Finite Group Databasebeta

← #11752630

Subgroups — #11752630

Order 960.

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

normal subgroups only

This group has 428 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
2C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C3×#4016C211yesmaximal, characteristic, complemented
4#91437C211yesmaximal, characteristic, complemented
5#91433C212yesmaximal
6#91403C212yesmaximal, complemented
7#91383C211yesmaximal, characteristic, complemented
8#91383C211yesmaximal, characteristic, complemented
9#91380C212yesmaximal, complemented
10#91347C211yesmaximal, characteristic, complemented
11#91334C212yesmaximal, complemented
12#65915—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×C4×D15C2211yescharacteristic
15C2×C4×D15C2211yescharacteristic
16C2×C5×Dic6C2211yescharacteristic
17C2×#1200C2212yes—
18C3×C42×C5C2211yescharacteristic
19#6714C2211yescharacteristic
20#6714C2211yescharacteristic
21C4⋊Dic15C2211yescharacteristic
22C5×C4⋊Dic3C2211yescharacteristic
23C5×Dic3⋊C4C2212yes—
24C4×C5×Dic3C2212yes—
25C3×C4⋊Dic5C2211yescharacteristic
26C3×C4⋊Dic5C2211yescharacteristic
27C3×#683C2212yes—
28C3×#683C2212yes—
29#6669C2212yes—
30#6668C2212yes—
31#6668C2212yes—
32#6667C2212yes—
33#6667C2212yes—
34#6667C2212yes—
35Dic3×Dic5C2212yes—
36#5694—51nomaximal, Hall
37C4×C5×Q8—31no—
38#4092—31no—
39#4092—31no—
40#4040—32no—
41#4038—31no—
42D5×C4⋊C4—31no—
43#4035—32no—
44#4022—32no—
45C4×D20—31no—
46#4018—32no—
47#4016D311yescharacteristic, complemented
48C22×D15C2311yescharacteristic
49C22×D15C2311yescharacteristic
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2311yescharacteristic
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55D60—22no—
56C4×D15—22no—
57C4×D15—22no—
58C2×C5×Dic3C2312yes—
59C2×C5×Dic3C2312yes—
60C5×Dic6—22no—
61C2×C3×Dic5C2312yes—
62C2×C3×Dic5C2312yes—
63#1200—24no—
64C3×#125—51no—
65#898—52no—
66#897—51no—
67#897—51no—
68#894—52no—
69#892—51no—
70#892—52no—
71D3×C4⋊C4—51no—
72#890—52no—
73C4×D12—51no—
74C4×Dic6D511yescharacteristic, complemented
75C2×C5×Q8—31no—
76C2×D20—31no—
77C2×C4×D5—31no—
78C2×C4×D5—31no—
79C2×C4×D5—32no—
80C5×C4⋊C4—32no—
81C5×C4⋊C4—31no—
82C42×C5—32no—
83C42×C5C2×D311yescharacteristic
84#685—31no—
85#685—31no—
86#685—32no—
87#685—32no—
88#685—32no—
89C4⋊Dic5—31no—
90C4⋊Dic5C2×D311yescharacteristic
91C4⋊Dic5C2×D311yescharacteristic
92#683—32no—
93#683—32no—
94#683—32no—
95#683C2×D312yes—
96#683C2×D312yes—
97C4×Dic5—32no—
98#552—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×D15—21no—
101C2×D15—21no—
102C2×D15—21no—
103C2×D15—21no—
104C2×D15—21no—
105C2×D15#4112yes—
106C3×C4×C5—21no—
107C3×C4×C5—21no—
108C3×C4×C5#4112yes—
109Dic15—21no—
110Dic15—21no—
111C3×Dic5—22no—
112C3×Dic5—22no—
113C5×Dic3—22no—
114C5×Dic3—22no—
115C2×D12—51no—
116C2×C4×D3—51no—
117C2×C4×D3—51no—
118C2×C4×D3—52no—
119C2×Dic6C2×D511yescharacteristic
120C3×C4⋊C4—52no—
121C3×C4⋊C4—52no—
122C3×C4⋊C4—51no—
123C3×C4⋊C4—51no—
124C3×C42C2×D511yescharacteristic
125(C2×D3)⋊C4—51no—
126(C2×D3)⋊C4—51no—
127(C2×D3)⋊C4—52no—
128(C2×D3)⋊C4—52no—
129(C2×D3)⋊C4—52no—
130C4⋊Dic3—51no—
131C4⋊Dic3—52no—
132C4⋊Dic3—52no—
133C4⋊Dic3C2×D511yescharacteristic
134Dic3⋊C4—52no—
135Dic3⋊C4C2×D512yes—
136C4×Dic3—52no—
137C4×Dic3C2×D512yes—
138C22×D5—31no—
139C22×D5—31no—
140C5×Q8—62no—
141C2×C4×C5—32no—
142C2×C4×C5—32no—
143C2×C4×C5C22×D311yescharacteristic
144C2×C4×C5C22×D311yescharacteristic
