Finite Group Databasebeta

← #14284433

Subgroups — #14284433

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5691C211yesmaximal, characteristic
2#11746878C211yesmaximal, characteristic, complemented
3#11746878C211yesmaximal, characteristic, complemented
4#11746364C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10602542—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#898—21no—
11C5×#897C411yescharacteristic
12C5×#895C411yescharacteristic
13C5×#894—21no—
14C5×#893—21no—
15C5×#893C411yescharacteristic
16C5×#892—21no—
17C5×#887C411yescharacteristic
18C5×#875C2211yescharacteristic
19C42×C5×D3C2211yescharacteristic
20#91087C2211yescharacteristic
21#91087C2211yescharacteristic
22C3×#3935C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24Dic3⋊#168—21no—
25Dic3⋊#168—21no—
26(C2×D3)⋊#168—21no—
27(C2×D3)⋊#168—21no—
28#68368—51nomaximal, Hall
29C5×#529—31no—
30#65215—31no—
31#65215—31no—
32#64763—31no—
33#64763D311yescharacteristic, complemented
34#64760—31no—
35#64760—31no—
36C2×C5×D12—21no—
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C4×C5×D3C2×C411yescharacteristic
40C2×C4×C5×D3D411yescharacteristic
41C2×C4×C5×D3D411yescharacteristic
42C2×C5×Dic6C2×C411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×C4⋊Dic3—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3D411yescharacteristic
60C4×C5×Dic3D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63#5691D511yescharacteristic
64#4705—51no—
65#4705—51no—
66C3×#330—51no—
67#4543—51no—
68#4464—51no—
69#4464—51no—
70C5×#126—61no—
71C5×#125C2×D311yescharacteristic
72C5×#124—31no—
73C5×#123—61no—
74C5×C22⋊Q8—31no—
75C5×#121—31no—
76C4×C5×Q8—31no—
77C4×C5×D4—31no—
78C4×C5×D4—61no—
79C5×#117—61no—
80C2×C42×C5—31no—
81C22⋊#168—61no—
82C22⋊#168—61no—
83C4⋊#168—61no—
84C4⋊#168—61no—
85#3935—31no—
86#3935—31no—
87#3935C2×D311yescharacteristic
88#3935C2×D311yescharacteristic
89#1535—151noSylow
90C22×C5×D3—21no—
91C22×C5×D3C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C5×Dic3—21no—
98C2×C5×Dic3C22⋊C411yescharacteristic
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C5×D12—41no—
102C5×D12—42no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C4×C5×D3—41no—
106C4×C5×D3—42no—
107C5×Dic6—41no—
108C3⋊#168—41no—
109C3⋊#168—41no—
110C3×#168—41no—
111C3×#168—41no—
112C3×#125C2×D511yescharacteristic
113#898—21no—
114#897Dic511yescharacteristic
115#895Dic511yescharacteristic
116#894—21no—
117#893—21no—
118#893Dic511yescharacteristic
119#892—21no—
120#887Dic511yescharacteristic
121#875C2×D511yescharacteristic
122C42×D3C2×D511yescharacteristic
123C3×#97—51no—
124C3×#97—51no—
125(C2×D3)⋊C8—101no—
126(C2×D3)⋊C8—101no—
127Dic3⋊C8—101no—
128Dic3⋊C8—101no—
129#803—51no—
130#803—51no—
131C2×C5×Q8—31no—
132C2×C5×D4—31no—
133C2×C5×D4—61no—
134C22×C4×C5—31no—
135C22×C4×C5—31no—
136C22×C4×C5—31no—
137C22×C4×C5—61no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4C4×D311yescharacteristic
143C5×C4⋊C4C4×D311yescharacteristic
144C5×C22⋊C4—61no—
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4—61no—
149C42×C5—31no—
150C42×C5—31no—
151C42×C5—31no—
152C42×C5—61no—
153C42×C5C22×D311yescharacteristic
154C2×#168—21no—
155C2×#168—21no—
156C2×#168—61no—
157C2×#168—61no—
158#529—31no—
159#432—151no—
160#432—151no—
161#330—51no—
162#330—151no—
163#329—151no—
164#329—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C5×D3—21no—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C5×D3—41no—
170C2×C5×D3—41no—
171C2×C5×D3—41no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5—41no—
177C5×Dic3—21no—
178C5×Dic3—21no—
179C5×Dic3—21no—
180C5×Dic3—41no—
181C2×D12—21no—
182C2×D12C2×Dic511yescharacteristic
183C2×C4×D3—21no—
184C2×C4×D3C2×Dic511yescharacteristic
185C2×C4×D3C22⋊D511yescharacteristic
186C2×C4×D3C22⋊D511yescharacteristic
187C2×Dic6C2×Dic511yescharacteristic
188C2×C3×C8—101no—
189C2×C3×C8—101no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4C2×Dic511yescharacteristic
193C3×C4⋊C4C2×Dic511yescharacteristic
194C3×C42C22×D511yescharacteristic
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200C4⋊Dic3—21no—
201Dic3⋊C4—21no—
