Finite Group Databasebeta

← #11753768

Subgroups — #11753768

Order 960.

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

normal subgroups only

This group has 424 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#91786C211yesmaximal, characteristic, complemented
2C5×#888C211yesmaximal, characteristic, complemented
3C3×#4038C211yesmaximal, characteristic, complemented
4#91455C212yesmaximal
5C4×#1202C211yesmaximal, characteristic
6#91387C212yesmaximal, complemented
7#91362C212yesmaximal, complemented
8#91360C211yesmaximal, characteristic, complemented
9#91347C211yesmaximal, characteristic, complemented
10#91340C211yesmaximal, characteristic, complemented
11Dic5×Dic6C212yesmaximal, complemented
12#66066—31nomaximal, Hall
13C2×C4×D15C2211yescharacteristic
14C2×Dic30C2211yescharacteristic
15C2×C5×Dic6C2212yes—
16C2×C3×C4×D5C2211yescharacteristic
17C2×#1202C2211yescharacteristic
18C3×C5×C4⋊C4C2211yescharacteristic
19#6714C2212yes—
20C4⋊Dic15C2212yes—
21C5×C4⋊Dic3C2211yescharacteristic
22C5×Dic3⋊C4C2212yes—
23C4×C5×Dic3C2211yescharacteristic
24C3×#685C2212yes—
25C3×C4⋊Dic5C2211yescharacteristic
26C3×C4×Dic5C2212yes—
27Dic3⋊Dic5C2211yescharacteristic
28Dic3⋊Dic5C2212yes—
29#6669C2212yes—
30#6667C2211yescharacteristic
31#6667C2212yes—
32#6665C2211yescharacteristic
33#6665C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5533—51nomaximal, Hall
37C5×C4⋊Q8—31no—
38#4093—32no—
39Q8×Dic5—32no—
40#4044—32no—
41#4044—32no—
42#4043—31no—
43#4043—31no—
44#4038—31no—
45#4038D311yescharacteristic, complemented
46C4×D20—31no—
47C4×Dic10—31no—
48C22×D15C2311yescharacteristic
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2311yescharacteristic
53C2×Dic15C2312yes—
54C4×D15—22no—
55Dic30—22no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C5×Dic6—24no—
60C2×C3×Dic5C2312yes—
61C2×C3×Dic5C2311yescharacteristic
62C3×C4×D5—22no—
63#1202—22no—
64C3×#117—51no—
65C4×#67—51no—
66#924—51no—
67#897—51no—
68#892—51no—
69#888D511yescharacteristic, complemented
70#887—51no—
71#885—52no—
72#879—52no—
73#876—52no—
74C4×Dic6—52no—
75C2×C5×Q8—32no—
76C2×D20—31no—
77C2×C4×D5—31no—
78C2×C4×D5C2×D311yescharacteristic
79C2×Dic10—31no—
80C5×C4⋊C4—32no—
81C5×C4⋊C4—31no—
82C5×C4⋊C4C2×D311yescharacteristic
83C42×C5—31no—
84#685—31no—
85#685—32no—
86#685—32no—
87#685—31no—
88#685—32no—
89#685C2×D312yes—
90C4⋊Dic5—32no—
91C4⋊Dic5—31no—
92C4⋊Dic5—32no—
93C4⋊Dic5C2×D311yescharacteristic
94#683—32no—
95C4×Dic5—32no—
96C4×Dic5—32no—
97C4×Dic5C2×D312yes—
98#556—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×D15—21no—
101C2×D15—21no—
102C2×D15—21no—
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C3×C4×C5—22no—
107C3×C4×C5#4112yes—
108Dic15—22no—
109Dic15—21no—
110C3×Dic5—21no—
111C3×Dic5—22no—
112C5×Dic3—22no—
113C5×Dic3—21no—
114C5×Dic3#4112yes—
115C22×C3×C4—51no—
116C2×#67—51no—
117C2×C4×D3—51no—
118C2×Dic6—51no—
119C2×Dic6C2×D512yes—
120C3×C4⋊C4—51no—
121C3×C4⋊C4C2×D511yescharacteristic
122C3×C22⋊C4—52no—
123C3×C42—52no—
124#217—51no—
125#217—52no—
126(C2×D3)⋊C4—52no—
127(C2×D3)⋊C4—51no—
128(C2×D3)⋊C4—52no—
129C4⋊Dic3—52no—
130C4⋊Dic3C2×D511yescharacteristic
131Dic3⋊C4—52no—
132Dic3⋊C4—51no—
133Dic3⋊C4—52no—
134Dic3⋊C4C2×D512yes—
135C4×Dic3—52no—
136C4×Dic3—52no—
137C4×Dic3C2×D511yescharacteristic
138C22×D5—31no—
139C22×D5C22×D311yescharacteristic
140C5×Q8—64no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—31no—
144C2×C4×C5C22×D312yes—
