Finite Group Databasebeta

← #11753819

Subgroups — #11753819

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#91777C211yesmaximal, characteristic, complemented
2C5×#897C211yesmaximal, characteristic, complemented
3C3×#4039C211yesmaximal, characteristic, complemented
4#91462C212yesmaximal, complemented
5#91456C211yesmaximal, characteristic
6#91447C212yesmaximal, complemented
7#91371C211yesmaximal, characteristic, complemented
8#91368C211yesmaximal, characteristic, complemented
9#91361C212yesmaximal, complemented
10#91360C212yesmaximal, complemented
11Dic5×Dic6C211yesmaximal, characteristic, complemented
12#65977—31nomaximal, Hall
13C2×Dic30C2212yes—
14C2×C4×C5×D3C2211yescharacteristic
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×D20C2211yescharacteristic
17C2×C3×C4×D5C2212yes—
18C2×#1201C2212yes—
19C3×C5×C4⋊C4C2211yescharacteristic
20C4⋊Dic15C2211yescharacteristic
21#6712C2212yes—
22C4×Dic15C2211yescharacteristic
23C5×(C2×D3)⋊C4C2212yes—
24C5×C4⋊Dic3C2212yes—
25C3×#685C2212yes—
26C3×C4×Dic5C2211yescharacteristic
27Dic3⋊Dic5C2212yes—
28Dic3⋊Dic5C2211yescharacteristic
29Dic3⋊Dic5C2211yescharacteristic
30(C2×D3)⋊Dic5C2211yescharacteristic
31(C2×D3)⋊Dic5C2211yescharacteristic
32#6665C2212yes—
33#6665C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5561—51nomaximal, Hall
37C5×C22⋊Q8—31no—
38#4093—31no—
39Q8×Dic5—31no—
40#4076—31no—
41#4072—31no—
42#4044—32no—
43#4043—32no—
44#4039D311yescharacteristic, complemented
45#4034—31no—
46#4031—32no—
47#4029—32no—
48C22×C5×D3C2311yescharacteristic
49C22×C3×D5C2312yes—
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2312yes—
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55Dic30—42no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C4×C5×D3—22no—
59C5×Dic6—22no—
60C2×C3×Dic5C2311yescharacteristic
61C2×C3×Dic5C2311yescharacteristic
62C3×D20—22no—
63C3×C4×D5—42no—
64#1201—42no—
65C3×C4×D4—51no—
66#938—51no—
67#936—51no—
68#929—52no—
69#924—52no—
70#897D511yescharacteristic, complemented
71#888—51no—
72#885—52no—
73#879—52no—
74#872—51no—
75C4×Dic6—51no—
76C2×C5×Q8—31no—
77C22×C4×C5—31no—
78C2×C22⋊D5—32no—
79C2×D20C2×D311yescharacteristic
80C2×C4×D5C2×D312yes—
81C2×Dic10—32no—
82C5×C4⋊C4—32no—
83C5×C4⋊C4C2×D311yescharacteristic
84C5×C22⋊C4—32no—
85C22⋊Dic5—31no—
86C22⋊Dic5—31no—
87#685—32no—
88#685—32no—
89#685—32no—
90#685C2×D312yes—
91C4⋊Dic5—31no—
92C4⋊Dic5—32no—
93C4⋊Dic5—31no—
94C4⋊Dic5—31no—
95#683—32no—
96C4×Dic5—31no—
97C4×Dic5—32no—
98C4×Dic5C2×D311yescharacteristic
99#542—151noSylow
100C22×C3×C5C2411yescharacteristic
101C2×C5×D3—21no—
102C2×C5×D3—21no—
103C2×C5×D3—21no—
104C2×C3×D5—22no—
105C2×C3×D5—22no—
106C2×C3×D5—22no—
107C3×C4×C5—22no—
108C3×C4×C5#4112yes—
109Dic15—22no—
110Dic15—21no—
111Dic15—21no—
112C3×Dic5—21no—
113C3×Dic5—21no—
114C5×Dic3—22no—
115C5×Dic3—21no—
116C2×C3×D4—51no—
117C22×C3×C4—52no—
118C2×#67—52no—
119C2×C4×D3C2×D511yescharacteristic
120C2×Dic6—52no—
121C2×Dic6C2×D511yescharacteristic
122C3×C4⋊C4C2×D511yescharacteristic
123C3×C22⋊C4—52no—
124C3×C42—51no—
125#217—52no—
126#217—52no—
127#217—52no—
128(C2×D3)⋊C4—51no—
129(C2×D3)⋊C4—51no—
130(C2×D3)⋊C4C2×D512yes—
131C4⋊Dic3—51no—
132C4⋊Dic3C2×D512yes—
133Dic3⋊C4—52no—
134Dic3⋊C4—52no—
135Dic3⋊C4—51no—
136Dic3⋊C4—51no—
137C4×Dic3—51no—
138C4×Dic3—52no—
139C23×C5—31no—
140C22×D5C22×D312yes—
141C5×Q8—62no—
142C2×C4×C5—32no—
143C2×C4×C5—31no—
144C2×C4×C5—62no—
145C2×C4×C5C22×D312yes—
146C2×C4×C5C22×D311yescharacteristic
