Finite Group Databasebeta

← #11752649

Subgroups — #11752649

Order 960.

432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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#91761C211yesmaximal, characteristic, complemented
2C5×#869C211yesmaximal, characteristic, complemented
3C3×#4021C211yesmaximal, characteristic, complemented
4#91465C211yesmaximal, characteristic
5#91455C212yesmaximal, complemented
6#91434C211yesmaximal, characteristic, complemented
7#91421C212yesmaximal, complemented
8#91413C212yesmaximal, complemented
9#91390C211yesmaximal, characteristic, complemented
10#91361C212yesmaximal, complemented
11#91331C211yesmaximal, characteristic, complemented
12#66067—31nomaximal, Hall
13C2×C4×D15C2211yescharacteristic
14C2×C5×Dic6C2212yes—
15C2×C3×D20C2211yescharacteristic
16C2×C3×Dic10C2211yescharacteristic
17C2×#1202C2212yes—
18C2×D5×Dic3C2212yes—
19C3×C42×C5C2211yescharacteristic
20#6714C2211yescharacteristic
21#6714C2211yescharacteristic
22#6712C2211yescharacteristic
23#6712C2211yescharacteristic
24C4×Dic15C2211yescharacteristic
25C5×C4⋊Dic3C2212yes—
26C5×C4⋊Dic3C2211yescharacteristic
27C5×C4⋊Dic3C2211yescharacteristic
28C3×#685C2212yes—
29C3×#685C2212yes—
30Dic3⋊Dic5C2212yes—
31#6668C2212yes—
32#6667C2212yes—
33#6665C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5682—51nomaximal, Hall
37C5×C4⋊Q8—31no—
38#4093—32no—
39#4092—32no—
40#4044—32no—
41#4043—31no—
42#4041—31no—
43#4040—32no—
44#4039—31no—
45#4033—31no—
46#4021D311yescharacteristic, complemented
47#4018—31no—
48C22×D15C2311yescharacteristic
49C22×C3×D5C2312yes—
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2311yescharacteristic
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56C4×D15—22no—
57C2×C5×Dic3C2312yes—
58C2×C5×Dic3C2312yes—
59C5×Dic6—42no—
60C2×C3×Dic5C2312yes—
61C3×D20—22no—
62C3×Dic10—22no—
63#1202—42no—
64D5×Dic3—42no—
65C3×#124—51no—
66#946—51no—
67Q8×Dic3—51no—
68#938—51no—
69D4×Dic3—51no—
70#886—52no—
71#885—52no—
72#879—52no—
73#878—52no—
74#872—51no—
75#869D511yescharacteristic, complemented
76C2×C5×Q8—32no—
77C2×D20—32no—
78C2×D20C2×D311yescharacteristic
79C2×C4×D5—31no—
80C2×C4×D5—32no—
81C2×Dic10C2×D311yescharacteristic
82C5×C4⋊C4—31no—
83C5×C4⋊C4—31no—
84C5×C4⋊C4—32no—
85C42×C5C2×D311yescharacteristic
86#685—32no—
87#685—32no—
88#685—31no—
89#685—31no—
90#685—32no—
91#685C2×D312yes—
92#685C2×D312yes—
93C4⋊Dic5—32no—
94#683—31no—
95#683—31no—
96#683—32no—
97C4×Dic5—31no—
98C4×Dic5—32no—
99#542—151noSylow
100C22×C3×C5C2411yescharacteristic
101C2×D15—21no—
102C2×D15—21no—
103C2×D15—21no—
104C2×C3×D5—22no—
105C2×C3×D5—22no—
106C2×C3×D5—22no—
107C3×C4×C5—21no—
108C3×C4×C5—21no—
109C3×C4×C5#4112yes—
110Dic15—21no—
111Dic15—21no—
112Dic15—21no—
113C3×Dic5—22no—
114C5×Dic3—22no—
115C5×Dic3—22no—
116C2×C3×Q8—51no—
117C2×C3×D4—51no—
118C2×#67—52no—
119C22×Dic3—52no—
120C2×C4×D3—51no—
121C2×Dic6C2×D512yes—
122C3×C22⋊C4—52no—
123C3×C22⋊C4—52no—
124C3×C42C2×D511yescharacteristic
125#217—52no—
126#217—52no—
127(C2×D3)⋊C4—51no—
128(C2×D3)⋊C4—51no—
129(C2×D3)⋊C4—52no—
130C4⋊Dic3—52no—
131C4⋊Dic3C2×D512yes—
132C4⋊Dic3C2×D511yescharacteristic
133C4⋊Dic3C2×D511yescharacteristic
134Dic3⋊C4—51no—
135Dic3⋊C4—51no—
136Dic3⋊C4—52no—
137C4×Dic3—51no—
138C4×Dic3—52no—
139C22×D5—31no—
140C22×D5C22×D312yes—
141C5×Q8—122no—
142C2×C4×C5—32no—
143C2×C4×C5—32no—
144C2×C4×C5C22×D311yescharacteristic
145C2×C4×C5C22×D311yescharacteristic
146C2×C4×C5C22×D311yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—31no—