202C4×Dic3—21no—
203C4×Dic3C2×Dic511yescharacteristic
204C4×Dic3C22⋊D511yescharacteristic
205C4×Dic3C22⋊D511yescharacteristic
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—31no—
209C23×C5—61no—
210C5×Q8—121no—
211C5×D4—121no—
212C5×D4—122no—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—31no—
218C2×C4×C5—61no—
219C2×C4×C5—121no—
220C2×C4×C5—121no—
221C2×C4×C5—121no—
222C2×C4×C5—122no—
223C2×C4×C5C2×C4×D311yescharacteristic
224C2×C4×C5D3×D411yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226#168—41no—
227#168—41no—
228#168—121no—
229#168—121no—
230#126—61no—
231#125D3×D511yescharacteristic
232#124—31no—
233#123—61no—
234C22⋊Q8—31no—
235#121—31no—
236C4×Q8—31no—
237C4×D4—31no—
238C4×D4—61no—
239#117—61no—
240C2×C42—31no—
241C4⋊C8—301no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244C22⋊C8—301no—
245#97—51no—
246#97—51no—
247#97—151no—
248#97—151no—
249C2×C3×C5#41311yescharacteristic
250C2×C3×C5#42111yescharacteristic
251C2×C3×C5#42111yescharacteristic
252C5×D3—41no—
253C5×D3—81no—
254C22×D3—21no—
255C22×D3C22⋊Dic511yescharacteristic
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4C22×Dic511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×Dic3—21no—
262C2×Dic3C22⋊Dic511yescharacteristic
263C2×Dic3C22⋊Dic511yescharacteristic
264C2×Dic3C22⋊Dic511yescharacteristic
265D12—41no—
266D12—42no—
267C4×D3—41no—
268C4×D3—41no—
269C4×D3—41no—
270C4×D3—42no—
271Dic6—41no—
272C3×C8—201no—
273C3×C8—201no—
274C3⋊C8—201no—
275C3⋊C8—201no—
276C22×C5—61no—
277C22×C5—61no—
278C22×C5—61no—
279C22×C5—121no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5D3×C22⋊C411yescharacteristic
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—41no—
287C4×C5—41no—
288C4×C5—61no—
289C4×C5—61no—
290C4×C5—61no—
291C4×C5—121no—
292C2×Q8—31no—
293C2×D4—31no—
294C2×D4—61no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—31no—
298C22×C4—61no—
299C2×C8—101no—
300C2×C8—101no—
301C2×C8—301no—
302C2×C8—301no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4D3×Dic511yescharacteristic
308C4⋊C4D3×Dic511yescharacteristic
309C22⋊C4—61no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C42—31no—
315C42—31no—
316C42—31no—
317C42—61no—
318C42C2×D3×D511yescharacteristic
319C3×C5#153511yescharacteristic, complemented, Hall
320C22×C3C2×C22⋊Dic511yescharacteristic
321C2×D3—21no—
322C2×D3—21no—
323C2×D3—21no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—41no—
332Dic3—21no—
333Dic3—21no—
334Dic3—21no—
335Dic3—41no—
336C2×C5—121no—
337C2×C5—241no—
338C2×C5#475111yescharacteristic
339C2×C5#482111yescharacteristic
340C2×C5#482111yescharacteristic
341C23—31no—
342C23—61no—
343Q8—121no—
344D4—121no—
345D4—122no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—61no—
352C2×C4—121no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4—122no—
356C2×C4C2×D3×Dic511yescharacteristic
357C2×C4D3×C22⋊D511yescharacteristic
358C2×C4D3×C22⋊D511yescharacteristic
359C8—201no—
360C8—201no—
361C8—601no—
362C8—601no—
363C2×C3#6552511yescharacteristic
364C2×C3#6552511yescharacteristic
365C2×C3#6552611yescharacteristic
366D3—41no—
367D3—81no—
368C5#6836811yescharacteristic, complemented, Sylow
369C22—61no—
370C22—61no—
371C22—61no—
372C22—121no—
373C22—121no—
374C22—121no—
375C22D3×C22⋊Dic511yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—61no—
382C4—61no—
383C4—61no—
384C4—121no—
385C3#1060254211yescharacteristic, complemented, Sylow
386C2—121no—
387C2—241no—
388C2#1174937211yescharacteristic
389C2#1174942911yescharacteristic
390C2#1174942911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#895C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1535
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #11746878C2semidirect
3. #11746878C2semidirect
4. #11746364C2semidirect
5. C3×#64763C2semidirect
6. #11745847C2semidirect
7. #11745847C2semidirect
33. #64763D3semidirect
319. C3×C5#1535semidirect
368. C5#68368semidirect
385. C3#10602542semidirect

Maximal subgroups

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

subgroupindex
C5×#56912
#117468782
#117463642
C3×#647632
#117458472
#106025423
#683685