Finite Group Databasebeta

← #14290638

Subgroups — #14290638

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D4×Q8C211yesmaximal, characteristic
2#11751181C211yesmaximal, characteristic, complemented
3#11751121C211yesmaximal, characteristic, complemented
4#11751120C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic
8#10602710—31nomaximal, Hall
9C22×C3×C5×Q8—21no—
10C3×C5×C4⋊Q8—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×C22⋊Q8—21no—
13C3×C5×C22⋊Q8—22no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×#6716—21no—
18#91758C2211yescharacteristic
19#91119—21no—
20#91094—21no—
21#91092—22no—
22#91092—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71917—51nomaximal, Hall
27C5×D4×Q8D311yescharacteristic
28#65368—31no—
29#65309—31no—
30#65308—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—42no—
37C2×C3×C5×Q8—42no—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C2×Dic30—21no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D412yes—
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53#6716—42no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C3×D4×Q8D511yescharacteristic
60#5080—51no—
61#5020—51no—
62#5019—51no—
63#4547—51no—
64#4535—51no—
65D4⋊(C3⋊C8)—51no—
66C22×C5×Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C5×C22⋊Q8—21no—
70C5×C22⋊Q8—22no—
71C4×C5×Q8C2×D311yescharacteristic
72C4×C5×D4—21no—
73C4×C5×D4C2×D311yescharacteristic
74C2×#687—61no—
75#4015—31no—
76#3967—61no—
77#3942—61no—
78#3940—61no—
79#3940—62no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1651—151noSylow
84C23×C3×C5—21no—
85C3×C5×Q8—21no—
86C3×C5×Q8—44no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×Q8SD1612yescomplemented
90C3×C5×D4—21no—
91C3×C5×D4SD1612yes—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—44no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×Dic15—41no—
103Dic30—41no—
104Dic30—41no—
105C3⋊#168—22no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C22×C3×Q8—21no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8—22no—
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4—21no—
115C3×C4×D4C2×D511yescharacteristic
116C2×#214—101no—
117#869—51no—
118#835—101no—
119#810—101no—
120#808—101no—
121#808—102no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C2×C5×Q8—22no—
126C2×C5×Q8—21no—
127C2×C5×Q8—42no—
128C2×C5×Q8—42no—
129C2×C5×Q8#6711yescharacteristic
130C2×C5×D4#6711yescharacteristic
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C2×Dic10—61no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C4⋊C4#6711yescharacteristic
139C5×C4⋊C4#6712yes—
140C5×C22⋊C4—22no—
141C5×C22⋊C4—21no—
142C42×C5—21no—
143C42×C5C22×D311yescharacteristic
144#687—122no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147C2×#168—61no—
148C2×#168—61no—
149C2×#168—61no—
150D4×Q8D1511yescharacteristic
151#498—151no—
152#475—151no—
153#461—151no—
154#332—151no—
155Q8⋊C8—151no—
156D4⋊C8—151no—
157C22×C3×C5—22no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5#12011yescharacteristic
161C3×C4×C5—22no—
162C3×C4×C5—21no—
163C3×C4×C5—42no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—81no—
171C2×C3×Q8—22no—
172C2×C3×Q8—21no—
173C2×C3×Q8—42no—
174C2×C3×Q8—42no—
175C2×C3×Q8C22⋊D511yescharacteristic
176C2×C3×D4C22⋊D511yescharacteristic
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C2×Dic6—101no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4C22⋊D511yescharacteristic
184C3×C4⋊C4C22⋊D512yes—
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C22⋊C4—22no—
187C3×C22⋊C4—21no—
188C3×C42—21no—
189C3×C42C22×D511yescharacteristic
190#214—202no—
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C5×Q8—21no—
198C5×Q8—44no—
199C5×Q8—41no—
200C5×Q8—41no—
201C5×Q8#21412yescomplemented
202C5×D4—21no—
203C5×D4#21512yes—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—22no—
207C2×C4×C5—21no—
