Finite Group Databasebeta

← #14307985

Subgroups — #14307985

Order 1920.

812 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 127 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×#91821C212yesmaximal, complemented
2#11756269C211yesmaximal, characteristic, complemented
3C3×C5×#390C211yesmaximal, characteristic, complemented
4C2×#91089C212yesmaximal, complemented
5#11746351C211yesmaximal, characteristic, complemented
6#10600457—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×#6817C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C3×C5×C22⋊C4—22no—
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6716—22no—
13#91821—24no—
14#91821—24no—
15C2×#6715—22no—
16#91819—22no—
17C2×#6710C2212yes—
18#91786—22no—
19#91784—22no—
20#91089—24no—
21#69664—51nomaximal, Hall
22C2×#4078—32no—
23#65844—31no—
24C5×#390D311yescharacteristic, complemented
25C2×#3937—32no—
26#64750—31no—
27C24×C3×C5—21no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4D412yescomplemented
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—22no—
36#6817—22no—
37#6817—22no—
38#6817—22no—
39#6817—22no—
40C2×D60—22no—
41C2×D60D412yes—
42C2×C4×D15—22no—
43C2×Dic30D412yes—
44C3×C5×C4⋊C4—22no—
45C3×C5×C22⋊C4—44no—
46C3×C42×C5—22no—
47#6716—28no—
48#6715—28no—
49#6714—24no—
50C4⋊Dic15—22no—
51#6710—22no—
52#6710D414yescomplemented
53C2×C3⋊#168—22no—
54C2×#932—52no—
55#5510—51no—
56C3×#390D511yescharacteristic, complemented
57C2×#805—52no—
58#4530—51no—
59C22×C5×D4C2×D311yescharacteristic
60C2×#709—32no—
61C2×C5×C4⋊C4C2×D311yescharacteristic
62C2×C5×C22⋊C4—22no—
63C2×C42×C5C2×D311yescharacteristic
64C2×#687—62no—
65#4078—64no—
66#4078—64no—
67C2×#686—62no—
68#4076—62no—
69C2×#681—32no—
70#4043—62no—
71#4041—62no—
72#3937—64no—
73#2006—151noSylow
74C23×C3×C5—22no—
75C23×C3×C5—42no—
76C23×C3×C5—42no—
77C23×C3×C5—41no—
78C23×C3×C5—41no—
79C23×C3×C5C2×D411yescharacteristic
80C22×D15—22no—
81C3×C5×D4—24no—
82C3×C5×D4—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—42no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D412yes—
90C2×C3×C4×C5C2×D412yes—
91C2×C3×C4×C5#4111yescharacteristic
92#1220—42no—
93#1220—42no—
94C2×Dic15—22no—
95D60—22no—
96D60—22no—
97D60—82no—
98C4×D15—42no—
99C4×D15—42no—
100Dic30—22no—
101Dic30—22no—
102C3⋊#168—24no—
103C22×C3×D4C2×D511yescharacteristic
104C2×#235—52no—
105C2×C3×C4⋊C4C2×D511yescharacteristic
106C2×C3×C22⋊C4—22no—
107C2×C3×C42C2×D511yescharacteristic
108C2×#214—102no—
109#932—104no—
110#932—104no—
111C2×#213—102no—
112#930—102no—
113C2×#208—52no—
114#897—102no—
115#895—102no—
116#805—104no—
117C24×C5—21no—
118C2×C5×D4—21no—
119C2×C5×D4—22no—
120C2×C5×D4—22no—
121C2×C5×D4D1212yescomplemented
122C22×C4×C5—21no—
123C22×C4×C5#6712yes—
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—62no—
126#709—62no—
127#709—62no—
128#709—62no—
129#709—62no—
130C2×D20—32no—
131C2×D20—62no—
132C2×C4×D5—62no—
133C2×Dic10—32no—
134C5×C4⋊C4—22no—
135C5×C22⋊C4—44no—
136C42×C5—22no—
137#687—68no—
138#686—68no—
139#685—64no—
140C4⋊Dic5—62no—
141#681—34no—
142#681—62no—
143C2×#168—62no—
144C2×AGL(1,ℤ/8)—152no—
145#537—151no—
146C2×#104—152no—
147#390D1511yescharacteristic, complemented
148#343—151no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—44no—
152C22×C3×C5—42no—
153C22×C3×C5—82no—
154C22×C3×C5—81no—
155C22×C3×C5—81no—
156C22×C3×C5#12011yescharacteristic
157C22×C3×C5#12111yescharacteristic
158C22×C3×C5#12711yescharacteristic
159C2×D15—42no—
160C2×D15—42no—
161C2×D15—42no—
162C3×C4×C5—42no—
163C3×C4×C5—42no—
164C3×C4×C5#12012yes—
165C3×C4×C5#12112yes—
166Dic15—42no—
167C24×C3—21no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4D2012yescomplemented
172C22×C3×C4—21no—
173C22×C3×C4C22⋊D512yes—
174C22×C3×C4C22×D511yescharacteristic
175C2×#67—102no—
176#235—102no—
177#235—102no—
178#235—102no—
179#235—102no—
180C2×D12—52no—
181C2×D12—102no—
182C2×C4×D3—102no—
183C2×Dic6—52no—
184C3×C4⋊C4—22no—
185C3×C22⋊C4—44no—
186C3×C42—22no—
187#214—108no—
188#213—108no—
189(C2×D3)⋊C4—104no—
190C4⋊Dic3—102no—
191#208—54no—
192#208—102no—
193C2×C3⋊C8—102no—
194C23×C5—22no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5—41no—
198C23×C5—41no—
199C23×C5C2×#6711yescharacteristic
200C22×D5—62no—
201C5×D4—24no—
202C5×D4—42no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—42no—
208C2×C4×C5C2×D1211yescharacteristic
209C2×C4×C5#23511yescharacteristic
210C2×C4×C5D3×D412yes—
