Finite Group Databasebeta

← #14285125

Subgroups — #14285125

Order 1920.

484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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#11756484C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3#11750934C211yesmaximal, characteristic, complemented
4C3×C5×#332C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746306C211yesmaximal, characteristic, complemented
8#10599219—31nomaximal, Hall
9C2×#6821—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91836—21no—
12#91784—21no—
13#91784C412yes—
14#91782—21no—
15#91782C412yes—
16#91763C2211yescharacteristic
17C42×D15C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21#91104—21no—
22#91099—21no—
23C8×Dic15—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68426—51nomaximal, Hall
27#66059—31no—
28#65124—31no—
29#65122—31no—
30C5×#332D311yescharacteristic, complemented
31#64767—31no—
32#64705—31no—
33#64705—31no—
34C2×C3×C5×Q8—21no—
35#6821—42no—
36#6821—42no—
37C2×D60—22no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60C2×C412yes—
41C2×C4×D15—22no—
42C2×C4×D15C2×C411yescharacteristic
43C2×C4×D15D411yescharacteristic
44C2×C4×D15D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4C2×C412yes—
49C3×C42×C5C2311yescharacteristic
50#6714—22no—
51#6714—22no—
52C4×Dic15C2×C411yescharacteristic
53C4×Dic15D411yescharacteristic
54C4×Dic15D411yescharacteristic
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5725—51no—
58#4835—51no—
59#4833—51no—
60C3×#332D511yescharacteristic, complemented
61#4547—51no—
62#4485—51no—
63#4485—51no—
64C2×#713—61no—
65C5×C4⋊Q8C2×D311yescharacteristic
66#4093—61no—
67#4041—32no—
68#4041—61no—
69#4039—32no—
70#4039—61no—
71#4020—31no—
72C42×D5—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—61no—
76#3952—61no—
77#3947—61no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1553—151noSylow
82C22×D15—22no—
83C22×D15C22⋊C411yescharacteristic
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92C2×Dic15C22⋊C411yescharacteristic
93D60—42no—
94D60—44no—
95D60—41no—
96D60—41no—
97D60—41no—
98D60—41no—
99C4×D15—21no—
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—21no—
103C4×D15—41no—
104C4×D15—44no—
105C3×C5×C8—41no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3⋊#168—41no—
109C2×#239—101no—
110C3×C4⋊Q8C2×D511yescharacteristic
111#947—101no—
112#895—52no—
113#895—101no—
114#893—52no—
115#893—101no—
116#874—51no—
117C42×D3—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×C4⋊C8C2×D511yescharacteristic
120(C2×D3)⋊C8—101no—
121(C2×D3)⋊C8—101no—
122#815—101no—
123C8×Dic3—101no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)—51no—
126C2×C5×Q8—21no—
127#713—122no—
128#713—122no—
129C2×D20—32no—
130C2×D20—62no—
131C2×D20—61no—
132C2×D20—61no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—62no—
137C2×C5×C8—21no—
138C2×C5×C8—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4C4×D312yes—
141C42×C5C22×D311yescharacteristic
142#685—62no—
143#685—62no—
144C4×Dic5—31no—
145C4×Dic5—31no—
146C4×Dic5—31no—
147C2×#168—61no—
148C2×#168—61no—
149#532—151no—
150#432—151no—
151#431—151no—
152#332—151no—
153#332D1511yescharacteristic, complemented
154#331—151no—
155#331—151no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C2×D15—21no—
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—42no—
161C2×D15—42no—
162C2×D15—42no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169Dic15—21no—
170Dic15—21no—
171Dic15—21no—
172C2×C3×Q8—21no—
173#239—202no—
174#239—202no—
175C2×D12—52no—
176C2×D12—102no—
177C2×D12—101no—
178C2×D12—101no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×C4×D3—102no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4C4×D512yes—
187C3×C42C22×D511yescharacteristic
188(C2×D3)⋊C4—102no—
189(C2×D3)⋊C4—102no—
190C4×Dic3—51no—
191C4×Dic3—51no—
192C4×Dic3—51no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C22×D5—31no—
196C22×D5—62no—
197C5×Q8—41no—
198C5×Q8—41no—
199C2×C4×C5—22no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×Dic5—31no—
204C2×Dic5—31no—
205C2×Dic5—31no—
206D20—122no—
207D20—124no—
208D20—121no—
