Finite Group Databasebeta

← #14284421

Subgroups — #14284421

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5479C211yesmaximal, characteristic
2#11751027C211yesmaximal, characteristic, complemented
3C3×#65215C211yesmaximal, characteristic, complemented
4#11745850C212yesmaximal, complemented
5#11745847C212yesmaximal, complemented
6#10602542—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C5×#930C411yescharacteristic
9C5×#929—21no—
10C4×C5×#67—21no—
11C5×#924C411yescharacteristic
12C5×#876—21no—
13C5×#875C2211yescharacteristic
14C4×C5×D12C411yescharacteristic
15C5×#872—21no—
16C5×#870C2211yescharacteristic
17C4×C5×Dic6C411yescharacteristic
18#91114—21no—
19C4⋊(C3⋊#168)—21no—
20#91087C2212yes—
21C3×C22⋊#168—21no—
22C3×C4⋊#168—21no—
23C3×#3935C2212yes—
24#70809—51nomaximal, Hall
25C5×#529—31no—
26#65215—31no—
27#65215D311yescharacteristic, complemented
28#64763—32no—
29#64760—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×C5×#67—21no—
34C2×C5×D12C2×C411yescharacteristic
35C2×C4×C5×D3—21no—
36C2×C5×Dic6C2×C411yescharacteristic
37C3×C42×C5C2×C411yescharacteristic
38C3×C42×C5D411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41C2×C3⋊#168—22no—
42C5×#217—21no—
43C5×(C2×D3)⋊C4—21no—
44C5×(C2×D3)⋊C4—21no—
45C5×(C2×D3)⋊C4—21no—
46C5×(C2×D3)⋊C4—21no—
47C5×C4⋊Dic3C2×C411yescharacteristic
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×Dic3⋊C4—21no—
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3—21no—
54C2×C3×#168—22no—
55#5479D511yescharacteristic
56C3×#432—51no—
57#4926—51no—
58#4465—52no—
59#4464—52no—
60C5×#126—61no—
61C5×#125—31no—
62C5×#124—31no—
63C5×#123—61no—
64C5×C22⋊Q8—31no—
65C5×#121—31no—
66C4×C5×Q8—31no—
67C4×C5×D4—31no—
68C4×C5×D4—61no—
69C5×#117—61no—
70C2×C42×C5C2×D311yescharacteristic
71C22⋊#168—21no—
72C22⋊#168—61no—
73C4⋊#168—21no—
74C4⋊#168—61no—
75#3935—32no—
76#3935C2×D312yes—
77#1535—151noSylow
78C23×C3×C5C22⋊C411yescharacteristic
79C22×C5×D3—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C5×#67—42no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×D12—41no—
94C4×C5×D3—42no—
95C5×Dic6—41no—
96C3⋊#168—42no—
97C3×#168—42no—
98C2×C3×C42C2×D511yescharacteristic
99#930Dic511yescharacteristic
100#929—21no—
101C4×#67—21no—
102#924Dic511yescharacteristic
103#876—21no—
104#875C2×D511yescharacteristic
105C4×D12Dic511yescharacteristic
106#872—21no—
107#870C2×D511yescharacteristic
108C4×Dic6Dic511yescharacteristic
109C3×C4⋊C8—101no—
110C3×C22⋊C8—101no—
111C3×#97—52no—
112#830—101no—
113C4⋊(C3⋊C8)—101no—
114#803—52no—
115C2×C5×Q8—31no—
116C2×C5×D4—31no—
117C2×C5×D4—61no—
118C22×C4×C5—61no—
119C22×C4×C5C4×D311yescharacteristic
120C22×C4×C5D1211yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C5×C4⋊C4—31no—
123C5×C4⋊C4—31no—
124C5×C4⋊C4—61no—
125C5×C4⋊C4—61no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C5×C22⋊C4—61no—
129C5×C22⋊C4—61no—
130C5×C22⋊C4—61no—
131C5×C22⋊C4—61no—
132C5×C22⋊C4—61no—
133C42×C5—61no—
134C42×C5C4×D311yescharacteristic
135C42×C5D1211yescharacteristic
136C42×C5#6711yescharacteristic
137C42×C5C22×D311yescharacteristic
138C2×#168—22no—
139C2×#168—62no—
140#529—31no—
141#432—51no—
142#432—151no—
143#330—152no—
144#329—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C5×D3—41no—
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C5×Dic3—41no—
159C5×Dic3—41no—
160C5×Dic3—41no—
161C22×C3×C4C2×Dic511yescharacteristic
162C22×C3×C4C22⋊D511yescharacteristic
163C22×C3×C4C22⋊D511yescharacteristic
164C2×#67—21no—
165C2×D12C2×Dic511yescharacteristic
166C2×C4×D3—21no—
167C2×Dic6C2×Dic511yescharacteristic
168C2×C3×C8—102no—
169C3×C42C2×Dic511yescharacteristic
170C3×C42C22⋊D511yescharacteristic
171C3×C42C22⋊D511yescharacteristic
172C3×C42C22×D511yescharacteristic
173#217—21no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—21no—
178C4⋊Dic3C2×Dic511yescharacteristic
