Finite Group Databasebeta

← #14301606

Subgroups — #14301606

Order 1920.

688 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C3×#66262C211yesmaximal, characteristic, complemented
2D5×#947C211yesmaximal, characteristic
3D5⋊#836C211yesmaximal, characteristic, complemented
4#11751706C212yesmaximal
5#11746523C212yesmaximal, complemented
6#10604563—31nomaximal, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×D5×D12C2211yescharacteristic
9D5⋊#208C2212yes—
10C3×Q8×AGL(1,𝔽5)—24no—
11C3×#4130—22no—
12C3×#4130C2212yes—
13#91836C411yescharacteristic, complemented
14C5×#947C411yescharacteristic, complemented
15D5×(C2×D3)⋊C4—22no—
16C4×D5×Dic3C2211yescharacteristic
17#91374C411yescharacteristic, complemented
18#91370C411yescharacteristic, complemented
19#91326—22no—
20#91234—22no—
21#91151—24no—
22#71661—51nomaximal, Hall
23#66262D311yescharacteristic, complemented
24D5×#124—31no—
25D5⋊#101—31no—
26#65767—32no—
27#64862—32no—
28C22×D3×D5—21no—
29C2×C3×C5×Q8C2×C411yescharacteristic
30C2×D60C2×C411yescharacteristic
31C2×C5×D12C2×C411yescharacteristic
32C3×Q8×D5—22no—
33C3×Q8×D5—22no—
34C2×C3×C4×D5D412yes—
35C2×C3×C4×D5C2311yescharacteristic
36C2×C3×Dic10C2×C411yescharacteristic
37C2×C3×Dic10D412yes—
38C2×#1203—21no—
39C2×D5×Dic3—21no—
40D5×D12—22no—
41D5×D12—22no—
42#6762—22no—
43#6758—22no—
44D5⋊(C3⋊C8)—22no—
45C3×C22⋊AGL(1,𝔽5)—22no—
46C3×C4⋊AGL(1,𝔽5)—24no—
47C3×C4⋊AGL(1,𝔽5)D414yes—
48C3×C4×AGL(1,𝔽5)—24no—
49C3×C4×AGL(1,𝔽5)—22no—
50#6714—22no—
51C4×Dic15C2×C411yescharacteristic
52C5×(C2×D3)⋊C4—22no—
53C4×C5×Dic3C2×C411yescharacteristic
54#6667—22no—
55(C2×D3)⋊Dic5—22no—
56Dic3×Dic5—21no—
57C3×#519—51no—
58C2×#947—51no—
59C2×#836—51no—
60#5001—52no—
61#4532—52no—
62C2×Q8×D5C2×D311yescharacteristic
63C2×D4×D5—31no—
64Q8×AGL(1,𝔽5)—24no—
65#4130—22no—
66#4130C2×D312yes—
67D5⋊M16—32no—
68C5×#124—31no—
69#4093—31no—
70#4082—31no—
71#4031—62no—
72D5×C22⋊C4—62no—
73#4021—31no—
74C42×D5—31no—
75#4007—64no—
76#4005—62no—
77#1888—151noSylow
78C22×D15—21no—
79C22×C5×D3—21no—
80C22×C3×D5C2×D411yescharacteristic
81C2×D3×D5—44no—
82C2×D3×D5—41no—
83C2×D3×D5—41no—
84C2×C3×AGL(1,𝔽5)—24no—
85C3×C5×Q8—22no—
86C2×C3×C4×C5C22⋊C412yes—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×Dic15—21no—
89D60—22no—
90C2×C5×Dic3—21no—
91C5×D12—22no—
92C2×C3×Dic5C22⋊C412yes—
93C2×C3×Dic5C2×D411yescharacteristic
94C3×C4×D5—22no—
95C3×C4×D5—22no—
96C3×C4×D5C2×D412yes—
97C3×C4×D5#4112yes—
98C3×Dic10—22no—
99C3×Dic10—24no—
100#1203—42no—
101D5×Dic3—42no—
102C3⋊#170—42no—
103C22×C3×Q8—51no—
104C22×D12—51no—
105C3×C4×Q8—104no—
106C3×#117—52no—
107C3×#117—102no—
108#947—51no—
109#947—51no—
110#947—51no—
111#947—102no—
112#947AGL(1,𝔽5)11yescharacteristic, complemented
113C2×(C2×D3)⋊C4—102no—
114C2×C4×Dic3—51no—
115C2×#208—52no—
116#836—102no—
117#809—104no—
118C23×D5—61no—
119C2×C5×Q8C4×D311yescharacteristic
120C2×C5×D4—31no—
121C2×C22⋊D5—61no—
122Q8×D5—22no—
123Q8×D5—22no—
124D4×D5—62no—
