Finite Group Databasebeta

← #14283220

Subgroups — #14283220

Order 1920.

484 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754451C211yesmaximal, characteristic
2#11750750C211yesmaximal, characteristic, complemented
3#11748338C211yesmaximal, characteristic, complemented
4C5×#4452C211yesmaximal, characteristic, complemented
5C3×#64671C211yesmaximal, characteristic
6#11745963C211yesmaximal, characteristic, complemented
7#11745955C211yesmaximal, characteristic
8#10599104—31nomaximal, Hall
9C2×#6712—21no—
10C2×C4×Dic15—21no—
11C2×C4×Dic15C2211yescharacteristic
12C5×#924C2211yescharacteristic
13C3×#4076C2211yescharacteristic
14#91559—21no—
15#91537—21no—
16#91434C411yescharacteristic, complemented
17#91394—21no—
18#91384C411yescharacteristic, complemented
19#91368C411yescharacteristic, complemented
20#91366—21no—
21#91344C411yescharacteristic, complemented
22C3×C5×#95C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90983—21no—
27#90954—21no—
28#68279—51nomaximal, Hall
29#65958—31no—
30#65008—31no—
31#64938—31no—
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671D311yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C22×Dic15D411yescharacteristic
41C2×C5×Dic6C2×C411yescharacteristic
42C2×C3×C22⋊D5—21no—
43C2×C3×D20C2×C411yescharacteristic
44C2×D5×Dic3—21no—
45#6712—24no—
46C4×Dic15—42no—
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15C2×C411yescharacteristic
49C4×Dic15D411yescharacteristic
50C4×Dic15D411yescharacteristic
51C5×#217—21no—
52C5×C4⋊Dic3C2×C411yescharacteristic
53C5×Dic3⋊C4—21no—
54C2×C5×C3⋊C8—21no—
55C3×#685—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic
57C2×C3×#168—21no—
58Dic3⋊Dic5—21no—
59Dic3⋊Dic5—21no—
60#6668—21no—
61#6665—21no—
62#6665—21no—
63#6665—21no—
64Dic3×Dic5—21no—
65#5600—51no—
66#4719—51no—
67#4649—51no—
68C3×#327—51no—
69#4537—51no—
70#4467—51no—
71#4452D511yescharacteristic, complemented
72C5×C22⋊Q8—31no—
73#4093—31no—
74Q8×Dic5—31no—
75#4076C2×D311yescharacteristic
76C2×#683—61no—
77C2×C4×Dic5—31no—
78C2×C4×Dic5—61no—
79#4044—61no—
80#4039—31no—
81#4038—61no—
82#4036—31no—
83#4032—61no—
84#4027—61no—
85C5×C22⋊C8—31no—
86C5×#95C2×D311yescharacteristic
87#3963—31no—
88C22⋊#168C2×D311yescharacteristic
89#3947—61no—
90#3946—61no—
91#1509—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C3×D5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—22no—
103C2×Dic15—22no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C2×Dic15C22⋊C411yescharacteristic
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C411yescharacteristic
109C2×Dic15C22⋊C411yescharacteristic
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C5×Dic6—41no—
113C3×C22⋊D5—41no—
114C3×C22⋊D5—41no—
115C2×C3×Dic5—21no—
116C3×D20—41no—
117D5×Dic3—42no—
118C3×#168—41no—
119C5×C3⋊C8—41no—
120C3×#121—51no—
121#936—51no—
122#935—101no—
123D4×Dic3—51no—
124D4×Dic3—101no—
125#924C2×D511yescharacteristic
126C2×Dic3⋊C4—101no—
127C2×C4×Dic3—51no—
128C2×C4×Dic3—101no—
129#890—51no—
130#887—51no—
131#879—101no—
132#877—101no—
133C3×C22⋊C8—51no—
134C3×#95C2×D511yescharacteristic
135C3⋊#95—51no—
136#830C2×D511yescharacteristic
137#815—101no—
138Dic3⋊C8—101no—
139C2×C5×Q8—31no—
140C22×C4×C5—21no—
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—21no—
143C22×Dic5—31no—
144C22×Dic5—31no—
145C22×Dic5—61no—
146C2×D20C4×D311yescharacteristic
147C2×C4×D5—61no—
148C2×C5×C8—61no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—61no—
151C5×C22⋊C4—61no—
152#685—21no—
153#685—61no—
154#685—61no—
155#685—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158C4⋊Dic5C4×D311yescharacteristic
159#683—61no—
160#683—64no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166C4×Dic5—122no—
167C2×#168—21no—
168#529—151no—
169#432—151no—
170C4×C4⋊C4—151no—
171#328—31no—
172#328—151no—
173#327—51no—
174#327—151no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—42no—
186Dic15—21no—
187Dic15—21no—
188Dic15—21no—
189Dic15—42no—
190Dic15#10412yes—
191C3×Dic5—41no—
192C5×Dic3—41no—
193C5×Dic3—41no—
194C2×C3×D4—51no—
195C2×C3×D4—101no—
196C22×C3×C4—21no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—51no—
199C22×Dic3—51no—
200C22×Dic3—101no—
201C22×Dic3—101no—
202C2×Dic6C4×D511yescharacteristic
203C2×C3×C8—101no—
204C3×C4⋊C4—51no—
205C3×C22⋊C4—101no—
206#217—21no—
207#217—101no—
208#217—101no—
209#217—101no—
210C4⋊Dic3—101no—
211C4⋊Dic3C4×D511yescharacteristic
212Dic3⋊C4—21no—
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215Dic3⋊C4—104no—
