Finite Group Databasebeta

← #14289315

Subgroups — #14289315

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#11752480C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic, complemented
3#11747083C211yesmaximal, characteristic, complemented
4#11747033C211yesmaximal, characteristic
5#11746277C211yesmaximal, characteristic, complemented
6C5×#4459C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10598994—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91370—21no—
14#91365—21no—
15#91341—22no—
16#91338—21no—
17#91331—21no—
18C2×#6657—21no—
19C2×#6652—21no—
20C3×C4×C5×C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3953—22no—
24#90965—21no—
25#90964—21no—
26#71197—51nomaximal, Hall
27#65876—31no—
28#65304—31no—
29#65137—31no—
30#64983D311yescharacteristic, complemented
31C5×D4⋊C8—31no—
32#64706—31no—
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×Dic10—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D412yes—
52#6668—22no—
53(C2×D3)⋊Dic5—22no—
54(C2×D3)⋊Dic5—22no—
55Dic3×Dic5—22no—
56#6657—42no—
57#6652—42no—
58#5732—51no—
59C3×#486—51no—
60#5075—51no—
61#5072—51no—
62#4547—51no—
63#4459D511yescharacteristic, complemented
64#4456—51no—
65C4×C5×D4—31no—
66#4082—61no—
67C2×#686—61no—
68#4072—61no—
69#4070—61no—
70C2×#677—61no—
71#4033—61no—
72#4025—62no—
73#4020C2×D311yescharacteristic
74#4015C2×D311yescharacteristic
75C4×Dic10—31no—
76C5×C4⋊C8—31no—
77C4×C5×C8C2×D311yescharacteristic
78#3953—22no—
79#3953—61no—
80#3941—61no—
81C4⋊#168—31no—
82#1628—151noSylow
83C22×C5×D3—21no—
84C22×C3×D5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90Dic30—21no—
91Dic30—21no—
92C2×C5×Dic3—21no—
93C5×D12—21no—
94C5×D12—21no—
95C4×C5×D3—41no—
96C4×C5×D3—41no—
97C2×C3×Dic5—22no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C5×C3⋊C8—41no—
108C3×C4⋊Q8—51no—
109C3×#127—51no—
110#947—101no—
111Q8×Dic3—101no—
112C2×#214—101no—
113C2×#213—101no—
114#898—102no—
115#897—101no—
116#892—101no—
117C4×D12C2×D511yescharacteristic
118C4×Dic6—51no—
119C3×#102—102no—
120C3×C4×C8C2×D511yescharacteristic
121#832—101no—
122#832—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C2×C5×D4—31no—
126C22×C4×C5—61no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20—21no—
130C2×Dic10—21no—
131C2×Dic10—31no—
132C2×C5×C8—21no—
133C2×C5×C8—61no—
134C5×C4⋊C4—31no—
135C5×C22⋊C4—61no—
136C42×C5C22×D311yescharacteristic
137C22⋊Dic5—62no—
138C22⋊Dic5—62no—
139#686—122no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4⋊Dic5#6712yes—
143#683—62no—
144#683—61no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—61no—
148#677—122no—
149#556—151no—
150#486—51no—
151#460—151no—
152#459—151no—
153#332—151no—
154Q8⋊C8—151no—
155D4⋊C8—31no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C2×C3×D5—81no—
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—42no—
171C5×Dic3—41no—
172C2×C3×Q8—101no—
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×D12D2011yescharacteristic
177C2×C4×D3—21no—
178C2×Dic6—51no—
179C2×C3×C8—21no—
180C3×C4⋊C4—52no—
181C3×C4⋊C4—101no—
182C3×C42C22×D511yescharacteristic
183#214—202no—
184#213—202no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—102no—
187(C2×D3)⋊C4—102no—
188C4⋊Dic3—51no—
189C4⋊Dic3—102no—
190C4⋊Dic3D2011yescharacteristic
191Dic3⋊C4—101no—
192C4×Dic3—102no—
193C4×Dic3—101no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C23×C5—61no—
197C22×D5—41no—
198C5×D4—61no—
199C5×D4—61no—
200C2×C4×C5—61no—
201C2×C4×C5—121no—
202C2×C4×C5—121no—
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5—22no—
207C2×Dic5—61no—
208C2×Dic5—61no—
209D20—42no—
210D20—41no—
211D20—41no—
212D20—41no—
213D20—41no—
214Dic10—41no—
215Dic10—41no—
216Dic10—61no—
