Finite Group Databasebeta

← #11750922

Subgroups — #11750922

Order 960.

308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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#41×D15C211yesmaximal, characteristic
2M16×D15C211yesmaximal, characteristic, complemented
3#91761C211yesmaximal, characteristic, complemented
4C3×C5×#104C211yesmaximal, characteristic, complemented
5#91121C211yesmaximal, characteristic, complemented
6#91109C211yesmaximal, characteristic, complemented
7#91089C211yesmaximal, characteristic, complemented
8#65110—31nomaximal, Hall
9C3×C5×#41C2211yescharacteristic
10#6821C411yescharacteristic, complemented
11Q8×D15C411yescharacteristic, complemented
12#6819—21no—
13#6819C411yescharacteristic, complemented
14D4×D15—21no—
15D4×D15C411yescharacteristic, complemented
16#6817—21no—
17#6817C2211yescharacteristic
18C2×C4×D15—21no—
19C2×C4×D15C2211yescharacteristic
20C3×C5×M16C2211yescharacteristic, complemented
21C3×C42×C5C2211yescharacteristic, complemented
22#6714—21no—
23#6712—21no—
24C4×Dic15C2211yescharacteristic, complemented
25#6710C2211yescharacteristic, complemented
26#6705—21no—
27C8×D15—21no—
28#4821—51nomaximal, Hall
29D5×#41—31no—
30D5×M16—31no—
31#4018—31no—
32C5×#104D311yescharacteristic, complemented
33#3969—31no—
34#3957—31no—
35#3937—31no—
36C22×D15—21no—
37C22×D15D411yescharacteristic
38C3×C5×Q8C2×C411yescharacteristic
39C3×C5×D4—21no—
40C3×C5×D4C2×C411yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C2311yescharacteristic
44#1220—21no—
45#1220—21no—
46#1220—21no—
47C2×Dic15—21no—
48C2×Dic15—21no—
49C2×Dic15D411yescharacteristic
50D60—21no—
51D60C2×C411yescharacteristic
52C4×D15—21no—
53C4×D15—21no—
54C4×D15—21no—
55C4×D15C2×C411yescharacteristic
56C4×D15C2×C411yescharacteristic
57C4×D15D411yescharacteristic
58C4×D15D411yescharacteristic
59Dic30—21no—
60Dic30C2×C411yescharacteristic
61C3×C5×C8—21no—
62C3⋊#168—21no—
63D3×#41—51no—
64D3×M16—51no—
65#872—51no—
66C3×#104D511yescharacteristic, complemented
67#837—51no—
68#825—51no—
69#805—51no—
70C5×#41C2×D311yescharacteristic
71#713—31no—
72Q8×D5—31no—
73#711—31no—
74#711—61no—
75D4×D5—31no—
76D4×D5—61no—
77#709—31no—
78#709—61no—
79C2×C4×D5—31no—
80C2×C4×D5—61no—
81C5×M16C2×D311yescharacteristic, complemented
82C42×C5C2×D311yescharacteristic, complemented
83#685—61no—
84#683—61no—
85C4×Dic5—31no—
86#681—31no—
87#676—61no—
88C8×D5—61no—
89#421—151noSylow
90C22×C3×C5—21no—
91C22×C3×C5C2×D411yescharacteristic
92C2×D15—21no—
93C2×D15—41no—
94C2×D15—42no—
95C2×D15C22⋊C411yescharacteristic
96C2×D15C22⋊C411yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—41no—
99C3×C4×C5C22×C411yescharacteristic
100C3×C4×C5C2×D411yescharacteristic
101Dic15—21no—
102Dic15—41no—
103Dic15C22⋊C411yescharacteristic
104Dic15C22⋊C411yescharacteristic
105C3×#41C2×D511yescharacteristic
106#239—51no—
107D3×Q8—51no—
108#237—51no—
109#237—101no—
110D3×D4—51no—
111D3×D4—101no—
112#235—51no—
113#235—101no—
114C2×C4×D3—51no—
115C2×C4×D3—101no—
116C3×M16C2×D511yescharacteristic, complemented
117C3×C42C2×D511yescharacteristic, complemented
118(C2×D3)⋊C4—101no—
119Dic3⋊C4—101no—
120C4×Dic3—51no—
121#208—51no—
122ΓL(1,𝔽25)—101no—
123D3×C8—101no—
124C22×D5—31no—
125C22×D5—61no—
126C5×Q8C4×D311yescharacteristic
127C5×D4—21no—
128C5×D4C4×D311yescharacteristic
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5C22×D311yescharacteristic
132C22⋊D5—61no—
133C22⋊D5—61no—
134C22⋊D5—61no—
135C2×Dic5—31no—
136C2×Dic5—61no—
137C2×Dic5—61no—
138D20—31no—
139D20—61no—
140C4×D5—31no—
141C4×D5—31no—
142C4×D5—31no—
143C4×D5—31no—
144C4×D5—61no—
145C4×D5—61no—
146C4×D5—61no—
147Dic10—31no—
148Dic10—61no—
149C5×C8—21no—
150#168—61no—
151C2×#41—151no—
152C2×M16—151no—
153#117—151no—
154#104—151no—
155#104—151no—
156#104—151no—
157#104D1511yescharacteristic, complemented
