Finite Group Databasebeta

← #14283217

Subgroups — #14283217

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#11754460C211yesmaximal, characteristic
2#11750750C211yesmaximal, characteristic, complemented
3#11748338C211yesmaximal, characteristic, complemented
4C5×#4451C211yesmaximal, characteristic
5C3×#64672C211yesmaximal, characteristic, complemented
6#11745960C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic
8#10599072—31nomaximal, Hall
9C2×#6712—21no—
10C2×C4×Dic15—21no—
11C2×C4×Dic15C2211yescharacteristic
12C5×#930C2211yescharacteristic
13C3×#4070C2211yescharacteristic
14#67⋊Dic5—21no—
15#91543—21no—
16#91435C411yescharacteristic, complemented
17#91400—21no—
18#91384C411yescharacteristic, complemented
19#91370C411yescharacteristic, complemented
20#91367—21no—
21#91331C411yescharacteristic, complemented
22C3×C5×#95C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90983—21no—
27#90954—21no—
28#68311—51nomaximal, Hall
29#65934—31no—
30#65008—31no—
31#64938—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672D311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C22×Dic15D411yescharacteristic
41C2×C5×#67—21no—
42C2×C5×D12C2×C411yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic
44C2×D3×Dic5—21no—
45#6712—24no—
46C4×Dic15—42no—
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15C2×C411yescharacteristic
49C4×Dic15D411yescharacteristic
50C4×Dic15D411yescharacteristic
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3C2×C411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—21no—
57C2×C3×#168—21no—
58Dic3⋊Dic5—21no—
59#6668—21no—
60#6668—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63(C2×D3)⋊Dic5—21no—
64Dic3×Dic5—21no—
65#5624—51no—
66#4719—51no—
67#4649—51no—
68C3×#328—51no—
69#4538—51no—
70#4470—51no—
71#4451D511yescharacteristic
72C5×#121—31no—
73#4082—31no—
74#4081—61no—
75D4×Dic5—31no—
76D4×Dic5—61no—
77#4070C2×D311yescharacteristic
78C2×#683—61no—
79C2×C4×Dic5—31no—
80C2×C4×Dic5—61no—
81#4036—31no—
82#4033—31no—
83#4025—61no—
84#4023—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×C5×D3—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
110C5×#67—41no—
111C5×#67—41no—
112C2×C5×Dic3—21no—
113C5×D12—41no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C3×Dic10—41no—
117D3×Dic5—42no—
118C3×#168—41no—
119C5×C3⋊C8—41no—
120C3×C22⋊Q8—51no—
121#947—51no—
122Q8×Dic3—51no—
123#930C2×D511yescharacteristic
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⋊C8—51no—
134C3×#95C2×D511yescharacteristic
135C3⋊#95—51no—
136#830C2×D511yescharacteristic
137#815—101no—
138Dic3⋊C8—101no—
139C2×C5×D4—31no—
140C2×C5×D4—61no—
141C22×C4×C5—21no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—31no—
144C22×Dic5—31no—
145C22×Dic5—61no—
146C22×Dic5—61no—
147C2×Dic10C4×D311yescharacteristic
148C2×C5×C8—61no—
149C5×C4⋊C4—31no—
150C5×C22⋊C4—61no—
151C22⋊Dic5—21no—
152C22⋊Dic5—61no—
153C22⋊Dic5—61no—
154C22⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5C4×D311yescharacteristic
157#683—21no—
158#683—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—21no—
168#529—151no—
169#432—151no—
170C4×C4⋊C4—151no—
171#328—51no—
172#328—151no—
173#327—31no—
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×C5×D3—41no—
181C2×C5×D3—41no—
182C2×C5×D3—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—
192C3×Dic5—41no—
193C5×Dic3—41no—
194C2×C3×Q8—51no—
195C22×C3×C4—21no—
196C22×C3×C4C22×D511yescharacteristic
197C2×#67—21no—
198C22×Dic3—51no—
199C22×Dic3—51no—
200C22×Dic3—101no—
201C2×D12C4×D511yescharacteristic
202C2×C4×D3—101no—
203C2×C3×C8—101no—
204C3×C4⋊C4—51no—
205C3×C4⋊C4—101no—
206C3×C22⋊C4—101no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—101no—
212C4⋊Dic3—101no—
213C4⋊Dic3C4×D511yescharacteristic
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×C5—61no—
224C23×C5D3×D411yescharacteristic
225C5×D4—121no—
226C5×D4—121no—
227C5×D4—121no—
228C2×C4×C5—22no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—61no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×Dic5—21no—
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—122no—
246C2×Dic5—121no—
247C2×Dic5—121no—
248Dic10—41no—
249C5×C8—121no—
250#168—41no—
251#126—301no—
252#125—151no—
253#124—151no—
254#123—301no—
255C22⋊Q8—51no—
256#121—31no—
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
275C5×D3—81no—
276C23×C3D4×D511yescharacteristic
277C22×D3—21no—
278C3×Q8—201no—
279C2×C3×C4—22no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4C2×C4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287#67—41no—
288#67—41no—
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—201no—
299C2×Dic3—201no—
300D12—41no—
301C4×D3—202no—
302C3×C8—201no—
303C3⋊C8—41no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—121no—
307C22×C5—121no—
308C22×C5—121no—
309C22×C5D3×C22⋊C411yescharacteristic
310C22×C5#91411yescharacteristic
311C22×C5#91811yescharacteristic
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—42no—
315C4×C5—121no—
316Dic5—32no—
317Dic5—41no—
318Dic5—41no—
319Dic5—61no—
320Dic5—61no—
321Dic5—61no—
322Dic5—122no—
323C2×Q8—51no—
324C2×D4—31no—
325C2×D4—61no—
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—101no—
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×C3D5×C22⋊C411yescharacteristic
356C22×C3#405711yescharacteristic
357C22×C3#406111yescharacteristic
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—41no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—201no—
365C3×C4—201no—
366Dic3—41no—
367Dic3—52no—
368Dic3—101no—
369Dic3—101no—
370Dic3—101no—
371Dic3—202no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—241no—
375C2×C5#474011yescharacteristic
376C2×C5#480311yescharacteristic
377C2×C5D3×#10411yescharacteristic
378C23—61no—
379C23#679011yescharacteristic
380Q8—201no—
381D4—121no—
382D4—121no—
383D4—121no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—101no—
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#6502911yescharacteristic
409C2×C3#6506011yescharacteristic
410C2×C3D5×#10411yescharacteristic
411D3—81no—
412C5#6831111yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—121no—
416C22—121no—
417C22—121no—
418C22#9147311yescharacteristic
419C22#9150011yescharacteristic
420C22#9152411yescharacteristic
421C4—21no—
422C4—21no—
423C4—42no—
424C4—121no—
425C4—152no—
426C4—201no—
427C4—201no—
428C4—301no—
429C4—301no—
430C4—301no—
431C4—602no—
432C3#1059907211yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—241no—
436C2#1174711211yescharacteristic
437C2#1174713111yescharacteristic
438C2#1174750911yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C22
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
5. C3×#64672C2semidirect
6. #11745960C2semidirect
16. #91435C4semidirect
18. #91384C4semidirect
19. #91370C4semidirect
21. #91331C4semidirect
35. #64672D3semidirect
352. C3×C5#1509semidirect
412. C5#68311semidirect
432. C3#10599072semidirect

Maximal subgroups

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

subgroupindex
#117544602
#117507502
#117483382
C5×#44512
C3×#646722
#117459602
#117459572
#105990723
#683115