Finite Group Databasebeta

← #11756374

Subgroups — #11756374

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
1C3×C5×#121C211yesmaximal, characteristic, complemented
2#91829C211yesmaximal, characteristic, complemented
3#91828C211yesmaximal, characteristic, complemented
4#91828C211yesmaximal, characteristic, complemented
5#91828C211yesmaximal, characteristic, complemented
6#91827C211yesmaximal, characteristic, complemented
7#91824C211yesmaximal, characteristic, complemented
8#91818C211yesmaximal, characteristic, complemented
9C4×#1220C211yesmaximal, characteristic, complemented
10#91783C211yesmaximal, characteristic, complemented
11#91778C211yesmaximal, characteristic, complemented
12#91773C211yesmaximal, characteristic, complemented
13#91772C211yesmaximal, characteristic, complemented
14#91770C211yesmaximal, characteristic, complemented
15#91766C211yesmaximal, characteristic, complemented
16#65949—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic
20C22×C3×C4×C5C2211yescharacteristic
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C2×#1220C2211yescharacteristic
24C2×#1220C2211yescharacteristic
25C2×#1220C2211yescharacteristic
26C2×#1220C2211yescharacteristic
27C22×Dic15C2211yescharacteristic
28C22×Dic15C2211yescharacteristic
29C2×D60C2211yescharacteristic
30C2×C4×D15C2211yescharacteristic
31C2×C4×D15C2211yescharacteristic
32C3×C5×C4⋊C4C2211yescharacteristic
33C3×C5×C22⋊C4C2211yescharacteristic
34C3×C5×C22⋊C4C2211yescharacteristic
35#6719C2211yescharacteristic
36#6719C2211yescharacteristic
37#6719C2211yescharacteristic
38#6719C2211yescharacteristic
39#6714C2211yescharacteristic
40#6714C2211yescharacteristic
41#6714C2211yescharacteristic
42#6714C2211yescharacteristic
43C4⋊Dic15C2211yescharacteristic
44#6712C2211yescharacteristic
45#6712C2211yescharacteristic
46#6712C2211yescharacteristic
47#6712C2211yescharacteristic
48#6712C2211yescharacteristic
49#6712C2211yescharacteristic
50C4×Dic15C2211yescharacteristic
51C4×Dic15C2211yescharacteristic
52#5615—51nomaximal, Hall
53C5×#121D311yescharacteristic, complemented
54#4086—31no—
55#4085—31no—
56#4085—31no—
57#4085—31no—
58#4084—31no—
59#4081—31no—
60#4075—31no—
61C4×C22⋊D5—31no—
62#4040—31no—
63#4035—31no—
64#4030—31no—
65#4029—31no—
66#4027—31no—
67#4023—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C3×C5×D4—41no—
74C3×C5×D4—41no—
75C3×C5×D4—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80C2×C3×C4×C5C2311yescharacteristic
81#1220—22no—
82#1220—22no—
83#1220—41no—
84#1220—41no—
85#1220—41no—
86#1220—41no—
87C2×Dic15—22no—
88C2×Dic15—41no—
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C2×Dic15C2311yescharacteristic
92C2×Dic15C2311yescharacteristic
93C2×Dic15C2311yescharacteristic
94C2×Dic15C2311yescharacteristic
95D60—41no—
96C4×D15—41no—
97C4×D15—41no—
98C3×#121D511yescharacteristic, complemented
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#889—51no—
109#884—51no—
110#883—51no—
111#67⋊C4—51no—
112#877—51no—
113C2×C5×D4C2×D311yescharacteristic
114C2×C5×D4C2×D311yescharacteristic
115C2×C5×D4C2×D311yescharacteristic
116C22×C4×C5C2×D311yescharacteristic
117C2×C22⋊D5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C22×Dic5—31no—
124C22×Dic5—31no—
125C2×D20—31no—
126C2×C4×D5—31no—
127C2×C4×D5—31no—
128C5×C4⋊C4C2×D311yescharacteristic
129C5×C22⋊C4C2×D311yescharacteristic
130C5×C22⋊C4C2×D311yescharacteristic
131C22⋊Dic5—31no—
132C22⋊Dic5—31no—
133C22⋊Dic5—31no—
134C22⋊Dic5—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139C4⋊Dic5—31no—
140#683—31no—
141#683—31no—
142#683—31no—
143#683—31no—
144#683—31no—
145#683—31no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148#540—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5C2411yescharacteristic
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×D15—21no—
163C2×D15—21no—
164C2×D15—21no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169Dic15—21no—
170Dic15—21no—
171Dic15—21no—
172Dic15—21no—
173Dic15—21no—
174Dic15#4112yes—
175C2×C3×D4C2×D511yescharacteristic
176C2×C3×D4C2×D511yescharacteristic
177C2×C3×D4C2×D511yescharacteristic
178C22×C3×C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
192C3×C22⋊C4C2×D511yescharacteristic
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⋊Dic3—51no—
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204Dic3⋊C4—51no—
205Dic3⋊C4—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4—51no—
208C4×Dic3—51no—
209C4×Dic3—51no—
210C23×C5C22×D311yescharacteristic
211C23×C5C22×D311yescharacteristic
212C23×C5C22×D311yescharacteristic
213C22×D5—31no—
214C22×D5—31no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—41no—
219C2×C4×C5C22×D311yescharacteristic
