Finite Group Databasebeta

← #14290008

Subgroups — #14290008

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, characteristic
2#11751171C211yesmaximal, characteristic, complemented
3#11751132C211yesmaximal, characteristic, complemented
4#11751108C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602713—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#127—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C5×#121—22no—
13C3×C5×#121—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×#6718—21no—
18#91758C2211yescharacteristic
19#91116—22no—
20#91116—21no—
21#91094—21no—
22#91091—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71920—51nomaximal, Hall
27C5×#550D311yescharacteristic
28#65359—31no—
29#65320—31no—
30#65296—31no—
31#64764—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C2×C3×C5×D4D412yes—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—21no—
45C2×Dic30—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53#6718—42no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C3×#550D511yescharacteristic
60#5070—51no—
61#5031—51no—
62#5007—51no—
63#4544—51no—
64#4535—51no—
65D4⋊(C3⋊C8)—51no—
66C2×C5×#41—21no—
67C5×#127—21no—
68C5×#127C2×D311yescharacteristic
69C5×#121—22no—
70C5×#121—21no—
71C4×C5×Q8C2×D311yescharacteristic
72C4×C5×D4—21no—
73C4×C5×D4C2×D311yescharacteristic
74C2×#689—61no—
75#4015—31no—
76#3964—61no—
77#3964—62no—
78#3942—61no—
79#3939—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1641—151noSylow
84C23×C3×C5—21no—
85C23×C3×C5—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8D812yes—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—44no—
91C3×C5×D4—42no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—82no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—44no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—41no—
107Dic30—41no—
108Dic30—41no—
109C3⋊#168—41no—
110C3⋊#168—41no—
111C3⋊#168—41no—
112C2×C3×#41—21no—
113C3×#127—21no—
114C3×#127C2×D511yescharacteristic
115C3×#121—22no—
116C3×#121—21no—
117C3×C4×Q8C2×D511yescharacteristic
118C3×C4×D4—21no—
119C3×C4×D4C2×D511yescharacteristic
120C2×#216—101no—
121#869—51no—
122#832—101no—
123#832—102no—
124#810—101no—
125#807—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)—51no—
128C4×C3⋊C8—51no—
129C5×#41—42no—
130C5×#41—42no—
131C2×C5×Q8#6711yescharacteristic
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4#6711yescharacteristic
137C2×C5×D4#6712yes—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C2×Dic10—61no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4#6711yescharacteristic
143C5×C4⋊C4#6711yescharacteristic
144C5×C22⋊C4—22no—
145C5×C22⋊C4—21no—
146C42×C5—21no—
147C42×C5C22×D311yescharacteristic
148#689—122no—
149C4⋊Dic5—61no—
150C4⋊Dic5—61no—
151C2×#168—61no—
152C2×#168—61no—
153C2×#168—61no—
154#550D1511yescharacteristic
155#486—151no—
156#474—151no—
157#462—151no—
158#331—151no—
159Q8⋊C8—151no—
160D4⋊C8—151no—
161C22×C3×C5—42no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5—42no—
165C22×C3×C5—42no—
166C22×C3×C5—41no—
167C22×C3×C5#12011yescharacteristic
168C3×C4×C5—22no—
169C3×C4×C5—21no—
170C3×C4×C5—41no—
171C3×C4×C5—41no—
172C3×C4×C5C2×D811yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5#13711yescharacteristic
176Dic15—81no—
177C3×#41—42no—
178C3×#41—42no—
179C2×C3×Q8C22⋊D511yescharacteristic
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4C22⋊D511yescharacteristic
185C2×C3×D4C22⋊D512yes—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C2×Dic6—101no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4C22⋊D511yescharacteristic
191C3×C4⋊C4C22⋊D511yescharacteristic
192C3×C22⋊C4—22no—
193C3×C22⋊C4—21no—
194C3×C42—21no—
195C3×C42C22×D511yescharacteristic
196#216—202no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C2×C3⋊C8—101no—
202C23×C5—21no—
203C23×C5—22no—
204C5×Q8—21no—
205C5×Q8#21312yes—
206C5×D4—21no—
207C5×D4—21no—
208C5×D4—42no—
209C5×D4—44no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C5×D4—41no—
