Finite Group Databasebeta

← #14285055

Subgroups — #14285055

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66059C211yesmaximal, characteristic
2D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3#11746871C211yesmaximal, characteristic, complemented
4#11746367C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599278—31nomaximal, Hall
9C2×C3×#713C412yes—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4093C412yes—
12C3×#4041—21no—
13C3×#4041—21no—
14C3×#4039—21no—
15C3×#4039—21no—
16C3×#4020C2211yescharacteristic
17C3×C42×D5C2211yescharacteristic
18C2×D5×C3⋊C8—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90982—21no—
24#90955—21no—
25#90952—21no—
26#71807—51nomaximal, Hall
27#66059D311yescharacteristic
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#333—31no—
31#64766—31no—
32#64705—31no—
33#64705—31no—
34C2×C3×C5×Q8C2×C412yes—
35C3×#713—44no—
36C2×C3×D20—22no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20C2×C412yes—
40C2×C3×C4×D5—22no—
41C2×C3×C4×D5C2×C411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—22no—
52C3×#685—22no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56D5×C3⋊C8—42no—
57C3×#532—51no—
58#4926—51no—
59C2×C4⋊(C3⋊C8)—51no—
60#4546—51no—
61#4546D511yescharacteristic, complemented
62#4544—51no—
63#4544—51no—
64C2×#713Dic312yes—
65C5×C4⋊Q8C2×D311yescharacteristic
66#4093Dic312yes—
67C2×C8×D5—61no—
68#4041—21no—
69#4041—21no—
70#4039—21no—
71#4039—21no—
72#4020C2×D311yescharacteristic
73C42×D5C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76#3952—61no—
77#3947—61no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1551—151noSylow
82C22×C3×D5—22no—
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×Q8—42no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×D20—42no—
93C3×D20—44no—
94C3×D20—41no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×C4×D5—22no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—21no—
103C3×C4×D5—44no—
104C3⋊#168—41no—
105C3⋊#168—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C2×C3×#41—52no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×#127—51no—
111C3×#124—52no—
112C3×#121—101no—
113C3×#121—101no—
114C3×C4×D4—101no—
115C3×C4×D4—101no—
116C2×C3×C42—51no—
117C22×C3⋊C8—101no—
118#830—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124#803—101no—
125C2×C5×Q8C2×Dic312yes—
126#713—44no—
127C2×D20—22no—
128C2×D20—21no—
129C2×D20—21no—
130C2×D20C2×Dic312yes—
131C2×C4×D5—22no—
132C2×C4×D5C2×Dic311yescharacteristic
133C2×C4×D5#6711yescharacteristic
134C2×C4×D5#6711yescharacteristic
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C42×C5C22×D311yescharacteristic
140#685—22no—
141#685—22no—
142C4×Dic5C2×Dic311yescharacteristic
143C4×Dic5#6711yescharacteristic
144C4×Dic5#6711yescharacteristic
145C2×#168—61no—
146C2×#168—61no—
147C8×D5—122no—
148#532—51no—
149#432—151no—
150C2×C4⋊C8—151no—
151#333—31no—
152#333—151no—
153#331—151no—
154#331—151no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—42no—
159C2×C3×D5—42no—
160C2×C3×D5—42no—
161C2×C3×D5#10012yes—
162C3×C4×C5—21no—
163C3×C4×C5—42no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×#41—204no—
172C2×C3×Q8C4×D512yes—
173C2×C3×D4—52no—
174C2×C3×D4—102no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4—102no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42—51no—
188C3×C42C22×D511yescharacteristic
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C2×C3⋊C8—101no—
193C2×C3⋊C8—202no—
194C22×D5—22no—
195C22×D5#21711yescharacteristic
196C5×Q8—42no—
197C2×C4×C5—22no—
198C2×C4×C5C22×Dic311yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×Dic5#21711yescharacteristic
202C2×Dic5#21711yescharacteristic
203C2×Dic5#21711yescharacteristic
204D20—42no—
205D20—44no—
206D20—41no—
207D20—41no—
208D20—41no—
209D20—41no—
210C4×D5—22no—
