Finite Group Databasebeta

← #11753375

Subgroups — #11753375

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#91782C211yesmaximal, characteristic, complemented
2C5×#888C211yesmaximal, characteristic, complemented
3C3×#4043C211yesmaximal, characteristic, complemented
4#91455C212yesmaximal, complemented
5#91450C211yesmaximal, characteristic
6#91383C212yesmaximal, complemented
7#91374C211yesmaximal, characteristic, complemented
8#91357C211yesmaximal, characteristic, complemented
9#91354C212yesmaximal, complemented
10#91345C212yesmaximal, complemented
11#91331C211yesmaximal, characteristic, complemented
12#66067—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×C4×D15C2212yes—
15C2×C5×Dic6C2212yes—
16C2×C3×C4×D5C2211yescharacteristic
17C2×C3×Dic10C2211yescharacteristic
18C2×#1202C2212yes—
19C3×C5×C4⋊C4C2211yescharacteristic
20#6714C2212yes—
21C4×Dic15C2211yescharacteristic
22C5×C4⋊Dic3C2211yescharacteristic
23C5×Dic3⋊C4C2212yes—
24C4×C5×Dic3C2211yescharacteristic
25C3×#685C2212yes—
26C3×C4⋊Dic5C2212yes—
27#6668C2212yes—
28#6668C2211yescharacteristic
29#6668C2211yescharacteristic
30#6667C2212yes—
31#6667C2212yes—
32#6667C2212yes—
33#6665C2211yescharacteristic
34#6665C2211yescharacteristic
35Dic3×Dic5C2212yes—
36#5643—51nomaximal, Hall
37C5×C4⋊Q8—31no—
38#4093—32no—
39#4092—32no—
40#4044—32no—
41#4043D311yescharacteristic, complemented
42#4041—31no—
43#4040—32no—
44#4039—31no—
45#4033—31no—
46#4021—31no—
47#4018—31no—
48C22×D15C2312yes—
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54D60—22no—
55C4×D15—42no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C5×Dic6—42no—
60C2×C3×Dic5C2312yes—
61C2×C3×Dic5C2311yescharacteristic
62C3×C4×D5—22no—
63C3×Dic10—22no—
64#1202—42no—
65C3×C22⋊Q8—51no—
66#947—51no—
67Q8×Dic3—51no—
68#930—51no—
69#926—51no—
70#898—52no—
71#897—52no—
72#893—51no—
73#888D511yescharacteristic, complemented
74#885—52no—
75#883—52no—
76C2×C5×Q8—32no—
77C2×D20—31no—
78C2×D20—32no—
79C2×C4×D5—32no—
80C2×C4×D5C2×D311yescharacteristic
81C2×Dic10C2×D311yescharacteristic
82C5×C4⋊C4—32no—
83C5×C4⋊C4—31no—
84C5×C4⋊C4C2×D311yescharacteristic
85C42×C5—31no—
86#685—31no—
87#685—31no—
88#685—32no—
89#685—32no—
90#685—32no—
91#685—32no—
92#685C2×D312yes—
93C4⋊Dic5C2×D312yes—
94#683—31no—
95#683—31no—
96#683—32no—
97C4×Dic5—31no—
98C4×Dic5—32no—
99#542—151noSylow
100C22×C3×C5C2411yescharacteristic
101C2×D15—22no—
102C2×D15—22no—
103C2×D15—22no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C2×C3×D5—21no—
107C3×C4×C5—22no—
108C3×C4×C5#4112yes—
109Dic15—21no—
110Dic15—21no—
111C3×Dic5—22no—
112C3×Dic5—21no—
113C5×Dic3—22no—
114C5×Dic3—21no—
115C5×Dic3—21no—
116C2×C3×Q8—51no—
117C22×C3×C4—51no—
118C2×#67—52no—
119C2×D12—51no—
120C2×C4×D3—52no—
121C2×Dic6C2×D512yes—
122C3×C4⋊C4—52no—
123C3×C4⋊C4C2×D511yescharacteristic
124C3×C22⋊C4—52no—
125#217—51no—
126#217—51no—
127(C2×D3)⋊C4—52no—
128(C2×D3)⋊C4—52no—
129(C2×D3)⋊C4—52no—
130(C2×D3)⋊C4—52no—
131C4⋊Dic3—52no—
132C4⋊Dic3—51no—
133C4⋊Dic3—51no—
134C4⋊Dic3C2×D511yescharacteristic
135Dic3⋊C4C2×D512yes—
136C4×Dic3—51no—
137C4×Dic3—52no—
138C4×Dic3C2×D511yescharacteristic
139C22×D5—32no—
140C22×D5C22×D311yescharacteristic
141C5×Q8—122no—
142C2×C4×C5—32no—
143C2×C4×C5—31no—
144C2×C4×C5—31no—
145C2×C4×C5C22×D312yes—
146C2×C4×C5C22×D311yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5C22×D312yes—
