Finite Group Databasebeta

← #11753533

Subgroups — #11753533

Order 960.

428 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#91779C211yesmaximal, characteristic, complemented
2C5×#892C211yesmaximal, characteristic, complemented
3C3×#4043C211yesmaximal, characteristic, complemented
4C4×#1201C211yesmaximal, characteristic
5#91414C212yesmaximal
6D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#91393C212yesmaximal, complemented
8#91381C212yesmaximal, complemented
9#91369C211yesmaximal, characteristic, complemented
10#91341C212yesmaximal, complemented
11#91331C211yesmaximal, characteristic, complemented
12#65863—31nomaximal, Hall
13C2×C4×C5×D3C2211yescharacteristic
14C2×C3×C4×D5C2211yescharacteristic
15C2×C3×Dic10C2211yescharacteristic
16C2×#1201C2211yescharacteristic
17C2×D5×Dic3C2212yes—
18C3×C5×C4⋊C4C2211yescharacteristic
19C4⋊Dic15C2211yescharacteristic
20C4⋊Dic15C2212yes—
21#6712C2212yes—
22C4×Dic15C2211yescharacteristic
23C5×(C2×D3)⋊C4C2212yes—
24C5×C4⋊Dic3C2211yescharacteristic
25C4×C5×Dic3C2212yes—
26C3×#685C2212yes—
27C3×C4⋊Dic5C2212yes—
28#6669C2212yes—
29#6669C2211yescharacteristic
30#6668C2212yes—
31#6668C2212yes—
32(C2×D3)⋊Dic5C2212yes—
33(C2×D3)⋊Dic5C2211yescharacteristic
34#6665C2211yescharacteristic
35Dic3×Dic5C2212yes—
36#5642—51nomaximal, Hall
37C5×#117—31no—
38C4×C22⋊D5—31no—
39#4070—31no—
40#4043D311yescharacteristic, complemented
41D5×C4⋊C4—31no—
42#4036—31no—
43#4033—31no—
44#4029—32no—
45#4025—32no—
46#4018—32no—
47#4016—32no—
48C22×C5×D3C2311yescharacteristic
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2311yescharacteristic
53C2×Dic15C2312yes—
54C2×Dic15C2311yescharacteristic
55C2×C5×Dic3C2312yes—
56C2×C5×Dic3C2311yescharacteristic
57C4×C5×D3—22no—
58C2×C3×Dic5C2312yes—
59C2×C3×Dic5C2311yescharacteristic
60C3×C4×D5—22no—
61C3×Dic10—22no—
62#1201—22no—
63D5×Dic3—24no—
64C3×C22⋊Q8—51no—
65#946—51no—
66Q8×Dic3—51no—
67C4×#67—51no—
68C2×C4⋊Dic3—51no—
69#898—52no—
70#892D511yescharacteristic, complemented
71#890—51no—
72#890—52no—
73#886—52no—
74#877—52no—
75C22×C4×C5—31no—
76C2×C22⋊D5—31no—
77C2×C4×D5—32no—
78C2×C4×D5C2×D311yescharacteristic
79C2×Dic10C2×D311yescharacteristic
80C5×C4⋊C4—31no—
81C5×C4⋊C4C2×D311yescharacteristic
82C5×C22⋊C4—32no—
83C42×C5—32no—
84C22⋊Dic5—31no—
85C22⋊Dic5—32no—
86#685—31no—
87#685C2×D312yes—
88C4⋊Dic5—32no—
89C4⋊Dic5—31no—
90C4⋊Dic5C2×D312yes—
91#683—32no—
92#683—32no—
93#683—32no—
94#683—31no—
95#683—32no—
96C4×Dic5—31no—
97C4×Dic5—32no—
98#552—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×C5×D3—21no—
101C2×C5×D3—21no—
102C2×C5×D3—21no—
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5#4112yes—
106C3×C4×C5—22no—
107C3×C4×C5#4112yes—
108Dic15—22no—
109Dic15—21no—
110Dic15—21no—
111C3×Dic5—22no—
112C3×Dic5—21no—
113C5×Dic3—22no—
114C5×Dic3—21no—
115C2×C3×Q8—51no—
116C22×C3×C4—51no—
117C2×#67—51no—
118C22×Dic3—52no—
119C2×C4×D3C2×D511yescharacteristic
120C3×C4⋊C4—52no—
121C3×C4⋊C4C2×D511yescharacteristic
122C3×C22⋊C4—52no—
123#217—51no—
124(C2×D3)⋊C4—52no—
125(C2×D3)⋊C4—51no—
126(C2×D3)⋊C4C2×D512yes—
127C4⋊Dic3—52no—
128C4⋊Dic3—51no—
129C4⋊Dic3—52no—
130C4⋊Dic3—52no—
131C4⋊Dic3C2×D511yescharacteristic
132Dic3⋊C4—52no—
133Dic3⋊C4—52no—
134Dic3⋊C4—51no—
135C4×Dic3—51no—
136C4×Dic3—52no—
137C4×Dic3C2×D512yes—
138C23×C5—31no—
139C22×D5C22×D311yescharacteristic
140C2×C4×C5—32no—
141C2×C4×C5—31no—
142C2×C4×C5—62no—
143C2×C4×C5C22×D312yes—
144C2×C4×C5C22×D311yescharacteristic
