Finite Group Databasebeta

← D5×#92259 #72247402

Subgroups — D5×#92259 #72247402

Order 4860.

492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 79 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#72247400C211yesmaximal, characteristic, complemented
2C5×#92259C211yesmaximal, characteristic, complemented
3D5×#6891C211yesmaximal, characteristic, complemented
4C32×D5×C3⋊D3C311yesmaximal, characteristic
5D3×D5×3−1+2—31nomaximal
6D5×(C3⋊D3)⋊C9C311yesmaximal, characteristic, complemented
7D5×(C3⋊D3)⋊C9C312yesmaximal, complemented
8C5×#6891C2211yescharacteristic, complemented, Hall
9C2×#92259—51nomaximal, Hall
10C32×C3⋊D15C2×C311yescharacteristic
11C32×C5×C3⋊D3C2×C311yescharacteristic
12C34×D5C2×C311yescharacteristic
133−1+2×D15—31no—
14C5×D3×3−1+2—31no—
15C3×D5×3−1+2—21no—
16C3×D5×3−1+2D311yescharacteristic, complemented
17C5⋊((C3⋊D3)⋊C9)C2×C311yescharacteristic, complemented
18C5⋊((C3⋊D3)⋊C9)C2×C312yescomplemented
19C5×(C3⋊D3)⋊C9C2×C311yescharacteristic, complemented
20C5×(C3⋊D3)⋊C9C2×C312yescomplemented
21D5×C32⋊C9—21no—
22D5×C32⋊C9—22no—
23D5×C32⋊C9C2×C311yescharacteristic, complemented
24D5×C32⋊C9C2×C312yescomplemented
25C3×D5×C3⋊D3—31no—
26C3×D5×C3⋊D3C3211yescharacteristic
27C32×D3×D5—31no—
28C32×D3×D5—91no—
29C2×D5×3−1+2—91no—
30D3×C9×D5—31no—
31D3×C9×D5—32no—
32C2×#6891—51no—
33#92259—51no—
34#92259D511yescharacteristic, direct product factor
35C34×C5C22×C311yescharacteristic
36C3×C5×3−1+2—21no—
37C3×C5×3−1+2C2×D311yescharacteristic, complemented
38C5×C32⋊C9—21no—
39C5×C32⋊C9—22no—
40C5×C32⋊C9C22×C311yescharacteristic, complemented
41C5×C32⋊C9C22×C312yescomplemented
42C2×C32×C3⋊D3—51no—
43C2×D3×3−1+2—151no—
44C2×(C3⋊D3)⋊C9—52no—
45C2×(C3⋊D3)⋊C9—51no—
46C3×C3⋊D15—31no—
47C3×C3⋊D15C2×C3211yescharacteristic
48C3×C5×C3⋊D3—31no—
49C3×C5×C3⋊D3C2×C3211yescharacteristic
50C32×D15—31no—
51C32×D15—91no—
52C32×C5×D3—31no—
53C32×C5×D3—91no—
54C33×D5—21no—
55C33×D5—31no—
56C33×D5—31no—
57C33×D5—63no—
58C33×D5—61no—
59C33×D5—61no—
60C33×D5C3×D311yescharacteristic
61C33×D5C2×C3211yescharacteristic
62C2×C5×3−1+2—91no—
63C9×D15—31no—
64C9×D15—32no—
65C5×D3×C9—31no—
66C5×D3×C9—32no—
67D5×3−1+2—31no—
68D5×3−1+2—61no—
69D5×3−1+2—62no—
70D5×3−1+2—61no—
71D5×3−1+2—91no—
72C3×C9×D5—22no—
73C3×C9×D5—21no—
74C3×C9×D5C3×D311yescharacteristic, complemented
75C3×C9×D5C3×D312yescomplemented
76#6891C2×D511yescharacteristic, complemented, Sylow
77C2×C32×D5—91no—
78D5×C3⋊D33−1+211yescharacteristic, complemented
79C3×D3×D5—31no—
80C3×D3×D5—91no—
81C3×D3×D5—91no—
82C3×D3×D5—93no—
83C2×C9×D5—91no—
84C2×C9×D5—92no—
85C2×C34—51no—
86C32×C3⋊D3—51no—
87C32×C3⋊D3C3×D511yescharacteristic
88C2×C3×3−1+2—51no—
89C2×C3×3−1+2—101no—
90D3×3−1+2—31no—
91D3×3−1+2—151no—
92C2×C32⋊C9—52no—
93C2×C32⋊C9—51no—
94C2×C32⋊C9—102no—
95C2×C32⋊C9—101no—
