Finite Group Databasebeta

← #14281888

Subgroups — #14281888

Order 1920.

424 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
1#11756238C211yesmaximal, characteristic
2C5×#4925C211yesmaximal, characteristic, complemented
3C3×#65214C211yesmaximal, characteristic, complemented
4#11745844C212yesmaximal, complemented
5#11745838C212yesmaximal, complemented
6#10601553—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8#91819C411yescharacteristic
9#91818—21no—
10C4×#1220—21no—
11#91813C411yescharacteristic
12#91765—21no—
13#91764C411yescharacteristic
14C4×D60C2211yescharacteristic
15#91761—21no—
16#91759C411yescharacteristic
17C4×Dic30C2211yescharacteristic
18C5×#830—21no—
19C5×C4⋊(C3⋊C8)—21no—
20C4×C5×C3⋊C8C2212yes—
21C3×C22⋊#168—21no—
22C3×C4⋊#168C2212yes—
23C3×C4×#168—21no—
24#70759—51nomaximal, Hall
25#65813—31no—
26C5×#431—31no—
27#65214D311yescharacteristic, complemented
28#64679—32no—
29#64676—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×#1220—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C3×C42×C5C2×C411yescharacteristic
38C3×C42×C5D411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41#6719—21no—
42#6714—21no—
43#6714—21no—
44#6714—21no—
45#6714—21no—
46C4⋊Dic15C2×C411yescharacteristic
47C4⋊Dic15C2×C411yescharacteristic
48#6712—21no—
49#6712—21no—
50#6712—21no—
51#6712—21no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—22no—
54C2×C3×#168—22no—
55#5479—51no—
56C3×#431—51no—
57#4925D511yescharacteristic, complemented
58#4484—52no—
59#4483—52no—
60C2×C42×C5C2×D311yescharacteristic
61#4076—31no—
62#4075—61no—
63C4×C22⋊D5—61no—
64#4070—31no—
65#4022—61no—
66#4021—31no—
67C4×D20—31no—
68#4018—61no—
69#4016—31no—
70C4×Dic10—31no—
71C5×C4⋊C8—61no—
72C5×C22⋊C8—61no—
73C4×C5×C8—32no—
74C22⋊#168—21no—
75C4⋊#168C2×D312yes—
76C4×#168—21no—
77#1482—151noSylow
78C23×C3×C5C22⋊C411yescharacteristic
79C22×D15—21no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
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
89#1220—42no—
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93D60—22no—
94C4×D15—42no—
95Dic30—22no—
96C3×#168—42no—
97C5×C3⋊C8—42no—
98C2×C3×C42C2×D511yescharacteristic
99#930—51no—
100#929—101no—
101C4×#67—101no—
102#924—51no—
103#876—101no—
104#875—51no—
105C4×D12—51no—
106#872—101no—
107#870—51no—
108C4×Dic6—51no—
109C3×C4⋊C8—52no—
110C3×C22⋊C8—101no—
111C3×C4×C8—101no—
112#830—21no—
113C4⋊(C3⋊C8)—21no—
114C4×C3⋊C8C2×D512yes—
115C22×C4×C5C4×D311yescharacteristic
116C22×C4×C5D1211yescharacteristic
117C22×C4×C5#6711yescharacteristic
118C2×C22⋊D5—61no—
119C2×D20—31no—
120C2×C4×D5—61no—
121C2×Dic10—31no—
122C2×C5×C8—62no—
123C42×C5C4×D311yescharacteristic
124C42×C5D1211yescharacteristic
125C42×C5#6711yescharacteristic
126C42×C5C22×D311yescharacteristic
127C22⋊Dic5—61no—
128#685—61no—
129#685—61no—
130#685—61no—
131#685—61no—
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134#683—61no—
135#683—61no—
136#683—61no—
137#683—61no—
138C4×Dic5—61no—
139C2×#168—22no—
140#529—151no—
141#431—31no—
142#431—51no—
143Q8⋊C8—152no—
144D4⋊C8—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—41no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5#13112yes—
157C3×C4×C5#13512yes—
158Dic15—41no—
159Dic15—41no—
160Dic15—41no—
161C22×C3×C4C4×D511yescharacteristic
162C22×C3×C4D2011yescharacteristic
163C22×C3×C4C22⋊D511yescharacteristic
164C2×#67—101no—
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×Dic6—51no—
168C2×C3×C8—102no—
169C3×C42C4×D511yescharacteristic
170C3×C42D2011yescharacteristic
171C3×C42C22⋊D511yescharacteristic
172C3×C42C22×D511yescharacteristic
173#217—101no—
174(C2×D3)⋊C4—101no—
175(C2×D3)⋊C4—101no—
176(C2×D3)⋊C4—101no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—22no—
186C23×C5(C2×D3)⋊C411yescharacteristic
187C22×D5—61no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—41no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5(C2×D3)⋊C411yescharacteristic
