Finite Group Databasebeta

← #14298411

Subgroups — #14298411

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91358C211yesmaximal, characteristic
2C3×#65415C211yesmaximal, characteristic
3#11748341C211yesmaximal, characteristic
4#11746375C211yesmaximal, characteristic, complemented
5C5×#4554C211yesmaximal, characteristic, complemented
6#11745987C211yesmaximal, characteristic, complemented
7#11745986C211yesmaximal, characteristic, complemented
8#10599784—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C2×#6665C412yes—
17C2×Dic3×Dic5C412yes—
18#91358—22no—
19#91358—22no—
20C3×#3952—22no—
21#90955—22no—
22#69974—51nomaximal, Hall
23C2×#4038—31no—
24#65415—31no—
25#65415D311yescharacteristic
26C5×#343—31no—
27#64774—31no—
28#64774—31no—
29#64750—31no—
30C23×C3×D5C2×C411yescharacteristic
31C22×C3×C4×C5C2311yescharacteristic
32C22×Dic15C2×C412yes—
33C22×C5×Dic3C2×C412yes—
34C22×C3×Dic5C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5D412yes—
40C2×C3×C4×D5D412yes—
41C3×C5×M16—21no—
42C3×C5×M16—21no—
43C2×C3×C5×C8—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46#6710—21no—
47#6710—21no—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×#208—21no—
52C5×#208—21no—
53C2×C5×C3⋊C8—21no—
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57#6665—24no—
58Dic3×Dic5—24no—
59C2×#926—51no—
60C3×#407—51no—
61#5207—51no—
62#4554—51no—
63#4554—51no—
64#4554—51no—
65#4554D511yescharacteristic, complemented
66C22×C4×D5C2×D311yescharacteristic
67C2×C5×M16—31no—
68C2×C5×M16C2×D311yescharacteristic
69C2×C5×C4⋊C4—31no—
70C2×#685—32no—
71C2×C4⋊Dic5—31no—
72C2×C4×Dic5—32no—
73C2×#681—31no—
74C2×#681C2×D311yescharacteristic
75#4038—62no—
76#4038—62no—
77#3952—22no—
78#3952—62no—
79#1822—151noSylow
80C23×C3×C5C22×C411yescharacteristic
81C22×C3×D5—21no—
82C22×C3×D5—21no—
83C22×C3×D5—41no—
84C22×C3×D5—41no—
85C22×C3×D5C22⋊C412yes—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×Dic15—22no—
93C2×Dic15—42no—
94C2×C5×Dic3—22no—
95C2×C5×Dic3—42no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5C22⋊C412yes—
99C3×C4×D5—22no—
100C3×C4×D5—22no—
101C3×C4×D5—22no—
102C3×C4×D5—22no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C23×C3×C4—51no—
108C2×C3×M16—51no—
109C2×C3×M16C2×D511yescharacteristic
110C2×#217—52no—
111#926—102no—
112#926—102no—
113C2×C4⋊Dic3—51no—
114C2×C4⋊Dic3C2×D511yescharacteristic
115C2×C4×Dic3—52no—
116C2×#208—51no—
117C2×#208C2×D511yescharacteristic
118C3×C22⋊C8—102no—
119#830—102no—
120C23×D5C4×D311yescharacteristic
121C22×C4×C5—32no—
122C22×C4×C5C22×D311yescharacteristic
123C22×Dic5—32no—
124C22×Dic5C4×D311yescharacteristic
125C2×C4×D5—21no—
126C2×C4×D5—21no—
127C2×C4×D5—21no—
128C2×C4×D5—21no—
129C2×C4×D5D1212yes—
130C2×C4×D5#6712yes—
131C5×M16—21no—
132C5×M16—21no—
133C5×M16—61no—
134C5×M16—61no—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139#685—64no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4×Dic5—64no—
143#681—21no—
144#681—21no—
145#681—61no—
146#681—61no—
147C2×#168—21no—
148C2×#168—61no—
149C2×#117—151no—
150#407—51no—
151#407—151no—
152#343—31no—
153#343—151no—
154#343—151no—
155#343—151no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C22×C3×C5#11711yescharacteristic
160C22×C3×C5#11711yescharacteristic
161C2×C3×D5—22no—
162C2×C3×D5—22no—
163C2×C3×D5—22no—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C3×C4×C5#12311yescharacteristic
167C3×C4×C5#12311yescharacteristic
168C3×C4×C5#12311yescharacteristic
169C3×C4×C5#12311yescharacteristic
170Dic15—42no—
171C3×Dic5—22no—
172C5×Dic3—42no—
173C24×C3—51no—
174C22×C3×C4—51no—
175C22×C3×C4—52no—
176C22×C3×C4—52no—
177C22×C3×C4—101no—
178C22×C3×C4—101no—
179C22×C3×C4—101no—
180C22×C3×C4—101no—
181C22×C3×C4C22×D511yescharacteristic
182C22×Dic3—52no—
183C22×Dic3C4×D512yes—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—101no—
187C3×M16—101no—
188C2×C3×C8—21no—
189C2×C3×C8—101no—
190#217—104no—
191C4⋊Dic3—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3—101no—
194C4⋊Dic3—101no—
195C4×Dic3—104no—
196#208—21no—
197#208—21no—
198#208—101no—
199#208—101no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—101no—
202C23×C5C2×C4×D311yescharacteristic
203C22×D5—21no—
204C22×D5—21no—
205C22×D5—41no—
206C22×D5—41no—
207C22×D5(C2×D3)⋊C412yes—
208C2×C4×C5—62no—
209C2×C4×C5—122no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5#23711yescharacteristic
212C2×C4×C5#23711yescharacteristic
213C2×C4×C5#23711yescharacteristic