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—44no—
216C5×C8—121no—
217C5×C8—121no—
218#168—121no—
219#168—121no—
220C2×#41—52no—
221C22×C8—301no—
222C4⋊Q8D3×D511yescharacteristic
223#127—51no—
224#124—52no—
225#121—101no—
226#121—101no—
227C4×D4—101no—
228C4×D4—101no—
229C2×C42—51no—
230C4⋊C8—31no—
231C4⋊C8—31no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234C4⋊C8—301no—
235C22⋊C8—301no—
236#97—301no—
237C2×C3×C5C2×#10011yescharacteristic
238C2×C3×C5#41611yescharacteristic
239C2×C3×C5#41711yescharacteristic
240C3×D5—22no—
241C3×D5—82no—
242C23×C3—51no—
243C23×C3—102no—
244C3×Q8—42no—
245C3×D4—202no—
246C3×D4—204no—
247C3×D4—201no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C2×C3×C4—22no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—102no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—204no—
261C2×C3×C4C2×C4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C3⋊C8—41no—
265C3⋊C8—41no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5C2×#21711yescharacteristic
269C2×D5—21no—
270C2×D5—21no—
271C2×D5—42no—
272C2×D5—42no—
273C2×D5—42no—
274C2×D5#83312yes—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5#94911yescharacteristic
278C4×C5#95011yescharacteristic
279C4×C5#95011yescharacteristic
280C4×C5#95111yescharacteristic
281Dic5—21no—
282Dic5—21no—
283Dic5—21no—
284#41—204no—
285C2×Q8D5×Dic312yes—
286C2×D4—52no—
287C2×D4—102no—
288C2×D4—101no—
289C2×D4—101no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—102no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—301no—
297C2×C8—301no—
298C2×C8—602no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C22⋊C4—102no—
302C22⋊C4—102no—
303C42—51no—
304C42—51no—
305C42—51no—
306C42C2×D3×D511yescharacteristic
307C3×C5#155111yescharacteristic, complemented, Hall
308C22×C3—52no—
309C22×C3—101no—
310C22×C3—101no—
311C22×C3—202no—
312C22×C3—202no—
313C22×C3—202no—
314C22×C3D5×C22⋊C411yescharacteristic
315C3×C4—21no—
316C3×C4—42no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4—101no—
320C3×C4#406011yescharacteristic
321C3×C4#406211yescharacteristic
322C3×C4#406411yescharacteristic
323C3×C4#406511yescharacteristic
324C2×C5C2×#83311yescharacteristic
325C2×C5#523211yescharacteristic
326C2×C5#523311yescharacteristic
327D5—22no—
328D5—82no—
329C23—51no—
330C23—102no—
331Q8—42no—
332D4—202no—
333D4—204no—
334D4—201no—
335D4—201no—
336D4—201no—
337D4—201no—
338C2×C4—22no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—51no—
342C2×C4—102no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—204no—
348C2×C4C2×D5×Dic311yescharacteristic
349C2×C4D5×#6711yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C8—121no—
352C8—121no—
353C8—601no—
354C8—601no—
355C2×C3—102no—
356C2×C3—402no—
357C2×C3D5×#10011yescharacteristic
358C2×C3#6509211yescharacteristic
359C2×C3#6509311yescharacteristic
360C5#7180711yescharacteristic, complemented, Sylow
361C22—52no—
362C22—101no—
363C22—101no—
364C22—202no—
365C22—202no—
366C22—202no—
367C22D5×#21711yescharacteristic
368C4—21no—
369C4—42no—
370C4—101no—
371C4—101no—
372C4—101no—
373C4#9150211yescharacteristic
374C4#9150811yescharacteristic
375C4#9151411yescharacteristic
376C4#9151611yescharacteristic
377C3#1059927811yescharacteristic, complemented, Sylow
378C2—102no—
379C2—402no—
380C2D5×#83311yescharacteristic
381C2#1174919811yescharacteristic
382C2#1174920711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1551
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. D5×C4⋊(C3⋊C8)C2semidirect
3. #11746871C2semidirect
4. #11746367C2semidirect
5. C5×#4546C2semidirect
6. #11745852C2semidirect
7. #11745852C2semidirect
61. #4546D5semidirect
307. C3×C5#1551semidirect
360. C5#71807semidirect
377. C3#10599278semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
D5×C4⋊(C3⋊C8)2
#117468712
#117463672
C5×#45462
#117458522
#105992783
#718075