Finite Group Databasebeta

← #11756468

Subgroups — #11756468

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×C5×#126C211yesmaximal, characteristic, complemented
2#91787C211yesmaximal, characteristic, complemented
3#91784C211yesmaximal, characteristic, complemented
4#91783C211yesmaximal, characteristic, complemented
5#91782C211yesmaximal, characteristic, complemented
6C4⋊C4×D15C211yesmaximal, characteristic, complemented
7#91778C211yesmaximal, characteristic, complemented
8#91775C211yesmaximal, characteristic, complemented
9#91773C211yesmaximal, characteristic, complemented
10#91773C211yesmaximal, characteristic, complemented
11#91773C211yesmaximal, characteristic, complemented
12#91770C211yesmaximal, characteristic, complemented
13#91770C211yesmaximal, characteristic, complemented
14C4×D60C211yesmaximal, characteristic, complemented
15#91761C211yesmaximal, characteristic, complemented
16#66043—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C22×Dic15C2211yescharacteristic
21C2×D60C2211yescharacteristic
22C2×D60C2211yescharacteristic
23C2×D60C2211yescharacteristic
24C2×C4×D15C2211yescharacteristic
25C2×C4×D15C2211yescharacteristic
26C2×C4×D15C2211yescharacteristic
27C2×C4×D15C2211yescharacteristic
28C2×C4×D15C2211yescharacteristic
29C3×C5×C4⋊C4C2211yescharacteristic
30C3×C5×C4⋊C4C2211yescharacteristic
31C3×C5×C4⋊C4C2211yescharacteristic
32C3×C5×C22⋊C4C2211yescharacteristic
33C3×C5×C22⋊C4C2211yescharacteristic
34C3×C5×C22⋊C4C2211yescharacteristic
35C3×C42×C5C2211yescharacteristic
36#6714C2211yescharacteristic
37#6714C2211yescharacteristic
38#6714C2211yescharacteristic
39#6714C2211yescharacteristic
40#6714C2211yescharacteristic
41#6714C2211yescharacteristic
42#6714C2211yescharacteristic
43C4⋊Dic15C2211yescharacteristic
44C4⋊Dic15C2211yescharacteristic
45#6712C2211yescharacteristic
46#6712C2211yescharacteristic
47#6712C2211yescharacteristic
48#6712C2211yescharacteristic
49#6712C2211yescharacteristic
50C4×Dic15C2211yescharacteristic
51C4×Dic15C2211yescharacteristic
52#5709—51nomaximal, Hall
53C5×#126D311yescharacteristic, complemented
54#4044—31no—
55#4041—31no—
56#4040—31no—
57#4039—31no—
58D5×C4⋊C4—31no—
59#4035—31no—
60#4032—31no—
61#4030—31no—
62#4030—31no—
63#4030—31no—
64#4027—31no—
65#4027—31no—
66C4×D20—31no—
67#4018—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78#1220—22no—
79#1220—22no—
80#1220—41no—
81C2×Dic15—41no—
82C2×Dic15C2311yescharacteristic
83C2×Dic15C2311yescharacteristic
84C2×Dic15C2311yescharacteristic
85C2×Dic15C2311yescharacteristic
86C2×Dic15C2311yescharacteristic
87D60—22no—
88D60—22no—
89D60—41no—
90C4×D15—22no—
91C4×D15—22no—
92C4×D15—41no—
93C4×D15—41no—
94C4×D15—41no—
95C3×#126D511yescharacteristic, complemented
96#898—51no—
97#895—51no—
98#894—51no—
99#893—51no—
100D3×C4⋊C4—51no—
101#889—51no—
102#886—51no—
103#884—51no—
104#884—51no—
105#884—51no—
106#67⋊C4—51no—
107#67⋊C4—51no—
108C4×D12—51no—
109#872—51no—
110C2×C22⋊D5—31no—
111C2×C22⋊D5—31no—
112C2×C22⋊D5—31no—
113C22×Dic5—31no—
114C2×D20—31no—
115C2×D20—31no—
116C2×D20—31no—
117C2×C4×D5—31no—
118C2×C4×D5—31no—
119C2×C4×D5—31no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C5×C4⋊C4C2×D311yescharacteristic
123C5×C4⋊C4C2×D311yescharacteristic
124C5×C4⋊C4C2×D311yescharacteristic
125C5×C22⋊C4C2×D311yescharacteristic
126C5×C22⋊C4C2×D311yescharacteristic
127C5×C22⋊C4C2×D311yescharacteristic
128C42×C5C2×D311yescharacteristic
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134#685—31no—
135#685—31no—
136C4⋊Dic5—31no—
137C4⋊Dic5—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×C5C2411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15#4112yes—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165Dic15—21no—
166Dic15—21no—
167Dic15—21no—
168Dic15—21no—
169Dic15#4112yes—
170C2×#67—51no—
171C2×#67—51no—
172C2×#67—51no—
173C22×Dic3—51no—
174C2×D12—51no—
175C2×D12—51no—
176C2×D12—51no—
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C3×C4⋊C4C2×D511yescharacteristic
183C3×C4⋊C4C2×D511yescharacteristic
184C3×C4⋊C4C2×D511yescharacteristic
185C3×C22⋊C4C2×D511yescharacteristic
186C3×C22⋊C4C2×D511yescharacteristic
187C3×C22⋊C4C2×D511yescharacteristic
188C3×C42C2×D511yescharacteristic
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—
194(C2×D3)⋊C4—51no—
195(C2×D3)⋊C4—51no—
196C4⋊Dic3—51no—
197C4⋊Dic3—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
206C22×D5—31no—
207C22×D5—31no—
208C22×D5—31no—