125D4×D5—62no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×C4×D5#6712yes—
129C2×C4×D5C22×D311yescharacteristic
130C2×Dic10C4×D311yescharacteristic
131C2×Dic10D1212yes—
132C22⋊AGL(1,𝔽5)—22no—
133#704—62no—
134C4⋊AGL(1,𝔽5)—24no—
135C4⋊AGL(1,𝔽5)#6714yes—
136C4×AGL(1,𝔽5)—24no—
137C4×AGL(1,𝔽5)—22no—
138#700—62no—
139D5⋊C8—62no—
140C5×C22⋊C4—62no—
141C42×C5—31no—
142C22⋊Dic5—62no—
143#685—62no—
144#685—62no—
145C4×Dic5—31no—
146C4×Dic5—61no—
147C2×#124—151no—
148#519—51no—
149#418—152no—
150C2×#101—151no—
151#339—152no—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×D15—42no—
154C2×D15—41no—
155C2×C5×D3—42no—
156C2×C5×D3—41no—
157C2×C3×D5—22no—
158C2×C3×D5#12011yescharacteristic
159C2×C3×D5#12311yescharacteristic
160D3×D5—82no—
161D3×D5—82no—
162C3×AGL(1,𝔽5)—44no—
163C3×C4×C5—22no—
164C3×C4×C5C4×D412yes—
165Dic15—41no—
166C3×Dic5—22no—
167C3×Dic5#12112yes—
168C5×Dic3—41no—
169C23×D3—101no—
170C2×C3×Q8—52no—
171C2×C3×Q8—51no—
172C2×C3×Q8—102no—
173C2×C3×Q8—102no—
174C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
175C22×C3×C4—51no—
176C22×C3×C4—52no—
177C22×Dic3—101no—
178C2×D12—51no—
179C2×D12—102no—
180C2×D12—102no—
181C2×D12—101no—
182C2×D12C2×AGL(1,𝔽5)11yescharacteristic
183C3×C4⋊C4—54no—
184C3×C4⋊C4—104no—
185C3×C22⋊C4—102no—
186C3×C42—102no—
187C3×C42—104no—
188(C2×D3)⋊C4—22no—
189(C2×D3)⋊C4—102no—
190(C2×D3)⋊C4—102no—
191(C2×D3)⋊C4—102no—
192C4×Dic3—51no—
193C4×Dic3—101no—
194C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
195#208—102no—
196#208—102no—
197C2×C3⋊C8—102no—
198C23×C5—61no—
199C22×D5—61no—
200C22×D5—124no—
201C22×D5—121no—
202C22×D5—121no—
203C22×D5C2×#6711yescharacteristic
204C2×AGL(1,𝔽5)—24no—
205C5×Q8—22no—
206C5×D4—62no—
207C2×C4×C5—61no—
208C2×C4×C5(C2×D3)⋊C412yes—
209C2×C4×C5C2×C4×D311yescharacteristic
210C22⋊D5—122no—
211C2×Dic5—61no—
212C2×Dic5(C2×D3)⋊C412yes—
213C2×Dic5C2×D1211yescharacteristic
214D20—62no—
215C4×D5—22no—
216C4×D5—22no—
217C4×D5—122no—
218C4×D5#23512yes—
219C4×D5C2×#6712yes—
220Dic10—22no—
221Dic10—24no—
222#170—122no—
223C22×Q8—51no—
224C22×D4—151no—
225C2×M16—152no—
226#124—31no—
227#124—151no—
228#124—151no—
229#124—151no—
230#124—302no—
231C4×Q8—104no—
232#117—52no—
233#117—102no—
234C2×C22⋊C4—302no—
235C2×C42—151no—
236#102—304no—
237#101—302no—
238C2×C3×C5—21no—
239C2×C3×C5#38611yescharacteristic
240D15—81no—
241C3×D5—21no—
242C3×D5#45412yes—
243C5×D3—81no—
244C23×C3—51no—
245C22×D3—21no—
246C22×D3—101no—
247C22×D3—201no—
248C22×D3—201no—
249C22×D3—204no—
250C3×Q8—22no—
251C3×Q8—104no—
252C3×Q8—102no—
253C2×C3×C4—51no—
254C2×C3×C4—52no—
255C2×C3×C4—52no—
256C2×C3×C4—52no—
257C2×C3×C4—102no—
258C2×C3×C4—102no—
259C2×C3×C4—104no—
260C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
261C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
262C2×Dic3—21no—
263C2×Dic3—101no—
264C2×Dic3—202no—
265D12—22no—
266D12—102no—
267D12—202no—
268C3⋊C8—202no—
269C22×C5—122no—
270C22×C5—121no—
271C22×C5C2×(C2×D3)⋊C411yescharacteristic
