Finite Group Databasebeta

← #14289062

Subgroups — #14289062

Order 1920.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752710C211yesmaximal, characteristic, complemented
2#11751173C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic, complemented
4C3×#65365C211yesmaximal, characteristic, complemented
5#11745861C211yesmaximal, characteristic, complemented
6#11745839C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601810—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6715—21no—
11C4×D60C2211yescharacteristic
12C2×C5×#213—21no—
13C4×C5×D12C2211yescharacteristic
14C2×C3×#687—22no—
15C3×#4015C2211yescharacteristic
16#91466—21no—
17#91460—21no—
18#91347—21no—
19#91338—21no—
20#91326—22no—
21#91116—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×#832—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26#71265—51nomaximal, Hall
27#65897—31no—
28C5×#459—31no—
29#65365D311yescharacteristic, complemented
30#65361—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×C5×D12D411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C3×Dic10D412yes—
42C2×#1203—22no—
43C3×C42×C5C2311yescharacteristic
44#6715—42no—
45#6714—21no—
46C4⋊Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C5×#213—42no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×#687—44no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6667—22no—
57(C2×D3)⋊Dic5—22no—
58Dic3×Dic5—22no—
59#5734—51no—
60C3×#492—51no—
61#5072—51no—
62#5072D511yescharacteristic, complemented
63#4546—51no—
64#4459—51no—
65#4459—51no—
66C2×C5×D8—61no—
67C5×#127C2×D311yescharacteristic
68C4×C5×D4—31no—
69#4084—61no—
70C2×#687—22no—
71C2×#686—61no—
72#4076—61no—
73#4072—61no—
74#4038—61no—
75#4031—62no—
76C4×D20—31no—
77#4015C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—61no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1624—151noSylow
84C23×C3×C5—41no—
85C22×D15—21no—
86C22×C5×D3—21no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96D60—21no—
97D60—21no—
98C4×D15—41no—
99C4×D15—41no—
100C2×C5×Dic3—21no—
101C5×D12—21no—
102C5×D12—21no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C2×C3×Dic5—22no—
106C3×Dic10—42no—
107#1203—82no—
108C3⋊#168—41no—
109C3×#168—22no—
110C5×C3⋊C8—41no—
111C2×C3×SD16—102no—
112C3×C4⋊Q8—51no—
113C3×#127C2×D511yescharacteristic
114#947—102no—
115C2×#213—21no—
116C2×#213—101no—
117#895—101no—
118#895—101no—
119#892—101no—
120#892—101no—
121C4×D12—51no—
122C4×D12C2×D511yescharacteristic
123C3×C4×C8—51no—
124#832—21no—
125#832—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—31no—
132C22×C4×C5—61no—
133C2×C22⋊D5—62no—
134C2×D20—31no—
135C2×C4×D5—61no—
136C2×Dic10#6712yes—
137C5×D8—122no—
138C2×C5×C8—61no—
139C5×C4⋊C4—31no—
140C5×C22⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142C22⋊Dic5—62no—
143#687—44no—
144#686—122no—
145#685—62no—
146#685—61no—
147C4⋊Dic5—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5—31no—
150C4×Dic5—62no—
151C2×#168—21no—
152C2×#168—61no—
153#555—151no—
154#492—51no—
155#459—31no—
156#459—151no—
157#333—151no—
158D4⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—81no—
161C22×C3×C5—81no—
162C22×C3×C5—81no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—41no—
165C2×D15—41no—
166C2×D15—41no—
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C2×C5×D3—41no—
170C3×C4×C5—21no—
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175Dic15—41no—
176C3×Dic5—42no—
177C5×Dic3—41no—
178C2×C3×Q8—52no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×D12—51no—
183C2×D12—102no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—101no—
187C3×SD16—204no—
188C2×C3×C8—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C42C22×D511yescharacteristic
192#213—42no—
193#213—202no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—102no—
196(C2×D3)⋊C4—102no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—51no—
199C4⋊Dic3C22⋊D511yescharacteristic
200C4×Dic3—102no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—101no—
203C23×C5—41no—
204C23×C5—61no—
205C22×D5—61no—
