Finite Group Databasebeta

← #14290871

Subgroups — #14290871

Order 1920.

480 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 96 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#11756314C211yesmaximal, characteristic
2C3×#65296C211yesmaximal, characteristic, complemented
3#11747085C211yesmaximal, characteristic, complemented
4#11746948C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10598978—31nomaximal, Hall
9C2×#6819—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91819—21no—
12C2×C4⋊Dic15—21no—
13#91786—21no—
14#91775—22no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6658—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90987—22no—
25#90971—21no—
26#71111—51nomaximal, Hall
27#65889—31no—
28#65296D311yescharacteristic, complemented
29#65130—31no—
30#64969—31no—
31C5×D4⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C22×Dic15—22no—
38#6819—42no—
39#6819—42no—
40C2×D60D411yescharacteristic
41C2×C4×D15—21no—
42C2×Dic30—21no—
43C2×C3×Dic10—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—22no—
50C4⋊Dic15—21no—
51C4⋊Dic15D411yescharacteristic
52C4⋊Dic15D412yes—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58#6658—42no—
59#5555—51no—
60C3×#474—51no—
61#5083—51no—
62#5080—51no—
63D4⋊(C3⋊C8)D511yescharacteristic, complemented
64#4483—51no—
65#4482—51no—
66C2×#711—61no—
67C4×C5×D4C2×D311yescharacteristic
68#4076—61no—
69C2×C4⋊Dic5—61no—
70C2×#677—61no—
71#4043—61no—
72#4032—62no—
73C4×D20—31no—
74#4015—31no—
75#4015C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3964—21no—
79#3949—62no—
80#3948—61no—
81#3939—21no—
82C4⋊#168C2×D311yescharacteristic
83#1654—151noSylow
84C23×C3×C5—21no—
85C22×D15—21no—
86C3×C5×D4—21no—
87C3×C5×D4SD1612yescomplemented
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—
95C2×Dic15—22no—
96C2×Dic15—21no—
97C2×Dic15—44no—
98D60—21no—
99D60—21no—
100C4×D15—41no—
101C4×D15—41no—
102Dic30—41no—
103Dic30—41no—
104C2×C3×Dic5—41no—
105C3×Dic10—41no—
106C3×Dic10—41no—
107C3×#168—41no—
108C5×C3⋊C8—22no—
109C5×C3⋊C8—41no—
110C2×#237—101no—
111C3×C4⋊Q8—51no—
112C3×C4×D4C2×D511yescharacteristic
113C2×#215—101no—
114#930—101no—
115C2×C4⋊Dic3—101no—
116#897—101no—
117#886—102no—
118C4×D12—51no—
119#869—51no—
120C3×#107—101no—
121C3×C4⋊C8—51no—
122C3×#102—101no—
123#835—101no—
124#808—102no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C4×C3⋊C8C2×D511yescharacteristic
127C2×C5×D4#6711yescharacteristic
128C22×C4×C5—21no—
129C2×C22⋊D5—62no—
130C22×Dic5—62no—
131#711—122no—
132#711—122no—
133C2×D20—31no—
134C2×C4×D5—61no—
135C2×Dic10—21no—
136C2×Dic10—61no—
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C5×C4⋊C4#6711yescharacteristic
140C5×C22⋊C4—21no—
141C42×C5C22×D311yescharacteristic
142#685—62no—
143#685—61no—
144C4⋊Dic5—21no—
145C4⋊Dic5—21no—
146C4⋊Dic5—31no—
147C4⋊Dic5—32no—
148C4⋊Dic5—62no—
149C4⋊Dic5—61no—
150C2×#168—21no—
151#677—122no—
152#547—151no—
153#498—151no—
154#474—51no—
155#461—151no—
156#332—151no—
157D4⋊C8—31no—
158D4⋊C8—151no—
159C22×C3×C5—22no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C2×D15—41no—
164C2×D15—41no—
165C2×D15—41no—
166C3×C4×C5—21no—
167C3×C4×C5—41no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172Dic15—42no—
173Dic15—41no—
174C3×Dic5—81no—
175C2×C3×Q8—101no—
176C2×C3×D4D2011yescharacteristic
177C22×C3×C4—21no—
178C2×#67—102no—
179C22×Dic3—102no—
180#237—202no—
181#237—202no—
182C2×D12—51no—
183C2×C4×D3—101no—
184C2×Dic6—101no—
185C2×C3×C8—101no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4D2011yescharacteristic
189C3×C22⋊C4—21no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192(C2×D3)⋊C4—102no—
193(C2×D3)⋊C4—101no—
194C4⋊Dic3—52no—
195C4⋊Dic3—51no—
196C4⋊Dic3—102no—
197C4⋊Dic3—101no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C23×C5—21no—
201C22×D5—61no—
202C5×D4—21no—
203C5×D4#21512yescomplemented
204C2×C4×C5—21no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C22⋊D5—124no—
211C2×Dic5—41no—
212C2×Dic5—62no—
213C2×Dic5—61no—
214C2×Dic5—124no—
215D20—61no—
216D20—61no—
217C4×D5—121no—
218C4×D5—121no—
219Dic10—41no—
220Dic10—41no—
