Finite Group Databasebeta

← #14313548

Subgroups — #14313548

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66159C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic
3C5×#5240C211yesmaximal, characteristic
4#11746009C214yesmaximal, complemented
5#10600852—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×Dic10C411yescharacteristic, complemented
8#91815—21no—
9C5×#926—21no—
10C3×#4090C412yescomplemented
11C3×#4082C2212yes—
12C3×#4081—21no—
13C3×#4081—21no—
14C3×#4072C411yescharacteristic, complemented
15C3×#4070—21no—
16C3×#4070—21no—
17#91118—21no—
18#91118C2212yes—
19C5×#834—21no—
20C5×#834C2212yes—
21#71871—51nomaximal, Hall
22#66159D311yescharacteristic
23C5×#410—31no—
24#65529—31no—
25#64693—34no—
26C3×C5×#41—41no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8C2×C411yescharacteristic
29C2×C3×C5×D4D411yescharacteristic
30C2×C3×C5×D4D411yescharacteristic
31C2×C3×C5×D4C2311yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×Dic5—21no—
36C2×C3×Dic10—21no—
37C2×C3×Dic10—41no—
38C2×C3×Dic10—41no—
39C2×C3×Dic10C2×C412yes—
40#6719—22no—
41C4⋊Dic15—41no—
42C4×Dic15—41no—
43C5×#217—22no—
44C5×C4⋊Dic3—41no—
45C4×C5×Dic3—41no—
46C3×C22⋊Dic5—21no—
47C3×C22⋊Dic5—22no—
48C3×C22⋊Dic5—22no—
49C3×C4⋊Dic5—21no—
50C3×#683—22no—
51C3×#683—22no—
52C3×C4×Dic5C2×C412yes—
53C3×#536—51no—
54#5240—51no—
55#5240D511yescharacteristic
56#4541—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×Dic10Dic311yescharacteristic, complemented
59C5×#117—61no—
60#4090Dic312yescomplemented
61#4082C2×D312yes—
62#4081—21no—
63#4081—21no—
64#4072—61no—
65#4072Dic311yescharacteristic, complemented
66#4070—21no—
67#4070—21no—
68C5×#99—32no—
69C5×#99—61no—
70#3966—32no—
71#3966—61no—
72#2129—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C3×C5×Q8—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
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×Dic15—42no—
91C2×C5×Dic3—42no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—42no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97C3×Dic10—42no—
98C2×C3×#41C2×D511yescharacteristic
99C22×C3×Q8—51no—
100C3×C4⋊Q8—52no—
101C3×#124—52no—
102C3×#123—101no—
103C3×#123—101no—
104C3×C22⋊Q8—101no—
105C3×C22⋊Q8—101no—
106C3×#117—51no—
107#926—21no—
108#926—101no—
109#834—21no—
110#834—52no—
111#834—101no—
112#834C2×D512yes—
113C5×#41—41no—
114C5×#41—41no—
115C2×C5×Q8C2×Dic311yescharacteristic
116C2×C5×D4#6711yescharacteristic
117C2×C5×D4#6711yescharacteristic
118C2×C5×D4C22×D311yescharacteristic
119C22×C4×C5C2×Dic311yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C22×Dic5—21no—
123C2×Dic10—21no—
124C2×Dic10—41no—
125C2×Dic10—41no—
126C2×Dic10C2×Dic312yes—
127C5×C4⋊C4—121no—
128C5×C22⋊C4—62no—
129C42×C5—121no—
130C22⋊Dic5—21no—
131C22⋊Dic5—22no—
132C22⋊Dic5—22no—
133C22⋊Dic5—62no—
134C4⋊Dic5—21no—
135C4⋊Dic5—121no—
136#683—22no—
137#683—22no—
138C4×Dic5—121no—
139C4×Dic5C2×Dic312yes—
140#536—51no—
141#410—31no—
142#410—151no—
143#354—154no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—41no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5#9911yescharacteristic
155C3×C4×C5#9911yescharacteristic
156Dic15—82no—
157C3×Dic5—42no—
158C3×Dic5—42no—
159C5×Dic3—82no—
160C3×#41—41no—
161C3×#41—41no—
162C2×C3×Q8—52no—
163C2×C3×Q8—101no—
164C2×C3×Q8—201no—
165C2×C3×Q8—201no—
166C2×C3×Q8C4×D511yescharacteristic
167C2×C3×D4D2011yescharacteristic
168C2×C3×D4C22⋊D511yescharacteristic
169C2×C3×D4C22×D511yescharacteristic
170C22×C3×C4—101no—
171C22×C3×C4C4×D511yescharacteristic
172C22×C3×C4D2011yescharacteristic
173C22×C3×C4C22⋊D511yescharacteristic
174C3×C4⋊C4—102no—
175C3×C4⋊C4—102no—
176C3×C4⋊C4—101no—
177C3×C22⋊C4—101no—
178C3×C22⋊C4—102no—
179C3×C22⋊C4—102no—
180C3×C42—52no—
181#217—22no—
182#217—102no—
183C4⋊Dic3—41no—
184C4⋊Dic3—201no—
185C4×Dic3—41no—
186C4×Dic3—201no—
187C23×C5#21711yescharacteristic
188C23×C5C2×#6711yescharacteristic
