Finite Group Databasebeta

← C5⋊D5×#953 #72231443

Subgroups — C5⋊D5×#953 #72231443

Order 4800.

5296 conjugacy classes of subgroups; only the 446 normal subgroups are shown.

normal subgroups only

This group has 5296 conjugacy classes of subgroups — too many to draw. Only its 446 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#72231437C213yesmaximal, complemented
2#72231435C211yesmaximal, characteristic, complemented
3#72231428C213yesmaximal, complemented
4C52×#953C211yesmaximal, characteristic, complemented
5#217×C5⋊D5C213yesmaximal, complemented
6C24×C3×C5⋊D5C211yesmaximal, characteristic, complemented
7C2×#67×C5⋊D5C213yesmaximal, complemented
8#120×C5⋊D5—31nomaximal, Hall
9C24×C3×C52C2211yescharacteristic, complemented
10C23×C3×C5⋊D5—212no—
11C23×C3×C5⋊D5C2213yes—
12C23×C3×C5⋊D5C2213yescomplemented
13C22×D3×C5⋊D5C2211yescharacteristic, complemented
14C2×#10597159C2213yescomplemented
15C2×C52×#67C2213yescomplemented
16#67×C5⋊D5—212no—
17C2×#10597115C2213yescomplemented
18C2×#10597114C2213yescomplemented
19C2×Dic3×C5⋊D5C2213yescomplemented
20#11925254C2213yescomplemented
21C52×#217C2213yescomplemented
22#11925118C2216yescomplemented
23D5×#953—56nomaximal
24C24×C5⋊D5D311yescharacteristic, complemented
25C2×D4×C5⋊D5—33no—
26C52×#120—31no—
27#11717273—31no—
28#11717257—33no—
29#11717202—33no—
30C22⋊C4×C5⋊D5—33no—
31C23×C3×C52—26no—
32C23×C3×C52C2313yes—
33C22×C3⋊(C5⋊D5)C2311yescharacteristic, complemented
34C22×C52×D3C2311yescharacteristic, complemented
35C22×C3×C5⋊D5—232no—
36C22×C3×C5⋊D5—26no—
37C22×C3×C5⋊D5—212no—
38C22×C3×C5⋊D5—212no—
39C22×C3×C5⋊D5D4112yescomplemented
40C22×C3×C5⋊D5C2313yes—
41C22×C3×C5⋊D5C2311yescharacteristic
42C2×D3×C5⋊D5—26no—
43#10597159—26no—
44C2×C3⋊#1039C2313yescomplemented
45C52×#67—26no—
46C2×C52×Dic3C2313yescomplemented
47#10597115—26no—
48#10597114—26no—
49Dic3×C5⋊D5—26no—
50C24×C3×D5—56no—
51C2×D5×#67—518no—
52#91842—56no—
53C5×#953D516yescomplemented
54#91564—518no—
55#91563—518no—
56D5×#217—518no—
57C24×C52C2×D311yescharacteristic, complemented
58C23×C5⋊D5—212no—
59C23×C5⋊D5—31no—
60C23×C5⋊D5C2×D313yes—
61C23×C5⋊D5C2×D313yescomplemented
62C2×C52×D4—33no—
63C2×C22⋊(C5⋊D5)—33no—
64C2×C22⋊(C5⋊D5)—33no—
65D4×C5⋊D5—612no—
66C2×C4⋊(C5⋊D5)—33no—
67C2×C4×C5⋊D5—33no—
68C52×C22⋊C4—33no—
69C22⋊#1039—33no—
70#87808—36no—
71D5×#120—156no—
72C22×C3×C52—28no—
73C22×C3×C52—26no—
74C22×C3×C52C2×D416yescomplemented
75C22×C3×C52C2411yescharacteristic
76C2×C3⋊(C5⋊D5)—23no—
77C2×C52×D3—23no—
78C2×C3×C5⋊D5—224no—
79C2×C3×C5⋊D5—26no—
80C2×C3×C5⋊D5—224no—
81C2×C3×C5⋊D5C2×D416yes—
