Finite Group Databasebeta

← #14284122

Subgroups — #14284122

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
1#11756238C211yesmaximal, characteristic
2C3×C4×C5×M16C211yesmaximal, characteristic, complemented
3#11751027C211yesmaximal, characteristic, complemented
4#11746286C212yesmaximal, complemented
5#11746285C212yesmaximal, complemented
6#10600654—31nomaximal, Hall
7C2×C3×C5×M16—21no—
8C2×C3×C42×C5C2211yescharacteristic
9#91819C411yescharacteristic
10#91818—21no—
11C4×#1220—21no—
12#91813C411yescharacteristic
13#91765—21no—
14#91764C2211yescharacteristic
15C4×D60C411yescharacteristic
16#91761—21no—
17#91759C2211yescharacteristic
18C4×Dic30C411yescharacteristic
19C3×C5×#97C2212yes—
20C3×C4×C5×C8—21no—
21#91114—21no—
22C4⋊(C3⋊#168)—21no—
23#91087C2212yes—
24#69861—51nomaximal, Hall
25#65813—31no—
26C4×C5×M16D311yescharacteristic, complemented
27#65215—31no—
28#64685—32no—
29#64684—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×C5×M16—24no—
38C2×C3×C5×C8—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C3×C42×C5C2311yescharacteristic
43#6719—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C4⋊Dic15C2×C411yescharacteristic
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—22no—
56#5479—51no—
57C3×C4×M16D511yescharacteristic, complemented
58#4926—51no—
59#4465—52no—
60#4464—52no—
61C2×C5×M16—21no—
62C2×C42×C5C2×D311yescharacteristic
63#4076—31no—
64#4075—61no—
65C4×C22⋊D5—61no—
66#4070—31no—
67#4022—61no—
68#4021—31no—
69C4×D20—31no—
70#4018—61no—
71#4016—31no—
72C4×Dic10—31no—
73C5×#97C2×D312yes—
74C4×C5×C8—21no—
75C22⋊#168—61no—
76C4⋊#168—61no—
77#3935—32no—
78#1529—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C22×D15—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
90#1220—42no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94D60—41no—
95C4×D15—42no—
96Dic30—41no—
97C3×C5×C8—24no—
98C3⋊#168—42no—
99C2×C3×M16—21no—
100C2×C3×C42C2×D511yescharacteristic
101#930—51no—
102#929—101no—
103C4×#67—101no—
104#924—51no—
105#876—101no—
106#875—51no—
107C4×D12—51no—
108#872—101no—
109#870—51no—
110C4×Dic6—51no—
111C3×#97C2×D512yes—
112C3×C4×C8—21no—
113#830—101no—
114C4⋊(C3⋊C8)—101no—
115#803—52no—
116C22×C4×C5C4×D311yescharacteristic
117C22×C4×C5D1211yescharacteristic
118C22×C4×C5#6711yescharacteristic
119C2×C22⋊D5—61no—
120C2×D20—31no—
121C2×C4×D5—61no—
122C2×Dic10—31no—
123C5×M16—24no—
124C2×C5×C8—22no—
125C42×C5C4×D311yescharacteristic
126C42×C5D1211yescharacteristic
127C42×C5#6711yescharacteristic
128C42×C5C22×D311yescharacteristic
129C22⋊Dic5—61no—
130#685—61no—
131#685—61no—
132#685—61no—
133#685—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—31no—
136#683—61no—
137#683—61no—
138#683—61no—
139#683—61no—
140C4×Dic5—61no—
141C2×#168—62no—
142#529—151no—
143#432—151no—
144C4×M16D1511yescharacteristic, complemented
145#330—152no—
146#329—152no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×D15—41no—
152C2×D15—41no—
153C2×D15—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—
160Dic15—41no—
161Dic15—41no—
162Dic15—41no—
163C22×C3×C4C4×D511yescharacteristic
164C22×C3×C4D2011yescharacteristic
165C22×C3×C4C22⋊D511yescharacteristic
166C2×#67—101no—
167C2×D12—51no—
168C2×C4×D3—101no—
169C2×Dic6—51no—
170C3×M16—24no—
171C2×C3×C8—22no—
172C3×C42C4×D511yescharacteristic
173C3×C42D2011yescharacteristic
174C3×C42C22⋊D511yescharacteristic
175C3×C42C22×D511yescharacteristic
176#217—101no—
177(C2×D3)⋊C4—101no—
178(C2×D3)⋊C4—101no—
179(C2×D3)⋊C4—101no—
180(C2×D3)⋊C4—101no—
181C4⋊Dic3—51no—
182C4⋊Dic3—51no—
183Dic3⋊C4—101no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—102no—
189C23×C5(C2×D3)⋊C411yescharacteristic
190C22×D5—61no—
191C2×C4×C5—22no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5(C2×D3)⋊C411yescharacteristic
195C2×C4×C5(C2×D3)⋊C411yescharacteristic
196C2×C4×C5(C2×D3)⋊C411yescharacteristic
197C2×C4×C5C2×C4×D311yescharacteristic
