Finite Group Databasebeta

← #14285319

Subgroups — #14285319

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752550C211yesmaximal, characteristic
2C5×#4835C211yesmaximal, characteristic, complemented
3#11747011C211yesmaximal, characteristic, complemented
4#11746306C211yesmaximal, characteristic, complemented
5C3×#64702C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10601612—31nomaximal, Hall
9C2×#6769—21no—
10#91763C2211yescharacteristic
11C42×C5×D3C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91460—21no—
14#91460C412yes—
15#91428—21no—
16#91428C412yes—
17#91374—21no—
18C2×#6650—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×(C2×D3)⋊C8—21no—
22C5×#815—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25Dic3⋊#168—21no—
26#68429—51nomaximal, Hall
27#65811—31no—
28C5×#432—31no—
29#65213—31no—
30#64705—31no—
31#64705—31no—
32#64702—31no—
33#64702D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60C2×C412yes—
37C2×C4×C5×D3C2×C411yescharacteristic
38C2×C4×C5×D3D411yescharacteristic
39C2×C4×C5×D3D411yescharacteristic
40C2×C3×Dic10—21no—
41C2×#1203—22no—
42C2×#1200—22no—
43#6769—42no—
44#6769—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C4×C5×Dic3C2×C411yescharacteristic
49C4×C5×Dic3D411yescharacteristic
50C4×C5×Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C412yes—
54C2×C3×#168—21no—
55#6667—22no—
56#6667—22no—
57#6650—42no—
58#5725—51no—
59#4837—51no—
60#4835D511yescharacteristic, complemented
61C3×#332—51no—
62#4547—51no—
63#4485—51no—
64#4485—51no—
65C2×#709—61no—
66C2×C42×C5—31no—
67#4076—32no—
68#4076—61no—
69C2×#681—61no—
70#4021—61no—
71#4020—31no—
72C4×D20—32no—
73C4×D20—61no—
74#4015C2×D311yescharacteristic
75C5×C4⋊C8—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×C22⋊C8—61no—
78C5×#97—61no—
79C4⋊#168—31no—
80C4⋊#168—61no—
81C4⋊#168C2×D311yescharacteristic
82#1557—151noSylow
83C22×D15—22no—
84C22×C5×D3C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88D60—42no—
89D60—41no—
90D60—41no—
91D60—41no—
92D60—41no—
93C2×C5×Dic3C22⋊C411yescharacteristic
94C2×C5×Dic3C22⋊C411yescharacteristic
95C2×C5×Dic3C22⋊C411yescharacteristic
96C4×C5×D3—21no—
97C4×C5×D3—21no—
98C4×C5×D3—21no—
99C4×C5×D3—21no—
100C4×C5×D3—41no—
101C2×C3×Dic5—22no—
102C3×Dic10—41no—
103C3×Dic10—41no—
104#1203—44no—
105#1200—44no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3×#168—41no—
109C5×C3⋊C8—41no—
110C2×#239—101no—
111C3×C4⋊Q8—51no—
112#947—101no—
113C2×ΓL(1,𝔽25)—101no—
114#895—52no—
115#895—101no—
116#893—52no—
117#893—101no—
118#874—51no—
119C42×D3C2×D511yescharacteristic
120C3×C4⋊C8—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122(C2×D3)⋊C8—21no—
123#815—21no—
124Dic3⋊C8—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C22×C4×C5—31no—
128C22×C4×C5—31no—
129C22×C4×C5—31no—
130C2×C22⋊D5—62no—
131#709—122no—
132#709—122no—
133C2×D20—32no—
134C2×D20—61no—
135C2×D20—61no—
136C2×C4×D5—62no—
137C2×Dic10—21no—
138C2×C5×C8—21no—
139C2×C5×C8—61no—
140C42×C5—31no—
141C42×C5—31no—
142C42×C5—31no—
143C42×C5C22×D311yescharacteristic
144#685—62no—
145#685—62no—
146C4⋊Dic5—21no—
147C4⋊Dic5C4×D312yes—
148#681—122no—
149C2×#168—21no—
150C2×#168—61no—
151#532—151no—
152#432—31no—
153#423—151no—
154#332—51no—
155#332—151no—
156#331—151no—
157#331—151no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×D15—42no—
160C2×D15—42no—
161C2×D15—42no—
162C2×C5×D3—21no—
163C2×C5×D3—21no—
164C2×C5×D3—21no—
165C3×C4×C5—21no—
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170C3×Dic5—42no—
171C5×Dic3—21no—
172C5×Dic3—21no—
173C5×Dic3—21no—
174C2×C3×Q8—101no—
175#239—202no—
176#239—202no—
177C2×D12—52no—
178C2×D12—102no—
179C2×D12—101no—
180C2×D12—101no—
181C2×C4×D3—102no—
182C2×C4×D3C4×D511yescharacteristic
183C2×C4×D3D2011yescharacteristic
184C2×C4×D3C22⋊D511yescharacteristic
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C3×C4⋊C4—52no—
188C3×C4⋊C4—101no—
189C3×C42C22×D511yescharacteristic
190(C2×D3)⋊C4—102no—
191(C2×D3)⋊C4—102no—
192C4×Dic3C4×D511yescharacteristic
193C4×Dic3D2011yescharacteristic
194C4×Dic3C22⋊D511yescharacteristic
195C2×C3⋊C8—21no—
196C2×C3⋊C8—101no—
197ΓL(1,𝔽25)—202no—
198C23×C5—31no—
199C22×D5—62no—
200C2×C4×C5—31no—
201C2×C4×C5—31no—
