Finite Group Databasebeta

← #11748913

Subgroups — #11748913

Order 960.

516 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1202C211yesmaximal, characteristic
2C2×#6714C211yesmaximal, characteristic, complemented
3C2×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#685C211yesmaximal, characteristic, complemented
5C2×#6667C211yesmaximal, characteristic, complemented
6C2×#6665C211yesmaximal, characteristic, complemented
7C2×Dic3×Dic5C211yesmaximal, characteristic, complemented
8#65277—31nomaximal, Hall
9C23×D15C2211yescharacteristic
10C23×C3×D5C2211yescharacteristic
11C22×C3×C4×C5C2211yescharacteristic
12C22×Dic15C2211yescharacteristic
13C22×C5×Dic3C2211yescharacteristic
14C22×C5×Dic3C2211yescharacteristic
15C22×C3×Dic5C2211yescharacteristic
16C2×#1202—22no—
17C2×#1202—22no—
18C2×#1202C414yescomplemented
19#6714—22no—
20C5×Dic3⋊C4—22no—
21C3×#685—22no—
22#6667—22no—
23#6665—22no—
24Dic3×Dic5—22no—
25#4957—51nomaximal, Hall
26C22×D20—31no—
27C2×C5×C4⋊C4—31no—
28C2×#685—31no—
29C2×#685—31no—
30C2×#685—31no—
31C2×#685D311yescharacteristic, complemented
32C2×C4×Dic5—31no—
33C23×C3×C5C2311yescharacteristic
34C22×D15—21no—
35C22×D15—21no—
36C22×D15—21no—
37C22×D15—21no—
38C22×D15—21no—
39C22×D15—21no—
40C22×D15C2×C412yes—
41C22×C3×D5—21no—
42C22×C3×D5—21no—
43C22×C3×D5—21no—
44C22×C3×D5—21no—
45C22×C3×D5—21no—
46C22×C3×D5—21no—
47C22×C3×D5C2×C412yes—
48C2×C3×C4×C5—21no—
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—21no—
51C2×Dic15—21no—
52C2×Dic15—21no—
53C2×Dic15D412yescomplemented
54C2×C5×Dic3—21no—
55C2×C5×Dic3—21no—
56C2×C5×Dic3—21no—
57C2×C5×Dic3C2×C412yes—
58C2×C5×Dic3D412yes—
59C2×C5×Dic3D412yes—
60C2×C3×Dic5—21no—
61C2×C3×Dic5—21no—
62C2×C3×Dic5D412yescomplemented
63#1202—28no—
64C22×#67—51no—
65C2×C3×C22⋊C4—51no—
66C2×#217—51no—
67C2×(C2×D3)⋊C4—51no—
68C2×(C2×D3)⋊C4—51no—
69C2×Dic3⋊C4D511yescharacteristic, complemented
70C2×C4×Dic3—51no—
71C23×D5—31no—
72C23×D5C2×D311yescharacteristic
73C22×C4×C5—31no—
74C22×C4×C5—31no—
75C22×C4×C5C2×D311yescharacteristic
76C22×Dic5—31no—
77C22×Dic5C2×D311yescharacteristic
78C2×D20—34no—
79C2×D20—62no—
80C2×D20—62no—
81C5×C4⋊C4—62no—
82#685—22no—
83#685—62no—
84#685—62no—
85#685—62no—
86C4×Dic5—62no—
87#390—151noSylow
88C22×C3×C5C22×C411yescharacteristic
89C22×C3×C5C2×D411yescharacteristic
90C22×C3×C5C2×D411yescharacteristic
91C22×C3×C5C2×D411yescharacteristic
92C22×C3×C5C2×D411yescharacteristic
93C22×C3×C5#4111yescharacteristic
94C22×C3×C5#4111yescharacteristic
95C2×D15—22no—
96C2×D15—22no—
97C2×D15—22no—
98C2×D15—41no—
99C2×D15—41no—
100C2×D15—41no—
101C2×D15—41no—
102C2×C3×D5—22no—
103C2×C3×D5—22no—
104C2×C3×D5—22no—
105C2×C3×D5—41no—
106C2×C3×D5—41no—
107C2×C3×D5—41no—
108C2×C3×D5—41no—
109C3×C4×C5—41no—
110Dic15—22no—
111C3×Dic5—22no—
112C5×Dic3—41no—
113C5×Dic3C22⋊C414yescomplemented
114C24×C3—51no—
115C23×D3—51no—
116C22×C3×C4—51no—
117C22×C3×C4C2×D511yescharacteristic
118C2×#67—54no—
