Finite Group Databasebeta

← #14289470

Subgroups — #14289470

Order 1920.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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#11756312C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic, complemented
3#11747075C211yesmaximal, characteristic, complemented
4#11746917C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745854C211yesmaximal, characteristic, complemented
7#11745844C211yesmaximal, characteristic, complemented
8#10598981—31nomaximal, Hall
9C2×#6817—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91829—21no—
12#91819—21no—
13#91782—21no—
14#91773—22no—
15#91763C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6658—22no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3940—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90990—21no—
25#90974—21no—
26#71141—51nomaximal, Hall
27#65887—31no—
28#65297D311yescharacteristic, complemented
29#65139—31no—
30#64982—31no—
31C5×D4⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C2×#1220—22no—
38#6817—42no—
39#6817—42no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60D412yes—
43C2×C4×D15—22no—
44C2×Dic30D411yescharacteristic
45C2×C3×Dic10—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—22no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58#6658—44no—
59#5553—51no—
60C3×#476—51no—
61#5091—51no—
62#5085—51no—
63D4⋊(C3⋊C8)D511yescharacteristic, complemented
64#4485—51no—
65#4484—51no—
66C2×#709—61no—
67C4×C5×D4C2×D311yescharacteristic
68#4086—61no—
69#4076—61no—
70C2×#677—62no—
71#4039—61no—
72#4030—62no—
73#4020—31no—
74#4015C2×D311yescharacteristic
75C4×Dic10—31no—
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3964—21no—
79#3950—61no—
80#3948—61no—
81#3940—21no—
82C4⋊#168C2×D311yescharacteristic
83#1631—151noSylow
84C23×C3×C5—21no—
85C22×D15—22no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—44no—
95#1220—82no—
96C2×Dic15—21no—
97C2×Dic15—21no—
98D60—42no—
99D60—41no—
100D60—41no—
101D60—41no—
102D60—41no—
103C4×D15—44no—
104Dic30—21no—
105Dic30SD1612yescomplemented
106C2×C3×Dic5—41no—
107C3×Dic10—42no—
108C3×#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C2×#235—101no—
112C3×C4⋊Q8—51no—
113C3×C4×D4C2×D511yescharacteristic
114C2×#215—102no—
115#940—101no—
116#930—101no—
117#893—101no—
118#884—102no—
119#874—51no—
120C4×Dic6—51no—
121C3×#106—101no—
122C3×C4⋊C8—51no—
123C3×#102—101no—
124#810—101no—
125#807—101no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—62no—
131C2×C22⋊D5—62no—
132#709—122no—
133#709—122no—
134C2×D20—32no—
135C2×D20—61no—
136C2×D20—61no—
137C2×C4×D5—62no—
138C2×Dic10—21no—
139C2×Dic10—31no—
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4#6711yescharacteristic
143C5×C22⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145#685—62no—
146C4⋊Dic5—21no—
147C4⋊Dic5—21no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—21no—
152#677—124no—
153#550—151no—
154#492—151no—
155#477—151no—
156#476—51no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—31no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—42no—
165C2×D15—42no—
166C2×D15—42no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—22no—
174Dic15—41no—
175C3×Dic5—81no—
176C2×C3×Q8—101no—
177C2×C3×D4D2011yescharacteristic
178C22×C3×C4—21no—
179C2×#67—102no—
180C2×#67—102no—
181#235—202no—
182#235—202no—
183C2×D12—52no—
184C2×D12—101no—
185C2×D12—101no—
186C2×C4×D3—102no—
187C2×Dic6—51no—
188C2×C3×C8—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4D2011yescharacteristic
192C3×C22⋊C4—21no—
193C3×C42C22×D511yescharacteristic
194#215—204no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3—51no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C23×C5—21no—
202C22×D5—62no—
203C5×D4—21no—
204C5×D4—21no—
205C2×C4×C5—21no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C22⋊D5—124no—
212C22⋊D5—242no—