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—51no—
220C4×Dic3—101no—
221C4×Dic3—202no—
222C2×C3⋊C8—21no—
223C23×C5D3×D411yescharacteristic
224C22×D5—21no—
225C5×Q8—121no—
226C2×C4×C5—22no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—61no—
231C2×C4×C5—61no—
232C2×C4×C5C2×C4×D311yescharacteristic
233C2×C4×C5D3×D411yescharacteristic
234C22⋊D5—41no—
235C22⋊D5—41no—
236C2×Dic5—21no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—62no—
242C2×Dic5—61no—
243C2×Dic5—61no—
244C2×Dic5—62no—
245C2×Dic5—121no—
246C2×Dic5—121no—
247D20—41no—
248C4×D5—122no—
249C5×C8—121no—
250#168—41no—
251#126—301no—
252#125—151no—
253#124—151no—
254#123—301no—
255C22⋊Q8—31no—
256#121—51no—
257C4×Q8—151no—
258C4×D4—151no—
259C4×D4—301no—
260#117—301no—
261C2×C4⋊C4—301no—
262C2×C42—151no—
263C2×C42—301no—
264C4⋊C8—301no—
265C22⋊C8—31no—
266C22⋊C8—51no—
267#97—301no—
268#95—151no—
269#95D3×D511yescharacteristic
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#41011yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275C3×D5—81no—
276C23×C3—101no—
277C23×C3D4×D511yescharacteristic
278C3×D4—201no—
279C3×D4—201no—
280C3×D4—201no—
281C2×C3×C4—22no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—101no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—51no—
291C2×Dic3—51no—
292C2×Dic3—51no—
293C2×Dic3—51no—
294C2×Dic3—102no—
295C2×Dic3—101no—
296C2×Dic3—101no—
297C2×Dic3—102no—
298C2×Dic3—202no—
299C2×Dic3—201no—
300C2×Dic3—201no—
301Dic6—41no—
302C3×C8—201no—
303C3⋊C8—41no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5D3×C22⋊C411yescharacteristic
307C22×C5#91111yescharacteristic
308C22×C5#91511yescharacteristic
309C2×D5—41no—
310C2×D5—41no—
311C2×D5—41no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—42no—
315C4×C5—121no—
316C4×C5—121no—
317Dic5—32no—
318Dic5—41no—
319Dic5—61no—
320Dic5—61no—
321Dic5—61no—
322Dic5—122no—
323C2×Q8—31no—
324C2×D4—51no—
325C2×D4—101no—
326C22×C4—21no—
327C22×C4—151no—
328C22×C4—151no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332C2×C8—61no—
333C2×C8—101no—
334C4⋊C4—31no—
335C4⋊C4—51no—
336C4⋊C4—61no—
337C4⋊C4—304no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C22⋊C4—61no—
342C22⋊C4—101no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C42—151no—
347C42—151no—
348C42—151no—
349C42—151no—
350C42—301no—
351C42—602no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—201no—
356C22×C3—201no—
357C22×C3—201no—
358C22×C3D5×C22⋊C411yescharacteristic
359C22×C3#406011yescharacteristic
360C22×C3#406411yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—201no—
365Dic3—41no—
366Dic3—41no—
367Dic3—52no—
368Dic3—101no—
369Dic3—101no—
370Dic3—101no—
371Dic3—202no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#474011yescharacteristic
375C2×C5#477111yescharacteristic
376C2×C5D3×#10411yescharacteristic
377D5—81no—
378C23—101no—
379C23#679011yescharacteristic
380Q8—121no—
381D4—201no—
382D4—201no—
383D4—201no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—101no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—302no—
396C2×C4—301no—
397C2×C4—301no—
398C2×C4—302no—
399C2×C4—602no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C4×D3×D511yescharacteristic
403C2×C4#677711yescharacteristic
404C8—121no—
405C8—201no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—401no—
409C2×C3#6502911yescharacteristic
410C2×C3#6509211yescharacteristic
411C2×C3D5×#10411yescharacteristic
412C5#6827911yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—201no—
416C22—201no—
417C22—201no—
418C22#9147311yescharacteristic
419C22#9149811yescharacteristic
420C22#9152211yescharacteristic
421C4—21no—
422C4—21no—
423C4—42no—
424C4—121no—
425C4—121no—
426C4—152no—
427C4—201no—
428C4—301no—
429C4—301no—
430C4—301no—
431C4—602no—
432C3#1059910411yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—401no—
436C2#1174711211yescharacteristic
437C2#1174713111yescharacteristic
438C2#1174750711yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C22
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750750C2semidirect
3. #11748338C2semidirect
4. C5×#4452C2semidirect
6. #11745963C2semidirect
16. #91434C4semidirect
18. #91384C4semidirect
19. #91368C4semidirect
21. #91344C4semidirect
71. #4452D5semidirect
352. C3×C5#1509semidirect
412. C5#68279semidirect
432. C3#10599104semidirect

Maximal subgroups

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

subgroupindex
#117544512
#117507502
#117483382
C5×#44522
C3×#646712
#117459632
#117459552
#105991043
#682795