Finite Group Databasebeta

← #14307139

Subgroups — #14307139

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754617C211yesmaximal, characteristic
2C4×#6712C211yesmaximal, characteristic
3#11748328C211yesmaximal, characteristic
4C5×#4523C211yesmaximal, characteristic
5C3×#64743C211yesmaximal, characteristic
6#11745975C211yesmaximal, characteristic
7#11745973C211yesmaximal, characteristic
8#10599523—31nomaximal, Hall
9C2×C3×C42×C5C2211yescharacteristic
10C2×#6712—21no—
11C2×C4×Dic15C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91576—21no—
18#91576—21no—
19#91470C411yescharacteristic, complemented
20#91470C411yescharacteristic, complemented
21C4×#1204—21no—
22C4×#1204—21no—
23#91384C411yescharacteristic, complemented
24#91384C411yescharacteristic, complemented
25#91115—21no—
26#90954—21no—
27#90951—21no—
28#68730—51nomaximal, Hall
29#65851—31no—
30M16×Dic5—31no—
31C4×#683—31no—
32C5×#339—31no—
33#64775—31no—
34#64752—31no—
35#64743D311yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C22×Dic15D411yescharacteristic
41C2×#1204—21no—
42C2×#1204—21no—
43C3×C42×C5—21no—
44C3×C42×C5—21no—
45#6712—24no—
46C4×Dic15—21no—
47C4×Dic15—21no—
48C4×Dic15C2×C411yescharacteristic
49C4×Dic15C2×C411yescharacteristic
50C4×Dic15D411yescharacteristic
51C4×Dic15D411yescharacteristic
52C5×#217—21no—
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×C4⋊Dic3C2×C411yescharacteristic
55C4×C5×Dic3—21no—
56C5×#208—21no—
57C5×#208Q812yescomplemented
58C2×C5×C3⋊C8—21no—
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5C2×C411yescharacteristic
61C3×C4⋊Dic5C2×C411yescharacteristic
62C3×C4×Dic5—21no—
63C3×#681—21no—
64C3×#681Q812yescomplemented
65C2×C3×#168—21no—
66Dic3⋊Dic5—21no—
67Dic3⋊Dic5—21no—
68#6669—21no—
69#6669—21no—
70#6668—21no—
71#6668—21no—
72#5517—51no—
73Dic3×M16—51no—
74C4×Dic3⋊C4—51no—
75C3×#339—51no—
76#4555—51no—
77#4532—51no—
78#4523D511yescharacteristic
79C2×C5×M16—31no—
80C5×#117—31no—
81C2×C42×C5C2×D311yescharacteristic
82#4072C2×D311yescharacteristic
83C2×#683—61no—
84C2×C4×Dic5—31no—
85C2×C4×Dic5—31no—
86C2×#681C2×D311yescharacteristic
87#4036—31no—
88#4036—31no—
89#4034—31no—
90#4034—31no—
91#4024—61no—
92#4024—61no—
93C4×Dic10—61no—
94C4×Dic10—61no—
95#3963—61no—
96#3947—61no—
97C8×Dic5—61no—
98#1986—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—22no—
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15C22⋊C411yescharacteristic
115C2×Dic15C22⋊C411yescharacteristic
116C2×Dic15C22⋊C411yescharacteristic
117C2×Dic15C22⋊C411yescharacteristic
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122#1204—42no—
123#1204—42no—
124C3×#168—22no—
125C5×C3⋊C8—22no—
126C2×C3×M16—51no—
127C3×#117—51no—
128C2×C3×C42C2×D511yescharacteristic
129#926C2×D511yescharacteristic
130C2×Dic3⋊C4—101no—
131C2×C4×Dic3—51no—
132C2×C4×Dic3—51no—
133C2×#208C2×D511yescharacteristic
134#890—51no—
135#890—51no—
136#888—51no—
137#888—51no—
138#878—101no—
139#878—101no—
140C4×Dic6—101no—
141C4×Dic6—101no—
142C3⋊#95—101no—
143#815—101no—
144C8×Dic3—101no—
145C22×C4×C5—21no—
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—31no—
148C22×Dic5—31no—
149C22×Dic5—61no—
150C2×Dic10—61no—
151C2×Dic10—61no—
152C5×M16—32no—
153C5×M16—61no—
154C2×C5×C8—61no—
155C5×C4⋊C4—31no—
156C5×C4⋊C4—31no—
157C5×C22⋊C4—61no—
158C42×C5—21no—
