Finite Group Databasebeta

← #14283173

Subgroups — #14283173

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×C22⋊Q8C211yesmaximal, characteristic
2#11748719C211yesmaximal, characteristic
3#11748505C211yesmaximal, characteristic
4#11746359C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745963C211yesmaximal, characteristic, complemented
7#11745962C211yesmaximal, characteristic, complemented
8#10602481—31nomaximal, Hall
9C2×C5×D3×Q8C411yescharacteristic, complemented
10C22×C4×C5×D3C2211yescharacteristic
11C3×C5×C22⋊Q8C2211yescharacteristic
12C5×#946C411yescharacteristic, complemented
13C5×#924C2211yescharacteristic
14C5×#897C411yescharacteristic, complemented
15C5×#896—21no—
16C5×D3×C4⋊C4—21no—
17C5×D3×C4⋊C4C411yescharacteristic, complemented
18C5×D3×C22⋊C4—21no—
19C5×#878—21no—
20C2×(C2×D3)⋊Dic5—21no—
21C2×Dic3×Dic5—21no—
22C2×#6650—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27(C2×D3)⋊#168—21no—
28#68335—51nomaximal, Hall
29C2×C5×C22⋊Q8—31no—
30C4×C22⋊Dic5—31no—
31#65496—31no—
32#64758—31no—
33#64758—31no—
34#64758—31no—
35#64758D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×C5×Dic3D411yescharacteristic
41C5×D3×Q8—42no—
42C2×C4×C5×D3—21no—
43C2×C4×C5×D3—21no—
44C2×C4×C5×D3—42no—
45C2×C4×C5×D3C2×C411yescharacteristic
46C2×C4×C5×D3C2×C411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C4×C5×D3D411yescharacteristic
49C2×C5×Dic6—21no—
50C2×C5×Dic6C2×C411yescharacteristic
51C22×C3×Dic5—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C2×C3⋊#168—21no—
56C5×#217—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3C2×C411yescharacteristic
61C5×Dic3⋊C4—21no—
62C5×Dic3⋊C4—21no—
63C5×Dic3⋊C4—21no—
64C2×C3×#168—21no—
65(C2×D3)⋊Dic5—24no—
66Dic3×Dic5—42no—
67#6650—42no—
68D3×C22⋊Q8D511yescharacteristic
69#4726—51no—
70#4666—51no—
71C3×#328—51no—
72#4538—51no—
73#4467—51no—
74#4452—51no—
75C22×C5×Q8—31no—
76C23×C4×C5—31no—
77C5×C22⋊Q8—31no—
78C5×C22⋊Q8—31no—
79C5×C22⋊Q8—31no—
80C5×C22⋊Q8—61no—
81C5×C22⋊Q8—61no—
82C5×C22⋊Q8C2×D311yescharacteristic
83C2×C5×C4⋊C4—31no—
84C2×C5×C4⋊C4—61no—
85C2×C5×C22⋊C4—61no—
86C2×C22⋊Dic5—61no—
87C2×C4×Dic5—61no—
88C2×#681—61no—
89#3963—31no—
90#3963C2×D311yescharacteristic
91C22⋊#168—31no—
92C22⋊#168—61no—
93C22⋊#168C2×D311yescharacteristic
94#1508—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—22no—
99C22×C5×D3—41no—
100C22×C5×D3C22⋊C411yescharacteristic
101C22×C5×D3C22⋊C411yescharacteristic
102C3×C5×Q8—41no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×Dic15—22no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3C22⋊C411yescharacteristic
115C2×C5×Dic3C22⋊C411yescharacteristic
116C4×C5×D3—22no—
117C4×C5×D3—22no—
118C4×C5×D3—41no—
119C4×C5×D3—41no—
120C4×C5×D3—42no—
121C4×C5×D3—42no—
122C5×Dic6—42no—
123C5×Dic6—41no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5—41no—
127C3⋊#168—41no—
128C3×#168—41no—
129C2×D3×Q8Dic511yescharacteristic, complemented
130C22×C4×D3C2×D511yescharacteristic
131C3×C22⋊Q8C2×D511yescharacteristic
132#946Dic511yescharacteristic, complemented
133C2×(C2×D3)⋊C4—101no—
134#924C2×D511yescharacteristic
135C2×C4×Dic3—101no—
136C2×ΓL(1,𝔽25)—101no—
137#897Dic511yescharacteristic, complemented
138#896—21no—
139D3×C4⋊C4—21no—
140D3×C4⋊C4Dic511yescharacteristic, complemented
141D3×C22⋊C4—21no—
142#878—21no—
143C3×C22⋊C8—51no—
144C3×#95—51no—
145C3⋊#95—51no—
146#830—51no—
147(C2×D3)⋊C8—101no—
148C24×C5—31no—
149C2×C5×Q8—31no—
150C2×C5×Q8—61no—
151C2×C5×Q8—122no—
152C2×C5×Q8C4×D311yescharacteristic
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—31no—
158C22×C4×C5—61no—
159C22×C4×C5—61no—
