Finite Group Databasebeta

← C5×#4961 #11750460

Subgroups — C5×#4961 #11750460

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#67C211yesmaximal, characteristic
2C2×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C5×#217C211yesmaximal, characteristic, complemented
4C2×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C5×C3⋊#95C211yesmaximal, characteristic, complemented
8C5×#394—31nomaximal, Hall
9C24×C3×C5C2211yescharacteristic
10C23×C5×D3C2211yescharacteristic
11C22×C3×C4×C5C2211yescharacteristic
12C22×C3×C4×C5C2211yescharacteristic
13C2×C5×#67—22no—
14C2×C5×#67—22no—
15C2×C5×#67—22no—
16C22×C5×Dic3C2211yescharacteristic
17C22×C5×Dic3C2211yescharacteristic
18C22×C5×Dic3C2211yescharacteristic
19C3×C5×C22⋊C4—22no—
20C5×#217—22no—
21C5×(C2×D3)⋊C4—22no—
22C5×(C2×D3)⋊C4—22no—
23C5×C4⋊Dic3—22no—
24#4961C511yesmaximal, characteristic, direct product factor, Hall
25C22×C5×D4—31no—
26C2×C5×C4⋊C4—31no—
27C2×C5×C22⋊C4—31no—
28C2×C5×C22⋊C4—31no—
29C2×C5×C22⋊C4—31no—
30C2×C5×C22⋊C4D311yescharacteristic, complemented
31C5×#95—31no—
32C23×C3×C5—21no—
33C23×C3×C5—21no—
34C23×C3×C5—21no—
35C23×C3×C5—21no—
36C23×C3×C5—21no—
37C23×C3×C5—21no—
38C23×C3×C5D412yes—
39C23×C3×C5C2311yescharacteristic
40C22×C5×D3—21no—
41C22×C5×D3—21no—
42C22×C5×D3—21no—
43C22×C5×D3—21no—
44C22×C5×D3—21no—
45C22×C5×D3—21no—
46C22×C5×D3D412yes—
47C2×C3×C4×C5—21no—
48C2×C3×C4×C5—21no—
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5D412yescomplemented
53C5×#67—28no—
54C2×C5×Dic3—21no—
55C2×C5×Dic3—21no—
56C2×C5×Dic3—21no—
57C2×C5×Dic3—21no—
58C2×C5×Dic3—21no—
59C2×C5×Dic3—21no—
60C2×C5×Dic3—21no—
61C2×C5×Dic3—21no—
62C2×C5×Dic3D412yes—
63C22×#67C2×C511yescharacteristic
64C2×C3×C22⋊C4C2×C511yescharacteristic, complemented
65C2×#217C2×C511yescharacteristic, complemented
66C2×(C2×D3)⋊C4C2×C511yescharacteristic, complemented
67C2×(C2×D3)⋊C4C2×C511yescharacteristic, complemented
68C2×C4⋊Dic3C2×C511yescharacteristic, complemented
69C3⋊#95C2×C511yescharacteristic, complemented
70C24×C5—31no—
71C24×C5C2×D311yescharacteristic
72C2×C5×D4—62no—
73C2×C5×D4—62no—
74C2×C5×D4—62no—
75C22×C4×C5—31no—
76C22×C4×C5—31no—
77C22×C4×C5—31no—
78C22×C4×C5C2×D311yescharacteristic
79C22×C4×C5C2×D311yescharacteristic
80C5×C4⋊C4—62no—
81C5×C22⋊C4—22no—
82C5×C22⋊C4—62no—
83C5×C22⋊C4—62no—
84C5×C22⋊C4—62no—
85#394—31noSylow
86C22×C3×C5—22no—
87C22×C3×C5—22no—
88C22×C3×C5—22no—
89C22×C3×C5—41no—
90C22×C3×C5—41no—
91C22×C3×C5—41no—
92C22×C3×C5—41no—
93C22×C3×C5C2×D411yescharacteristic
94C22×C3×C5C2×D411yescharacteristic
95C22×C3×C5C2×D411yescharacteristic
96C22×C3×C5C2×D411yescharacteristic
97C22×C3×C5#4111yescharacteristic
98C22×C3×C5#4111yescharacteristic
99C22×C3×C5#4111yescharacteristic
100C2×C5×D3—22no—
101C2×C5×D3—22no—
102C2×C5×D3—22no—
103C2×C5×D3—41no—
104C2×C5×D3—41no—
105C2×C5×D3—41no—
106C2×C5×D3—41no—
107C3×C4×C5—22no—
