Finite Group Databasebeta

← #14289295

Subgroups — #14289295

Order 1920.

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

normal subgroups only

This group has 432 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#11752508C211yesmaximal, characteristic, complemented
2#11751176C211yesmaximal, characteristic, complemented
3C5×#5070C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic
5#11745858C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10601990—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6716—21no—
11C4×Dic30C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C2×C3×#686—21no—
14C3×C4×D20C2211yescharacteristic
15#91368—21no—
16#91361—22no—
17#91360—21no—
18#91358—21no—
19#91344—21no—
20#91116—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#832—22no—
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3964—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71019—51nomaximal, Hall
27#66066—31no—
28C5×#486—31no—
29#65364—31no—
30#65361D311yescharacteristic
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×Dic6—21no—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C3×C42×C5C2311yescharacteristic
42#6716—42no—
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3D412yes—
49C2×C5×C3⋊C8—21no—
50C3×#686—42no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6665—22no—
56#6665—22no—
57Dic3×Dic5—22no—
58#5542—51no—
59C3×#459—51no—
60#5075—51no—
61#5070D511yescharacteristic, complemented
62D4⋊(C3⋊C8)—51no—
63#4484—51no—
64#4482—51no—
65C5×C4⋊Q8—31no—
66C5×#127C2×D311yescharacteristic
67#4093—61no—
68Q8×Dic5—61no—
69C2×#687—61no—
70C2×#686—21no—
71#4044—62no—
72#4043—61no—
73#4038—61no—
74C4×D20C2×D311yescharacteristic
75C4×Dic10—31no—
76C5×#102—62no—
77C4×C5×C8—31no—
78#3964—21no—
79#3964—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1628—151noSylow
83C23×C3×C5—41no—
84C22×C3×D5—21no—
85C3×C5×D4—42no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95Dic30—21no—
96Dic30—21no—
97C2×C5×Dic3—22no—
98C5×Dic6—41no—
99C5×Dic6—41no—
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20—21no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105C3⋊#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×C3×D8—101no—
109C3×#127C2×D511yescharacteristic
110C3×C4×D4—51no—
111#936—101no—
112C2×#214—101no—
113#926—101no—
114#924—101no—
115#887—101no—
116#879—102no—
117#869C2×D511yescharacteristic
118C4×Dic6—51no—
119C3×C4⋊C8—51no—
120C3×#102—101no—
121#832—22no—
122#832—101no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8—61no—
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×D20#6711yescharacteristic
130C2×C4×D5—21no—
131C2×Dic10—31no—
132C2×C5×C8—61no—
133C5×C4⋊C4—32no—
134C5×C4⋊C4—61no—
135C42×C5C22×D311yescharacteristic
136#687—122no—
137#686—42no—
138#685—21no—
139#685—62no—
140#685—62no—
141C4⋊Dic5—31no—
142C4⋊Dic5—62no—
143C4⋊Dic5#6711yescharacteristic
144#683—61no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—21no—
148C2×#168—61no—
149#556—151no—
150#486—31no—
151#460—151no—
152#459—51no—
153#332—151no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5—81no—
157C22×C3×C5—81no—
158C22×C3×C5—81no—
159C22×C3×C5#12011yescharacteristic
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168Dic15—41no—
169Dic15—41no—
170C3×Dic5—41no—
171C5×Dic3—42no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—51no—
176C22×C3×C4—101no—
177C2×Dic6—21no—
178C2×Dic6—51no—
179C3×D8—202no—
180C2×C3×C8—101no—
181C3×C4⋊C4—51no—
182C3×C22⋊C4—101no—
183C3×C42C22×D511yescharacteristic
184#217—102no—
185#217—102no—
186#214—202no—
187C4⋊Dic3—21no—
188C4⋊Dic3—51no—
189C4⋊Dic3C22⋊D512yes—
190Dic3⋊C4—102no—
191Dic3⋊C4—101no—
192C4×Dic3—102no—
193C4×Dic3—101no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C23×C5—41no—
197C22×D5—21no—
198C5×Q8—121no—
199C5×Q8—121no—
200C5×D4—42no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—41no—