189C23×C5C2×#6711yescharacteristic
190C5×Q8—41no—
191C5×D4—41no—
192C5×D4—41no—
193C5×D4—41no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—122no—
201C2×C4×C5#21711yescharacteristic
202C2×C4×C5#21711yescharacteristic
203C2×C4×C5#21711yescharacteristic
204C2×C4×C5C22×Dic311yescharacteristic
205C2×Dic5—22no—
206C2×Dic5—22no—
207C2×Dic5—42no—
208C2×Dic5—122no—
209Dic10—41no—
210Dic10—41no—
211Dic10—42no—
212C2×#41D3×D511yescharacteristic
213C22×Q8—51no—
214C4⋊Q8—52no—
215#124—52no—
216#123—101no—
217#123—101no—
218C22⋊Q8—101no—
219C22⋊Q8—101no—
220#117—51no—
221#117—61no—
222#117—301no—
223#99—32no—
224#99—61no—
225#99—152no—
226#99—301no—
227C2×C3×C5—21no—
228C2×C3×C5—41no—
229C2×C3×C5—41no—
230C2×C3×C5—41no—
231C2×C3×C5C2×#9911yescharacteristic
232C23×C3#68511yescharacteristic
233C23×C3C2×D2011yescharacteristic
234C23×C3C2×C22⋊D511yescharacteristic
235C3×Q8—41no—
236C3×Q8—202no—
237C3×Q8—201no—
238C3×Q8—201no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—102no—
249C2×C3×C4—102no—
250C2×C3×C4—202no—
251C2×C3×C4#68511yescharacteristic
252C2×C3×C4#68511yescharacteristic
253C2×C3×C4#68511yescharacteristic
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×Dic3—42no—
256C2×Dic3—202no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5C2×#21711yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—242no—
268C4×C5#83411yescharacteristic
269C4×C5#83411yescharacteristic
270Dic5—42no—
271Dic5—42no—
272Dic5—242no—
273#41—41no—
274#41—41no—
275C2×Q8—52no—
276C2×Q8—101no—
277C2×Q8—201no—
278C2×Q8—201no—
279C2×Q8D5×Dic311yescharacteristic
280C2×D4#120111yescharacteristic
281C2×D4#120211yescharacteristic
282C2×D4C2×D3×D511yescharacteristic
283C22×C4—101no—
284C22×C4D5×Dic311yescharacteristic
285C22×C4#120111yescharacteristic
286C22×C4#120211yescharacteristic
287C4⋊C4—102no—
288C4⋊C4—102no—
289C4⋊C4—101no—
290C4⋊C4—121no—
291C4⋊C4—601no—
292C22⋊C4—62no—
293C22⋊C4—101no—
294C22⋊C4—102no—
295C22⋊C4—102no—
296C22⋊C4—302no—
297C42—52no—
298C42—121no—
299C42—601no—
300C3×C5#212911yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C2×#68511yescharacteristic
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—202no—
312C3×C4—202no—
313C3×C4#393811yescharacteristic
314C3×C4#393811yescharacteristic
315Dic3—82no—
316Dic3—402no—
317C2×C5—21no—
318C2×C5—41no—
319C2×C5—41no—
320C2×C5—41no—
321C2×C5C2×#83411yescharacteristic
322C23#666511yescharacteristic
323C23C2×#120111yescharacteristic
324C23C2×#120211yescharacteristic
325Q8—41no—
326Q8—202no—
327Q8—201no—
328Q8—201no—
329D4—41no—
330D4—41no—
331D4—41no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—102no—
339C2×C4—102no—
340C2×C4—122no—
341C2×C4—202no—
342C2×C4—602no—
343C2×C4#666511yescharacteristic
344C2×C4#666511yescharacteristic
345C2×C4#666511yescharacteristic
346C2×C4C2×D5×Dic311yescharacteristic
347C2×C3—21no—
348C2×C3—41no—
349C2×C3—41no—
350C2×C3—41no—
351C2×C3C2×#393811yescharacteristic
352C5#7187111yescharacteristic, complemented, Sylow
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C2×#666511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—202no—
364C4—202no—
365C4—242no—
366C4—1202no—
367C4#9099511yescharacteristic
368C4#9099511yescharacteristic
369C3#1060085211yescharacteristic, complemented, Sylow
370C2—21no—
371C2—41no—
372C2—41no—
373C2—41no—
374C2C2×#9099511yescharacteristic
subgroupG/H
centerC2C2×#90995
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2129
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #11746009C2semidirect
7. C22×C3×Dic10C4semidirect
10. C3×#4090C4semidirect
14. C3×#4072C4semidirect
58. C22×Dic10Dic3semidirect
60. #4090Dic3semidirect
65. #4072Dic3semidirect
300. C3×C5#2129semidirect
352. C5#71871semidirect
369. C3#10600852semidirect

Maximal subgroups

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

subgroupindex
C3×#661592
#117513412
C5×#52402
#117460092
#106008523
#718715