Finite Group Databasebeta

← #11752837

Subgroups — #11752837

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1202C211yesmaximal, characteristic, complemented
2C2×#6766C211yesmaximal, characteristic, complemented
3C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C5×#878C211yesmaximal, characteristic, complemented
5C3×#4028C211yesmaximal, characteristic, complemented
6#91572C211yesmaximal, characteristic, complemented
7Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
8D5×#217C211yesmaximal, characteristic, complemented
9#91465C211yesmaximal, characteristic, complemented
10#91455C211yesmaximal, characteristic, complemented
11#91413C211yesmaximal, characteristic, complemented
12#91409C211yesmaximal, characteristic, complemented
13#91409C211yesmaximal, characteristic, complemented
14#91396C211yesmaximal, characteristic, complemented
15#91354C211yesmaximal, characteristic, complemented
16#65964—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C23×C3×D5C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic, complemented
20C2×C4×D15C2211yescharacteristic, complemented
21C22×C5×Dic3C2211yescharacteristic
22C2×C5×Dic6C2211yescharacteristic, complemented
23C2×C3×C22⋊D5C2211yescharacteristic
24C2×C3×D20C2211yescharacteristic, complemented
25C2×C3×D20C2211yescharacteristic, complemented
26C2×#1202—24no—
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic
29C2×#1202C2211yescharacteristic
30C2×#1202C2211yescharacteristic
31C2×#1202C2211yescharacteristic, complemented
32C2×#1202C2211yescharacteristic, complemented
33C2×D5×Dic3C2211yescharacteristic, complemented
34C2×D5×Dic3C2211yescharacteristic, complemented
35C2×D5×Dic3C2211yescharacteristic, complemented
36#6766—24no—
37C3×C5×C22⋊C4C2211yescharacteristic
38#6719C2211yescharacteristic
39#6714C2211yescharacteristic, complemented
40#6714C2211yescharacteristic, complemented
41C5×#217C2211yescharacteristic
42C5×C4⋊Dic3C2211yescharacteristic, complemented
43C5×Dic3⋊C4C2211yescharacteristic, complemented
44C5×Dic3⋊C4C2211yescharacteristic, complemented
45C3×#685C2211yescharacteristic, complemented
46C3×#685C2211yescharacteristic, complemented
47#6668C2211yescharacteristic, complemented
48#6667C2211yescharacteristic, complemented
49#6667C2211yescharacteristic, complemented
50#6665C2211yescharacteristic, complemented
51#6665C2211yescharacteristic, complemented
52#6665C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5591—51nomaximal, Hall
55C2×#713—31no—
56C22×D20—31no—
57C5×C22⋊Q8—31no—
58#4093—31no—
59C4×C22⋊D5—31no—
60#4041—31no—
61#4041—31no—
62#4041—31no—
63#4040—31no—
64#4040—31no—
65#4039—31no—
66#4028—31no—
67#4028D311yescharacteristic, complemented
68D5×C22⋊C4—31no—
69D5×C22⋊C4—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15—22no—
72C22×D15—22no—
73C22×D15—41no—
74C22×D15C2311yescharacteristic
75C22×D15C2311yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—22no—
78C22×C3×D5—41no—
79C22×C3×D5C2311yescharacteristic
80C22×C3×D5C2311yescharacteristic
81C22×C3×D5C2311yescharacteristic
82C2×C3×C4×C5C2311yescharacteristic
83C2×C3×C4×C5C2311yescharacteristic
84C2×Dic15C2311yescharacteristic
85C2×Dic15C2311yescharacteristic
86C4×D15—22no—
87C4×D15—41no—
88C2×C5×Dic3—22no—