208C2×C4×C5—44no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5C2×#6711yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—121no—
215Dic10—121no—
216Dic10—121no—
217#168—62no—
218#168—121no—
219#168—121no—
220C22×Q8—21no—
221C2×SD16—301no—
222C4⋊Q8—21no—
223C4⋊Q8—151no—
224C4⋊Q8C2×D1511yescharacteristic
225C22⋊Q8—21no—
226C22⋊Q8—22no—
227C4×Q8C2×D1511yescharacteristic
228C4×D4—21no—
229C4×D4C2×D1511yescharacteristic
230#106—301no—
231#106—302no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234#103—301no—
235#103—301no—
236C4×C8—151no—
237C2×C3×C5—42no—
238C2×C3×C5#44811yescharacteristic
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45611yescharacteristic
241C23×C3—21no—
242C3×Q8—21no—
243C3×Q8—44no—
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8#68712yescomplemented
247C3×D4—21no—
248C3×D4#68812yes—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—44no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4C2×C22⋊D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×Dic3—201no—
260Dic6—201no—
261Dic6—201no—
262C3⋊C8—102no—
263C3⋊C8—201no—
264C3⋊C8—201no—
265C22×C5—22no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5#95311yescharacteristic
269C4×C5—22no—
270C4×C5—21no—
271C4×C5—42no—
272C4×C5—41no—
273C4×C5—41no—
274C4×C5#93211yescharacteristic
275C4×C5C2×#21411yescharacteristic
276C4×C5C2×#21511yescharacteristic
277C4×C5#94211yescharacteristic
278Dic5—241no—
279C2×Q8—22no—
280C2×Q8—21no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—301no—
284C2×Q8#122011yescharacteristic
285C2×D4#122011yescharacteristic
286C22×C4—22no—
287C22×C4—21no—
288SD16—602no—
289C2×C8—301no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—301no—
296C4⋊C4—301no—
297C4⋊C4#122011yescharacteristic
298C4⋊C4#122011yescharacteristic
299C4⋊C4#122012yes—
300C22⋊C4—22no—
301C22⋊C4—21no—
302C42—21no—
303C42C22×D1511yescharacteristic
304C3×C5#165111yescharacteristic, complemented, Hall
305C22×C3—22no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3#409911yescharacteristic
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—42no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4#407811yescharacteristic
315C3×C4C2×#68711yescharacteristic
316C3×C4C2×#68811yescharacteristic
317C3×C4#408811yescharacteristic
318Dic3—401no—
319C2×C5—42no—
320C2×C5#521811yescharacteristic
321C2×C5#522711yescharacteristic
322C2×C5#524611yescharacteristic
323C23—21no—
324Q8—21no—
325Q8—44no—
326Q8—41no—
327Q8—41no—
328Q8—601no—
329Q8—601no—
330Q8#671612yescomplemented
331D4—21no—
332D4#671712yes—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—601no—
341C2×C4C2×#122011yescharacteristic
342C2×C4C2×#122011yescharacteristic
343C2×C4C2×#122011yescharacteristic
344C8—302no—
345C8—601no—
346C8—601no—
347C2×C3—42no—
348C2×C3#6550711yescharacteristic
349C2×C3#6551611yescharacteristic
350C2×C3#6553511yescharacteristic
351C5#7191711yescharacteristic, complemented, Sylow
352C22—22no—
353C22—41no—
354C22—41no—
355C22#9184211yescharacteristic
356C4—22no—
357C4—21no—
358C4—42no—
359C4—41no—
360C4—41no—
361C4—1201no—
362C4#9182111yescharacteristic
363C4C2×#671611yescharacteristic
364C4C2×#671711yescharacteristic
365C4#9183111yescharacteristic
366C3#1060271011yescharacteristic, complemented, Sylow
367C2—42no—
368C2#1175131911yescharacteristic
369C2#1175132811yescharacteristic
370C2#1175134711yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4×Q8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterD4×Q8D15
hypocenterC3×C5#1651
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #11751181C2semidirect
3. #11751121C2semidirect
5. #11746368C2semidirect
6. #11746356C2semidirect
89. C3×C5×Q8SD16semidirect
201. C5×Q8#214semidirect
246. C3×Q8#687semidirect
304. C3×C5#1651semidirect
330. Q8#6716semidirect
351. C5#71917semidirect
366. C3#10602710semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4×Q82
#117511812
#117511212
#117511202
#117463682
#117463562
D4⋊(C3⋊#168)2
#106027103
#719175