119C2×#67—102no—
120C2×#67—102no—
121C22×Dic3—51no—
122C22×Dic3C2×D511yescharacteristic
123C22×Dic3C2×D511yescharacteristic
124C3×C22⋊C4—102no—
125#217—102no—
126(C2×D3)⋊C4—102no—
127(C2×D3)⋊C4—102no—
128Dic3⋊C4—22no—
129C4×Dic3—102no—
130C23×C5C22×D311yescharacteristic
131C22×D5—21no—
132C22×D5—21no—
133C22×D5—21no—
134C22×D5—21no—
135C22×D5—21no—
136C22×D5—21no—
137C22×D5—32no—
138C22×D5—61no—
139C22×D5—61no—
140C22×D5—61no—
141C22×D5—61no—
142C22×D5—61no—
143C22×D5—61no—
144C22×D5C4×D312yes—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—32no—
149C2×C4×C5—32no—
150C2×C4×C5—32no—
151C2×C4×C5—61no—
152C2×C4×C5—61no—
153C2×C4×C5—61no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—32no—
157C2×Dic5—61no—
158C2×Dic5—61no—
159C2×Dic5#6712yescomplemented
160D20—68no—
161C22×D4—151no—
162C2×C4⋊C4—31no—
163C2×C22⋊C4—51no—
164C2×C22⋊C4—151no—
165C2×C22⋊C4—151no—
166C2×C22⋊C4—151no—
167C2×C42—151no—
168C2×C3×C5C2×C22⋊C411yescharacteristic
169C2×C3×C5C4×D411yescharacteristic
170C2×C3×C5C4×D411yescharacteristic
171C2×C3×C5#12111yescharacteristic
172C2×C3×C5#12111yescharacteristic
173C2×C3×C5#12411yescharacteristic
174C2×C3×C5#12711yescharacteristic
175D15—42no—
176C3×D5—42no—
177C23×C3—52no—
178C23×C3—101no—
179C23×C3—101no—
180C23×C3—101no—
181C23×C3—101no—
182C23×C3—101no—
183C23×C3—101no—
184C23×C3C22×D511yescharacteristic
185C22×D3—52no—
186C22×D3—101no—
187C22×D3—101no—
188C22×D3—101no—
189C22×D3—101no—
190C22×D3—101no—
191C22×D3—101no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—52no—
196C2×C3×C4—101no—
197C2×C3×C4—101no—
198#67—108no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—52no—
203C2×Dic3—101no—
204C2×Dic3—101no—
205C2×Dic3C4×D512yes—
206C2×Dic3D2012yes—
207C2×Dic3C22⋊D512yes—
208C22×C5C2×C4×D311yescharacteristic
209C22×C5#23511yescharacteristic
210C22×C5D3×D411yescharacteristic
211C22×C5D3×D411yescharacteristic
212C22×C5D3×D411yescharacteristic
213C22×C5#23711yescharacteristic
214C22×C5C2×#6711yescharacteristic
215C2×D5—22no—
216C2×D5—22no—
217C2×D5—22no—
218C2×D5—41no—
219C2×D5—41no—
220C2×D5—41no—
221C2×D5—41no—
222C2×D5—62no—
223C2×D5—62no—
224C2×D5—62no—
225C2×D5—121no—
226C2×D5—121no—
227C2×D5—121no—
228C2×D5—121no—
229C4×C5—34no—
230C4×C5—41no—
231C4×C5—121no—
232Dic5—22no—
233Dic5—62no—
234C24—51no—
235C24—151no—
236C2×D4—154no—
237C2×D4—302no—
238C2×D4—302no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—51no—
242C22×C4—151no—
243C22×C4D3×D511yescharacteristic
244C4⋊C4—62no—
245C22⋊C4—102no—
246C22⋊C4—302no—
247C22⋊C4—302no—
248C22⋊C4—302no—
249C42—302no—
250C3×C5#39011yescharacteristic, complemented, Hall
251C22×C3—102no—
252C22×C3—102no—
253C22×C3—102no—
254C22×C3—201no—
255C22×C3—201no—
256C22×C3—201no—
257C22×C3—201no—
258C22×C3C2×C4×D511yescharacteristic
259C22×C3C2×D2011yescharacteristic
260C22×C3D4×D511yescharacteristic
261C22×C3D4×D511yescharacteristic
262C22×C3#71311yescharacteristic
