Finite Group Databasebeta

← #14284345

Subgroups — #14284345

Order 1920.

496 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 84 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#11752751C211yesmaximal, characteristic
2#11750806C211yesmaximal, characteristic, complemented
3#11746940C211yesmaximal, characteristic, complemented
4C5×#4464C211yesmaximal, characteristic, complemented
5C3×#64684C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599140—31nomaximal, Hall
9C2×#6777C411yescharacteristic
10C2×D15⋊Q8C411yescharacteristic
11C42×D15C2211yescharacteristic
12C5×#875C2211yescharacteristic
13C3×#4021C2211yescharacteristic
14#91473—21no—
15#91473—21no—
16#91464—21no—
17#91464—21no—
18#91370C411yescharacteristic
19#91368C411yescharacteristic
20C3×C5×#97C2211yescharacteristic, complemented
21#91104—21no—
22#91098—21no—
23#91087C2211yescharacteristic, complemented
24C5×#803C2211yescharacteristic, complemented
25C3×#3935C2211yescharacteristic, complemented
26#90983—21no—
27#90957—21no—
28#68347—51nomaximal, Hall
29D5×#124—31no—
30#64994—31no—
31#64994—31no—
32C5×#329—31no—
33#64760—31no—
34#64684—31no—
35#64684D311yescharacteristic, complemented
36C22×D3×D5—21no—
37C2×C4×D15C2×C411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C4×D15D411yescharacteristic
40C2×C5×D12C2×C411yescharacteristic
41C2×C5×Dic6C2×C411yescharacteristic
42C2×C3×D20C2×C411yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic
44C2×#1204—21no—
45C2×#1201—21no—
46C2×#1200—21no—
47#6777—42no—
48D15⋊Q8—42no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51C4×Dic15C2×C411yescharacteristic
52C4×Dic15D411yescharacteristic
53C4×Dic15D411yescharacteristic
54C2×C3⋊#168—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C2×C5×C3⋊C8—21no—
58C3×#685—21no—
59C3×#685—21no—
60C2×C3×#168—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63#6665—21no—
64#6665—21no—
65D3×#124—51no—
66#4705—51no—
67#4705—51no—
68C3×#329—51no—
69#4540—51no—
70#4464—51no—
71#4464D511yescharacteristic, complemented
72C2×Q8×D5—31no—
73C2×D4×D5—31no—
74C5×#124—31no—
75#4093—31no—
76#4082—31no—
77#4031—61no—
78#4031—61no—
79D5×C22⋊C4—61no—
80D5×C22⋊C4—61no—
81#4021C2×D311yescharacteristic
82C42×D5—31no—
83C5×#97—31no—
84C5×#97C2×D311yescharacteristic, complemented
85#3952—61no—
86#3952—61no—
87#3946—61no—
88#3946—61no—
89#3935—31no—
90#3935C2×D311yescharacteristic, complemented
91#1533—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C22×C5×D3—21no—
94C22×C3×D5—21no—
95C2×D3×D5—42no—
96C2×D3×D5—42no—
97C2×D3×D5—42no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15C22⋊C411yescharacteristic
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C4×D15—22no—
105C4×D15—41no—
106C4×D15—41no—
107C2×C5×Dic3—21no—
108C5×D12—41no—
109C5×Dic6—41no—
110C2×C3×Dic5—21no—
111C3×D20—41no—
112C3×Dic10—41no—
113#1204—42no—
114#1201—42no—
115#1200—42no—
116C3×C5×C8—41no—
117C3⋊#168—41no—
118C3×#168—41no—
119C5×C3⋊C8—41no—
120C2×D3×Q8—51no—
121C2×D3×D4—51no—
122C3×#124—51no—
123#947—51no—
124#936—51no—
125#885—101no—
126#885—101no—
127D3×C22⋊C4—101no—
128D3×C22⋊C4—101no—
129#875C2×D511yescharacteristic
130C42×D3—51no—
131C3×#97—51no—
132C3×#97C2×D511yescharacteristic, complemented
133(C2×D3)⋊C8—101no—