96(C3⋊D3)⋊C9—52no—
97(C3⋊D3)⋊C9—51no—
98(C3⋊D3)⋊C9C3×D512yescomplemented
99(C3⋊D3)⋊C9C3×D511yescharacteristic, complemented
100C33×C5—21no—
101C33×C5—31no—
102C33×C5—31no—
103C33×C5—63no—
104C33×C5—61no—
105C33×C5—61no—
106C33×C5C2×C3×D311yescharacteristic
107C33×C5C22×C3211yescharacteristic
108C5×3−1+2—31no—
109C5×3−1+2—61no—
110C5×3−1+2—62no—
111C5×3−1+2—61no—
112C3×C5×C9—22no—
113C3×C5×C9—21no—
114C3×C5×C9C2×C3×D311yescharacteristic, complemented
115C3×C5×C9C2×C3×D312yescomplemented
116C2×C3×C3⋊D3—51no—
117C2×C3×C3⋊D3—151no—
118C2×C32×D3—151no—
119C2×C32×D3—451no—
120C22×3−1+2—451no—
121C2×D3×C9—152no—
122C2×D3×C9—151no—
123C2×C32×C5—91no—
124C3⋊D15C2×3−1+211yescharacteristic, complemented
125C5×C3⋊D3C2×3−1+211yescharacteristic, complemented
126C3×D15—31no—
127C3×D15—91no—
128C3×D15—91no—
129C3×D15—93no—
130C3×C5×D3—31no—
131C3×C5×D3—91no—
132C3×C5×D3—91no—
133C3×C5×D3—93no—
134C32×D5—23no—
135C32×D5—21no—
136C32×D5—21no—
137C32×D5—33no—
138C32×D5—31no—
139C32×D5—31no—
140C32×D5—61no—
141C32×D5—61no—
142C32×D5—61no—
143C32×D5—63no—
144C32×D5—63no—
145C32×D5—63no—
146C32×D5—61no—
147C32×D5—61no—
148C32×D5—63no—
149C32×D5—91no—
150C32×D5(C3⋊D3)⋊C311yescharacteristic
151C32×D5C2×3−1+211yescharacteristic, complemented
152C32×D5C32×D311yescharacteristic
153C2×C5×C9—91no—
154C2×C5×C9—92no—
155C9×D5—31no—
156C9×D5—62no—
157C9×D5—62no—
158C9×D5—61no—
159C9×D5—91no—
160C9×D5—92no—
161C34C2×C3×D511yescharacteristic
162C3×3−1+2—21no—
163C3×3−1+2D3×D511yescharacteristic, complemented
164C32⋊C9—22no—
165C32⋊C9—21no—
166C32⋊C9C2×C3×D512yescomplemented
167C32⋊C9C2×C3×D511yescharacteristic, complemented
168C2×C3×D5—91no—
169C2×C3×D5—271no—
170D3×D5—31no—
171D3×D5—91no—
172C2×C33—51no—
173C2×C33—51no—
174C2×C33—101no—
175C2×C33—151no—
176C2×C33—151no—
177C2×C33—301no—
178C2×C33—301no—
179C2×C33—303no—
180C3×C3⋊D3—31no—
181C3×C3⋊D3—51no—
182C3×C3⋊D3—151no—
183C3×C3⋊D3C32×D511yescharacteristic
184C32×D3—31no—
185C32×D3—91no—
186C32×D3—151no—
187C32×D3—451no—
188C2×3−1+2—91no—
189C2×3−1+2—301no—
190C2×3−1+2—301no—
191C2×3−1+2—301no—
192C2×3−1+2—302no—
193C2×3−1+2—451no—
194C2×C3×C9—52no—
195C2×C3×C9—51no—
196C2×C3×C9—102no—
197C2×C3×C9—101no—
198D3×C9—32no—
199D3×C9—31no—
200D3×C9—152no—
201D3×C9—151no—
202C32×C5—23no—
203C32×C5—21no—
204C32×C5—21no—
205C32×C5—33no—
206C32×C5—31no—
207C32×C5—31no—
208C32×C5—61no—
209C32×C5—61no—
210C32×C5—61no—
211C32×C5—63no—
212C32×C5—63no—
213C32×C5—63no—
214C32×C5—63no—
215C32×C5—61no—
216C32×C5—61no—
217C32×C5C2×(C3⋊D3)⋊C311yescharacteristic
218C32×C5C22×3−1+211yescharacteristic, complemented
219C32×C5C2×C32×D311yescharacteristic
220C5×C9—31no—
221C5×C9—62no—
222C5×C9—62no—
223C5×C9—61no—
224C22×C32—451no—
225C2×C3⋊D3—51no—
226C2×C3×D3—151no—
227C2×C3×D3—451no—
228C2×C3×D3—451no—
229C2×C3×D3—453no—