217Dic10—61no—
218C5×C8—41no—
219C5×C8—121no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8—51no—
224#127—51no—
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—151no—
229C4×Q8—301no—
230C4×D4—31no—
231#117—301no—
232C4⋊C8—31no—
233C4⋊C8—151no—
234#102—102no—
235#102—301no—
236#102—301no—
237C4×C8D3×D511yescharacteristic
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—161no—
242C5×D3—81no—
243C23×C3—201no—
244C22×D3—21no—
245C3×Q8—201no—
246C3×Q8—201no—
247C3×D4—202no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C3×D4—201no—
252C2×C3×C4—102no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—101no—
258C2×Dic3—101no—
259D12—21no—
260D12—21no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—101no—
264Dic6—101no—
265C3×C8—41no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5—121no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5#93711yescharacteristic
272C2×D5—81no—
273C2×D5—81no—
274C2×D5—81no—
275C4×C5—21no—
276C4×C5—121no—
277C4×C5#91111yescharacteristic
278C4×C5#91211yescharacteristic
279C4×C5#91411yescharacteristic
280C4×C5#91611yescharacteristic
281Dic5—42no—
282Dic5—121no—
283Dic5—121no—
284C2×Q8—101no—
285C2×Q8—151no—
286C2×D4—31no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—101no—
290C22×C4—61no—
291SD16—602no—
292D8—602no—
293C2×C8—21no—
294C2×C8—61no—
295C2×C8—301no—
296C4⋊C4—31no—
297C4⋊C4—52no—
298C4⋊C4—101no—
299C4⋊C4—151no—
300C4⋊C4—302no—
301C4⋊C4—301no—
302C22⋊C4—61no—
303C22⋊C4—302no—
304C22⋊C4—302no—
305C42—302no—
306C42—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—401no—
310C22×C3—401no—
311C22×C3—401no—
312C22×C3#402811yescharacteristic
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—202no—
318C3×C4#405011yescharacteristic
319C3×C4#405411yescharacteristic
320C3×C4#405711yescharacteristic
321C3×C4#406211yescharacteristic
322Dic3—41no—
323Dic3—201no—
324Dic3—201no—
325C2×C5—241no—
326C2×C5#506211yescharacteristic
327C2×C5#515811yescharacteristic
328C2×C5#517211yescharacteristic
329D5—161no—
330C23—61no—
331C23—201no—
332Q8—201no—
333Q8—201no—
334Q8—301no—
335Q8—301no—
336D4—61no—
337D4—61no—
338D4—202no—
339D4—201no—
340D4—201no—
341D4—201no—
342D4—201no—
343C2×C4—61no—
344C2×C4—102no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4D3×D2011yescharacteristic
350C2×C4#677711yescharacteristic
351C2×C4D5×#6711yescharacteristic
352C8—41no—
353C8—121no—
354C8—601no—
355C2×C3—801no—
356C2×C3#6502311yescharacteristic
357C2×C3#6507011yescharacteristic
358C2×C3#6511611yescharacteristic
359D3—81no—
360C5#7119711yescharacteristic, complemented, Sylow
361C22—121no—
362C22—121no—
363C22—121no—
364C22—401no—
365C22—401no—
366C22—401no—
367C22#9147411yescharacteristic
368C4—21no—
369C4—121no—
370C4—202no—
371C4—601no—
372C4—601no—
373C4#9125411yescharacteristic
374C4#9125711yescharacteristic
375C4#9127311yescharacteristic
376C4#9127611yescharacteristic
377C3#1059899411yescharacteristic, complemented, Sylow
378C2—241no—
379C2—801no—
380C2#1174712111yescharacteristic
381C2#1174788911yescharacteristic
382C2#1174814911yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11747033C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1628
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752480C2semidirect
2. C3×#64983C2semidirect
3. #11747083C2semidirect
5. #11746277C2semidirect
6. C5×#4459C2semidirect
7. #11745855C2semidirect
30. #64983D3semidirect
63. #4459D5semidirect
308. C3×C5#1628semidirect
360. C5#71197semidirect
377. C3#10598994semidirect

Maximal subgroups

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

subgroupindex
#117524802
C3×#649832
#117470832
#117470332
#117462772
C5×#44592
#117458552
#105989943
#711975