Finite Group Databasebeta

← #11753800

Subgroups — #11753800

Order 960.

428 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C4⋊C4×D15C211yesmaximal, characteristic, complemented
2C5×#890C211yesmaximal, characteristic, complemented
3C3×#4043C211yesmaximal, characteristic, complemented
4C4×#1202C211yesmaximal, characteristic
5#91390C211yesmaximal, characteristic, complemented
6#91361C212yesmaximal, complemented
7#91358C211yesmaximal, characteristic, complemented
8#91354C212yesmaximal
9#91347C212yesmaximal, complemented
10#91346C212yesmaximal, complemented
11Dic3×Dic10C211yesmaximal, characteristic, complemented
12#66028—31nomaximal, Hall
13C2×C4×D15C2211yescharacteristic
14C2×C4×D15C2212yes—
15C2×C3×C4×D5C2211yescharacteristic
16C2×C3×Dic10C2211yescharacteristic
17C2×#1202C2211yescharacteristic
18C3×C5×C4⋊C4C2211yescharacteristic
19C4⋊Dic15C2211yescharacteristic
20#6712C2212yes—
21C5×C4⋊Dic3C2212yes—
22C5×C4⋊Dic3C2211yescharacteristic
23C5×Dic3⋊C4C2212yes—
24C4×C5×Dic3C2211yescharacteristic
25C3×#685C2212yes—
26C3×C4⋊Dic5C2212yes—
27Dic3⋊Dic5C2211yescharacteristic
28Dic3⋊Dic5C2212yes—
29#6668C2212yes—
30#6667C2211yescharacteristic
31#6667C2212yes—
32#6665C2211yescharacteristic
33#6665C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5639—51nomaximal, Hall
37C5×#125—31no—
38#4044—32no—
39#4043—31no—
40#4043D311yescharacteristic, complemented
41#4040—32no—
42#4038—31no—
43#4038—32no—
44D5×C4⋊C4—31no—
45#4036—32no—
46C4×D20—31no—
47C4×Dic10—31no—
48C22×D15C2311yescharacteristic
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2312yes—
53C2×Dic15C2311yescharacteristic
54C4×D15—24no—
55C4×D15—22no—
56C2×C5×Dic3C2311yescharacteristic
57C2×C5×Dic3C2312yes—
58C2×C5×Dic3C2311yescharacteristic
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2312yes—
61C3×C4×D5—22no—
62C3×Dic10—22no—
63#1202—22no—
64C3×C22⋊Q8—51no—
65#946—51no—
66Q8×Dic3—51no—
67C4×#67—51no—
68#926—51no—
69#892—52no—
70D3×C4⋊C4—51no—
71#890D511yescharacteristic, complemented
72#889—52no—
73#883—52no—
74#879—52no—
75C2×D20—31no—
76C2×C4×D5—31no—
77C2×C4×D5—32no—
78C2×C4×D5C2×D311yescharacteristic
79C2×Dic10C2×D311yescharacteristic
80C5×C4⋊C4—32no—
81C5×C4⋊C4—31no—
82C5×C4⋊C4—32no—
83C5×C4⋊C4C2×D311yescharacteristic
84C42×C5—31no—
85#685—31no—
86#685—32no—
87#685—31no—
88#685—32no—
89#685C2×D312yes—
90C4⋊Dic5—31no—
91C4⋊Dic5—31no—
92C4⋊Dic5—32no—
93C4⋊Dic5C2×D312yes—
94#683—32no—
95#683—32no—
96C4×Dic5—32no—
97C4×Dic5—32no—
98#552—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×D15—21no—
101C2×D15—21no—
102C2×D15#4112yes—
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C3×C4×C5—22no—
107C3×C4×C5#4112yes—
108Dic15—21no—
109Dic15—22no—
110C3×Dic5—22no—
111C3×Dic5—21no—
112C5×Dic3—21no—
113C5×Dic3—21no—
114C5×Dic3—22no—
115C2×C3×Q8—51no—
116C22×C3×C4—51no—
117C2×#67—51no—
118C2×C4×D3—52no—
119C2×C4×D3—51no—
120C3×C4⋊C4—52no—
121C3×C4⋊C4C2×D511yescharacteristic
122C3×C22⋊C4—52no—
123#217—51no—
124#217—52no—
125(C2×D3)⋊C4—52no—
126(C2×D3)⋊C4—51no—
127C4⋊Dic3—51no—
128C4⋊Dic3—52no—
129C4⋊Dic3C2×D512yes—
130C4⋊Dic3C2×D511yescharacteristic
131Dic3⋊C4—52no—
132Dic3⋊C4—52no—
133Dic3⋊C4—51no—
134Dic3⋊C4C2×D512yes—
135C4×Dic3—52no—
136C4×Dic3—52no—
137C4×Dic3C2×D511yescharacteristic
138C22×D5—31no—
139C22×D5C22×D311yescharacteristic
140C2×C4×C5—31no—
141C2×C4×C5—32no—
142C2×C4×C5—31no—
143C2×C4×C5C22×D312yes—
