Finite Group Databasebeta

← #11753752

Subgroups — #11753752

Order 960.

436 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
1#91785C211yesmaximal, characteristic, complemented
2C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#4044C211yesmaximal, characteristic, complemented
4#91454C211yesmaximal, characteristic
5#91452C211yesmaximal, characteristic, complemented
6C4×#1203C211yesmaximal, characteristic, complemented
7#91441C211yesmaximal, characteristic, complemented
8#91431C211yesmaximal, characteristic, complemented
9#91413C211yesmaximal, characteristic, complemented
10#91378C211yesmaximal, characteristic, complemented
11#91365C211yesmaximal, characteristic, complemented
12#91354C211yesmaximal, characteristic, complemented
13#91351C211yesmaximal, characteristic, complemented
14#91345C211yesmaximal, characteristic, complemented
15#91335C211yesmaximal, characteristic, complemented
16#65849—31nomaximal, Hall
17C2×C4×D15C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C2×C4×C5×D3C2211yescharacteristic
20C2×C4×C5×D3C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic
22C2×#1203C2211yescharacteristic
23C2×#1202C2211yescharacteristic
24C2×#1201C2211yescharacteristic
25C2×D5×Dic3C2211yescharacteristic
26C3×C5×C4⋊C4C2211yescharacteristic
27#6714C2211yescharacteristic
28#6714C2211yescharacteristic
29#6712C2211yescharacteristic
30#6712C2211yescharacteristic
31C5×C4⋊Dic3C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C3×#685C2211yescharacteristic
35C3×#685C2211yescharacteristic
36C3×#685C2211yescharacteristic
37C3×C4⋊Dic5C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×C4×Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6668C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49(C2×D3)⋊Dic5C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5707—51nomaximal, Hall
53C2×C5×C4⋊C4—31no—
54#4076—31no—
55#4075—31no—
56#4075—31no—
57C4×C22⋊D5—31no—
58C4×C22⋊D5—31no—
59#4070—31no—
60#4044—31no—
61#4044D311yescharacteristic, complemented
62#4042—31no—
63#4042—31no—
64#4040—31no—
65#4040—31no—
66#4035—31no—
67#4035—31no—
68C22×D15C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C4×D15—41no—
78Dic30—41no—
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C4×C5×D3—22no—
83C4×C5×D3—41no—
84C4×C5×D3—41no—
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88#1203—22no—
89#1202—41no—
90#1201—22no—
91D5×Dic3—41no—
92C3×#126—51no—
93#898—51no—
94#897—51no—
95#896—51no—
96#894—51no—
97D3×C4⋊C4D511yescharacteristic, complemented
98#890—51no—
99#886—51no—
100#884—51no—
101#883—51no—
102#883—51no—
103#67⋊C4—51no—
104#878—51no—
105C4×D12—51no—
106#870—51no—
107C22×C4×C5—31no—
108C22×C4×C5—31no—
109C22×C4×C5—31no—
110C2×C22⋊D5—31no—
111C2×C22⋊D5—31no—
112C2×D20—31no—
113C2×C4×D5—31no—
114C2×C4×D5—31no—
115C2×Dic10—31no—
116C5×C4⋊C4—31no—
117C5×C4⋊C4—31no—
118C5×C4⋊C4—31no—
119C5×C4⋊C4C2×D311yescharacteristic
120C22⋊Dic5—31no—
121C22⋊Dic5—31no—
122#685—31no—
123#685—31no—
124#685—31no—
125#685—31no—
126#685—31no—
127#685C2×D311yescharacteristic
128#685C2×D311yescharacteristic
129#685C2×D311yescharacteristic
130C4⋊Dic5—31no—
131C4⋊Dic5C2×D311yescharacteristic
132#683—31no—
133#683—31no—
134#683—31no—
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683C2×D311yescharacteristic
140C4×Dic5—31no—
141C4×Dic5C2×D311yescharacteristic
142#539—151noSylow
143C22×C3×C5C2411yescharacteristic
144C2×D15—21no—
145C2×D15—21no—
146C2×D15—21no—
147C2×C5×D3—21no—
148C2×C5×D3—21no—
149C2×C5×D3#4112yes—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156Dic15—21no—
157Dic15—21no—
158Dic15—21no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C5×Dic3—21no—
165C2×#67—51no—
166C2×#67—51no—
167C22×Dic3—51no—
168C2×D12—51no—
169C2×C4×D3—51no—
170C2×C4×D3C2×D511yescharacteristic
171C2×C4×D3C2×D511yescharacteristic
172C2×C4×D3C2×D511yescharacteristic
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4C2×D511yescharacteristic
177C3×C22⋊C4—51no—
178C3×C22⋊C4—51no—
179C3×C22⋊C4—51no—
180C3×C42—51no—
181#217—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)⋊C4—51no—
188C4⋊Dic3—51no—
189C4⋊Dic3—51no—
190C4⋊Dic3—51no—
191C4⋊Dic3—51no—
192C4⋊Dic3C2×D511yescharacteristic
193Dic3⋊C4—51no—
194Dic3⋊C4—51no—
195Dic3⋊C4—51no—
196Dic3⋊C4—51no—
197Dic3⋊C4C2×D511yescharacteristic
198Dic3⋊C4C2×D511yescharacteristic
199C4×Dic3—51no—
200C23×C5—31no—
201C22×D5—31no—
202C22×D5C22×D311yescharacteristic
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—62no—
207C2×C4×C5—121no—
208C2×C4×C5—121no—
209C2×C4×C5C22×D311yescharacteristic
