Finite Group Databasebeta

← #14285142

Subgroups — #14285142

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66050C211yesmaximal, characteristic
2#11746871C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746365C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599179—31nomaximal, Hall
9C2×C3×#711—21no—
10C3×C5×#127C2211yescharacteristic
11C3×#4084—21no—
12C3×#4084C412yes—
13C3×#4082—21no—
14C3×D4×Dic5—21no—
15C3×D4×Dic5C412yes—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90955—21no—
23#90955—21no—
24#90952—21no—
25Dic5×C3⋊C8—21no—
26#71808—51nomaximal, Hall
27#66050D311yescharacteristic
28#65124—31no—
29#65122—31no—
30C5×#331—31no—
31#64764—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C412yes—
37C2×C3×C22⋊D5—22no—
38C22×C3×Dic5—22no—
39C3×#711—42no—
40C3×#711—42no—
41C2×C3×C4×D5C2×C411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×Dic10—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5—22no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C412yes—
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57C3×#532—51no—
58#4926—51no—
59#4925—51no—
60#4547—51no—
61#4547—51no—
62#4544—51no—
63#4544D511yescharacteristic, complemented
64C2×#711—21no—
65C5×#127C2×D311yescharacteristic
66#4084—21no—
67#4084Dic312yes—
68#4082—21no—
69D4×Dic5—21no—
70D4×Dic5Dic312yes—
71C42×D5C2×D311yescharacteristic
72#4015C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3952—61no—
77#3947—61no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1553—151noSylow
82C23×C3×C5—22no—
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×D4—42no—
85C3×C5×D4—41no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C3×C22⋊D5—44no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—44no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C22⋊C411yescharacteristic
98C3×C4×D5—21no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C5×C3⋊C8—41no—
108C5×C3⋊C8—41no—
109C2×C3×#41—101no—
110C3×C4⋊Q8—51no—
111C3×#127C2×D511yescharacteristic
112C3×#124—101no—
113C3×#121—52no—
114C3×#121—101no—
115C3×C4×D4—52no—
116C3×C4×D4—101no—
117C2×C3×C42—51no—
118#830—101no—
119#830—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124#803—101no—
125C4×C3⋊C8—101no—
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×C5×D4C2×Dic312yes—
129C2×C22⋊D5—22no—
130C22×Dic5—22no—
131#711—42no—
132#711—42no—
133C2×C4×D5C2×Dic311yescharacteristic
134C2×C4×D5#6711yescharacteristic
135C2×C4×D5#6711yescharacteristic
136C2×Dic10—21no—
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C42×C5C22×D311yescharacteristic
140C22⋊Dic5—22no—
141C22⋊Dic5—22no—
142C4⋊Dic5—21no—
143C4⋊Dic5C2×Dic312yes—
144C4×Dic5C2×Dic311yescharacteristic
145C4×Dic5#6711yescharacteristic
146C4×Dic5#6711yescharacteristic
147C2×#168—61no—
148C2×#168—61no—
149#532—51no—
150#432—151no—
151#431—151no—
152#332—151no—
153#332—151no—
154#331—31no—
155#331—151no—
156C22×C3×C5—42no—
157C22×C3×C5—42no—
158C22×C3×C5—42no—
159C22×C3×C5C2×C22⋊C411yescharacteristic
160C2×C3×D5—21no—
161C2×C3×D5—21no—
162C2×C3×D5—21no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×Dic5—42no—
172C3×#41—202no—
173C3×#41—202no—
174C2×C3×Q8—101no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—102no—
178C2×C3×D4C4×D512yes—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C22×C3×C4—102no—
183C3×C4⋊C4—52no—
184C3×C4⋊C4—101no—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42C22×D511yescharacteristic
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C23×C5—22no—
196C22×D5#21711yescharacteristic
197C5×D4—42no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C2×C4×C5C22×Dic311yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C22⋊D5—44no—
206C2×Dic5—22no—
207C2×Dic5—44no—
208C2×Dic5#21711yescharacteristic
209C2×Dic5#21711yescharacteristic
210C2×Dic5#21711yescharacteristic
