Finite Group Databasebeta

← D5⋊#4465 #14283909

Subgroups — D5⋊#4465 #14283909

Order 1920.

464 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 106 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
1D5×#870C211yesmaximal, characteristic
2#11752335C211yesmaximal, characteristic
3C3×#65676C211yesmaximal, characteristic
4#11746507C212yesmaximal, complemented
5#11746506C212yesmaximal, complemented
6D5⋊#330—31nomaximal, Hall
7C2×D5⋊(C3⋊C8)—21no—
8C2×C3×D5⋊C8—21no—
9#91759C411yescharacteristic
10C5×#870C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12D5×C4⋊Dic3C411yescharacteristic
13D5×C4⋊Dic3C411yescharacteristic
14D5×Dic3⋊C4—21no—
15D5×Dic3⋊C4—21no—
16#91388C2211yescharacteristic
17#91388C2211yescharacteristic
18#91378—21no—
19#91378—21no—
20#91231—21no—
21#91231C2212yes—
22C3×#4002—21no—
23C3×#4002C2212yes—
24C2×#4465—51nomaximal, Hall
25D5×#125—31no—
26#65676—31no—
27#65676D311yescharacteristic
28#64870—32no—
29#64870—32no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×D5×Dic3—21no—
34C2×D5×Dic3—21no—
35C2×C3⋊#170—22no—
36D5⋊(C3⋊C8)—24no—
37C2×C3×#170—22no—
38C3×D5⋊C8—24no—
39C3×C42×C5C2×C411yescharacteristic
40C4⋊Dic15C2×C411yescharacteristic
41C4⋊Dic15C2×C411yescharacteristic
42#6712—21no—
43#6712—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×C4⋊Dic3C2×C411yescharacteristic
46C5×Dic3⋊C4—21no—
47C5×Dic3⋊C4—21no—
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5C2311yescharacteristic
51Dic3⋊Dic5—21no—
52Dic3⋊Dic5—21no—
53#6669—21no—
54#6669—21no—
55#6668—21no—
56#6668—21no—
57C2×#870—51no—
58C2×C3×#97—51no—
59C2×#803—51no—
60#4465—52no—
61#4465—52no—
62C2×D5⋊C8—21no—
63C2×D5⋊C8—61no—
64C5×#125—31no—
65D5×C4⋊C4—31no—
66D5×C4⋊C4—31no—
67D5×C4⋊C4—61no—
68D5×C4⋊C4—61no—
69#4036—31no—
70#4036—31no—
71#4035—61no—
72#4035—61no—
73C42×D5C2×D311yescharacteristic
74#4016—31no—
75#4002—21no—
76#4002—32no—
77#4002—61no—
78#4002C2×D312yes—
79C2×#330—151noSylow
80C22×C3×D5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×Dic15—21no—
85C2×Dic15—21no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C2×C3×Dic5C2×D411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5—22no—
94D5×Dic3—42no—
95D5×Dic3—42no—
96C3⋊#170—24no—
97C3×#170—24no—
98C22×C3×C8—101no—
99C2×C3×C42—51no—
100C2×C4⋊Dic3—51no—
101C2×C4⋊Dic3—51no—
102C2×Dic3⋊C4—101no—
103C2×Dic3⋊C4—101no—
104C22×C3⋊C8—101no—
105#870—51no—
106#870—51no—
107#870—51no—
108#870—101no—
109#870—101no—
110#870AGL(1,𝔽5)11yescharacteristic
111C3×#97—52no—
112C3×#97—101no—
113#803—52no—
114#803—101no—
115C2×C4×D5—61no—
116C2×C4×D5—61no—
117C2×C4×D5C4×D311yescharacteristic
118C2×C4×D5D1211yescharacteristic
119C2×C4×D5#6711yescharacteristic
120C2×#170—22no—
121C2×#170—62no—
122D5⋊C8—24no—
123D5⋊C8—64no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C42×C5C4×D311yescharacteristic
129C4⋊Dic5—31no—
130C4⋊Dic5—31no—
131C4⋊Dic5—61no—
132C4⋊Dic5—61no—
133#683—61no—
134#683—61no—
135#683—61no—
136#683—61no—
137#683—61no—
138#683—61no—
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142C2×#125—151no—
143C2×#97—51no—
144C2×#97—151no—
145#330—152no—
146#330—152no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C2×C3×D5#10112yes—
149C2×C3×D5#10412yes—
150C2×C3×D5#10412yes—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154Dic15—41no—
155Dic15—41no—
156C3×Dic5—21no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C5×Dic3—41no—
160C5×Dic3—41no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C22×Dic3—101no—
165C22×Dic3—101no—
166C2×C3×C8—102no—
167C2×C3×C8—104no—
168C3×C42—51no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42C2×AGL(1,𝔽5)11yescharacteristic
172C4⋊Dic3—51no—
173C4⋊Dic3—51no—
174C4⋊Dic3—101no—
175C4⋊Dic3—101no—
