Finite Group Databasebeta

← #11753649

Subgroups — #11753649

Order 960.

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

normal subgroups only

This group has 480 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#91782C211yesmaximal, characteristic, complemented
2C5×#890C211yesmaximal, characteristic, complemented
3C3×#4041C211yesmaximal, characteristic, complemented
4#91465C212yesmaximal, complemented
5#91458C211yesmaximal, characteristic, complemented
6#91450C211yesmaximal, characteristic, complemented
7#91434C211yesmaximal, characteristic, complemented
8#91413C212yesmaximal, complemented
9#91409C212yesmaximal, complemented
10#91357C211yesmaximal, characteristic, complemented
11#91354C212yesmaximal, complemented
12#66032—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×C4×D15C2212yes—
15C2×C3×D20C2211yescharacteristic
16C2×C3×D20C2212yes—
17C2×C3×C4×D5C2211yescharacteristic
18C2×#1202C2212yes—
19C2×#1202C2212yes—
20C2×#1202C2212yes—
21C2×D5×Dic3C2212yes—
22C3×C5×C4⋊C4C2211yescharacteristic
23#6714C2212yes—
24C4×Dic15C2211yescharacteristic
25C5×C4⋊Dic3C2212yes—
26C5×C4⋊Dic3C2211yescharacteristic
27C5×Dic3⋊C4C2212yes—
28C4×C5×Dic3C2211yescharacteristic
29C3×#685C2212yes—
30#6668C2211yescharacteristic
31#6668C2211yescharacteristic
32#6667C2212yes—
33#6665C2211yescharacteristic
34#6665C2212yes—
35#6665C2211yescharacteristic
36#5619—51nomaximal, Hall
37C5×#125—31no—
38#4041—32no—
39#4041—32no—
40#4041—31no—
41#4041D311yescharacteristic, complemented
42#4040—32no—
43#4040—32no—
44#4039—31no—
45#4039—31no—
46#4020—31no—
47#4018—31no—
48C22×D15C2312yes—
49C22×C3×D5C2311yescharacteristic
50C22×C3×D5C2312yes—
51C2×C3×C4×C5C2312yes—
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55D60—22no—
56C4×D15—42no—
57C2×C5×Dic3C2312yes—
58C2×C5×Dic3C2311yescharacteristic
59C2×C5×Dic3C2311yescharacteristic
60C2×C3×Dic5C2311yescharacteristic
61C3×D20—22no—
62C3×D20—42no—
63C3×C4×D5—22no—
64#1202—42no—
65#1202—42no—
66#1202—42no—
67D5×Dic3—42no—
68C3×#121—51no—
69#940—51no—
70#939—52no—
71#938—52no—
72D4×Dic3—51no—
73#930—51no—
74#926—51no—
75#893—51no—
76#890D511yescharacteristic, complemented
77#886—52no—
78#883—52no—
79C2×D20—31no—
80C2×D20—32no—
81C2×D20—32no—
82C2×D20—32no—
83C2×D20C2×D311yescharacteristic
84C2×D20C2×D312yes—
85C2×C4×D5—32no—
86C2×C4×D5—32no—
87C2×C4×D5C2×D311yescharacteristic
88C5×C4⋊C4—32no—
89C5×C4⋊C4—31no—
90C5×C4⋊C4—32no—
91C5×C4⋊C4C2×D311yescharacteristic
92C42×C5—31no—
93#685—31no—
94#685—31no—
95#685—32no—
96#685—32no—
97#685—32no—
98#685C2×D312yes—
99#683—31no—
100#683—31no—
101C4×Dic5—31no—
102#540—151noSylow
103C22×C3×C5C2411yescharacteristic
104C2×D15—22no—
105C2×D15—22no—
106C2×D15—22no—
107C2×C3×D5—21no—
108C2×C3×D5—22no—
109C2×C3×D5—22no—
110C2×C3×D5—21no—
111C2×C3×D5—22no—
112C2×C3×D5—21no—
113C3×C4×C5—22no—
114C3×C4×C5#4112yes—
115Dic15—21no—
116Dic15—21no—
117C3×Dic5—21no—
118C5×Dic3—22no—
119C5×Dic3—21no—
120C5×Dic3—21no—
121C2×C3×D4—51no—
122C2×C3×D4—52no—
123C22×C3×C4—51no—
124C2×#67—52no—
125C2×#67—52no—
126C2×#67—52no—
127C22×Dic3—52no—
128C2×D12—51no—
129C2×C4×D3—52no—
130C3×C4⋊C4C2×D511yescharacteristic
131C3×C22⋊C4—52no—
132#217—52no—
133#217—51no—
134#217—51no—
135(C2×D3)⋊C4—52no—
136(C2×D3)⋊C4—52no—
137C4⋊Dic3—51no—
138C4⋊Dic3—51no—
139C4⋊Dic3C2×D512yes—
140C4⋊Dic3C2×D511yescharacteristic
141Dic3⋊C4C2×D512yes—
142C4×Dic3—51no—
143C4×Dic3C2×D511yescharacteristic
144C22×D5—32no—
145C22×D5C22×D311yescharacteristic
146C22×D5C22×D312yes—
147C2×C4×C5—31no—
148C2×C4×C5—31no—
149C2×C4×C5—32no—
150C2×C4×C5C22×D312yes—
151C2×C4×C5C22×D311yescharacteristic
152C2×Dic5—31no—
153C2×Dic5—31no—
154C2×Dic5C22×D311yescharacteristic
