Finite Group Databasebeta

← #14309013

Subgroups — #14309013

Order 1920.

580 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755432C211yesmaximal, characteristic
2#11751044C211yesmaximal, characteristic
3#11749473C211yesmaximal, characteristic
4#11749473C211yesmaximal, characteristic
5C5×#4527C211yesmaximal, characteristic
6C3×#64747C211yesmaximal, characteristic
7#11746020C211yesmaximal, characteristic
8#10599749—31nomaximal, Hall
9C23×Dic15C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C2×C5×#217C2211yescharacteristic
13C2×C5×#217C2211yescharacteristic
14C2×C3×C22⋊Dic5C2211yescharacteristic
15C2×C3×C22⋊Dic5C2211yescharacteristic
16#91576—22no—
17#91575—22no—
18#91574—22no—
19#91115—22no—
20#90994—22no—
21#90994—22no—
22#68956—51nomaximal, Hall
23#65817—31no—
24#65232—31no—
25#65232—31no—
26#65232—31no—
27C5×#342—31no—
28#64747—31no—
29#64747D311yescharacteristic
30C24×C3×C5C2311yescharacteristic
31C22×C3×C4×C5—21no—
32C22×Dic15—21no—
33C22×Dic15—21no—
34C22×Dic15—21no—
35C22×Dic15—21no—
36C22×Dic15—21no—
37C22×Dic15—21no—
38C22×Dic15D412yes—
39C22×Dic15Q812yescomplemented
40C22×C5×Dic3—21no—
41C22×C5×Dic3D412yes—
42C22×C3×Dic5—21no—
43C22×C3×Dic5D412yes—
44C2×#1204—22no—
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47#6719—21no—
48#6719—21no—
49C5×#217—21no—
50C5×#217—21no—
51C5×#217—21no—
52C5×#217—21no—
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—21no—
57Dic3⋊Dic5—22no—
58#6669—22no—
59#6668—22no—
60#5483—51no—
61#4943—51no—
62#4943—51no—
63#4943—51no—
64C3×#342—51no—
65#4527—51no—
66#4527D511yescharacteristic
67C23×Dic5—31no—
68C2×C5×C22⋊C4—31no—
69C2×C5×C22⋊C4—31no—
70C2×C5×C22⋊C4C2×D311yescharacteristic
71C2×C22⋊Dic5—31no—
72C2×C22⋊Dic5C2×D311yescharacteristic
73C2×C22⋊Dic5C2×D311yescharacteristic
74#4070—62no—
75#4024—62no—
76#4024—62no—
77#3963—62no—
78#3963—62no—
79#3963—62no—
80#2030—151noSylow
81C23×C3×C5—42no—
82C23×C3×C5C2×D411yescharacteristic
83C23×C3×C5C2×D411yescharacteristic
84C23×C3×C5C2×D411yescharacteristic
85C23×C3×C5C2×Q811yescharacteristic
86C23×C3×C5#4111yescharacteristic
87C23×C3×C5#4111yescharacteristic
88C23×C3×C5#4111yescharacteristic
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5—41no—
91C2×Dic15—22no—
92C2×Dic15—22no—
93C2×Dic15—22no—
94C2×Dic15—22no—
95C2×Dic15—41no—
96C2×Dic15—41no—
97C2×Dic15—41no—
98C2×Dic15—41no—
99C2×Dic15—42no—
100C2×C5×Dic3—22no—
101C2×C5×Dic3—42no—
102C2×C5×Dic3—42no—
103C2×C5×Dic3—41no—
104C2×C3×Dic5—22no—
105C2×C3×Dic5—42no—
106C2×C3×Dic5—42no—
107C2×C3×Dic5—41no—
108#1204—82no—
109C23×Dic3—51no—
110C2×C3×C22⋊C4—51no—
111C2×C3×C22⋊C4—51no—
112C2×C3×C22⋊C4C2×D511yescharacteristic
113C2×#217—51no—
114C2×#217C2×D511yescharacteristic
115C2×#217C2×D511yescharacteristic
116#924—102no—
117#878—102no—
118#878—102no—
119C3⋊#95—102no—
120C3⋊#95—102no—
121C3⋊#95—102no—
122C24×C5C22×D311yescharacteristic
123C22×C4×C5—21no—
124C22×C4×C5—32no—
125C22×C4×C5—61no—
126C22×Dic5—21no—
127C22×Dic5—32no—
128C22×Dic5—32no—
129C22×Dic5—61no—
130C22×Dic5—61no—
131C22×Dic5—61no—
132C22×Dic5—61no—
133C22×Dic5—61no—
134C22×Dic5—61no—
135C22×Dic5D1212yes—
136C2×Dic10—62no—
137C5×C22⋊C4—21no—
