Finite Group Databasebeta

← #14295668

Subgroups — #14295668

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#235C211yesmaximal, characteristic
2C2×C5×#825C211yesmaximal, characteristic
3C3×M16×Dic5C211yesmaximal, characteristic, complemented
4#11748611C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic
6#11746376C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10601147—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16Dic5×#67—22no—
17Dic5×D12C412yescomplemented
18C4×D3×Dic5—21no—
19#91371—21no—
20Dic5×Dic6C412yescomplemented
21C5×#825C414yescomplemented
22C3×#3947—21no—
23C3×C8×Dic5—21no—
24#90994—22no—
25#90978C414yescomplemented
26#69866—51nomaximal, Hall
27#41×Dic5—31no—
28C2×C5×#104—31no—
29C2×#3969—31no—
30M16×Dic5D311yescharacteristic, complemented
31#65221—31no—
32#64775—31no—
33#64743—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C2×C5×#67—21no—
37C22×C5×Dic3—21no—
38C5×#235—21no—
39C5×#235—21no—
40C5×#235C2×C412yes—
41C5×#235C2×C412yes—
42C2×C5×D12C2×C411yescharacteristic
43C2×C4×C5×D3—21no—
44C2×C5×Dic6C2×C411yescharacteristic
45C22×C3×Dic5D412yes—
46C2×D3×Dic5—22no—
47C3×C5×M16—21no—
48C3×C5×M16C2×C412yescomplemented
49C2×C3×C5×C8—21no—
50#6719—21no—
51C4⋊Dic15C2×C412yes—
52C4×Dic15—21no—
53C4×Dic15—21no—
54C4×Dic15C2×C412yescomplemented
55C4×C5×Dic3—21no—
56C4×C5×Dic3C2×C412yescomplemented
57C3×C4×Dic5C2×C412yes—
58C3×C4×Dic5D411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×#681—21no—
61C3×#681C2×C412yescomplemented
62C2×C3×#168—21no—
63Dic3⋊Dic5—22no—
64(C2×D3)⋊Dic5—22no—
65Dic3×Dic5—22no—
66C4×#235—51no—
67C3×C4×M16—51no—
68C2×#825—51no—
69C2×#825D511yescharacteristic
70#4932—51no—
71#4555—51no—
72#4555—51no—
73C2×C5×#41—31no—
74C2×C5×M16C2×D311yescharacteristic
75C2×C42×C5—31no—
76Q8×Dic5—32no—
77D4×Dic5—32no—
78D4×Dic5—62no—
79#4072—31no—
80#4072—61no—
81C2×C4×Dic5—31no—
82C2×C4×Dic5—61no—
83C2×C4×Dic5C2×D311yescharacteristic
84C2×#681C2×D311yescharacteristic
85C5×#104—34no—
86#3969—34no—
87#3963—62no—
88#3947—21no—
89C8×Dic5—21no—
90#1759—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C5×D3—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×Dic15—22no—
100C2×Dic15—22no—
101C2×Dic15—42no—
102C5×#67—22no—
103C5×#67—22no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3—42no—
107C5×D12—21no—
108C5×D12C4212yes—
109C4×C5×D3—22no—
110C4×C5×D3—22no—
111C5×Dic6—21no—
112C5×Dic6C4212yes—
113C2×C3×Dic5—42no—
114C2×C3×Dic5C22⋊C412yes—
115C2×C3×Dic5C22⋊C412yes—
116D3×Dic5—44no—
117C3×C5×C8—22no—
118C3×#168—22no—
119C2×#235C2×D511yescharacteristic
120C2×C3×M16—51no—
121C2×C3×M16C2×D511yescharacteristic
122C2×C3×C42—51no—
123C4×#67—102no—
124#926—51no—
125C2×C4×Dic3—51no—
126C2×C4×Dic3C2×D511yescharacteristic
127C4×D12—52no—
128#872—101no—
129C42×D3—101no—
130C4×Dic6—52no—
131C3×#97—101no—
132C3×C4×C8—101no—
133C3⋊#95—102no—
134#825—54no—
135#825Dic514yescomplemented
136C5×#41—32no—
137C5×#41—32no—
138C5×#41—61no—
139C5×#41—61no—
140C2×C5×Q8—31no—
141C2×C5×D4—31no—
142C2×C5×D4—61no—
143C22×C4×C5—61no—
144C22×C4×C5—61no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—61no—
147C22×Dic5—62no—
148C22×Dic5D1212yes—
149C5×M16—21no—
150C5×M16C4×D312yescomplemented
151C2×C5×C8—21no—
152C42×C5—32no—
