Finite Group Databasebeta

← D5×#4207⋊C2 #72247482

Subgroups — D5×#4207⋊C2 #72247482

Order 3240.

430 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 57 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#4207⋊D5C211yesmaximal, characteristic, complemented
2#4207⋊D5C211yesmaximal, characteristic, complemented
3#4208⋊D5C211yesmaximal, characteristic, complemented
4C5×#4207⋊C2C211yesmaximal, characteristic, complemented
5D5×#4208C211yesmaximal, characteristic, complemented
6D5×#4207C211yesmaximal, characteristic, complemented
7D5×#4207C211yesmaximal, characteristic, complemented
8D5×((C3⋊D3)⋊C3)⋊C2—31nomaximal
9D3×D5×D9—31nomaximal
10D3×D5×D9—31nomaximal
11C5⋊#4208C2211yescharacteristic, complemented
12C5⋊#4207C2211yescharacteristic, complemented
13C5⋊#4207C2211yescharacteristic, complemented
14C5×#4208C2211yescharacteristic, complemented
15C5×#4207C2211yescharacteristic, complemented
16C5×#4207C2211yescharacteristic, complemented
17D5×#737C2211yescharacteristic, complemented
18C2×#4207⋊C2—51nomaximal, Hall
19#272⋊D5—31no—
20D15⋊D9—31no—
21D15⋊D9—31no—
22((C3⋊D3)⋊C3)⋊D5—31no—
23((C3⋊D3)⋊C3)⋊D5—31no—
24D9×D15—31no—
25D9×D15—31no—
26D3×D45—31no—
27D3×D45—31no—
28C5×((C3⋊D3)⋊C3)⋊C2—31no—
29C5×D3×D9—31no—
30C5×D3×D9—31no—
31D5×#272D311yescharacteristic
32D5×C3⋊D9D311yescharacteristic, complemented
33D5×C3⋊D9D311yescharacteristic, complemented
34D5×AGL(1,ℤ/9)—61no—
35D5×AGL(1,ℤ/9)—61no—
36D5×(C3⋊D3)⋊C3—31no—
37D5×(C3⋊D3)⋊C3—31no—
38D3×C9×D5—31no—
39D3×C9×D5—31no—
40D3×C9×D5—61no—
41C3×D5×D9—31no—
42C3×D5×D9—31no—
43C5×#737C2311yescharacteristic, complemented, Hall
44D32×D5—91no—
45D32×D5—91no—
46C2×D5×D9—91no—
47C2×#4208—51no—
48C2×#4207—51no—
49C2×#4207—51no—
50#4207⋊C2—51no—
51#4207⋊C2—51no—
52#4207⋊C2—51no—
53#4207⋊C2D511yescharacteristic, direct product factor
54C5⋊#272C2×D311yescharacteristic
55C3⋊D45C2×D311yescharacteristic, complemented
56C3⋊D45C2×D311yescharacteristic, complemented
57C5×#272C2×D311yescharacteristic
58C5×C3⋊D9C2×D311yescharacteristic, complemented
59C5×C3⋊D9C2×D311yescharacteristic, complemented
60C5⋊AGL(1,ℤ/9)—61no—
61C5⋊AGL(1,ℤ/9)—61no—
62C5⋊((C3⋊D3)⋊C3)—31no—
63C5⋊((C3⋊D3)⋊C3)—31no—
64C9×D15—31no—
65C9×D15—31no—
66C9×D15—61no—
67C3×D45—31no—
68C3×D45—31no—
69C5×AGL(1,ℤ/9)—61no—
70C5×AGL(1,ℤ/9)—61no—
71C5×(C3⋊D3)⋊C3—31no—
72C5×(C3⋊D3)⋊C3—31no—
73C5×D3×C9—31no—
74C5×D3×C9—31no—
75C5×D3×C9—61no—
76C3×C5×D9—31no—
77C3×C5×D9—31no—
78D5×3−1+2—21no—
79D5×3−1+2—21no—
80D5×3−1+2—41no—
81D5×H(3,𝔽3)C2×D311yescharacteristic
82C3×C9×D5—21no—
83C3×C9×D5C2×D311yescharacteristic, complemented
84C3×C9×D5C2×D311yescharacteristic, complemented
85C2×((C3⋊D3)⋊C3)⋊C2—151no—
86C2×D3×D9—151no—
87C2×D3×D9—151no—
88(C3⋊D3)⋊D5—91no—
89(C3⋊D3)⋊D5—91no—
90D3×D15—91no—
91D3×D15—91no—
92D3×D15—91no—
93D3×D15—91no—
94C5×D32—91no—
95C5×D32—91no—
96D5×C3⋊D3—31no—
97D5×C3⋊D3—31no—
98C3×D3×D5—31no—
99C3×D3×D5—31no—
100C3×D3×D5—61no—
101C3×D3×D5—91no—
102C3×D3×D5—91no—
103C2×D45—91no—
104C2×C5×D9—91no—
105C2×C9×D5—91no—
106D5×D9—31no—
