Finite Group Databasebeta

← #11753698

Subgroups — #11753698

Order 960.

580 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6765C211yesmaximal, characteristic, complemented
2C2×D5×Dic6C211yesmaximal, characteristic, complemented
3#91776C211yesmaximal, characteristic, complemented
4C5×#897C211yesmaximal, characteristic, complemented
5C3×#4041C211yesmaximal, characteristic, complemented
6#91464C212yesmaximal, complemented
7C4×#1201C211yesmaximal, characteristic, complemented
8#91434C212yesmaximal, complemented
9#91430C212yesmaximal, complemented
10#91408C212yesmaximal, complemented
11#91368C211yesmaximal, characteristic, complemented
12#65967—31nomaximal, Hall
13C2×Dic30C2211yescharacteristic
14C2×C4×C5×D3C2211yescharacteristic
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×D20C2212yes—
17C2×C3×D20C2211yescharacteristic
18C2×C3×C4×D5C2211yescharacteristic
19C2×#1204C2212yes—
20C2×#1201C2211yescharacteristic
21C2×#1201C2212yes—
22C2×D5×Dic3C2212yes—
23C2×D5×Dic3C2212yes—
24#6765—24no—
25D5×Dic6—24no—
26C3×C5×C4⋊C4C2211yescharacteristic
27#6712C2212yes—
28C4×Dic15C2212yes—
29C4×Dic15C2211yescharacteristic
30C5×(C2×D3)⋊C4C2212yes—
31C5×C4⋊Dic3C2212yes—
32C3×#685C2212yes—
33#6669C2211yescharacteristic
34(C2×D3)⋊Dic5C2211yescharacteristic
35#6665C2212yes—
36#6665C2211yescharacteristic
37#6665C2212yes—
38#5598—51nomaximal, Hall
39C2×Q8×D5—31no—
40C2×#709—31no—
41C5×C22⋊Q8—31no—
42#4093—31no—
43C4×C22⋊D5—31no—
44#4042—32no—
45#4041D311yescharacteristic, complemented
46#4039—32no—
47#4033—31no—
48#4031—32no—
49#4030—32no—
50C22×C5×D3C2311yescharacteristic
51C22×C3×D5C2312yes—
52C22×C3×D5C2311yescharacteristic
53C2×C3×C4×C5C2312yes—
54C2×C3×C4×C5C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56C2×Dic15C2311yescharacteristic
57C2×Dic15C2312yes—
58Dic30D414yescomplemented
59C2×C5×Dic3C2312yes—
60C2×C5×Dic3C2311yescharacteristic
61C4×C5×D3—22no—
62C5×Dic6—22no—
63C2×C3×Dic5C2311yescharacteristic
64C3×D20—24no—
65C3×D20—22no—
66C3×C4×D5—22no—
67#1204—24no—
68#1201—22no—
69#1201—24no—
70D5×Dic3—24no—
71D5×Dic3—24no—
72C2×#237—51no—
73C22×Dic6—51no—
74C3×#121—51no—
75#939—52no—
76#936—51no—
77D4×Dic3—52no—
78C4×#67—51no—
79#897D511yescharacteristic, complemented
80#887—51no—
81#885—52no—
82#878—52no—
83C2×C5×Q8—31no—
84C22×C4×C5—31no—
85C2×C22⋊D5—32no—
86C2×C22⋊D5—31no—
87Q8×D5—64no—
88#709—64no—
89C2×D20C2×D311yescharacteristic
90C2×D20C2×D312yes—
91C2×C4×D5—32no—
92C2×C4×D5—32no—
93C2×C4×D5C2×D311yescharacteristic
94C2×Dic10—31no—
95C2×Dic10—32no—
96C5×C4⋊C4—32no—
97C5×C4⋊C4C2×D311yescharacteristic
98C5×C22⋊C4—32no—
