Finite Group Databasebeta

← #14282823

Subgroups — #14282823

Order 1920.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756550C211yesmaximal, characteristic
2C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
3C4×#6719C211yesmaximal, characteristic, complemented
4#11746291C212yesmaximal, complemented
5#11746288C212yesmaximal, complemented
6#10600735—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C411yescharacteristic, complemented
9C22×C3×C5×C8—21no—
10#91842—21no—
11C2×#6719—21no—
12#91819C411yescharacteristic, complemented
13#91819C2211yescharacteristic
14#91818—21no—
15C4×#1220—21no—
16C4×#1220—21no—
17#91815C411yescharacteristic, complemented
18#91813C411yescharacteristic, complemented
19#91813C2211yescharacteristic
20C2×C4×Dic15—21no—
21C3×C5×C22⋊C8—21no—
22C3×C5×C22⋊C8C2212yes—
23#91115C2212yes—
24#69942—51nomaximal, Hall
25#66125—31no—
26C2×C5×C22⋊C8D311yescharacteristic, complemented
27C4×C22⋊Dic5—31no—
28#64690—32no—
29#64687—32no—
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×#1220—21no—
40C2×#1220—21no—
41C22×Dic15—22no—
42#6817—42no—
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×Dic30C2×C411yescharacteristic
46C2×C3×C5×C8—22no—
47C2×C3×C5×C8—42no—
48#6719—24no—
49#6719—21no—
50#6719—21no—
51#6719—21no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15C2×C411yescharacteristic
55C4⋊Dic15C2×C411yescharacteristic
56#6712—21no—
57#6712—21no—
58C4×Dic15—21no—
59C4×Dic15—42no—
60#5791—51no—
61C2×C3×C22⋊C8D511yescharacteristic, complemented
62C4×#217—51no—
63#4470—52no—
64#4467—52no—
65C23×C4×C5C2×D311yescharacteristic
66C2×#709—31no—
67C22×C5×C8—21no—
68#4099—61no—
69C2×C22⋊Dic5—61no—
70#4076—31no—
71#4076—31no—
72#4075—61no—
73C4×C22⋊D5—61no—
74C4×C22⋊D5—61no—
75#4072—31no—
76#4070—31no—
77#4070—31no—
78C2×C4×Dic5—61no—
79C5×C22⋊C8—21no—
80C5×C22⋊C8C2×D312yes—
81#3963—32no—
82#1501—151noSylow
83C23×C3×C5—22no—
84C23×C3×C5—22no—
85C23×C3×C5—41no—
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×D15—21no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100#1220—42no—
101#1220—42no—
102#1220—42no—
103C2×Dic15—24no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—42no—
108C2×Dic15—42no—
109D60—41no—
110C4×D15—42no—
111Dic30—41no—
112C3×C5×C8—42no—
113C23×C3×C4C2×D511yescharacteristic
114C2×#235—51no—
115C22×C3×C8—21no—
116#953—101no—
117C2×#217—101no—
118#930—51no—
119#930—51no—
120#929—101no—
121C4×#67—101no—
122C4×#67—101no—
123#926—51no—
124#924—51no—
125#924—51no—
126C2×C4×Dic3—101no—
127C3×C22⋊C8—21no—
128C3×C22⋊C8C2×D512yes—
129C3⋊#95—52no—
130C24×C5D1211yescharacteristic
131C22×C4×C5—42no—
132C22×C4×C5C4×D311yescharacteristic
133C22×C4×C5C4×D311yescharacteristic
134C22×C4×C5D1211yescharacteristic
135C22×C4×C5#6711yescharacteristic
136C22×C4×C5#6711yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C2×C22⋊D5—61no—
139C2×C22⋊D5—61no—
140C2×C22⋊D5—61no—
141C22×Dic5—62no—
142#709—122no—
143C2×D20—31no—
144C2×C4×D5—61no—
145C2×Dic10—31no—
146C2×C5×C8—22no—
147C2×C5×C8—42no—
148C22⋊Dic5—64no—
149C22⋊Dic5—61no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152#685—61no—
153#685—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—31no—
