Finite Group Databasebeta

← #14281947

Subgroups — #14281947

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2C4×#6710C211yesmaximal, characteristic, complemented
3C2×C5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#11745840C212yesmaximal, complemented
5#11745834C212yesmaximal, complemented
6#10601220—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C2×#6710—21no—
9C22×C5×C3⋊C8—21no—
10C3×#4076C411yescharacteristic
11C3×#4075—21no—
12C3×C4×C22⋊D5—21no—
13C3×#4070C411yescharacteristic
14C3×#4022—21no—
15C3×#4021C411yescharacteristic
16C3×C4×D20C2211yescharacteristic
17C3×#4018—21no—
18C3×#4016C411yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91087—21no—
21C4×C3⋊#168C2212yes—
22C5×C4⋊(C3⋊C8)—21no—
23C5×C4⋊(C3⋊C8)C2212yes—
24#71751—51nomaximal, Hall
25#65813D311yescharacteristic
26C2×C5×C4⋊C8—31no—
27C4×#681—31no—
28#64704—32no—
29#64703—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×C3×C22⋊D5—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×Dic10C2×C411yescharacteristic
37C3×C42×C5C2×C411yescharacteristic
38C3×C42×C5D411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41#6710—24no—
42C2×C3⋊#168—22no—
43C2×C5×C3⋊C8—22no—
44C2×C5×C3⋊C8—42no—
45C3×C22⋊Dic5—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×#685—21no—
49C3×#685—21no—
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×#529—51no—
58C2×C4⋊(C3⋊C8)D511yescharacteristic, complemented
59C4×#208—51no—
60#4535—52no—
61D4⋊(C3⋊C8)—52no—
62C22×C5×C8—61no—
63C2×C42×C5C2×D311yescharacteristic
64#4076Dic311yescharacteristic
65#4075—21no—
66C4×C22⋊D5—21no—
67#4070Dic311yescharacteristic
68C2×#681—61no—
69#4022—21no—
70#4021Dic311yescharacteristic
71C4×D20C2×D311yescharacteristic
72#4018—21no—
73#4016Dic311yescharacteristic
74C4×Dic10C2×D311yescharacteristic
75C5×C4⋊C8—32no—
76C5×C4⋊C8—61no—
77#3935—61no—
78C4×#168—32no—
79#1483—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×C3×D5—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C3×C22⋊D5—42no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C3×D20—22no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×Dic10—22no—
100C3⋊#168—24no—
101C5×C3⋊C8—42no—
102C3×#126—101no—
103C3×#125—51no—
104C3×#124—51no—
105C3×#123—101no—
106C3×C22⋊Q8—51no—
107C3×#121—51no—
108C3×C4×Q8—51no—
109C3×C4×D4—51no—
110C3×C4×D4—101no—
111C3×#117—101no—
112C2×C3×C42C2×D511yescharacteristic
113C2×#208—101no—
114C22×C3⋊C8—21no—
115C4⋊(C3⋊C8)—21no—
116C4⋊(C3⋊C8)C2×D512yes—
117#803—101no—
118C4×C3⋊C8—52no—
119C22×C4×C5C2×Dic311yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C2×C22⋊D5—21no—
123C2×D20C2×Dic311yescharacteristic
124C2×C4×D5—21no—
125C2×Dic10C2×Dic311yescharacteristic
126C2×C5×C8—62no—
127C2×C5×C8—122no—
128C42×C5C2×Dic311yescharacteristic
129C42×C5#6711yescharacteristic
130C42×C5#6711yescharacteristic
131C42×C5C22×D311yescharacteristic
132C22⋊Dic5—21no—
133#685—21no—
134#685—21no—
135#685—21no—
136#685—21no—
137C4⋊Dic5C2×Dic311yescharacteristic
138C4⋊Dic5C2×Dic311yescharacteristic
139#683—21no—
140#683—21no—
141#683—21no—
142#683—21no—
143C4×Dic5—21no—
144#681—64no—
145C2×#168—62no—
146#529—51no—
147C2×C4⋊C8—31no—
148C4×M16—151no—
149Q8⋊C8—152no—
150D4⋊C8—152no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5#10412yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C2×C3×D5—41no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5#13112yes—
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—41no—
166C3×Dic5—41no—
167C3×Dic5—41no—
168C2×C3×Q8—51no—
169C2×C3×D4—51no—
170C2×C3×D4—101no—
171C22×C3×C4—101no—
172C22×C3×C4C4×D511yescharacteristic
173C22×C3×C4D2011yescharacteristic
174C22×C3×C4C22⋊D511yescharacteristic
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C22⋊C4—101no—
182C3×C22⋊C4—101no—
183C3×C22⋊C4—101no—
184C3×C22⋊C4—101no—
185C3×C22⋊C4—101no—
186C3×C42—101no—
187C3×C42C4×D511yescharacteristic
188C3×C42D2011yescharacteristic
189C3×C42C22⋊D511yescharacteristic
190C3×C42C22×D511yescharacteristic
191#208—104no—
192C2×C3⋊C8—22no—
193C2×C3⋊C8—42no—
194C2×C3⋊C8—102no—
195C23×C5#21711yescharacteristic