108C3×C4×C5—41no—
109C5×Dic3—22no—
110C5×Dic3—41no—
111C5×Dic3—41no—
112C24×C3C22×C511yescharacteristic
113C23×D3C22×C511yescharacteristic
114C22×C3×C4C22×C511yescharacteristic
115C22×C3×C4C22×C511yescharacteristic
116C2×#67—22no—
117C2×#67—22no—
118C2×#67—22no—
119C22×Dic3C22×C511yescharacteristic
120C22×Dic3C22×C511yescharacteristic
121C22×Dic3C22×C511yescharacteristic
122C3×C22⋊C4—22no—
123#217—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—22no—
126C4⋊Dic3—22no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—32no—
134C23×C5—61no—
135C23×C5—61no—
136C23×C5—61no—
137C23×C5—61no—
138C23×C5—61no—
139C23×C5—61no—
140C23×C5D1212yes—
141C23×C5C22×D311yescharacteristic
142C5×D4—68no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—32no—
149C2×C4×C5—61no—
150C2×C4×C5—61no—
151C2×C4×C5—61no—
152C2×C4×C5—61no—
153C2×C4×C5—61no—
154C2×C4×C5—61no—
155C2×C4×C5—61no—
156C2×C4×C5—61no—
157C2×C4×C5#6712yescomplemented
158C22×D4—31no—
159C2×C4⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4C5×D311yescharacteristic, complemented
164#95—31no—
165C2×C3×C5—42no—
166C2×C3×C5#12011yescharacteristic
167C2×C3×C5#12111yescharacteristic
168C2×C3×C5#12111yescharacteristic
169C2×C3×C5#12111yescharacteristic
170C2×C3×C5#12311yescharacteristic
171C2×C3×C5#12311yescharacteristic
172C2×C3×C5#12411yescharacteristic
173C5×D3—42no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3C5×D412yes—
181C23×C3C23×C511yescharacteristic
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—21no—
188C22×D3C5×D412yes—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4C5×D412yescomplemented
195#67—28no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3C5×D412yes—
205C22×C5—22no—
206C22×C5—22no—
207C22×C5—22no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—62no—
213C22×C5—62no—
214C22×C5—62no—
215C22×C5—121no—
216C22×C5—121no—
217C22×C5—121no—
218C22×C5—121no—
219C22×C5C2×D1211yescharacteristic
220C22×C5#23511yescharacteristic
221C22×C5D3×D411yescharacteristic
222C22×C5D3×D411yescharacteristic
223C22×C5#23711yescharacteristic
224C22×C5#23711yescharacteristic
225C22×C5C2×#6711yescharacteristic
226C4×C5—22no—
227C4×C5—41no—
228C4×C5—62no—
229C4×C5—121no—
230C4×C5—121no—
231C24—31no—
232C24C2×C5×D311yescharacteristic
233C2×D4—62no—
234C2×D4—62no—
235C2×D4—62no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4C2×C5×D311yescharacteristic
240C22×C4C2×C5×D311yescharacteristic
241C4⋊C4—62no—
242C22⋊C4—22no—
243C22⋊C4—62no—
244C22⋊C4—62no—
245C22⋊C4—62no—
246C3×C5#39411yescharacteristic, complemented, Hall
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3C2×C5×D411yescharacteristic
255C22×C3C2×C5×D411yescharacteristic
256C22×C3C2×C5×D411yescharacteristic
257C22×C3C2×C5×D411yescharacteristic
258C22×C3C5×#4111yescharacteristic
259C22×C3C5×#4111yescharacteristic
260C22×C3C5×#4111yescharacteristic
