Finite Group Databasebeta

← #14307994

Subgroups — #14307994

Order 1920.

812 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#91797C212yesmaximal, complemented
2#11756269C211yesmaximal, characteristic, complemented
3C2×#91109C212yesmaximal, complemented
4#11751089C211yesmaximal, characteristic, complemented
5C3×C5×#343C211yesmaximal, characteristic, complemented
6#10599801—31nomaximal, Hall
7C2×#6817C2212yes—
8C22×D60C2211yescharacteristic
9C2×C3×C5×M16C2212yes—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11#91819—22no—
12C2×#6714—22no—
13C2×C4×Dic15C2211yescharacteristic
14#91797—24no—
15#91797—24no—
16C2×D120—22no—
17C2×#6706—22no—
18#91786—22no—
19#91784—22no—
20#91109—24no—
21#69008—51nomaximal, Hall
22C2×#4054—32no—
23#65844—31no—
24C2×#3957—32no—
25#65277—31no—
26C5×#343D311yescharacteristic, complemented
27C23×D15—21no—
28C22×C3×C4×C5D412yes—
29C22×C3×C4×C5C2311yescharacteristic
30C2×#1220—22no—
31C22×Dic15—21no—
32#6817—22no—
33#6817—22no—
34#6817—22no—
35#6817—22no—
36C2×D60—22no—
37C2×D60—22no—
38C2×D60—21no—
39C2×D60—22no—
40C2×D60D412yes—
41C2×D60D412yescomplemented
42C2×C4×D15—22no—
43C2×Dic30D412yes—
44C3×C5×M16—22no—
45C3×C5×M16D414yescomplemented
46C2×C3×C5×C8—22no—
47C3×C5×C4⋊C4—22no—
48#6714—24no—
49#6714—44no—
50C4⋊Dic15—22no—
51C4×Dic15—22no—
52D120—28no—
53#6706—28no—
54C2×#908—52no—
55#5510—51no—
56C2×#825—52no—
57#4988—51no—
58C3×#343D511yescharacteristic, complemented
59C2×#709—32no—
60C22×D20—31no—
61C2×C5×M16C2×D312yes—
62C2×C5×C4⋊C4C2×D311yescharacteristic
63#4076—62no—
64C2×#685—62no—
65C2×C4×Dic5—31no—
66#4054—64no—
67#4054—64no—
68C2×D40—62no—
69C2×#677—62no—
70#4043—62no—
71#4041—62no—
72#3957—64no—
73#2006—151noSylow
74C23×C3×C5C2×D411yescharacteristic
75C22×D15—22no—
76C22×D15—22no—
77C22×D15—42no—
78C22×D15—42no—
79C22×D15—41no—
80C22×D15—41no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—42no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D412yes—
85C2×C3×C4×C5C2×D412yes—
86C2×C3×C4×C5#4111yescharacteristic
87#1220—42no—
88#1220—42no—
89C2×Dic15—22no—
90C2×Dic15—22no—
91C2×Dic15—41no—
92C2×Dic15—41no—
93D60—24no—
94D60—22no—
95D60—22no—
96D60—42no—
97D60—82no—
98C4×D15—42no—
99C4×D15—42no—
100Dic30—22no—
101Dic30—22no—
102C3×C5×C8—24no—
103C2×#235—52no—
104C22×D12—51no—
105C2×C3×M16C2×D512yes—
106C2×C3×C4⋊C4C2×D511yescharacteristic
107#930—102no—
108C2×(C2×D3)⋊C4—102no—
109C2×C4×Dic3—51no—
110#908—104no—
111#908—104no—
112C2×D24—102no—
113C2×#204—102no—
114#897—102no—
115#895—102no—
116#825—104no—
117C23×D5—61no—
118C22×C4×C5D1212yes—
119C22×C4×C5C22×D311yescharacteristic
120C2×C22⋊D5—62no—
121C22×Dic5—61no—
122#709—62no—
123#709—62no—
124#709—62no—
125#709—62no—
126C2×D20—32no—
127C2×D20—32no—
128C2×D20—62no—
129C2×D20—62no—
130C2×D20—61no—
131C2×D20—62no—
132C2×C4×D5—62no—
133C2×Dic10—32no—
134C5×M16—22no—
135C5×M16D1214yescomplemented
136C2×C5×C8—22no—
137C5×C4⋊C4—22no—
138#685—64no—
139#685—124no—
