Finite Group Databasebeta

← #11753772

Subgroups — #11753772

Order 960.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91783C211yesmaximal, characteristic, complemented
2C5×#889C211yesmaximal, characteristic, complemented
3C3×#4041C211yesmaximal, characteristic, complemented
4#91465C211yesmaximal, characteristic, complemented
5#91459C211yesmaximal, characteristic, complemented
6#91458C211yesmaximal, characteristic, complemented
7#91444C211yesmaximal, characteristic, complemented
8#91409C211yesmaximal, characteristic, complemented
9#91409C211yesmaximal, characteristic, complemented
10#91409C211yesmaximal, characteristic, complemented
11#91407C211yesmaximal, characteristic, complemented
12#91396C211yesmaximal, characteristic, complemented
13#91393C211yesmaximal, characteristic, complemented
14#91356C211yesmaximal, characteristic, complemented
15#91348C211yesmaximal, characteristic, complemented
16#66032—31nomaximal, Hall
17C2×D60C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C3×D20C2211yescharacteristic
20C2×C3×D20C2211yescharacteristic
21C2×C3×D20C2211yescharacteristic
22C2×C3×C4×D5C2211yescharacteristic
23C2×#1202C2211yescharacteristic
24C2×#1202C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic
29C2×#1200C2211yescharacteristic
30C2×D5×Dic3C2211yescharacteristic
31C2×D5×Dic3C2211yescharacteristic
32C3×C5×C4⋊C4C2211yescharacteristic
33#6714C2211yescharacteristic
34#6714C2211yescharacteristic
35#6714C2211yescharacteristic
36#6712C2211yescharacteristic
37C5×C4⋊Dic3C2211yescharacteristic
38C5×Dic3⋊C4C2211yescharacteristic
39C5×Dic3⋊C4C2211yescharacteristic
40C5×Dic3⋊C4C2211yescharacteristic
41C5×Dic3⋊C4C2211yescharacteristic
42C4×C5×Dic3C2211yescharacteristic
43C3×#685C2211yescharacteristic
44C3×#685C2211yescharacteristic
45#6669C2211yescharacteristic
46#6667C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5615—51nomaximal, Hall
53C5×#125—31no—
54#4041—31no—
55#4041—31no—
56#4041—31no—
57#4041—31no—
58#4041—31no—
59#4041D311yescharacteristic, complemented
60#4040—31no—
61#4040—31no—
62#4040—31no—
63#4040—31no—
64#4039—31no—
65#4039—31no—
66#4020—31no—
67#4018—31no—
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C22×C3×D5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78D60—41no—
79C4×D15—41no—
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C3×D20—41no—
86C3×D20—41no—
87C3×D20—41no—
88C3×C4×D5—41no—
89#1202—22no—
90#1202—22no—
91#1202—41no—
92#1202—41no—
93#1202—41no—
94#1202—41no—
95#1200—41no—
96D5×Dic3—22no—
97D5×Dic3—41no—
98C3×#121—51no—
99#940—51no—
100#939—51no—
101#939—51no—
102#939—51no—
103#938—51no—
104#935—51no—
105#929—51no—
106C4×#67—51no—
107#894—51no—
108#889D511yescharacteristic, complemented
109#884—51no—
110#883—51no—
111#67⋊C4—51no—
112#877—51no—
113C2×D20—31no—
114C2×D20—31no—
115C2×D20—31no—
116C2×D20—31no—
117C2×D20—31no—
118C2×D20—31no—
119C2×D20—31no—
120C2×D20C2×D311yescharacteristic
121C2×D20C2×D311yescharacteristic
122C2×D20C2×D311yescharacteristic
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×C4×D5—31no—
126C2×C4×D5—31no—
127C2×C4×D5C2×D311yescharacteristic
128C5×C4⋊C4—31no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4C2×D311yescharacteristic