89C2×C5×Dic3C2311yescharacteristic
90C2×C5×Dic3C2311yescharacteristic
91C2×C5×Dic3C2311yescharacteristic
92C2×C5×Dic3C2311yescharacteristic
93C5×Dic6—22no—
94C3×C22⋊D5—22no—
95C2×C3×Dic5C2311yescharacteristic
96C3×D20—22no—
97C3×D20—41no—
98#1202—22no—
99#1202—22no—
100#1202—22no—
101#1202—22no—
102#1202—41no—
103#1202D414yescomplemented
104D5×Dic3—22no—
105D5×Dic3—22no—
106D5×Dic3—41no—
107C22×#67—51no—
108C2×#237—51no—
109C3×#120—51no—
110C2×#217—51no—
111#939—51no—
112#939—51no—
113#938—51no—
114#937—51no—
115D4×Dic3—51no—
116#886—51no—
117#885—51no—
118#883—51no—
119#67⋊C4—51no—
120D3×C22⋊C4—51no—
121#878D511yescharacteristic, complemented
122C23×D5—31no—
123C23×D5C2×D311yescharacteristic
124C2×C5×Q8—31no—
125C22×C4×C5—31no—
126C2×C22⋊D5C2×D311yescharacteristic
127#713—64no—
128C2×D20—31no—
129C2×D20—31no—
130C2×D20—31no—
131C2×D20—31no—
132C2×D20—31no—
133C2×D20—31no—
134C2×D20—64no—
135C2×D20C2×D311yescharacteristic, complemented
136C2×D20C2×D311yescharacteristic, complemented
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5—31no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—31no—
145C5×C22⋊C4—31no—
146C5×C22⋊C4C2×D311yescharacteristic
147C22⋊Dic5—31no—
148#685—31no—
149#685—31no—
150#685—31no—
151#685—31no—
152#685—31no—
153#685—31no—
154#685—31no—
155#685C2×D311yescharacteristic, complemented
156#685C2×D311yescharacteristic, complemented
157#683—31no—
158C4×Dic5—31no—
159#546—151noSylow
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5#4112yescomplemented
163C22×C3×C5C2411yescharacteristic
164C2×D15—21no—
165C2×D15—21no—
166C2×D15—21no—
167C2×D15—21no—
168C2×D15—21no—
169C2×D15—44no—
170C2×D15C2×D412yes—
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C2×C3×D5—44no—
180C2×C3×D5C2×D412yes—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183Dic15—21no—
184Dic15—21no—
185C3×Dic5—21no—
186C5×Dic3—21no—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3C2×D412yes—
190C24×C3—51no—
191C23×D3—51no—
192C2×C3×D4—51no—
193C2×C3×D4—51no—
194C2×C3×D4—51no—
195C2×#67—51no—
196C2×#67—51no—
197C2×#67—51no—
198C2×#67—51no—
199C2×#67—51no—
200C2×#67—51no—
201C2×#67—104no—
202C22×Dic3—51no—
203C22×Dic3—51no—
204C22×Dic3—51no—
205C22×Dic3C2×D511yescharacteristic
206#237—104no—
207C2×C4×D3—51no—
208C2×C4×D3—51no—
209C2×Dic6C2×D511yescharacteristic, complemented
210C3×C22⋊C4—51no—
211C3×C22⋊C4—51no—
212C3×C22⋊C4C2×D511yescharacteristic
213#217—51no—
214#217—51no—
215#217—51no—
216#217—51no—
217#217C2×D511yescharacteristic
218(C2×D3)⋊C4—51no—
219(C2×D3)⋊C4—51no—
220(C2×D3)⋊C4—51no—
221(C2×D3)⋊C4—51no—
222C4⋊Dic3—51no—
223C4⋊Dic3C2×D511yescharacteristic, complemented
224Dic3⋊C4C2×D511yescharacteristic, complemented
225Dic3⋊C4C2×D511yescharacteristic, complemented
226C4×Dic3—51no—
227C23×C5C22×D311yescharacteristic
228C22×D5—22no—
229C22×D5—22no—
230C22×D5—31no—
231C22×D5—31no—
232C22×D5—41no—
233C22×D5—62no—
234C22×D5—62no—
235C22×D5—121no—
236C22×D5C22×D311yescharacteristic
237C22×D5C22×D311yescharacteristic
238C22×D5C22×D311yescharacteristic
239C5×Q8—62no—
240C2×C4×C5—31no—
241C2×C4×C5—31no—
242C2×C4×C5—31no—
243C2×C4×C5—31no—
244C2×C4×C5—62no—
245C2×C4×C5C22×D311yescharacteristic
246C2×C4×C5C22×D311yescharacteristic
247C22⋊D5—22no—
248C2×Dic5—31no—
249C2×Dic5—31no—