230C22×C9—452no—
231C22×C9—451no—
232C2×C3×C5—91no—
233C2×C3×C5—271no—
234D15—31no—
235D15—91no—
236C3×D5—21no—
237C3×D5—31no—
238C3×D5—31no—
239C3×D5—63no—
240C3×D5—61no—
241C3×D5—61no—
242C3×D5—91no—
243C3×D5—271no—
244C3×D5C3×(C3⋊D3)⋊C311yescharacteristic
245C3×D5D3×3−1+211yescharacteristic
246C5×D3—31no—
247C5×D3—91no—
248C33—21no—
249C33—31no—
250C33—31no—
251C33—63no—
252C33—61no—
253C33—61no—
254C33C3×D3×D511yescharacteristic
255C33C2×C32×D511yescharacteristic
2563−1+2—61no—
2573−1+2—61no—
2583−1+2—62no—
2593−1+2—61no—
260C3×C9—21no—
261C3×C9—22no—
262C3×C9C3×D3×D512yescomplemented
263C3×C9C3×D3×D511yescharacteristic, complemented
264C2×D5—91noHall
265C2×C32—51no—
266C2×C32—51no—
267C2×C32—51no—
268C2×C32—91no—
269C2×C32—101no—
270C2×C32—101no—
271C2×C32—103no—
272C2×C32—151no—
273C2×C32—151no—
274C2×C32—153no—
275C2×C32—301no—
276C2×C32—301no—
277C2×C32—301no—
278C2×C32—301no—
279C2×C32—301no—
280C2×C32—303no—
281C2×C32—303no—
282C2×C32—303no—
283C2×C32—303no—
284C2×C32—451no—
285C3⋊D3—51no—
286C3⋊D3D5×3−1+211yescharacteristic, complemented
287C3×D3—31no—
288C3×D3—91no—
289C3×D3—91no—
290C3×D3—93no—
291C3×D3—151no—
292C3×D3—451no—
293C3×D3—451no—
294C3×D3—453no—
295C2×C9—92no—
296C2×C9—91no—
297C2×C9—152no—
298C2×C9—301no—
299C2×C9—302no—
300C2×C9—301no—
301C2×C9—452no—
302C2×C9—451no—
303C3×C5—21no—
304C3×C5—31no—
305C3×C5—31no—
306C3×C5—63no—
307C3×C5—61no—
308C3×C5—61no—
309C3×C5C2×C3×(C3⋊D3)⋊C311yescharacteristic
310C3×C5C2×D3×3−1+211yescharacteristic
311C22×C3—451no—
312C22×C3—1351no—
313C2×D3—151no—
314C2×D3—451no—
315C2×C5—91no—
316D5—91no—
317D5#9225911yescharacteristic, direct product factor
318C32—23no—
319C32—21no—
320C32—21no—
321C32—33no—
322C32—31no—
323C32—31no—
324C32—61no—
325C32—61no—
326C32—61no—
327C32—63no—
328C32—63no—
329C32—63no—
330C32—63no—
331C32—61no—
332C32—61no—
333C32D5×(C3⋊D3)⋊C311yescharacteristic
334C32C2×D5×3−1+211yescharacteristic, complemented
335C32C32×D3×D511yescharacteristic
336C9—32no—
337C9—61no—
338C9—61no—
339C9—62no—
340C2×C3—51no—
341C2×C3—51no—
342C2×C3—91no—
343C2×C3—101no—
344C2×C3—151no—
345C2×C3—151no—
346C2×C3—271no—
347C2×C3—301no—
348C2×C3—301no—
349C2×C3—303no—
350C2×C3—451no—
351C2×C3—1351no—
352D3—31no—
353D3—91no—
354D3—151no—
355D3—451no—
356C5C2×#9225911yescharacteristic, complemented, Sylow
357C22—451noSylow
358C3—21no—
359C3—31no—
360C3—31no—
361C3—63no—
362C3—61no—
363C3—61no—
364C3C3×D5×(C3⋊D3)⋊C311yescharacteristic
365C3D3×D5×3−1+211yescharacteristic
366C2—51no—
367C2—91no—
368C2—451no—
subgroupG/H
centerC3C3×D5×(C3⋊D3)⋊C3
commutator, cosocleC33×C5C22×C32
FrattiniC32C32×D3×D5
FittingC5×#6891C22
socleC32×C5C2×C32×D3
prime radicalC32×D5×C3⋊D3C3
hypercenterC32D5×(C3⋊D3)⋊C3
hypocenterC32×C5C22×3−1+2
LCSG ▷ C33×C5 ▷ C32×C5
UCSC1 ◁ C3 ◁ C32