210C2×C4×C5C22×D311yescharacteristic
211C2×C4×C5C22×D311yescharacteristic
212C22⋊D5—62no—
213C22⋊D5—62no—
214C2×Dic5—31no—
215C2×Dic5—31no—
216C2×Dic5—31no—
217C2×Dic5C22×D311yescharacteristic
218C2×Dic5C22×D311yescharacteristic
219C2×Dic5C22×D311yescharacteristic
220D20—121no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—121no—
224#126—51no—
225#126—151no—
226#125—151no—
227#125—151no—
228#123—151no—
229#123—151no—
230#123—151no—
231#123—151no—
232C22⋊Q8—151no—
233C22⋊Q8—151no—
234C22⋊Q8—151no—
235#121—151no—
236C4×D4—151no—
237C4×D4—151no—
238C2×C4⋊C4—31no—
239C2×C3×C5C2×#4111yescharacteristic
240C2×C3×C5H(5,𝔽2)11yescharacteristic
241C2×C3×C52−1+411yescharacteristic
242D15—41no—
243C3×D5—41no—
244C5×D3—22no—
245C23×C3—51no—
246C22×D3—51no—
247C22×D3C22×D511yescharacteristic
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4C22×D511yescharacteristic
252C2×C3×C4C22×D511yescharacteristic
253C2×C3×C4C22×D511yescharacteristic
254#67—102no—
255#67—201no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—201no—
260C2×Dic3C22×D511yescharacteristic
261C2×Dic3C22×D511yescharacteristic
262C2×Dic3C22×D511yescharacteristic
263D12—102no—
264C4×D3—22no—
265C4×D3—41no—
266C4×D3—41no—
267C4×D3—201no—
268Dic6—201no—
269C22×C5—32no—
270C22×C5—61no—
271C22×C5—61no—
272C22×C5C23×D311yescharacteristic
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—21no—
276C2×D5—61no—
277C2×D5—61no—
278C2×D5—61no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—61no—
283C4×C5—61no—
284C4×C5—61no—
285Dic5—21no—
286Dic5—21no—
287Dic5—21no—
288Dic5—61no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—151no—
292C2×D4—151no—
293C2×D4—151no—
294C2×D4—151no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—31no—
298C22×C4—151no—
299C22×C4—151no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—151no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C4⋊C4—151no—
311C4⋊C4—151no—
312C4⋊C4—151no—
313C4⋊C4D3×D511yescharacteristic
314C22⋊C4—51no—
315C22⋊C4—51no—
316C22⋊C4—51no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C22⋊C4—151no—
322C22⋊C4—151no—
323C22⋊C4—151no—
324C42—51no—
325C42—151no—
326C3×C5#53911yescharacteristic, complemented, Hall
327C22×C3—101no—
328C22×C3—101no—
329C22×C3—101no—
330C22×C3C23×D511yescharacteristic
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—101no—
334C2×D3—101no—
335C2×D3—101no—
336C2×D3#70912yes—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—101no—
343Dic3—21no—
344Dic3—21no—
345Dic3—21no—
346Dic3—101no—
347Dic3—101no—
348Dic3—101no—
349C2×C5—62no—
350C2×C5D3×#4111yescharacteristic
351C2×C5#100911yescharacteristic
352C2×C5#101011yescharacteristic
353D5—41no—
354D5—121no—
355C23—31no—
356C23—51no—
357C23—151no—
358Q8—601no—
359D4—302no—
360D4—302no—
361D4—601no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—62no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—151no—
372C2×C4—151no—
373C2×C4—151no—
374C2×C4—601no—
375C2×C4—601no—
376C2×C4C2×D3×D511yescharacteristic
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—201no—
380C2×C3C2×#70911yescharacteristic
381C2×C3#414411yescharacteristic
382C2×C3#414711yescharacteristic
383D3—22no—
384D3—201no—
385C5#570711yescharacteristic, complemented, Sylow
386C22—32no—
387C22—61no—
388C22—61no—
389C22—101no—
390C22—101no—
391C22—101no—
392C22—301no—
393C22—301no—
394C22—301no—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—61no—
400C4—61no—
401C4—61no—
402C4—101no—
403C4—101no—
404C4—101no—
405C4—301no—
406C4—301no—
407C4—301no—
408C3#6584911yescharacteristic, complemented, Sylow
409C2—62no—
410C2—201no—
411C2—601no—
412C2D3×#70911yescharacteristic
413C2#9202711yescharacteristic
414C2#9202811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radical#91454C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#539
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. #91785C2semidirect
2. C5×D3×C4⋊C4C2semidirect
3. C3×#4044C2semidirect
5. #91452C2semidirect
6. C4×#1203C2semidirect
7. #91441C2semidirect
8. #91431C2semidirect
9. #91413C2semidirect
10. #91378C2semidirect
11. #91365C2semidirect
12. #91354C2semidirect
13. #91351C2semidirect
14. #91345C2semidirect
15. #91335C2semidirect
61. #4044D3semidirect
97. D3×C4⋊C4D5semidirect
326. C3×C5#539semidirect
385. C5#5707semidirect
408. C3#65849semidirect

Maximal subgroups

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

subgroupindex
#917852
C5×D3×C4⋊C42
C3×#40442
#914542
#914522
C4×#12032
#914412
#914312
#914132
#913782
#913652
#913542
#913512
#913452
#913352
#658493
#57075