156#683—61no—
157#683—61no—
158C4×Dic5—61no—
159C4×Dic5—122no—
160#525—151no—
161C2×C22⋊C8D1511yescharacteristic, complemented
162C4×C22⋊C4—151no—
163#328—152no—
164#327—152no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—44no—
173C22×C3×C5#10412yes—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C22×C3×C5#13512yes—
176C2×D15—41no—
177C2×D15—41no—
178C2×D15—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—21no—
182C3×C4×C5#9912yes—
183Dic15—44no—
184Dic15—41no—
185Dic15—41no—
186Dic15—41no—
187C24×C3D2011yescharacteristic
188C22×C3×C4—42no—
189C22×C3×C4C4×D511yescharacteristic
190C22×C3×C4C4×D511yescharacteristic
191C22×C3×C4D2011yescharacteristic
192C22×C3×C4C22⋊D511yescharacteristic
193C22×C3×C4C22⋊D511yescharacteristic
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—101no—
196C2×#67—101no—
197C2×#67—101no—
198C22×Dic3—102no—
199#235—202no—
200C2×D12—51no—
201C2×C4×D3—101no—
202C2×Dic6—51no—
203C2×C3×C8—22no—
204C2×C3×C8—42no—
205#217—104no—
206#217—101no—
207#217—101no—
208#217—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3—51no—
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215C4×Dic3—101no—
216C4×Dic3—202no—
217C23×C5—22no—
218C23×C5—22no—
219C23×C5—41no—
220C23×C5(C2×D3)⋊C411yescharacteristic
221C23×C5(C2×D3)⋊C411yescharacteristic
222C23×C5C2×D1211yescharacteristic
223C22×D5—61no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5(C2×D3)⋊C411yescharacteristic
231C2×C4×C5(C2×D3)⋊C411yescharacteristic
232C2×C4×C5C2×C4×D311yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C22⋊D5—122no—
235C22⋊D5—122no—
236C22⋊D5—122no—
237C2×Dic5—64no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241C2×Dic5—122no—
242C2×Dic5—122no—
243D20—121no—
244C4×D5—122no—
245Dic10—121no—
246C5×C8—42no—
247C2×#41—151no—
248C23×C4C2×D1511yescharacteristic
249C22×C8—21no—
250#123—301no—
251C22⋊Q8—151no—
252C22⋊Q8—151no—
253#121—151no—
254#121—151no—
255#120—301no—
256C4×D4—301no—
257C4×D4—301no—
258#117—151no—
259C2×C22⋊C4—301no—
260C2×C42—301no—
261C22⋊C8—21no—
262C22⋊C8C2×D1512yes—
263#95—152no—
264C2×C3×C5—22no—
265C2×C3×C5—22no—
266C2×C3×C5—41no—
267C2×C3×C5C2×#9911yescharacteristic
268C2×C3×C5#41611yescharacteristic
269C2×C3×C5C2×#10411yescharacteristic
270D15—81no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—41no—
274C23×C3#68511yescharacteristic
275C23×C3#68511yescharacteristic
276C23×C3C2×D2011yescharacteristic
277C22×D3—101no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4#68511yescharacteristic
285C2×C3×C4#68511yescharacteristic
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288#67—202no—
289#67—202no—
290#67—202no—
291C2×Dic3—104no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—101no—
295C2×Dic3—202no—
296C2×Dic3—202no—
297D12—201no—
298C4×D3—202no—
299Dic6—201no—
300C3×C8—42no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—44no—
309C22×C5#82512yes—
310C22×C5#90412yes—
311C22×C5C2×(C2×D3)⋊C411yescharacteristic
312C2×D5—121no—
313C2×D5—121no—
314C2×D5—121no—
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—21no—
318C4×C5#80612yes—
319Dic5—124no—
320Dic5—121no—
