Finite Group Databasebeta

← #11752633

Subgroups — #11752633

Order 960.

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

normal subgroups only

This group has 476 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×D60C211yesmaximal, characteristic, complemented
2C4×C5×D12C211yesmaximal, characteristic, complemented
3C3×#4016C211yesmaximal, characteristic, complemented
4#91466C211yesmaximal, characteristic, complemented
5#91466C211yesmaximal, characteristic, complemented
6#91446C212yesmaximal, complemented
7#91437C211yesmaximal, characteristic, complemented
8#91420C212yesmaximal, complemented
9#91351C212yesmaximal, complemented
10#91347C211yesmaximal, characteristic, complemented
11#91342C212yesmaximal, complemented
12#65892—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×C4×D15C2211yescharacteristic
15C2×C4×D15C2211yescharacteristic
16C2×C5×D12C2211yescharacteristic
17C2×C4×C5×D3C2212yes—
18C2×#1203C2212yes—
19C2×#1203C2212yes—
20C2×#1200C2212yes—
21C3×C42×C5C2211yescharacteristic
22#6714C2211yescharacteristic
23#6714C2211yescharacteristic
24C4⋊Dic15C2211yescharacteristic
25C5×(C2×D3)⋊C4C2212yes—
26C5×C4⋊Dic3C2211yescharacteristic
27C3×C4⋊Dic5C2211yescharacteristic
28C3×C4⋊Dic5C2211yescharacteristic
29C3×#683C2212yes—
30C3×#683C2212yes—
31#6669C2212yes—
32#6667C2212yes—
33(C2×D3)⋊Dic5C2212yes—
34(C2×D3)⋊Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5695—51nomaximal, Hall
37C4×C5×D4—31no—
38#4084—31no—
39#4084—31no—
40#4075—32no—
41C4×C22⋊D5—32no—
42#4038—31no—
43D5×C4⋊C4—31no—
44#4030—32no—
45#4025—32no—
46C4×D20—31no—
47#4016D311yescharacteristic, complemented
48C22×D15C2311yescharacteristic
49C22×D15C2311yescharacteristic
50C22×C5×D3C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×C3×C4×C5C2311yescharacteristic
53C2×C3×C4×C5C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56D60—22no—
57C4×D15—22no—
58C4×D15—22no—
59C2×C5×Dic3C2312yes—
60C5×D12—22no—
61C4×C5×D3—42no—
62C2×C3×Dic5C2312yes—
63C2×C3×Dic5C2312yes—
64#1203—24no—
65#1203—42no—
66#1200—42no—
67C3×#125—51no—
68#898—52no—
69#895—51no—
70#895—51no—
71#895—52no—
72#894—52no—
73#893—52no—
74#892—51no—
75D3×C4⋊C4—51no—
76C4×D12—51no—
77C4×D12D511yescharacteristic, complemented
78C2×C5×D4—31no—
79C22×C4×C5—32no—
80C2×C22⋊D5—32no—
81C2×C22⋊D5—32no—
82C2×D20—31no—
83C2×C4×D5—31no—
84C2×C4×D5—31no—
85C2×C4×D5—32no—
86C5×C4⋊C4—31no—
87C5×C22⋊C4—32no—
88C42×C5C2×D311yescharacteristic
89C22⋊Dic5—32no—
90C22⋊Dic5—32no—
91#685—31no—
92#685—31no—
93#685—32no—
94C4⋊Dic5—31no—
95C4⋊Dic5C2×D311yescharacteristic
96C4⋊Dic5C2×D311yescharacteristic
97#683—32no—
98#683C2×D312yes—
99#683C2×D312yes—
100C4×Dic5—32no—
101#553—151noSylow
102C22×C3×C5C2411yescharacteristic
103C2×D15—21no—
104C2×D15—21no—
105C2×D15—21no—
106C2×D15—21no—
107C2×D15—21no—
108C2×D15#4112yes—
109C2×C5×D3—22no—
110C2×C5×D3—22no—
111C2×C5×D3—22no—
112C3×C4×C5—21no—
113C3×C4×C5—21no—
114C3×C4×C5#4112yes—
115Dic15—21no—
116Dic15—21no—
117C3×Dic5—22no—
118C3×Dic5—22no—
119C5×Dic3—22no—
120C2×D12—52no—
121C2×D12—51no—
122C2×D12—52no—
123C2×D12C2×D511yescharacteristic
124C2×C4×D3—51no—
125C2×C4×D3—51no—
126C2×C4×D3—52no—
127C2×C4×D3C2×D512yes—
128C3×C4⋊C4—52no—
129C3×C4⋊C4—52no—
130C3×C4⋊C4—51no—
131C3×C4⋊C4—51no—
132C3×C42C2×D511yescharacteristic
133(C2×D3)⋊C4—52no—
134(C2×D3)⋊C4—52no—
135(C2×D3)⋊C4—51no—
136(C2×D3)⋊C4—51no—
137(C2×D3)⋊C4—52no—
138(C2×D3)⋊C4C2×D512yes—
139C4⋊Dic3—51no—
140C4⋊Dic3C2×D511yescharacteristic
141Dic3⋊C4—52no—
142C4×Dic3—52no—
143C23×C5—32no—
144C22×D5—31no—
145C22×D5—31no—
146C5×D4—62no—
147C2×C4×C5—32no—
148C2×C4×C5—122no—
149C2×C4×C5C22×D311yescharacteristic
150C2×C4×C5C22×D311yescharacteristic
151C2×C4×C5C22×D311yescharacteristic