153C42×C5—61no—
154C22⋊Dic5—61no—
155C22⋊Dic5—62no—
156C4⋊Dic5—32no—
157C4⋊Dic5—62no—
158C4×Dic5—32no—
159C4×Dic5—61no—
160C4×Dic5—61no—
161C4×Dic5—62no—
162C4×Dic5C4×D312yes—
163C4×Dic5#6711yescharacteristic
164C4×Dic5#6711yescharacteristic
165#681—21no—
166#681C4×D312yescomplemented
167C2×#168—21no—
168C4×#41—151no—
169C2×#104—31no—
170C2×#104—151no—
171C4×M16—51no—
172#376—151no—
173#339—151no—
174#339—151no—
175C22×C3×C5—22no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5C4×D411yescharacteristic
178C22×C3×C5C4×D411yescharacteristic
179C2×C5×D3—22no—
180C2×C5×D3—42no—
181C3×C4×C5C2×C4211yescharacteristic
182C3×C4×C5#11711yescharacteristic
183C3×C4×C5C4×D411yescharacteristic
184C3×C4×C5C4×D411yescharacteristic
185Dic15—42no—
186Dic15—42no—
187C3×Dic5—22no—
188C3×Dic5—22no—
189C5×Dic3—22no—
190C5×Dic3—42no—
191C22×C3×C4—52no—
192C22×C3×C4C22×D511yescharacteristic
193C2×#67—21no—
194C22×Dic3—21no—
195C22×Dic3—101no—
196#235—21no—
197#235—21no—
198#235C4×D512yes—
199#235C2×Dic512yes—
200C2×D12C4×D511yescharacteristic
201C2×C4×D3—21no—
202C2×C4×D3—102no—
203C2×Dic6C4×D511yescharacteristic
204C3×M16—21no—
205C3×M16—52no—
206C3×M16—101no—
207C3×M16C2×Dic512yescomplemented
208C2×C3×C8—21no—
209C2×C3×C8—101no—
210C3×C42—52no—
211C3×C42—51no—
212C3×C42—51no—
213#217—101no—
214(C2×D3)⋊C4—102no—
215C4⋊Dic3—52no—
216Dic3⋊C4—102no—
217C4×Dic3—21no—
218C4×Dic3—52no—
219C4×Dic3—102no—
220C4×Dic3—101no—
221C4×Dic3—101no—
222C4×Dic3C2×Dic512yescomplemented
223C23×C5—61no—
224C23×C5C2×D1211yescharacteristic
225C5×Q8—32no—
226C5×Q8—61no—
227C5×D4—32no—
228C5×D4—62no—
229C5×D4—62no—
230C5×D4—61no—
231C2×C4×C5—61no—
232C2×C4×C5—62no—
233C2×C4×C5—62no—
234C2×C4×C5—62no—
235C2×C4×C5—122no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5#23511yescharacteristic
240C2×C4×C5#23511yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C2×Dic5—42no—
243C2×Dic5—62no—
244C2×Dic5—62no—
245C2×Dic5—124no—
246C2×Dic5—122no—
247C2×Dic5(C2×D3)⋊C412yes—
248C2×Dic5(C2×D3)⋊C412yes—
249C5×C8—22no—
250#168—22no—
251C2×#41—31no—
252C2×M16—51no—
253C2×M16D3×D511yescharacteristic
254C4×Q8—152no—
255C4×D4—152no—
256C4×D4—302no—
257#117—151no—
258#117—301no—
259C2×C42—31no—
260C2×C42—51no—
261C2×C42—151no—
262C2×C42—301no—
263#104—34no—
264#104—154no—
265#97—101no—
266C4×C8—101no—
267#95—302no—
268C2×C3×C5—21no—
269C2×C3×C5—21no—
270C2×C3×C5C4×C22⋊C411yescharacteristic
271C2×C3×C5#42112yes—
272C5×D3—42no—
273C23×C3D4×D511yescharacteristic
274C22×D3—21no—
275C2×C3×C4—52no—
276C2×C3×C4—52no—
277C2×C3×C4—202no—
278C2×C3×C4C2×C4×D511yescharacteristic
279C2×C3×C4C2×C4×D511yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4#71111yescharacteristic
282C2×C3×C4#71111yescharacteristic
283C2×C3×C4C22×Dic511yescharacteristic
284#67—22no—
285#67—22no—
286C2×Dic3—21no—
287C2×Dic3—22no—
288C2×Dic3—42no—
289C2×Dic3—102no—
290C2×Dic3—102no—
291C2×Dic3—202no—
292D12—21no—
293D12C4×Dic512yes—
294C4×D3—22no—
295C4×D3—22no—
296C4×D3—204no—
297Dic6—21no—
298Dic6C4×Dic512yes—
299C3×C8—22no—
300C3×C8—102no—
301C22×C5—22no—
302C22×C5—62no—
303C22×C5—122no—
304C22×C5C4×D1211yescharacteristic
305C22×C5C4×D1211yescharacteristic
306C22×C5C2×(C2×D3)⋊C411yescharacteristic
307C4×C5—62no—
308C4×C5—122no—
309C4×C5C42×D311yescharacteristic