263C22×C3#71311yescharacteristic
264C22×C3C2×C22⋊D511yescharacteristic
265C2×D3—102no—
266C2×D3—102no—
267C2×D3—102no—
268C2×D3—201no—
269C2×D3—201no—
270C2×D3—201no—
271C2×D3—201no—
272C3×C4—41no—
273C3×C4—102no—
274Dic3—41no—
275Dic3—102no—
276Dic3#68514yescomplemented
277C2×C5D3×C22⋊C411yescharacteristic
278C2×C5#67⋊C411yescharacteristic
279C2×C5#88411yescharacteristic
280C2×C5#88511yescharacteristic
281C2×C5C4×#6711yescharacteristic
282C2×C5#93911yescharacteristic
283C2×C5#94011yescharacteristic
284D5—42no—
285D5—122no—
286C23—52no—
287C23—101no—
288C23—101no—
289C23—101no—
290C23—101no—
291C23—101no—
292C23—101no—
293C23—152no—
294C23—301no—
295C23—301no—
296C23—301no—
297C23—301no—
298C23—301no—
299C23—301no—
300C23C2×D3×D511yescharacteristic
301D4—308no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—32no—
308C2×C4—52no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—152no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C3—202no—
318C2×C3#403911yescharacteristic
319C2×C3#403911yescharacteristic
320C2×C3#404111yescharacteristic
321C2×C3#404111yescharacteristic
322C2×C3C2×#68511yescharacteristic
323C2×C3#408611yescharacteristic
324C2×C3#409311yescharacteristic
325D3—202no—
326C5#495711yescharacteristic, complemented, Sylow
327C22—102no—
328C22—102no—
329C22—102no—
330C22—201no—
331C22—201no—
332C22—201no—
333C22—201no—
334C22—302no—
335C22—302no—
336C22—302no—
337C22—601no—
338C22—601no—
339C22—601no—
340C22—601no—
341C22#676611yescharacteristic
342C22#677311yescharacteristic
343C22C4×D3×D511yescharacteristic
344C22D3×D2011yescharacteristic
345C22D5×#6711yescharacteristic
346C22D3×C22⋊D511yescharacteristic
347C22#679011yescharacteristic
348C4—34no—
349C4—41no—
350C4—102no—
351C4—121no—
352C4—302no—
353C3#6527711yescharacteristic, complemented, Sylow
354C2—202no—
355C2—602no—
356C2#9139611yescharacteristic
357C2#9140911yescharacteristic
358C2#9144411yescharacteristic
359C2#9145511yescharacteristic
360C2#9145911yescharacteristic
361C2D3×#68511yescharacteristic
362C2#9156711yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×D5
commutatorC22×C3×C5C22×C4
FittingC22×C3×C4×C5C22
socle, cosocleC23×C3×C5C23
prime radicalC22×#1202C2
hypercenterC22×C4D3×D5
hypocenterC3×C5#390
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#6714C2semidirect
3. C2×C5×Dic3⋊C4C2semidirect
4. C2×C3×#685C2semidirect
5. C2×#6667C2semidirect
6. C2×#6665C2semidirect
7. C2×Dic3×Dic5C2semidirect
18. C2×#1202C4semidirect
31. C2×#685D3semidirect
53. C2×Dic15D4semidirect
62. C2×C3×Dic5D4semidirect
69. C2×Dic3⋊C4D5semidirect
113. C5×Dic3C22⋊C4semidirect
159. C2×Dic5#67semidirect
250. C3×C5#390semidirect
276. Dic3#685semidirect
326. C5#4957semidirect
353. C3#65277semidirect

Maximal subgroups

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

subgroupindex
C22×#12022
C2×#67142
C2×C5×Dic3⋊C42
C2×C3×#6852
C2×#66672
C2×#66652
C2×Dic3×Dic52
#652773
#49575