Finite Group Databasebeta

← #14313305

Subgroups — #14313305

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#536C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic
3#11751338C211yesmaximal, characteristic
4#11746360C214yesmaximal, complemented
5#10602663—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×C5×Q8C411yescharacteristic, complemented
8C3×C5×C4⋊Q8—21no—
9C3×C5×#124—21no—
10C3×C5×#123C412yescomplemented
11C3×C5×#123C2212yes—
12C3×C5×C22⋊Q8—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×#117C411yescharacteristic, complemented
15#91815—21no—
16C2×#6710—21no—
17#91120—21no—
18#91118—21no—
19#91118C2212yes—
20#91117C2212yes—
21#71870—51nomaximal, Hall
22C5×#536D311yescharacteristic
23#65529—31no—
24#65526—31no—
25#64759—34no—
26C3×C5×#41—41no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8—21no—
29C2×C3×C5×Q8—21no—
30C2×C3×C5×Q8—41no—
31C2×C3×C5×Q8—41no—
32C2×C3×C5×Q8D411yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4C2311yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C412yes—
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C22⋊C4—22no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4C2×C412yes—
46C3×C42×C5—21no—
47#6719—22no—
48C4⋊Dic15—41no—
49C4×Dic15—41no—
50#6710—22no—
51#6710—41no—
52C2×C3⋊#168—41no—
53C3×#536D511yescharacteristic
54#5240—51no—
55#5237—51no—
56#4539—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×C5×Q8Dic311yescharacteristic, complemented
59C5×C4⋊Q8—21no—
60C5×#124—21no—
61C5×#123Dic312yescomplemented
62C5×#123C2×D312yes—
63C5×C22⋊Q8—21no—
64C5×C22⋊Q8—21no—
65C5×#117Dic311yescharacteristic, complemented
66#4072—61no—
67C2×#681—61no—
68#3968—61no—
69#3966—32no—
70#3966—61no—
71#3965—32no—
72#2123—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22×C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C3×C5×Q8—41no—
77C3×C5×Q8—42no—
78C3×C5×Q8—41no—
79C3×C5×Q8—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—42no—
97C3⋊#168—42no—
98C2×C3×#41C2×D511yescharacteristic
99C22×C3×Q8Dic511yescharacteristic, complemented
100C3×C4⋊Q8—21no—
101C3×#124—21no—
102C3×#123Dic512yescomplemented
103C3×#123C2×D512yes—
104C3×C22⋊Q8—21no—
105C3×C22⋊Q8—21no—
106C3×#117Dic511yescharacteristic, complemented
107#926—101no—
108C2×#208—101no—
109#836—101no—
110#834—52no—
111#834—101no—
112#833—52no—
113C5×#41—41no—
114C5×#41—41no—
115C2×C5×Q8—21no—
116C2×C5×Q8—21no—
117C2×C5×Q8—41no—
118C2×C5×Q8—41no—
119C2×C5×Q8#6711yescharacteristic
120C2×C5×D4C2×Dic311yescharacteristic
121C2×C5×D4#6711yescharacteristic
122C2×C5×D4C22×D311yescharacteristic
123C22×C4×C5C2×Dic311yescharacteristic
124C22×C4×C5C2×Dic312yes—
125C22×C4×C5#6711yescharacteristic
126C22×C4×C5#6711yescharacteristic
127C5×C4⋊C4—21no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—22no—
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4C2×Dic312yes—
133C42×C5—21no—
134C22⋊Dic5—62no—
135C4⋊Dic5—121no—
136C4×Dic5—121no—
137#681—62no—
138#681—121no—
139C2×#168—121no—
140#536D1511yescharacteristic
141#413—151no—
142#410—151no—
143#352—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—42no—
155C3×C4×C5—42no—
156C3×C4×C5#9911yescharacteristic
157C3×C4×C5#9911yescharacteristic
158Dic15—82no—
159C3×#41—41no—
160C3×#41—41no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—41no—
164C2×C3×Q8—41no—
165C2×C3×Q8C22⋊D511yescharacteristic
166C2×C3×D4C2×Dic511yescharacteristic
167C2×C3×D4C22⋊D511yescharacteristic
168C2×C3×D4C22×D511yescharacteristic
169C22×C3×C4C2×Dic511yescharacteristic
170C22×C3×C4C2×Dic512yes—
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22⋊D511yescharacteristic
173C3×C4⋊C4—21no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C22⋊C4—22no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4C2×Dic512yes—
179C3×C42—21no—
180#217—102no—
181C4⋊Dic3—201no—
182C4×Dic3—201no—
183#208—102no—
184#208—201no—
185C2×C3⋊C8—201no—
186C23×C5#21711yescharacteristic
187C23×C5C22×Dic311yescharacteristic
188C23×C5C2×#6711yescharacteristic
189C5×Q8—41no—