202C2×C4×C5—31no—
203C2×C4×C5—61no—
204C2×C4×C5—61no—
205C2×C4×C5—61no—
206C2×C4×C5—61no—
207C2×C4×C5—121no—
208C2×C4×C5C2×C4×D311yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C22⋊D5—124no—
212C2×Dic5—22no—
213D20—122no—
214D20—121no—
215D20—121no—
216D20—121no—
217D20—121no—
218C4×D5—124no—
219Dic10—41no—
220Dic10—41no—
221C5×C8—41no—
222C5×C8—121no—
223#168—41no—
224#168—121no—
225C2×#41—301no—
226C2×M16—301no—
227C4⋊Q8—51no—
228#127—151no—
229#124—301no—
230#121—152no—
231#121—301no—
232C4×D4—152no—
233C4×D4—301no—
234C2×C42—31no—
235C4⋊C8—31no—
236C4⋊C8—51no—
237C4⋊C8—151no—
238C4⋊C8—301no—
239C4⋊C8D3×D511yescharacteristic
240C22⋊C8—61no—
241#97—61no—
242C2×C3×C5#41311yescharacteristic
243C2×C3×C5#41711yescharacteristic
244C2×C3×C5#41811yescharacteristic
245D15—82no—
246C5×D3—41no—
247C22×D3—102no—
248C22×D3#68511yescharacteristic
249C3×Q8—201no—
250C3×Q8—201no—
251C2×C3×C4—102no—
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C2×Dic3#68511yescharacteristic
256C2×Dic3#68511yescharacteristic
257C2×Dic3#68511yescharacteristic
258D12—202no—
259D12—204no—
260D12—201no—
261D12—201no—
262D12—201no—
263D12—201no—
264C4×D3—21no—
265C4×D3—21no—
266C4×D3—21no—
267C4×D3—21no—
268C4×D3—41no—
269C4×D3—204no—
270C3×C8—41no—
271C3×C8—201no—
272C3⋊C8—41no—
273C3⋊C8—201no—
274C22×C5—61no—
275C22×C5—61no—
276C22×C5—61no—
277C22×C5D3×C22⋊C411yescharacteristic
278C2×D5—122no—
279C2×D5—122no—
280C2×D5—122no—
281C4×C5—21no—
282C4×C5—61no—
283C4×C5—61no—
284C4×C5—61no—
285C4×C5#91111yescharacteristic
286C4×C5#91411yescharacteristic
287C4×C5#91411yescharacteristic
288C4×C5#91811yescharacteristic
289Dic5—42no—
290#41—602no—
291#41—602no—
292C2×Q8—101no—
293C2×D4—152no—
294C2×D4—302no—
295C2×D4—301no—
296C2×D4—301no—
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—31no—
300C22×C4—302no—
301M16—602no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—101no—
305C2×C8—301no—
306C4⋊C4—52no—
307C4⋊C4—101no—
308C22⋊C4—302no—
309C22⋊C4—302no—
310C42—31no—
311C42—31no—
312C42—31no—
313C42C2×D3×D511yescharacteristic
314C3×C5#155711yescharacteristic, complemented, Hall
315C22×C3C2×#68511yescharacteristic
316C2×D3—21no—
317C2×D3—21no—
318C2×D3—21no—
319C2×D3—202no—
320C2×D3—202no—
321C2×D3—202no—
322C3×C4—21no—
323C3×C4—202no—
324C3×C4#405411yescharacteristic
325C3×C4#405511yescharacteristic
326C3×C4#409511yescharacteristic
327C3×C4#409511yescharacteristic
328Dic3—21no—
329Dic3—21no—
330Dic3—21no—
331C2×C5—121no—
332C2×C5#475111yescharacteristic
333C2×C5#477011yescharacteristic
334C2×C5#480311yescharacteristic
335D5—242no—
336C23—31no—
337C23—302no—
338Q8—201no—
339Q8—201no—
340D4—602no—
341D4—604no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—102no—
354C2×C4—121no—
355C2×C4—604no—
356C2×C4C4×D3×D511yescharacteristic
357C2×C4D3×D2011yescharacteristic
358C2×C4D3×C22⋊D511yescharacteristic
359C8—41no—
360C8—121no—
361C8—201no—
362C8—601no—
363C2×C3#6529011yescharacteristic
364C2×C3#6542111yescharacteristic
365C2×C3#6542211yescharacteristic
366D3—41no—
367D3—402no—
368C5#6842911yescharacteristic, complemented, Sylow
369C22—61no—
370C22—61no—
371C22—61no—
372C22—602no—
373C22—602no—
374C22—602no—
375C22D3×#68511yescharacteristic
376C4—21no—
377C4—61no—
378C4—61no—
379C4—61no—
380C4—202no—
381C4#9125311yescharacteristic
382C4#9126311yescharacteristic
383C4#9148011yescharacteristic
384C4#9150411yescharacteristic
385C3#1060161211yescharacteristic, complemented, Sylow
386C2—121no—
387C2—1202no—
388C2#1174747711yescharacteristic
389C2#1174760811yescharacteristic
390C2#1174823511yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11752550C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1557
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4835C2semidirect
3. #11747011C2semidirect
4. #11746306C2semidirect
5. C3×#64702C2semidirect
6. #11745856C2semidirect
7. #11745854C2semidirect
33. #64702D3semidirect
60. #4835D5semidirect
314. C3×C5#1557semidirect
368. C5#68429semidirect
385. C3#10601612semidirect

Maximal subgroups

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

subgroupindex
#117525502
C5×#48352
#117470112
#117463062
C3×#647022
#117458562
#117458542
#106016123
#684295