Finite Group Databasebeta

← #11752978

Subgroups — #11752978

Order 960.

424 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#91774C211yesmaximal, characteristic
2C5×#877C211yesmaximal, characteristic, complemented
3C3×#4025C211yesmaximal, characteristic, complemented
4#91575C211yesmaximal, characteristic, complemented
5#91556C211yesmaximal, characteristic
6#91530C211yesmaximal, characteristic, complemented
7#91526C211yesmaximal, characteristic
8C4×#1204C211yesmaximal, characteristic, complemented
9#91429C211yesmaximal, characteristic, complemented
10#91402C211yesmaximal, characteristic, complemented
11#91380C211yesmaximal, characteristic, complemented
12#91380C211yesmaximal, characteristic, complemented
13#91340C211yesmaximal, characteristic, complemented
14#91328C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#65867—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C22×C5×Dic3C2211yescharacteristic
20C2×#1204C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×#1200C2211yescharacteristic
23C3×C5×C22⋊C4C2211yescharacteristic
24#6719C2211yescharacteristic
25#6714C2211yescharacteristic
26#6714C2211yescharacteristic
27C4×Dic15C2211yescharacteristic
28C5×#217C2211yescharacteristic
29C5×Dic3⋊C4C2211yescharacteristic
30C5×Dic3⋊C4C2211yescharacteristic
31C4×C5×Dic3C2211yescharacteristic
32C4×C5×Dic3C2211yescharacteristic
33C3×C22⋊Dic5C2211yescharacteristic
34C3×C22⋊Dic5C2211yescharacteristic
35C3×C4⋊Dic5C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×C4×Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5702—51nomaximal, Hall
53C5×#117—31no—
54C4×C22⋊D5—31no—
55#4070—31no—
56#4043—31no—
57#4038—31no—
58#4034—31no—
59#4033—31no—
60#4031—31no—
61#4031—31no—
62#4025—31no—
63#4025D311yescharacteristic, complemented
64#4022—31no—
65#4022—31no—
66C4×Dic10—31no—
67C4×Dic10—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72#1220—22no—
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76Dic30—22no—
77C2×C5×Dic3—22no—
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86#1204—22no—
87#1204—22no—
88#1200—22no—
89C3×#126—51no—
90#898—51no—
91#898—51no—
92#896—51no—
93#888—51no—
94#887—51no—
95#887—51no—
96#885—51no—
97#885—51no—
98#67⋊C4—51no—
99#879—51no—
100#878—51no—
101#877D511yescharacteristic, complemented
102#872—51no—
103C4×Dic6—51no—
104C22×C4×C5—31no—
105C2×C22⋊D5—31no—
106C2×C4×D5—31no—
107C2×Dic10—31no—
108C2×Dic10—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⋊Dic5—31no—
117C22⋊Dic5C2×D311yescharacteristic
118C22⋊Dic5C2×D311yescharacteristic
119#685—31no—
120#685—31no—
121#685—31no—
122#685—31no—
123#685—31no—
124C4⋊Dic5—31no—
125C4⋊Dic5—31no—
126C4⋊Dic5C2×D311yescharacteristic
127#683—31no—
128#683—31no—
129#683—31no—
130#683—31no—
131#683—31no—
132#683C2×D311yescharacteristic
133#683C2×D311yescharacteristic
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5C2×D311yescharacteristic
139#556—151noSylow
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
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#4112yes—
160C2×#67—51no—
161C22×Dic3C2×D511yescharacteristic
162C2×C4×D3—51no—
163C2×Dic6—51no—
164C2×Dic6—51no—
165C2×Dic6—51no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4—51no—
169C3×C22⋊C4—51no—
170C3×C22⋊C4—51no—
171C3×C22⋊C4C2×D511yescharacteristic
172C3×C42—51no—
173#217—51no—
174#217C2×D511yescharacteristic
175(C2×D3)⋊C4—51no—
176(C2×D3)⋊C4—51no—
177(C2×D3)⋊C4—51no—
178(C2×D3)⋊C4—51no—
179(C2×D3)⋊C4—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—51no—
182Dic3⋊C4—51no—
183Dic3⋊C4—51no—
184Dic3⋊C4—51no—
185Dic3⋊C4—51no—
186Dic3⋊C4—51no—
187Dic3⋊C4C2×D511yescharacteristic
188Dic3⋊C4C2×D511yescharacteristic
189C4×Dic3—51no—
