Finite Group Databasebeta

← #11756299

Subgroups — #11756299

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2#91828C211yesmaximal, characteristic, complemented
3#91828C211yesmaximal, characteristic, complemented
4#91819C211yesmaximal, characteristic, complemented
5#91818C211yesmaximal, characteristic, complemented
6C4×#1220C211yesmaximal, characteristic, complemented
7C2×#6712C211yesmaximal, characteristic, complemented
8#91783C211yesmaximal, characteristic, complemented
9#91778C211yesmaximal, characteristic, complemented
10#91773C211yesmaximal, characteristic, complemented
11#91770C211yesmaximal, characteristic, complemented
12#91770C211yesmaximal, characteristic, complemented
13#91768C211yesmaximal, characteristic, complemented
14#91765C211yesmaximal, characteristic, complemented
15#91761C211yesmaximal, characteristic, complemented
16#65874—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C22×C3×C4×C5C2211yescharacteristic
19C22×C3×C4×C5C2211yescharacteristic
20C2×#1220C2211yescharacteristic
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C2×#1220C2211yescharacteristic
24C22×Dic15C2211yescharacteristic
25C22×Dic15C2211yescharacteristic
26C2×D60C2211yescharacteristic
27C2×C4×D15C2211yescharacteristic
28C2×C4×D15C2211yescharacteristic
29C3×C5×C4⋊C4C2211yescharacteristic
30C3×C5×C22⋊C4C2211yescharacteristic
31C3×C5×C22⋊C4C2211yescharacteristic
32C3×C42×C5C2211yescharacteristic
33#6719C2211yescharacteristic
34#6719C2211yescharacteristic
35#6714C2211yescharacteristic
36#6714C2211yescharacteristic
37#6714C2211yescharacteristic
38#6714C2211yescharacteristic
39#6714C2211yescharacteristic
40#6714C2211yescharacteristic
41C4⋊Dic15C2211yescharacteristic
42#6712C2211yescharacteristic
43#6712C2211yescharacteristic
44#6712C2211yescharacteristic
45#6712C2211yescharacteristic
46#6712C2211yescharacteristic
47#6712C2211yescharacteristic
48#6712C2211yescharacteristic
49#6712C2211yescharacteristic
50C4×Dic15C2211yescharacteristic
51C4×Dic15C2211yescharacteristic
52#5540—51nomaximal, Hall
53C4×C5×D4D311yescharacteristic, complemented
54#4085—31no—
55#4085—31no—
56#4076—31no—
57#4075—31no—
58C4×C22⋊D5—31no—
59C2×#683—31no—
60#4040—31no—
61#4035—31no—
62#4030—31no—
63#4027—31no—
64#4027—31no—
65#4025—31no—
66#4022—31no—
67#4018—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C3×C5×D4—22no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80#1220—22no—
81#1220—22no—
82#1220—22no—
83#1220—41no—
84C2×Dic15—22no—
85C2×Dic15—41no—
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C2×Dic15C2311yescharacteristic
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C2×Dic15C2311yescharacteristic
92D60—41no—
93C4×D15—22no—
94C4×D15—41no—
95C3×C4×D4D511yescharacteristic, complemented
96#939—51no—
97#939—51no—
98#930—51no—
99#929—51no—
100C4×#67—51no—
101C2×Dic3⋊C4—51no—
102#894—51no—
103#889—51no—
104#884—51no—
105#67⋊C4—51no—
106#67⋊C4—51no—
107#879—51no—
108#876—51no—
109#872—51no—
110C2×C5×D4C2×D311yescharacteristic
111C22×C4×C5C2×D311yescharacteristic
112C22×C4×C5C2×D311yescharacteristic
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5—31no—
116C2×C22⋊D5—31no—
117C22×Dic5—31no—
118C22×Dic5—31no—
119C2×D20—31no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C5×C4⋊C4C2×D311yescharacteristic
123C5×C22⋊C4C2×D311yescharacteristic
124C5×C22⋊C4C2×D311yescharacteristic
125C42×C5C2×D311yescharacteristic
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134C4⋊Dic5—31no—
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683—31no—
142#683—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145#553—151noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#4112yes—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164Dic15—21no—
165Dic15—21no—
166Dic15—21no—
167Dic15—21no—
168Dic15—21no—
169Dic15#4112yes—
170C2×C3×D4C2×D511yescharacteristic
171C22×C3×C4C2×D511yescharacteristic
172C22×C3×C4C2×D511yescharacteristic
173C2×#67—51no—
174C2×#67—51no—
175C2×#67—51no—
176C2×#67—51no—
177C22×Dic3—51no—
178C22×Dic3—51no—
179C2×D12—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C3×C4⋊C4C2×D511yescharacteristic
183C3×C22⋊C4C2×D511yescharacteristic
184C3×C22⋊C4C2×D511yescharacteristic
185C3×C42C2×D511yescharacteristic
186#217—51no—
187#217—51no—
188(C2×D3)⋊C4—51no—
189(C2×D3)⋊C4—51no—
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194C4⋊Dic3—51no—
195Dic3⋊C4—51no—
196Dic3⋊C4—51no—
197Dic3⋊C4—51no—
198Dic3⋊C4—51no—
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203C4×Dic3—51no—
204C4×Dic3—51no—
205C23×C5C22×D311yescharacteristic
206C23×C5C22×D311yescharacteristic
207C22×D5—31no—
208C22×D5—31no—
209C5×D4—22no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5C22×D311yescharacteristic
213C2×C4×C5C22×D311yescharacteristic
