Finite Group Databasebeta

← #11752814

Subgroups — #11752814

Order 960.

428 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91770C211yesmaximal, characteristic
2C5×#877C211yesmaximal, characteristic, complemented
3C3×#4023C211yesmaximal, characteristic, complemented
4#91576C211yesmaximal, characteristic, complemented
5#91546C211yesmaximal, characteristic
6C2×#6669C211yesmaximal, characteristic, complemented
7#91542C211yesmaximal, characteristic
8C4×#1204C211yesmaximal, characteristic, complemented
9#91387C211yesmaximal, characteristic, complemented
10#91386C211yesmaximal, characteristic, complemented
11#91382C211yesmaximal, characteristic, complemented
12#91380C211yesmaximal, characteristic, complemented
13#91379C211yesmaximal, characteristic, complemented
14#91378C211yesmaximal, characteristic, complemented
15#91377C211yesmaximal, characteristic, complemented
16#65865—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C22×C5×Dic3C2211yescharacteristic
21C22×C3×Dic5C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C3×C5×C22⋊C4C2211yescharacteristic
24#6714C2211yescharacteristic
25#6712C2211yescharacteristic
26C4×Dic15C2211yescharacteristic
27C5×#217C2211yescharacteristic
28C5×Dic3⋊C4C2211yescharacteristic
29C5×Dic3⋊C4C2211yescharacteristic
30C4×C5×Dic3C2211yescharacteristic
31C4×C5×Dic3C2211yescharacteristic
32C3×C22⋊Dic5C2211yescharacteristic
33C3×#683C2211yescharacteristic
34C3×#683C2211yescharacteristic
35C3×C4×Dic5C2211yescharacteristic
36C3×C4×Dic5C2211yescharacteristic
37Dic3⋊Dic5C2211yescharacteristic
38Dic3⋊Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40#6669C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50#6667C2211yescharacteristic
51#6667C2211yescharacteristic
52#5531—51nomaximal, Hall
53C5×#117—31no—
54#4075—31no—
55C2×#683—31no—
56#4044—31no—
57#4042—31no—
58#4035—31no—
59#4035—31no—
60#4032—31no—
61#4027—31no—
62#4024—31no—
63#4023D311yescharacteristic, complemented
64#4022—31no—
65#4018—31no—
66#4016—31no—
67C4×Dic10—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72#1220—22no—
73C2×Dic15—22no—
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C4×D15—22no—
78C2×C5×Dic3—22no—
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C3×Dic5—22no—
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88#1204—22no—
89C3×#117—51no—
90#929—51no—
91C2×Dic3⋊C4—51no—
92#898—51no—
93#896—51no—
94#889—51no—
95#889—51no—
96#886—51no—
97#67⋊C4—51no—
98#878—51no—
99#877D511yescharacteristic, complemented
100#876—51no—
101#872—51no—
102#870—51no—
103C4×Dic6—51no—
104C22×C4×C5—31no—
105C2×C22⋊D5—31no—
106C22×Dic5—31no—
107C22×Dic5C2×D311yescharacteristic
108C2×C4×D5—31no—
109C2×Dic10—31no—
110C5×C4⋊C4—31no—
111C5×C4⋊C4—31no—
112C5×C22⋊C4—31no—
113C5×C22⋊C4C2×D311yescharacteristic
114C42×C5—31no—
115C42×C5—31no—
116C22⋊Dic5C2×D311yescharacteristic
117#685—31no—
118#685—31no—
119#685—31no—
120#685—31no—
121#685—31no—
122C4⋊Dic5—31no—
123C4⋊Dic5—31no—
124C4⋊Dic5—31no—
125#683—31no—
126#683—31no—
127#683—31no—
128#683—31no—
129#683—31no—
130#683—31no—
131#683—31no—
132#683—31no—
133#683—31no—
134#683C2×D311yescharacteristic
135#683C2×D311yescharacteristic
136C4×Dic5—31no—
137C4×Dic5C2×D311yescharacteristic
138C4×Dic5C2×D311yescharacteristic
139#552—151noSylow
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5#4112yes—
143C22×C3×C5C2411yescharacteristic
144C2×D15—21no—
145C2×D15—21no—
146C2×D15—21no—
147C3×C4×C5—21no—
148C3×C4×C5—21no—
149Dic15—21no—
150Dic15—21no—
151Dic15#4112yes—
152C3×Dic5—21no—
153C3×Dic5—21no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C5×Dic3—21no—
157C5×Dic3—21no—
158C5×Dic3—21no—
159C5×Dic3—21no—
160C22×C3×C4—51no—
161C2×#67—51no—
162C22×Dic3—51no—
163C22×Dic3C2×D511yescharacteristic
164C2×C4×D3—51no—
165C2×Dic6—51no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C22⋊C4—51no—
169C3×C22⋊C4C2×D511yescharacteristic
170C3×C42—51no—
171C3×C42—51no—
172#217C2×D511yescharacteristic
173(C2×D3)⋊C4—51no—
174(C2×D3)⋊C4—51no—
175(C2×D3)⋊C4—51no—
176(C2×D3)⋊C4—51no—
177(C2×D3)⋊C4—51no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181Dic3⋊C4—51no—
182Dic3⋊C4—51no—
183Dic3⋊C4—51no—
184Dic3⋊C4—51no—
185Dic3⋊C4—51no—
186Dic3⋊C4—51no—
187Dic3⋊C4—51no—
188Dic3⋊C4—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4C2×D511yescharacteristic
191Dic3⋊C4C2×D511yescharacteristic
192C4×Dic3—51no—
193C4×Dic3C2×D511yescharacteristic
194C4×Dic3C2×D511yescharacteristic
