Finite Group Databasebeta

← #11755210

Subgroups — #11755210

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#91833C211yesmaximal, characteristic, complemented
2C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C3×#4093C211yesmaximal, characteristic
4C4×#1204C211yesmaximal, characteristic, complemented
5#91434C211yesmaximal, characteristic
6#91430C212yesmaximal, complemented
7#91393C212yesmaximal, complemented
8#91364C211yesmaximal, characteristic
9#91363C212yesmaximal, complemented
10#91361C212yesmaximal, complemented
11#91333C211yesmaximal, characteristic, complemented
12#65902—31nomaximal, Hall
13C2×C3×C5×Q8C2211yescharacteristic
14C2×Dic30C2211yescharacteristic
15C2×C3×D20C2211yescharacteristic
16C2×#1204C2211yescharacteristic
17C2×D5×Dic3C2212yes—
18#6712C2212yes—
19#6712C2212yes—
20C4×Dic15C2211yescharacteristic
21C5×C4⋊Dic3C2212yes—
22C5×C4⋊Dic3C2211yescharacteristic
23C4×C5×Dic3C2212yes—
24C4×C5×Dic3C2211yescharacteristic
25C3×#685C2212yes—
26C3×#685C2212yes—
27C3×C4×Dic5C2211yescharacteristic
28Dic3⋊Dic5C2211yescharacteristic
29#6669C2211yescharacteristic
30#6669C2212yes—
31#6668C2211yescharacteristic
32#6665C2212yes—
33#6665C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5671—51nomaximal, Hall
37C4×C5×Q8—31no—
38#4093D311yescharacteristic
39#4090—31no—
40#4044—32no—
41#4042—32no—
42#4039—31no—
43#4033—31no—
44#4022—32no—
45#4021—31no—
46#4018—32no—
47C4×Dic10—31no—
48C22×C3×D5C2312yes—
49C3×C5×Q8—22no—
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2312yes—
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55Dic30—22no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2311yescharacteristic
61C3×D20—22no—
62#1204—22no—
63D5×Dic3—24no—
64C3×#124—51no—
65Q8×Dic3D511yescharacteristic, complemented
66#944—51no—
67#936—51no—
68D4×Dic3—51no—
69#879—52no—
70#879—52no—
71#878—52no—
72#877—52no—
73C4×Dic6—51no—
74C4×Dic6—51no—
75C2×C5×Q8C2×D311yescharacteristic
76C2×D20C2×D311yescharacteristic
77C2×C4×D5—32no—
78C2×Dic10—31no—
79C2×Dic10—31no—
80C5×C4⋊C4—31no—
81C5×C4⋊C4—32no—
82C42×C5—31no—
83C42×C5—32no—
84#685—32no—
85#685—32no—
86#685—32no—
87#685C2×D312yes—
88#685C2×D312yes—
89C4⋊Dic5—31no—
90#683—32no—
91#683—32no—
92#683—31no—
93#683—31no—
94#683—32no—
95C4×Dic5—31no—
96C4×Dic5—32no—
97C4×Dic5C2×D311yescharacteristic
98#556—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×C3×D5—22no—
101C2×C3×D5—22no—
102C2×C3×D5—22no—
103C3×C4×C5—22no—
104C3×C4×C5#4112yes—
105Dic15—22no—
106Dic15—21no—
107Dic15#4112yes—
108C3×Dic5—21no—
109C3×Dic5—21no—
110C5×Dic3—22no—
111C5×Dic3—21no—
112C5×Dic3—21no—
113C2×C3×Q8C2×D511yescharacteristic
114C2×C3×D4—51no—
115C22×Dic3—52no—
116C2×Dic6—51no—
117C2×Dic6—51no—
118C3×C22⋊C4—52no—
119C3×C22⋊C4—52no—
120C3×C42—51no—
121#217—52no—
122#217—52no—
123#217—52no—
124C4⋊Dic3—51no—
125C4⋊Dic3C2×D511yescharacteristic
126C4⋊Dic3C2×D512yes—
127Dic3⋊C4—52no—
128Dic3⋊C4—52no—
129Dic3⋊C4—51no—
130Dic3⋊C4—52no—
131Dic3⋊C4—51no—
132C4×Dic3—51no—
133C4×Dic3—52no—
134C4×Dic3C2×D511yescharacteristic
135C4×Dic3C2×D512yes—
136C22×D5C22×D312yes—
137C5×Q8—22no—
138C2×C4×C5—32no—
139C2×C4×C5—31no—
140C2×C4×C5—31no—
141C2×C4×C5C22×D312yes—
142C2×C4×C5C22×D311yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—31no—