250C2×Dic5C22×D311yescharacteristic
251D20—22no—
252D20—34no—
253D20—41no—
254D20—62no—
255D20—62no—
256D20—62no—
257D20—62no—
258D20—121no—
259C4×D5—62no—
260C4×D5—62no—
261C4×D5—62no—
262C4×D5—121no—
263C4×D5—121no—
264C2×#41—151no—
265C22×D4—151no—
266#124—151no—
267#123—151no—
268#123—151no—
269C22⋊Q8—31no—
270#121—151no—
271#121—151no—
272#121—151no—
273#120—51no—
274#120—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C22⋊C4—151no—
278C2×C22⋊C4—151no—
279C2×C3×C5—22no—
280C2×C3×C5C22×D411yescharacteristic
281C2×C3×C5C2×#4111yescharacteristic
282C2×C3×C5H(5,𝔽2)11yescharacteristic
283D15—22no—
284D15—41no—
285C3×D5—22no—
286C3×D5—41no—
287C3×D5—41no—
288C23×C3—51no—
289C23×C3—51no—
290C23×C3—51no—
291C23×C3—102no—
292C23×C3—102no—
293C23×C3—201no—
294C23×C3C22×D511yescharacteristic
295C22×D3—51no—
296C22×D3—51no—
297C22×D3—102no—
298C22×D3—102no—
299C22×D3—201no—
300C3×D4—102no—
301C3×D4—102no—
302C3×D4—201no—
303C2×C3×C4—51no—
304C2×C3×C4C22×D511yescharacteristic
305C2×C3×C4C22×D511yescharacteristic
306#67—54no—
307#67—102no—
308#67—102no—
309#67—102no—
310#67—102no—
311#67—201no—
312C2×Dic3—22no—
313C2×Dic3—51no—
314C2×Dic3—51no—
315C2×Dic3—102no—
316C2×Dic3—102no—
317C2×Dic3—201no—
318C2×Dic3C22×D511yescharacteristic
319C2×Dic3C22×D511yescharacteristic
320C2×Dic3C22×D511yescharacteristic
321C2×Dic3C22×D511yescharacteristic
322C4×D3—102no—
323C4×D3—201no—
324Dic6—22no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5#23712yescomplemented
328C22×C5C23×D311yescharacteristic
329C2×D5—21no—
330C2×D5—21no—
331C2×D5—21no—
332C2×D5—21no—
333C2×D5—21no—
334C2×D5—21no—
335C2×D5—21no—
336C2×D5—21no—
337C2×D5—32no—
338C2×D5—44no—
339C2×D5—61no—
340C2×D5—61no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—61no—
344C2×D5—124no—
345C2×D5D3×D412yes—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—32no—
349C4×C5—61no—
350C4×C5—61no—
351C4×C5—61no—
352Dic5—21no—
353Dic5—61no—
354Dic5—61no—
355C24—51no—
356C24—151no—
357#41—304no—
358C2×Q8—31no—
359C2×D4—51no—
360C2×D4—51no—
361C2×D4—51no—
362C2×D4—151no—
363C2×D4—151no—
364C2×D4—151no—
365C2×D4—151no—
366C2×D4—151no—
367C2×D4—151no—
368C2×D4—304no—
369C22×C4—31no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4—151no—
375C4⋊C4—31no—
376C4⋊C4—31no—
377C4⋊C4—31no—
378C4⋊C4—151no—
379C22⋊C4—31no—
380C22⋊C4—51no—
381C22⋊C4—51no—
382C22⋊C4—151no—
383C22⋊C4—151no—
384C22⋊C4—151no—
385C22⋊C4—151no—
386C22⋊C4—151no—
387C22⋊C4—151no—
388C22⋊C4—151no—
389C22⋊C4—151no—
390C22⋊C4D3×D511yescharacteristic
391C42—151no—
392C3×C5#54611yescharacteristic, complemented, Hall
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—52no—
396C22×C3—101no—
397C22×C3—101no—
398C22×C3—101no—
399C22×C3—101no—
400C22×C3—101no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3—101no—
404C22×C3—204no—
405C22×C3#71312yescomplemented
406C22×C3C23×D511yescharacteristic
407C2×D3—52no—
408C2×D3—101no—
409C2×D3—101no—
410C2×D3—101no—
411C2×D3—101no—
412C2×D3—101no—
413C2×D3—204no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—101no—
417Dic3—21no—
418Dic3—21no—
419Dic3—21no—
420Dic3—101no—
421Dic3—101no—
422Dic3D4×D512yes—
423C2×C5—22no—
424C2×C5C2×D3×D411yescharacteristic
425C2×C5C2×#23711yescharacteristic