190C4×Dic3—51no—
191C4×Dic3—51no—
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—31no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5C22×D311yescharacteristic
209C2×Dic5C22×D311yescharacteristic
210C2×Dic5C22×D311yescharacteristic
211C2×Dic5C22×D311yescharacteristic
212C4×D5—62no—
213Dic10—62no—
214Dic10—62no—
215Dic10—62no—
216C4⋊Q8—151no—
217#126—51no—
218#126—151no—
219#126—151no—
220#126—151no—
221#124—151no—
222#124—151no—
223C22⋊Q8—151no—
224C22⋊Q8—151no—
225C4×Q8—151no—
226C4×Q8—151no—
227C4×Q8—151no—
228C4×D4—151no—
229#117—31no—
230#117—151no—
231C2×C3×C5—41no—
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×C4C22×D511yescharacteristic
243C2×C3×C4C22×D511yescharacteristic
244#67—102no—
245C2×Dic3—22no—
246C2×Dic3—51no—
247C2×Dic3—51no—
248C2×Dic3—51no—
249C2×Dic3C22×D511yescharacteristic
250C2×Dic3C22×D511yescharacteristic
251C2×Dic3C22×D511yescharacteristic
252C2×Dic3C22×D511yescharacteristic
253C4×D3—102no—
254Dic6—102no—
255Dic6—102no—
256Dic6—102no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5C23×D311yescharacteristic
261C2×D5—61no—
262C2×D5—61no—
263C2×D5—61no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—32no—
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×Q8—151no—
279C2×Q8—151no—
280C2×D4—151no—
281C22×C4—31no—
282C22×C4—151no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—51no—
288C4⋊C4—151no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—151no—
292C4⋊C4—151no—
293C4⋊C4—151no—
294C4⋊C4—151no—
295C22⋊C4—31no—
296C22⋊C4—51no—
297C22⋊C4—51no—
298C22⋊C4—151no—
299C22⋊C4—151no—
300C22⋊C4—151no—
301C22⋊C4—151no—
302C22⋊C4—151no—
303C22⋊C4—151no—
304C22⋊C4D3×D511yescharacteristic
305C42—31no—
306C42—31no—
307C42—51no—
308C42—151no—
309C42—151no—
310C42—151no—
311C42—151no—
312C3×C5#55611yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
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—52no—
330Dic3—101no—
331Dic3—101no—
332Dic3#70912yes—
333C2×C5—41no—
334C2×C5D3×#4111yescharacteristic
335C2×C5D3×#4111yescharacteristic
336C2×C5#101011yescharacteristic
337D5—121no—
338C23—151no—
339C23C2×D3×D511yescharacteristic
340Q8—302no—
341Q8—302no—
342Q8—302no—
343D4—302no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—62no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—151no—
356C2×C4—302no—
357C2×C4C2×D3×D511yescharacteristic
358C2×C4C2×D3×D511yescharacteristic
359C2×C3—41no—
360C2×C3C2×#70911yescharacteristic
361C2×C3D5×#4111yescharacteristic
362C2×C3#415011yescharacteristic
363D3—201no—
364C5#570211yescharacteristic, complemented, Sylow
365C22—21no—
366C22—21no—
367C22—21no—
368C22—301no—
369C22—301no—
370C22—301no—
371C22C22×D3×D511yescharacteristic
372C4—21no—
373C4—21no—
374C4—32no—
375C4—61no—
376C4—61no—
377C4—61no—
378C4—101no—
379C4—101no—
380C4—101no—
381C4—101no—
382C4—152no—
383C4—301no—
384C4—301no—
385C3#6586711yescharacteristic, complemented, Sylow
386C2—41no—
387C2—601no—
388C2D3×#70911yescharacteristic
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#556
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×#4025C2semidirect
4. #91575C2semidirect
6. #91530C2semidirect
8. C4×#1204C2semidirect
9. #91429C2semidirect
10. #91402C2semidirect
11. #91380C2semidirect
12. #91380C2semidirect
13. #91340C2semidirect
14. #91328C2semidirect
15. #91325C2semidirect
63. #4025D3semidirect
101. #877D5semidirect
312. C3×C5#556semidirect
364. C5#5702semidirect
385. C3#65867semidirect

Maximal subgroups

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

subgroupindex
#917742
C5×#8772
C3×#40252
#915752
#915562
#915302
#915262
C4×#12042
#914292
#914022
#913802
#913402
#913282
#913252
#658673
#57025