Finite Group Databasebeta

← #14302017

Subgroups — #14302017

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5791C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic, complemented
3#11751308C211yesmaximal, characteristic, complemented
4C2×#90979C212yesmaximal, complemented
5#11745977C212yesmaximal, complemented
6#10602505—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C5×#235C2211yescharacteristic
9C2×#6710C2212yes—
10C5×#953—21no—
11C5×#930C412yescomplemented
12C5×#929—21no—
13C4×C5×#67—22no—
14C5×#926C2211yescharacteristic
15C5×#924C412yescomplemented
16C2×C3×C22⋊Dic5—21no—
17C3×#4072—24no—
18C2×C3×C4⋊Dic5—21no—
19C2×C3×C4×Dic5C2212yes—
20#91114—22no—
21#90979—24no—
22#71591—51nomaximal, Hall
23C5×#525—31no—
24C2×#4072D311yescharacteristic, complemented
25C2×#3969—32no—
26#65496—31no—
27#64752—32no—
28C24×C3×C5D411yescharacteristic
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5C2×C412yes—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C5×#67—22no—
36C2×C5×#67—21no—
37C5×#235—22no—
38C5×#235—22no—
39C2×C5×D12C2×C411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C5×Dic6C2×C411yescharacteristic
42C22×C3×Dic5—22no—
43#6710—22no—
44#6710—22no—
45C2×C3⋊#168—22no—
46C5×#217—22no—
47C5×#217—21no—
48C5×(C2×D3)⋊C4—22no—
49C5×C4⋊Dic3C2×C412yes—
50C5×Dic3⋊C4—22no—
51C4×C5×Dic3—21no—
52C3×C22⋊Dic5—24no—
53C3×C4⋊Dic5—24no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5D414yescomplemented
56C2×C3×#117—51no—
57#5791D511yescharacteristic
58#5207—51no—
59C2×#805—52no—
60#4523—52no—
61C2×C5×#41—31no—
62C23×C4×C5C2×D311yescharacteristic
63C5×#123—61no—
64C5×C22⋊Q8—32no—
65C5×#121—32no—
66C5×#120—61no—
67C4×C5×D4—62no—
68C5×#117—31no—
69C2×C22⋊Dic5—21no—
70#4072—24no—
71C2×C4⋊Dic5—21no—
72C2×C4×Dic5C2×D312yes—
73C2×#681—32no—
74#3969—64no—
75C22⋊#168—62no—
76#1897—151noSylow
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—42no—
80C23×C3×C5C22⋊C412yes—
81C23×C3×C5C2×D411yescharacteristic
82C22×C5×D3—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—24no—
86C2×C3×C4×C5—24no—
87C2×C3×C4×C5C22⋊C412yes—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D412yes—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4112yes—
92C5×#67—44no—
93C5×#67—41no—
94C5×#67—41no—
95C2×C5×Dic3—22no—
96C2×C5×Dic3—21no—
97C5×D12—22no—
98C4×C5×D3—42no—
99C5×Dic6—22no—
100C2×C3×Dic5—24no—
101C2×C3×Dic5—44no—
102C3⋊#168—42no—
103C23×C3×C4C2×D511yescharacteristic
104C2×#235C2×D511yescharacteristic
105C3×#117—104no—
106C2×C3×C4⋊C4—101no—
107C2×C3×C22⋊C4—101no—
108C2×C3×C42—52no—
109#953—21no—
110#930Dic512yescomplemented
111#929—21no—
112C4×#67—22no—
113#926C2×D511yescharacteristic
114#924Dic512yescomplemented
115C2×#208—52no—
116#830—102no—
117#805—104no—
118C24×C5#6711yescharacteristic
119C5×#41—62no—
120C5×#41—62no—
121C2×C5×Q8—31no—
122C2×C5×D4—31no—
123C2×C5×D4—62no—
124C2×C5×D4—61no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—61no—