272C2×D5—22no—
273C2×D5—122no—
274C2×D5—121no—
275C2×D5—242no—
276C2×D5—242no—
277C2×D5#92911yescharacteristic
278C2×D5#95311yescharacteristic
279AGL(1,𝔽5)—44no—
280C4×C5—22no—
281C4×C5—121no—
282C4×C5C4×#6712yes—
283Dic5—22no—
284Dic5—121no—
285Dic5#93012yes—
286C24—301no—
287C2×Q8—52no—
288C2×Q8—51no—
289C2×Q8—102no—
290C2×Q8—102no—
291C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
292C2×D4—31no—
293C2×D4—151no—
294C2×D4—302no—
295C2×D4—302no—
296C2×D4—301no—
297C22×C4—51no—
298C22×C4—52no—
299C22×C4—301no—
300M16—302no—
301M16—302no—
302C2×C8—302no—
303C4⋊C4—54no—
304C4⋊C4—104no—
305C22⋊C4—62no—
306C22⋊C4—102no—
307C22⋊C4—302no—
308C22⋊C4—302no—
309C22⋊C4—302no—
310C42—31no—
311C42—102no—
312C42—104no—
313C42—151no—
314C42—301no—
315C3×C5#188811yescharacteristic, complemented, Hall
316C22×C3—51no—
317C22×C3—51no—
318C22×C3—102no—
319C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
320C2×D3—42no—
321C2×D3—41no—
322C2×D3—202no—
323C2×D3—201no—
324C2×D3—402no—
325C2×D3—402no—
326C3×C4—22no—
327C3×C4—52no—
328C3×C4—102no—
329C3×C4—204no—
330C3×C4D4×AGL(1,𝔽5)12yes—
331Dic3—41no—
332Dic3—201no—
333C2×C5—21no—
334C2×C5—241no—
335C2×C5#521311yescharacteristic
336D5—21no—
337D5—241no—
338D5#524512yes—
339C23—51no—
340C23—61no—
341C23—301no—
342C23—601no—
343C23—601no—
344C23—604no—
345Q8—22no—
346Q8—104no—
347Q8—102no—
348D4—62no—
349D4—302no—
350D4—602no—
351C2×C4—51no—
352C2×C4—52no—
353C2×C4—52no—
354C2×C4—52no—
355C2×C4—61no—
356C2×C4—102no—
357C2×C4—102no—
358C2×C4—104no—
359C2×C4—301no—
360C2×C4—602no—
361C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
362C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
363C8—602no—
364C2×C3—21no—
365C2×C3—52no—
366C2×C3—101no—
367C2×C3#6577911yescharacteristic
368D3—81no—
369D3—401no—
370C5#7166111yescharacteristic, complemented, Sylow
371C22—51no—
372C22—51no—
373C22—102no—
374C22—122no—
375C22—121no—
376C22—602no—
377C22—601no—
378C22—1202no—
379C22—1202no—
380C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
381C4—22no—
382C4—52no—
383C4—102no—
384C4—121no—
385C4—204no—
386C4—601no—
387C4AGL(1,𝔽5)×#6712yes—
388C3#1060456311yescharacteristic, complemented, Sylow
389C2—21no—
390C2—52no—
391C2—101no—
392C2—241no—
393C2—1201no—
394C2#1175202211yescharacteristic
subgroupG/H
centerC2#11752022
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC2×C3×C5#386
prime radicalC2×D5×D12C22
cosocleC2×C3×C4×D5C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66262C2semidirect
3. D5⋊#836C2semidirect
5. #11746523C2semidirect
13. #91836C4semidirect
14. C5×#947C4semidirect
17. #91374C4semidirect
18. #91370C4semidirect
23. #66262D3semidirect
112. #947AGL(1,𝔽5)semidirect
315. C3×C5#1888semidirect
370. C5#71661semidirect
388. C3#10604563semidirect

Maximal subgroups

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

subgroupindex
C3×#662622
D5×#9472
D5⋊#8362
#117517062
#117465232
#106045633
#716615