160C22×C4×C5—122no—
161C22×C4×C5C22×D311yescharacteristic
162C22×Dic5—21no—
163C22×Dic5—61no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—31no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4—61no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4C4×D311yescharacteristic
171C5×C22⋊C4—21no—
172C5×C22⋊C4—61no—
173C5×C22⋊C4—61no—
174C5×C22⋊C4—61no—
175C22⋊Dic5—64no—
176C4×Dic5—122no—
177#681—122no—
178C2×#168—21no—
179C2×#168—61no—
180C2×C22⋊Q8—31no—
181#407—151no—
182C4×C22⋊C4—151no—
183#328—51no—
184#328—151no—
185#328—151no—
186#328—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#13711yescharacteristic
191C22×C3×C5#13711yescharacteristic
192C2×C5×D3—21no—
193C2×C5×D3—21no—
194C2×C5×D3—21no—
195C2×C5×D3—21no—
196C2×C5×D3—21no—
197C2×C5×D3—42no—
198C2×C5×D3—42no—
199C2×C5×D3#10412yes—
200C3×C4×C5—21no—
201C3×C4×C5—21no—
202C3×C4×C5—41no—
203C3×C4×C5—41no—
204Dic15—42no—
205C3×Dic5—42no—
206C5×Dic3—21no—
207C5×Dic3—41no—
208C5×Dic3—41no—
209C5×Dic3#9912yes—
210C23×D3C22⋊D511yescharacteristic
211C2×C3×Q8C2×Dic511yescharacteristic
212C22×C3×C4—101no—
213C22×C3×C4C22×D511yescharacteristic
214C22×Dic3—101no—
215C22×Dic3C22⋊D511yescharacteristic
216D3×Q8—42no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—42no—
220C2×C4×D3C2×Dic511yescharacteristic
221C2×C4×D3C2×Dic511yescharacteristic
222C2×C4×D3C22⋊D511yescharacteristic
223C2×C4×D3C22⋊D511yescharacteristic
224C2×Dic6—21no—
225C2×Dic6C2×Dic511yescharacteristic
226C2×C3×C8—101no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4C2×Dic511yescharacteristic
229C3×C22⋊C4—21no—
230#217—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—104no—
234C4⋊Dic3—21no—
235C4⋊Dic3C2×Dic511yescharacteristic
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238Dic3⋊C4—21no—
239C4×Dic3—202no—
240C2×C3⋊C8—101no—
241ΓL(1,𝔽25)—202no—
242C23×C5—31no—
243C23×C5—31no—
244C23×C5—62no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—121no—
248C23×C5D3×D411yescharacteristic
249C5×Q8—41no—
250C5×Q8—121no—
251C5×Q8—122no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—31no—
255C2×C4×C5—31no—
256C2×C4×C5—41no—
257C2×C4×C5—62no—
258C2×C4×C5—62no—
259C2×C4×C5—62no—
260C2×C4×C5—61no—
261C2×C4×C5—61no—
262C2×C4×C5—121no—
263C2×C4×C5—121no—
264C2×C4×C5—122no—
265C2×C4×C5—122no—
266C2×C4×C5C2×C4×D311yescharacteristic
267C2×C4×C5D3×D411yescharacteristic
268C2×Dic5—22no—
269C2×Dic5—41no—
270C2×Dic5—41no—
271C2×Dic5—62no—
272C2×Dic5—121no—
273C2×Dic5—121no—
274#168—41no—
275#168—121no—
276C22×Q8—31no—
277C23×C4—31no—
278C2×M16—301no—
279C22⋊Q8—31no—
280C22⋊Q8—31no—
281C22⋊Q8—31no—
282C22⋊Q8—61no—
283C22⋊Q8—61no—
284C22⋊Q8D3×D511yescharacteristic
285C2×C4⋊C4—31no—
286C2×C4⋊C4—61no—
287C2×C22⋊C4—61no—
288C2×C22⋊C4—301no—
289C2×C42—301no—
290C22⋊C8—51no—
291C22⋊C8—151no—
292C22⋊C8—301no—
293#95—51no—
294#95—151no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5C2×#9911yescharacteristic
298C2×C3×C5#41911yescharacteristic
299C2×C3×C5C2×#10411yescharacteristic
300C5×D3—22no—
301C5×D3—41no—
302C23×C3C2×C22⋊D511yescharacteristic
303C22×D3—21no—
304C22×D3—21no—
305C22×D3—22no—
306C22×D3—41no—
307C22×D3C22⋊Dic511yescharacteristic
308C22×D3C22⋊Dic511yescharacteristic
309C3×Q8—41no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—41no—
313C2×C3×C4—102no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4C22×Dic511yescharacteristic
317C2×C3×C4C2×C22⋊D511yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—102no—
322C2×Dic3—201no—
323C2×Dic3—201no—
324C2×Dic3C22⋊Dic511yescharacteristic
325C2×Dic3C22⋊Dic511yescharacteristic