134(C2×D3)⋊C8—101no—
135Dic3⋊C8—101no—
136Dic3⋊C8—101no—
137#803—51no—
138#803C2×D511yescharacteristic, complemented
139C23×D5—61no—
140C2×C5×Q8—31no—
141C2×C5×D4—31no—
142C2×C22⋊D5—61no—
143Q8×D5—122no—
144D4×D5—122no—
145C2×D20C4×D311yescharacteristic
146C2×C4×D5—31no—
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—61no—
150C2×Dic10—61no—
151C2×Dic10C4×D311yescharacteristic
152C2×C5×C8—21no—
153C2×C5×C8—61no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C42×C5C22×D311yescharacteristic
157C22⋊Dic5—61no—
158C22⋊Dic5—61no—
159#685—21no—
160#685—21no—
161#685—61no—
162#685—61no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—31no—
166C2×#168—21no—
167C2×#168—61no—
168C2×#124—151no—
169#432—151no—
170#432—151no—
171#329—31no—
172#329—51no—
173#329—151no—
174#329—151no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C2×D15—21no—
177C2×D15—21no—
178C2×D15#10012yes—
179C2×C5×D3—41no—
180C2×C5×D3—41no—
181C2×C5×D3—41no—
182C2×C3×D5—41no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185D3×D5—84no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189Dic15—21no—
190Dic15—21no—
191Dic15—21no—
192C3×Dic5—41no—
193C5×Dic3—41no—
194C23×D3—101no—
195C2×C3×Q8—51no—
196C2×C3×D4—51no—
197C2×#67—101no—
198D3×Q8—202no—
199D3×D4—202no—
200C2×D12C4×D511yescharacteristic
201C2×C4×D3—51no—
202C2×C4×D3—51no—
203C2×C4×D3—51no—
204C2×C4×D3—101no—
205C2×Dic6—101no—
206C2×Dic6C4×D511yescharacteristic
207C2×C3×C8—21no—
208C2×C3×C8—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C42C22×D511yescharacteristic
212#217—101no—
213#217—101no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—101no—
217(C2×D3)⋊C4—101no—
218C4×Dic3—51no—
219C4×Dic3—51no—
220C4×Dic3—51no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C23×C5—61no—
224C22×D5—21no—
225C22×D5—31no—
226C22×D5—122no—
227C22×D5—122no—
228C22×D5—122no—
229C5×Q8—121no—
230C5×D4—121no—
231C2×C4×C5—61no—
232C2×C4×C5C2×C4×D311yescharacteristic
233C2×C4×C5D3×D411yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C22⋊D5—122no—
236C2×Dic5—21no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—31no—
240D20—41no—
241C4×D5—62no—
242C4×D5—122no—
243C4×D5—121no—
244C4×D5—121no—
245Dic10—41no—
246Dic10—122no—
247C5×C8—41no—
248C5×C8—121no—
249#168—41no—
250#168—121no—
251C22×Q8—151no—
252C22×D4—151no—
253#124—31no—
254#124—51no—
255#124—151no—
256#124—151no—
257#124—301no—
258#124—301no—
259C2×C22⋊C4—301no—
260C2×C22⋊C4—301no—
261C2×C42—151no—
262C4⋊C8—301no—
263C4⋊C8—301no—
264C22⋊C8—301no—
265C22⋊C8—301no—
266#97—31no—
267#97—51no—
268#97—151no—
269#97D3×D511yescharacteristic, complemented
270C2×C3×C5C2×#10011yescharacteristic
271C2×C3×C5#42111yescharacteristic
272C2×C3×C5#42111yescharacteristic
273D15—22no—
274C3×D5—81no—
275C5×D3—81no—
276C23×C3—101no—
277C22×D3—21no—
278C22×D3—51no—
279C22×D3—202no—
280C22×D3—202no—
281C22×D3—202no—
282C3×Q8—201no—
283C3×D4—201no—
284C2×C3×C4—101no—
285C2×C3×C4C2×C4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288#67—202no—
289C2×Dic3—21no—
290C2×Dic3—51no—
291C2×Dic3—51no—
292C2×Dic3—51no—
293D12—41no—
294C4×D3—102no—
295C4×D3—202no—
296C4×D3—201no—
297C4×D3—201no—
298Dic6—41no—
299Dic6—202no—
300C3×C8—41no—
301C3×C8—201no—