214C2×C4×C5C22×D311yescharacteristic
215C2×C4×C5C22×D311yescharacteristic
216C2×C4×C5C22×D311yescharacteristic
217C22⋊D5—62no—
218C22⋊D5—62no—
219C22⋊D5—62no—
220C22⋊D5—121no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—31no—
227C2×Dic5—62no—
228C2×Dic5—121no—
229D20—121no—
230C4×D5—62no—
231C4×D5—121no—
232#126—151no—
233#126—151no—
234#125—151no—
235#123—151no—
236#123—151no—
237#121—151no—
238#121—151no—
239#121—151no—
240#121—151no—
241C4×D4—151no—
242C4×D4—151no—
243C4×D4—151no—
244C4×D4D1511yescharacteristic, complemented
245#117—151no—
246C2×C4⋊C4—151no—
247C2×C3×C5—22no—
248C2×C3×C5—41no—
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5C2×#4111yescharacteristic
251C2×C3×C5H(5,𝔽2)11yescharacteristic
252D15—41no—
253D15—41no—
254C23×C3C22×D511yescharacteristic
255C23×C3C22×D511yescharacteristic
256C22×D3—51no—
257C22×D3—51no—
258C3×D4—22no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4C22×D511yescharacteristic
262C2×C3×C4C22×D511yescharacteristic
263C2×C3×C4C22×D511yescharacteristic
264C2×C3×C4C22×D511yescharacteristic
265C2×C3×C4C22×D511yescharacteristic
266#67—102no—
267#67—102no—
268#67—102no—
269#67—201no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—51no—
275C2×Dic3—51no—
276C2×Dic3—102no—
277C2×Dic3—201no—
278D12—201no—
279C4×D3—102no—
280C4×D3—201no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5#23512yes—
287C22×C5C23×D311yescharacteristic
288C2×D5—61no—
289C2×D5—61no—
290C2×D5—61no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299Dic5—32no—
300Dic5—61no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5—61no—
305C2×D4—151no—
306C2×D4—151no—
307C2×D4—151no—
308C2×D4—151no—
309C2×D4—151no—
310C2×D4C2×D1511yescharacteristic
311C22×C4—151no—
312C22×C4—151no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4C2×D1511yescharacteristic
316C22×C4C2×D1511yescharacteristic
317C4⋊C4—151no—
318C4⋊C4—151no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C4⋊C4—151no—
326C4⋊C4C2×D1511yescharacteristic
327C22⋊C4—151no—
328C22⋊C4—151no—
329C22⋊C4—151no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4C2×D1511yescharacteristic
336C22⋊C4C2×D1511yescharacteristic
337C42—151no—
338C42—151no—
339C42C2×D1511yescharacteristic
340C3×C5#55311yescharacteristic, complemented, Hall
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3#70912yes—
347C22×C3C23×D511yescharacteristic
348C2×D3—101no—
349C2×D3—101no—
350C2×D3—101no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359Dic3—52no—
360Dic3—101no—
361Dic3—101no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5—22no—
366C2×C5—41no—
367C2×C5C2×#23511yescharacteristic
368C2×C5#100411yescharacteristic
369C2×C5D3×#4111yescharacteristic
370D5—121no—
371D5—121no—
372C23—151no—
373C23—151no—
374C23C22×D1511yescharacteristic
375C23C22×D1511yescharacteristic
376D4—22no—
377D4—302no—
378D4—302no—
379D4—302no—
380D4—601no—
381D4—601no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—151no—
385C2×C4—151no—
386C2×C4—151no—
387C2×C4—151no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—302no—
391C2×C4—302no—
392C2×C4—601no—
393C2×C4—601no—
394C2×C4C22×D1511yescharacteristic
395C2×C4C22×D1511yescharacteristic
396C2×C4C22×D1511yescharacteristic
397C2×C4C22×D1511yescharacteristic
398C2×C4C22×D1511yescharacteristic
399C2×C3—22no—
400C2×C3—41no—
401C2×C3C2×#70911yescharacteristic
402C2×C3#414411yescharacteristic
403C2×C3D5×#4111yescharacteristic
404D3—201no—
405D3—201no—
406C5#554011yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—301no—
413C22—301no—
414C22—301no—
415C22—301no—
416C22—301no—
417C22—301no—
418C22#681712yes—
419C22C23×D1511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—152no—
426C4—301no—
427C4—301no—
428C4—301no—
429C4—301no—
430C4—301no—
431C3#6587411yescharacteristic, complemented, Sylow
432C2—22no—
433C2—41no—
434C2—601no—
435C2—601no—
436C2C2×#681711yescharacteristic
437C2#9209511yescharacteristic
438C2#41×D1511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C4×C5×D4C2
hypercenterC4×D4D15
hypocenterC3×C5#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×C5×D4C2semidirect
2. #91828C2semidirect
3. #91828C2semidirect
4. #91819C2semidirect
5. #91818C2semidirect
6. C4×#1220C2semidirect
7. C2×#6712C2semidirect
8. #91783C2semidirect
9. #91778C2semidirect
10. #91773C2semidirect
11. #91770C2semidirect
12. #91770C2semidirect
13. #91768C2semidirect
14. #91765C2semidirect
15. #91761C2semidirect
53. C4×C5×D4D3semidirect
95. C3×C4×D4D5semidirect
244. C4×D4D15semidirect
340. C3×C5#553semidirect
406. C5#5540semidirect
431. C3#65874semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×D42
#918282
#918192
#918182
C4×#12202
C2×#67122
#917832
#917782
#917732
#917702
#917682
#917652
#917612
#658743
#55405