134C42×C5—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685C2×D311yescharacteristic
144#685C2×D311yescharacteristic
145#683—31no—
146#683—31no—
147C4×Dic5—31no—
148#540—151noSylow
149C22×C3×C5C2411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C2×C3×D5—21no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—21no—
169Dic15—21no—
170C3×Dic5—21no—
171C5×Dic3—21no—
172C5×Dic3—21no—
173C5×Dic3—21no—
174C5×Dic3#4112yes—
175C2×C3×D4—51no—
176C2×C3×D4—51no—
177C2×C3×D4—51no—
178C22×C3×C4—51no—
179C2×#67—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67—51no—
184C2×#67—51no—
185C22×Dic3—51no—
186C22×Dic3—51no—
187C2×D12—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C3×C4⋊C4C2×D511yescharacteristic
191C3×C22⋊C4—51no—
192C3×C22⋊C4—51no—
193#217—51no—
194#217—51no—
195#217—51no—
196#217—51no—
197(C2×D3)⋊C4—51no—
198(C2×D3)⋊C4—51no—
199(C2×D3)⋊C4—51no—
200(C2×D3)⋊C4—51no—
201C4⋊Dic3C2×D511yescharacteristic
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204Dic3⋊C4C2×D511yescharacteristic
205Dic3⋊C4C2×D511yescharacteristic
206Dic3⋊C4C2×D511yescharacteristic
207Dic3⋊C4C2×D511yescharacteristic
208C4×Dic3—51no—
209C4×Dic3C2×D511yescharacteristic
210C22×D5—31no—
211C22×D5—31no—
212C22×D5C22×D311yescharacteristic
213C22×D5C22×D311yescharacteristic
214C22×D5C22×D311yescharacteristic
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5C22×D311yescharacteristic
220C2×C4×C5C22×D311yescharacteristic
221C2×C4×C5C22×D311yescharacteristic
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5C22×D311yescharacteristic
225D20—41no—
226D20—41no—
227D20—41no—
228D20—62no—
229D20—62no—
230D20—121no—
231D20—121no—
232D20—121no—
233D20—121no—
234D20—121no—
235C4×D5—41no—
236C4×D5—62no—
237C4×D5—121no—
238C4×D5—121no—
239C4×D5—121no—
240#127—151no—
241#125—31no—
242#123—151no—
243#123—151no—
244#123—151no—
245#123—151no—
246#121—51no—
247#121—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#121—151no—
252C4×D4—151no—
253C4×D4—151no—
254#117—151no—
255C2×C3×C5C2×#4111yescharacteristic
256C2×C3×C5H(5,𝔽2)11yescharacteristic
257C2×C3×C5H(5,𝔽2)11yescharacteristic
258D15—41no—
259D15—41no—
260C3×D5—41no—
261C3×D5—41no—
262C3×D5—41no—
263C23×C3—51no—
264C23×C3—51no—
265C23×C3—51no—
266C22×D3—51no—
267C22×D3—51no—
268C3×D4—201no—
269C3×D4—201no—
270C3×D4—201no—
271C2×C3×C4—51no—
272C2×C3×C4—201no—
273C2×C3×C4C22×D511yescharacteristic
274C2×C3×C4C22×D511yescharacteristic
275C2×C3×C4C22×D511yescharacteristic
276#67—102no—
277#67—102no—
278#67—201no—
279#67—201no—
280#67—201no—
281#67—201no—
282C2×Dic3—51no—
283C2×Dic3—51no—
284C2×Dic3—102no—
285C2×Dic3—201no—
286C2×Dic3C22×D511yescharacteristic
287C2×Dic3C22×D511yescharacteristic
288C2×Dic3C22×D511yescharacteristic
289C2×Dic3C22×D511yescharacteristic
290D12—201no—
291C4×D3—201no—
292C4×D3—201no—
293C22×C5C23×D311yescharacteristic
294C2×D5—21no—
295C2×D5—21no—
296C2×D5—21no—
297C2×D5—21no—
298C2×D5—21no—
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—61no—
304C2×D5—61no—
305C2×D5—61no—
306C2×D5—61no—
307C2×D5—61no—
308C2×D5—61no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—21no—
312C4×C5—32no—
313C4×C5—61no—
