Finite Group Databasebeta

← #14282491

Subgroups — #14282491

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752494C211yesmaximal, characteristic
2C3×C4×C8×D5C211yesmaximal, characteristic, complemented
3#11746871C211yesmaximal, characteristic, complemented
4#11746280C211yesmaximal, characteristic, complemented
5C5×#4456C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10599034—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C2×C3×C8×D5—21no—
12C3×C42×D5C2211yescharacteristic
13#91450C411yescharacteristic
14C4×#1202—21no—
15#91388C411yescharacteristic
16#91387—21no—
17#91386—21no—
18#91375C411yescharacteristic
19#91359C411yescharacteristic
20#91348—21no—
21C3×C4×C5×C8C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C8×Dic5—21no—
25C3×C4×#168C2211yescharacteristic
26#90955—21no—
27#90952—21no—
28#69736—51nomaximal, Hall
29#65914—31no—
30#65124—31no—
31C4×C8×D5D311yescharacteristic, complemented
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15—21no—
38C2×C5×Dic6C2×C411yescharacteristic
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×#1202—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—21no—
46C4⋊Dic15C2×C411yescharacteristic
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56C3×C8×D5—24no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6669—21no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63#6665—21no—
64#5479—51no—
65C2×C3×C4×C8—51no—
66#4926—51no—
67#4459—51no—
68#4459—51no—
69#4456—51no—
70#4456D511yescharacteristic, complemented
71C4×C5×Q8—31no—
72#4093—31no—
73#4092—31no—
74C2×C8×D5—21no—
75#4044—61no—
76#4041—31no—
77#4040—61no—
78#4036—31no—
79C4×D20—31no—
80C4×D20—61no—
81#4018—61no—
82C42×D5C2×D311yescharacteristic
83C5×C4⋊C8—31no—
84C4×C5×C8C2×D311yescharacteristic
85#3952—61no—
86#3947—61no—
87C8×Dic5—21no—
88C4⋊#168—31no—
89C4×#168C2×D311yescharacteristic
90#1494—151noSylow
91C22×D15—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97D60—21no—
98D60—21no—
99C4×D15—41no—
100C4×D15—41no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—21no—
103C5×Dic6—21no—
104C5×Dic6—21no—
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C22⋊C411yescharacteristic
108C3×C4×D5—22no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113#1202—42no—
114C3×C5×C8—22no—
115C3⋊#168—41no—
116C3×#168—22no—
117C5×C3⋊C8—41no—
118C22×C3×C8—101no—
119C2×C3×C42—51no—
120#930—51no—
121#929—101no—
122C4×#67—101no—
123#924—51no—
124#876—101no—
125#875—51no—
126C4×D12—51no—
127#872—101no—
128#870—51no—
129C4×Dic6C2×D511yescharacteristic
130C3×C4×C8—51no—
131C3×C4×C8—101no—
132C3×C4×C8C2×D511yescharacteristic
133#830—101no—
134C4⋊(C3⋊C8)—51no—
135C4⋊(C3⋊C8)C2×D511yescharacteristic
136#803—101no—
137C2×C5×Q8—31no—
138C2×D20—31no—
139C2×D20—61no—
140C2×C4×D5—61no—
141C2×C4×D5C4×D311yescharacteristic
142C2×C4×D5D1211yescharacteristic
143C2×C4×D5#6711yescharacteristic
144C2×C5×C8—21no—
145C2×C5×C8—61no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—61no—
148C42×C5—61no—
149C42×C5C22×D311yescharacteristic
150#685—61no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157#683—61no—
158#683—61no—
159C4×Dic5C4×D311yescharacteristic
160C4×Dic5D1211yescharacteristic
161C4×Dic5#6711yescharacteristic
162C2×#168—21no—
163C2×#168—61no—
164C8×D5—24no—
165#529—151no—
166#432—151no—
167C2×C4×C8—51no—
168Q8⋊C8—31no—
169Q8⋊C8—151no—
170D4⋊C8—151no—
171D4⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×D15—41no—
174C2×D15—41no—
175C2×D15—41no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5#10412yes—
179C3×C4×C5—21no—
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5#13511yescharacteristic
184Dic15—41no—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C2×#67—101no—
194C2×D12—51no—
195C2×C4×D3—101no—
196C2×Dic6C4×D511yescharacteristic
197C2×C3×C8—21no—
198C2×C3×C8—104no—
199C2×C3×C8—101no—
200C3×C42—51no—
201C3×C42—51no—
202C3×C42—51no—
203C3×C42C22×D511yescharacteristic
204#217—101no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209C4⋊Dic3—51no—
210C4⋊Dic3C4×D511yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—101no—
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215C4×Dic3—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—101no—
218C22×D5—61no—
219C22×D5(C2×D3)⋊C411yescharacteristic
220C5×Q8—61no—
221C5×Q8—61no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5C2×C4×D311yescharacteristic
225C2×C4×C5C2×D1211yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C2×Dic5—61no—
