Finite Group Databasebeta

← #14313161

Subgroups — #14313161

Order 1920.

528 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#11756587C211yesmaximal, characteristic
2C5×#5240C211yesmaximal, characteristic, complemented
3C3×#65526C211yesmaximal, characteristic, complemented
4#11746005C212yesmaximal, complemented
5#11745999C212yesmaximal, complemented
6#10600849—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×C4×D15C411yescharacteristic, complemented
9#91835—21no—
10#91827—21no—
11#91826C411yescharacteristic, complemented
12#91826C2211yescharacteristic
13#91824C411yescharacteristic, complemented
14#91824C2211yescharacteristic
15C4×#1220—21no—
16C4×#1220—21no—
17#91815C411yescharacteristic, complemented
18C5×#926—21no—
19C2×C3×#681—21no—
20C5×#834—21no—
21C5×#834C2212yes—
22C3×#3968—21no—
23C3×#3965C2212yes—
24#70145—51nomaximal, Hall
25#66162—31no—
26C5×#410—31no—
27#65526D311yescharacteristic, complemented
28#64692—32no—
29#64691—32no—
30C23×D15C2×C411yescharacteristic
31C3×C5×#41—41no—
32C3×C5×#41—41no—
33C2×C3×C5×Q8D411yescharacteristic
34C2×C3×C5×D4C2×C411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C22×Dic15C2×C411yescharacteristic
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15—41no—
46C2×C4×D15—41no—
47#6719—21no—
48#6719—21no—
49#6719C2×C411yescharacteristic
50#6719C2×C411yescharacteristic
51#6714—21no—
52#6714—21no—
53C4⋊Dic15—21no—
54#6712—21no—
55#6712—21no—
56C4×Dic15—21no—
57C5×#217—22no—
58C5×C4⋊Dic3—41no—
59C4×C5×Dic3—41no—
60C3×#681—22no—
61C3×#681—41no—
62C2×C3×#168—41no—
63#5828—51no—
64C3×#413—51no—
65#5240D511yescharacteristic, complemented
66#4476—52no—
67#4475—52no—
68C2×C5×#41C2×D311yescharacteristic
69C22×C4×D5—31no—
70C5×#117—61no—
71#4092—61no—
72#4084—61no—
73#4083—31no—
74#4083—31no—
75#4081—31no—
76#4081—31no—
77C4×C22⋊D5—61no—
78C4×C22⋊D5—61no—
79#4072—31no—
80C2×#681—21no—
81C5×#99—32no—
82C5×#99—61no—
83#3968—21no—
84#3965C2×D312yes—
85#2120—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22×C411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×D15—21no—
90C22×D15—42no—
91C22×D15—41no—
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C22⋊C411yescharacteristic
103C2×C3×C4×C5C22⋊C411yescharacteristic
104C2×C3×C4×C5C22⋊C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106#1220—42no—
107#1220—42no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—21no—
111C2×Dic15—41no—
112C4×D15—42no—
113C4×D15—41no—
114C4×D15—41no—
115C2×C5×Dic3—42no—
116C3×#168—42no—
117C2×C3×#41C2×D511yescharacteristic
118C22×C4×D3—51no—
119C2×C3×M16—101no—
120#946—101no—
121#938—101no—
122#937—51no—
123#937—51no—
124#935—51no—
125#935—51no—
126C4×#67—101no—
127C4×#67—101no—
128#926—21no—
129#926—51no—
130C3×#101—101no—
131C3×#100—52no—
132#834—21no—
133#834C2×D512yes—
134C23×D5—31no—
135C5×#41—41no—
136C5×#41—41no—
137C2×C5×Q8#6711yescharacteristic
138C2×C5×D4C4×D311yescharacteristic
139C2×C5×D4D1211yescharacteristic
140C2×C5×D4C22×D311yescharacteristic
141C22×C4×C5C4×D311yescharacteristic
142C22×C4×C5D1211yescharacteristic
143C22×C4×C5#6711yescharacteristic
144C2×C22⋊D5—61no—
145C2×C22⋊D5—61no—
146C22×Dic5—31no—
147C2×C4×D5—61no—
148C2×C4×D5—61no—