82C2×C3×C5⋊D5C2×D416yescomplemented
83D3×C5⋊D5—44no—
84C3⋊#1039—23no—
85C52×Dic3—23no—
86C24×C3×C5C2×D516yescomplemented
87C23×C3×D5—518no—
88C23×C3×D5—518no—
89C23×C3×D5—1072no—
90C22×D3×D5—56no—
91C2×#1220—518no—
92C2×C5×#67C2×D5118yescomplemented
93D5×#67—1072no—
94C2×#1202—518no—
95C2×#1201—518no—
96C2×D5×Dic3—518no—
97#6719—518no—
98C5×#217C2×D5118yescomplemented
99#6665—536no—
100C23×C52—26no—
101C23×C52—31no—
102C23×C52C22×D313yes—
103C22×C5⋊D5—232no—
104C22×C5⋊D5—26no—
105C22×C5⋊D5—212no—
106C22×C5⋊D5—212no—
107C22×C5⋊D5—31no—
108C22×C5⋊D5—66no—
109C22×C5⋊D5#67112yescomplemented
110C22×C5⋊D5C22×D313yes—
111C22×C5⋊D5C22×D311yescharacteristic
112C52×D4—66no—
113C2×C4×C52—33no—
114C22⋊(C5⋊D5)—66no—
115C22⋊(C5⋊D5)—66no—
116C2×#1039—33no—
117C4⋊(C5⋊D5)—66no—
118C4×C5⋊D5—66no—
119C2×#953—251noHall
120C24×D5—56no—
121C2×D4×D5—1518no—
122C5×#120—36no—
123#4099—156no—
124#4083—1518no—
125#4028—1518no—
126D5×C22⋊C4—1518no—
127C2×C3×C52—26no—
128C2×C3×C52C22×D413yes—
129C3⋊(C5⋊D5)—41no—
130C52×D3—41no—
131C3×C5⋊D5—26no—
132C3×C5⋊D5#12014yescomplemented
133C23×C3×C5—236no—
134C23×C3×C5C22×D5118yes—
135C22×D15—56no—
136C22×C5×D3C22×D516yescomplemented
137C22×C3×D5—56no—
138C22×C3×D5—572no—
139C22×C3×D5—518no—
140C22×C3×D5—1072no—
141C22×C3×D5—1072no—
142C22×C3×D5—10192no—
143C22×C3×D5—1036no—
144C2×D3×D5—1036no—
145#1220—1036no—
146C2×Dic15—518no—
147C5×#67—236no—
148C2×C5×Dic3C22×D5118yescomplemented
149#1202—1036no—
150#1201—1036no—
151D5×Dic3—1036no—
152C22×C52—28no—
153C22×C52—26no—
154C22×C52—63no—
155C22×C52C2×#6716yescomplemented
156C22×C52C23×D311yescharacteristic
157C2×C5⋊D5—224no—
158C2×C5⋊D5—26no—
159C2×C5⋊D5—224no—
160C2×C5⋊D5—63no—
161C2×C5⋊D5—124no—
162C2×C5⋊D5C2×#6716yes—
163C2×C5⋊D5C2×#6716yescomplemented
164C4×C52—63no—
165#1039—63no—
166C25×C3—251no—
167C22×#67—253no—
168#953—251no—
169#953—253no—
170#953—253no—
171#953C5⋊D511yescharacteristic, direct product factor
172C2×#217—253no—
173C24×C5D3×D516yescomplemented
174C23×D5—518no—
175C23×D5—518no—
176C23×D5—1072no—
177C23×D5—156no—
178C2×C5×D4—318no—
179C2×C22⋊D5—1518no—
180C2×C22⋊D5—1518no—
181D4×D5—3072no—
182C2×D20—1518no—
183C2×C4×D5—1518no—
184C5×C22⋊C4—318no—
185C22⋊Dic5—1518no—
186#685—1536no—
187C3×C52C2×#12011yescharacteristic, complemented, Hall
188C2×#120—751noSylow
189C22×C3×C5—248no—
190C22×C3×C5—236no—
191C22×C3×C5D4×D5136yescomplemented
192C22×C3×C5C23×D516yes—
193C2×D15—1018no—
194C2×C5×D3—218no—
195C2×C3×D5—536no—
196C2×C3×D5—536no—
197C2×C3×D5—10144no—
198C2×C3×D5—10144no—
199C2×C3×D5—1036no—
200D3×D5—2024no—
201Dic15—1018no—
202C5×Dic3—218no—