179C4⋊Dic3C2×Dic511yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—21no—
182Dic3⋊C4—21no—
183Dic3⋊C4—21no—
184C4×Dic3—21no—
185C2×C3⋊C8—102no—
186C23×C5—61no—
187C23×C5(C2×D3)⋊C411yescharacteristic
188C5×Q8—121no—
189C5×D4—121no—
190C5×D4—122no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—61no—
195C2×C4×C5—61no—
196C2×C4×C5—61no—
197C2×C4×C5—122no—
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5(C2×D3)⋊C411yescharacteristic
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204#168—42no—
205#168—122no—
206#126—61no—
207#125—31no—
208#124—31no—
209#123—61no—
210C22⋊Q8—31no—
211#121—31no—
212C4×Q8—31no—
213C4×D4—31no—
214C4×D4—61no—
215#117—61no—
216C2×C42D3×D511yescharacteristic
217C4⋊C8—101no—
218C4⋊C8—301no—
219C22⋊C8—101no—
220C22⋊C8—301no—
221#97—52no—
222#97—152no—
223C2×C3×C5—41no—
224C2×C3×C5#41311yescharacteristic
225C2×C3×C5#42111yescharacteristic
226C2×C3×C5#42111yescharacteristic
227C5×D3—81no—
228C23×C3C22⋊Dic511yescharacteristic
229C22×D3—21no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4C22⋊Dic511yescharacteristic
234C2×C3×C4C22⋊Dic511yescharacteristic
235C2×C3×C4C22⋊Dic511yescharacteristic
236C2×C3×C4C22×Dic511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239#67—42no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243D12—41no—
244C4×D3—42no—
245Dic6—41no—
246C3×C8—202no—
247C3⋊C8—202no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5—121no—
254C22×C5C2×(C2×D3)⋊C411yescharacteristic
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—121no—
262C4×C5—121no—
263C4×C5—121no—
264C2×Q8—31no—
265C2×D4—31no—
266C2×D4—61no—
267C22×C4—61no—
268C22×C4D3×Dic511yescharacteristic
269C22×C4#120111yescharacteristic
270C22×C4#120311yescharacteristic
271C2×C8—102no—
272C2×C8—302no—
273C4⋊C4—31no—
274C4⋊C4—31no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C22⋊C4—61no—
280C22⋊C4—61no—
281C22⋊C4—61no—
282C22⋊C4—61no—
283C22⋊C4—61no—
284C42—61no—
285C42D3×Dic511yescharacteristic
286C42#120111yescharacteristic
287C42#120311yescharacteristic
288C42C2×D3×D511yescharacteristic
289C3×C5#153511yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3C2×C22⋊Dic511yescharacteristic
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303Dic3—41no—
304Dic3—41no—
305Dic3—41no—
306C2×C5—41no—
307C2×C5—241no—
308C2×C5#500511yescharacteristic
309C2×C5#513211yescharacteristic
310C2×C5#513911yescharacteristic
311C23—61no—
312C23(C2×D3)⋊Dic511yescharacteristic
313Q8—121no—
314D4—121no—
315D4—122no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—122no—
323C2×C4(C2×D3)⋊Dic511yescharacteristic
324C2×C4(C2×D3)⋊Dic511yescharacteristic
325C2×C4(C2×D3)⋊Dic511yescharacteristic
326C2×C4C2×D3×Dic511yescharacteristic
327C2×C4C2×#120111yescharacteristic
328C2×C4C2×#120311yescharacteristic
329C8—202no—
330C8—602no—
331C2×C3—41no—
332C2×C3#6552511yescharacteristic
333C2×C3#6552511yescharacteristic
334C2×C3#6552611yescharacteristic
335D3—81no—
336C5#7080911yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22C2×(C2×D3)⋊Dic511yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—121no—
351C4—121no—
352C4—121no—
353C3#1060254211yescharacteristic, complemented, Sylow
354C2—41no—
355C2—241no—
356C2#1174835511yescharacteristic
357C2#1174842411yescharacteristic
358C2#1174842511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C4
cosocleC3×C42×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1535
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751027C2semidirect
3. C3×#65215C2semidirect
4. #11745850C2semidirect
5. #11745847C2semidirect
27. #65215D3semidirect
289. C3×C5#1535semidirect
336. C5#70809semidirect
353. C3#10602542semidirect

Maximal subgroups

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

subgroupindex
C5×#54792
#117510272
C3×#652152
#117458502
#117458472
#106025423
#708095