Finite Group Databasebeta

← #14281938

Subgroups — #14281938

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752682C211yesmaximal, characteristic
2C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×#6649C211yesmaximal, characteristic, complemented
4#11746305C211yesmaximal, characteristic, complemented
5C5×#4483C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10598963—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C2×C3×C8×D5—21no—
12C3×C42×D5C2211yescharacteristic
13#91449C411yescharacteristic
14#91447—21no—
15C4×#1201—21no—
16#91388C411yescharacteristic
17#91373C411yescharacteristic
18#91372—21no—
19#91371—21no—
20#91360C411yescharacteristic
21C2×#6649—21no—
22C3×C5×C4⋊C8C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25C3×#3946—21no—
26C3×C4⋊#168C2211yescharacteristic
27#90952—21no—
28#70427—51nomaximal, Hall
29#65891—31no—
30D5×C4⋊C8D311yescharacteristic, complemented
31C4×#676—31no—
32C5×D4⋊C8—31no—
33D4⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×Dic30C2×C411yescharacteristic
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×#1201—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15C2×C411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56C3×C8×D5—42no—
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60(C2×D3)⋊Dic5—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63#6665—21no—
64#6649—24no—
65#5479—51no—
66C2×C3×C4⋊C8—51no—
67C4×#208—51no—
68#4484—51no—
69#4484—51no—
70#4483—51no—
71#4483D511yescharacteristic, complemented
72C4×C5×D4—31no—
73#4084—31no—
74#4082—31no—
75C4×C22⋊D5—61no—
76#4072—61no—
77C2×#676—61no—
78C2×C8×D5—21no—
79#4043—31no—
80#4036—31no—
81#4029—61no—
82#4025—61no—
83C42×D5C2×D311yescharacteristic
84C4×Dic10—31no—
85C5×C4⋊C8C2×D311yescharacteristic
86C4×C5×C8—31no—
87#3947—61no—
88#3946—21no—
89C4⋊#168C2×D311yescharacteristic
90C4×#168—31no—
91#1483—151noSylow
92C22×C5×D3—21no—
93C22×C3×D5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99Dic30—21no—
100Dic30—21no—
101C2×C5×Dic3—21no—
102C5×D12—21no—
103C5×D12—21no—
104C4×C5×D3—41no—
105C4×C5×D3—41no—
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C22⋊C411yescharacteristic
108C2×C3×Dic5C22⋊C411yescharacteristic
109C3×C4×D5—22no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5—21no—
114#1201—42no—
115C3×C5×C8—41no—
116C3⋊#168—22no—
117C3×#168—41no—
118C5×C3⋊C8—22no—
119C22×C3×C8—101no—
120C2×C3×C42—51no—
121#930—51no—
122#929—101no—
123C4×#67—101no—
124#924—51no—
125C2×#208—101no—
126#876—101no—
127#875—51no—
128C4×D12C2×D511yescharacteristic
129#872—101no—
130#870—51no—
131C4×Dic6—51no—
132C3×C4⋊C8—51no—
133C3×C4⋊C8—101no—
134C3×C4⋊C8C2×D511yescharacteristic
135#803—101no—
136C4×C3⋊C8—51no—
137C4×C3⋊C8C2×D511yescharacteristic
138C2×C5×D4—31no—
139C22×C4×C5—61no—
140C2×C22⋊D5—61no—
141C2×C4×D5C4×D311yescharacteristic
142C2×C4×D5D1211yescharacteristic
143C2×C4×D5#6711yescharacteristic
144C2×Dic10—31no—
145C2×C5×C8—21no—
146C2×C5×C8—61no—
147C5×C4⋊C4—31no—