107D5×D9—31no—
108D5×D9—61no—
109D5×D9—61no—
110D5×D9—91no—
111D5×D9—91no—
112C2×#737—51no—
113#4208—51no—
114#4208C2×D511yescharacteristic, complemented
115#4207—51no—
116#4207—51no—
117#4207C2×D511yescharacteristic, complemented
118#4207C2×D511yescharacteristic, complemented
119C5×3−1+2—21no—
120C5×3−1+2—21no—
121C5×3−1+2—41no—
122C5×H(3,𝔽3)C22×D311yescharacteristic
123C3×C5×C9—21no—
124C3×C5×C9C22×D311yescharacteristic, complemented
125C3×C5×C9C22×D311yescharacteristic, complemented
126C2×D3×D5—271no—
127C2×D3×D5—271no—
128C2×D3×D5—271no—
129C2×#272—51no—
130C2×C3⋊D9—51no—
131C2×C3⋊D9—51no—
132C2×AGL(1,ℤ/9)—301no—
133C2×AGL(1,ℤ/9)—301no—
134C2×(C3⋊D3)⋊C3—151no—
135C2×(C3⋊D3)⋊C3—151no—
136C2×D3×C9—151no—
137C2×D3×C9—151no—
138C2×D3×C9—301no—
139C2×C3×D9—151no—
140C2×C3×D9—151no—
141((C3⋊D3)⋊C3)⋊C2—31no—
142((C3⋊D3)⋊C3)⋊C2—151no—
143((C3⋊D3)⋊C3)⋊C2—151no—
144((C3⋊D3)⋊C3)⋊C2—151no—
145D3×D9—31no—
146D3×D9—31no—
147D3×D9—151no—
148D3×D9—151no—
149D3×D9—151no—
150D3×D9—151no—
151D3×D9—151no—
152D3×D9—151no—
153C3⋊D15—31no—
154C3⋊D15—31no—
155C5×C3⋊D3—31no—
156C5×C3⋊D3—31no—
157C3×D15—31no—
158C3×D15—31no—
159C3×D15—61no—
160C3×D15—91no—
161C3×D15—91no—
162C3×C5×D3—31no—
163C3×C5×D3—31no—
164C3×C5×D3—61no—
165C3×C5×D3—91no—
166C3×C5×D3—91no—
167C32×D5—21no—
168C32×D5D3211yescharacteristic
169C32×D5D3211yescharacteristic
170C2×C5×C9—91no—
171D45—31no—
172D45—31no—
173D45—61no—
174D45—61no—
175C9×D5—21no—
176C9×D5—21no—
177C9×D5—41no—
178C9×D5—91no—
179C9×D5D3211yescharacteristic
180C5×D9—31no—
181C5×D9—31no—
182C5×D9—61no—
183C5×D9—61no—
184#737C22×D511yescharacteristic, complemented, Sylow
185C2×D32—451no—
186C2×D32—451no—
187C22×D9—451no—
188C2×D15—271no—
189C2×D15—271no—
190C2×D15—271no—
191C2×C5×D3—271no—
192C2×C5×D3—271no—
193C2×C5×D3—271no—
194C2×C3×D5—91no—
195C2×C3×D5—271no—
196C2×C3×D5—271no—
197D3×D5—31no—
198D3×D5—31no—
199D3×D5—61no—
200D3×D5—91no—
201D3×D5—91no—
202D3×D5—271no—
203D3×D5—271no—
204D3×D5—271no—
205D3×D5—271no—
206D3×D5—271no—
207D3×D5—271no—
208D3×D5—271no—
209D3×D5—541no—
210C2×3−1+2—101no—
211C2×3−1+2—101no—
212C2×3−1+2—201no—
213C2×H(3,𝔽3)—51no—
214C2×C3×C9—51no—
215C2×C3×C9—51no—
216C2×C3×C9—101no—
217#272—51no—
218#272D3×D511yescharacteristic
219C3⋊D9—51no—
220C3⋊D9—51no—
221C3⋊D9D3×D511yescharacteristic, complemented
222C3⋊D9D3×D511yescharacteristic, complemented
223AGL(1,ℤ/9)—61no—
224AGL(1,ℤ/9)—61no—
225AGL(1,ℤ/9)—301no—
226AGL(1,ℤ/9)—301no—
227(C3⋊D3)⋊C3—31no—
228(C3⋊D3)⋊C3—31no—
229(C3⋊D3)⋊C3—151no—
230(C3⋊D3)⋊C3—151no—
231D3×C9—31no—
232D3×C9—31no—
233D3×C9—61no—
234D3×C9—151no—
235D3×C9—151no—
236D3×C9—301no—
237C3×D9—31no—
238C3×D9—31no—
239C3×D9—151no—
240C3×D9—151no—
241C32×C5—21no—
242C32×C5C2×D3211yescharacteristic
243C32×C5C2×D3211yescharacteristic
244C5×C9—21no—
245C5×C9—21no—
246C5×C9—41no—
247C5×C9C2×D3211yescharacteristic
248C22×D5—811noHall
249C2×C3⋊D3—151no—
250C2×C3⋊D3—151no—
251C2×C3×D3—151no—
252C2×C3×D3—151no—
253C2×C3×D3—301no—
254C2×C3×D3—451no—
255C2×C3×D3—451no—
256D32—91no—