150C2×Dic5C22×D312yes—
151D20—22no—
152D20—122no—
153C4×D5—62no—
154C4×D5—122no—
155Dic10—22no—
156C4⋊Q8—31no—
157#126—152no—
158#124—51no—
159#124—152no—
160#123—152no—
161C22⋊Q8—152no—
162C22⋊Q8—151no—
163#121—151no—
164C4×Q8—151no—
165C4×D4—151no—
166#117—151no—
167C2×C3×C5C2×#4111yescharacteristic
168C2×C3×C5H(5,𝔽2)11yescharacteristic
169C2×C3×C52−1+411yescharacteristic
170D15—41no—
171C3×D5—42no—
172C23×C3—52no—
173C22×D3—51no—
174C3×Q8—102no—
175C3×D4—102no—
176C2×C3×C4—52no—
177C2×C3×C4C22×D511yescharacteristic
178C2×C3×C4C22×D511yescharacteristic
179C2×C3×C4C22×D511yescharacteristic
180#67—202no—
181C2×Dic3—51no—
182C2×Dic3—51no—
183C2×Dic3—51no—
184C2×Dic3—202no—
185C2×Dic3C22×D512yes—
186C2×Dic3C22×D512yes—
187C4×D3—102no—
188Dic6—42no—
189C22×C5C23×D311yescharacteristic
190C2×D5—22no—
191C2×D5—22no—
192C2×D5—22no—
193C2×D5—61no—
194C2×D5—61no—
195C2×D5—61no—
196C4×C5—21no—
197C4×C5—21no—
198C4×C5—62no—
199C4×C5—62no—
200C4×C5#23712yes—
201Dic5—22no—
202Dic5—61no—
203Dic5—61no—
204Dic5—61no—
205C2×Q8—32no—
206C2×Q8—51no—
207C2×D4—51no—
208C2×D4—152no—
209C22×C4—152no—
210C22×C4—151no—
211C4⋊C4—31no—
212C4⋊C4—31no—
213C4⋊C4—32no—
214C4⋊C4—152no—
215C4⋊C4—152no—
216C4⋊C4—151no—
217C4⋊C4—151no—
218C22⋊C4—52no—
219C22⋊C4—52no—
220C22⋊C4—152no—
221C22⋊C4—152no—
222C22⋊C4—152no—
223C22⋊C4—151no—
224C22⋊C4—151no—
225C42—152no—
226C42—151no—
227C42D3×D511yescharacteristic
228C3×C5#54211yescharacteristic, complemented, Hall
229C22×C3—102no—
230C22×C3—102no—
231C22×C3—102no—
232C22×C3C23×D511yescharacteristic
233C2×D3—101no—
234C2×D3—101no—
235C2×D3—101no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—102no—
239C3×C4#71312yes—
240Dic3—22no—
241Dic3—22no—
242Dic3—101no—
243Dic3—101no—
244Dic3—101no—
245C2×C5C2×#23711yescharacteristic
246C2×C5#100911yescharacteristic
247C2×C5#101011yescharacteristic
248D5—42no—
249D5—121no—
250C23—52no—
251C23—151no—
252Q8—102no—
253Q8—122no—
254D4—102no—
255D4—602no—
256C2×C4—32no—
257C2×C4—32no—
258C2×C4—52no—
259C2×C4—151no—
260C2×C4—151no—
261C2×C4—151no—
262C2×C4—302no—
263C2×C4—602no—
264C2×C4C2×D3×D511yescharacteristic
265C2×C4C2×D3×D511yescharacteristic
266C2×C4C2×D3×D511yescharacteristic
267C2×C3—202no—
268C2×C3#414411yescharacteristic
269C2×C3C2×#71311yescharacteristic
270C2×C3#414711yescharacteristic
271D3—201no—
272C5#568211yescharacteristic, complemented, Sylow
273C22—102no—
274C22—102no—
275C22—102no—
276C22—301no—
277C22—301no—
278C22—301no—
279C22C22×D3×D511yescharacteristic
280C4—21no—
281C4—21no—
282C4—62no—
283C4—62no—
284C4—102no—
285C4—301no—
286C4—301no—
287C4—301no—
288C4#676612yes—
289C3#6606711yescharacteristic, complemented, Sylow
290C2—202no—
291C2—601no—
292C2C2×#676611yescharacteristic
293C2#9200011yescharacteristic
294C2#9201811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radical#91465C2
hypercenterC42D3×D5
hypocenterC3×C5#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #91761C2semidirect
2. C5×#869C2semidirect
3. C3×#4021C2semidirect
5. #91455C2semidirect
6. #91434C2semidirect
7. #91421C2semidirect
8. #91413C2semidirect
9. #91390C2semidirect
10. #91361C2semidirect
11. #91331C2semidirect
46. #4021D3semidirect
75. #869D5semidirect
228. C3×C5#542semidirect
272. C5#5682semidirect
289. C3#66067semidirect

Maximal subgroups

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

subgroupindex
#917612
C5×#8692
C3×#40212
#914652
#914552
#914342
#914212
#914132
#913902
#913612
#913312
#660673
#56825