209D20—121no—
210D20—121no—
211D20—121no—
212C4×D5—61no—
213C4×D5—61no—
214C4×D5—61no—
215C4×D5—61no—
216C4×D5—121no—
217C4×D5—124no—
218C5×C8—41no—
219C5×C8—41no—
220#168—121no—
221#168—121no—
222C2×#41—301no—
223C4⋊Q8C2×D1511yescharacteristic
224#127—151no—
225#124—301no—
226#121—152no—
227#121—301no—
228C4×D4—152no—
229C4×D4—301no—
230C2×C42—151no—
231C4⋊C8—151no—
232C4⋊C8—151no—
233C4⋊C8C2×D1511yescharacteristic
234C4⋊C8C2×D1511yescharacteristic
235C22⋊C8—301no—
236C22⋊C8—301no—
237#97—301no—
238C4×C8—301no—
239C2×C3×C5#41311yescharacteristic
240C2×C3×C5#41611yescharacteristic
241C2×C3×C5#41811yescharacteristic
242D15—41no—
243D15—82no—
244C22×D3—51no—
245C22×D3—102no—
246C3×Q8—41no—
247C3×Q8—41no—
248C2×C3×C4—22no—
249C2×C3×C4C2×C4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×Dic3—51no—
253C2×Dic3—51no—
254C2×Dic3—51no—
255D12—202no—
256D12—204no—
257D12—201no—
258D12—201no—
259D12—201no—
260D12—201no—
261C4×D3—101no—
262C4×D3—101no—
263C4×D3—101no—
264C4×D3—101no—
265C4×D3—201no—
266C4×D3—204no—
267C3×C8—41no—
268C3×C8—41no—
269C3⋊C8—201no—
270C3⋊C8—201no—
271C22×C5D3×C22⋊C411yescharacteristic
272C2×D5—61no—
273C2×D5—61no—
274C2×D5—61no—
275C2×D5—122no—
276C2×D5—122no—
277C2×D5—122no—
278C4×C5—21no—
279C4×C5—42no—
280C4×C5#91111yescharacteristic
281C4×C5#91411yescharacteristic
282C4×C5#91611yescharacteristic
283C4×C5#91911yescharacteristic
284Dic5—61no—
285Dic5—61no—
286Dic5—61no—
287#41—602no—
288#41—602no—
289C2×Q8—21no—
290C2×D4—152no—
291C2×D4—302no—
292C2×D4—301no—
293C2×D4—301no—
294C22×C4—151no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—302no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—301no—
301C2×C8—301no—
302C4⋊C4—21no—
303C4⋊C4C4×D1512yes—
304C22⋊C4—302no—
305C22⋊C4—302no—
306C42—151no—
307C42—151no—
308C42—151no—
309C42C22×D1511yescharacteristic
310C3×C5#155311yescharacteristic, complemented, Hall
311C22×C3D5×C22⋊C411yescharacteristic
312C2×D3—101no—
313C2×D3—101no—
314C2×D3—101no—
315C2×D3—202no—
316C2×D3—202no—
317C2×D3—202no—
318C3×C4—21no—
319C3×C4—42no—
320C3×C4#405711yescharacteristic
321C3×C4#406011yescharacteristic
322C3×C4#406211yescharacteristic
323C3×C4#406511yescharacteristic
324Dic3—101no—
325Dic3—101no—
326Dic3—101no—
327C2×C5#475111yescharacteristic
328C2×C5#477011yescharacteristic
329C2×C5#480411yescharacteristic
330D5—121no—
331D5—242no—
332C23—151no—
333C23—302no—
334Q8—41no—
335Q8—41no—
336D4—602no—
337D4—604no—
338D4—601no—
339D4—601no—
340D4—601no—
341D4—601no—
342C2×C4—22no—
343C2×C4—151no—
344C2×C4—151no—
345C2×C4—151no—
346C2×C4—301no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4—301no—
350C2×C4—601no—
351C2×C4—604no—
352C2×C4C2×C4×D1511yescharacteristic
353C2×C4D4×D1511yescharacteristic
354C2×C4D4×D1511yescharacteristic
355C8—41no—
356C8—41no—
357C8—601no—
358C8—601no—
359C2×C3#6504011yescharacteristic
360C2×C3#6505911yescharacteristic
361C2×C3#6509311yescharacteristic
362D3—201no—
363D3—402no—
364C5#6842611yescharacteristic, complemented, Sylow
365C22—301no—
366C22—301no—
367C22—301no—
368C22—602no—
369C22—602no—
370C22—602no—
371C22C22⋊C4×D1511yescharacteristic
372C4—21no—
373C4—42no—
374C4—301no—
375C4—301no—
376C4—301no—
377C4#9180011yescharacteristic
378C4#9180311yescharacteristic
379C4#9180511yescharacteristic
380C4#9180811yescharacteristic
381C3#1059921911yescharacteristic, complemented, Sylow
382C2—601no—
383C2—1202no—
384C2#1175085211yescharacteristic
385C2#1175087111yescharacteristic
386C2#1175090511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756484C2
cosocleC3×C42×C5C23
hypercenter#332D15
hypocenterC3×C5#1553
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. #11750934C2semidirect
4. C3×C5×#332C2semidirect
5. #11746368C2semidirect
6. #11746306C2semidirect
7. #11746306C2semidirect
30. C5×#332D3semidirect
60. C3×#332D5semidirect
153. #332D15semidirect
310. C3×C5#1553semidirect
364. C5#68426semidirect
381. C3#10599219semidirect

Maximal subgroups

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

subgroupindex
#117564842
#117509362
#117509342
C3×C5×#3322
#117463682
#117463062
#105992193
#684265