203C2×C52—26no—
204C2×C52—121no—
205C2×C52C22×#6713yes—
206C5⋊D5—26no—
207C5⋊D5—121no—
208C5⋊D5#95314yesdirect product factor
209C24×C3—253no—
210C24×C3—253no—
211C24×C3—5012no—
212C24×C3C2×C5⋊D511yescharacteristic, complemented
213C23×D3—251no—
214C2×#67—253no—
215C2×#67—253no—
216C2×#67—253no—
217C2×#67—5012no—
218C2×#67C2×C5⋊D513yescomplemented
219C22×Dic3—253no—
220#217—253no—
221#217—256no—
222#217C2×C5⋊D513yescomplemented
223C23×C5—236no—
224C23×C5—36no—
225C23×C5C2×D3×D5118yes—
226C22×D5—56no—
227C22×D5—572no—
228C22×D5—518no—
229C22×D5—1072no—
230C22×D5—1072no—
231C22×D5—10192no—
232C22×D5—1036no—
233C22×D5—156no—
234C22×D5—3036no—
235C5×D4—636no—
236C2×C4×C5—318no—
237C22⋊D5—3036no—
238C22⋊D5—3036no—
239C2×Dic5—1518no—
240D20—3036no—
241C4×D5—3036no—
242C25—251no—
243C22×D4—753no—
244#120—31no—
245#120—753no—
246#120—753no—
247#120—751no—
248C2×C22⋊C4—753no—
249C2×C3×C5—236no—
250C2×C3×C5C2×D4×D5118yes—
251D15—206no—
252C3×D5—524no—
253C3×D5—1036no—
254C5×D3—46no—
255C52C2×#95311yescharacteristic, complemented, Sylow
256C23×C3—26no—
257C23×C3—251no—
258C23×C3—2512no—
259C23×C3—253no—
260C23×C3—5012no—
261C23×C3—5012no—
262C23×C3—5032no—
263C23×C3—506no—
264C23×C3C22×C5⋊D513yes—
265C22×D3—251no—
266C22×D3—506no—
267C22×D3C22×C5⋊D511yescharacteristic, complemented
268#67—26no—
269#67—506no—
270#67—506no—
271#67—506no—
272C2×Dic3—253no—
273C2×Dic3—506no—
274C2×Dic3C22×C5⋊D513yescomplemented
275C22×C5—248no—
276C22×C5—236no—
277C22×C5—618no—
278C22×C5D5×#67136yescomplemented
279C22×C5C22×D3×D516yes—
280C2×D5—536no—
281C2×D5—536no—
282C2×D5—10144no—
283C2×D5—10144no—
284C2×D5—1036no—
285C2×D5—3018no—
286C2×D5—6024no—
287C4×C5—618no—
288Dic5—3018no—
289C24—253no—
290C24—253no—
291C24—5012no—
292C24—751no—
293C24D3×C5⋊D511yescharacteristic, complemented
294C2×D4—33no—
295C2×D4—753no—
296C2×D4—753no—
297C2×D4—753no—
298C2×D4—15012no—
299C22×C4—753no—
300C22⋊C4—33no—
301C22⋊C4—756no—
302C22⋊C4—753no—
303C3×C5D5×#12016yescomplemented
304C22×C3—28no—
305C22×C3—26no—
306C22×C3—256no—
307C22×C3—256no—
308C22×C3—5024no—
309C22×C3—5024no—
310C22×C3—506no—
311C22×C3D4×C5⋊D516yescomplemented
312C22×C3C23×C5⋊D511yescharacteristic
313C2×D3—23no—
314C2×D3—503no—
315C2×D3—1004no—
316Dic3—23no—
317Dic3—503no—
318C2×C5—236no—
319C2×C5—126no—
320C2×C5C2×D5×#67118yes—
321D5—524no—
322D5—1036no—
323D5—606no—
324C23—26no—
325C23—31no—
326C23—251no—
327C23—253no—
328C23—2512no—
329C23—5012no—
330C23—5012no—
331C23—5032no—
332C23—506no—
333C23—751no—
334C23—1506no—
335C23C2×D3×C5⋊D513yes—
336D4—66no—
337D4—1506no—
338D4—1506no—
339D4—1506no—
