Finite Group Databasebeta

← #14284149

Subgroups — #14284149

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2#11751027C211yesmaximal, characteristic, complemented
3C4×C5×#208C211yesmaximal, characteristic, complemented
4#11745849C212yesmaximal, complemented
5#11745846C212yesmaximal, complemented
6#10600654—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C2×C5×#208—21no—
9C3×#4076C411yescharacteristic
10C3×#4075—21no—
11C3×C4×C22⋊D5—21no—
12C3×#4070C411yescharacteristic
13C3×#4022—21no—
14C3×#4021C2211yescharacteristic
15C3×C4×D20C411yescharacteristic
16C3×#4018—21no—
17C3×#4016C2211yescharacteristic
18C3×C4×Dic10C411yescharacteristic
19#91114—21no—
20C4⋊(C3⋊#168)—21no—
21#91087C2212yes—
22C5×#803C2212yes—
23C4×C5×C3⋊C8—21no—
24#71747—51nomaximal, Hall
25#65813D311yescharacteristic
26C4×C5×M16—31no—
27#65215—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
41C2×C3⋊#168—22no—
42C5×#208—24no—
43C2×C5×C3⋊C8—22no—
44C3×C22⋊Dic5—21no—
45C3×#685—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×#685—21no—
49C3×C4⋊Dic5C2×C411yescharacteristic
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×#683—21no—
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×C4×Dic5—21no—
56C3×#529—51no—
57#4926—51no—
58C4×#208D511yescharacteristic, complemented
59#4543—52no—
60#4540—52no—
61C2×C5×M16—61no—
62C2×C42×C5C2×D311yescharacteristic
63#4076Dic311yescharacteristic
64#4075—21no—
65C4×C22⋊D5—21no—
66#4070Dic311yescharacteristic
67#4022—21no—
68#4021C2×D311yescharacteristic
69C4×D20Dic311yescharacteristic
70#4018—21no—
71#4016C2×D311yescharacteristic
72C4×Dic10Dic311yescharacteristic
73C5×#97—32no—
74C4×C5×C8—61no—
75C22⋊#168—61no—
76C4⋊#168—61no—
77#3935—32no—
78#1529—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C22×C3×D5—21no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C3×C22⋊D5—42no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C3×D20—41no—
95C3×C4×D5—42no—
96C3×Dic10—41no—
97C3⋊#168—42no—
98C5×C3⋊C8—24no—
99C3×#126—101no—
100C3×#125—51no—
101C3×#124—51no—
102C3×#123—101no—
103C3×C22⋊Q8—51no—
104C3×#121—51no—
105C3×C4×Q8—51no—
106C3×C4×D4—51no—
107C3×C4×D4—101no—
108C3×#117—101no—
109C2×C3×C42C2×D511yescharacteristic
110C2×#208—21no—
111#830—101no—
112C4⋊(C3⋊C8)—101no—
113#803—52no—
114#803C2×D512yes—
115C4×C3⋊C8—21no—
116C22×C4×C5C2×Dic311yescharacteristic
117C22×C4×C5#6711yescharacteristic
118C22×C4×C5#6711yescharacteristic
119C2×C22⋊D5—21no—
120C2×D20C2×Dic311yescharacteristic
121C2×C4×D5—21no—
122C2×Dic10C2×Dic311yescharacteristic
123C5×M16—64no—
124C2×C5×C8—62no—
125C42×C5C2×Dic311yescharacteristic
126C42×C5#6711yescharacteristic
127C42×C5#6711yescharacteristic
128C42×C5C22×D311yescharacteristic
129C22⋊Dic5—21no—
130#685—21no—
131#685—21no—
132#685—21no—
133#685—21no—
134C4⋊Dic5C2×Dic311yescharacteristic
135C4⋊Dic5C2×Dic311yescharacteristic
136#683—21no—
137#683—21no—
138#683—21no—
139#683—21no—
140C4×Dic5—21no—
141C2×#168—62no—
142#529—51no—
143#432—151no—
144C4×M16—31no—
145#330—152no—
146#329—152no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×C3×D5—41no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5#10412yes—
160C3×Dic5—41no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C2×C3×Q8—51no—
164C2×C3×D4—51no—
165C2×C3×D4—101no—
166C22×C3×C4—101no—
167C22×C3×C4C4×D511yescharacteristic
168C22×C3×C4D2011yescharacteristic
169C22×C3×C4C22⋊D511yescharacteristic
170C3×C4⋊C4—51no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C22⋊C4—101no—
177C3×C22⋊C4—101no—
178C3×C22⋊C4—101no—
179C3×C22⋊C4—101no—
180C3×C22⋊C4—101no—
181C3×C42—101no—
182C3×C42C4×D511yescharacteristic
183C3×C42D2011yescharacteristic
184C3×C42C22⋊D511yescharacteristic
185C3×C42C22×D511yescharacteristic
186#208—24no—
187C2×C3⋊C8—22no—
188C2×C3⋊C8—102no—
189C23×C5#21711yescharacteristic
190C22×D5—21no—