195C23×C5C22×D311yescharacteristic
196C22×D5—31no—
197C2×C4×C5—31no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5—62no—
202C2×C4×C5C22×D311yescharacteristic
203C2×C4×C5C22×D311yescharacteristic
204C22⋊D5—62no—
205C2×Dic5—22no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—31no—
209C2×Dic5—62no—
210C2×Dic5C22×D311yescharacteristic
211C2×Dic5C22×D311yescharacteristic
212C2×Dic5C22×D311yescharacteristic
213C2×Dic5C22×D311yescharacteristic
214C4×D5—62no—
215Dic10—62no—
216#126—151no—
217#126—151no—
218#125—151no—
219#125—151no—
220#125—151no—
221#123—151no—
222#123—151no—
223C22⋊Q8—151no—
224C22⋊Q8—151no—
225C4×Q8—151no—
226C4×D4—151no—
227#117—31no—
228#117—51no—
229#117—151no—
230C2×C4⋊C4—151no—
231C2×C3×C5—22no—
232C2×C3×C5C2×#4111yescharacteristic
233C2×C3×C5C2×#4111yescharacteristic
234C2×C3×C52−1+411yescharacteristic
235D15—41no—
236C23×C3C22×D511yescharacteristic
237C22×D3—51no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—51no—
242C2×C3×C4—102no—
243C2×C3×C4C22×D511yescharacteristic
244C2×C3×C4C22×D511yescharacteristic
245#67—102no—
246C2×Dic3—22no—
247C2×Dic3—51no—
248C2×Dic3—51no—
249C2×Dic3—51no—
250C2×Dic3—102no—
251C2×Dic3C22×D511yescharacteristic
252C2×Dic3C22×D511yescharacteristic
253C2×Dic3C22×D511yescharacteristic
254C2×Dic3C22×D511yescharacteristic
255C4×D3—102no—
256Dic6—102no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5#23512yes—
260C22×C5C23×D311yescharacteristic
261C2×D5—61no—
262C2×D5—61no—
263C2×D5—61no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—61no—
267C4×C5—61no—
268C4×C5—61no—
269C4×C5—61no—
270Dic5—21no—
271Dic5—21no—
272Dic5—21no—
273Dic5—21no—
274Dic5—32no—
275Dic5—61no—
276Dic5—61no—
277C2×Q8—151no—
278C2×D4—151no—
279C22×C4—31no—
280C22×C4—51no—
281C22×C4—151no—
282C22×C4—151no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—151no—
288C4⋊C4—151no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—151no—
292C4⋊C4—151no—
293C4⋊C4—151no—
294C4⋊C4—151no—
295C4⋊C4—151no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C22⋊C4—31no—
300C22⋊C4—51no—
301C22⋊C4—151no—
302C22⋊C4—151no—
303C22⋊C4—151no—
304C22⋊C4—151no—
305C22⋊C4—151no—
306C22⋊C4D3×D511yescharacteristic
307C42—31no—
308C42—31no—
309C42—51no—
310C42—51no—
311C42—151no—
312C3×C5#55211yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—21no—
315C22×C3#70912yes—
316C22×C3C23×D511yescharacteristic
317C2×D3—101no—
318C2×D3—101no—
319C2×D3—101no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—101no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—101no—
326Dic3—21no—
327Dic3—21no—
328Dic3—21no—
329Dic3—21no—
330Dic3—52no—
331Dic3—101no—
332Dic3—101no—
333C2×C5—22no—
334C2×C5C2×#23511yescharacteristic
335C2×C5D3×#4111yescharacteristic
336C2×C5#101011yescharacteristic
337D5—121no—
338C23—151no—
339C23C2×D3×D511yescharacteristic
340Q8—302no—
341D4—302no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—62no—
351C2×C4—102no—
352C2×C4—151no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—302no—
356C2×C4—302no—
357C2×C4C2×D3×D511yescharacteristic
358C2×C4C2×D3×D511yescharacteristic
359C2×C3—22no—
360C2×C3C2×#70911yescharacteristic
361C2×C3D5×#4111yescharacteristic
362C2×C3#415011yescharacteristic
363D3—201no—
364C5#553111yescharacteristic, complemented, Sylow
365C22—21no—
366C22—21no—
367C22—301no—
368C22—301no—
369C22—301no—
370C22#677112yes—
371C22C22×D3×D511yescharacteristic
372C4—21no—
373C4—21no—
374C4—61no—
375C4—61no—
376C4—61no—
377C4—61no—
378C4—101no—
379C4—101no—
380C4—101no—
381C4—101no—
382C4—152no—
383C4—301no—
384C4—301no—
385C3#6586511yescharacteristic, complemented, Sylow
386C2—22no—
387C2—601no—
388C2C2×#677111yescharacteristic
389C2#9202011yescharacteristic
390C2#9202411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC2×#1220C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#877C2semidirect
3. C3×#4023C2semidirect
4. #91576C2semidirect
6. C2×#6669C2semidirect
8. C4×#1204C2semidirect
9. #91387C2semidirect
10. #91386C2semidirect
11. #91382C2semidirect
12. #91380C2semidirect
13. #91379C2semidirect
14. #91378C2semidirect
15. #91377C2semidirect
63. #4023D3semidirect
99. #877D5semidirect
312. C3×C5#552semidirect
364. C5#5531semidirect
385. C3#65865semidirect

Maximal subgroups

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

subgroupindex
#917702
C5×#8772
C3×#40232
#915762
#915462
C2×#66692
#915422
C4×#12042
#913872
#913862
#913822
#913802
#913792
#913782
#913772
#658653
#55315