138C5×C22⋊C4—21no—
139C5×C22⋊C4—61no—
140C5×C22⋊C4—61no—
141C5×C22⋊C4—61no—
142C5×C22⋊C4—61no—
143C22⋊Dic5—21no—
144C22⋊Dic5—21no—
145C22⋊Dic5—21no—
146C22⋊Dic5—21no—
147C22⋊Dic5—61no—
148C22⋊Dic5—61no—
149C4⋊Dic5—62no—
150#683—62no—
151#683—62no—
152#543—151no—
153#381—151no—
154#381—151no—
155#381—151no—
156#342—31no—
157#342—51no—
158#342—151no—
159C22×C3×C5—22no—
160C22×C3×C5—22no—
161C22×C3×C5—22no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5C22⋊Q811yescharacteristic
169C22×C3×C5C22⋊Q811yescharacteristic
170C22×C3×C5#12411yescharacteristic
171C22×C3×C5#12411yescharacteristic
172C22×C3×C5#12411yescharacteristic
173C3×C4×C5—81no—
174Dic15—42no—
175Dic15—42no—
176C3×Dic5—42no—
177C3×Dic5—81no—
178C5×Dic3—42no—
179C5×Dic3—81no—
180C24×C3C22×D511yescharacteristic
181C22×C3×C4—21no—
182C22×C3×C4—52no—
183C22×C3×C4—101no—
184C22×Dic3—21no—
185C22×Dic3—52no—
186C22×Dic3—52no—
187C22×Dic3—101no—
188C22×Dic3—101no—
189C22×Dic3—101no—
190C22×Dic3—101no—
191C22×Dic3—101no—
192C22×Dic3—101no—
193C22×Dic3D2012yes—
194C2×Dic6—102no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—101no—
198C3×C22⋊C4—101no—
199C3×C22⋊C4—101no—
200C3×C22⋊C4—101no—
201#217—21no—
202#217—21no—
203#217—21no—
204#217—21no—
205#217—101no—
206#217—101no—
207C4⋊Dic3—102no—
208Dic3⋊C4—102no—
209Dic3⋊C4—102no—
210C23×C5—42no—
211C23×C5C2×D1211yescharacteristic
212C23×C5#23511yescharacteristic
213C23×C5#23511yescharacteristic
214C23×C5D3×D411yescharacteristic
215C23×C5D3×D411yescharacteristic
216C23×C5#23711yescharacteristic
217C23×C5D3×Q811yescharacteristic
218C2×C4×C5—42no—
219C2×C4×C5—41no—
220C2×C4×C5—62no—
221C2×C4×C5—122no—
222C2×C4×C5—122no—
223C2×C4×C5—121no—
224C2×Dic5—22no—
225C2×Dic5—42no—
226C2×Dic5—42no—
227C2×Dic5—41no—
228C2×Dic5—62no—
229C2×Dic5—62no—
230C2×Dic5—62no—
231C2×Dic5—62no—
232C2×Dic5—121no—
233C2×Dic5—121no—
234C2×Dic5—121no—
235C2×Dic5—121no—
236C2×Dic5—122no—
237Dic10—242no—
238C23×C4—151no—
239C22⋊Q8—302no—
240C22⋊Q8—302no—
241C22⋊Q8—302no—
242C2×C22⋊C4—31no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—51no—
245C2×C22⋊C4—51no—
246C2×C22⋊C4—151no—
247C2×C22⋊C4D3×D511yescharacteristic
248#95—302no—
249#95—302no—
250#95—302no—
251C2×C3×C5—21no—
252C2×C3×C5—21no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5—21no—
257C2×C3×C5#39311yescharacteristic
258C2×C3×C5#45812yes—
259C23×C3—42no—
260C23×C3C2×D2011yescharacteristic
261C23×C3#70911yescharacteristic
262C23×C3#70911yescharacteristic
263C23×C3D4×D511yescharacteristic
264C23×C3D4×D511yescharacteristic
265C23×C3#71111yescharacteristic
266C23×C3Q8×D511yescharacteristic
267C2×C3×C4—42no—
268C2×C3×C4—41no—
269C2×C3×C4—102no—
270C2×C3×C4—202no—
271C2×C3×C4—202no—
272C2×C3×C4—201no—
273C2×Dic3—22no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3—41no—
277C2×Dic3—102no—
278C2×Dic3—102no—
279C2×Dic3—102no—
280C2×Dic3—102no—
281C2×Dic3—201no—
282C2×Dic3—201no—
283C2×Dic3—201no—
284C2×Dic3—201no—
285C2×Dic3—202no—
286Dic6—402no—
287C22×C5—22no—
288C22×C5—22no—
289C22×C5—22no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5—41no—
293C22×C5—41no—
294C22×C5#87511yescharacteristic