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C22⋊D5—122no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203C2×Dic5—61no—
204D20—121no—
205C4×D5—122no—
206Dic10—121no—
207C5×C8—24no—
208#168—122no—
209C2×M16—21no—
210#126—301no—
211#125—151no—
212#124—151no—
213#123—301no—
214C22⋊Q8—151no—
215#121—151no—
216C4×Q8—151no—
217C4×D4—151no—
218C4×D4—301no—
219#117—301no—
220C2×C42C2×D1511yescharacteristic
221C4⋊C8—301no—
222C22⋊C8—301no—
223#97—152no—
224#97C2×D1512yes—
225C4×C8—21no—
226C2×C3×C5—41no—
227C2×C3×C5#41311yescharacteristic
228C2×C3×C5C2×#10411yescharacteristic
229C2×C3×C5#42111yescharacteristic
230D15—81no—
231C23×C3#68511yescharacteristic
232C22×D3—101no—
233C2×C3×C4—22no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4#68511yescharacteristic
237C2×C3×C4#68511yescharacteristic
238C2×C3×C4#68511yescharacteristic
239C2×C3×C4C2×C4×D511yescharacteristic
240C2×C3×C4C2×D2011yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242#67—202no—
243C2×Dic3—101no—
244C2×Dic3—101no—
245C2×Dic3—101no—
246D12—201no—
247C4×D3—202no—
248Dic6—201no—
249C3×C8—24no—
250C3⋊C8—202no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5C2×(C2×D3)⋊C411yescharacteristic
255C2×D5—121no—
256C2×D5—121no—
257C2×D5—121no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5#80512yes—
264Dic5—121no—
265Dic5—121no—
266Dic5—121no—
267C2×Q8—151no—
268C2×D4—151no—
269C2×D4—301no—
270C22×C4—301no—
271C22×C4C4×D1511yescharacteristic
272C22×C4D6011yescharacteristic
273C22×C4#122011yescharacteristic
274M16—24no—
275C2×C8—22no—
276C2×C8—302no—
277C4⋊C4—151no—
278C4⋊C4—151no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—301no—
284C22⋊C4—301no—
285C22⋊C4—301no—
286C22⋊C4—301no—
287C22⋊C4—301no—
288C42—301no—
289C42C4×D1511yescharacteristic
290C42D6011yescharacteristic
291C42#122011yescharacteristic
292C42C22×D1511yescharacteristic
293C3×C5#152911yescharacteristic, complemented, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3C2×#68511yescharacteristic
298C2×D3—201no—
299C2×D3—201no—
300C2×D3—201no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4#393712yes—
307Dic3—201no—
308Dic3—201no—
309Dic3—201no—
310C2×C5—41no—
311C2×C5C2×#80511yescharacteristic
312C2×C5#513211yescharacteristic
313C2×C5#513911yescharacteristic
314D5—241no—
315C23—301no—
316C23#671411yescharacteristic
317Q8—601no—
318D4—601no—
319D4—602no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—301no—
324C2×C4—301no—
325C2×C4—301no—
326C2×C4—602no—
327C2×C4#671411yescharacteristic
328C2×C4#671411yescharacteristic
329C2×C4#671411yescharacteristic
330C2×C4C2×C4×D1511yescharacteristic
331C2×C4C2×D6011yescharacteristic
332C2×C4C2×#122011yescharacteristic
333C8—24no—
334C8—602no—
335C2×C3—41no—
336C2×C3C2×#393711yescharacteristic
337C2×C3#6542111yescharacteristic
338C2×C3#6542811yescharacteristic
339D3—401no—
340C5#6986111yescharacteristic, complemented, Sylow
341C22—21no—
342C22—21no—
343C22—21no—
344C22—601no—
345C22—601no—
346C22—601no—
347C22C2×#671411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—601no—
354C4—601no—
355C4—601no—
356C4#9108912yes—
357C3#1060065411yescharacteristic, complemented, Sylow
358C2—41no—
359C2—1201no—
360C2C2×#9108911yescharacteristic
361C2#1175123311yescharacteristic
362C2#1175124011yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C4×C5×M16C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C4
cosocleC3×C42×C5C23
hypercenterC4×M16D15
hypocenterC3×C5#1529
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×M16C2semidirect
3. #11751027C2semidirect
4. #11746286C2semidirect
5. #11746285C2semidirect
26. C4×C5×M16D3semidirect
57. C3×C4×M16D5semidirect
144. C4×M16D15semidirect
293. C3×C5#1529semidirect
340. C5#69861semidirect
357. C3#10600654semidirect

Maximal subgroups

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

subgroupindex
#117562382
C3×C4×C5×M162
#117510272
#117462862
#117462852
#106006543
#698615