128C22×C4×C5C4×D312yes—
129C22×C4×C5D1212yes—
130C22×C4×C5#6711yescharacteristic
131C22×C4×C5C22×D311yescharacteristic
132C22×Dic5—22no—
133C5×C4⋊C4—32no—
134C5×C4⋊C4—62no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—61no—
137C5×C22⋊C4—62no—
138C42×C5—61no—
139C22⋊Dic5—24no—
140C4⋊Dic5—24no—
141C4×Dic5—22no—
142C4×Dic5#6714yescomplemented
143#681—62no—
144#681—62no—
145C2×#168—62no—
146#525—31no—
147C2×#117—51no—
148C2×#104—152no—
149#407—151no—
150#339—152no—
151C22×C3×C5—22no—
152C22×C3×C5—22no—
153C22×C3×C5—22no—
154C22×C3×C5—22no—
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12311yescharacteristic
160C2×C5×D3—41no—
161C2×C5×D3—42no—
162C3×C4×C5—22no—
163C3×C4×C5C4×D412yes—
164C3×C4×C5#12112yes—
165C3×Dic5—44no—
166C5×Dic3—41no—
167C5×Dic3—42no—
168C24×C3C22⋊D511yescharacteristic
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—102no—
172C22×C3×C4C2×Dic512yes—
173C22×C3×C4C22⋊D511yescharacteristic
174C22×C3×C4C22⋊D512yes—
175C22×C3×C4C22×D511yescharacteristic
176C2×#67—22no—
177C2×#67—21no—
178#235—22no—
179#235—22no—
180C2×D12C2×Dic511yescharacteristic
181C2×C4×D3—21no—
182C2×Dic6C2×Dic511yescharacteristic
183C3×C4⋊C4—104no—
184C3×C22⋊C4—104no—
185C3×C42—54no—
186C3×C42—102no—
187#217—22no—
188#217—21no—
189(C2×D3)⋊C4—22no—
190C4⋊Dic3C2×Dic512yes—
191Dic3⋊C4—22no—
192C4×Dic3—21no—
193#208—102no—
194#208—102no—
195C2×C3⋊C8—102no—
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—42no—
199C23×C5—61no—
200C23×C5(C2×D3)⋊C412yes—
201C23×C5C2×#6711yescharacteristic
202C5×Q8—62no—
203C5×D4—62no—
204C5×D4—124no—
205C5×D4—121no—
206C5×D4—121no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—24no—
210C2×C4×C5—24no—
211C2×C4×C5—62no—
212C2×C4×C5—61no—
213C2×C4×C5—122no—
214C2×C4×C5(C2×D3)⋊C412yes—
215C2×C4×C5C2×C4×D311yescharacteristic
216C2×C4×C5C2×D1211yescharacteristic
217C2×C4×C5#23512yes—
218C2×C4×C5C2×#6712yes—
219C2×Dic5—24no—
220C2×Dic5—44no—
221#168—122no—
222C2×#41—31no—
223C23×C4D3×D511yescharacteristic
224C2×M16—152no—
225#123—61no—
226C22⋊Q8—32no—
227#121—32no—
228#120—61no—
229C4×D4—62no—
230#117—31no—
231#117—104no—
232C2×C4⋊C4—101no—
233C2×C22⋊C4—101no—
234C2×C42—52no—
235#104—304no—
236C22⋊C8—302no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—42no—
240C2×C3×C5#38611yescharacteristic
241C2×C3×C5#42112yes—
242C5×D3—81no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—42no—
246C23×C3C22⋊Dic512yes—
247C23×C3C2×C22⋊D511yescharacteristic
248C22×D3—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—104no—
254C2×C3×C4—204no—
255C2×C3×C4C22⋊Dic512yes—
256C2×C3×C4D4×D512yes—
257C2×C3×C4#71112yes—
258C2×C3×C4C22×Dic511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260#67—44no—
261#67—41no—
262#67—41no—
263C2×Dic3—22no—
264C2×Dic3—21no—
265D12—22no—
266C4×D3—42no—
267Dic6—22no—
268C3⋊C8—202no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—22no—
272C22×C5—22no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5—121no—
