Finite Group Databasebeta

← #14281347

Subgroups — #14281347

Order 1920.

644 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91819C211yesmaximal, characteristic
2C5×#5207C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊#168C211yesmaximal, characteristic, complemented
4#11745950C214yesmaximal, complemented
5#10600763—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×#1220C412yes—
8C22×D60C411yescharacteristic
9#91819—21no—
10#91819—21no—
11#91819—21no—
12#91819—21no—
13C2×#6714C2212yes—
14C2×C4⋊Dic15C411yescharacteristic
15C2×C5×#208—21no—
16C22×C3×#168—21no—
17C5×#830—21no—
18C5×#830C2212yes—
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yes—
21#69921—51nomaximal, Hall
22C2×#4076—31no—
23C5×#407—31no—
24C2×C22⋊#168D311yescharacteristic, complemented
25#64688—34no—
26C24×C3×C5C2×C411yescharacteristic
27C23×D15C2×C412yes—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—22no—
36C2×#1220—22no—
37C2×#1220—44no—
38C22×Dic15C2×C412yes—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—42no—
42#6714—22no—
43#6714—22no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C5×#208—42no—
47C2×C5×C3⋊C8—22no—
48C2×C3×#168—22no—
49C2×C3×#168—42no—
50C2×#930—51no—
51C2×C3×C22⋊C8—51no—
52#5207D511yescharacteristic, complemented
53#4468—54no—
54C23×C4×C5C2×D311yescharacteristic
55C22×C22⋊D5—32no—
56C22×D20—31no—
57C2×C5×M16—61no—
58#4076—61no—
59#4076—61no—
60#4076—61no—
61#4076—61no—
62C2×#685—32no—
63C2×C4⋊Dic5—31no—
64C22×#168—21no—
65C5×C22⋊C8—32no—
66C5×C22⋊C8—61no—
67C22⋊#168—21no—
68C22⋊#168C2×D312yes—
69#1471—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22×C411yescharacteristic
76C22×D15—22no—
77C22×D15—24no—
78C22×D15—42no—
79C22×D15—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90#1220—44no—
91#1220—44no—
92C2×Dic15—22no—
93C2×Dic15—42no—
94D60—42no—
95D60—42no—
96C3×#168—42no—
97C5×C3⋊C8—42no—
98C23×C3×C4C2×D511yescharacteristic
99C22×#67—52no—
100C22×D12—51no—
101C22×C3×C8—101no—
102#930—101no—
103#930—101no—
104#930—101no—
105#930—101no—
106C2×(C2×D3)⋊C4—52no—
107C2×C4⋊Dic3—51no—
108C2×#208—21no—
109C3×C22⋊C8—52no—
110C3×C22⋊C8—101no—
111#830—21no—
112#830C2×D512yes—
113C24×C5C4×D311yescharacteristic
114C23×D5—32no—
115C22×C4×C5—42no—
116C22×C4×C5C4×D311yescharacteristic
117C22×C4×C5D1211yescharacteristic
118C22×C4×C5D1211yescharacteristic
119C22×C4×C5#6711yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5C22×D311yescharacteristic
122C2×C22⋊D5—62no—
123C2×C22⋊D5—62no—
124C2×C22⋊D5—124no—
125C22×Dic5—32no—
126C2×D20—61no—
127C2×D20—61no—
128C2×D20—122no—
129C5×M16—122no—
130C2×C5×C8—62no—
131#685—62no—
132#685—62no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135C2×#168—22no—
136C2×#168—42no—
137C2×#121—151no—
138#407—31no—
139C2×C22⋊C8—51no—
140#323—154no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—44no—
149C22×C3×C5#10012yes—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C22×C3×C5#13112yes—
152C2×D15—42no—
153C2×D15—42no—
154C2×D15—42no—
155C2×D15—84no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5#9912yes—
160Dic15—42no—
161C24×C3C4×D511yescharacteristic
162C23×D3—52no—
163C22×C3×C4—42no—
164C22×C3×C4C4×D511yescharacteristic
165C22×C3×C4D2011yescharacteristic
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C22×C3×C4C22⋊D511yescharacteristic
169C22×C3×C4C22×D511yescharacteristic
170C2×#67—102no—
171C2×#67—102no—
172C2×#67—204no—
173C22×Dic3—52no—
174C2×D12—101no—
175C2×D12—101no—
176C2×D12—202no—
177C2×C3×C8—102no—
178C2×C3×C8—202no—
179(C2×D3)⋊C4—102no—
180(C2×D3)⋊C4—102no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183#208—42no—
184C2×C3⋊C8—22no—
185C23×C5—22no—
186C23×C5—22no—
187C23×C5—41no—
188C23×C5(C2×D3)⋊C411yescharacteristic
189C23×C5(C2×D3)⋊C411yescharacteristic
190C23×C5C2×C4×D311yescharacteristic
191C22×D5—62no—
192C22×D5—64no—
193C22×D5—122no—
194C22×D5—122no—
195C2×C4×C5—22no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5(C2×D3)⋊C411yescharacteristic
202C2×C4×C5(C2×D3)⋊C411yescharacteristic
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C22⋊D5—124no—
206C22⋊D5—124no—