194C2×C4×C5C2×C4×D311yescharacteristic
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C22⋊D5—122no—
198C2×Dic5—61no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201D20—62no—
202C4×D5—122no—
203Dic10—62no—
204C5×C8—122no—
205#168—42no—
206#126—301no—
207#125—151no—
208#124—151no—
209#123—301no—
210C22⋊Q8—151no—
211#121—151no—
212C4×Q8—151no—
213C4×D4—151no—
214C4×D4—301no—
215#117—301no—
216C2×C42D3×D511yescharacteristic
217C4⋊C8—52no—
218C4⋊C8—61no—
219C22⋊C8—61no—
220C22⋊C8—101no—
221C4×C8—32no—
222C4×C8—101no—
223C2×C3×C5—41no—
224C2×C3×C5#40811yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#42111yescharacteristic
227D15—81no—
228C23×C3#68511yescharacteristic
229C22×D3—101no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—41no—
233C2×C3×C4#68511yescharacteristic
234C2×C3×C4#68511yescharacteristic
235C2×C3×C4#68511yescharacteristic
236C2×C3×C4C2×C4×D511yescharacteristic
237C2×C3×C4C2×D2011yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239#67—202no—
240C2×Dic3—101no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243D12—102no—
244C4×D3—202no—
245Dic6—102no—
246C3×C8—202no—
247C3⋊C8—42no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C2×(C2×D3)⋊C411yescharacteristic
252C2×D5—121no—
253C2×D5—121no—
254C2×D5—121no—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5#90112yes—
260C4×C5#95012yes—
261Dic5—121no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—151no—
265C2×D4—151no—
266C2×D4—301no—
267C22×C4—301no—
268C22×C4#120011yescharacteristic
269C22×C4#120211yescharacteristic
270C22×C4#120311yescharacteristic
271C2×C8—62no—
272C2×C8—102no—
273C4⋊C4—151no—
274C4⋊C4—151no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C22⋊C4—301no—
280C22⋊C4—301no—
281C22⋊C4—301no—
282C22⋊C4—301no—
283C22⋊C4—301no—
284C42—301no—
285C42#120011yescharacteristic
286C42#120211yescharacteristic
287C42#120311yescharacteristic
288C42C2×D3×D511yescharacteristic
289C3×C5#148211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3C2×#68511yescharacteristic
294C2×D3—201no—
295C2×D3—201no—
296C2×D3—201no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4#405012yes—
302C3×C4#405312yes—
303Dic3—201no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—41no—
307C2×C5#500211yescharacteristic
308C2×C5#511011yescharacteristic
309C2×C5#513911yescharacteristic
310D5—241no—
311C23—301no—
312C23#666711yescharacteristic
313Q8—302no—
314D4—302no—
315D4—602no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—301no—
320C2×C4—301no—
321C2×C4—301no—
322C2×C4—602no—
323C2×C4#666711yescharacteristic
324C2×C4#666711yescharacteristic
325C2×C4#666711yescharacteristic
326C2×C4C2×#120011yescharacteristic
327C2×C4C2×#120211yescharacteristic
328C2×C4C2×#120311yescharacteristic
329C8—122no—
330C8—202no—
331C2×C3—41no—
332C2×C3#6529411yescharacteristic
333C2×C3#6540211yescharacteristic
334C2×C3#6541811yescharacteristic
335D3—401no—
336C5#7075911yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—601no—
341C22—601no—
342C22—601no—
343C22C2×#666711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—601no—
349C4—601no—
350C4—601no—
351C4#9129012yes—
352C4#9131112yes—
353C3#1060155311yescharacteristic, complemented, Sylow
354C2—41no—
355C2—1201no—
356C2#1174834911yescharacteristic
357C2#1174841111yescharacteristic
358C2#1174842811yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C4
cosocleC3×C42×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C5×#4925C2semidirect
3. C3×#65214C2semidirect
4. #11745844C2semidirect
5. #11745838C2semidirect
27. #65214D3semidirect
57. #4925D5semidirect
289. C3×C5#1482semidirect
336. C5#70759semidirect
353. C3#10601553semidirect

Maximal subgroups

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

subgroupindex
#117562382
C5×#49252
C3×#652142
#117458442
#117458382
#106015533
#707595