310C4×C5#87211yescharacteristic
311C4×C5C4×#6711yescharacteristic
312C4×C5C4×#6711yescharacteristic
313Dic5—22no—
314Dic5—22no—
315Dic5—122no—
316Dic5—122no—
317#41—32no—
318#41—32no—
319#41—61no—
320#41—61no—
321C2×Q8—31no—
322C2×D4—31no—
323C2×D4—61no—
324C22×C4—52no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4—302no—
328C22×C4—301no—
329C22×C4C2×D3×D511yescharacteristic
330M16—21no—
331M16—52no—
332M16—101no—
333M16D3×Dic512yescomplemented
334C2×C8—21no—
335C2×C8—101no—
336C4⋊C4—152no—
337C4⋊C4—302no—
338C22⋊C4—302no—
339C22⋊C4—301no—
340C42—32no—
341C42—52no—
342C42—51no—
343C42—51no—
344C42—61no—
345C42—152no—
346C42—302no—
347C42—301no—
348C42—301no—
349C3×C5#175911yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#402711yescharacteristic
353C22×C3D4×Dic511yescharacteristic
354C2×D3—22no—
355C2×D3—42no—
356C3×C4—102no—
357C3×C4—102no—
358C3×C4#402311yescharacteristic
359C3×C4#402711yescharacteristic
360C3×C4C2×C4×Dic511yescharacteristic
361C3×C4D4×Dic511yescharacteristic
362Dic3—22no—
363Dic3—42no—
364Dic3—202no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5—122no—
369C2×C5C4×(C2×D3)⋊C411yescharacteristic
370C2×C5#513912yes—
371C23—61no—
372C23D5×D1211yescharacteristic
373Q8—32no—
374Q8—61no—
375D4—32no—
376D4—62no—
377D4—62no—
378D4—61no—
379C2×C4—52no—
380C2×C4—52no—
381C2×C4—61no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—122no—
386C2×C4—202no—
387C2×C4—302no—
388C2×C4—302no—
389C2×C4—604no—
390C2×C4—602no—
391C2×C4#677211yescharacteristic
392C2×C4C4×D3×D511yescharacteristic
393C2×C4C4×D3×D511yescharacteristic
394C2×C4C2×D3×Dic511yescharacteristic
395C2×C4#678211yescharacteristic
396C2×C4D5×#6711yescharacteristic
397C8—22no—
398C8—102no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3#6511012yes—
402C2×C3C22⋊C4×Dic511yescharacteristic
403D3—42no—
404C5#6986611yescharacteristic, complemented, Sylow
405C22—22no—
406C22—62no—
407C22—122no—
408C22#9140511yescharacteristic
409C22Dic5×D1211yescharacteristic
410C22D5×(C2×D3)⋊C411yescharacteristic
411C4—62no—
412C4—102no—
413C4—102no—
414C4—122no—
415C4—602no—
416C4—602no—
417C4C4×D3×Dic511yescharacteristic
418C4#9139811yescharacteristic
419C4#9144011yescharacteristic
420C4Dic5×#6711yescharacteristic
421C3#1060114711yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—122no—
425C2#1174822912yes—
426C2Dic5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1759
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×M16×Dic5C2semidirect
4. #11748611C2semidirect
6. #11746376C2semidirect
7. #11745976C2semidirect
17. Dic5×D12C4semidirect
20. Dic5×Dic6C4semidirect
21. C5×#825C4semidirect
25. #90978C4semidirect
30. M16×Dic5D3semidirect
48. C3×C5×M16C2×C4semidirect
54. C4×Dic15C2×C4semidirect
56. C4×C5×Dic3C2×C4semidirect
61. C3×#681C2×C4semidirect
135. #825Dic5semidirect
150. C5×M16C4×D3semidirect
166. #681C4×D3semidirect
207. C3×M16C2×Dic5semidirect
222. C4×Dic3C2×Dic5semidirect
333. M16D3×Dic5semidirect
349. C3×C5#1759semidirect
404. C5#69866semidirect
421. C3#10601147semidirect

Maximal subgroups

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

subgroupindex
Dic5×#2352
C2×C5×#8252
C3×M16×Dic52
#117486112
C2×#909782
#117463762
#117459762
#106011473
#698665