Finite Group Databasebeta

← #14283942

Subgroups — #14283942

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2C4×#6710C211yesmaximal, characteristic, complemented
3C2×C5×#803C211yesmaximal, characteristic, complemented
4#11745849C212yesmaximal, complemented
5#11745846C212yesmaximal, complemented
6#10600590—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C2×#6710—21no—
9C22×C5×C3⋊C8—21no—
10C3×#4076C411yescharacteristic
11C3×#4075—21no—
12C3×C4×C22⋊D5—21no—
13C3×#4070C411yescharacteristic
14C3×#4022—21no—
15C3×#4021C2211yescharacteristic
16C3×C4×D20C411yescharacteristic
17C3×#4018—21no—
18C3×#4016C2211yescharacteristic
19C3×C4×Dic10C411yescharacteristic
20#91087C2212yes—
21C4×C3⋊#168—21no—
22C5×#803—21no—
23C5×#803C2212yes—
24#71746—51nomaximal, Hall
25#65813D311yescharacteristic
26C2×C5×#97—31no—
27C4×#681—31no—
28#64685—32no—
29#64684—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×C3×C22⋊D5—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×Dic10C2×C411yescharacteristic
37C3×C42×C5C2×C411yescharacteristic
38C3×C42×C5D411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41#6710—24no—
42C2×C3⋊#168—22no—
43C2×C5×C3⋊C8—24no—
44C2×C5×C3⋊C8—22no—
45C3×C22⋊Dic5—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×#685—21no—
49C3×#685—21no—
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×#529—51no—
58C4×#208—51no—
59C2×#803D511yescharacteristic, complemented
60#4543—52no—
61#4540—52no—
62C22×C5×C8—61no—
63C2×C42×C5C2×D311yescharacteristic
64#4076Dic311yescharacteristic
65#4075—21no—
66C4×C22⋊D5—21no—
67#4070Dic311yescharacteristic
68C2×#681—61no—
69#4022—21no—
70#4021C2×D311yescharacteristic
71C4×D20Dic311yescharacteristic
72#4018—21no—
73#4016C2×D311yescharacteristic
74C4×Dic10Dic311yescharacteristic
75C5×#97—32no—
76C5×#97—61no—
77#3935—32no—
78C4×#168—61no—
79#1524—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×C3×D5—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C3×C22⋊D5—42no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—41no—
96C3×C4×D5—42no—
97C3×Dic10—41no—
98C3⋊#168—24no—
99C5×C3⋊C8—24no—
100C3×#126—101no—
101C3×#125—51no—
102C3×#124—51no—
103C3×#123—101no—
104C3×C22⋊Q8—51no—
105C3×#121—51no—
106C3×C4×Q8—51no—
107C3×C4×D4—51no—
108C3×C4×D4—101no—
109C3×#117—101no—
110C2×C3×C42C2×D511yescharacteristic
111C2×#208—101no—
112C22×C3⋊C8—21no—
113#803—21no—
114#803—52no—
115#803C2×D512yes—
116C4×C3⋊C8—101no—
117C22×C4×C5C2×Dic311yescharacteristic
118C22×C4×C5#6711yescharacteristic
119C22×C4×C5#6711yescharacteristic
120C2×C22⋊D5—21no—
121C2×D20C2×Dic311yescharacteristic
122C2×C4×D5—21no—
123C2×Dic10C2×Dic311yescharacteristic
124C2×C5×C8—64no—
125C2×C5×C8—62no—
126C42×C5C2×Dic311yescharacteristic
127C42×C5#6711yescharacteristic
128C42×C5#6711yescharacteristic
129C42×C5C22×D311yescharacteristic
130C22⋊Dic5—21no—
131#685—21no—
132#685—21no—
133#685—21no—
134#685—21no—
135C4⋊Dic5C2×Dic311yescharacteristic
136C4⋊Dic5C2×Dic311yescharacteristic
137#683—21no—
138#683—21no—
139#683—21no—
140#683—21no—
141C4×Dic5—21no—
142#681—64no—
143C2×#168—62no—
144#529—51no—
145C4×M16—151no—
146C2×#97—31no—
147#330—152no—
148#329—152no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#10412yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C2×C3×D5—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5#10412yes—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C2×C3×Q8—51no—
166C2×C3×D4—51no—
167C2×C3×D4—101no—
168C22×C3×C4—101no—
169C22×C3×C4C4×D511yescharacteristic
170C22×C3×C4D2011yescharacteristic
171C22×C3×C4C22⋊D511yescharacteristic
172C3×C4⋊C4—51no—
173C3×C4⋊C4—51no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C22⋊C4—101no—
179C3×C22⋊C4—101no—
180C3×C22⋊C4—101no—
181C3×C22⋊C4—101no—
182C3×C22⋊C4—101no—
183C3×C42—101no—
184C3×C42C4×D511yescharacteristic
185C3×C42D2011yescharacteristic
186C3×C42C22⋊D511yescharacteristic
187C3×C42C22×D511yescharacteristic
188#208—104no—
189C2×C3⋊C8—24no—
190C2×C3⋊C8—22no—
191C2×C3⋊C8—102no—