191C2×C4×C5—22no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5#21711yescharacteristic
195C2×C4×C5#21711yescharacteristic
196C2×C4×C5#21711yescharacteristic
197C2×C4×C5C22×Dic311yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C22⋊D5—42no—
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—21no—
204D20—41no—
205C4×D5—42no—
206Dic10—41no—
207C5×C8—64no—
208#168—122no—
209C2×M16—61no—
210#126—101no—
211#125—51no—
212#124—51no—
213#123—101no—
214C22⋊Q8—51no—
215#121—51no—
216C4×Q8—51no—
217C4×D4—51no—
218C4×D4—101no—
219#117—101no—
220C2×C42D3×D511yescharacteristic
221C4⋊C8—301no—
222C22⋊C8—301no—
223#97—32no—
224#97—152no—
225C4×C8—61no—
226C2×C3×C5—41no—
227C2×C3×C5#41311yescharacteristic
228C2×C3×C5C2×#10411yescharacteristic
229C2×C3×C5#42111yescharacteristic
230C3×D5—81no—
231C23×C3—101no—
232C23×C3#68511yescharacteristic
233C3×Q8—201no—
234C3×D4—201no—
235C3×D4—202no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—202no—
243C2×C3×C4#68511yescharacteristic
244C2×C3×C4#68511yescharacteristic
245C2×C3×C4#68511yescharacteristic
246C2×C3×C4C2×C4×D511yescharacteristic
247C2×C3×C4C2×D2011yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C3⋊C8—24no—
250C3⋊C8—202no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5C2×#21711yescharacteristic
255C2×D5—41no—
256C2×D5—41no—
257C2×D5—41no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5#83712yes—
264Dic5—41no—
265Dic5—41no—
266Dic5—41no—
267C2×Q8—51no—
268C2×D4—51no—
269C2×D4—101no—
270C22×C4—101no—
271C22×C4D5×Dic311yescharacteristic
272C22×C4#120111yescharacteristic
273C22×C4#120211yescharacteristic
274M16—64no—
275C2×C8—62no—
276C2×C8—302no—
277C4⋊C4—51no—
278C4⋊C4—51no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C22⋊C4—101no—
284C22⋊C4—101no—
285C22⋊C4—101no—
286C22⋊C4—101no—
287C22⋊C4—101no—
288C42—101no—
289C42D5×Dic311yescharacteristic
290C42#120111yescharacteristic
291C42#120211yescharacteristic
292C42C2×D3×D511yescharacteristic
293C3×C5#152911yescharacteristic, complemented, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—201no—
298C22×C3—201no—
299C22×C3—201no—
300C22×C3C2×#68511yescharacteristic
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—201no—
307C3×C4—201no—
308C3×C4—201no—
309C3×C4#393712yes—
310C2×C5—41no—
311C2×C5C2×#83711yescharacteristic
312C2×C5#523611yescharacteristic
313C2×C5#523711yescharacteristic
314D5—81no—
315C23—101no—
316C23#666511yescharacteristic
317Q8—201no—
318D4—201no—
319D4—202no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—101no—
324C2×C4—101no—
325C2×C4—101no—
326C2×C4—202no—
327C2×C4#666511yescharacteristic
328C2×C4#666511yescharacteristic
329C2×C4#666511yescharacteristic
330C2×C4C2×D5×Dic311yescharacteristic
331C2×C4C2×#120111yescharacteristic
332C2×C4C2×#120211yescharacteristic
333C8—64no—
334C8—602no—
335C2×C3—41no—
336C2×C3—401no—
337C2×C3C2×#393711yescharacteristic
338C2×C3#6542111yescharacteristic
339C2×C3#6542811yescharacteristic
340C5#7174711yescharacteristic, complemented, Sylow
341C22—21no—
342C22—21no—
343C22—21no—
344C22—201no—
345C22—201no—
346C22—201no—
347C22C2×#666511yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—201no—
354C4—201no—
355C4—201no—
356C4#9097712yes—
357C3#1060065411yescharacteristic, complemented, Sylow
358C2—41no—
359C2—401no—
360C2#1174835311yescharacteristic
361C2C2×#9097711yescharacteristic
362C2#1174842011yescharacteristic
subgroupG/H
centerC22C2×#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#1529
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. C4×C5×#208C2semidirect
4. #11745849C2semidirect
5. #11745846C2semidirect
58. C4×#208D5semidirect
293. C3×C5#1529semidirect
340. C5#71747semidirect
357. C3#10600654semidirect

Maximal subgroups

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

subgroupindex
C3×#658132
#117510272
C4×C5×#2082
#117458492
#117458462
#106006543
#717475