Finite Group Databasebeta

← #11753796

Subgroups — #11753796

Order 960.

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

normal subgroups only

This group has 424 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
1#91777C211yesmaximal, characteristic, complemented
2C5×#897C211yesmaximal, characteristic, complemented
3C3×#4038C211yesmaximal, characteristic, complemented
4#91462C212yesmaximal
5C4×#1201C211yesmaximal, characteristic
6#91372C212yesmaximal, complemented
7#91361C212yesmaximal, complemented
8#91359C211yesmaximal, characteristic, complemented
9#91344C211yesmaximal, characteristic, complemented
10#91338C211yesmaximal, characteristic, complemented
11#91333C212yesmaximal, complemented
12#65975—31nomaximal, Hall
13C2×Dic30C2212yes—
14C2×C4×C5×D3C2211yescharacteristic
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×C4×D5C2211yescharacteristic
17C2×#1201C2211yescharacteristic
18C3×C5×C4⋊C4C2211yescharacteristic
19C4⋊Dic15C2211yescharacteristic
20#6712C2212yes—
21C4×Dic15C2211yescharacteristic
22C5×(C2×D3)⋊C4C2212yes—
23C5×C4⋊Dic3C2212yes—
24C3×#685C2212yes—
25C3×C4⋊Dic5C2211yescharacteristic
26C3×C4×Dic5C2212yes—
27Dic3⋊Dic5C2212yes—
28#6669C2211yescharacteristic
29#6669C2212yes—
30(C2×D3)⋊Dic5C2211yescharacteristic
31(C2×D3)⋊Dic5C2212yes—
32#6665C2211yescharacteristic
33#6665C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5533—51nomaximal, Hall
37C5×C22⋊Q8—31no—
38#4092—31no—
39Q8×Dic5—31no—
40C4×C22⋊D5—31no—
41#4072—31no—
42#4044—32no—
43#4038D311yescharacteristic, complemented
44#4034—31no—
45#4033—32no—
46#4031—32no—
47#4025—32no—
48C22×C5×D3C2311yescharacteristic
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2312yes—
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55Dic30—24no—
56C2×C5×Dic3C2311yescharacteristic
57C2×C5×Dic3C2312yes—
58C4×C5×D3—22no—
59C5×Dic6—22no—
60C2×C3×Dic5C2312yes—
61C2×C3×Dic5C2311yescharacteristic
62C3×C4×D5—22no—
63#1201—22no—
64C3×#117—51no—
65C4×#67—51no—
66#924—51no—
67#897D511yescharacteristic, complemented
68#892—51no—
69#888—51no—
70#887—51no—
71#885—52no—
72#879—52no—
73#876—52no—
74C4×Dic6—52no—
75C2×C5×Q8—31no—
76C22×C4×C5—31no—
77C2×C22⋊D5—31no—
78C2×C4×D5C2×D311yescharacteristic
79C2×Dic10—32no—
80C5×C4⋊C4—32no—
81C5×C4⋊C4C2×D311yescharacteristic
82C5×C22⋊C4—32no—
83C22⋊Dic5—31no—
84C22⋊Dic5—32no—
85#685—32no—
86#685—31no—
87#685C2×D312yes—
88C4⋊Dic5—31no—
89C4⋊Dic5—32no—
90C4⋊Dic5C2×D311yescharacteristic
91#683—32no—
92#683—32no—
93#683—31no—
94C4×Dic5—31no—
95C4×Dic5—32no—
96C4×Dic5—32no—
97C4×Dic5C2×D312yes—
98#556—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—21no—
106C3×C4×C5—22no—
107C3×C4×C5#4112yes—
108Dic15—22no—
109Dic15—21no—
110Dic15#4112yes—
111C3×Dic5—21no—
112C3×Dic5—22no—
113C5×Dic3—22no—
114C5×Dic3—21no—
115C22×C3×C4—51no—
116C2×#67—51no—
117C2×C4×D3C2×D511yescharacteristic
118C2×Dic6—52no—
119C2×Dic6C2×D511yescharacteristic
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—51no—
127(C2×D3)⋊C4—52no—
128(C2×D3)⋊C4C2×D512yes—
129C4⋊Dic3—51no—
130C4⋊Dic3C2×D512yes—
131Dic3⋊C4—52no—
132Dic3⋊C4—51no—
133Dic3⋊C4—52no—
134Dic3⋊C4—52no—
135C4×Dic3—51no—
136C4×Dic3—52no—
137C4×Dic3—52no—
138C23×C5—31no—
139C22×D5C22×D311yescharacteristic