145C2×Dic5—32no—
146C2×Dic5C22×D311yescharacteristic
147C2×Dic5C22×D311yescharacteristic
148D20—22no—
149C4×D5—64no—
150Dic10—62no—
151Dic10—62no—
152C4⋊Q8—151no—
153#126—152no—
154#126—152no—
155#124—51no—
156#124—151no—
157C22⋊Q8—152no—
158C4×Q8—31no—
159C4×Q8—151no—
160C4×Q8—151no—
161C4×D4—151no—
162#117—152no—
163C2×C3×C5C2×#4111yescharacteristic
164C2×C3×C5C2×#4111yescharacteristic
165C2×C3×C52−1+411yescharacteristic
166C3×D5—42no—
167C23×C3—52no—
168C3×Q8—22no—
169C3×D4—102no—
170C2×C3×C4—51no—
171C2×C3×C4—51no—
172C2×C3×C4C22×D512yes—
173C2×C3×C4C22×D511yescharacteristic
174C2×Dic3—51no—
175C2×Dic3—51no—
176C2×Dic3—52no—
177C2×Dic3—104no—
178C2×Dic3C22×D512yes—
179C2×Dic3C22×D511yescharacteristic
180C2×Dic3C22×D511yescharacteristic
181Dic6—102no—
182Dic6—102no—
183C22×C5C23×D311yescharacteristic
184C2×D5—22no—
185C2×D5—22no—
186C2×D5—22no—
187C4×C5—22no—
188C4×C5—61no—
189C4×C5—62no—
190C4×C5—61no—
191C4×C5#23712yes—
192Dic5—21no—
193Dic5—21no—
194Dic5—32no—
195Dic5—62no—
196Dic5—61no—
197C2×Q8—151no—
198C2×Q8—151no—
199C2×Q8D3×D511yescharacteristic
200C2×D4—51no—
201C22×C4—152no—
202C4⋊C4—31no—
203C4⋊C4—32no—
204C4⋊C4—151no—
205C4⋊C4—152no—
206C4⋊C4—151no—
207C4⋊C4—151no—
208C4⋊C4—152no—
209C4⋊C4—152no—
210C22⋊C4—52no—
211C22⋊C4—52no—
212C22⋊C4—152no—
213C22⋊C4—152no—
214C22⋊C4—152no—
215C42—32no—
216C42—31no—
217C42—51no—
218C42—152no—
219C42—151no—
220C3×C5#55611yescharacteristic, complemented, Hall
221C22×C3—102no—
222C22×C3—102no—
223C22×C3—102no—
224C22×C3C23×D511yescharacteristic
225C3×C4—22no—
226C3×C4—101no—
227C3×C4—101no—
228C3×C4#70912yes—
229Dic3—21no—
230Dic3—21no—
231Dic3—22no—
232Dic3—52no—
233Dic3—102no—
234Dic3—101no—
235C2×C5C2×#23711yescharacteristic
236C2×C5D3×#4111yescharacteristic
237C2×C5#101011yescharacteristic
238D5—42no—
239C23—52no—
240Q8—22no—
241Q8—302no—
242Q8—302no—
243D4—102no—
244C2×C4—31no—
245C2×C4—32no—
246C2×C4—31no—
247C2×C4—51no—
248C2×C4—51no—
249C2×C4—151no—
250C2×C4—151no—
251C2×C4—152no—
252C2×C4—304no—
253C2×C4C2×D3×D512yes—
254C2×C4C2×D3×D511yescharacteristic
255C2×C3—202no—
256C2×C3C2×#70911yescharacteristic
257C2×C3#414711yescharacteristic
258C2×C3D5×#4111yescharacteristic
259C5#567111yescharacteristic, complemented, Sylow
260C22—102no—
261C22—102no—
262C22—102no—
263C22C22×D3×D511yescharacteristic
264C4—22no—
265C4—61no—
266C4—62no—
267C4—61no—
268C4—101no—
269C4—101no—
270C4—152no—
271C4—301no—
272C4—302no—
273C4#677912yes—
274C3#6590211yescharacteristic, complemented, Sylow
275C2—202no—
276C2#9202811yescharacteristic
277C2#9203411yescharacteristic
278C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radicalC2×C3×D20C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #91833C2semidirect
2. C5×Q8×Dic3C2semidirect
4. C4×#1204C2semidirect
6. #91430C2semidirect
7. #91393C2semidirect
9. #91363C2semidirect
10. #91361C2semidirect
11. #91333C2semidirect
65. Q8×Dic3D5semidirect
220. C3×C5#556semidirect
259. C5#5671semidirect
274. C3#65902semidirect

Maximal subgroups

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

subgroupindex
#918332
C5×Q8×Dic32
C3×#40932
C4×#12042
#914342
#914302
#913932
#913642
#913632
#913612
#913332
#659023
#56715