155D20—22no—
156D20—42no—
157D20—62no—
158D20—122no—
159D20—122no—
160D20—122no—
161C4×D5—22no—
162C4×D5—122no—
163C4×D5—122no—
164#127—151no—
165#125—31no—
166#123—152no—
167#123—152no—
168#121—51no—
169#121—151no—
170#121—152no—
171#121—152no—
172C4×D4—151no—
173C4×D4—151no—
174#117—151no—
175C2×C3×C5C2×#4111yescharacteristic
176C2×C3×C5H(5,𝔽2)11yescharacteristic
177C2×C3×C5H(5,𝔽2)11yescharacteristic
178D15—42no—
179C3×D5—41no—
180C3×D5—42no—
181C23×C3—51no—
182C23×C3—52no—
183C22×D3—52no—
184C3×D4—102no—
185C3×D4—202no—
186C2×C3×C4—51no—
187C2×C3×C4—102no—
188C2×C3×C4C22×D512yes—
189C2×C3×C4C22×D511yescharacteristic
190#67—202no—
191#67—202no—
192#67—202no—
193C2×Dic3—51no—
194C2×Dic3—51no—
195C2×Dic3—202no—
196C2×Dic3C22×D511yescharacteristic
197C2×Dic3C22×D511yescharacteristic
198C2×Dic3C22×D512yes—
199D12—102no—
200C4×D3—202no—
201C22×C5C23×D311yescharacteristic
202C2×D5—21no—
203C2×D5—22no—
204C2×D5—21no—
205C2×D5—22no—
206C2×D5—22no—
207C2×D5—21no—
208C2×D5—62no—
209C2×D5—62no—
210C2×D5—62no—
211C4×C5—22no—
212C4×C5—61no—
213C4×C5—62no—
214C4×C5—61no—
215C4×C5#23712yes—
216Dic5—21no—
217Dic5—61no—
218Dic5—61no—
219C2×D4—51no—
220C2×D4—52no—
221C2×D4—152no—
222C2×D4—152no—
223C2×D4—152no—
224C2×D4—151no—
225C22×C4—51no—
226C22×C4—152no—
227C22×C4—152no—
228C4⋊C4—31no—
229C4⋊C4—32no—
230C4⋊C4—32no—
231C4⋊C4—151no—
232C4⋊C4—151no—
233C4⋊C4D3×D511yescharacteristic
234C22⋊C4—52no—
235C22⋊C4—152no—
236C22⋊C4—151no—
237C22⋊C4—151no—
238C22⋊C4—152no—
239C22⋊C4—152no—
240C42—31no—
241C42—151no—
242C3×C5#54011yescharacteristic, complemented, Hall
243C22×C3—101no—
244C22×C3—102no—
245C22×C3—102no—
246C22×C3—101no—
247C22×C3—102no—
248C22×C3—101no—
249C22×C3C23×D511yescharacteristic
250C2×D3—102no—
251C2×D3—102no—
252C2×D3—102no—
253C3×C4—22no—
254C3×C4—101no—
255C3×C4#71312yes—
256Dic3—22no—
257Dic3—21no—
258Dic3—21no—
259Dic3—101no—
260Dic3—101no—
261C2×C5C2×#23711yescharacteristic
262C2×C5#100411yescharacteristic
263C2×C5#100911yescharacteristic
264D5—41no—
265D5—42no—
266D5—122no—
267C23—52no—
268C23—51no—
269C23—152no—
270D4—102no—
271D4—202no—
272D4—302no—
273D4—602no—
274D4—602no—
275D4—602no—
276C2×C4—31no—
277C2×C4—31no—
278C2×C4—32no—
279C2×C4—51no—
280C2×C4—102no—
281C2×C4—151no—
282C2×C4—151no—
283C2×C4—602no—
284C2×C4—602no—
285C2×C4C2×D3×D512yes—
286C2×C4C2×D3×D511yescharacteristic
287C2×C3—201no—
288C2×C3—202no—
289C2×C3C2×#71311yescharacteristic
290C2×C3#414911yescharacteristic
291C2×C3#414911yescharacteristic
292D3—202no—
293C5#561911yescharacteristic, complemented, Sylow
294C22—101no—
295C22—102no—
296C22—101no—
297C22—102no—
298C22—102no—
299C22—101no—
300C22—302no—
301C22—302no—
302C22—302no—
303C22C22×D3×D511yescharacteristic
304C4—22no—
305C4—61no—
306C4—62no—
307C4—61no—
308C4—101no—
309C4—301no—
310C4—301no—
311C4#676612yes—
312C3#6603211yescharacteristic, complemented, Sylow
313C2—201no—
314C2—202no—
315C2—602no—
316C2C2×#676611yescharacteristic
317C2#9202611yescharacteristic
318C2#9203511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#540
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. #91782C2semidirect
2. C5×#890C2semidirect
3. C3×#4041C2semidirect
4. #91465C2semidirect
5. #91458C2semidirect
6. #91450C2semidirect
7. #91434C2semidirect
8. #91413C2semidirect
9. #91409C2semidirect
10. #91357C2semidirect
11. #91354C2semidirect
41. #4041D3semidirect
76. #890D5semidirect
242. C3×C5#540semidirect
293. C5#5619semidirect
312. C3#66032semidirect

Maximal subgroups

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

subgroupindex
#917822
C5×#8902
C3×#40412
#914652
#914582
#914502
#914342
#914132
#914092
#913572
#913542
#660323
#56195