302C3⋊C8—41no—
303C3⋊C8—201no—
304C22×C5—121no—
305C22×C5—121no—
306C22×C5—121no—
307C22×C5D3×C22⋊C411yescharacteristic
308C2×D5—32no—
309C2×D5—41no—
310C2×D5—41no—
311C2×D5—41no—
312C2×D5—61no—
313C2×D5—61no—
314C2×D5—244no—
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—21no—
318C4×C5—121no—
319Dic5—41no—
320Dic5—61no—
321Dic5—61no—
322Dic5—61no—
323C24—301no—
324C2×Q8—31no—
325C2×Q8—51no—
326C2×Q8—301no—
327C2×Q8—602no—
328C2×D4—31no—
329C2×D4—51no—
330C2×D4—301no—
331C2×D4—602no—
332C22×C4—151no—
333C22×C4—151no—
334C22×C4—151no—
335C22×C4—301no—
336C2×C8—21no—
337C2×C8—61no—
338C2×C8—101no—
339C2×C8—301no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C22⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C22⋊C4—301no—
347C22⋊C4—301no—
348C42—151no—
349C42—151no—
350C42—151no—
351C42C2×D3×D511yescharacteristic
352C3×C5#153311yescharacteristic, complemented, Hall
353C22×C3—201no—
354C22×C3—201no—
355C22×C3—201no—
356C22×C3D5×C22⋊C411yescharacteristic
357C2×D3—41no—
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—52no—
361C2×D3—101no—
362C2×D3—101no—
363C2×D3—404no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—201no—
368Dic3—41no—
369Dic3—101no—
370Dic3—101no—
371Dic3—101no—
372C2×C5—241no—
373C2×C5D3×#10011yescharacteristic
374C2×C5#482111yescharacteristic
375C2×C5#482111yescharacteristic
376D5—62no—
377D5—81no—
378C23—61no—
379C23—101no—
380C23—151no—
381C23—602no—
382C23—602no—
383C23—602no—
384Q8—121no—
385Q8—201no—
386Q8—602no—
387D4—121no—
388D4—201no—
389D4—602no—
390C2×C4—61no—
391C2×C4—101no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4—602no—
399C2×C4C4×D3×D511yescharacteristic
400C2×C4#677711yescharacteristic
401C2×C4#679011yescharacteristic
402C8—41no—
403C8—121no—
404C8—201no—
405C8—601no—
406C2×C3—401no—
407C2×C3D5×#10011yescharacteristic
408C2×C3#6511011yescharacteristic
409C2×C3#6511011yescharacteristic
410D3—81no—
411D3—102no—
412C5#6834711yescharacteristic, complemented, Sylow
413C22—121no—
414C22—121no—
415C22—121no—
416C22—152no—
417C22—201no—
418C22—201no—
419C22—201no—
420C22—301no—
421C22—301no—
422C22—1204no—
423C22#9147311yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—121no—
428C4—201no—
429C4—301no—
430C4—301no—
431C4—301no—
432C3#1059914011yescharacteristic, complemented, Sylow
433C2—241no—
434C2—302no—
435C2—401no—
436C2#1174711311yescharacteristic
437C2#1174822411yescharacteristic
438C2#1174823711yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6777C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11750806C2semidirect
3. #11746940C2semidirect
4. C5×#4464C2semidirect
5. C3×#64684C2semidirect
6. #11745847C2semidirect
7. #11745846C2semidirect
20. C3×C5×#97C22semidirect
23. #91087C22semidirect
24. C5×#803C22semidirect
25. C3×#3935C22semidirect
35. #64684D3semidirect
71. #4464D5semidirect
84. C5×#97C2×D3semidirect
90. #3935C2×D3semidirect
132. C3×#97C2×D5semidirect
138. #803C2×D5semidirect
269. #97D3×D5semidirect
352. C3×C5#1533semidirect
412. C5#68347semidirect
432. C3#10599140semidirect

Maximal subgroups

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

subgroupindex
#117527512
#117508062
#117469402
C5×#44642
C3×#646842
#117458472
#117458462
#105991403
#683475