148C5×C22⋊C4—61no—
149C42×C5C22×D311yescharacteristic
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152C22⋊Dic5—61no—
153#685—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—61no—
156C4⋊Dic5—61no—
157#683—61no—
158#683—61no—
159C4×Dic5—61no—
160C4×Dic5C4×D311yescharacteristic
161C4×Dic5D1211yescharacteristic
162C4×Dic5#6711yescharacteristic
163C2×#168—21no—
164C2×#168—61no—
165#676—64no—
166C8×D5—42no—
167#529—151no—
168C2×C4⋊C8—51no—
169C4×M16—151no—
170Q8⋊C8—151no—
171Q8⋊C8—151no—
172D4⋊C8—31no—
173D4⋊C8—151no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C5×D3—41no—
176C2×C5×D3—41no—
177C2×C5×D3—41no—
178C2×C3×D5—21no—
179C2×C3×D5—21no—
180C2×C3×D5#10412yes—
181C3×C4×C5—21no—
182C3×C4×C5#13111yescharacteristic
183C3×C4×C5#13111yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5#13711yescharacteristic
186Dic15—41no—
187Dic15—41no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C3×Dic5—21no—
191C5×Dic3—41no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C2×#67—101no—
196C2×D12C4×D511yescharacteristic
197C2×C4×D3—21no—
198C2×Dic6—51no—
199C2×C3×C8—21no—
200C2×C3×C8—101no—
201C2×C3×C8—202no—
202C3×C42—51no—
203C3×C42—51no—
204C3×C42—51no—
205C3×C42C22×D511yescharacteristic
206#217—101no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3C4×D511yescharacteristic
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217C4×Dic3—101no—
218#208—104no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—101no—
221C23×C5—61no—
222C22×D5(C2×D3)⋊C411yescharacteristic
223C5×D4—61no—
224C5×D4—61no—
225C2×C4×C5—61no—
226C2×C4×C5—121no—
227C2×C4×C5—121no—
228C2×C4×C5C2×C4×D311yescharacteristic
229C2×C4×C5C2×D1211yescharacteristic
230C2×C4×C5C2×#6711yescharacteristic
231C22⋊D5—122no—
232C2×Dic5—61no—
233C2×Dic5—61no—
234C2×Dic5(C2×D3)⋊C411yescharacteristic
235C2×Dic5(C2×D3)⋊C411yescharacteristic
236C2×Dic5(C2×D3)⋊C411yescharacteristic
237C4×D5—22no—
238C4×D5—21no—
239C4×D5—21no—
240C4×D5—21no—
241C4×D5—21no—
242Dic10—61no—
243Dic10—61no—
244C5×C8—41no—
245C5×C8—62no—
246#168—41no—
247#168—62no—
248C2×M16—301no—
249C22×C8—101no—
250#126—301no—
251#125—151no—
252#124—151no—
253#123—301no—
254C22⋊Q8—151no—
255#121—151no—
256C4×Q8—151no—
257C4×D4—31no—
258C4×D4—301no—
259#117—301no—
260C2×C42—51no—
261C4⋊C8—51no—
262C4⋊C8—101no—
263C4⋊C8D3×D511yescharacteristic
264#97—301no—
265C4×C8—31no—
266C4×C8—151no—
267C2×C3×C5#40811yescharacteristic
268C2×C3×C5#41711yescharacteristic
269C2×C3×C5C2×#10411yescharacteristic
270C3×D5—22no—
271C5×D3—81no—
272C23×C3—51no—
273C22×D3—21no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—102no—
278C2×C3×C4—101no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285#67—202no—
286C2×Dic3—21no—
287C2×Dic3—101no—
288C2×Dic3—101no—
289D12—21no—
290D12—21no—
291C4×D3—41no—
292C4×D3—41no—
293Dic6—101no—
294Dic6—101no—
295C3×C8—41no—
296C3×C8—201no—
297C3⋊C8—22no—
298C3⋊C8—102no—
299C22×C5—121no—
300C22×C5—121no—
301C22×C5—121no—
302C22×C5C2×(C2×D3)⋊C411yescharacteristic