149C2×C4×D5—121no—
150C2×C4×D5—121no—
151C5×C4⋊C4—121no—
152C5×C22⋊C4—62no—
153C42×C5—121no—
154C22⋊Dic5—31no—
155C22⋊Dic5—31no—
156C22⋊Dic5—61no—
157C22⋊Dic5—61no—
158#685—61no—
159#685—61no—
160C4⋊Dic5—61no—
161#683—61no—
162#683—61no—
163C4×Dic5—61no—
164#681—22no—
165#681—41no—
166C2×#168—41no—
167#525—151no—
168#413—51no—
169#410—31no—
170#352—152no—
171AΣL(1,𝔽16)—152no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×D15—22no—
180C2×D15—41no—
181C2×D15—42no—
182C2×D15—41no—
183C2×D15—42no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187C3×C4×C5#9911yescharacteristic
188C3×C4×C5#9911yescharacteristic
189Dic15—41no—
190Dic15—41no—
191Dic15—41no—
192C5×Dic3—82no—
193C23×D3—51no—
194C3×#41—41no—
195C3×#41—41no—
196C2×C3×Q8D2011yescharacteristic
197C2×C3×D4C4×D511yescharacteristic
198C2×C3×D4C22⋊D511yescharacteristic
199C2×C3×D4C22×D511yescharacteristic
200C22×C3×C4C4×D511yescharacteristic
201C22×C3×C4D2011yescharacteristic
202C22×C3×C4C22⋊D511yescharacteristic
203C2×#67—101no—
204C2×#67—101no—
205C22×Dic3—51no—
206C2×C4×D3—101no—
207C2×C4×D3—101no—
208C2×C4×D3—201no—
209C2×C4×D3—201no—
210C3×M16—102no—
211C3×M16—201no—
212C2×C3×C8—201no—
213#217—22no—
214#217—51no—
215#217—51no—
216#217—101no—
217#217—101no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4⋊Dic3—41no—
221C4⋊Dic3—101no—
222Dic3⋊C4—101no—
223Dic3⋊C4—101no—
224C4×Dic3—41no—
225C4×Dic3—101no—
226C23×C5(C2×D3)⋊C411yescharacteristic
227C23×C5C2×C4×D311yescharacteristic
228C23×C5C2×D1211yescharacteristic
229C22×D5—61no—
230C22×D5—122no—
231C22×D5—121no—
232C5×Q8—41no—
233C5×D4—41no—
234C5×D4—41no—
235C5×D4—41no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—122no—
243C2×C4×C5(C2×D3)⋊C411yescharacteristic
244C2×C4×C5(C2×D3)⋊C411yescharacteristic
245C2×C4×C5(C2×D3)⋊C411yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—122no—
248C22⋊D5—122no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—61no—
252C2×Dic5—121no—
253C4×D5—122no—
254C4×D5—121no—
255C4×D5—121no—
256#168—42no—
257C2×#41D3×D511yescharacteristic
258C23×C4—151no—
259C2×M16—101no—
260#123—151no—
261#123—151no—
262C22⋊Q8—301no—
263#121—301no—
264#120—151no—
265#120—151no—
266C4×D4—301no—
267C4×D4—301no—
268#117—61no—
269#117—151no—
270#101—101no—
271#100—52no—
272#99—32no—
273#99—61no—
274C2×C3×C5—21no—
275C2×C3×C5—41no—
276C2×C3×C5—41no—
277C2×C3×C5—41no—
278C2×C3×C5C2×#9911yescharacteristic
279D15—42no—
280C23×C3#68511yescharacteristic
281C23×C3C2×C4×D511yescharacteristic
282C23×C3C2×C22⋊D511yescharacteristic
283C22×D3—101no—
284C22×D3—202no—
285C22×D3—201no—
286C3×Q8—41no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—41no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4#68511yescharacteristic
297C2×C3×C4#68511yescharacteristic
298C2×C3×C4#68511yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300#67—202no—
301#67—202no—
302C2×Dic3—42no—
303C2×Dic3—101no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306C2×Dic3—201no—
307C4×D3—202no—
308C4×D3—201no—
309C4×D3—201no—
310C3×C8—202no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—41no—
317C22×C5C2×(C2×D3)⋊C411yescharacteristic
318C2×D5—62no—
319C2×D5—121no—
320C2×D5—122no—