209C2×C4×C5C22×D311yescharacteristic
210C2×C4×C5C22×D311yescharacteristic
211C2×C4×C5C22×D311yescharacteristic
212C2×C4×C5C22×D311yescharacteristic
213C2×C4×C5C22×D311yescharacteristic
214C2×C4×C5C22×D311yescharacteristic
215C22⋊D5—62no—
216C22⋊D5—62no—
217C22⋊D5—121no—
218C2×Dic5—31no—
219C2×Dic5—31no—
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—121no—
224D20—62no—
225D20—62no—
226D20—121no—
227C4×D5—62no—
228C4×D5—62no—
229C4×D5—121no—
230C4×D5—121no—
231C4×D5—121no—
232#126—151no—
233#126D1511yescharacteristic, complemented
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×D4—151no—
245#117—151no—
246C2×C4⋊C4—151no—
247C2×C3×C5—41no—
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5H(5,𝔽2)11yescharacteristic
251D15—22no—
252D15—41no—
253D15—41no—
254C23×C3C22×D511yescharacteristic
255C22×D3—51no—
256C22×D3—51no—
257C22×D3—51no—
258C2×C3×C4C22×D511yescharacteristic
259C2×C3×C4C22×D511yescharacteristic
260C2×C3×C4C22×D511yescharacteristic
261C2×C3×C4C22×D511yescharacteristic
262C2×C3×C4C22×D511yescharacteristic
263C2×C3×C4C22×D511yescharacteristic
264#67—102no—
265#67—102no—
266#67—201no—
267C2×Dic3—51no—
268C2×Dic3—51no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—201no—
273D12—102no—
274D12—102no—
275D12—201no—
276C4×D3—102no—
277C4×D3—102no—
278C4×D3—201no—
279C4×D3—201no—
280C4×D3—201no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5C23×D311yescharacteristic
285C2×D5—32no—
286C2×D5—61no—
287C2×D5—61no—
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—
299C4×C5—21no—
300Dic5—32no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5—61no—
305C2×D4—151no—
306C2×D4—151no—
307C2×D4—151no—
308C2×D4—151no—
309C2×D4—151no—
310C2×D4—151no—
311C22×C4—151no—
312C22×C4—151no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—151no—
318C4⋊C4—151no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4C2×D1511yescharacteristic
325C4⋊C4C2×D1511yescharacteristic
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⋊C4C2×D1511yescharacteristic
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×C3C23×D511yescharacteristic
345C2×D3—52no—
346C2×D3—101no—
347C2×D3—101no—
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—
359C3×C4—21no—
360Dic3—52no—
361Dic3—101no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5—41no—
366C2×C5D3×#4111yescharacteristic
367C2×C5D3×#4111yescharacteristic
368C2×C5#100911yescharacteristic
369D5—62no—
370D5—121no—
371D5—121no—
372C23—151no—
373C23—151no—
374C23—151no—
375C23C22×D1511yescharacteristic
376D4—302no—
377D4—302no—
378D4—302no—
379D4—302no—
380D4—601no—
381D4—601no—
382C2×C4—151no—
383C2×C4—151no—
384C2×C4—151no—
385C2×C4—151no—
386C2×C4—151no—
387C2×C4—302no—
388C2×C4—302no—
389C2×C4—601no—
390C2×C4—601no—
391C2×C4—601no—
392C2×C4—601no—
393C2×C4C22×D1511yescharacteristic
394C2×C4C22×D1511yescharacteristic
395C2×C4C22×D1511yescharacteristic
396C2×C4C22×D1511yescharacteristic
397C2×C4C22×D1511yescharacteristic
398C2×C4C22×D1511yescharacteristic
399C2×C3—41no—
400C2×C3D5×#4111yescharacteristic
401C2×C3D5×#4111yescharacteristic
402C2×C3#414911yescharacteristic
403D3—102no—
404D3—201no—
405D3—201no—
406C5#570911yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—152no—
411C22—301no—
412C22—301no—
413C22—301no—
414C22—301no—
415C22—301no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C23×D1511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—152no—
427C4—301no—
428C4—301no—
429C4—301no—
430C4—301no—
431C3#6604311yescharacteristic, complemented, Sylow
432C2—41no—
433C2—302no—
434C2—601no—
435C2—601no—
436C2#41×D1511yescharacteristic
437C2#41×D1511yescharacteristic
438C2#9210011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#126C2
hypercenter#126D15
hypocenterC3×C5#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. C3×C5×#126C2semidirect
2. #91787C2semidirect
3. #91784C2semidirect
4. #91783C2semidirect
5. #91782C2semidirect
6. C4⋊C4×D15C2semidirect
7. #91778C2semidirect
8. #91775C2semidirect
9. #91773C2semidirect
10. #91773C2semidirect
11. #91773C2semidirect
12. #91770C2semidirect
13. #91770C2semidirect
14. C4×D60C2semidirect
15. #91761C2semidirect
53. C5×#126D3semidirect
95. C3×#126D5semidirect
233. #126D15semidirect
340. C3×C5#553semidirect
406. C5#5709semidirect
431. C3#66043semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1262
#917872
#917842
#917832
#917822
C4⋊C4×D152
#917782
#917752
#917732
#917702
C4×D602
#917612
#660433
#57095