147C22⋊D5—122no—
148C2×Dic5—31no—
149C2×Dic5—32no—
150C2×Dic5—31no—
151C2×Dic5C22×D311yescharacteristic
152C2×Dic5C22×D311yescharacteristic
153D20—22no—
154C4×D5—42no—
155Dic10—122no—
156C4⋊Q8—151no—
157#126—152no—
158#124—152no—
159#124—151no—
160#123—152no—
161C22⋊Q8—31no—
162C22⋊Q8—152no—
163#121—151no—
164C4×Q8—151no—
165C4×D4—51no—
166#117—151no—
167C2×C3×C5C2×#4111yescharacteristic
168C2×C3×C5H(5,𝔽2)11yescharacteristic
169C2×C3×C52−1+411yescharacteristic
170C3×D5—42no—
171C5×D3—41no—
172C23×C3—52no—
173C22×D3C22×D511yescharacteristic
174C3×D4—102no—
175C2×C3×C4—51no—
176C2×C3×C4—51no—
177C2×C3×C4—202no—
178C2×C3×C4C22×D512yes—
179C2×C3×C4C22×D511yescharacteristic
180#67—202no—
181C2×Dic3—51no—
182C2×Dic3—52no—
183C2×Dic3—51no—
184C2×Dic3C22×D512yes—
185C2×Dic3C22×D511yescharacteristic
186C4×D3—22no—
187Dic6—22no—
188Dic6—202no—
189C22×C5—61no—
190C22×C5—61no—
191C22×C5—61no—
192C22×C5C23×D311yescharacteristic
193C2×D5—22no—
194C2×D5—22no—
195C2×D5—22no—
196C4×C5—22no—
197C4×C5—61no—
198C4×C5—62no—
199C4×C5#23512yes—
200Dic5—21no—
201Dic5—21no—
202Dic5—61no—
203Dic5—62no—
204Dic5—61no—
205C2×Q8—31no—
206C2×Q8—152no—
207C2×D4—51no—
208C2×D4—152no—
209C22×C4—31no—
210C22×C4—52no—
211C4⋊C4—32no—
212C4⋊C4—151no—
213C4⋊C4—151no—
214C4⋊C4—152no—
215C4⋊C4—151no—
216C4⋊C4—152no—
217C4⋊C4D3×D511yescharacteristic
218C22⋊C4—32no—
219C22⋊C4—52no—
220C22⋊C4—152no—
221C22⋊C4—152no—
222C22⋊C4—152no—
223C22⋊C4—151no—
224C22⋊C4—151no—
225C42—51no—
226C42—152no—
227C42—151no—
228C3×C5#54211yescharacteristic, complemented, Hall
229C22×C3—102no—
230C22×C3—102no—
231C22×C3—102no—
232C22×C3C23×D511yescharacteristic
233C2×D3—21no—
234C2×D3—21no—
235C2×D3—21no—
236C3×C4—22no—
237C3×C4—101no—
238C3×C4—101no—
239C3×C4#71112yes—
240Dic3—22no—
241Dic3—21no—
242Dic3—101no—
243Dic3—101no—
244Dic3—102no—
245C2×C5—121no—
246C2×C5C2×#23511yescharacteristic
247C2×C5#100411yescharacteristic
248C2×C5#101011yescharacteristic
249D5—42no—
250C23—31no—
251C23—52no—
252Q8—62no—
253Q8—602no—
254D4—102no—
255D4—602no—
256C2×C4—32no—
257C2×C4—31no—
258C2×C4—51no—
259C2×C4—51no—
260C2×C4—62no—
261C2×C4—151no—
262C2×C4—151no—
263C2×C4—152no—
264C2×C4—202no—
265C2×C4C2×D3×D512yes—
266C2×C4C2×D3×D511yescharacteristic
267C2×C3—202no—
268C2×C3C2×#71111yescharacteristic
269C2×C3#414711yescharacteristic
270C2×C3#414911yescharacteristic
271D3—41no—
272C5#556111yescharacteristic, complemented, Sylow
273C22—61no—
274C22—61no—
275C22—61no—
276C22—102no—
277C22—102no—
278C22—102no—
279C22C22×D3×D511yescharacteristic
280C4—22no—
281C4—61no—
282C4—62no—
283C4—101no—
284C4—101no—
285C4—302no—
286C4—301no—
287C4—301no—
288C4#677212yes—
289C3#6597711yescharacteristic, complemented, Sylow
290C2—121no—
291C2—202no—
292C2C2×#677211yescharacteristic
293C2#9202611yescharacteristic
294C2#9202811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radical#91456C2
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. #91777C2semidirect
2. C5×#897C2semidirect
3. C3×#4039C2semidirect
4. #91462C2semidirect
6. #91447C2semidirect
7. #91371C2semidirect
8. #91368C2semidirect
9. #91361C2semidirect
10. #91360C2semidirect
11. Dic5×Dic6C2semidirect
44. #4039D3semidirect
70. #897D5semidirect
228. C3×C5#542semidirect
272. C5#5561semidirect
289. C3#65977semidirect

Maximal subgroups

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

subgroupindex
#917772
C5×#8972
C3×#40392
#914622
#914562
#914472
#913712
#913682
#913612
#913602
Dic5×Dic62
#659773
#55615