321C2×D5—121no—
322C2×D5—122no—
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—21no—
326C4×C5—242no—
327C4×C5#80611yescharacteristic
328C4×C5#80611yescharacteristic
329Dic5—121no—
330Dic5—121no—
331Dic5—121no—
332C24—151no—
333#41—41no—
334#41—41no—
335C2×Q8#120211yescharacteristic
336C2×D4—301no—
337C2×D4—301no—
338C2×D4#120011yescharacteristic
339C2×D4#120311yescharacteristic
340C2×D4C2×D3×D511yescharacteristic
341C22×C4—151no—
342C22×C4—301no—
343C22×C4—301no—
344C22×C4—601no—
345C22×C4—601no—
346C22×C4#120011yescharacteristic
347C22×C4#120211yescharacteristic
348C22×C4#120311yescharacteristic
349M16—102no—
350M16—201no—
351C2×C8—201no—
352C4⋊C4—121no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C4⋊C4—301no—
356C22⋊C4—62no—
357C22⋊C4—151no—
358C22⋊C4—151no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C22⋊C4—301no—
362C22⋊C4—301no—
363C42—121no—
364C42—301no—
365C3×C5#212011yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3C2×#68511yescharacteristic
373C2×D3—102no—
374C2×D3—201no—
375C2×D3—202no—
376C2×D3—201no—
377C2×D3—202no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4#393811yescharacteristic
382C3×C4#393811yescharacteristic
383Dic3—82no—
384Dic3—201no—
385Dic3—201no—
386Dic3—201no—
387C2×C5—21no—
388C2×C5—41no—
389C2×C5—41no—
390C2×C5—41no—
391C2×C5C2×#80611yescharacteristic
392D5—122no—
393C23—301no—
394C23—601no—
395C23—602no—
396C23#666711yescharacteristic
397C23C2×#120011yescharacteristic
398C23C2×#120311yescharacteristic
399Q8—41no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—602no—
404D4—602no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—122no—
412C2×C4—301no—
413C2×C4—301no—
414C2×C4—301no—
415C2×C4—602no—
416C2×C4—601no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4#666711yescharacteristic
420C2×C4#666711yescharacteristic
421C2×C4#666711yescharacteristic
422C2×C4C2×#120211yescharacteristic
423C8—202no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—41no—
428C2×C3C2×#393811yescharacteristic
429D3—202no—
430C5#7014511yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—302no—
438C22—601no—
439C22—602no—
440C22—602no—
441C22—601no—
442C22C2×#666711yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—242no—
447C4—601no—
448C4—601no—
449C4—601no—
450C4#9099711yescharacteristic
451C4#9099711yescharacteristic
452C3#1060084911yescharacteristic, complemented, Sylow
453C2—21no—
454C2—41no—
455C2—41no—
456C2—41no—
457C2—602no—
458C2C2×#9099711yescharacteristic
subgroupG/H
centerC4#90997
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radical#11756587C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2120
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C5×#5240C2semidirect
3. C3×#65526C2semidirect
4. #11746005C2semidirect
5. #11745999C2semidirect
8. C22×C4×D15C4semidirect
11. #91826C4semidirect
13. #91824C4semidirect
17. #91815C4semidirect
27. #65526D3semidirect
65. #5240D5semidirect
365. C3×C5#2120semidirect
430. C5#70145semidirect
452. C3#10600849semidirect

Maximal subgroups

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

subgroupindex
#117565872
C5×#52402
C3×#655262
#117460052
#117459992
#106008493
#701455