150C2×Dic5C22×D311yescharacteristic
151D20—62no—
152D20—122no—
153C4×D5—22no—
154C4×D5—122no—
155Dic10—22no—
156C4⋊Q8—31no—
157#126—152no—
158#124—151no—
159#124—152no—
160#123—152no—
161C22⋊Q8—51no—
162C22⋊Q8—152no—
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—42no—
171C3×D5—41no—
172C23×C3—51no—
173C22×D3—52no—
174C3×Q8—102no—
175C2×C3×C4—52no—
176C2×C3×C4—51no—
177C2×C3×C4—102no—
178C2×C3×C4C22×D512yes—
179C2×C3×C4C22×D511yescharacteristic
180#67—202no—
181C2×Dic3—51no—
182C2×Dic3—51no—
183C2×Dic3C22×D512yes—
184C2×Dic3C22×D511yescharacteristic
185C2×Dic3C22×D511yescharacteristic
186D12—102no—
187C4×D3—202no—
188Dic6—42no—
189C22×C5C23×D311yescharacteristic
190C2×D5—21no—
191C2×D5—21no—
192C2×D5—21no—
193C2×D5—62no—
194C2×D5—62no—
195C2×D5—62no—
196C4×C5—22no—
197C4×C5—61no—
198C4×C5—62no—
199C4×C5—61no—
200C4×C5#23712yes—
201Dic5—22no—
202Dic5—21no—
203Dic5—61no—
204Dic5—61no—
205C2×Q8—32no—
206C2×Q8—51no—
207C2×D4—152no—
208C2×D4—151no—
209C22×C4—51no—
210C22×C4—152no—
211C4⋊C4—31no—
212C4⋊C4—32no—
213C4⋊C4—52no—
214C4⋊C4—151no—
215C4⋊C4—151no—
216C4⋊C4—152no—
217C4⋊C4D3×D511yescharacteristic
218C22⋊C4—52no—
219C22⋊C4—152no—
220C22⋊C4—152no—
221C22⋊C4—152no—
222C22⋊C4—151no—
223C22⋊C4—151no—
224C22⋊C4—152no—
225C42—31no—
226C42—152no—
227C42—151no—
228C3×C5#54211yescharacteristic, complemented, Hall
229C22×C3—101no—
230C22×C3—101no—
231C22×C3—101no—
232C22×C3C23×D511yescharacteristic
233C2×D3—102no—
234C2×D3—102no—
235C2×D3—102no—
236C3×C4—22no—
237C3×C4—101no—
238C3×C4—102no—
239C3×C4#71312yes—
240Dic3—21no—
241Dic3—22no—
242Dic3—21no—
243Dic3—101no—
244Dic3—101no—
245C2×C5C2×#23711yescharacteristic
246C2×C5#100711yescharacteristic
247C2×C5#100911yescharacteristic
248D5—41no—
249D5—122no—
250C23—51no—
251C23—152no—
252Q8—102no—
253Q8—122no—
254D4—302no—
255D4—602no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—32no—
259C2×C4—52no—
260C2×C4—51no—
261C2×C4—102no—
262C2×C4—151no—
263C2×C4—151no—
264C2×C4—602no—
265C2×C4C2×D3×D512yes—
266C2×C4C2×D3×D511yescharacteristic
267C2×C3—201no—
268C2×C3#414411yescharacteristic
269C2×C3C2×#71311yescharacteristic
270C2×C3#414711yescharacteristic
271D3—202no—
272C5#564311yescharacteristic, complemented, Sylow
273C22—101no—
274C22—101no—
275C22—101no—
276C22—302no—
277C22—302no—
278C22—302no—
279C22C22×D3×D511yescharacteristic
280C4—22no—
281C4—62no—
282C4—61no—
283C4—61no—
284C4—101no—
285C4—102no—
286C4—301no—
287C4—301no—
288C4#676612yes—
289C3#6606711yescharacteristic, complemented, Sylow
290C2—201no—
291C2—602no—
292C2C2×#676611yescharacteristic
293C2#9202711yescharacteristic
294C2#9202911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radical#91450C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#542
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×#888C2semidirect
3. C3×#4043C2semidirect
4. #91455C2semidirect
6. #91383C2semidirect
7. #91374C2semidirect
8. #91357C2semidirect
9. #91354C2semidirect
10. #91345C2semidirect
11. #91331C2semidirect
41. #4043D3semidirect
73. #888D5semidirect
228. C3×C5#542semidirect
272. C5#5643semidirect
289. C3#66067semidirect

Maximal subgroups

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

subgroupindex
#917822
C5×#8882
C3×#40432
#914552
#914502
#913832
#913742
#913572
#913542
#913452
#913312
#660673
#56435