426C2×C5#100411yescharacteristic
427D5—22no—
428D5—41no—
429D5—41no—
430D5—62no—
431D5—121no—
432C23—51no—
433C23—51no—
434C23—51no—
435C23—102no—
436C23—102no—
437C23—151no—
438C23—151no—
439C23—201no—
440C23—302no—
441C23—302no—
442C23—601no—
443C23C2×D3×D511yescharacteristic
444Q8—62no—
445D4—102no—
446D4—102no—
447D4—154no—
448D4—201no—
449D4—302no—
450D4—302no—
451D4—302no—
452D4—302no—
453D4—601no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—51no—
459C2×C4—62no—
460C2×C4—151no—
461C2×C4—151no—
462C2×C4—302no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4C2×D3×D511yescharacteristic
468C2×C4C2×D3×D511yescharacteristic
469C2×C3—22no—
470C2×C3—102no—
471C2×C3—201no—
472C2×C3—201no—
473C2×C3C2×D4×D511yescharacteristic
474C2×C3C2×#71311yescharacteristic
475C2×C3#414911yescharacteristic
476D3—102no—
477D3—201no—
478C5#559111yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—52no—
482C22—101no—
483C22—101no—
484C22—101no—
485C22—101no—
486C22—101no—
487C22—101no—
488C22—101no—
489C22—101no—
490C22—152no—
491C22—204no—
492C22—301no—
493C22—301no—
494C22—301no—
495C22—301no—
496C22—301no—
497C22—604no—
498C22#676612yescomplemented
499C22C22×D3×D511yescharacteristic
500C4—21no—
501C4—21no—
502C4—32no—
503C4—61no—
504C4—61no—
505C4—61no—
506C4—101no—
507C4—301no—
508C4—301no—
509C3#6596411yescharacteristic, complemented, Sylow
510C2—22no—
511C2—102no—
512C2—201no—
513C2—201no—
514C2—302no—
515C2—601no—
516C2C2×#676611yescharacteristic
517C2D3×D4×D511yescharacteristic
518C2#9202611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#1202C2semidirect
2. C2×#6766C2semidirect
3. C22⋊C4×D15C2semidirect
4. C5×#878C2semidirect
5. C3×#4028C2semidirect
6. #91572C2semidirect
7. Dic3×C22⋊D5C2semidirect
8. D5×#217C2semidirect
9. #91465C2semidirect
10. #91455C2semidirect
11. #91413C2semidirect
12. #91409C2semidirect
13. #91409C2semidirect
14. #91396C2semidirect
15. #91354C2semidirect
19. C2×C4×D15C22semidirect
20. C2×C4×D15C22semidirect
22. C2×C5×Dic6C22semidirect
24. C2×C3×D20C22semidirect
25. C2×C3×D20C22semidirect
31. C2×#1202C22semidirect
32. C2×#1202C22semidirect
33. C2×D5×Dic3C22semidirect
34. C2×D5×Dic3C22semidirect
35. C2×D5×Dic3C22semidirect
39. #6714C22semidirect
40. #6714C22semidirect
42. C5×C4⋊Dic3C22semidirect
43. C5×Dic3⋊C4C22semidirect
44. C5×Dic3⋊C4C22semidirect
45. C3×#685C22semidirect
46. C3×#685C22semidirect
47. #6668C22semidirect
48. #6667C22semidirect
49. #6667C22semidirect
50. #6665C22semidirect
51. #6665C22semidirect
52. #6665C22semidirect
53. Dic3×Dic5C22semidirect
67. #4028D3semidirect
103. #1202D4semidirect
121. #878D5semidirect
135. C2×D20C2×D3semidirect
136. C2×D20C2×D3semidirect
155. #685C2×D3semidirect
156. #685C2×D3semidirect
162. C22×C3×C5#41semidirect
209. C2×Dic6C2×D5semidirect
223. C4⋊Dic3C2×D5semidirect
224. Dic3⋊C4C2×D5semidirect
225. Dic3⋊C4C2×D5semidirect
327. C22×C5#237semidirect
392. C3×C5#546semidirect
405. C22×C3#713semidirect
478. C5#5591semidirect
498. C22#6766semidirect
509. C3#65964semidirect

Maximal subgroups

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

subgroupindex
C22×#12022
C2×#67662
C22⋊C4×D152
C5×#8782
C3×#40282
#915722
Dic3×C22⋊D52
D5×#2172
#914652
#914552
#914132
#914092
#913962
#913542
#659643
#55915