340C2×C4—33no—
341C2×C4—753no—
342C2×C4—1506no—
343C2×C3—26no—
344C2×C3—254no—
345C2×C3—506no—
346C2×C3C2×D4×C5⋊D513yes—
347D3—41no—
348D3—1001no—
349C5D5×#95316yescomplemented
350C22—28no—
351C22—26no—
352C22—63no—
353C22—256no—
354C22—256no—
355C22—3004no—
356C22—5024no—
357C22—5024no—
358C22—506no—
359C22—1503no—
360C22#67×C5⋊D516yescomplemented
361C22C22×D3×C5⋊D511yescharacteristic
362C4—63no—
363C4—1503no—
364C3#120×C5⋊D511yescharacteristic, complemented, Sylow
365C2—26no—
366C2—121no—
367C2—254no—
368C2—3001no—
369C2—506no—
370C2C2×#67×C5⋊D513yes—
subgroupG/H
center, FrattiniC22C22×D3×C5⋊D5
commutator, socle, cosocleC22×C3×C52C24
FittingC24×C3×C52C22
hypercenterC24D3×C5⋊D5
hypocenterC3×C52C2×#120
LCSG ▷ C22×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. #72231437C2semidirect
2. #72231435C2semidirect
3. #72231428C2semidirect
4. C52×#953C2semidirect
5. #217×C5⋊D5C2semidirect
6. C24×C3×C5⋊D5C2semidirect
7. C2×#67×C5⋊D5C2semidirect
9. C24×C3×C52C22semidirect
12. C23×C3×C5⋊D5C22semidirect
13. C22×D3×C5⋊D5C22semidirect
14. C2×#10597159C22semidirect
15. C2×C52×#67C22semidirect
17. C2×#10597115C22semidirect
18. C2×#10597114C22semidirect
19. C2×Dic3×C5⋊D5C22semidirect
20. #11925254C22semidirect
21. C52×#217C22semidirect
22. #11925118C22semidirect
24. C24×C5⋊D5D3semidirect
33. C22×C3⋊(C5⋊D5)C23semidirect
34. C22×C52×D3C23semidirect
39. C22×C3×C5⋊D5D4semidirect
44. C2×C3⋊#1039C23semidirect
46. C2×C52×Dic3C23semidirect
53. C5×#953D5semidirect
57. C24×C52C2×D3semidirect
61. C23×C5⋊D5C2×D3semidirect
74. C22×C3×C52C2×D4semidirect
82. C2×C3×C5⋊D5C2×D4semidirect
86. C24×C3×C5C2×D5semidirect
92. C2×C5×#67C2×D5semidirect
98. C5×#217C2×D5semidirect
109. C22×C5⋊D5#67semidirect
132. C3×C5⋊D5#120semidirect
136. C22×C5×D3C22×D5semidirect
148. C2×C5×Dic3C22×D5semidirect
155. C22×C52C2×#67semidirect
163. C2×C5⋊D5C2×#67semidirect
171. #953C5⋊D5direct (N × H)
173. C24×C5D3×D5semidirect
187. C3×C52C2×#120semidirect
191. C22×C3×C5D4×D5semidirect
208. C5⋊D5#953direct (N × H)
212. C24×C3C2×C5⋊D5semidirect
218. C2×#67C2×C5⋊D5semidirect
222. #217C2×C5⋊D5semidirect
255. C52C2×#953semidirect
267. C22×D3C22×C5⋊D5semidirect
274. C2×Dic3C22×C5⋊D5semidirect
278. C22×C5D5×#67semidirect
293. C24D3×C5⋊D5semidirect
303. C3×C5D5×#120semidirect
311. C22×C3D4×C5⋊D5semidirect
349. C5D5×#953semidirect
360. C22#67×C5⋊D5semidirect
364. C3#120×C5⋊D5semidirect

Maximal subgroups

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

subgroupindex
#722314372
#722314352
#722314282
C52×#9532
#217×C5⋊D52
C24×C3×C5⋊D52
C2×#67×C5⋊D52
#120×C5⋊D53
D5×#9535