221Dic10—121no—
222Dic10—121no—
223C5×C8—62no—
224C5×C8—121no—
225#168—41no—
226C2×#41—301no—
227C2×SD16—301no—
228C4⋊Q8—51no—
229C4⋊Q8—151no—
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—151no—
234C4×D4D3×D511yescharacteristic
235C2×C4⋊C4—301no—
236#107—101no—
237#106—302no—
238C4⋊C8—31no—
239C4⋊C8—51no—
240#103—301no—
241#102—101no—
242C4×C8—31no—
243C2×C3×C5—42no—
244C2×C3×C5#44911yescharacteristic
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45611yescharacteristic
247D15—81no—
248C23×C3—21no—
249C22×D3—101no—
250C3×Q8—201no—
251C3×Q8—201no—
252C3×D4—21no—
253C3×D4#67712yescomplemented
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—201no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261#67—204no—
262C2×Dic3—102no—
263C2×Dic3—101no—
264C2×Dic3—204no—
265D12—101no—
266D12—101no—
267C4×D3—201no—
268C4×D3—201no—
269Dic6—201no—
270Dic6—201no—
271C3×C8—201no—
272C3⋊C8—22no—
273C3⋊C8—41no—
274C22×C5—22no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5#93711yescharacteristic
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—121no—
281C4×C5—21no—
282C4×C5—41no—
283C4×C5#91111yescharacteristic
284C4×C5#91211yescharacteristic
285C4×C5C2×#21511yescharacteristic
286C4×C5#94911yescharacteristic
287Dic5—81no—
288Dic5—122no—
289Dic5—121no—
290#41—602no—
291#41—602no—
292C2×Q8—101no—
293C2×Q8—301no—
294C2×D4—151no—
295C2×D4—302no—
296C2×D4#120211yescharacteristic
297C22×C4—21no—
298C22×C4—302no—
299C22×C4—301no—
300SD16—602no—
301C2×C8—61no—
302C2×C8—61no—
303C2×C8—101no—
304C4⋊C4—101no—
305C4⋊C4—101no—
306C4⋊C4—151no—
307C4⋊C4—152no—
308C4⋊C4—302no—
309C4⋊C4—301no—
310C4⋊C4#120211yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—302no—
313C22⋊C4—301no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3—22no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3#402811yescharacteristic
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—401no—
326C3×C4C2×#67711yescharacteristic
327C3×C4#405411yescharacteristic
328C3×C4#405711yescharacteristic
329C3×C4#406211yescharacteristic
330Dic3—202no—
331Dic3—201no—
332C2×C5—42no—
333C2×C5#504611yescharacteristic
334C2×C5#515811yescharacteristic
335C2×C5#520511yescharacteristic
336D5—241no—
337C23—21no—
338C23—301no—
339Q8—201no—
340Q8—201no—
341Q8—601no—
342Q8—601no—
343D4—21no—
344D4—301no—
345D4—301no—
346D4—604no—
347D4#665812yescomplemented
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—201no—
352C2×C4—301no—
353C2×C4—302no—
354C2×C4—604no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4C2×#120211yescharacteristic
358C2×C4#679011yescharacteristic
359C2×C4#679011yescharacteristic
360C8—62no—
361C8—121no—
362C8—201no—
363C2×C3—42no—
364C2×C3#6502011yescharacteristic
365C2×C3#6507011yescharacteristic
366C2×C3#6511511yescharacteristic
367D3—401no—
368C5#7111111yescharacteristic, complemented, Sylow
369C22—22no—
370C22—41no—
371C22—41no—
372C22—601no—
373C22—601no—
374C22—601no—
375C22#9157211yescharacteristic
376C4—21no—
377C4—41no—
378C4—401no—
379C4—601no—
380C4—602no—
381C4#9130111yescharacteristic
382C4C2×#665811yescharacteristic
383C4#9148211yescharacteristic
384C4#9149711yescharacteristic
385C3#1059897811yescharacteristic, complemented, Sylow
386C2—42no—
387C2—1201no—
388C2#1174855111yescharacteristic
389C2#1174904211yescharacteristic
390C2#1174942411yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radical#11756314C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1654
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×#65296C2semidirect
3. #11747085C2semidirect
4. #11746948C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745860C2semidirect
7. #11745838C2semidirect
28. #65296D3semidirect
63. D4⋊(C3⋊C8)D5semidirect
87. C3×C5×D4SD16semidirect
203. C5×D4#215semidirect
253. C3×D4#677semidirect
315. C3×C5#1654semidirect
347. D4#6658semidirect
368. C5#71111semidirect
385. C3#10598978semidirect

Maximal subgroups

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

subgroupindex
#117563142
C3×#652962
#117470852
#117469482
C5×D4⋊(C3⋊C8)2
#117458602
#117458382
#105989783
#711115