152C22⋊D5—64no—
153C22⋊D5—122no—
154C2×Dic5—31no—
155C2×Dic5—31no—
156C2×Dic5C22×D312yes—
157C2×Dic5C22×D312yes—
158D20—62no—
159C4×D5—62no—
160C4×D5—62no—
161C4×D5—122no—
162#126—152no—
163#125—51no—
164#123—152no—
165#121—152no—
166#121—151no—
167#121—151no—
168C4×D4—31no—
169C4×D4—152no—
170C4×D4—151no—
171#117—151no—
172C2×C4⋊C4—151no—
173C2×C3×C5C2×#4111yescharacteristic
174C2×C3×C5C2×#4111yescharacteristic
175C2×C3×C5H(5,𝔽2)11yescharacteristic
176D15—22no—
177D15—41no—
178C5×D3—42no—
179C22×D3—51no—
180C22×D3—51no—
181C22×D3C22×D512yes—
182C2×C3×C4—52no—
183C2×C3×C4—52no—
184C2×C3×C4C22×D511yescharacteristic
185C2×C3×C4C22×D511yescharacteristic
186C2×C3×C4C22×D511yescharacteristic
187C2×Dic3—51no—
188C2×Dic3—51no—
189C2×Dic3C22×D512yes—
190D12—22no—
191D12—102no—
192D12—104no—
193D12—202no—
194C4×D3—42no—
195C4×D3—102no—
196C4×D3—102no—
197C4×D3—202no—
198C22×C5—62no—
199C22×C5—62no—
200C22×C5—62no—
201C22×C5C23×D311yescharacteristic
202C2×D5—32no—
203C2×D5—61no—
204C2×D5—61no—
205C2×D5—61no—
206C2×D5—61no—
207C2×D5—61no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—62no—
211C4×C5#23912yes—
212Dic5—22no—
213Dic5—22no—
214Dic5—61no—
215Dic5—61no—
216C2×D4—31no—
217C2×D4—152no—
218C2×D4—152no—
219C2×D4—151no—
220C22×C4—32no—
221C22×C4—152no—
222C22×C4—151no—
223C22×C4—151no—
224C4⋊C4—31no—
225C4⋊C4—51no—
226C4⋊C4—51no—
227C4⋊C4—52no—
228C4⋊C4—52no—
229C4⋊C4—152no—
230C4⋊C4—151no—
231C22⋊C4—32no—
232C22⋊C4—152no—
233C22⋊C4—152no—
234C22⋊C4—152no—
235C22⋊C4—151no—
236C22⋊C4—151no—
237C42—152no—
238C42D3×D511yescharacteristic
239C3×C5#55311yescharacteristic, complemented, Hall
240C22×C3C23×D511yescharacteristic
241C2×D3—22no—
242C2×D3—22no—
243C2×D3—22no—
244C2×D3—52no—
245C2×D3—101no—
246C2×D3—101no—
247C2×D3—101no—
248C2×D3—101no—
249C2×D3—101no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—102no—
253C3×C4—102no—
254C3×C4#70912yes—
255Dic3—22no—
256Dic3—101no—
257Dic3—101no—
258C2×C5—122no—
259C2×C5C2×#23911yescharacteristic
260C2×C5D3×#4111yescharacteristic
261C2×C5#100911yescharacteristic
262D5—62no—
263D5—121no—
264C23—32no—
265C23—151no—
266C23—151no—
267D4—62no—
268D4—302no—
269D4—304no—
270D4—602no—
271C2×C4—32no—
272C2×C4—52no—
273C2×C4—52no—
274C2×C4—122no—
275C2×C4—151no—
276C2×C4—151no—
277C2×C4—302no—
278C2×C4—302no—
279C2×C4—602no—
280C2×C4C2×D3×D511yescharacteristic
281C2×C4C2×D3×D511yescharacteristic
282C2×C4C2×D3×D511yescharacteristic
283C2×C3C2×#70911yescharacteristic
284C2×C3#414411yescharacteristic
285C2×C3D5×#4111yescharacteristic
286D3—42no—
287D3—102no—
288D3—201no—
289C5#569511yescharacteristic, complemented, Sylow
290C22—62no—
291C22—62no—
292C22—62no—
293C22—152no—
294C22—301no—
295C22—301no—
296C22—301no—
297C22—301no—
298C22—301no—
299C22C22×D3×D511yescharacteristic
300C4—21no—
301C4—21no—
302C4—62no—
303C4—102no—
304C4—102no—
305C4—301no—
306C4—301no—
307C4#676912yes—
308C3#6589211yescharacteristic, complemented, Sylow
309C2—122no—
310C2—302no—
311C2—601no—
312C2C2×#676911yescharacteristic
313C2#9201611yescharacteristic
314C2#9201811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×D60C2semidirect
2. C4×C5×D12C2semidirect
3. C3×#4016C2semidirect
4. #91466C2semidirect
5. #91466C2semidirect
6. #91446C2semidirect
7. #91437C2semidirect
8. #91420C2semidirect
9. #91351C2semidirect
10. #91347C2semidirect
11. #91342C2semidirect
47. #4016D3semidirect
77. C4×D12D5semidirect
239. C3×C5#553semidirect
289. C5#5695semidirect
308. C3#65892semidirect

Maximal subgroups

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

subgroupindex
C4×D602
C4×C5×D122
C3×#40162
#914662
#914462
#914372
#914202
#913512
#913472
#913422
#658923
#56955