145C2×C4×C5C22×D311yescharacteristic
146C2×Dic5—31no—
147C2×Dic5—32no—
148C2×Dic5C22×D312yes—
149C2×Dic5C22×D311yescharacteristic
150D20—62no—
151C4×D5—22no—
152C4×D5—62no—
153Dic10—62no—
154C4⋊Q8—31no—
155#126—152no—
156#126—152no—
157#124—152no—
158C22⋊Q8—151no—
159C22⋊Q8—151no—
160C4×Q8—151no—
161C4×Q8—152no—
162C4×D4—151no—
163#117—51no—
164#117—151no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168D15—41no—
169C3×D5—41no—
170C23×C3—51no—
171C22×D3—51no—
172C2×C3×C4—52no—
173C2×C3×C4—51no—
174C2×C3×C4—102no—
175C2×C3×C4C22×D512yes—
176C2×C3×C4C22×D511yescharacteristic
177#67—102no—
178C2×Dic3—51no—
179C2×Dic3—52no—
180C2×Dic3C22×D512yes—
181C2×Dic3C22×D511yescharacteristic
182C2×Dic3C22×D511yescharacteristic
183C4×D3—102no—
184Dic6—24no—
185Dic6—102no—
186C22×C5C23×D311yescharacteristic
187C2×D5—21no—
188C2×D5—21no—
189C2×D5—21no—
190C2×D5—61no—
191C2×D5—61no—
192C2×D5—61no—
193C4×C5—22no—
194C4×C5—32no—
195C4×C5—62no—
196C4×C5—61no—
197C4×C5#23512yes—
198Dic5—21no—
199Dic5—22no—
200Dic5—62no—
201Dic5—61no—
202C2×Q8—32no—
203C2×Q8—151no—
204C2×D4—151no—
205C22×C4—51no—
206C22×C4—151no—
207C4⋊C4—31no—
208C4⋊C4—32no—
209C4⋊C4—51no—
210C4⋊C4—151no—
211C4⋊C4—152no—
212C4⋊C4—152no—
213C4⋊C4—152no—
214C4⋊C4D3×D511yescharacteristic
215C22⋊C4—52no—
216C22⋊C4—152no—
217C22⋊C4—151no—
218C22⋊C4—151no—
219C22⋊C4—152no—
220C22⋊C4—152no—
221C42—31no—
222C42—52no—
223C42—152no—
224C42—152no—
225C3×C5#55611yescharacteristic, complemented, Hall
226C22×C3—101no—
227C22×C3—101no—
228C22×C3—101no—
229C22×C3C23×D511yescharacteristic
230C2×D3—101no—
231C2×D3—101no—
232C2×D3—101no—
233C3×C4—22no—
234C3×C4—101no—
235C3×C4—102no—
236C3×C4#71312yes—
237Dic3—22no—
238Dic3—21no—
239Dic3—102no—
240Dic3—101no—
241Dic3#71112yes—
242C2×C5C2×#23511yescharacteristic
243C2×C5D3×#4111yescharacteristic
244C2×C5#101011yescharacteristic
245D5—41no—
246D5—121no—
247C23—51no—
248C23—151no—
249Q8—64no—
250Q8—302no—
251D4—302no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—32no—
255C2×C4—51no—
256C2×C4—52no—
257C2×C4—102no—
258C2×C4—151no—
259C2×C4—152no—
260C2×C4—302no—
261C2×C4C2×D3×D512yes—
262C2×C4C2×D3×D511yescharacteristic
263C2×C3—201no—
264C2×C3C2×#71111yescharacteristic
265C2×C3C2×#71311yescharacteristic
266C2×C3#414711yescharacteristic
267D3—201no—
268C5#553311yescharacteristic, complemented, Sylow
269C22—101no—
270C22—101no—
271C22—101no—
272C22—301no—
273C22—301no—
274C22—301no—
275C22C22×D3×D511yescharacteristic
276C4—22no—
277C4—32no—
278C4—62no—
279C4—61no—
280C4—101no—
281C4—102no—
282C4—301no—
283C4—302no—
284C4#677312yes—
285C3#6606611yescharacteristic, complemented, Sylow
286C2—201no—
287C2—601no—
288C2C2×#677311yescharacteristic
289C2D3×#71111yescharacteristic
290C2#9202811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1202C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#556
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. #91786C2semidirect
2. C5×#888C2semidirect
3. C3×#4038C2semidirect
6. #91387C2semidirect
7. #91362C2semidirect
8. #91360C2semidirect
9. #91347C2semidirect
10. #91340C2semidirect
11. Dic5×Dic6C2semidirect
45. #4038D3semidirect
69. #888D5semidirect
225. C3×C5#556semidirect
268. C5#5533semidirect
285. C3#66066semidirect

Maximal subgroups

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

subgroupindex
#917862
C5×#8882
C3×#40382
#914552
C4×#12022
#913872
#913622
#913602
#913472
#913402
Dic5×Dic62
#660663
#55335