321Dic5—121no—
322Dic5—121no—
323C24D6011yescharacteristic
324#41—602no—
325C2×Q8—151no—
326C2×D4—151no—
327C2×D4—301no—
328C2×D4—301no—
329C2×D4—301no—
330C22×C4—42no—
331C22×C4—302no—
332C22×C4—301no—
333C22×C4C4×D1511yescharacteristic
334C22×C4C4×D1511yescharacteristic
335C22×C4D6011yescharacteristic
336C22×C4#122011yescharacteristic
337C22×C4#122011yescharacteristic
338C22×C4C22×D1511yescharacteristic
339C2×C8—22no—
340C2×C8—42no—
341C4⋊C4—151no—
342C4⋊C4—151no—
343C4⋊C4—301no—
344C4⋊C4—301no—
345C22⋊C4—304no—
346C22⋊C4—301no—
347C22⋊C4—301no—
348C22⋊C4—301no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C42—301no—
352C42—602no—
353C3×C5#150111yescharacteristic, complemented, Hall
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—44no—
362C22×C3#395712yes—
363C22×C3#405012yes—
364C22×C3C2×#68511yescharacteristic
365C2×D3—201no—
366C2×D3—201no—
367C2×D3—201no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4#393812yes—
372Dic3—204no—
373Dic3—201no—
374Dic3—201no—
375Dic3—201no—
376C2×C5—22no—
377C2×C5—22no—
378C2×C5—41no—
379C2×C5C2×#80611yescharacteristic
380C2×C5#511311yescharacteristic
381C2×C5C2×#82511yescharacteristic
382D5—241no—
383C23—22no—
384C23—22no—
385C23—41no—
386C23—301no—
387C23#671411yescharacteristic
388C23#671411yescharacteristic
389C23C2×D6011yescharacteristic
390Q8—601no—
391D4—601no—
392D4—602no—
393D4—602no—
394D4—602no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—304no—
402C2×C4—301no—
403C2×C4—301no—
404C2×C4—301no—
405C2×C4—602no—
406C2×C4—602no—
407C2×C4—602no—
408C2×C4#671411yescharacteristic
409C2×C4#671411yescharacteristic
410C2×C4C2×C4×D1511yescharacteristic
411C2×C4C2×#122011yescharacteristic
412C8—42no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—41no—
416C2×C3C2×#393811yescharacteristic
417C2×C3#6540211yescharacteristic
418C2×C3C2×#395711yescharacteristic
419D3—401no—
420C5#6994211yescharacteristic, complemented, Sylow
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—601no—
430C22—601no—
431C22—601no—
432C22#9110912yes—
433C22#9179312yes—
434C22C2×#671411yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—604no—
439C4—601no—
440C4—601no—
441C4—601no—
442C4#9109012yes—
443C3#1060073511yescharacteristic, complemented, Sylow
444C2—22no—
445C2—22no—
446C2—41no—
447C2—1201no—
448C2C2×#9109011yescharacteristic
449C2#1175121411yescharacteristic
450C2C2×#9110911yescharacteristic
subgroupG/H
centerC2×C4#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×C22⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C22⋊C8D15
hypocenterC3×C5#1501
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×C22⋊C8C2semidirect
3. C4×#6719C2semidirect
4. #11746291C2semidirect
5. #11746288C2semidirect
8. C2×#6817C4semidirect
12. #91819C4semidirect
17. #91815C4semidirect
18. #91813C4semidirect
26. C2×C5×C22⋊C8D3semidirect
61. C2×C3×C22⋊C8D5semidirect
161. C2×C22⋊C8D15semidirect
353. C3×C5#1501semidirect
420. C5#69942semidirect
443. C3#10600735semidirect

Maximal subgroups

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

subgroupindex
#117565502
C2×C3×C5×C22⋊C82
C4×#67192
#117462912
#117462882
#106007353
#699425