Finite Group Databasebeta

← #14283201

Subgroups — #14283201

Order 1920.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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#11756383C211yesmaximal, characteristic
2#11750820C211yesmaximal, characteristic, complemented
3#11750750C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic
7#11746272C211yesmaximal, characteristic
8#10599104—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10#91836C411yescharacteristic, complemented
11Q8×Dic15C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C2×#6712—21no—
14C2×C4×Dic15—21no—
15C2×C4×Dic15C2211yescharacteristic
16#91787—21no—
17#91782C411yescharacteristic, complemented
18#91781—21no—
19#91779C411yescharacteristic, complemented
20#91775—21no—
21#91770—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24#91115C2211yescharacteristic
25#91114C2211yescharacteristic
26#91099—21no—
27#91098—21no—
28#68311—51nomaximal, Hall
29#65958—31no—
30#65008—31no—
31#64938—31no—
32C5×#328D311yescharacteristic, complemented
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42C22×Dic15D411yescharacteristic
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C22⋊C4—21no—
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15C2×C411yescharacteristic
56#6712—24no—
57#6712—21no—
58C4×Dic15—21no—
59C4×Dic15—42no—
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15C2×C411yescharacteristic
62C4×Dic15D411yescharacteristic
63C4×Dic15D411yescharacteristic
64C2×C3⋊#168—21no—
65#5624—51no—
66#4719—51no—
67#4649—51no—
68C3×#328D511yescharacteristic, complemented
69#4538—51no—
70#4470—51no—
71#4451—51no—
72C5×C22⋊Q8C2×D311yescharacteristic
73#4093—31no—
74Q8×Dic5—31no—
75#4076—31no—
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⋊C8C2×D311yescharacteristic
86C5×#95C2×D311yescharacteristic
87#3963—31no—
88C22⋊#168—31no—
89#3947—61no—
90#3946—61no—
91#1509—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—21no—
94C3×C5×Q8—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103#1220—41no—
104#1220—41no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—22no—
108C2×Dic15—22no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15C22⋊C411yescharacteristic
113C2×Dic15C22⋊C411yescharacteristic
114C2×Dic15C22⋊C411yescharacteristic
115C2×Dic15C22⋊C411yescharacteristic
116D60—41no—
117C4×D15—42no—
118C3×C5×C8—41no—
119C3⋊#168—41no—
120C3×C22⋊Q8C2×D511yescharacteristic
121#947—51no—
122Q8×Dic3—51no—
123#930—51no—
124C2×Dic3⋊C4—101no—
125C2×C4×Dic3—51no—
126C2×C4×Dic3—101no—
127#898—101no—
128#893—51no—
129#892—101no—
130#890—51no—
131#886—101no—
132#67⋊C4—101no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×#95C2×D511yescharacteristic
135C3⋊#95—51no—
136#830—51no—
137#815—101no—
138Dic3⋊C8—101no—
139C2×C5×Q8C4×D311yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—61no—
143C22×Dic5—31no—
144C22×Dic5—31no—
145C22×Dic5—61no—
146C2×D20—31no—
147C2×C4×D5—61no—
148C2×C5×C8—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4C4×D311yescharacteristic
151C5×C22⋊C4—21no—
152#685—61no—
153#685—61no—
154#685—61no—
155#685—61no—
156C4⋊Dic5—31no—
157C4⋊Dic5—61no—
158C4⋊Dic5—61no—
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—61no—
168#529—151no—
169#432—151no—
170C4×C4⋊C4—151no—
171#328—151no—
172#328D1511yescharacteristic, complemented
173#327—151no—
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×D15—41no—
181C2×D15—41no—
182C2×D15—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—42no—
186C3×C4×C5—41no—
187C3×C4×C5—41no—
188Dic15—21no—
189Dic15—21no—
190Dic15—21no—
191Dic15—42no—
192Dic15—41no—
193Dic15#10412yes—
194C2×C3×Q8C4×D511yescharacteristic
195C22×C3×C4—21no—
196C22×C3×C4C22×D511yescharacteristic
197C2×#67—101no—
198C22×Dic3—51no—
199C22×Dic3—51no—
200C22×Dic3—101no—
201C2×D12—51no—
202C2×C4×D3—101no—
203C2×C3×C8—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4C4×D511yescharacteristic
206C3×C22⋊C4—21no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3—101no—
213C4⋊Dic3—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—101no—
223C23×C5D3×D411yescharacteristic
224C22×D5—61no—
225C5×Q8—41no—
226C2×C4×C5—22no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5C2×C4×D311yescharacteristic