140C5×Q8—62no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—62no—
144C2×C4×C5C22×D312yes—
145C2×C4×C5C22×D311yescharacteristic
146C22⋊D5—62no—
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—32no—
150C2×Dic5C22×D312yes—
151C2×Dic5C22×D311yescharacteristic
152C4×D5—22no—
153Dic10—64no—
154C4⋊Q8—151no—
155#126—152no—
156#126—152no—
157#124—152no—
158C22⋊Q8—31no—
159C22⋊Q8—151no—
160C4×Q8—152no—
161C4×Q8—151no—
162C4×D4—151no—
163#117—51no—
164#117—151no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168C3×D5—41no—
169C5×D3—41no—
170C23×C3—51no—
171C22×D3C22×D511yescharacteristic
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—51no—
180C2×Dic3—52no—
181C2×Dic3C22×D511yescharacteristic
182C2×Dic3C22×D512yes—
183C4×D3—22no—
184Dic6—22no—
185Dic6—104no—
186C22×C5—61no—
187C22×C5—61no—
188C22×C5—61no—
189C22×C5C23×D311yescharacteristic
190C2×D5—21no—
191C2×D5—21no—
192C2×D5—21no—
193C4×C5—22no—
194C4×C5—61no—
195C4×C5—62no—
196C4×C5#23512yes—
197Dic5—21no—
198Dic5—22no—
199Dic5—32no—
200Dic5—62no—
201Dic5—61no—
202C2×Q8—31no—
203C2×Q8—152no—
204C2×D4—151no—
205C22×C4—31no—
206C22×C4—51no—
207C4⋊C4—32no—
208C4⋊C4—51no—
209C4⋊C4—151no—
210C4⋊C4—152no—
211C4⋊C4—152no—
212C4⋊C4—151no—
213C4⋊C4—152no—
214C4⋊C4D3×D511yescharacteristic
215C22⋊C4—32no—
216C22⋊C4—52no—
217C22⋊C4—151no—
218C22⋊C4—152no—
219C22⋊C4—152no—
220C22⋊C4—151no—
221C42—52no—
222C42—152no—
223C42—152no—
224C42—151no—
225C3×C5#55611yescharacteristic, complemented, Hall
226C22×C3—101no—
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#71112yes—
237Dic3—22no—
238Dic3—21no—
239Dic3—52no—
240Dic3—101no—
241Dic3—102no—
242C2×C5—121no—
243C2×C5C2×#23511yescharacteristic
244C2×C5D3×#4111yescharacteristic
245C2×C5#101011yescharacteristic
246D5—41no—
247C23—31no—
248C23—51no—
249Q8—62no—
250Q8—304no—
251D4—302no—
252C2×C4—31no—
253C2×C4—32no—
254C2×C4—51no—
255C2×C4—52no—
256C2×C4—62no—
257C2×C4—102no—
258C2×C4—151no—
259C2×C4—151no—
260C2×C4—152no—
261C2×C4C2×D3×D512yes—
262C2×C4C2×D3×D511yescharacteristic
263C2×C3—201no—
264C2×C3C2×#71111yescharacteristic
265C2×C3#414711yescharacteristic
266C2×C3D5×#4111yescharacteristic
267D3—41no—
268C5#553311yescharacteristic, complemented, Sylow
269C22—61no—
270C22—61no—
271C22—61no—
272C22—101no—
273C22—101no—
274C22—101no—
275C22C22×D3×D511yescharacteristic
276C4—22no—
277C4—61no—
278C4—62no—
279C4—101no—
280C4—102no—
281C4—152no—
282C4—302no—
283C4—301no—
284C4#677212yes—
285C3#6597511yescharacteristic, complemented, Sylow
286C2—121no—
287C2—201no—
288C2C2×#677211yescharacteristic
289C2#9202411yescharacteristic
290C2#9202811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1201C22
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. #91777C2semidirect
2. C5×#897C2semidirect
3. C3×#4038C2semidirect
6. #91372C2semidirect
7. #91361C2semidirect
8. #91359C2semidirect
9. #91344C2semidirect
10. #91338C2semidirect
11. #91333C2semidirect
43. #4038D3semidirect
67. #897D5semidirect
225. C3×C5#556semidirect
268. C5#5533semidirect
285. C3#65975semidirect

Maximal subgroups

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

subgroupindex
#917772
C5×#8972
C3×#40382
#914622
C4×#12012
#913722
#913612
#913592
#913442
#913382
#913332
#659753
#55335