190C5×Q8—42no—
191C5×Q8—41no—
192C5×Q8—41no—
193C5×D4—41no—
194C5×D4—41no—
195C5×D4—41no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—42no—
205C2×C4×C5#21711yescharacteristic
206C2×C4×C5#21711yescharacteristic
207C2×C4×C5#21711yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—122no—
210#168—122no—
211C2×#41C2×D1511yescharacteristic
212C22×Q8Dic1511yescharacteristic, complemented
213C2×M16—301no—
214C4⋊Q8—21no—
215#124—21no—
216#123Dic1512yescomplemented
217#123C2×D1512yes—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#117—301no—
221#117Dic1511yescharacteristic, complemented
222#101—301no—
223#100—152no—
224#99—152no—
225#99—301no—
226C2×C3×C5—21no—
227C2×C3×C5—41no—
228C2×C3×C5—41no—
229C2×C3×C5—41no—
230C2×C3×C5C2×#9911yescharacteristic
231C23×C3C22⋊Dic511yescharacteristic
232C23×C3C22×Dic511yescharacteristic
233C23×C3C2×C22⋊D511yescharacteristic
234C3×Q8—41no—
235C3×Q8—42no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—42no—
250C2×C3×C4C22⋊Dic511yescharacteristic
251C2×C3×C4C22⋊Dic511yescharacteristic
252C2×C3×C4C22⋊Dic511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×Dic3—202no—
255C3⋊C8—202no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5C2×#21711yescharacteristic
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—42no—
267C4×C5—42no—
268C4×C5#83411yescharacteristic
269C4×C5#83411yescharacteristic
270Dic5—242no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8#122011yescharacteristic
278C2×D4C2×Dic1511yescharacteristic
279C2×D4#122011yescharacteristic
280C2×D4C22×D1511yescharacteristic
281C22×C4C2×Dic1511yescharacteristic
282C22×C4C2×Dic1512yes—
283C22×C4#122011yescharacteristic
284C22×C4#122011yescharacteristic
285M16—302no—
286M16—601no—
287C2×C8—601no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—601no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—302no—
295C22⋊C4C2×Dic1512yes—
296C42—21no—
297C42—601no—
298C3×C5#212311yescharacteristic, complemented, Hall
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3C2×C22⋊Dic511yescharacteristic
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—42no—
310C3×C4—42no—
311C3×C4#396611yescharacteristic
312C3×C4#396611yescharacteristic
313Dic3—402no—
314C2×C5—21no—
315C2×C5—41no—
316C2×C5—41no—
317C2×C5—41no—
318C2×C5C2×#83411yescharacteristic
319C23#671911yescharacteristic
320C23C22×Dic1511yescharacteristic
321C23C2×#122011yescharacteristic
322Q8—41no—
323Q8—42no—
324Q8—41no—
325Q8—41no—
326D4—41no—
327D4—41no—
328D4—41no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—602no—
339C2×C4#671911yescharacteristic
340C2×C4#671911yescharacteristic
341C2×C4#671911yescharacteristic
342C2×C4C2×#122011yescharacteristic
343C8—602no—
344C2×C3—21no—
345C2×C3—41no—
346C2×C3—41no—
347C2×C3—41no—
348C2×C3C2×#396611yescharacteristic
349C5#7187011yescharacteristic, complemented, Sylow
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C2×#671911yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—42no—
362C4—1202no—
363C4#9111811yescharacteristic
364C4#9111811yescharacteristic
365C3#1060266311yescharacteristic, complemented, Sylow
366C2—21no—
367C2—41no—
368C2—41no—
369C2—41no—
370C2C2×#9111811yescharacteristic
subgroupG/H
centerC2C2×#91118
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C22×D15
FittingC3×C5×#536C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C5×D4C23
hypercenter#536D15
hypocenterC3×C5#2123
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
4. #11746360C2semidirect
7. C22×C3×C5×Q8C4semidirect
10. C3×C5×#123C4semidirect
14. C3×C5×#117C4semidirect
58. C22×C5×Q8Dic3semidirect
61. C5×#123Dic3semidirect
65. C5×#117Dic3semidirect
99. C22×C3×Q8Dic5semidirect
102. C3×#123Dic5semidirect
106. C3×#117Dic5semidirect
212. C22×Q8Dic15semidirect
216. #123Dic15semidirect
221. #117Dic15semidirect
298. C3×C5#2123semidirect
349. C5#71870semidirect
365. C3#10602663semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5362
#117513412
#117513382
#117463602
#106026633
#718705