205C2×C4×C5—62no—
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—21no—
210C2×Dic5—61no—
211C2×Dic5—61no—
212D20—21no—
213D20—21no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—61no—
217Dic10—61no—
218C5×C8—121no—
219#168—41no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—101no—
223C4⋊Q8—31no—
224#127D3×D511yescharacteristic
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—151no—
229C4×Q8—301no—
230C4×D4—51no—
231#117—301no—
232C4⋊C8—51no—
233C4⋊C8—151no—
234#102—62no—
235#102—101no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5—161no—
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#44911yescharacteristic
241C2×C3×C5#45411yescharacteristic
242C3×D5—81no—
243C23×C3—41no—
244C23×C3—101no—
245C3×D4—42no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—101no—
251C3×D4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—201no—
254C2×C3×C4—201no—
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×Dic3—22no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261Dic6—41no—
262Dic6—41no—
263Dic6—101no—
264Dic6—101no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5—81no—
269C22×C5—81no—
270C22×C5—81no—
271C22×C5#93711yescharacteristic
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—122no—
277C4×C5#91111yescharacteristic
278C4×C5#91211yescharacteristic
279C4×C5#93211yescharacteristic
280C4×C5#95011yescharacteristic
281Dic5—41no—
282Dic5—121no—
283Dic5—121no—
284C2×Q8—61no—
285C2×Q8—151no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—51no—
290C22×C4—101no—
291SD16—602no—
292D8—202no—
293C2×C8—61no—
294C2×C8—101no—
295C2×C8—301no—
296C4⋊C4—32no—
297C4⋊C4—51no—
298C4⋊C4—61no—
299C4⋊C4—151no—
300C4⋊C4—302no—
301C4⋊C4—301no—
302C22⋊C4—101no—
303C22⋊C4—302no—
304C22⋊C4—302no—
305C42—302no—
306C42—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—81no—
310C22×C3—81no—
311C22×C3—81no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—201no—
318C3×C4#405711yescharacteristic
319C3×C4#405811yescharacteristic
320C3×C4#406011yescharacteristic
321C3×C4#406211yescharacteristic
322Dic3—42no—
323Dic3—201no—
324Dic3—201no—
325C2×C5—161no—
326C2×C5#503711yescharacteristic
327C2×C5#515811yescharacteristic
328C2×C5#520111yescharacteristic
329D5—81no—
330C23—41no—
331C23—101no—
332Q8—121no—
333Q8—121no—
334Q8—301no—
335Q8—301no—
336D4—42no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—101no—
342D4—101no—
343C2×C4—62no—
344C2×C4—101no—
345C2×C4—201no—
346C2×C4—201no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4D5×#6711yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—201no—
354C8—601no—
355C2×C3—161no—
356C2×C3—401no—
357C2×C3#6535111yescharacteristic
358C2×C3#6544711yescharacteristic
359C2×C3#6546111yescharacteristic
360C5#7101911yescharacteristic, complemented, Sylow
361C22—81no—
362C22—81no—
363C22—81no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22#9157711yescharacteristic
368C4—21no—
369C4—122no—
370C4—201no—
371C4—601no—
372C4—601no—
373C4#9148911yescharacteristic
374C4#9149011yescharacteristic
375C4#9149711yescharacteristic
376C4#9149811yescharacteristic
377C3#1060199011yescharacteristic, complemented, Sylow
378C2—161no—
379C2—401no—
380C2#1174915811yescharacteristic
381C2#1174915911yescharacteristic
382C2#1174916711yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC3×#65361C2
hypercenter#127D3×D5
hypocenterC3×C5#1628
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. #11752508C2semidirect
2. #11751176C2semidirect
3. C5×#5070C2semidirect
5. #11745858C2semidirect
6. #11745844C2semidirect
7. #11745835C2semidirect
61. #5070D5semidirect
308. C3×C5#1628semidirect
360. C5#71019semidirect
377. C3#10601990semidirect

Maximal subgroups

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

subgroupindex
#117525082
#117511762
C5×#50702
C3×#653612
#117458582
#117458442
#117458352
#106019903
#710195