192C23×C5#21711yescharacteristic
193C22×D5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—41no—
197C2×C4×C5#21711yescharacteristic
198C2×C4×C5#21711yescharacteristic
199C2×C4×C5#21711yescharacteristic
200C2×C4×C5C22×Dic311yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C22⋊D5—42no—
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—21no—
207D20—41no—
208C4×D5—42no—
209Dic10—41no—
210C5×C8—64no—
211#168—64no—
212C2×M16—301no—
213C22×C8—61no—
214#126—101no—
215#125—51no—
216#124—51no—
217#123—101no—
218C22⋊Q8—51no—
219#121—51no—
220C4×Q8—51no—
221C4×D4—51no—
222C4×D4—101no—
223#117—101no—
224C2×C42D3×D511yescharacteristic
225#97—32no—
226#97—61no—
227#97—152no—
228C4×C8—301no—
229C2×C3×C5—22no—
230C2×C3×C5#41311yescharacteristic
231C2×C3×C5C2×#10411yescharacteristic
232C2×C3×C5C2×#10411yescharacteristic
233C3×D5—81no—
234C23×C3—101no—
235C23×C3#68511yescharacteristic
236C3×Q8—201no—
237C3×D4—201no—
238C3×D4—202no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—41no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—202no—
246C2×C3×C4#68511yescharacteristic
247C2×C3×C4#68511yescharacteristic
248C2×C3×C4#68511yescharacteristic
249C2×C3×C4C2×C4×D511yescharacteristic
250C2×C3×C4C2×D2011yescharacteristic
251C2×C3×C4C2×C22⋊D511yescharacteristic
252C3⋊C8—24no—
253C3⋊C8—104no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5#83712yes—
257C22×C5C2×#21711yescharacteristic
258C2×D5—41no—
259C2×D5—41no—
260C2×D5—41no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5#83712yes—
267Dic5—41no—
268Dic5—41no—
269Dic5—41no—
270C2×Q8—51no—
271C2×D4—51no—
272C2×D4—101no—
273C22×C4—101no—
274C22×C4D5×Dic311yescharacteristic
275C22×C4#120111yescharacteristic
276C22×C4#120211yescharacteristic
277M16—304no—
278C2×C8—64no—
279C2×C8—62no—
280C2×C8—302no—
281C4⋊C4—51no—
282C4⋊C4—51no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4—101no—
287C22⋊C4—101no—
288C22⋊C4—101no—
289C22⋊C4—101no—
290C22⋊C4—101no—
291C22⋊C4—101no—
292C42—101no—
293C42D5×Dic311yescharacteristic
294C42#120111yescharacteristic
295C42#120211yescharacteristic
296C42C2×D3×D511yescharacteristic
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—201no—
301C22×C3—201no—
302C22×C3—201no—
303C22×C3#395712yes—
304C22×C3C2×#68511yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—201no—
311C3×C4—201no—
312C3×C4—201no—
313C3×C4#393712yes—
314C2×C5—22no—
315C2×C5C2×#83711yescharacteristic
316C2×C5C2×#83711yescharacteristic
317C2×C5#523711yescharacteristic
318D5—81no—
319C23—101no—
320C23#666511yescharacteristic
321Q8—201no—
322D4—201no—
323D4—202no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—202no—
331C2×C4#666511yescharacteristic
332C2×C4#666511yescharacteristic
333C2×C4#666511yescharacteristic
334C2×C4C2×D5×Dic311yescharacteristic
335C2×C4C2×#120111yescharacteristic
336C2×C4C2×#120211yescharacteristic
337C8—64no—
338C8—304no—
339C2×C3—22no—
340C2×C3—401no—
341C2×C3C2×#393711yescharacteristic
342C2×C3#6542111yescharacteristic
343C2×C3C2×#395711yescharacteristic
344C5#7174611yescharacteristic, complemented, Sylow
345C22—21no—
346C22—21no—
347C22—201no—
348C22—201no—
349C22—201no—
350C22#9097612yes—
351C22C2×#666511yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—201no—
358C4—201no—
359C4—201no—
360C4#9097712yes—
361C3#1060059011yescharacteristic, complemented, Sylow
362C2—22no—
363C2—401no—
364C2#1174835311yescharacteristic
365C2C2×#9097611yescharacteristic
366C2C2×#9097711yescharacteristic
subgroupG/H
centerC2×C4#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C4
cosocleC3×C42×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#6710C2semidirect
3. C2×C5×#803C2semidirect
4. #11745849C2semidirect
5. #11745846C2semidirect
59. C2×#803D5semidirect
297. C3×C5#1524semidirect
344. C5#71746semidirect
361. C3#10600590semidirect

Maximal subgroups

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

subgroupindex
C3×#658132
C4×#67102
C2×C5×#8032
#117458492
#117458462
#106005903
#717465