257D32—91no—
258D32—451no—
259D32—451no—
260D32—451no—
261D32—451no—
262D32—451no—
263D32—451no—
264C22×C9—451no—
265C2×D9—91no—
266C2×D9—151no—
267C2×D9—151no—
268C2×D9—301no—
269C2×D9—301no—
270C2×D9—451no—
271C2×D9—451no—
272C2×D9—451no—
273C2×C3×C5—91no—
274C2×C3×C5—271no—
275C2×C3×C5—271no—
276D15—31no—
277D15—31no—
278D15—61no—
279D15—91no—
280D15—91no—
281D15—271no—
282D15—541no—
283C3×D5—31no—
284C3×D5—61no—
285C3×D5—91no—
286C3×D5—121no—
287C3×D5—271no—
288C3×D5—271no—
289C3×D5#111311yescharacteristic
290C5×D3—31no—
291C5×D3—31no—
292C5×D3—61no—
293C5×D3—91no—
294C5×D3—91no—
295C5×D3—271no—
296C5×D3—541no—
2973−1+2—21no—
2983−1+2—21no—
2993−1+2—41no—
300H(3,𝔽3)C2×D3×D511yescharacteristic
301C3×C9—21no—
302C3×C9C2×D3×D511yescharacteristic, complemented
303C3×C9C2×D3×D511yescharacteristic, complemented
304C22×D3—1351no—
305C22×D3—1351no—
306C22×D3—1351no—
307C22×C5—811no—
308C2×D5—91no—
309C2×D5—271no—
310C2×D5—271no—
311C2×D5—811no—
312C2×D5—811no—
313C2×D5—811no—
314C2×C32—51no—
315C2×C32—51no—
316C2×C32—101no—
317C3⋊D3—31no—
318C3⋊D3—31no—
319C3⋊D3—151no—
320C3⋊D3—151no—
321C3×D3—31no—
322C3×D3—31no—
323C3×D3—61no—
324C3×D3—91no—
325C3×D3—91no—
326C3×D3—151no—
327C3×D3—151no—
328C3×D3—301no—
329C3×D3—451no—
330C3×D3—451no—
331C2×C9—51no—
332C2×C9—91no—
333C2×C9—101no—
334C2×C9—101no—
335C2×C9—201no—
336C2×C9—451no—
337D9—31no—
338D9—31no—
339D9—61no—
340D9—61no—
341D9—151no—
342D9—151no—
343D9—301no—
344D9—301no—
345C3×C5—31no—
346C3×C5—61no—
347C3×C5—121no—
348C3×C5C2×#111311yescharacteristic
349C22×C3—451no—
350C22×C3—1351no—
351C22×C3—1351no—
352C2×D3—151no—
353C2×D3—151no—
354C2×D3—271no—
355C2×D3—271no—
356C2×D3—271no—
357C2×D3—301no—
358C2×D3—451no—
359C2×D3—451no—
360C2×D3—1351no—
361C2×D3—1351no—
362C2×D3—1351no—
363C2×D3—1351no—
364C2×D3—1351no—
365C2×D3—1351no—
366C2×D3—1351no—
367C2×D3—1351no—
368C2×D3—1351no—
369C2×D3—1351no—
370C2×D3—1351no—
371C2×C5—91no—
372C2×C5—271no—
373C2×C5—271no—
374D5—91no—
375D5—271no—
376D5—271no—
377D5#4207⋊C211yescharacteristic, direct product factor
378C32—21no—
379C32D32×D511yescharacteristic
380C32D32×D511yescharacteristic
381C9—21no—
382C9—21no—
383C9—41no—
384C9D32×D511yescharacteristic
385C23—4051noSylow
386C2×C3—51no—
387C2×C3—91no—
388C2×C3—151no—
389C2×C3—151no—
390C2×C3—271no—
391C2×C3—271no—
392C2×C3—451no—
393C2×C3—601no—
394C2×C3—1351no—
395C2×C3—1351no—
396D3—31no—
397D3—31no—
398D3—61no—
399D3—91no—
400D3—91no—
401D3—151no—
402D3—151no—
403D3—271no—
404D3—271no—
405D3—301no—
406D3—451no—
407D3—451no—
408D3—1351no—
409D3—1351no—
410C5C2×#4207⋊C211yescharacteristic, complemented, Sylow
411C22—451no—
412C22—811no—
413C22—1351no—
414C22—1351no—
415C22—4051no—
416C22—4051no—
417C22—4051no—
418C3—31no—
419C3—31no—
420C3—121no—
421C3D5×#111311yescharacteristic
422C2—51no—
423C2—91no—
424C2—271no—
425C2—271no—
426C2—451no—
427C2—1351no—
428C2—1351no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×#737C23
FrattiniC3D5×#1113
socleC3×C5C2×#1113
LCSG ▷ C5×#737
UCSC1