303C2×D5—21no—
304C2×D5—21no—
305C2×D5#82512yes—
306C4×C5—21no—
307C4×C5—121no—
308C4×C5#90111yescharacteristic
309C4×C5#90111yescharacteristic
310C4×C5#93211yescharacteristic
311C4×C5#94211yescharacteristic
312Dic5—21no—
313Dic5—21no—
314Dic5—21no—
315Dic5—121no—
316Dic5—121no—
317C2×Q8—151no—
318C2×D4—31no—
319C2×D4—301no—
320C22×C4—51no—
321C22×C4—51no—
322C22×C4—51no—
323C22×C4—61no—
324M16—304no—
325C2×C8—21no—
326C2×C8—61no—
327C2×C8—101no—
328C2×C8—202no—
329C2×C8—301no—
330C4⋊C4—31no—
331C4⋊C4—151no—
332C4⋊C4—301no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C22⋊C4—61no—
337C22⋊C4—301no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C42—51no—
342C42—51no—
343C42—51no—
344C42—301no—
345C42C2×D3×D511yescharacteristic
346C3×C5#148311yescharacteristic, complemented, Hall
347C22×C3—52no—
348C22×C3—101no—
349C22×C3—101no—
350C22×C3D5×C22⋊C411yescharacteristic
351C2×D3—41no—
352C2×D3—41no—
353C2×D3—41no—
354C3×C4—21no—
355C3×C4—101no—
356C3×C4—101no—
357C3×C4—101no—
358C3×C4#404711yescharacteristic
359C3×C4#405311yescharacteristic
360C3×C4#405711yescharacteristic
361C3×C4#406111yescharacteristic
362Dic3—41no—
363Dic3—201no—
364Dic3—201no—
365C2×C5—241no—
366C2×C5#496611yescharacteristic
367C2×C5#511011yescharacteristic
368C2×C5C2×#82511yescharacteristic
369D5—22no—
370C23—51no—
371C23—61no—
372Q8—301no—
373Q8—301no—
374D4—61no—
375D4—61no—
376D4—602no—
377C2×C4—51no—
378C2×C4—51no—
379C2×C4—51no—
380C2×C4—61no—
381C2×C4—102no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—301no—
389C2×C4—301no—
390C2×C4C4×D3×D511yescharacteristic
391C2×C4D5×D1211yescharacteristic
392C2×C4D5×#6711yescharacteristic
393C8—41no—
394C8—62no—
395C8—201no—
396C8—302no—
397C2×C3—102no—
398C2×C3#6501611yescharacteristic
399C2×C3#6506011yescharacteristic
400C2×C3D5×#10411yescharacteristic
401D3—81no—
402C5#7042711yescharacteristic, complemented, Sylow
403C22—52no—
404C22—101no—
405C22—101no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22D5×(C2×D3)⋊C411yescharacteristic
410C4—21no—
411C4—101no—
412C4—101no—
413C4—101no—
414C4—121no—
415C4—601no—
416C4—601no—
417C4#9126511yescharacteristic
418C4#9126611yescharacteristic
419C4#9148911yescharacteristic
420C4#9151311yescharacteristic
421C3#1059896311yescharacteristic, complemented, Sylow
422C2—102no—
423C2—241no—
424C2#1174749811yescharacteristic
425C2#1174813411yescharacteristic
426C2D5×#82511yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91449C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×D5×C4⋊C8C2semidirect
3. C4×#6649C2semidirect
4. #11746305C2semidirect
5. C5×#4483C2semidirect
6. #11745844C2semidirect
7. #11745836C2semidirect
30. D5×C4⋊C8D3semidirect
71. #4483D5semidirect
346. C3×C5#1483semidirect
402. C5#70427semidirect
421. C3#10598963semidirect

Maximal subgroups

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

subgroupindex
#117526822
C3×D5×C4⋊C82
C4×#66492
#117463052
C5×#44832
#117458442
#117458362
#105989633
#704275