211C2×C4×C5D3×D412yes—
212C22⋊D5—122no—
213C22⋊D5—122no—
214C2×Dic5—62no—
215D20—62no—
216D20—62no—
217D20—242no—
218C4×D5—122no—
219C4×D5—122no—
220Dic10—62no—
221Dic10—62no—
222#168—64no—
223C2×#41—152no—
224C22×D4C2×D1511yescharacteristic
225AGL(1,ℤ/8)—304no—
226AGL(1,ℤ/8)—304no—
227C2×SD16—302no—
228C2×D8—302no—
229C2×M16—152no—
230C22⋊Q8—302no—
231#121—302no—
232#121—302no—
233C2×C4⋊C4C2×D1511yescharacteristic
234C2×C22⋊C4—22no—
235C2×C42C2×D1511yescharacteristic
236#104—304no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—82no—
240C2×C3×C5#39211yescharacteristic
241C2×C3×C5#45311yescharacteristic
242C2×C3×C5#45411yescharacteristic
243D15—82no—
244C23×C3—22no—
245C23×C3—42no—
246C23×C3—42no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3C2×C22⋊D511yescharacteristic
250C22×D3—102no—
251C3×D4—24no—
252C3×D4—42no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4#70911yescharacteristic
260C2×C3×C4D4×D512yes—
261C2×C3×C4D4×D512yes—
262#67—202no—
263#67—202no—
264C2×Dic3—102no—
265D12—102no—
266D12—102no—
267D12—402no—
268C4×D3—202no—
269C4×D3—202no—
270Dic6—102no—
271Dic6—102no—
272C3⋊C8—104no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—44no—
276C22×C5—42no—
277C22×C5—82no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5#93011yescharacteristic
281C22×C5#93711yescharacteristic
282C22×C5#94011yescharacteristic
283C2×D5—122no—
284C2×D5—122no—
285C2×D5—122no—
286C4×C5—42no—
287C4×C5—42no—
288C4×C5#88212yes—
289C4×C5#88412yes—
290Dic5—122no—
291C24—21no—
292#41—302no—
293#41—302no—
294#41—302no—
295#41—302no—
296C2×Q8—152no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—152no—
301C2×D4—302no—
302C2×D4—302no—
303C2×D4D6012yescomplemented
304C22×C4—21no—
305C22×C4—302no—
306C22×C4#122012yes—
307C22×C4C22×D1511yescharacteristic
308SD16—308no—
309D8—308no—
310M16—154no—
311M16—302no—
312C2×C8—302no—
313C4⋊C4—22no—
314C4⋊C4—302no—
315C22⋊C4—44no—
316C22⋊C4—304no—
317C42—22no—
318C3×C5#200611yescharacteristic, complemented, Hall
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—44no—
322C22×C3—42no—
323C22×C3—82no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3#407611yescharacteristic
327C22×C3#408311yescharacteristic
328C22×C3#408611yescharacteristic
329C2×D3—202no—
330C2×D3—202no—
331C2×D3—202no—
332C3×C4—42no—
333C3×C4—42no—
334C3×C4#402812yes—
335C3×C4#403012yes—
336Dic3—202no—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—82no—
340C2×C5#496011yescharacteristic
341C2×C5#506211yescharacteristic
342C2×C5#507711yescharacteristic
343D5—242no—
344C23—22no—
345C23—42no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—302no—
350C23C2×#122011yescharacteristic
351Q8—302no—
352Q8—302no—
353D4—24no—
354D4—42no—
355D4—302no—
356D4—302no—
357D4—602no—
358D4—602no—
359D4—1202no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—302no—
366C2×C4—602no—
367C2×C4—602no—
368C2×C4C2×D6011yescharacteristic
369C2×C4#681711yescharacteristic
370C2×C4D4×D1512yes—
371C2×C4D4×D1512yes—
372C8—304no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—82no—
376C2×C3#6524911yescharacteristic
377C2×C3#6535111yescharacteristic
378C2×C3#6536611yescharacteristic
379D3—402no—
380C5#6966411yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—44no—
384C22—42no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—602no—
389C22—602no—
390C22—602no—
391C22#9181911yescharacteristic
392C22#9182611yescharacteristic
393C22#9182911yescharacteristic
394C4—42no—
395C4—42no—
396C4—602no—
397C4#9177112yes—
398C4#9177312yes—
399C3#1060045711yescharacteristic, complemented, Sylow
400C2—21no—
401C2—21no—
402C2—82no—
403C2—1202no—
404C2#1175106111yescharacteristic
405C2#1175116311yescharacteristic
406C2#1175117811yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#390C2
socleC22×C3×C5#120
hypercenter#390D15
hypocenterC3×C5#2006
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#91821C2semidirect
2. #11756269C2semidirect
3. C3×C5×#390C2semidirect
4. C2×#91089C2semidirect
5. #11746351C2semidirect
24. C5×#390D3semidirect
31. C2×C3×C5×D4D4semidirect
52. #6710D4semidirect
56. C3×#390D5semidirect
121. C2×C5×D4D12semidirect
147. #390D15semidirect
171. C2×C3×D4D20semidirect
303. C2×D4D60semidirect
318. C3×C5#2006semidirect
380. C5#69664semidirect
399. C3#10600457semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
#117562692
C3×C5×#3902
C2×#910892
#117463512
#106004573
#696645