99C22⋊Dic5—31no—
100#685—32no—
101#685—32no—
102#685—31no—
103#685C2×D312yes—
104#683—32no—
105#683—31no—
106C4×Dic5—32no—
107C4×Dic5—31no—
108#548—151noSylow
109C22×C3×C5C2411yescharacteristic
110C2×C5×D3—21no—
111C2×C5×D3—21no—
112C2×C5×D3—21no—
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5—22no—
116C2×C3×D5—22no—
117C2×C3×D5—22no—
118C2×C3×D5#4112yescomplemented
119C3×C4×C5—22no—
120C3×C4×C5C2×D412yes—
121Dic15—21no—
122Dic15—21no—
123Dic15C2×D414yes—
124C3×Dic5—21no—
125C5×Dic3—21no—
126C5×Dic3—22no—
127C2×C3×D4—52no—
128C2×C3×D4—51no—
129C22×C3×C4—51no—
130C2×#67—52no—
131C2×#67—51no—
132C22×Dic3—52no—
133C22×Dic3—52no—
134#237—104no—
135C2×C4×D3C2×D511yescharacteristic
136C2×Dic6—51no—
137C2×Dic6—52no—
138C2×Dic6—104no—
139C2×Dic6C2×D511yescharacteristic
140C3×C4⋊C4C2×D511yescharacteristic
141C3×C22⋊C4—52no—
142#217—52no—
143#217—52no—
144#217—51no—
145(C2×D3)⋊C4—51no—
146(C2×D3)⋊C4C2×D512yes—
147C4⋊Dic3C2×D512yes—
148Dic3⋊C4—52no—
149Dic3⋊C4—51no—
150C4×Dic3—52no—
151C4×Dic3—51no—
152C23×C5—31no—
153C22×D5C22×D312yes—
154C22×D5C22×D311yescharacteristic
155C5×Q8—62no—
156C2×C4×C5—31no—
157C2×C4×C5—32no—
158C2×C4×C5—62no—
159C2×C4×C5C22×D312yes—
160C2×C4×C5C22×D311yescharacteristic
161C22⋊D5—64no—
162C22⋊D5—62no—
163C2×Dic5—32no—
164C2×Dic5—31no—
165C2×Dic5—31no—
166C2×Dic5C22×D311yescharacteristic
167D20—24no—
168D20—22no—
169C4×D5—22no—
170C4×D5—64no—
171C4×D5—64no—
172Dic10—34no—
173Dic10—64no—
174C2×#41—151no—
175C22×Q8—151no—
176#124—152no—
177#124—151no—
178C22⋊Q8—31no—
179C22⋊Q8—152no—
180#121—51no—
181#121—152no—
182C4×Q8—151no—
183C4×D4—152no—
184C4×D4—151no—
185C2×C3×C5C22×D411yescharacteristic
186C2×C3×C5C2×#4111yescharacteristic
187C2×C3×C52−1+411yescharacteristic
188C3×D5—22no—
189C3×D5—42no—
190C5×D3—41no—
191C23×C3—51no—
192C23×C3—52no—
193C22×D3C22×D511yescharacteristic
194C3×D4—104no—
195C3×D4—102no—
196C2×C3×C4—51no—
197C2×C3×C4—102no—
198C2×C3×C4C22×D512yes—
199C2×C3×C4C22×D511yescharacteristic
200#67—104no—
201#67—102no—
202C2×Dic3—52no—
203C2×Dic3—51no—
204C2×Dic3—51no—
205C2×Dic3—104no—
206C2×Dic3—104no—
207C2×Dic3C22×D511yescharacteristic
208C2×Dic3C22×D512yes—
209C4×D3—22no—
210Dic6—22no—
211Dic6—54no—
212Dic6—104no—
213C22×C5—61no—
214C22×C5—61no—
215C22×C5—61no—
216C22×C5C23×D311yescharacteristic
217C2×D5—21no—
218C2×D5—21no—
219C2×D5—22no—
220C2×D5—22no—
221C2×D5—22no—
222C2×D5#23712yescomplemented
223C4×C5—22no—
224C4×C5—62no—
225C4×C5—61no—
226C4×C5D3×D412yes—
227Dic5—21no—
228Dic5—34no—
229Dic5—61no—
230Dic5—61no—
231#41—304no—
232C2×Q8—31no—
233C2×Q8—152no—
234C2×Q8—151no—
235C2×Q8—304no—