Complements

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

NH ≅ G/Ntype
1. #72247400C2semidirect
2. C5×#92259C2semidirect
3. D5×#6891C2semidirect
6. D5×(C3⋊D3)⋊C9C3semidirect
7. D5×(C3⋊D3)⋊C9C3semidirect
8. C5×#6891C22semidirect
16. C3×D5×3−1+2D3semidirect
17. C5⋊((C3⋊D3)⋊C9)C2×C3semidirect
18. C5⋊((C3⋊D3)⋊C9)C2×C3semidirect
19. C5×(C3⋊D3)⋊C9C2×C3semidirect
20. C5×(C3⋊D3)⋊C9C2×C3semidirect
23. D5×C32⋊C9C2×C3semidirect
24. D5×C32⋊C9C2×C3semidirect
34. #92259D5direct (N × H)
37. C3×C5×3−1+2C2×D3semidirect
40. C5×C32⋊C9C22×C3semidirect
41. C5×C32⋊C9C22×C3semidirect
74. C3×C9×D5C3×D3semidirect
75. C3×C9×D5C3×D3semidirect
76. #6891C2×D5semidirect
78. D5×C3⋊D33−1+2semidirect
98. (C3⋊D3)⋊C9C3×D5semidirect
99. (C3⋊D3)⋊C9C3×D5semidirect
114. C3×C5×C9C2×C3×D3semidirect
115. C3×C5×C9C2×C3×D3semidirect
124. C3⋊D15C2×3−1+2semidirect
125. C5×C3⋊D3C2×3−1+2semidirect
151. C32×D5C2×3−1+2semidirect
163. C3×3−1+2D3×D5semidirect
166. C32⋊C9C2×C3×D5semidirect
167. C32⋊C9C2×C3×D5semidirect
218. C32×C5C22×3−1+2semidirect
262. C3×C9C3×D3×D5semidirect
263. C3×C9C3×D3×D5semidirect
286. C3⋊D3D5×3−1+2semidirect
317. D5#92259direct (N × H)
334. C32C2×D5×3−1+2semidirect
356. C5C2×#92259semidirect

Maximal subgroups

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

subgroupindex
#722474002
C5×#922592
D5×#68912
C32×D5×C3⋊D33
D3×D5×3−1+23
D5×(C3⋊D3)⋊C93
C2×#922595