261C2×D3—22no—
262C2×D3—22no—
263C2×D3—22no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C3×C4—22no—
269C3×C4—41no—
270Dic3—22no—
271Dic3—41no—
272Dic3—41no—
273C2×C5—42no—
274C2×C5—122no—
275C2×C5#88211yescharacteristic
276C2×C5#88311yescharacteristic
277C2×C5#88511yescharacteristic
278C2×C5#88611yescharacteristic
279C2×C5#93011yescharacteristic
280C2×C5#93811yescharacteristic
281C2×C5#93911yescharacteristic
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—32no—
289C23—61no—
290C23—61no—
291C23—61no—
292C23—61no—
293C23—61no—
294C23—61no—
295C23C5×D1212yes—
296C23C22×C5×D311yescharacteristic
297D4—68no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—32no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4C5×#6712yescomplemented
313C2×C3—42no—
314C2×C3C5×#12011yescharacteristic
315C2×C3C5×#12111yescharacteristic
316C2×C3C5×#12111yescharacteristic
317C2×C3C5×#12111yescharacteristic
318C2×C3C5×#12311yescharacteristic
319C2×C3C5×#12311yescharacteristic
320C2×C3C5×#12411yescharacteristic
321D3—42no—
322C5#496111yescharacteristic, direct product factor, Sylow
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—62no—
331C22—62no—
332C22—62no—
333C22—121no—
334C22—121no—
335C22—121no—
336C22—121no—
337C22C2×C5×D1211yescharacteristic
338C22C5×#23511yescharacteristic
339C22C5×D3×D411yescharacteristic
340C22C5×D3×D411yescharacteristic
341C22C5×#23711yescharacteristic
342C22C5×#23711yescharacteristic
343C22C2×C5×#6711yescharacteristic
344C4—22no—
345C4—41no—
346C4—62no—
347C4—121no—
348C4—121no—
349C3C5×#39411yescharacteristic, complemented, Sylow
350C2—42no—
351C2—122no—
352C2C5×#88211yescharacteristic
353C2C5×#88311yescharacteristic
354C2C5×#88511yescharacteristic
355C2C5×#88611yescharacteristic
356C2C5×#93011yescharacteristic
357C2C5×#93811yescharacteristic
358C2C5×#93911yescharacteristic
subgroupG/H
centerC23×C5C22×D3
commutator, cosocleC23×C3C23×C5
FrattiniC23C22×C5×D3
FittingC2×C3×C5×C22⋊C4C2
socleC23×C3×C5C23
prime radicalC22×C5×#67C2
hypercenterC2×C5×C22⋊C4D3
hypocenterC3C5×#394
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×C22⋊C4C2semidirect
3. C2×C5×#217C2semidirect
4. C2×C5×(C2×D3)⋊C4C2semidirect
5. C2×C5×(C2×D3)⋊C4C2semidirect
6. C2×C5×C4⋊Dic3C2semidirect
7. C5×C3⋊#95C2semidirect
24. #4961C5direct (N × H)
30. C2×C5×C22⋊C4D3semidirect
52. C2×C3×C4×C5D4semidirect
64. C2×C3×C22⋊C4C2×C5semidirect
65. C2×#217C2×C5semidirect
66. C2×(C2×D3)⋊C4C2×C5semidirect
67. C2×(C2×D3)⋊C4C2×C5semidirect
68. C2×C4⋊Dic3C2×C5semidirect
69. C3⋊#95C2×C5semidirect
157. C2×C4×C5#67semidirect
163. C2×C22⋊C4C5×D3semidirect
194. C2×C3×C4C5×D4semidirect
246. C3×C5#394semidirect
312. C2×C4C5×#67semidirect
322. C5#4961direct (N × H)
349. C3C5×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#672
C2×C3×C5×C22⋊C42
C2×C5×#2172
C2×C5×(C2×D3)⋊C42
C2×C5×C4⋊Dic32
C5×C3⋊#952
C5×#3943
#49615