Finite Group Databasebeta

← #14284401

Subgroups — #14284401

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756238C211yesmaximal, characteristic
2C3×C5×#432C211yesmaximal, characteristic, complemented
3#11751027C211yesmaximal, characteristic, complemented
4#11746286C212yesmaximal, complemented
5#11746285C212yesmaximal, complemented
6#10601603—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8#91819C411yescharacteristic
9#91818—21no—
10C4×#1220—21no—
11#91813C411yescharacteristic
12#91765—21no—
13#91764C2211yescharacteristic
14C4×D60C411yescharacteristic
15#91761—21no—
16#91759C2211yescharacteristic
17C4×Dic30C411yescharacteristic
18C3×C5×C4⋊C8—21no—
19C3×C5×C22⋊C8—21no—
20C3×C5×#97C2212yes—
21#91114—21no—
22C4⋊(C3⋊#168)—21no—
23#91087C2212yes—
24#70810—51nomaximal, Hall
25#65813—31no—
26C5×#432D311yescharacteristic, complemented
27#65215—31no—
28#64685—32no—
29#64684—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×#1220—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C2×C3×C5×C8—22no—
38C3×C42×C5C2×C411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5C2311yescharacteristic
42#6719—21no—
43#6714—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C4⋊Dic15C2×C411yescharacteristic
49#6712—21no—
50#6712—21no—
51#6712—21no—
52#6712—21no—
53C4×Dic15—21no—
54C2×C3⋊#168—22no—
55#5479—51no—
56C3×#432D511yescharacteristic, complemented
57#4926—51no—
58#4465—52no—
59#4464—52no—
60C2×C42×C5C2×D311yescharacteristic
61#4076—31no—
62#4075—61no—
63C4×C22⋊D5—61no—
64#4070—31no—
65#4022—61no—
66#4021—31no—
67C4×D20—31no—
68#4018—61no—
69#4016—31no—
70C4×Dic10—31no—
71C5×C4⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×#97C2×D312yes—
74C22⋊#168—61no—
75C4⋊#168—61no—
76#3935—32no—
77#1535—151noSylow
78C23×C3×C5C22⋊C411yescharacteristic
79C22×D15—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89#1220—42no—
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93D60—41no—
94C4×D15—42no—
95Dic30—41no—
96C3×C5×C8—42no—
97C3⋊#168—42no—
98C2×C3×C42C2×D511yescharacteristic
99#930—51no—
100#929—101no—
101C4×#67—101no—
102#924—51no—
103#876—101no—
104#875—51no—
105C4×D12—51no—
106#872—101no—
107#870—51no—
108C4×Dic6—51no—
109C3×C4⋊C8—21no—
110C3×C22⋊C8—21no—
111C3×#97C2×D512yes—
112#830—101no—
113C4⋊(C3⋊C8)—101no—
114#803—52no—
115C22×C4×C5C4×D311yescharacteristic
116C22×C4×C5D1211yescharacteristic
117C22×C4×C5#6711yescharacteristic
118C2×C22⋊D5—61no—
119C2×D20—31no—
120C2×C4×D5—61no—
121C2×Dic10—31no—
122C2×C5×C8—22no—
123C42×C5C4×D311yescharacteristic
124C42×C5D1211yescharacteristic
125C42×C5#6711yescharacteristic
126C42×C5C22×D311yescharacteristic
127C22⋊Dic5—61no—
128#685—61no—
129#685—61no—
130#685—61no—
131#685—61no—
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134#683—61no—
135#683—61no—
136#683—61no—
137#683—61no—
138C4×Dic5—61no—
139C2×#168—62no—
140#529—151no—
141#432—151no—
142#432D1511yescharacteristic, complemented
143#330—152no—
144#329—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—41no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158Dic15—41no—
159Dic15—41no—
160Dic15—41no—
161C22×C3×C4C4×D511yescharacteristic
162C22×C3×C4D2011yescharacteristic
163C22×C3×C4C22⋊D511yescharacteristic
164C2×#67—101no—
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×Dic6—51no—
168C2×C3×C8—22no—
169C3×C42C4×D511yescharacteristic
170C3×C42D2011yescharacteristic
171C3×C42C22⋊D511yescharacteristic
172C3×C42C22×D511yescharacteristic
173#217—101no—
174(C2×D3)⋊C4—101no—
175(C2×D3)⋊C4—101no—
176(C2×D3)⋊C4—101no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—102no—
186C23×C5(C2×D3)⋊C411yescharacteristic
187C22×D5—61no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5(C2×D3)⋊C411yescharacteristic
194C2×C4×C5C2×C4×D311yescharacteristic
