×C22⋊C4—62no—
116C5×C22⋊C4—62no—
117C42×C5—31no—
118C42×C5—32no—
119C42×C5C22×D311yescharacteristic
120C2×#168—22no—
121C2×#168—62no—
122C2×#124—31no—
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×C5×D3—22no—
131C2×C5×D3—41no—
132C2×C5×D3—42no—
133C2×C5×D3—84no—
134C2×C5×D3#10012yes—
135C3×C4×C5—21no—
136C3×C4×C5—22no—
137C3×C4×C5—41no—
138C5×Dic3—21no—
139C5×Dic3—22no—
140C5×Dic3—41no—
141C23×D3—21no—
142C2×C3×Q8C2×Dic511yescharacteristic
143C2×C3×D4C2×Dic511yescharacteristic
144C2×#67—21no—
145D3×Q8—42no—
146D3×D4—42no—
147C2×D12C2×Dic511yescharacteristic
148C2×C4×D3—21no—
149C2×C4×D3C2×Dic511yescharacteristic
150C2×C4×D3C22⋊D512yes—
151C2×Dic6—21no—
152C2×Dic6C2×Dic511yescharacteristic
153C2×C3×C8—102no—
154C3×C22⋊C4—22no—
155C3×C42C22×D511yescharacteristic
156#217—22no—
157(C2×D3)⋊C4—22no—
158(C2×D3)⋊C4—22no—
159C4×Dic3C2×Dic511yescharacteristic
160C4×Dic3C22⋊D512yes—
161C2×C3⋊C8—102no—
162C23×C5—21no—
163C23×C5—31no—
164C23×C5—61no—
165C23×C5—122no—
166C23×C5—124no—
167C5×Q8—41no—
168C5×Q8—121no—
169C5×Q8—122no—
170C5×D4—41no—
171C5×D4—121no—
172C5×D4—122no—
173C2×C4×C5—21no—
174C2×C4×C5—32no—
175C2×C4×C5—31no—
176C2×C4×C5—62no—
177C2×C4×C5—61no—
178C2×C4×C5—122no—
179C2×C4×C5—122no—
180C2×C4×C5C2×C4×D311yescharacteristic
181C2×C4×C5D3×D412yes—
182#168—42no—
183#168—122no—
184C22×Q8—31no—
185C22×D4—31no—
186#124—31no—
187#124—31no—
188#124—31no—
189#124—62no—
190#124D3×D511yescharacteristic
191C2×C22⋊C4—62no—
192C2×C42—31no—
193C4⋊C8—302no—
194C22⋊C8—302no—
195#97—52no—
196#97—152no—
197C2×C3×C5—81no—
198C2×C3×C5C2×#10011yescharacteristic
199C2×C3×C5#42112yes—
200C5×D3—22no—
201C5×D3—81no—
202C23×C3—21no—
203C22×D3—21no—
204C22×D3—44no—
205C22×D3—42no—
206C22×D3C22⋊Dic511yescharacteristic
207C3×Q8—41no—
208C3×D4—41no—
209C2×C3×C4—21no—
210C2×C3×C4C22×Dic511yescharacteristic
211C2×C3×C4C2×C22⋊D512yes—
212#67—42no—
213C2×Dic3—21no—
214C2×Dic3C22⋊Dic512yes—
215C2×Dic3C22⋊Dic511yescharacteristic
216D12—41no—
217C4×D3—22no—
218C4×D3—42no—
219C4×D3—42no—
220Dic6—42no—
221Dic6—41no—
222C3×C8—202no—
223C3⋊C8—202no—
224C22×C5—32no—
225C22×C5—41no—
226C22×C5—42no—
227C22×C5—62no—
228C22×C5—121no—
229C22×C5—122no—
230C22×C5—244no—
231C22×C5D3×C22⋊C411yescharacteristic
232C4×C5—21no—
233C4×C5—22no—
234C4×C5—41no—
235C4×C5—61no—
236C4×C5—62no—
237C4×C5—121no—
238C24—61no—
239C2×Q8—31no—
240C2×Q8—61no—
241C2×Q8—122no—
242C2×Q8D3×Dic511yescharacteristic
243C2×D4—31no—
244C2×D4—61no—
245C2×D4—122no—
246C2×D4D3×Dic511yescharacteristic
247C22×C4—31no—
248C22×C4—32no—
249C22×C4—61no—
250C2×C8—102no—
251C2×C8—302no—
252C22⋊C4—22no—
253C22⋊C4—62no—
254C22⋊C4—62no—
255C22⋊C4—62no—
256C42—31no—
257C42—32no—
258C42C2×D3×D511yescharacteristic
259C3×C5#153311yescharacteristic, complemented, Hall
260C22×C3—41no—
261C22×C3—42no—
262C22×C3C2×C22⋊Dic511yescharacteristic
263C2×D3—22no—
264C2×D3—41no—
265C2×D3—42no—
266C2×D3—84no—
267C2×D3#396512yes—
268C3×C4—21no—
269C3×C4—22no—
270C3×C4—41no—
271Dic3—21no—
272Dic3—22no—
273Dic3—41no—
274C2×C5—62no—
275C2×C5—81no—
276C2×C5—241no—
277C2×C5D3×#10011yescharacteristic
278C2×C5#482112yes—
279C23—21no—
280C23—31no—
281C23—61no—
282C23—122no—
283C23—124no—
284Q8—41no—
285Q8—121no—
286Q8—122no—
287D4—41no—
288D4—121no—
289D4—122no—
290C2×C4—21no—
291C2×C4—32no—
292C2×C4—31no—
293C2×C4—62no—
294C2×C4—61no—
295C2×C4—122no—
296C2×C4—122no—
297C2×C4C2×D3×Dic511yescharacteristic
298C2×C4D3×C22⋊D512yes—
299C8—202no—
300C8—602no—
301C2×C3—81no—
302C2×C3C2×#396511yescharacteristic
303C2×C3#6552512yes—
304D3—22no—
305D3—81no—
306C5#6834711yescharacteristic, complemented, Sylow
307C22—32no—
308C22—41no—
309C22—42no—
310C22—62no—
311C22—121no—
312C22—122no—
313C22—244no—
314C22D3×C22⋊Dic511yescharacteristic
315C4—21no—
316C4—22no—
317C4—41no—
318C4—61no—
319C4—62no—
320C4—121no—
321C3#1060251211yescharacteristic, complemented, Sylow
322C2—62no—
323C2—81no—
324C2—241no—
325C2D3×#396511yescharacteristic
326C2#1174942912yes—
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×D3×D4C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11746878C2semidirect
3. #11746361C2semidirect
4. C3×#64760C2semidirect
5. #11745847C2semidirect
16. #91087C22semidirect
17. C3×#3935C22semidirect
25. #64760D3semidirect
64. #3935C2×D3semidirect
259. C3×C5#1533semidirect
306. C5#68347semidirect
321. C3#10602512semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1242
#117468782
#117463612
C3×#647602
#117458472
#106025123
#683475