140C4⋊Dic5—62no—
141C4×Dic5—62no—
142D40—68no—
143#677—68no—
144C2×AGL(1,ℤ/8)—152no—
145#537—151no—
146C2×#104—152no—
147#390—151no—
148#343D1511yescharacteristic, complemented
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#12011yescharacteristic
152C22×C3×C5#12111yescharacteristic
153C22×C3×C5#12711yescharacteristic
154C2×D15—44no—
155C2×D15—42no—
156C2×D15—42no—
157C2×D15—42no—
158C2×D15—42no—
159C2×D15—82no—
160C2×D15—81no—
161C2×D15—81no—
162C3×C4×C5—42no—
163C3×C4×C5#12012yes—
164C3×C4×C5#12112yes—
165Dic15—42no—
166Dic15—42no—
167C23×D3—101no—
168C22×C3×C4D2012yes—
169C22×C3×C4C22×D511yescharacteristic
170C2×#67—102no—
171C22×Dic3—101no—
172#235—102no—
173#235—102no—
174#235—102no—
175#235—102no—
176C2×D12—52no—
177C2×D12—52no—
178C2×D12—102no—
179C2×D12—102no—
180C2×D12—101no—
181C2×D12—102no—
182C2×C4×D3—102no—
183C2×Dic6—52no—
184C3×M16—22no—
185C3×M16D2014yescomplemented
186C2×C3×C8—22no—
187C3×C4⋊C4—22no—
188(C2×D3)⋊C4—104no—
189(C2×D3)⋊C4—204no—
190C4⋊Dic3—102no—
191C4×Dic3—102no—
192D24—108no—
193#204—108no—
194C23×C5C2×D1211yescharacteristic
195C22×D5—62no—
196C22×D5—62no—
197C22×D5—122no—
198C22×D5—122no—
199C22×D5—121no—
200C22×D5—121no—
201C2×C4×C5—22no—
202C2×C4×C5—42no—
203C2×C4×C5C2×D1212yes—
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D412yes—
206C2×C4×C5#23911yescharacteristic
207C22⋊D5—122no—
208C22⋊D5—122no—
209C2×Dic5—62no—
210C2×Dic5—62no—
211C2×Dic5—121no—
212C2×Dic5—121no—
213D20—64no—
214D20—62no—
215D20—62no—
216D20—122no—
217D20—242no—
218C4×D5—122no—
219C4×D5—122no—
220Dic10—62no—
221Dic10—62no—
222C5×C8—24no—
223C2×#41—152no—
224C22×D4—151no—
225AGL(1,ℤ/8)—304no—
226AGL(1,ℤ/8)—304no—
227C2×SD16—302no—
228C2×D8—302no—
229C2×M16C2×D1512yes—
230C22⋊Q8—302no—
231#121—302no—
232#121—302no—
233C2×C4⋊C4C2×D1511yescharacteristic
234C2×C22⋊C4—302no—
235C2×C42—151no—
236#104—304no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5#39211yescharacteristic
240C2×C3×C5#45311yescharacteristic
241C2×C3×C5#45411yescharacteristic
242D15—82no—
243D15—82no—
244C23×C3C2×D2011yescharacteristic
245C22×D3—102no—
246C22×D3—102no—
247C22×D3—202no—
248C22×D3—202no—
249C22×D3—201no—
250C22×D3—201no—
251C2×C3×C4—22no—
252C2×C3×C4—42no—
253C2×C3×C4C2×D2012yes—
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D512yes—
256C2×C3×C4#71311yescharacteristic
257#67—202no—
258#67—202no—
259C2×Dic3—102no—
260C2×Dic3—102no—
261C2×Dic3—201no—
262C2×Dic3—201no—
263D12—104no—
264D12—102no—
265D12—102no—
266D12—202no—
267D12—402no—
268C4×D3—202no—
269C4×D3—202no—
270Dic6—102no—
271Dic6—102no—
272C3×C8—24no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5#87411yescharacteristic
276C22×C5#88211yescharacteristic
277C22×C5#89511yescharacteristic
278C2×D5—124no—
279C2×D5—122no—
280C2×D5—122no—
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—242no—
284C2×D5—241no—
285C2×D5—241no—
286C4×C5—42no—
287C4×C5#88212yes—
288C4×C5#89512yes—
289Dic5—122no—