295C22×C5#88211yescharacteristic
296C22×C5#88511yescharacteristic
297C22×C5#88511yescharacteristic
298C22×C5#89611yescharacteristic
299C22×C5#89611yescharacteristic
300C22×C5#89711yescharacteristic
301C4×C5—81no—
302C4×C5—122no—
303C4×C5—241no—
304Dic5—42no—
305Dic5—81no—
306Dic5—122no—
307Dic5—122no—
308C24C2×D3×D511yescharacteristic
309C2×Q8—302no—
310C22×C4—21no—
311C22×C4—32no—
312C22×C4—52no—
313C22×C4—61no—
314C22×C4—101no—
315C22×C4—152no—
316C22×C4—152no—
317C22×C4—301no—
318C22×C4—301no—
319C22×C4—301no—
320C22×C4—301no—
321C22×C4—301no—
322C22×C4—301no—
323C4⋊C4—302no—
324C4⋊C4—302no—
325C4⋊C4—302no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—61no—
329C22⋊C4—61no—
330C22⋊C4—61no—
331C22⋊C4—61no—
332C22⋊C4—101no—
333C22⋊C4—101no—
334C22⋊C4—101no—
335C22⋊C4—101no—
336C22⋊C4—301no—
337C22⋊C4—301no—
338C3×C5#203011yescharacteristic, complemented, Hall
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3#402111yescharacteristic
347C22×C3#402811yescharacteristic
348C22×C3#403111yescharacteristic
349C22×C3#403111yescharacteristic
350C22×C3#404211yescharacteristic
351C22×C3#404211yescharacteristic
352C22×C3#404311yescharacteristic
353C3×C4—81no—
354C3×C4—202no—
355C3×C4—401no—
356Dic3—42no—
357Dic3—81no—
358Dic3—202no—
359Dic3—202no—
360C2×C5—21no—
361C2×C5—21no—
362C2×C5—21no—
363C2×C5—21no—
364C2×C5—21no—
365C2×C5—21no—
366C2×C5#467311yescharacteristic
367C2×C5#474212yes—
368C23—42no—
369C23D15⋊Q811yescharacteristic
370C23#677111yescharacteristic
371C23D5×D1211yescharacteristic
372C23D3×D2011yescharacteristic
373C23#677911yescharacteristic
374C23#678211yescharacteristic
375C23#679011yescharacteristic
376Q8—1202no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—62no—
380C2×C4—102no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—121no—
384C2×C4—202no—
385C2×C4—202no—
386C2×C4—201no—
387C2×C4—302no—
388C2×C4—302no—
389C2×C4—302no—
390C2×C4—302no—
391C2×C4—601no—
392C2×C4—601no—
393C2×C4—601no—
394C2×C4—601no—
395C2×C4—602no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3#6496211yescharacteristic
403C2×C3#6503112yes—
404C5#6895611yescharacteristic, complemented, Sylow
405C22—22no—
406C22—22no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22#9135011yescharacteristic
413C22#9135311yescharacteristic
414C22#9137711yescharacteristic
415C22#9141911yescharacteristic
416C22#9142911yescharacteristic
417C22#9147611yescharacteristic
418C22#9152611yescharacteristic
419C4—81no—
420C4—122no—
421C4—202no—
422C4—241no—
423C4—401no—
424C4—602no—
425C4—602no—
426C3#1059974911yescharacteristic, complemented, Sylow
427C2—21no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2#1174713612yes—
434C2#1174857911yescharacteristic
subgroupG/H
centerC22#91476
commutator, prime radical, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2030
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
39. C22×Dic15Q8semidirect
338. C3×C5#2030semidirect
404. C5#68956semidirect
426. C3#10599749semidirect

Maximal subgroups

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

subgroupindex
#117554322
#117510442
#117494732
C5×#45272
C3×#647472
#117460202
#105997493
#689565