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C22⋊D5—122no—
198C2×Dic5—61no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201D20—121no—
202C4×D5—122no—
203Dic10—121no—
204C5×C8—42no—
205#168—122no—
206#126—301no—
207#125—151no—
208#124—151no—
209#123—301no—
210C22⋊Q8—151no—
211#121—151no—
212C4×Q8—151no—
213C4×D4—151no—
214C4×D4—301no—
215#117—301no—
216C2×C42C2×D1511yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—301no—
219C22⋊C8—21no—
220C22⋊C8—301no—
221#97—152no—
222#97C2×D1512yes—
223C2×C3×C5—41no—
224C2×C3×C5#41311yescharacteristic
225C2×C3×C5#42111yescharacteristic
226C2×C3×C5#42111yescharacteristic
227D15—81no—
228C23×C3#68511yescharacteristic
229C22×D3—101no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4#68511yescharacteristic
234C2×C3×C4#68511yescharacteristic
235C2×C3×C4#68511yescharacteristic
236C2×C3×C4C2×C4×D511yescharacteristic
237C2×C3×C4C2×D2011yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239#67—202no—
240C2×Dic3—101no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243D12—201no—
244C4×D3—202no—
245Dic6—201no—
246C3×C8—42no—
247C3⋊C8—202no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C2×(C2×D3)⋊C411yescharacteristic
252C2×D5—121no—
253C2×D5—121no—
254C2×D5—121no—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261Dic5—121no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—151no—
265C2×D4—151no—
266C2×D4—301no—
267C22×C4—301no—
268C22×C4C4×D1511yescharacteristic
269C22×C4D6011yescharacteristic
270C22×C4#122011yescharacteristic
271C2×C8—22no—
272C2×C8—302no—
273C4⋊C4—151no—
274C4⋊C4—151no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C22⋊C4—301no—
280C22⋊C4—301no—
281C22⋊C4—301no—
282C22⋊C4—301no—
283C22⋊C4—301no—
284C42—301no—
285C42C4×D1511yescharacteristic
286C42D6011yescharacteristic
287C42#122011yescharacteristic
288C42C22×D1511yescharacteristic
289C3×C5#153511yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3C2×#68511yescharacteristic
294C2×D3—201no—
295C2×D3—201no—
296C2×D3—201no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303Dic3—201no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—41no—
307C2×C5#500511yescharacteristic
308C2×C5#513211yescharacteristic
309C2×C5#513911yescharacteristic
310D5—241no—
311C23—301no—
312C23#671411yescharacteristic
313Q8—601no—
314D4—601no—
315D4—602no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—301no—
320C2×C4—301no—
321C2×C4—301no—
322C2×C4—602no—
323C2×C4#671411yescharacteristic
324C2×C4#671411yescharacteristic
325C2×C4#671411yescharacteristic
326C2×C4C2×C4×D1511yescharacteristic
327C2×C4C2×D6011yescharacteristic
328C2×C4C2×#122011yescharacteristic
329C8—42no—
330C8—602no—
331C2×C3—41no—
332C2×C3#6529411yescharacteristic
333C2×C3#6542111yescharacteristic
334C2×C3#6542811yescharacteristic
335D3—401no—
336C5#7081011yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—601no—
341C22—601no—
342C22—601no—
343C22C2×#671411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—601no—
351C4—601no—
352C4—601no—
353C3#1060160311yescharacteristic, complemented, Sylow
354C2—41no—
355C2—1201no—
356C2#1175110611yescharacteristic
357C2#1175123311yescharacteristic
358C2#1175124011yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#432C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C4
cosocleC3×C42×C5C23
hypercenter#432D15
hypocenterC3×C5#1535
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C3×C5×#432C2semidirect
3. #11751027C2semidirect
4. #11746286C2semidirect
5. #11746285C2semidirect
26. C5×#432D3semidirect
56. C3×#432D5semidirect
142. #432D15semidirect
289. C3×C5#1535semidirect
336. C5#70810semidirect
353. C3#10601603semidirect

Maximal subgroups

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

subgroupindex
#117562382
C3×C5×#4322
#117510272
#117462862
#117462852
#106016033
#708105