290Dic5—122no—
291C24—301no—
292#41—302no—
293#41—302no—
294#41—302no—
295#41—302no—
296C2×Q8—152no—
297C2×D4—152no—
298C2×D4—152no—
299C2×D4—302no—
300C2×D4—302no—
301C2×D4—302no—
302C2×D4—302no—
303C2×D4—301no—
304C22×C4—301no—
305C22×C4—302no—
306C22×C4D6012yes—
307C22×C4C22×D1511yescharacteristic
308SD16—308no—
309D8—308no—
310M16—22no—
311M16D6014yescomplemented
312C2×C8—22no—
313C4⋊C4—22no—
314C4⋊C4—302no—
315C22⋊C4—304no—
316C22⋊C4—604no—
317C42—302no—
318C3×C5#200611yescharacteristic, complemented, Hall
319C22×C3—21no—
320C22×C3—21no—
321C22×C3#402011yescharacteristic
322C22×C3#402811yescharacteristic
323C22×C3#404111yescharacteristic
324C2×D3—204no—
325C2×D3—202no—
326C2×D3—202no—
327C2×D3—202no—
328C2×D3—202no—
329C2×D3—402no—
330C2×D3—401no—
331C2×D3—401no—
332C3×C4—42no—
333C3×C4#402812yes—
334C3×C4#404112yes—
335Dic3—202no—
336Dic3—202no—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5#467111yescharacteristic
340C2×C5#474711yescharacteristic
341C2×C5#475311yescharacteristic
342D5—242no—
343D5—242no—
344C23—302no—
345C23—302no—
346C23—602no—
347C23—602no—
348C23—601no—
349C23—601no—
350C23C2×D6011yescharacteristic
351Q8—302no—
352Q8—302no—
353D4—302no—
354D4—304no—
355D4—302no—
356D4—602no—
357D4—602no—
358D4—602no—
359D4—1202no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—302no—
363C2×C4—302no—
364C2×C4—601no—
365C2×C4—601no—
366C2×C4—602no—
367C2×C4—602no—
368C2×C4C2×D6012yes—
369C2×C4D4×D1511yescharacteristic
370C2×C4D4×D1512yes—
371C2×C4#682111yescharacteristic
372C8—24no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3#6496011yescharacteristic
376C2×C3#6503611yescharacteristic
377C2×C3#6504211yescharacteristic
378D3—402no—
379D3—402no—
380C5#6900811yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—604no—
384C22—602no—
385C22—602no—
386C22—602no—
387C22—602no—
388C22—1202no—
389C22—1201no—
390C22—1201no—
391C22#9176311yescharacteristic
392C22#9177111yescharacteristic
393C22#9178411yescharacteristic
394C4—42no—
395C4—602no—
396C4—602no—
397C4#9177112yes—
398C4#9178412yes—
399C3#1059980111yescharacteristic, complemented, Sylow
400C2—21no—
401C2—21no—
402C2—1202no—
403C2—1202no—
404C2#1175077211yescharacteristic
405C2#1175084811yescharacteristic
406C2#1175085411yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#343C2
socleC22×C3×C5#120
hypercenter#343D15
hypocenterC3×C5#2006
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#91797C2semidirect
2. #11756269C2semidirect
3. C2×#91109C2semidirect
4. #11751089C2semidirect
5. C3×C5×#343C2semidirect
26. C5×#343D3semidirect
41. C2×D60D4semidirect
45. C3×C5×M16D4semidirect
58. C3×#343D5semidirect
135. C5×M16D12semidirect
148. #343D15semidirect
185. C3×M16D20semidirect
311. M16D60semidirect
318. C3×C5#2006semidirect
380. C5#69008semidirect
399. C3#10599801semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
#117562692
C2×#911092
#117510892
C3×C5×#3432
#105998013
#690085