176C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
177C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
178Dic3⋊C4—21no—
179Dic3⋊C4—21no—
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186C2×C3⋊C8—102no—
187C2×C3⋊C8—104no—
188C22×D5(C2×D3)⋊C411yescharacteristic
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×Dic5—61no—
195C2×Dic5—61no—
196C2×Dic5(C2×D3)⋊C411yescharacteristic
197C2×Dic5C2×D1211yescharacteristic
198C2×Dic5C2×#6711yescharacteristic
199C4×D5—22no—
200C4×D5—22no—
201C4×D5—22no—
202C4×D5—122no—
203C4×D5—122no—
204#170—24no—
205#170—64no—
206C22×C8—101no—
207C22×C8—301no—
208#125—31no—
209#125—151no—
210#125—151no—
211#125—151no—
212#125—301no—
213#125—301no—
214C2×C4⋊C4—151no—
215C2×C4⋊C4—151no—
216C2×C4⋊C4—301no—
217C2×C4⋊C4—301no—
218C2×C42—51no—
219#97—52no—
220#97—101no—
221#97—152no—
222#97—301no—
223C2×C3×C5C2×#10111yescharacteristic
224C2×C3×C5C2×#10411yescharacteristic
225C2×C3×C5C2×#10411yescharacteristic
226C3×D5#33014yescomplemented
227C23×C3—51no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4—102no—
232C2×C3×C4—102no—
233C2×C3×C4—102no—
234C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
235C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
236C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241C2×Dic3—202no—
242C2×Dic3—202no—
243C3×C8—104no—
244C3⋊C8—104no—
245C22×C5C2×(C2×D3)⋊C411yescharacteristic
246C2×D5#80512yes—
247C2×D5#82412yes—
248C2×D5#82512yes—
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—121no—
253C4×C5—121no—
254Dic5—21no—
255Dic5—21no—
256Dic5—21no—
257Dic5—121no—
258Dic5—121no—
259C22×C4—51no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—301no—
263C22×C4—301no—
264C2×C8—102no—
265C2×C8—104no—
266C2×C8—302no—
267C2×C8—304no—
268C4⋊C4—31no—
269C4⋊C4—31no—
270C4⋊C4—61no—
271C4⋊C4—61no—
272C4⋊C4—151no—
273C4⋊C4—151no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C42—51no—
283C42—51no—
284C42—51no—
285C42D3×AGL(1,𝔽5)11yescharacteristic
286C3×C5C2×#33011yescharacteristic, complemented, Hall
287C22×C3—52no—
288C22×C3—52no—
289C22×C3—52no—
290C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—101no—
295C3×C4—101no—
296C3×C4—101no—
297Dic3—41no—
298Dic3—41no—
299Dic3—201no—
300Dic3—201no—
301C2×C5C2×#80511yescharacteristic
302C2×C5C2×#82411yescharacteristic
303C2×C5C2×#82511yescharacteristic
304D5#446514yescomplemented
305C23—51no—
306C2×C4—51no—
307C2×C4—51no—
308C2×C4—51no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—102no—
312C2×C4—102no—
313C2×C4—102no—
314C2×C4—301no—
315C2×C4—301no—
316C2×C4—602no—
317C2×C4—602no—
318C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
319C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
320C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
321C8—104no—
322C8—304no—
323C2×C3—54no—
324C2×C3D5⋊#10111yescharacteristic
325C2×C3D5⋊#10411yescharacteristic
326C2×C3D5⋊#10411yescharacteristic
327C5C2×#446511yescharacteristic, complemented, Sylow
328C22—52no—
329C22—52no—
330C22—52no—
331C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—101no—
336C4—101no—
337C4—101no—
338C4—121no—
339C4—121no—
340C4—601no—
341C4—601no—
342C3D5⋊#33011yescharacteristic, complemented, Sylow
343C2—54no—
344C2D5⋊#82511yescharacteristic
345C2D5⋊#80511yescharacteristic
346C2D5⋊#82411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#330
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746507C2semidirect
5. #11746506C2semidirect
226. C3×D5#330semidirect
286. C3×C5C2×#330semidirect
304. D5#4465semidirect
327. C5C2×#4465semidirect
342. C3D5⋊#330semidirect

Maximal subgroups

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

subgroupindex
D5×#8702
#117523352
C3×#656762
#117465072
#117465062
D5⋊#3303
C2×#44655