159C42×C5—21no—
160C42×C5—61no—
161C22⋊Dic5—21no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164C4⋊Dic5C4×D311yescharacteristic
165C4⋊Dic5C4×D311yescharacteristic
166#683—61no—
167#683—61no—
168#683—61no—
169#683—61no—
170#683—64no—
171C4×Dic5—21no—
172C4×Dic5—31no—
173C4×Dic5—31no—
174C4×Dic5—31no—
175C4×Dic5—31no—
176C4×Dic5—61no—
177C4×Dic5—61no—
178#681—21no—
179#681Dic612yescomplemented
180C2×#168—21no—
181#533—151no—
182C4×M16—151no—
183C4×C4⋊C4—151no—
184#339—31no—
185#339—51no—
186#339—151no—
187#339—151no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C22×C3×C5#12411yescharacteristic
192C22×C3×C5C4⋊Q811yescharacteristic
193C3×C4×C5—42no—
194C3×C4×C5C4×Q811yescharacteristic
195C3×C4×C5C4×Q811yescharacteristic
196C3×C4×C5C22⋊Q811yescharacteristic
197C3×C4×C5C22⋊Q811yescharacteristic
198Dic15—21no—
199Dic15—21no—
200Dic15—21no—
201Dic15—42no—
202Dic15#10412yes—
203C3×Dic5—41no—
204C3×Dic5—41no—
205C5×Dic3—41no—
206C5×Dic3—41no—
207C22×C3×C4—21no—
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—51no—
210C22×Dic3—51no—
211C22×Dic3—101no—
212C2×Dic6—101no—
213C2×Dic6—101no—
214C3×M16—52no—
215C3×M16—101no—
216C2×C3×C8—101no—
217C3×C4⋊C4—51no—
218C3×C4⋊C4—51no—
219C3×C22⋊C4—101no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—101no—
223#217—21no—
224C4⋊Dic3—101no—
225C4⋊Dic3—101no—
226C4⋊Dic3C4×D511yescharacteristic
227C4⋊Dic3C4×D511yescharacteristic
228Dic3⋊C4—101no—
229Dic3⋊C4—101no—
230Dic3⋊C4—101no—
231Dic3⋊C4—101no—
232Dic3⋊C4—104no—
233C4×Dic3—21no—
234C4×Dic3—51no—
235C4×Dic3—51no—
236C4×Dic3—51no—
237C4×Dic3—51no—
238C4×Dic3—101no—
239C4×Dic3—101no—
240#208—21no—
241#208Dic1012yescomplemented
242C2×C3⋊C8—21no—
243C23×C5D3×D411yescharacteristic
244C2×C4×C5—22no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—61no—
248C2×C4×C5—61no—
249C2×C4×C5C2×Dic611yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23711yescharacteristic
254C2×C4×C5D3×Q811yescharacteristic
255C2×Dic5—21no—
256C2×Dic5—21no—
257C2×Dic5—31no—
258C2×Dic5—31no—
259C2×Dic5—31no—
260C2×Dic5—31no—
261C2×Dic5—62no—
262C2×Dic5—62no—
263C2×Dic5—121no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266Dic10—122no—
267Dic10—122no—
268C5×C8—62no—
269#168—22no—
270C2×M16—31no—
271C2×M16—51no—
272C4⋊Q8—151no—
273C4⋊Q8—151no—
274#125—151no—
275#125—151no—
276C22⋊Q8—301no—
277C22⋊Q8—301no—
278C4×Q8—301no—
279C4×Q8—301no—
280#117—31no—
281#117—51no—
282C2×C4⋊C4—301no—
283C2×C42—151no—
284C2×C42—151no—
285C2×C42D3×D511yescharacteristic
286#97—301no—
287C4×C8—301no—
288#95—301no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5#39111yescharacteristic
292C2×C3×C5C2×#10411yescharacteristic
293C2×C3×C5#42111yescharacteristic
294C23×C3D4×D511yescharacteristic
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4C2×Dic1011yescharacteristic
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4Q8×D511yescharacteristic
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—51no—
309C2×Dic3—51no—
310C2×Dic3—51no—
311C2×Dic3—51no—
312C2×Dic3—102no—
313C2×Dic3—102no—
314C2×Dic3—201no—
315C2×Dic3—201no—
316C2×Dic3—201no—
317Dic6—202no—
318Dic6—202no—
319C3×C8—102no—
320C3⋊C8—22no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5D3×C22⋊C411yescharacteristic
324C22×C5#88511yescharacteristic
325C22×C5#88811yescharacteristic