213C2×Dic5—41no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216D20—122no—
217D20—121no—
218D20—121no—
219D20—121no—
220D20—121no—
221C4×D5—124no—
222Dic10—32no—
223Dic10—42no—
224Dic10—61no—
225C5×C8—62no—
226C5×C8—121no—
227#168—41no—
228C2×#41—301no—
229C2×SD16—302no—
230C4⋊Q8—51no—
231#127—151no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8—151no—
236C4×D4—301no—
237C4×D4D3×D511yescharacteristic
238#107—301no—
239#106—101no—
240C4⋊C8—31no—
241C4⋊C8—51no—
242#103—301no—
243#102—101no—
244C4×C8—31no—
245C2×C3×C5—81no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249D15—82no—
250C23×C3—21no—
251C22×D3—102no—
252C3×Q8—202no—
253C3×D4—21no—
254C3×D4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—201no—
259C2×C3×C4C2×D2011yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—101no—
265C2×Dic3—101no—
266D12—202no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—204no—
272Dic6—52no—
273Dic6—101no—
274C3×C8—201no—
275C3⋊C8—22no—
276C3⋊C8—41no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5#93711yescharacteristic
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5D3×SD1611yescharacteristic
287C4×C5#91411yescharacteristic
288C4×C5#94211yescharacteristic
289C4×C5#95011yescharacteristic
290Dic5—62no—
291Dic5—81no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—101no—
296C2×Q8—151no—
297C2×D4—152no—
298C2×D4—302no—
299C2×D4—302no—
300C2×D4—301no—
301C2×D4—301no—
302C2×D4#120211yescharacteristic
303C22×C4—21no—
304C22×C4—302no—
305SD16—604no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—101no—
309C4⋊C4—101no—
310C4⋊C4—101no—
311C4⋊C4—151no—
312C4⋊C4—301no—
313C4⋊C4#120211yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—302no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3#402811yescharacteristic
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—401no—
329C3×C4#405011yescharacteristic
330C3×C4#405511yescharacteristic
331C3×C4#405711yescharacteristic
332C3×C4D5×SD1611yescharacteristic
333Dic3—102no—
334Dic3—201no—
335C2×C5—81no—
336C2×C5#504711yescharacteristic
337C2×C5#516911yescharacteristic
338C2×C5#519811yescharacteristic
339D5—242no—
340C23—21no—
341C23—302no—
342Q8—152no—
343Q8—202no—
344Q8—301no—
345D4—21no—
346D4—21no—
347D4—602no—
348D4—604no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—1202no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—201no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—604no—
361C2×C4C2×#120211yescharacteristic
362C2×C4#679011yescharacteristic
363C2×C4#679011yescharacteristic
364C8—62no—
365C8—121no—
366C8—201no—
367C2×C3—81no—
368C2×C3#6502211yescharacteristic
369C2×C3#6506511yescharacteristic
370C2×C3#6511111yescharacteristic
371D3—402no—
372C5#7114111yescharacteristic, complemented, Sylow
373C22—41no—
374C22—41no—
375C22—41no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9157211yescharacteristic
380C4—21no—
381C4—41no—
382C4—302no—
383C4—401no—
384C4—601no—
385C4#9131111yescharacteristic
386C4#9131511yescharacteristic
387C4#9148711yescharacteristic
388C4#9150011yescharacteristic
389C3#1059898111yescharacteristic, complemented, Sylow
390C2—81no—
391C2—1202no—
392C2#1174855211yescharacteristic
393C2#1174906411yescharacteristic
394C2#1174942111yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radical#11756312C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65297C2semidirect
3. #11747075C2semidirect
4. #11746917C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745854C2semidirect
7. #11745844C2semidirect
28. #65297D3semidirect
63. D4⋊(C3⋊C8)D5semidirect
105. Dic30SD16semidirect
318. C3×C5#1631semidirect
372. C5#71141semidirect
389. C3#10598981semidirect

Maximal subgroups

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

subgroupindex
#117563122
C3×#652972
#117470752
#117469172
C5×D4⋊(C3⋊C8)2
#117458542
#117458442
#105989813
#711415