276C22×C5—122no—
277C22×C5C2×(C2×D3)⋊C411yescharacteristic
278C22×C5#92911yescharacteristic
279C22×C5#95311yescharacteristic
280C4×C5—22no—
281C4×C5—121no—
282C4×C5—122no—
283C4×C5C4×#6712yes—
284C4×C5#93012yes—
285Dic5—44no—
286C24#120111yescharacteristic
287#41—62no—
288#41—62no—
289C2×Q8—31no—
290C2×D4—31no—
291C2×D4—62no—
292C2×D4—61no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—61no—
296C22×C4—102no—
297C22×C4D3×Dic512yes—
298C22×C4#120111yescharacteristic
299C22×C4#120312yes—
300C22×C4C2×D3×D511yescharacteristic
301M16—302no—
302M16—302no—
303C2×C8—302no—
304C4⋊C4—32no—
305C4⋊C4—62no—
306C4⋊C4—104no—
307C22⋊C4—62no—
308C22⋊C4—61no—
309C22⋊C4—62no—
310C22⋊C4—104no—
311C42—54no—
312C42—61no—
313C42—102no—
314C3×C5#189711yescharacteristic, complemented, Hall
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3#408111yescharacteristic
322C22×C3#408311yescharacteristic
323C22×C3C2×C22⋊Dic511yescharacteristic
324C2×D3—41no—
325C2×D3—42no—
326C3×C4—22no—
327C3×C4—204no—
328C3×C4D4×Dic512yes—
329C3×C4#408512yes—
330Dic3—41no—
331Dic3—42no—
332C2×C5—21no—
333C2×C5—21no—
334C2×C5—42no—
335C2×C5—241no—
336C2×C5#500512yes—
337C2×C5#521311yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—61no—
342C23(C2×D3)⋊Dic512yes—
343C23C2×#120111yescharacteristic
344Q8—62no—
345D4—62no—
346D4—124no—
347D4—121no—
348D4—121no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—62no—
354C2×C4—61no—
355C2×C4—104no—
356C2×C4—122no—
357C2×C4—204no—
358C2×C4(C2×D3)⋊Dic512yes—
359C2×C4C2×D3×Dic511yescharacteristic
360C2×C4#678212yes—
361C2×C4C2×#120311yescharacteristic
362C2×C4D5×#6712yes—
363C8—602no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—42no—
367C2×C3#6550911yescharacteristic
368C2×C3#6552512yes—
369D3—81no—
370C5#7159111yescharacteristic, complemented, Sylow
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—122no—
378C22—121no—
379C22C2×(C2×D3)⋊Dic511yescharacteristic
380C22#9153911yescharacteristic
381C22#9156311yescharacteristic
382C4—22no—
383C4—122no—
384C4—121no—
385C4—204no—
386C4Dic5×#6712yes—
387C4#9156612yes—
388C3#1060250511yescharacteristic, complemented, Sylow
389C2—21no—
390C2—21no—
391C2—42no—
392C2—241no—
393C2#1174842512yes—
394C2#1174949211yescharacteristic
subgroupG/H
centerC2×C4C2×#1203
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5791C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1897
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4072C2semidirect
3. #11751308C2semidirect
4. C2×#90979C2semidirect
5. #11745977C2semidirect
11. C5×#930C4semidirect
15. C5×#924C4semidirect
24. C2×#4072D3semidirect
55. C3×C4×Dic5D4semidirect
110. #930Dic5semidirect
114. #924Dic5semidirect
142. C4×Dic5#67semidirect
314. C3×C5#1897semidirect
370. C5#71591semidirect
388. C3#10602505semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
C2×C3×#40722
#117513082
C2×#909792
#117459772
#106025053
#715915