Finite Group Databasebeta

← #11754459

Subgroups — #11754459

Order 960.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#1220C211yesmaximal, characteristic, complemented
2C5×#929C211yesmaximal, characteristic, complemented
3C3×#4070C211yesmaximal, characteristic, complemented
4#91558C211yesmaximal, characteristic
5#91530C211yesmaximal, characteristic, complemented
6#91526C211yesmaximal, characteristic, complemented
7#91525C211yesmaximal, characteristic, complemented
8#91436C211yesmaximal, characteristic, complemented
9#91400C211yesmaximal, characteristic, complemented
10#91377C211yesmaximal, characteristic, complemented
11#91355C211yesmaximal, characteristic, complemented
12#91345C211yesmaximal, characteristic, complemented
13#91327C211yesmaximal, characteristic, complemented
14#91326C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#65996—31nomaximal, Hall
17C22×C3×C4×C5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C3×Dic10C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1203C2211yescharacteristic
25C2×D3×Dic5C2211yescharacteristic
26#6719C2211yescharacteristic
27#6714C2211yescharacteristic
28#6712C2211yescharacteristic
29C4×Dic15C2211yescharacteristic
30C5×#217C2211yescharacteristic
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×(C2×D3)⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C3×C22⋊Dic5C2211yescharacteristic
36C3×C22⋊Dic5C2211yescharacteristic
37C3×C4⋊Dic5C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×#683C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5640—51nomaximal, Hall
53C5×#123—31no—
54#4085—31no—
55#4082—31no—
56C4×C22⋊D5—31no—
57#4070D311yescharacteristic, complemented
58#4044—31no—
59#4042—31no—
60#4034—31no—
61#4033—31no—
62#4031—31no—
63#4031—31no—
64#4029—31no—
65#4025—31no—
66#4024—31no—
67#4023—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74#1220—22no—
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C4×D15—41no—
79C5×#67—41no—
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C3×Dic10—41no—
88#1204—22no—
89#1204—41no—
90#1203—41no—
91D3×Dic5—22no—
92C3×C22⋊Q8—51no—
93#947—51no—
94#944—51no—
95#929D511yescharacteristic, complemented
96C4×#67—51no—
97#898—51no—
98#896—51no—
99#896—51no—
100#894—51no—
101#892—51no—
102#887—51no—
103#885—51no—
104#885—51no—
105#884—51no—
106#879—51no—
107C2×C5×D4—31no—
108C22×C4×C5C2×D311yescharacteristic
109C2×C22⋊D5—31no—
110C2×C22⋊D5—31no—
111C22×Dic5—31no—
112C2×C4×D5—31no—
113C2×Dic10—31no—
114C2×Dic10—31no—
115C2×Dic10C2×D311yescharacteristic
116C5×C4⋊C4—31no—
117C5×C4⋊C4—31no—
118C5×C22⋊C4—31no—
119C5×C22⋊C4—31no—
120C5×C22⋊C4—31no—
121C22⋊Dic5—31no—
122C22⋊Dic5—31no—
123C22⋊Dic5—31no—
124C22⋊Dic5C2×D311yescharacteristic
125C22⋊Dic5C2×D311yescharacteristic
126#685—31no—
127#685—31no—
128#685—31no—
129#685—31no—
130C4⋊Dic5—31no—
131C4⋊Dic5C2×D311yescharacteristic
132#683—31no—
133#683—31no—
134#683—31no—
135#683—31no—
136#683C2×D311yescharacteristic
137#683C2×D311yescharacteristic
138C4×Dic5—31no—
139C4×Dic5—31no—
140C4×Dic5—31no—
141C4×Dic5—31no—
142#542—151noSylow
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×C5×D3—21no—
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155Dic15—21no—
156Dic15—21no—
157Dic15#4112yes—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C5×Dic3—21no—
165C2×C3×Q8—51no—
166C22×C3×C4C2×D511yescharacteristic
167C2×#67—51no—
168C2×#67C2×D511yescharacteristic
169C2×D12—51no—
170C2×C4×D3—51no—
171C2×C4×D3—51no—
172C2×Dic6—51no—
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C22⋊C4—51no—
178C3×C22⋊C4—51no—
179#217—51no—
180#217C2×D511yescharacteristic
181(C2×D3)⋊C4—51no—
182(C2×D3)⋊C4—51no—
183(C2×D3)⋊C4—51no—
184(C2×D3)⋊C4—51no—
185(C2×D3)⋊C4—51no—
186(C2×D3)⋊C4—51no—
187(C2×D3)⋊C4C2×D511yescharacteristic
188(C2×D3)⋊C4C2×D511yescharacteristic
189C4⋊Dic3—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4C2×D511yescharacteristic
195Dic3⋊C4C2×D511yescharacteristic
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3—51no—
200C23×C5—31no—
201C23×C5C22×D311yescharacteristic
202C22×D5—31no—
203C5×D4—121no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5—41no—
208C2×C4×C5C22×D311yescharacteristic
209C2×C4×C5C22×D311yescharacteristic
210C22⋊D5—62no—
211C22⋊D5—121no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—62no—
216C2×Dic5C22×D311yescharacteristic
217C2×Dic5C22×D311yescharacteristic