Complements

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

NH ≅ G/Ntype
1. #4207⋊D5C2semidirect
2. #4207⋊D5C2semidirect
3. #4208⋊D5C2semidirect
4. C5×#4207⋊C2C2semidirect
5. D5×#4208C2semidirect
6. D5×#4207C2semidirect
7. D5×#4207C2semidirect
11. C5⋊#4208C22semidirect
12. C5⋊#4207C22semidirect
13. C5⋊#4207C22semidirect
14. C5×#4208C22semidirect
15. C5×#4207C22semidirect
16. C5×#4207C22semidirect
17. D5×#737C22semidirect
32. D5×C3⋊D9D3semidirect
33. D5×C3⋊D9D3semidirect
43. C5×#737C23semidirect
53. #4207⋊C2D5direct (N × H)
55. C3⋊D45C2×D3semidirect
56. C3⋊D45C2×D3semidirect
58. C5×C3⋊D9C2×D3semidirect
59. C5×C3⋊D9C2×D3semidirect
83. C3×C9×D5C2×D3semidirect
84. C3×C9×D5C2×D3semidirect
114. #4208C2×D5semidirect
117. #4207C2×D5semidirect
118. #4207C2×D5semidirect
124. C3×C5×C9C22×D3semidirect
125. C3×C5×C9C22×D3semidirect
184. #737C22×D5semidirect
221. C3⋊D9D3×D5semidirect
222. C3⋊D9D3×D5semidirect
302. C3×C9C2×D3×D5semidirect
303. C3×C9C2×D3×D5semidirect
377. D5#4207⋊C2direct (N × H)
410. C5C2×#4207⋊C2semidirect

Maximal subgroups

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

subgroupindex
#4207⋊D52
#4208⋊D52
C5×#4207⋊C22
D5×#42082
D5×#42072
D5×((C3⋊D3)⋊C3)⋊C23
D3×D5×D93
C2×#4207⋊C25