214C5×D4—82no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—44no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×Dic5—121no—
225Dic10—121no—
226Dic10—121no—
227#168—121no—
228#168—121no—
229#168—121no—
230C2×#41—21no—
231C2×Q16—301no—
232C4⋊Q8—151no—
233#127—21no—
234#127C2×D1511yescharacteristic
235#121—22no—
236#121—21no—
237C4×Q8C2×D1511yescharacteristic
238C4×D4—21no—
239C4×D4C2×D1511yescharacteristic
240#107—301no—
241C4⋊C8—151no—
242C4⋊C8—151no—
243#103—301no—
244#102—301no—
245#102—302no—
246C4×C8—151no—
247C2×C3×C5—81no—
248C2×C3×C5—82no—
249C2×C3×C5#44711yescharacteristic
250C2×C3×C5#45211yescharacteristic
251C2×C3×C5#45511yescharacteristic
252C23×C3—21no—
253C23×C3—22no—
254C3×Q8—21no—
255C3×Q8#68612yes—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—42no—
259C3×D4—44no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—82no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—44no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4C2×C22⋊D511yescharacteristic
272C2×C3×C4C2×C22⋊D511yescharacteristic
273C2×C3×C4C2×C22⋊D511yescharacteristic
274C2×Dic3—201no—
275Dic6—201no—
276Dic6—201no—
277C3⋊C8—201no—
278C3⋊C8—201no—
279C3⋊C8—201no—
280C22×C5—42no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—42no—
284C22×C5—42no—
285C22×C5—41no—
286C22×C5#95311yescharacteristic
287C4×C5—22no—
288C4×C5—21no—
289C4×C5—41no—
290C4×C5—41no—
291C4×C5C2×#21311yescharacteristic
292C4×C5#93211yescharacteristic
293C4×C5#95011yescharacteristic
294C4×C5#95111yescharacteristic
295Dic5—241no—
296#41—42no—
297#41—42no—
298C2×Q8—301no—
299C2×Q8#122011yescharacteristic
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4#122011yescharacteristic
305C2×D4#122012yes—
306C22×C4—22no—
307C22×C4—21no—
308Q16—602no—
309C2×C8—301no—
310C2×C8—301no—
311C2×C8—301no—
312C4⋊C4—21no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4#122011yescharacteristic
316C4⋊C4#122011yescharacteristic
317C22⋊C4—22no—
318C22⋊C4—21no—
319C42—21no—
320C42C22×D1511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—42no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—41no—
328C22×C3#409911yescharacteristic
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4C2×#68611yescharacteristic
334C3×C4#407811yescharacteristic
335C3×C4#409611yescharacteristic
336C3×C4#409711yescharacteristic
337Dic3—401no—
338C2×C5—81no—
339C2×C5—82no—
340C2×C5#521711yescharacteristic
341C2×C5#523911yescharacteristic
342C2×C5#524211yescharacteristic
343C23—21no—
344C23—22no—
345Q8—21no—
346Q8—601no—
347Q8—601no—
348Q8#671512yes—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—44no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—82no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—601no—
365C2×C4C2×#122011yescharacteristic
366C2×C4C2×#122011yescharacteristic
367C2×C4C2×#122011yescharacteristic
368C8—601no—
369C8—601no—
370C8—601no—
371C2×C3—81no—
372C2×C3—82no—
373C2×C3#6550611yescharacteristic
374C2×C3#6552811yescharacteristic
375C2×C3#6553111yescharacteristic
376C5#7192011yescharacteristic, complemented, Sylow
377C22—42no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22#9184211yescharacteristic
384C4—22no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—1201no—
389C4C2×#671511yescharacteristic
390C4#9182111yescharacteristic
391C4#9183911yescharacteristic
392C4#9184011yescharacteristic
393C3#1060271311yescharacteristic, complemented, Sylow
394C2—81no—
395C2—82no—
396C2#1175131811yescharacteristic
397C2#1175134011yescharacteristic
398C2#1175134311yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#550C2
socleC22×C3×C5#120
hypercenter#550D15
hypocenterC3×C5#1641
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
2. #11751171C2semidirect
3. #11751132C2semidirect
4. #11751108C2semidirect
5. #11746365C2semidirect
6. #11746356C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
321. C3×C5#1641semidirect
376. C5#71920semidirect
393. C3#10602713semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5502
#117511712
#117511322
#117511082
#117463652
#117463562
D4⋊(C3⋊#168)2
#106027133
#719205