214C2×C4×C5#23711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×Dic5—21no—
217C2×Dic5—21no—
218C2×Dic5—62no—
219C2×Dic5—122no—
220C2×Dic5(C2×D3)⋊C412yes—
221C4×D5—22no—
222C4×D5—22no—
223C4×D5—22no—
224C4×D5—22no—
225C5×C8—41no—
226C5×C8—121no—
227#168—41no—
228#168—121no—
229C23×C4—51no—
230C2×M16—31no—
231C2×M16—51no—
232C2×M16—151no—
233C2×M16D3×D511yescharacteristic
234#117—302no—
235#117—302no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—151no—
238C2×C22⋊C4—152no—
239C2×C42—152no—
240C22⋊C8—102no—
241C22⋊C8—302no—
242C2×C3×C5—21no—
243C2×C3×C5—21no—
244C2×C3×C5#38111yescharacteristic
245C2×C3×C5#41311yescharacteristic
246C2×C3×C5#41311yescharacteristic
247C3×D5—42no—
248C23×C3—52no—
249C23×C3—101no—
250C23×C3—101no—
251C23×C3—201no—
252C23×C3—201no—
253C23×C3C2×C4×D511yescharacteristic
254C2×C3×C4—52no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—102no—
258C2×C3×C4—102no—
259C2×C3×C4—102no—
260C2×C3×C4—102no—
261C2×C3×C4#70911yescharacteristic
262C2×C3×C4#70911yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4#71111yescharacteristic
266C2×C3×C4#71311yescharacteristic
267C2×Dic3—22no—
268C2×Dic3—42no—
269C2×Dic3—102no—
270C2×Dic3—202no—
271C3×C8—41no—
272C3×C8—201no—
273C3⋊C8—41no—
274C3⋊C8—201no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5#87711yescharacteristic
278C22×C5#87711yescharacteristic
279C22×C5C2×(C2×D3)⋊C411yescharacteristic
280C2×D5—22no—
281C2×D5—22no—
282C2×D5—22no—
283C2×D5—42no—
284C2×D5—42no—
285C4×C5—122no—
286C4×C5#88611yescharacteristic
287C4×C5#88611yescharacteristic
288C4×C5#93511yescharacteristic
289C4×C5#93511yescharacteristic
290Dic5—22no—
291Dic5—122no—
292C24—51no—
293C22×C4—32no—
294C22×C4—51no—
295C22×C4—52no—
296C22×C4—52no—
297C22×C4—101no—
298C22×C4—101no—
299C22×C4—101no—
300C22×C4—101no—
301C22×C4—152no—
302C22×C4C2×D3×D511yescharacteristic
303M16—21no—
304M16—21no—
305M16—61no—
306M16—61no—
307M16—101no—
308M16—101no—
309M16—301no—
310M16—301no—
311C2×C8—21no—
312C2×C8—61no—
313C2×C8—101no—
314C2×C8—301no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C22⋊C4—304no—
320C42—304no—
321C3×C5#182211yescharacteristic, complemented, Hall
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—102no—
325C22×C3—102no—
326C22×C3—102no—
327C22×C3—202no—
328C22×C3—202no—
329C22×C3#401811yescharacteristic
330C22×C3D5×C22⋊C411yescharacteristic
331C22×C3#403811yescharacteristic
332C3×C4—102no—
333C3×C4#402911yescharacteristic
334C3×C4#402911yescharacteristic
335C3×C4#404011yescharacteristic
336C3×C4#404011yescharacteristic
337Dic3—42no—
338Dic3—202no—
339C2×C5—21no—
340C2×C5—21no—
341C2×C5#494311yescharacteristic
342C2×C5#513211yescharacteristic
343C2×C5#513211yescharacteristic
344D5—42no—
345C23—52no—
346C23—101no—
347C23—101no—
348C23—201no—
349C23—201no—
350C23C4×D3×D511yescharacteristic
351C2×C4—52no—
352C2×C4—62no—
353C2×C4—101no—
354C2×C4—101no—
355C2×C4—102no—
356C2×C4—102no—
357C2×C4—102no—
358C2×C4—102no—
359C2×C4—122no—
360C2×C4—302no—
361C2×C4—602no—
362C2×C4#676511yescharacteristic
363C2×C4#676611yescharacteristic
364C2×C4D5×D1211yescharacteristic
365C2×C4#677911yescharacteristic
366C2×C4#678011yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C8—41no—
369C8—121no—
370C8—201no—
371C8—601no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—202no—
375C2×C3#6495311yescharacteristic
376C2×C3#6503411yescharacteristic
377C2×C3#6504011yescharacteristic
378C5#6997411yescharacteristic, complemented, Sylow
379C22—21no—
380C22—21no—
381C22—102no—
382C22—102no—
383C22—102no—
384C22—202no—
385C22—202no—
386C22#9139311yescharacteristic
387C22#9139411yescharacteristic
388C22D5×(C2×D3)⋊C411yescharacteristic
389C4—102no—
390C4—122no—
391C4—602no—
392C4#9140711yescharacteristic
393C4#9141311yescharacteristic
394C4#9141411yescharacteristic
395C4#9154811yescharacteristic
396C3#1059978411yescharacteristic, complemented, Sylow
397C2—21no—
398C2—21no—
399C2—202no—
400C2#1174823011yescharacteristic
401C2#1174823111yescharacteristic
402C2#1174887111yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11746375C2semidirect
5. C5×#4554C2semidirect
6. #11745987C2semidirect
7. #11745986C2semidirect
65. #4554D5semidirect
321. C3×C5#1822semidirect
378. C5#69974semidirect
396. C3#10599784semidirect

Maximal subgroups

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

subgroupindex
C2×#913582
C3×#654152
#117483412
#117463752
C5×#45542
#117459872
#117459862
#105997843
#699745