314C4×C5—61no—
315C4×C5—61no—
316Dic5—21no—
317Dic5—61no—
318Dic5—61no—
319C2×D4—51no—
320C2×D4—51no—
321C2×D4—51no—
322C2×D4—151no—
323C2×D4—151no—
324C2×D4—151no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C22×C4—51no—
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—31no—
337C4⋊C4—31no—
338C4⋊C4—31no—
339C4⋊C4—151no—
340C4⋊C4—151no—
341C4⋊C4D3×D511yescharacteristic
342C22⋊C4—51no—
343C22⋊C4—51no—
344C22⋊C4—151no—
345C22⋊C4—151no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C42—31no—
353C42—151no—
354C3×C5#54011yescharacteristic, complemented, Hall
355C22×C3—101no—
356C22×C3—101no—
357C22×C3—101no—
358C22×C3—101no—
359C22×C3—101no—
360C22×C3—101no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3—101no—
364C22×C3C23×D511yescharacteristic
365C2×D3—101no—
366C2×D3—101no—
367C2×D3—101no—
368C2×D3—101no—
369C2×D3—101no—
370C2×D3—101no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—101no—
375Dic3—21no—
376Dic3—21no—
377Dic3—21no—
378Dic3—101no—
379Dic3—101no—
380Dic3#71312yes—
381C2×C5#100411yescharacteristic
382C2×C5#100411yescharacteristic
383C2×C5D3×#4111yescharacteristic
384D5—41no—
385D5—41no—
386D5—41no—
387D5—121no—
388D5—121no—
389C23—51no—
390C23—51no—
391C23—51no—
392C23—151no—
393C23—151no—
394D4—201no—
395D4—201no—
396D4—201no—
397D4—302no—
398D4—302no—
399D4—601no—
400D4—601no—
401D4—601no—
402D4—601no—
403D4—601no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—51no—
409C2×C4—151no—
410C2×C4—151no—
411C2×C4—201no—
412C2×C4—302no—
413C2×C4—601no—
414C2×C4—601no—
415C2×C4—601no—
416C2×C4C2×D3×D511yescharacteristic
417C2×C4C2×D3×D511yescharacteristic
418C2×C4C2×D3×D511yescharacteristic
419C2×C3—201no—
420C2×C3—201no—
421C2×C3—201no—
422C2×C3C2×#71311yescharacteristic
423C2×C3#414911yescharacteristic
424C2×C3#414911yescharacteristic
425D3—201no—
426D3—201no—
427C5#561511yescharacteristic, complemented, Sylow
428C22—101no—
429C22—101no—
430C22—101no—
431C22—101no—
432C22—101no—
433C22—101no—
434C22—101no—
435C22—101no—
436C22—101no—
437C22—301no—
438C22—301no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22—301no—
443C22C22×D3×D511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—32no—
448C4—61no—
449C4—61no—
450C4—61no—
451C4—101no—
452C4—301no—
453C4—301no—
454C3#6603211yescharacteristic, complemented, Sylow
455C2—201no—
456C2—201no—
457C2—201no—
458C2—601no—
459C2—601no—
460C2#9201711yescharacteristic
461C2#9202611yescharacteristic
462C2D3×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #91783C2semidirect
2. C5×#889C2semidirect
3. C3×#4041C2semidirect
4. #91465C2semidirect
5. #91459C2semidirect
6. #91458C2semidirect
7. #91444C2semidirect
8. #91409C2semidirect
9. #91409C2semidirect
10. #91409C2semidirect
11. #91407C2semidirect
12. #91396C2semidirect
13. #91393C2semidirect
14. #91356C2semidirect
15. #91348C2semidirect
59. #4041D3semidirect
108. #889D5semidirect
354. C3×C5#540semidirect
427. C5#5615semidirect
454. C3#66032semidirect

Maximal subgroups

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

subgroupindex
#917832
C5×#8892
C3×#40412
#914652
#914592
#914582
#914442
#914092
#914072
#913962
#913932
#913562
#913482
#660323
#56155