236C2×D4—52no—
237C2×D4—51no—
238C2×D4—151no—
239C2×D4—152no—
240C22×C4—31no—
241C22×C4—51no—
242C22×C4—152no—
243C22×C4—152no—
244C4⋊C4—32no—
245C4⋊C4—151no—
246C4⋊C4—152no—
247C4⋊C4D3×D511yescharacteristic
248C22⋊C4—32no—
249C22⋊C4—52no—
250C22⋊C4—151no—
251C22⋊C4—152no—
252C22⋊C4—152no—
253C22⋊C4—151no—
254C42—152no—
255C42—151no—
256C3×C5#54811yescharacteristic, complemented, Hall
257C22×C3—52no—
258C22×C3—101no—
259C22×C3—101no—
260C22×C3—102no—
261C22×C3—102no—
262C22×C3—102no—
263C22×C3C23×D511yescharacteristic
264C2×D3—21no—
265C2×D3—21no—
266C2×D3—21no—
267C3×C4—22no—
268C3×C4—101no—
269C3×C4D4×D512yes—
270Dic3—22no—
271Dic3—21no—
272Dic3—54no—
273Dic3—101no—
274Dic3—101no—
275C2×C5—121no—
276C2×C5C2×D3×D411yescharacteristic
277C2×C5C2×#23711yescharacteristic
278C2×C5#101011yescharacteristic
279D5—22no—
280D5—42no—
281C23—31no—
282C23—51no—
283C23—52no—
284Q8—62no—
285Q8—154no—
286Q8—304no—
287D4—104no—
288D4—102no—
289D4—304no—
290D4—302no—
291C2×C4—32no—
292C2×C4—31no—
293C2×C4—51no—
294C2×C4—62no—
295C2×C4—102no—
296C2×C4—152no—
297C2×C4—151no—
298C2×C4—151no—
299C2×C4—304no—
300C2×C4—304no—
301C2×C4C2×D3×D512yes—
302C2×C4C2×D3×D511yescharacteristic
303C2×C3—102no—
304C2×C3—202no—
305C2×C3C2×D4×D511yescharacteristic
306C2×C3#414711yescharacteristic
307C2×C3D5×#4111yescharacteristic
308D3—41no—
309C5#559811yescharacteristic, complemented, Sylow
310C22—52no—
311C22—61no—
312C22—61no—
313C22—61no—
314C22—101no—
315C22—101no—
316C22—102no—
317C22—102no—
318C22—102no—
319C22C22×D3×D511yescharacteristic
320C4—22no—
321C4—61no—
322C4—62no—
323C4—101no—
324C4—154no—
325C4—301no—
326C4—301no—
327C4#677712yes—
328C3#6596711yescharacteristic, complemented, Sylow
329C2—102no—
330C2—121no—
331C2—202no—
332C2C2×#677711yescharacteristic
333C2D5×#23711yescharacteristic
334C2#9202811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#548
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. C2×#6765C2semidirect
2. C2×D5×Dic6C2semidirect
3. #91776C2semidirect
4. C5×#897C2semidirect
5. C3×#4041C2semidirect
6. #91464C2semidirect
7. C4×#1201C2semidirect
8. #91434C2semidirect
9. #91430C2semidirect
10. #91408C2semidirect
11. #91368C2semidirect
45. #4041D3semidirect
58. Dic30D4semidirect
79. #897D5semidirect
118. C2×C3×D5#41semidirect
222. C2×D5#237semidirect
256. C3×C5#548semidirect
309. C5#5598semidirect
328. C3#65967semidirect

Maximal subgroups

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

subgroupindex
C2×#67652
C2×D5×Dic62
#917762
C5×#8972
C3×#40412
#914642
C4×#12012
#914342
#914302
#914082
#913682
#659673
#55985