206C5×D4—42no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—61no—
212C5×D4—61no—
213C2×C4×C5—61no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5C2×#6711yescharacteristic
219C22⋊D5—242no—
220C2×Dic5—22no—
221C2×Dic5—61no—
222D20—61no—
223D20—61no—
224C4×D5—121no—
225C4×D5—121no—
226Dic10—42no—
227C5×C8—121no—
228#168—22no—
229#168—121no—
230C2×SD16—102no—
231C2×D8—61no—
232C2×D8—301no—
233C4⋊Q8—51no—
234#127D3×D511yescharacteristic
235#124—302no—
236#121—301no—
237#121—301no—
238C4×D4—31no—
239C4×D4—151no—
240#117—301no—
241#117—301no—
242C4⋊C8—31no—
243C4⋊C8—151no—
244#102—61no—
245#102—301no—
246C4×C8—51no—
247C2×C3×C5—161no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251D15—81no—
252C5×D3—81no—
253C23×C3—41no—
254C22×D3—21no—
255C22×D3—101no—
256C3×Q8—202no—
257C3×D4—42no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C2×C3×C4—102no—
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—101no—
268D12—21no—
269D12—21no—
270D12—101no—
271D12—101no—
272D12—402no—
273C4×D3—41no—
274C4×D3—41no—
275C4×D3—201no—
276C4×D3—201no—
277C3×C8—102no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5—121no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5#93711yescharacteristic
287C2×D5—121no—
288C2×D5—121no—
289C2×D5—121no—
290C4×C5—21no—
291C4×C5—121no—
292C4×C5#91411yescharacteristic
293C4×C5#91411yescharacteristic
294C4×C5#91611yescharacteristic
295C4×C5#91611yescharacteristic
296Dic5—42no—
297Dic5—121no—
298C2×Q8—52no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—31no—
303C2×D4—151no—
304C2×D4—302no—
305C22×C4—61no—
306C22×C4—301no—
307SD16—204no—
308D8—122no—
309D8—602no—
310C2×C8—61no—
311C2×C8—101no—
312C2×C8—301no—
313C4⋊C4—31no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C22⋊C4—61no—
318C22⋊C4—302no—
319C22⋊C4—302no—
320C22⋊C4—301no—
321C42—302no—
322C42C2×D3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3#408311yescharacteristic
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—201no—
332C2×D3—201no—
333C2×D3—201no—
334C3×C4—21no—
335C3×C4—202no—
336C3×C4#405711yescharacteristic
337C3×C4#405811yescharacteristic
338C3×C4#407811yescharacteristic
339C3×C4#409611yescharacteristic
340Dic3—41no—
341Dic3—201no—
342C2×C5—161no—
343C2×C5—241no—
344C2×C5#507711yescharacteristic
345C2×C5#517211yescharacteristic
346C2×C5#517211yescharacteristic
347D5—241no—
348C23—41no—
349C23—61no—
350C23—301no—
351Q8—202no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—61no—
358D4—61no—
359D4—301no—
360D4—301no—
361D4—1202no—
362C2×C4—61no—
363C2×C4—102no—
364C2×C4—121no—
365C2×C4—121no—
366C2×C4—301no—
367C2×C4—601no—
368C2×C4—601no—
369C2×C4D5×#6711yescharacteristic
370C2×C4D3×C22⋊D511yescharacteristic
371C2×C4#679011yescharacteristic
372C8—102no—
373C8—121no—
374C8—601no—
375C2×C3—161no—
376C2×C3#6532611yescharacteristic
377C2×C3#6544711yescharacteristic
378C2×C3#6548711yescharacteristic
379D3—81no—
380D3—401no—
381C5#7126511yescharacteristic, complemented, Sylow
382C22—81no—
383C22—81no—
384C22—81no—
385C22—121no—
386C22—121no—
387C22—121no—
388C22—601no—
389C22—601no—
390C22—601no—
391C22#9157711yescharacteristic
392C4—21no—
393C4—121no—
394C4—202no—
395C4—601no—
396C4#9149511yescharacteristic
397C4#9149611yescharacteristic
398C4#9149911yescharacteristic
399C4#9150011yescharacteristic
400C3#1060181011yescharacteristic, complemented, Sylow
401C2—161no—
402C2—241no—
403C2—1201no—
404C2#1174916111yescharacteristic
405C2#1174916211yescharacteristic
406C2#1174916311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11752710C2semidirect
2. #11751173C2semidirect
3. C5×#5072C2semidirect
4. C3×#65365C2semidirect
5. #11745861C2semidirect
6. #11745839C2semidirect
7. #11745837C2semidirect
29. #65365D3semidirect
62. #5072D5semidirect
323. C3×C5#1624semidirect
381. C5#71265semidirect
400. C3#10601810semidirect

Maximal subgroups

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

subgroupindex
#117527102
#117511732
C5×#50722
C3×#653652
#117458612
#117458392
#117458372
#106018103
#712655