220C2×C4×C5C22×D311yescharacteristic
221C2×C4×C5C22×D311yescharacteristic
222C2×C4×C5C22×D311yescharacteristic
223C22⋊D5—62no—
224C22⋊D5—62no—
225C22⋊D5—121no—
226C22⋊D5—121no—
227C22⋊D5—121no—
228C22⋊D5—121no—
229C2×Dic5—31no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—62no—
236C2×Dic5—121no—
237D20—121no—
238C4×D5—121no—
239C4×D5—121no—
240#127—151no—
241#125—151no—
242#123—151no—
243#123—151no—
244#123—151no—
245#123—151no—
246#121—151no—
247#121—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#121D1511yescharacteristic, complemented
252C4×D4—151no—
253C4×D4—151no—
254#117—151no—
255C2×C3×C5—41no—
256C2×C3×C5—41no—
257C2×C3×C5—41no—
258C2×C3×C5C2×#4111yescharacteristic
259C2×C3×C5H(5,𝔽2)11yescharacteristic
260C2×C3×C5H(5,𝔽2)11yescharacteristic
261D15—41no—
262D15—41no—
263C23×C3C22×D511yescharacteristic
264C23×C3C22×D511yescharacteristic
265C23×C3C22×D511yescharacteristic
266C22×D3—51no—
267C22×D3—51no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—41no—
271C2×C3×C4—41no—
272C2×C3×C4C22×D511yescharacteristic
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—51no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—102no—
289C2×Dic3—201no—
290D12—201no—
291C4×D3—201no—
292C4×D3—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5C23×D311yescharacteristic
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—21no—
313Dic5—32no—
314Dic5—61no—
315Dic5—61no—
316Dic5—61no—
317Dic5—61no—
318Dic5—61no—
319C2×D4—151no—
320C2×D4—151no—
321C2×D4—151no—
322C2×D4—151no—
323C2×D4—151no—
324C2×D4—151no—
325C2×D4—151no—
326C2×D4C2×D1511yescharacteristic
327C2×D4C2×D1511yescharacteristic
328C2×D4C2×D1511yescharacteristic
329C22×C4—151no—
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4C2×D1511yescharacteristic
334C4⋊C4—151no—
335C4⋊C4—151no—
336C4⋊C4—151no—
337C4⋊C4—151no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C4⋊C4—151no—
341C4⋊C4C2×D1511yescharacteristic
342C22⋊C4—151no—
343C22⋊C4—151no—
344C22⋊C4—151no—
345C22⋊C4—151no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4C2×D1511yescharacteristic
351C22⋊C4C2×D1511yescharacteristic
352C42—151no—
353C42—151no—
354C3×C5#54011yescharacteristic, complemented, Hall
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
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—21no—
375Dic3—52no—
376Dic3—101no—
377Dic3—101no—
378Dic3—101no—
379Dic3—101no—
380Dic3—101no—
381C2×C5—41no—
382C2×C5—41no—
383C2×C5—41no—
384C2×C5#100411yescharacteristic
385C2×C5#100411yescharacteristic
386C2×C5D3×#4111yescharacteristic
387D5—121no—
388D5—121no—
389C23—151no—
390C23—151no—
391C23C22×D1511yescharacteristic
392C23C22×D1511yescharacteristic
393C23C22×D1511yescharacteristic
394D4—41no—
395D4—41no—
396D4—41no—
397D4—302no—
398D4—302no—
399D4—601no—
400D4—601no—
401D4—601no—
402D4—601no—
403D4—601no—
404C2×C4—41no—
405C2×C4—151no—
406C2×C4—151no—
407C2×C4—151no—
408C2×C4—151no—
409C2×C4—151no—
410C2×C4—151no—
411C2×C4—302no—
412C2×C4—601no—
413C2×C4—601no—
414C2×C4—601no—
415C2×C4C22×D1511yescharacteristic
416C2×C4C22×D1511yescharacteristic
417C2×C4C22×D1511yescharacteristic
418C2×C4C22×D1511yescharacteristic
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3#414411yescharacteristic
423C2×C3#414411yescharacteristic
424C2×C3D5×#4111yescharacteristic
425D3—201no—
426D3—201no—
427C5#561511yescharacteristic, complemented, Sylow
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—301no—
438C22—301no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22—301no—
443C22C23×D1511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—152no—
449C4—301no—
450C4—301no—
451C4—301no—
452C4—301no—
453C4—301no—
454C3#6594911yescharacteristic, complemented, Sylow
455C2—41no—
456C2—41no—
457C2—41no—
458C2—601no—
459C2—601no—
460C2#9209511yescharacteristic
461C2#9209511yescharacteristic
462C2#41×D1511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#121C2
hypercenter#121D15
hypocenterC3×C5#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×C5×#121C2semidirect
2. #91829C2semidirect
3. #91828C2semidirect
4. #91828C2semidirect
5. #91828C2semidirect
6. #91827C2semidirect
7. #91824C2semidirect
8. #91818C2semidirect
9. C4×#1220C2semidirect
10. #91783C2semidirect
11. #91778C2semidirect
12. #91773C2semidirect
13. #91772C2semidirect
14. #91770C2semidirect
15. #91766C2semidirect
53. C5×#121D3semidirect
98. C3×#121D5semidirect
251. #121D15semidirect
354. C3×C5#540semidirect
427. C5#5615semidirect
454. C3#65949semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1212
#918292
#918282
#918272
#918242
#918182
C4×#12202
#917832
#917782
#917732
#917722
#917702
#917662
#659493
#56155