Finite Group Databasebeta

← #14313498

Subgroups — #14313498

Order 1920.

540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756474C211yesmaximal, characteristic
2#11750841C212yesmaximal, complemented
3C3×C5×#353C211yesmaximal, characteristic, complemented
4#11746366C211yesmaximal, characteristic, complemented
5#11746295C212yesmaximal, complemented
6#10599945—31nomaximal, Hall
7C2×#6819C2211yescharacteristic
8C2×D4×D15C411yescharacteristic, complemented
9C3×C5×#127C2211yescharacteristic
10#91829C2211yescharacteristic
11#91828—22no—
12#91826—22no—
13#91825C411yescharacteristic, complemented
14#91766—22no—
15#91764C411yescharacteristic, complemented
16#91761C411yescharacteristic, complemented
17C3×C5×#99C2212yescomplemented
18#91118C2212yescomplemented
19#91090—22no—
20#69152—51nomaximal, Hall
21#66049—31no—
22#65029—32no—
23C5×#353D311yescharacteristic, complemented
24#64765—31no—
25#64694—32no—
26C23×D15—21no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C3×C5×D4C2311yescharacteristic
30C2×#1220—22no—
31C2×#1220—21no—
32C2×#1220D412yes—
33C22×Dic15D412yes—
34#6819—42no—
35D4×D15—42no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15C2×C411yescharacteristic
38C2×Dic30C2×C411yescharacteristic
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2×C411yescharacteristic
41#6719—22no—
42#6719—22no—
43#6714—21no—
44#6714—22no—
45#6712—21no—
46#6712—42no—
47C4×Dic15—42no—
48C4×Dic15C2×C411yescharacteristic
49#5715—51no—
50#4740—52no—
51C3×#353D511yescharacteristic, complemented
52#4545—51no—
53#4474—52no—
54C2×#711—31no—
55C2×D4×D5—31no—
56C5×#127C2×D311yescharacteristic
57#4086—31no—
58#4085—62no—
59#4083—62no—
60#4082—31no—
61#4023—62no—
62#4021—31no—
63#4018—31no—
64C5×#99C2×D312yescomplemented
65#3966—32no—
66#3938—62no—
67#2128—151noSylow
68C23×C3×C5—21no—
69C23×C3×C5C2×D412yes—
70C22×D15—21no—
71C22×D15—42no—
72C22×D15—82no—
73C22×D15C22⋊C411yescharacteristic
74C3×C5×D4—41no—
75C3×C5×D4—41no—
76C3×C5×D4—82no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5C22×C411yescharacteristic
80#1220—42no—
81#1220—42no—
82#1220—82no—
83C2×Dic15—22no—
84C2×Dic15—22no—
85C2×Dic15—21no—
86C2×Dic15—42no—
87C2×Dic15C22⋊C412yes—
88C2×Dic15C22⋊C411yescharacteristic
89D60—41no—
90C4×D15—22no—
91Dic30—41no—
92C2×#237—51no—
93C2×D3×D4—51no—
94C3×#127C2×D511yescharacteristic
95#940—51no—
96#939—102no—
97#937—102no—
98#936—51no—
99#877—102no—
100#875—51no—
101#872—51no—
102C3×#99C2×D512yescomplemented
103#834—52no—
104#806—102no—
105C23×D5—61no—
106C2×C5×D4—22no—
107C2×C5×D4C4×D311yescharacteristic
108C2×C5×D4C22×D311yescharacteristic
109C2×C22⋊D5—32no—
110C2×C22⋊D5—61no—
111C2×C22⋊D5—62no—
112C22×Dic5—32no—
113#711—122no—
114D4×D5—122no—
115C2×D20—31no—
116C2×C4×D5—31no—
117C2×Dic10—31no—
118C5×C22⋊C4—22no—
119C42×C5C4×D311yescharacteristic
120C22⋊Dic5—62no—
121C22⋊Dic5—62no—
122#685—62no—
123#685—61no—
124#683—61no—
125#683—122no—
126C4×Dic5—31no—
127C4×Dic5—122no—
128#535—151no—
129#410—152no—
130#353—151no—
131#353—152no—
132#353D1511yescharacteristic, complemented
133C22×C3×C5—22no—
134C22×C3×C5—42no—
135C22×C3×C5—42no—
136C22×C3×C5—41no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C2×D15—21no—
139C2×D15—41no—
140C2×D15—42no—
141C2×D15—41no—
142C2×D15—84no—
143C3×C4×C5—21no—
144C3×C4×C5—41no—
145C3×C4×C5—82no—
146Dic15—22no—
147Dic15—41no—
148Dic15—82no—
149Dic15#9912yes—
150C23×D3—101no—
151C2×C3×D4—22no—
152C2×C3×D4C4×D511yescharacteristic
153C2×C3×D4C22×D511yescharacteristic
154C2×#67—52no—
155C2×#67—101no—
156C2×#67—102no—
157C22×Dic3—52no—
158#237—202no—
159D3×D4—202no—
160C2×D12—51no—
161C2×C4×D3—51no—
162C2×Dic6—51no—
163C3×C22⋊C4—22no—
164C3×C42C4×D511yescharacteristic
165#217—102no—
166#217—102no—
167(C2×D3)⋊C4—102no—
168(C2×D3)⋊C4—101no—
169Dic3⋊C4—101no—
170Dic3⋊C4—202no—
171C4×Dic3—51no—
172C4×Dic3—202no—
173C23×C5—21no—
174C23×C5D3×D412yes—
175C22×D5—31no—
176C22×D5—61no—
177C22×D5—122no—
178C22×D5—242no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—82no—
182C2×C4×C5—21no—
183C2×C4×C5—42no—