145C2×C4×C5C22×D311yescharacteristic
146C2×Dic5—31no—
147C2×Dic5—31no—
148C2×Dic5C22×D312yes—
149C2×Dic5C22×D312yes—
150D20—62no—
151C4×D5—64no—
152C4×D5—62no—
153C4×D5—62no—
154#126—152no—
155#125—51no—
156#125—152no—
157#123—152no—
158C22⋊Q8—151no—
159C22⋊Q8—151no—
160C4×Q8—31no—
161C4×D4—151no—
162#117—152no—
163#117—151no—
164C2×C4⋊C4—151no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168D15—22no—
169D15—41no—
170C22×D3—51no—
171C22×D3—51no—
172C2×C3×C4—52no—
173C2×C3×C4—52no—
174C2×C3×C4C22×D511yescharacteristic
175C2×C3×C4C22×D511yescharacteristic
176C2×C3×C4C22×D511yescharacteristic
177C2×Dic3—51no—
178C2×Dic3—51no—
179C2×Dic3C22×D512yes—
180C2×Dic3C22×D512yes—
181D12—102no—
182C4×D3—104no—
183C4×D3—102no—
184C4×D3—102no—
185Dic6—22no—
186C22×C5C23×D311yescharacteristic
187C2×D5—32no—
188C2×D5—61no—
189C2×D5—61no—
190C2×D5—61no—
191C2×D5—61no—
192C2×D5—61no—
193C4×C5—21no—
194C4×C5—21no—
195C4×C5—62no—
196C4×C5—62no—
197C4×C5#23912yes—
198Dic5—22no—
199Dic5—22no—
200Dic5—61no—
201Dic5—61no—
202C2×Q8—31no—
203C2×D4—151no—
204C22×C4—152no—
205C22×C4—151no—
206C22×C4—151no—
207C4⋊C4—31no—
208C4⋊C4—32no—
209C4⋊C4—51no—
210C4⋊C4—51no—
211C4⋊C4—52no—
212C4⋊C4—52no—
213C4⋊C4—152no—
214C4⋊C4—152no—
215C4⋊C4—152no—
216C4⋊C4—151no—
217C22⋊C4—152no—
218C22⋊C4—152no—
219C22⋊C4—152no—
220C22⋊C4—151no—
221C22⋊C4—151no—
222C42—32no—
223C42—152no—
224C42D3×D511yescharacteristic
225C3×C5#55211yescharacteristic, complemented, Hall
226C22×C3C23×D511yescharacteristic
227C2×D3—52no—
228C2×D3—101no—
229C2×D3—101no—
230C2×D3—101no—
231C2×D3—101no—
232C2×D3—101no—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—102no—
236C3×C4—102no—
237C3×C4#70912yes—
238Dic3—22no—
239Dic3—22no—
240Dic3—101no—
241Dic3—101no—
242C2×C5C2×#23911yescharacteristic
243C2×C5D3×#4111yescharacteristic
244C2×C5#101011yescharacteristic
245D5—62no—
246D5—121no—
247C23—151no—
248C23—151no—
249Q8—62no—
250D4—302no—
251C2×C4—32no—
252C2×C4—32no—
253C2×C4—52no—
254C2×C4—52no—
255C2×C4—151no—
256C2×C4—151no—
257C2×C4—304no—
258C2×C4—302no—
259C2×C4—302no—
260C2×C4C2×D3×D511yescharacteristic
261C2×C4C2×D3×D511yescharacteristic
262C2×C4C2×D3×D511yescharacteristic
263C2×C3C2×#70911yescharacteristic
264C2×C3#414711yescharacteristic
265C2×C3D5×#4111yescharacteristic
266D3—102no—
267D3—201no—
268C5#569411yescharacteristic, complemented, Sylow
269C22—152no—
270C22—301no—
271C22—301no—
272C22—301no—
273C22—301no—
274C22—301no—
275C22C22×D3×D511yescharacteristic
276C4—21no—
277C4—21no—
278C4—62no—
279C4—62no—
280C4—102no—
281C4—102no—
282C4—301no—
283C4—301no—
284C4#676912yes—
285C3#6591511yescharacteristic, complemented, Sylow
286C2—302no—
287C2—601no—
288C2#9200011yescharacteristic
289C2C2×#676911yescharacteristic
290C2#9201611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radicalC2×D60C22
hypercenterC42D3×D5
hypocenterC3×C5#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C5×Dic6C2semidirect
3. C3×#4016C2semidirect
4. #91437C2semidirect
6. #91403C2semidirect
7. #91383C2semidirect
8. #91383C2semidirect
9. #91380C2semidirect
10. #91347C2semidirect
11. #91334C2semidirect
47. #4016D3semidirect
74. C4×Dic6D5semidirect
225. C3×C5#552semidirect
268. C5#5694semidirect
285. C3#65915semidirect

Maximal subgroups

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

subgroupindex
C4×D602
C4×C5×Dic62
C3×#40162
#914372
#914332
#914032
#913832
#913802
#913472
#913342
#659153
#56945