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—41no—
329C4×D3—41no—
330C4×D3—42no—
331C4×D3—42no—
332Dic6—42no—
333Dic6—41no—
334C3×C8—201no—
335C3⋊C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—32no—
339C22×C5—61no—
340C22×C5—61no—
341C22×C5—61no—
342C22×C5—61no—
343C22×C5—61no—
344C22×C5—122no—
345C22×C5—122no—
346C22×C5D3×C22⋊C411yescharacteristic
347C22×C5#91511yescharacteristic
348C22×C5#91811yescharacteristic
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—32no—
352C4×C5—41no—
353C4×C5—41no—
354C4×C5—61no—
355C4×C5—121no—
356C4×C5—121no—
357Dic5—42no—
358Dic5—122no—
359C24—31no—
360C2×Q8—31no—
361C2×Q8—61no—
362C2×Q8—122no—
363C2×Q8D3×Dic511yescharacteristic
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—101no—
372C22×C4—122no—
373C22×C4—301no—
374C22×C4C2×D3×D511yescharacteristic
375M16—602no—
376C2×C8—101no—
377C2×C8—301no—
378C4⋊C4—21no—
379C4⋊C4—31no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—61no—
384C4⋊C4D3×Dic511yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—304no—
390C42—602no—
391C3×C5#150811yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3#408811yescharacteristic
395C22×C3#408811yescharacteristic
396C22×C3C2×C22⋊Dic511yescharacteristic
397C2×D3—21no—
398C2×D3—21no—
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—21no—
402C2×D3—42no—
403C2×D3—42no—
404C2×D3#396912yes—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—202no—
410Dic3—21no—
411Dic3—41no—
412Dic3—41no—
413Dic3—202no—
414Dic3#396612yes—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—62no—
418C2×C5—121no—
419C2×C5D3×#9911yescharacteristic
420C2×C5#480211yescharacteristic
421C2×C5D3×#10411yescharacteristic
422C23—31no—
423C23—31no—
424C23—62no—
425C23—61no—
426C23—61no—
427C23—121no—
428C23D3×C22⋊D511yescharacteristic
429Q8—41no—
430Q8—121no—
431Q8—122no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—41no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—102no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—122no—
446C2×C4—122no—
447C2×C4—201no—
448C2×C4—201no—
449C2×C4—302no—
450C2×C4—601no—
451C2×C4—601no—
452C2×C4C2×D3×Dic511yescharacteristic
453C2×C4D3×C22⋊D511yescharacteristic
454C8—201no—
455C8—601no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3C2×#396611yescharacteristic
459C2×C3#6551411yescharacteristic
460C2×C3C2×#396911yescharacteristic
461D3—22no—
462D3—41no—
463C5#6833511yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—32no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—122no—
473C22—122no—
474C22#9151811yescharacteristic
475C22#9152011yescharacteristic
476C22D3×C22⋊Dic511yescharacteristic
477C4—21no—
478C4—21no—
479C4—32no—
480C4—41no—
481C4—41no—
482C4—61no—
483C4—121no—
484C4—121no—
485C4—202no—
486C4—602no—
487C3#1060248111yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—62no—
491C2—121no—
492C2D3×#396611yescharacteristic
493C2#1174921311yescharacteristic
494C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746359C2semidirect
5. C3×#64758C2semidirect
6. #11745963C2semidirect
7. #11745962C2semidirect
9. C2×C5×D3×Q8C4semidirect
12. C5×#946C4semidirect
14. C5×#897C4semidirect
17. C5×D3×C4⋊C4C4semidirect
35. #64758D3semidirect
129. C2×D3×Q8Dic5semidirect
132. #946Dic5semidirect
137. #897Dic5semidirect
140. D3×C4⋊C4Dic5semidirect
391. C3×C5#1508semidirect
463. C5#68335semidirect
487. C3#10602481semidirect

Maximal subgroups

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

subgroupindex
C5×D3×C22⋊Q82
#117487192
#117485052
#117463592
C3×#647582
#117459632
#117459622
#106024813
#683355