145C22⋊D5—62no—
146C2×Dic5—31no—
147C2×Dic5—31no—
148C2×Dic5—32no—
149C2×Dic5C22×D312yes—
150C2×Dic5C22×D311yescharacteristic
151C4×D5—22no—
152C4×D5—64no—
153Dic10—22no—
154#126—152no—
155#125—152no—
156#125—151no—
157#123—152no—
158C22⋊Q8—51no—
159C22⋊Q8—151no—
160C4×Q8—151no—
161C4×D4—151no—
162#117—31no—
163#117—152no—
164C2×C4⋊C4—151no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168C3×D5—22no—
169C5×D3—41no—
170C23×C3—51no—
171C22×D3C22×D511yescharacteristic
172C3×Q8—102no—
173C2×C3×C4—52no—
174C2×C3×C4—51no—
175C2×C3×C4—102no—
176C2×C3×C4C22×D512yes—
177C2×C3×C4C22×D511yescharacteristic
178#67—102no—
179C2×Dic3—51no—
180C2×Dic3—51no—
181C2×Dic3—52no—
182C2×Dic3—104no—
183C2×Dic3C22×D512yes—
184C2×Dic3C22×D511yescharacteristic
185C4×D3—22no—
186C22×C5—61no—
187C22×C5—61no—
188C22×C5—61no—
189C22×C5C23×D311yescharacteristic
190C2×D5—21no—
191C2×D5—21no—
192C2×D5#23912yes—
193C4×C5—22no—
194C4×C5—61no—
195C4×C5—62no—
196C4×C5#23712yes—
197Dic5—22no—
198Dic5—21no—
199Dic5—62no—
200Dic5—61no—
201Dic5—61no—
202C2×Q8—51no—
203C2×D4—151no—
204C22×C4—31no—
205C22×C4—51no—
206C22×C4—152no—
207C4⋊C4—31no—
208C4⋊C4—52no—
209C4⋊C4—152no—
210C4⋊C4—152no—
211C4⋊C4—151no—
212C4⋊C4—152no—
213C4⋊C4—151no—
214C4⋊C4—152no—
215C4⋊C4—152no—
216C4⋊C4D3×D511yescharacteristic
217C22⋊C4—32no—
218C22⋊C4—52no—
219C22⋊C4—151no—
220C22⋊C4—151no—
221C22⋊C4—152no—
222C42—32no—
223C42—152no—
224C42—151no—
225C3×C5#55211yescharacteristic, complemented, Hall
226C22×C3—52no—
227C22×C3—101no—
228C22×C3—101no—
229C22×C3C23×D511yescharacteristic
230C2×D3—21no—
231C2×D3—21no—
232C2×D3—21no—
233C3×C4—22no—
234C3×C4—101no—
235C3×C4—102no—
236C3×C4#70912yes—
237Dic3—21no—
238Dic3—22no—
239Dic3—102no—
240Dic3—101no—
241Dic3—101no—
242C2×C5—121no—
243C2×C5C2×#23711yescharacteristic
244C2×C5C2×#23911yescharacteristic
245C2×C5#101011yescharacteristic
246D5—22no—
247C23—31no—
248C23—51no—
249Q8—102no—
250D4—302no—
251C2×C4—31no—
252C2×C4—32no—
253C2×C4—52no—
254C2×C4—51no—
255C2×C4—62no—
256C2×C4—102no—
257C2×C4—151no—
258C2×C4—151no—
259C2×C4—152no—
260C2×C4—304no—
261C2×C4C2×D3×D512yes—
262C2×C4C2×D3×D511yescharacteristic
263C2×C3—102no—
264C2×C3C2×#70911yescharacteristic
265C2×C3D5×#4111yescharacteristic
266C2×C3#415011yescharacteristic
267D3—41no—
268C5#564211yescharacteristic, complemented, Sylow
269C22—52no—
270C22—61no—
271C22—61no—
272C22—61no—
273C22—101no—
274C22—101no—
275C22C22×D3×D511yescharacteristic
276C4—22no—
277C4—61no—
278C4—62no—
279C4—101no—
280C4—102no—
281C4—301no—
282C4—302no—
283C4—301no—
284C4#676512yes—
285C3#6586311yescharacteristic, complemented, Sylow
286C2—102no—
287C2—121no—
288C2C2×#676511yescharacteristic
289C2#9202011yescharacteristic
290C2D5×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1201C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#552
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. #91779C2semidirect
2. C5×#892C2semidirect
3. C3×#4043C2semidirect
6. D5×C4⋊Dic3C2semidirect
7. #91393C2semidirect
8. #91381C2semidirect
9. #91369C2semidirect
10. #91341C2semidirect
11. #91331C2semidirect
40. #4043D3semidirect
70. #892D5semidirect
225. C3×C5#552semidirect
268. C5#5642semidirect
285. C3#65863semidirect

Maximal subgroups

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

subgroupindex
#917792
C5×#8922
C3×#40432
C4×#12012
#914142
D5×C4⋊Dic32
#913932
#913812
#913692
#913412
#913312
#658633
#56425