158C2×C3×C5—21no—
159C2×C3×C5—41no—
160C2×C3×C5C2×C22⋊C411yescharacteristic
161D15—21no—
162D15—21no—
163D15—41no—
164C22×D3—51no—
165C22×D3—101no—
166C3×Q8C4×D511yescharacteristic
167C3×D4—21no—
168C3×D4C4×D511yescharacteristic
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4C22×D511yescharacteristic
172#67—101no—
173#67—101no—
174#67—101no—
175C2×Dic3—51no—
176C2×Dic3—101no—
177C2×Dic3—101no—
178D12—51no—
179D12—101no—
180C4×D3—51no—
181C4×D3—51no—
182C4×D3—51no—
183C4×D3—51no—
184C4×D3—101no—
185C4×D3—101no—
186C4×D3—101no—
187Dic6—51no—
188Dic6—101no—
189C3×C8—21no—
190C3⋊C8—101no—
191C22×C5—21no—
192C22×C5D3×D411yescharacteristic
193C2×D5—31no—
194C2×D5—31no—
195C2×D5—61no—
196C2×D5—121no—
197C2×D5—122no—
198C4×C5—21no—
199C4×C5—41no—
200C4×C5C2×C4×D311yescharacteristic
201C4×C5D3×D411yescharacteristic
202Dic5—31no—
203Dic5—31no—
204Dic5—61no—
205Dic5—121no—
206#41—151no—
207#41—151no—
208#41—151no—
209#41—301no—
210#41—301no—
211#41C2×D1511yescharacteristic
212C2×Q8—151no—
213C2×D4—151no—
214C2×D4—301no—
215C22×C4—151no—
216C22×C4—301no—
217M16—151no—
218M16—301no—
219M16C2×D1511yescharacteristic, complemented
220C2×C8—301no—
221C4⋊C4—301no—
222C22⋊C4—301no—
223C42—151no—
224C42C2×D1511yescharacteristic, complemented
225C3×C5#42111yescharacteristic, complemented, Hall
226C22×C3—21no—
227C22×C3D4×D511yescharacteristic
228C2×D3—51no—
229C2×D3—51no—
230C2×D3—101no—
231C2×D3—201no—
232C2×D3—202no—
233C3×C4—21no—
234C3×C4—41no—
235C3×C4C2×C4×D511yescharacteristic
236C3×C4D4×D511yescharacteristic
237Dic3—51no—
238Dic3—51no—
239Dic3—101no—
240Dic3—201no—
241C2×C5—21no—
242C2×C5—41no—
243C2×C5D3×C22⋊C411yescharacteristic
244D5—61no—
245D5—61no—
246D5—121no—
247C23—151no—
248C23—301no—
249Q8—151no—
250Q8—301no—
251Q8C4×D1511yescharacteristic
252D4—21no—
253D4—151no—
254D4—301no—
255D4—301no—
256D4—301no—
257D4—301no—
258D4C4×D1511yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—151no—
262C2×C4—151no—
263C2×C4—151no—
264C2×C4—151no—
265C2×C4—151no—
266C2×C4—301no—
267C2×C4—301no—
268C2×C4—301no—
269C2×C4—301no—
270C2×C4—301no—
271C2×C4C22×D1511yescharacteristic
272C8—21no—
273C8—301no—
274C2×C3—21no—
275C2×C3—41no—
276C2×C3D5×C22⋊C411yescharacteristic
277D3—101no—
278D3—101no—
279D3—201no—
280C5#482111yescharacteristic, complemented, Sylow
281C22—21no—
282C22—151no—
283C22—151no—
284C22—301no—
285C22—601no—
286C22—602no—
287C22D4×D1511yescharacteristic
288C4—21no—
289C4—41no—
290C4—151no—
291C4—151no—
292C4—301no—
293C4—601no—
294C4C2×C4×D1511yescharacteristic
295C4D4×D1511yescharacteristic
296C3#6511011yescharacteristic, complemented, Sylow
297C2—21no—
298C2—41no—
299C2—301no—
300C2—301no—
301C2—601no—
302C2C22⋊C4×D1511yescharacteristic
subgroupG/H
centerC4D4×D15
commutatorC3×C4×C5C22×C4
FrattiniC2×C4C22×D15
FittingC3×C5×#104C2
socleC2×C3×C5C2×C22⋊C4
prime radical#41×D15C2
cosocleC2×C3×C4×C5C23
hypercenter#104D15
hypocenterC3×C5#421
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D15C2semidirect
3. #91761C2semidirect
4. C3×C5×#104C2semidirect
5. #91121C2semidirect
6. #91109C2semidirect
7. #91089C2semidirect
10. #6821C4semidirect
11. Q8×D15C4semidirect
13. #6819C4semidirect
15. D4×D15C4semidirect
20. C3×C5×M16C22semidirect
21. C3×C42×C5C22semidirect
24. C4×Dic15C22semidirect
25. #6710C22semidirect
32. C5×#104D3semidirect
66. C3×#104D5semidirect
81. C5×M16C2×D3semidirect
82. C42×C5C2×D3semidirect
116. C3×M16C2×D5semidirect
117. C3×C42C2×D5semidirect
157. #104D15semidirect
219. M16C2×D15semidirect
224. C42C2×D15semidirect
225. C3×C5#421semidirect
280. C5#4821semidirect
296. C3#65110semidirect

Maximal subgroups

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

subgroupindex
#41×D152
M16×D152
#917612
C3×C5×#1042
#911212
#911092
#910892
#651103
#48215