207C2×Dic5—62no—
208C2×Dic5—122no—
209D20—122no—
210D20—122no—
211C5×C8—122no—
212#168—42no—
213C22×D4—152no—
214C22×D4—151no—
215C23×C4D3×D511yescharacteristic
216C2×M16—61no—
217C22×C8—101no—
218#121—301no—
219#121—301no—
220#121—301no—
221#121—301no—
222C2×C4⋊C4—151no—
223C2×C22⋊C4—152no—
224C22⋊C8—32no—
225C22⋊C8—52no—
226C22⋊C8—61no—
227C22⋊C8—101no—
228C2×C3×C5—22no—
229C2×C3×C5—22no—
230C2×C3×C5—41no—
231C2×C3×C5#40811yescharacteristic
232C2×C3×C5C2×#9911yescharacteristic
233C2×C3×C5C2×#10011yescharacteristic
234D15—82no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—41no—
238C23×C3#68511yescharacteristic
239C23×C3#68511yescharacteristic
240C23×C3C2×C4×D511yescharacteristic
241C22×D3—102no—
242C22×D3—104no—
243C22×D3—202no—
244C22×D3—202no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4#68511yescharacteristic
252C2×C3×C4#68511yescharacteristic
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255#67—204no—
256#67—204no—
257C2×Dic3—102no—
258C2×Dic3—202no—
259D12—202no—
260D12—202no—
261C3×C8—202no—
262C3⋊C8—42no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—44no—
271C22×C5#82312yes—
272C22×C5#90112yes—
273C22×C5C2×(C2×D3)⋊C411yescharacteristic
274C2×D5—122no—
275C2×D5—122no—
276C2×D5—122no—
277C2×D5—244no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5#80612yes—
282Dic5—122no—
283C24—152no—
284C24#120011yescharacteristic
285C2×D4—302no—
286C2×D4—302no—
287C2×D4—301no—
288C2×D4—301no—
289C2×D4—602no—
290C2×D4—604no—
291C22×C4—42no—
292C22×C4—152no—
293C22×C4#120011yescharacteristic
294C22×C4#120211yescharacteristic
295C22×C4#120211yescharacteristic
296C22×C4#120311yescharacteristic
297C22×C4#120311yescharacteristic
298C22×C4C2×D3×D511yescharacteristic
299M16—122no—
300C2×C8—62no—
301C2×C8—102no—
302C2×C8—202no—
303C4⋊C4—301no—
304C4⋊C4—301no—
305C22⋊C4—302no—
306C22⋊C4—302no—
307C3×C5#147111yescharacteristic, complemented, Hall
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—44no—
316C22×C3#395512yes—
317C22×C3#405312yes—
318C22×C3C2×#68511yescharacteristic
319C2×D3—202no—
320C2×D3—202no—
321C2×D3—202no—
322C2×D3—404no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4#393812yes—
327Dic3—202no—
328C2×C5—22no—
329C2×C5—22no—
330C2×C5—41no—
331C2×C5C2×#80611yescharacteristic
332C2×C5#511011yescharacteristic
333C2×C5C2×#82311yescharacteristic
334D5—242no—
335C23—22no—
336C23—22no—
337C23—41no—
338C23—302no—
339C23—304no—
340C23—602no—
341C23—602no—
342C23#666711yescharacteristic
343C23#666711yescharacteristic
344C23C2×#120011yescharacteristic
345D4—602no—
346D4—604no—
347D4—604no—
348D4—602no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—302no—
356C2×C4—602no—
357C2×C4#666711yescharacteristic
358C2×C4#666711yescharacteristic
359C2×C4C2×#120211yescharacteristic
360C2×C4C2×#120311yescharacteristic
361C8—122no—
362C8—202no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—41no—
366C2×C3C2×#393811yescharacteristic
367C2×C3#6541811yescharacteristic
368C2×C3C2×#395511yescharacteristic
369D3—402no—
370C5#6992111yescharacteristic, complemented, Sylow
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—602no—
380C22—602no—
381C22—602no—
382C22—1204no—
383C22#9096012yes—
384C22#9129012yes—
385C22C2×#666711yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—602no—
390C4#9099712yes—
391C3#1060076311yescharacteristic, complemented, Sylow
392C2—22no—
393C2—22no—
394C2—41no—
395C2—1202no—
396C2#1174834911yescharacteristic
397C2C2×#9096011yescharacteristic
398C2C2×#9099711yescharacteristic
subgroupG/H
centerC22C2×#6667
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91819C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1471
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C5×#5207C2semidirect
3. C2×C3×C22⋊#168C2semidirect
4. #11745950C2semidirect
24. C2×C22⋊#168D3semidirect
52. #5207D5semidirect
307. C3×C5#1471semidirect
370. C5#69921semidirect
391. C3#10600763semidirect

Maximal subgroups

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

subgroupindex
C2×#918192
C5×#52072
C2×C3×C22⋊#1682
#117459502
#106007633
#699215