326C4×C5—42no—
327C4×C5—121no—
328C4×C5—121no—
329C4×C5C4×Dic611yescharacteristic
330C4×C5#87811yescharacteristic
331C4×C5#88711yescharacteristic
332C4×C5#89611yescharacteristic
333Dic5—32no—
334Dic5—41no—
335Dic5—41no—
336Dic5—61no—
337Dic5—61no—
338Dic5—61no—
339Dic5—122no—
340C2×Q8—301no—
341C2×Q8—301no—
342C22×C4—21no—
343C22×C4—151no—
344C22×C4—151no—
345C22×C4—301no—
346C22×C4C2×D3×D511yescharacteristic
347M16—32no—
348M16—52no—
349M16—61no—
350M16—101no—
351C2×C8—61no—
352C2×C8—101no—
353C4⋊C4—31no—
354C4⋊C4—31no—
355C4⋊C4—51no—
356C4⋊C4—51no—
357C4⋊C4—304no—
358C4⋊C4—301no—
359C4⋊C4—301no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—301no—
363C4⋊C4—301no—
364C22⋊C4—61no—
365C22⋊C4—101no—
366C42—21no—
367C42—21no—
368C42—61no—
369C42—101no—
370C42—151no—
371C42—151no—
372C42—151no—
373C42—151no—
374C42—301no—
375C42—301no—
376C3×C5#198611yescharacteristic, complemented, Hall
377C22×C3—21no—
378C22×C3—21no—
379C22×C3D5×C22⋊C411yescharacteristic
380C22×C3#403111yescharacteristic
381C22×C3#403411yescharacteristic
382C3×C4—42no—
383C3×C4—201no—
384C3×C4—201no—
385C3×C4C4×Dic1011yescharacteristic
386C3×C4#402411yescharacteristic
387C3×C4#403311yescharacteristic
388C3×C4#404211yescharacteristic
389Dic3—41no—
390Dic3—41no—
391Dic3—52no—
392Dic3—101no—
393Dic3—101no—
394Dic3—101no—
395Dic3—202no—
396C2×C5—21no—
397C2×C5—21no—
398C2×C5#464611yescharacteristic
399C2×C5D3×#10411yescharacteristic
400C2×C5#482111yescharacteristic
401C23#679011yescharacteristic
402Q8—602no—
403Q8—602no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—101no—
410C2×C4—101no—
411C2×C4—151no—
412C2×C4—151no—
413C2×C4—151no—
414C2×C4—151no—
415C2×C4—302no—
416C2×C4—302no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4—601no—
420C2×C4D5×Dic611yescharacteristic
421C2×C4D3×Dic1011yescharacteristic
422C2×C4C4×D3×D511yescharacteristic
423C2×C4#677711yescharacteristic
424C2×C4#677911yescharacteristic
425C2×C4#678211yescharacteristic
426C8—62no—
427C8—102no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3#6493511yescharacteristic
431C2×C3D5×#10411yescharacteristic
432C2×C3#6511011yescharacteristic
433C5#6873011yescharacteristic, complemented, Sylow
434C22—21no—
435C22—21no—
436C22#9132811yescharacteristic
437C22#9147311yescharacteristic
438C22#9152611yescharacteristic
439C4—42no—
440C4—121no—
441C4—121no—
442C4—152no—
443C4—201no—
444C4—201no—
445C4—301no—
446C4—301no—
447C4—301no—
448C4—602no—
449C4#9132311yescharacteristic
450C4#9132411yescharacteristic
451C4#9143011yescharacteristic
452C4#9143611yescharacteristic
453C3#1059952311yescharacteristic, complemented, Sylow
454C2—21no—
455C2—21no—
456C2#1174711211yescharacteristic
457C2#1174711311yescharacteristic
458C2#1174863211yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1986
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
19. #91470C4semidirect
20. #91470C4semidirect
23. #91384C4semidirect
24. #91384C4semidirect
57. C5×#208Q8semidirect
64. C3×#681Q8semidirect
179. #681Dic6semidirect
241. #208Dic10semidirect
376. C3×C5#1986semidirect
433. C5#68730semidirect
453. C3#10599523semidirect

Maximal subgroups

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

subgroupindex
#117546172
C4×#67122
#117483282
C5×#45232
C3×#647432
#117459752
#117459732
#105995233
#687305