218C2×Dic5C22×D311yescharacteristic
219C2×Dic5C22×D311yescharacteristic
220C4×D5—121no—
221Dic10—41no—
222Dic10—62no—
223Dic10—121no—
224C4⋊Q8—151no—
225#126—151no—
226#126—151no—
227#124—151no—
228#124—151no—
229#124—151no—
230#123—31no—
231#123—151no—
232C22⋊Q8—51no—
233C22⋊Q8—151no—
234C22⋊Q8—151no—
235#121—151no—
236C4×Q8—151no—
237C4×D4—151no—
238#117—151no—
239C2×C3×C5—41no—
240C2×C3×C5C2×#4111yescharacteristic
241C2×C3×C5H(5,𝔽2)11yescharacteristic
242C2×C3×C52−1+411yescharacteristic
243D15—41no—
244C5×D3—41no—
245C23×C3C22×D511yescharacteristic
246C22×D3—51no—
247C22×D3C22×D511yescharacteristic
248C3×Q8—201no—
249C2×C3×C4—41no—
250C2×C3×C4—51no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4C22×D511yescharacteristic
255C2×C3×C4C22×D511yescharacteristic
256#67—41no—
257#67—102no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3C22×D511yescharacteristic
262C2×Dic3C22×D511yescharacteristic
263C2×Dic3C22×D511yescharacteristic
264D12—201no—
265C4×D3—102no—
266C4×D3—201no—
267Dic6—102no—
268Dic6—201no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—61no—
273C22×C5—61no—
274C22×C5—61no—
275C22×C5C23×D311yescharacteristic
276C2×D5—61no—
277C2×D5—61no—
278C2×D5—61no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—61no—
282C4×C5—61no—
283C4×C5—61no—
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287Dic5—21no—
288Dic5—32no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—51no—
292C2×Q8—151no—
293C2×Q8—151no—
294C2×D4—31no—
295C2×D4—151no—
296C2×D4—151no—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4D3×D511yescharacteristic
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—51no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—151no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C22⋊C4—31no—
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—51no—
314C22⋊C4—51no—
315C22⋊C4—151no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C22⋊C4—151no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#54211yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3C23×D511yescharacteristic
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—21no—
334C2×D3—101no—
335C2×D3—101no—
336C2×D3—101no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—101no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—101no—
343Dic3—21no—
344Dic3—21no—
345Dic3—21no—
346Dic3—52no—
347Dic3—101no—
348Dic3—101no—
349C2×C5—41no—
350C2×C5—121no—
351C2×C5#100411yescharacteristic
352C2×C5#100711yescharacteristic
353C2×C5D3×#4111yescharacteristic
354D5—121no—
355C23—31no—
356C23—151no—
357C23C2×D3×D511yescharacteristic
358Q8—201no—
359Q8—302no—
360Q8—601no—
361D4—121no—
362D4—302no—
363D4—601no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—41no—
368C2×C4—51no—
369C2×C4—51no—
370C2×C4—51no—
371C2×C4—51no—
372C2×C4—151no—
373C2×C4—151no—
374C2×C4—151no—
375C2×C4—302no—
376C2×C4—601no—
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—41no—
380C2×C3#414411yescharacteristic
381C2×C3D5×#4111yescharacteristic
382C2×C3#415011yescharacteristic
383D3—41no—
384D3—201no—
385C5#564011yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—61no—
390C22—61no—
391C22—61no—
392C22—301no—
393C22—301no—
394C22—301no—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—61no—
399C4—61no—
400C4—61no—
401C4—101no—
402C4—101no—
403C4—101no—
404C4—101no—
405C4—152no—
406C4—301no—
407C4—301no—
408C3#6599611yescharacteristic, complemented, Sylow
409C2—41no—
410C2—121no—
411C2—601no—
412C2#9200411yescharacteristic
413C2#9201611yescharacteristic
414C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
prime radical#91558C2
hypercenterC22×C4D3×D5
hypocenterC3×C5#542
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. C4×#1220C2semidirect
2. C5×#929C2semidirect
3. C3×#4070C2semidirect
5. #91530C2semidirect
6. #91526C2semidirect
7. #91525C2semidirect
8. #91436C2semidirect
9. #91400C2semidirect
10. #91377C2semidirect
11. #91355C2semidirect
12. #91345C2semidirect
13. #91327C2semidirect
14. #91326C2semidirect
15. #91325C2semidirect
57. #4070D3semidirect
95. #929D5semidirect
326. C3×C5#542semidirect
385. C5#5640semidirect
408. C3#65996semidirect

Maximal subgroups

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

subgroupindex
C4×#12202
C5×#9292
C3×#40702
#915582
#915302
#915262
#915252
#914362
#914002
#913772
#913552
#913452
#913272
#913262
#913252
#659963
#56405