144C2×C4×C5C22×D311yescharacteristic
145C2×Dic5—32no—
146C2×Dic5—31no—
147C2×Dic5C22×D311yescharacteristic
148C2×Dic5C22×D312yes—
149D20—62no—
150C4×D5—22no—
151C4×D5—64no—
152C4×D5—62no—
153Dic10—22no—
154#126—152no—
155#125—31no—
156#125—152no—
157#123—152no—
158C22⋊Q8—51no—
159C22⋊Q8—151no—
160C4×Q8—151no—
161C4×D4—151no—
162#117—152no—
163#117—151no—
164C2×C4⋊C4—151no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168D15—22no—
169C3×D5—41no—
170C23×C3—51no—
171C22×D3—51no—
172C3×Q8—102no—
173C2×C3×C4—51no—
174C2×C3×C4—52no—
175C2×C3×C4—102no—
176C2×C3×C4C22×D512yes—
177C2×C3×C4C22×D511yescharacteristic
178#67—102no—
179C2×Dic3—52no—
180C2×Dic3—51no—
181C2×Dic3C22×D511yescharacteristic
182C2×Dic3C22×D512yes—
183C2×Dic3C22×D511yescharacteristic
184C4×D3—104no—
185C4×D3—102no—
186C22×C5C23×D311yescharacteristic
187C2×D5—21no—
188C2×D5—21no—
189C2×D5—21no—
190C2×D5—32no—
191C2×D5—61no—
192C2×D5—61no—
193C4×C5—22no—
194C4×C5—61no—
195C4×C5—62no—
196C4×C5—61no—
197C4×C5#23712yes—
198Dic5—22no—
199Dic5—21no—
200Dic5—61no—
201Dic5—62no—
202C2×Q8—51no—
203C2×D4—151no—
204C22×C4—51no—
205C22×C4—152no—
206C22×C4—151no—
207C4⋊C4—31no—
208C4⋊C4—32no—
209C4⋊C4—32no—
210C4⋊C4—52no—
211C4⋊C4—151no—
212C4⋊C4—152no—
213C4⋊C4—152no—
214C4⋊C4—151no—
215C4⋊C4—152no—
216C4⋊C4D3×D511yescharacteristic
217C22⋊C4—52no—
218C22⋊C4—151no—
219C22⋊C4—152no—
220C22⋊C4—152no—
221C22⋊C4—151no—
222C42—31no—
223C42—152no—
224C42—152no—
225C3×C5#55211yescharacteristic, complemented, Hall
226C22×C3—101no—
227C22×C3—101no—
228C22×C3—101no—
229C22×C3C23×D511yescharacteristic
230C2×D3—52no—
231C2×D3—101no—
232C2×D3—101no—
233C3×C4—22no—
234C3×C4—101no—
235C3×C4—102no—
236C3×C4#71312yes—
237Dic3—21no—
238Dic3—21no—
239Dic3—22no—
240Dic3—101no—
241Dic3—102no—
242C2×C5C2×#23711yescharacteristic
243C2×C5#100711yescharacteristic
244C2×C5D3×#4111yescharacteristic
245D5—41no—
246D5—62no—
247C23—51no—
248C23—151no—
249Q8—102no—
250D4—302no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—32no—
254C2×C4—51no—
255C2×C4—52no—
256C2×C4—102no—
257C2×C4—152no—
258C2×C4—151no—
259C2×C4—304no—
260C2×C4—302no—
261C2×C4C2×D3×D512yes—
262C2×C4C2×D3×D511yescharacteristic
263C2×C3—201no—
264C2×C3C2×#71311yescharacteristic
265C2×C3D5×#4111yescharacteristic
266C2×C3#415011yescharacteristic
267D3—102no—
268C5#563911yescharacteristic, complemented, Sylow
269C22—101no—
270C22—101no—
271C22—101no—
272C22—152no—
273C22—301no—
274C22—301no—
275C22C22×D3×D511yescharacteristic
276C4—22no—
277C4—61no—
278C4—61no—
279C4—62no—
280C4—101no—
281C4—102no—
282C4—301no—
283C4—302no—
284C4#676612yes—
285C3#6602811yescharacteristic, complemented, Sylow
286C2—201no—
287C2—302no—
288C2C2×#676611yescharacteristic
289C2#9202411yescharacteristic
290C2#9203011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1202C22
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. C4⋊C4×D15C2semidirect
2. C5×#890C2semidirect
3. C3×#4043C2semidirect
5. #91390C2semidirect
6. #91361C2semidirect
7. #91358C2semidirect
9. #91347C2semidirect
10. #91346C2semidirect
11. Dic3×Dic10C2semidirect
40. #4043D3semidirect
71. #890D5semidirect
225. C3×C5#552semidirect
268. C5#5639semidirect
285. C3#66028semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D152
C5×#8902
C3×#40432
C4×#12022
#913902
#913612
#913582
#913542
#913472
#913462
Dic3×Dic102
#660283
#56395