184C2×C4×C5C2×C4×D311yescharacteristic
185C22⋊D5—122no—
186C22⋊D5—122no—
187C22⋊D5—242no—
188C2×Dic5—31no—
189C2×Dic5—32no—
190C2×Dic5—62no—
191C2×Dic5—62no—
192C2×Dic5—61no—
193C2×Dic5—122no—
194D20—121no—
195C4×D5—62no—
196Dic10—121no—
197C2×#41—151no—
198C22×D4—151no—
199#127—151no—
200#127C2×D1511yescharacteristic
201#124—151no—
202#124—151no—
203#121—302no—
204#120—302no—
205#117—151no—
206#117—302no—
207#99—152no—
208#99—302no—
209#99C2×D1512yescomplemented
210C2×C3×C5—21no—
211C2×C3×C5—42no—
212C2×C3×C5—81no—
213C2×C3×C5C2×#9911yescharacteristic
214D15—41no—
215D15—81no—
216C23×C3—21no—
217C23×C3D4×D512yes—
218C22×D3—51no—
219C22×D3—101no—
220C22×D3—202no—
221C22×D3—402no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—82no—
225C2×C3×C4—21no—
226C2×C3×C4—42no—
227C2×C3×C4C2×C4×D511yescharacteristic
228#67—202no—
229#67—202no—
230#67—402no—
231C2×Dic3—51no—
232C2×Dic3—52no—
233C2×Dic3—102no—
234C2×Dic3—102no—
235C2×Dic3—101no—
236C2×Dic3—202no—
237D12—201no—
238C4×D3—102no—
239Dic6—201no—
240C22×C5—22no—
241C22×C5—42no—
242C22×C5—42no—
243C22×C5—41no—
244C22×C5D3×C22⋊C411yescharacteristic
245C2×D5—61no—
246C2×D5—121no—
247C2×D5—122no—
248C2×D5—121no—
249C2×D5—244no—
250C4×C5—21no—
251C4×C5—41no—
252C4×C5—82no—
253Dic5—32no—
254Dic5—62no—
255Dic5—121no—
256Dic5—242no—
257C24—301no—
258#41—602no—
259C2×Q8—151no—
260C2×D4—22no—
261C2×D4—152no—
262C2×D4—151no—
263C2×D4—301no—
264C2×D4—302no—
265C2×D4—602no—
266C2×D4C4×D1511yescharacteristic
267C2×D4C22×D1511yescharacteristic
268C22×C4—152no—
269C22×C4—151no—
270C4⋊C4—301no—
271C4⋊C4—602no—
272C22⋊C4—22no—
273C22⋊C4—302no—
274C22⋊C4—301no—
275C22⋊C4—302no—
276C22⋊C4—302no—
277C42—151no—
278C42—602no—
279C42C4×D1511yescharacteristic
280C3×C5#212811yescharacteristic, complemented, Hall
281C22×C3—22no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—41no—
285C22×C3D5×C22⋊C411yescharacteristic
286C2×D3—101no—
287C2×D3—201no—
288C2×D3—202no—
289C2×D3—201no—
290C2×D3—404no—
291C3×C4—21no—
292C3×C4—41no—
293C3×C4—82no—
294Dic3—52no—
295Dic3—102no—
296Dic3—201no—
297Dic3—402no—
298C2×C5—21no—
299C2×C5—42no—
300C2×C5—81no—
301C2×C5D3×#9911yescharacteristic
302D5—121no—
303D5—241no—
304C23—21no—
305C23—151no—
306C23—301no—
307C23—602no—
308C23—1202no—
309C23D4×D1512yes—
310Q8—601no—
311D4—41no—
312D4—41no—
313D4—82no—
314D4—601no—
315D4—602no—
316D4—602no—
317D4—1202no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—151no—
321C2×C4—152no—
322C2×C4—302no—
323C2×C4—302no—
324C2×C4—302no—
325C2×C4—301no—
326C2×C4—602no—
327C2×C4C2×C4×D1511yescharacteristic
328C2×C3—21no—
329C2×C3—42no—
330C2×C3—81no—
331C2×C3D5×#9911yescharacteristic
332D3—201no—
333D3—401no—
334C5#6915211yescharacteristic, complemented, Sylow
335C22—22no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—301no—
340C22—601no—
341C22—602no—
342C22—601no—
343C22—1204no—
344C22C22⋊C4×D1511yescharacteristic
345C4—21no—
346C4—41no—
347C4—82no—
348C4—152no—
349C4—302no—
350C4—601no—
351C4—1202no—
352C3#1059994511yescharacteristic, complemented, Sylow
353C2—21no—
354C2—42no—
355C2—81no—
356C2—601no—
357C2—1201no—
358C2D15×#9911yescharacteristic
subgroupG/H
centerC2D15×#99
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C22×D15
FittingC3×C5×#353C2
socleC2×C3×C5C2×#99
prime radical#11756474C2
cosocleC2×C3×C5×D4C23
hypercenter#353D15
hypocenterC3×C5#2128
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #11750841C2semidirect
3. C3×C5×#353C2semidirect
4. #11746366C2semidirect
5. #11746295C2semidirect
8. C2×D4×D15C4semidirect
13. #91825C4semidirect
15. #91764C4semidirect
16. #91761C4semidirect
17. C3×C5×#99C22semidirect
18. #91118C22semidirect
23. C5×#353D3semidirect
51. C3×#353D5semidirect
64. C5×#99C2×D3semidirect
102. C3×#99C2×D5semidirect
132. #353D15semidirect
209. #99C2×D15semidirect
280. C3×C5#2128semidirect
334. C5#69152semidirect
352. C3#10599945semidirect

Maximal subgroups

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

subgroupindex
#117564742
#117508412
C3×C5×#3532
#117463662
#117462952
#105999453
#691525