228C2×Dic5(C2×D3)⋊C411yescharacteristic
229C2×Dic5(C2×D3)⋊C411yescharacteristic
230C2×Dic5(C2×D3)⋊C411yescharacteristic
231D20—61no—
232D20—61no—
233D20—122no—
234C4×D5—22no—
235C4×D5—21no—
236C4×D5—21no—
237C4×D5—21no—
238C4×D5—21no—
239C4×D5—121no—
240C4×D5—121no—
241C5×C8—22no—
242C5×C8—121no—
243#168—22no—
244#168—121no—
245C22×C8—101no—
246#126—301no—
247#125—151no—
248#124—151no—
249#123—301no—
250C22⋊Q8—151no—
251#121—151no—
252C4×Q8—31no—
253C4×D4—151no—
254C4×D4—301no—
255#117—301no—
256C2×C42—51no—
257C4⋊C8—31no—
258C4⋊C8—151no—
259C22⋊C8—301no—
260#97—301no—
261C4×C8—51no—
262C4×C8—101no—
263C4×C8D3×D511yescharacteristic
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267D15—81no—
268C3×D5—22no—
269C23×C3—51no—
270C22×D3—101no—
271C2×C3×C4—51no—
272C2×C3×C4—51no—
273C2×C3×C4—51no—
274C2×C3×C4—102no—
275C2×C3×C4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—101no—
278C2×C3×C4—101no—
279C2×C3×C4C2×C4×D511yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282#67—202no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—101no—
286D12—101no—
287D12—101no—
288C4×D3—201no—
289C4×D3—201no—
290Dic6—21no—
291Dic6—21no—
292C3×C8—22no—
293C3×C8—102no—
294C3⋊C8—41no—
295C3⋊C8—201no—
296C22×C5C2×(C2×D3)⋊C411yescharacteristic
297C2×D5—21no—
298C2×D5—21no—
299C2×D5—121no—
300C2×D5—121no—
301C2×D5—121no—
302C2×D5#80512yes—
303C4×C5—21no—
304C4×C5—121no—
305C4×C5—121no—
306C4×C5#90111yescharacteristic
307C4×C5#90111yescharacteristic
308C4×C5#90411yescharacteristic
309C4×C5#90411yescharacteristic
310Dic5—21no—
311Dic5—21no—
312Dic5—21no—
313Dic5—121no—
314C2×Q8—31no—
315C2×D4—151no—
316C2×D4—301no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—301no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—104no—
324C2×C8—101no—
325C2×C8—301no—
326C4⋊C4—31no—
327C4⋊C4—61no—
328C4⋊C4—151no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—301no—
332C22⋊C4—301no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—51no—
338C42—51no—
339C42—51no—
340C42—61no—
341C42C2×D3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—52no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3D5×C22⋊C411yescharacteristic
347C2×D3—201no—
348C2×D3—201no—
349C2×D3—201no—
350C3×C4—21no—
351C3×C4—101no—
352C3×C4—101no—
353C3×C4—101no—
354C3×C4#404711yescharacteristic
355C3×C4#405311yescharacteristic
356C3×C4#406211yescharacteristic
357C3×C4#406511yescharacteristic
358Dic3—41no—
359Dic3—41no—
360Dic3—201no—
361C2×C5C2×#80511yescharacteristic
362C2×C5#511011yescharacteristic
363C2×C5#511311yescharacteristic
364D5—22no—
365D5—241no—
366C23—51no—
367C23—301no—
368Q8—61no—
369Q8—61no—
370D4—301no—
371D4—301no—
372D4—602no—
373C2×C4—51no—
374C2×C4—51no—
375C2×C4—51no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—102no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—301no—
384C2×C4—601no—
385C2×C4—601no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4D5×D1211yescharacteristic
388C2×C4D5×#6711yescharacteristic
389C8—22no—
390C8—102no—
391C8—121no—
392C8—601no—
393C2×C3—102no—
394C2×C3#6501611yescharacteristic
395C2×C3#6509311yescharacteristic
396C2×C3D5×#10411yescharacteristic
397D3—401no—
398C5#6973611yescharacteristic, complemented, Sylow
399C22—52no—
400C22—101no—
401C22—101no—
402C22—601no—
403C22—601no—
404C22—601no—
405C22D5×(C2×D3)⋊C411yescharacteristic
406C4—21no—
407C4—101no—
408C4—101no—
409C4—101no—
410C4—121no—
411C4—121no—
412C4—601no—
413C4#9126511yescharacteristic
414C4#9126611yescharacteristic
415C4#9126911yescharacteristic
416C4#9127111yescharacteristic
417C3#1059903411yescharacteristic, complemented, Sylow
418C2—102no—
419C2—1201no—
420C2D5×#80511yescharacteristic
421C2#1174764211yescharacteristic
422C2#1174813411yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91450C4
cosocleC3×C42×C5C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#1494
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×C4×C8×D5C2semidirect
3. #11746871C2semidirect
4. #11746280C2semidirect
5. C5×#4456C2semidirect
6. #11745843C2semidirect
7. #11745839C2semidirect
31. C4×C8×D5D3semidirect
70. #4456D5semidirect
342. C3×C5#1494semidirect
398. C5#69736semidirect
417. C3#10599034semidirect

Maximal subgroups

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

subgroupindex
#117524942
C3×C4×C8×D52
#117468712
#117462802
C5×#44562
#117458432
#117458392
#105990343
#697365