196C22×D5—21no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5#21711yescharacteristic
202C2×C4×C5#21711yescharacteristic
203C2×C4×C5#21711yescharacteristic
204C2×C4×C5C22×Dic311yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C22⋊D5—42no—
208C2×Dic5—21no—
209C2×Dic5—21no—
210C2×Dic5—21no—
211D20—22no—
212C4×D5—41no—
213C4×D5—41no—
214Dic10—22no—
215C5×C8—122no—
216#168—64no—
217C2×M16—301no—
218C22×C8—61no—
219#126—101no—
220#125—51no—
221#124—51no—
222#123—101no—
223C22⋊Q8—51no—
224#121—51no—
225C4×Q8—51no—
226C4×D4—51no—
227C4×D4—101no—
228#117—101no—
229C2×C42D3×D511yescharacteristic
230C4⋊C8—32no—
231C4⋊C8—61no—
232#97—301no—
233C4×C8—152no—
234C2×C3×C5—22no—
235C2×C3×C5#40811yescharacteristic
236C2×C3×C5#41711yescharacteristic
237C2×C3×C5C2×#10411yescharacteristic
238C3×D5—81no—
239C23×C3—101no—
240C23×C3#68511yescharacteristic
241C3×Q8—102no—
242C3×D4—102no—
243C3×D4—202no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4#68511yescharacteristic
254C2×C3×C4#68511yescharacteristic
255C2×C3×C4#68511yescharacteristic
256C2×C3×C4C2×C4×D511yescharacteristic
257C2×C3×C4C2×D2011yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C3⋊C8—42no—
260C3⋊C8—104no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5#83712yes—
264C22×C5C2×#21711yescharacteristic
265C2×D5—41no—
266C2×D5—41no—
267C2×D5—41no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5#94812yes—
273C4×C5#94911yescharacteristic
274C4×C5#95111yescharacteristic
275Dic5—41no—
276Dic5—41no—
277Dic5—41no—
278C2×Q8—51no—
279C2×D4—51no—
280C2×D4—101no—
281C22×C4—101no—
282C22×C4D5×Dic311yescharacteristic
283C22×C4#120111yescharacteristic
284C22×C4#120211yescharacteristic
285M16—304no—
286C2×C8—62no—
287C2×C8—122no—
288C2×C8—302no—
289C4⋊C4—51no—
290C4⋊C4—51no—
291C4⋊C4—101no—
292C4⋊C4—101no—
293C4⋊C4—101no—
294C4⋊C4—101no—
295C22⋊C4—101no—
296C22⋊C4—101no—
297C22⋊C4—101no—
298C22⋊C4—101no—
299C22⋊C4—101no—
300C42—101no—
301C42D5×Dic311yescharacteristic
302C42#120111yescharacteristic
303C42#120211yescharacteristic
304C42C2×D3×D511yescharacteristic
305C3×C5#148311yescharacteristic, complemented, Hall
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—201no—
309C22×C3—201no—
310C22×C3—201no—
311C22×C3#395712yes—
312C22×C3C2×#68511yescharacteristic
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—201no—
318C3×C4—201no—
319C3×C4—201no—
320C3×C4#404712yes—
321C3×C4#407811yescharacteristic
322C3×C4#408811yescharacteristic
323C2×C5—22no—
324C2×C5#523211yescharacteristic
325C2×C5#523411yescharacteristic
326C2×C5C2×#83711yescharacteristic
327D5—81no—
328C23—101no—
329C23#666511yescharacteristic
330Q8—102no—
331D4—102no—
332D4—202no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—101no—
340C2×C4—201no—
341C2×C4—201no—
342C2×C4#666511yescharacteristic
343C2×C4#666511yescharacteristic
344C2×C4#666511yescharacteristic
345C2×C4C2×D5×Dic311yescharacteristic
346C2×C4C2×#120111yescharacteristic
347C2×C4C2×#120211yescharacteristic
348C8—122no—
349C8—304no—
350C2×C3—22no—
351C2×C3—401no—
352C2×C3#6525511yescharacteristic
353C2×C3#6539911yescharacteristic
354C2×C3C2×#395711yescharacteristic
355C5#7175111yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—201no—
359C22—201no—
360C22—201no—
361C22#9097612yes—
362C22C2×#666511yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—201no—
368C4—201no—
369C4—201no—
370C4#9128312yes—
371C4#9129911yescharacteristic
372C4#9130711yescharacteristic
373C3#1060122011yescharacteristic, complemented, Sylow
374C2—22no—
375C2—401no—
376C2#1174834211yescharacteristic
377C2#1174836811yescharacteristic
378C2C2×#9097611yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C4
cosocleC3×C42×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#6710C2semidirect
3. C2×C5×C4⋊(C3⋊C8)C2semidirect
4. #11745840C2semidirect
5. #11745834C2semidirect
58. C2×C4⋊(C3⋊C8)D5semidirect
305. C3×C5#1483semidirect
355. C5#71751semidirect
373. C3#10601220semidirect

Maximal subgroups

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

subgroupindex
C3×#658132
C4×#67102
C2×C5×C4⋊(C3⋊C8)2
#117458402
#117458342
#106012203
#717515