233C2×C4×C5D3×D411yescharacteristic
234C22⋊D5—121no—
235C22⋊D5—121no—
236C2×Dic5—31no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—31no—
240C2×Dic5—62no—
241C2×Dic5—61no—
242C2×Dic5—61no—
243C2×Dic5—62no—
244C2×Dic5—61no—
245C2×Dic5—121no—
246C2×Dic5—121no—
247D20—121no—
248C4×D5—122no—
249C5×C8—41no—
250#168—121no—
251#126—301no—
252#125—151no—
253#124—151no—
254#123—301no—
255C22⋊Q8C2×D1511yescharacteristic
256#121—151no—
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—151no—
266C22⋊C8C2×D1511yescharacteristic
267#97—301no—
268#95—151no—
269#95C2×D1511yescharacteristic
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#41011yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275D15—81no—
276C23×C3D4×D511yescharacteristic
277C22×D3—101no—
278C3×Q8—41no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4C2×C4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287#67—201no—
288#67—201no—
289C2×Dic3—51no—
290C2×Dic3—51no—
291C2×Dic3—51no—
292C2×Dic3—51no—
293C2×Dic3—102no—
294C2×Dic3—101no—
295C2×Dic3—101no—
296C2×Dic3—102no—
297C2×Dic3—101no—
298C2×Dic3—201no—
299C2×Dic3—201no—
300D12—201no—
301C4×D3—202no—
302C3×C8—41no—
303C3⋊C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5D3×C22⋊C411yescharacteristic
307C22×C5#91411yescharacteristic
308C22×C5#91811yescharacteristic
309C2×D5—121no—
310C2×D5—121no—
311C2×D5—121no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—42no—
315C4×C5—41no—
316C4×C5—41no—
317Dic5—32no—
318Dic5—61no—
319Dic5—61no—
320Dic5—61no—
321Dic5—122no—
322Dic5—121no—
323C2×Q8C4×D1511yescharacteristic
324C2×D4—151no—
325C2×D4—301no—
326C22×C4—21no—
327C22×C4—151no—
328C22×C4—151no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4C22×D1511yescharacteristic
332C2×C8—21no—
333C2×C8—301no—
334C4⋊C4—21no—
335C4⋊C4—151no—
336C4⋊C4—301no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—304no—
340C4⋊C4C4×D1511yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—301no—
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×C3D5×C22⋊C411yescharacteristic
356C22×C3#406011yescharacteristic
357C22×C3#406411yescharacteristic
358C2×D3—201no—
359C2×D3—201no—
360C2×D3—201no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4—41no—
366Dic3—52no—
367Dic3—101no—
368Dic3—101no—
369Dic3—101no—
370Dic3—202no—
371Dic3—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#474011yescharacteristic
375C2×C5#480311yescharacteristic
376C2×C5D3×#10411yescharacteristic
377D5—241no—
378C23—301no—
379C23D4×D1511yescharacteristic
380Q8—41no—
381D4—601no—
382D4—601no—
383D4—601no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—302no—
395C2×C4—301no—
396C2×C4—301no—
397C2×C4—302no—
398C2×C4—301no—
399C2×C4—602no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C2×C4×D1511yescharacteristic
403C2×C4D4×D1511yescharacteristic
404C8—41no—
405C8—601no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3#6502911yescharacteristic
409C2×C3#6509211yescharacteristic
410C2×C3D5×#10411yescharacteristic
411D3—401no—
412C5#6831111yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—601no—
416C22—601no—
417C22—601no—
418C22C22⋊C4×D1511yescharacteristic
419C22#9180311yescharacteristic
420C22#9180711yescharacteristic
421C4—21no—
422C4—21no—
423C4—42no—
424C4—41no—
425C4—41no—
426C4—152no—
427C4—301no—
428C4—301no—
429C4—301no—
430C4—602no—
431C4—601no—
432C3#1059910411yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—1201no—
436C2#1175084111yescharacteristic
437C2#1175090411yescharacteristic
438C2D15×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenter#328D15
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #11750820C2semidirect
3. #11750750C2semidirect
4. C3×C5×#328C2semidirect
5. #11746359C2semidirect
10. #91836C4semidirect
11. Q8×Dic15C4semidirect
17. #91782C4semidirect
19. #91779C4semidirect
32. C5×#328D3semidirect
68. C3×#328D5semidirect
172. #328D15semidirect
352. C3×C5#1509semidirect
412. C5#68311semidirect
432. C3#10599104semidirect

Maximal subgroups

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

subgroupindex
#117563832
#117508202
#117507502
C3×C5×#3282
#117463592
#117462912
#117462722
#105991043
#683115