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—41no—
216Dic10—41no—
217Dic10—41no—
218C5×C8—121no—
219C5×C8—121no—
220#168—121no—
221#168—121no—
222C2×#41—101no—
223C4⋊Q8—51no—
224#127D3×D511yescharacteristic
225#124—101no—
226#121—52no—
227#121—101no—
228C4×D4—52no—
229C4×D4—101no—
230C2×C42—51no—
231C4⋊C8—31no—
232C4⋊C8—31no—
233C4⋊C8—151no—
234C4⋊C8—151no—
235C22⋊C8—301no—
236C22⋊C8—301no—
237#97—301no—
238C4×C8—301no—
239C2×C3×C5—82no—
240C2×C3×C5#41311yescharacteristic
241C2×C3×C5#41611yescharacteristic
242C2×C3×C5#41811yescharacteristic
243C3×D5—41no—
244C23×C3—22no—
245C23×C3—51no—
246C3×Q8—201no—
247C3×Q8—201no—
248C3×D4—42no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—204no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4—102no—
262C2×C3×C4—201no—
263C2×C3×C4—204no—
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C3⋊C8—41no—
268C3⋊C8—41no—
269C3⋊C8—201no—
270C3⋊C8—201no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5C2×#21711yescharacteristic
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—21no—
278C4×C5—21no—
279C4×C5#93211yescharacteristic
280C4×C5#93211yescharacteristic
281C4×C5#95011yescharacteristic
282C4×C5#95011yescharacteristic
283Dic5—21no—
284Dic5—21no—
285Dic5—21no—
286Dic5—42no—
287#41—202no—
288#41—202no—
289C2×Q8—101no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—102no—
293C2×D4D5×Dic312yes—
294C22×C4—51no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—102no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—301no—
301C2×C8—301no—
302C4⋊C4—52no—
303C4⋊C4—101no—
304C22⋊C4—102no—
305C22⋊C4—102no—
306C42—51no—
307C42—51no—
308C42—51no—
309C42C2×D3×D511yescharacteristic
310C3×C5#155311yescharacteristic, complemented, Hall
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—101no—
315C22×C3—101no—
316C22×C3—101no—
317C22×C3D5×C22⋊C411yescharacteristic
318C3×C4—21no—
319C3×C4—101no—
320C3×C4—101no—
321C3×C4—101no—
322C3×C4—202no—
323C3×C4#405711yescharacteristic
324C3×C4#405811yescharacteristic
325C3×C4#406011yescharacteristic
326C3×C4#406211yescharacteristic
327C2×C5—82no—
328C2×C5#521511yescharacteristic
329C2×C5#523311yescharacteristic
330C2×C5#523711yescharacteristic
331D5—41no—
332C23—22no—
333C23—51no—
334Q8—201no—
335Q8—201no—
336D4—42no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—204no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—102no—
350C2×C4—201no—
351C2×C4—204no—
352C2×C4C2×D5×Dic311yescharacteristic
353C2×C4D5×#6711yescharacteristic
354C2×C4D5×#6711yescharacteristic
355C8—121no—
356C8—121no—
357C8—601no—
358C8—601no—
359C2×C3—82no—
360C2×C3—201no—
361C2×C3#6503411yescharacteristic
362C2×C3#6505911yescharacteristic
363C2×C3#6506111yescharacteristic
364C5#7180811yescharacteristic, complemented, Sylow
365C22—42no—
366C22—42no—
367C22—42no—
368C22—101no—
369C22—101no—
370C22—101no—
371C22D5×#21711yescharacteristic
372C4—21no—
373C4—101no—
374C4—101no—
375C4—101no—
376C4—202no—
377C4#9148911yescharacteristic
378C4#9149011yescharacteristic
379C4#9149111yescharacteristic
380C4#9149211yescharacteristic
381C3#1059917911yescharacteristic, complemented, Sylow
382C2—82no—
383C2—201no—
384C2#1174896111yescharacteristic
385C2#1174896211yescharacteristic
386C2#1174912311yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66050C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1553
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746871C2semidirect
3. #11746869C2semidirect
4. #11746365C2semidirect
5. C5×#4544C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
63. #4544D5semidirect
310. C3×C5#1553semidirect
364. C5#71808semidirect
381. C3#10599179semidirect

Maximal subgroups

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

subgroupindex
C3×#660502
#117468712
#117468692
#117463652
C5×#45442
#117458562
#117458552
#105991793
#718085