Finite Group Databasebeta

← #14283956

Subgroups — #14283956

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5691C211yesmaximal, characteristic
2#11747005C211yesmaximal, characteristic, complemented
3D3×#3935C211yesmaximal, characteristic, complemented
4#11746364C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10602539—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
20C2×#6650—21no—
21C2×D3×#168—21no—
22#91087C2211yescharacteristic
23#91087C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25C3×#3935C2211yescharacteristic
26#90953—21no—
27Dic3×#168—21no—
28#68361—51nomaximal, Hall
29C5×#529—31no—
30C4×#681—31no—
31C2×#3935—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#6650—24no—
64D3×#168—24no—
65#5691D511yescharacteristic
66#4707—51no—
67D3×#97—51no—
68C3×#330—51no—
69#4543—51no—
70#4464—51no—
71#4464—51no—
72C5×#126—61no—
73C5×#125C2×D311yescharacteristic
74C5×#124—31no—
75C5×#123—61no—
76C5×C22⋊Q8—31no—
77C5×#121—31no—
78C4×C5×Q8—31no—
79C4×C5×D4—31no—
80C4×C5×D4—61no—
81C5×#117—61no—
82C2×C42×C5—31no—
83C2×#681—61no—
84C22×#168—61no—
85#3935—31no—
86#3935—31no—
87#3935—61no—
88#3935C2×D311yescharacteristic
89#3935C2×D311yescharacteristic
90C4×#168—61no—
91#1524—151noSylow
92C22×C5×D3—21no—
93C22×C5×D3C22⋊C411yescharacteristic
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C5×Dic3—21no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C5×D12—41no—
104C5×D12—42no—
105C4×C5×D3—22no—
106C4×C5×D3—22no—
107C4×C5×D3—41no—
108C4×C5×D3—42no—
109C5×Dic6—41no—
110C3⋊#168—22no—
111C3⋊#168—22no—
112C3×#168—22no—
113C3×#168—22no—
114C3×#125C2×D511yescharacteristic
115C2×ΓL(1,𝔽25)—101no—
116C2×D3×C8—101no—
117#898—21no—
118#897Dic511yescharacteristic
119#895Dic511yescharacteristic
120#894—21no—
121#893—21no—
122#893Dic511yescharacteristic
123#892—21no—
124#887Dic511yescharacteristic
125#875C2×D511yescharacteristic
126C42×D3C2×D511yescharacteristic
127C3×#97—51no—
128C3×#97—51no—
129#815—101no—
130C8×Dic3—101no—
131#803—51no—
132#803—51no—
133C2×C5×Q8—31no—
134C2×C5×D4—31no—
135C2×C5×D4—61no—
136C22×C4×C5—31no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C22×C4×C5—61no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4C4×D311yescharacteristic
145C5×C4⋊C4C4×D311yescharacteristic
146C5×C22⋊C4—61no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4—61no—
149C5×C22⋊C4—61no—
150C5×C22⋊C4—61no—
151C42×C5—31no—
152C42×C5—31no—
153C42×C5—31no—
154C42×C5—61no—
155C42×C5C22×D311yescharacteristic
156#681—64no—
157C2×#168—21no—
158C2×#168—21no—
159C2×#168—64no—
160C2×#168—61no—
161C2×#168—61no—
162#529—31no—
163C4×M16—151no—
164C2×#97—151no—
165#330—51no—
166#330—151no—
167#329—151no—
168#329—151no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×C5×D3—21no—
171C2×C5×D3—21no—
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C5×D3#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C5×Dic3—21no—
182C5×Dic3—21no—
183C5×Dic3—41no—
184C5×Dic3#10412yes—
185C2×D12—21no—
186C2×D12C2×Dic511yescharacteristic
187C2×C4×D3—21no—
188C2×C4×D3C2×Dic511yescharacteristic
189C2×C4×D3C22⋊D511yescharacteristic
190C2×C4×D3C22⋊D511yescharacteristic
191C2×Dic6C2×Dic511yescharacteristic
192C2×C3×C8—101no—
193C2×C3×C8—101no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C2×Dic511yescharacteristic
197C3×C4⋊C4C2×Dic511yescharacteristic
198C3×C42C22×D511yescharacteristic
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204C4⋊Dic3—21no—
205Dic3⋊C4—21no—
206C4×Dic3—21no—
207C4×Dic3C2×Dic511yescharacteristic
208C4×Dic3C22⋊D511yescharacteristic
209C4×Dic3C22⋊D511yescharacteristic
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212ΓL(1,𝔽25)—104no—
213D3×C8—104no—
214C23×C5—31no—
215C23×C5—61no—
216C5×Q8—121no—
217C5×D4—121no—
218C5×D4—122no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—62no—
225C2×C4×C5—62no—
226C2×C4×C5—61no—
227C2×C4×C5—121no—
228C2×C4×C5—122no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232#168—22no—
233#168—22no—
234#168—62no—
235#168—62no—
236C2×M16—301no—
237C22×C8—301no—
238#126—61no—
239#125D3×D511yescharacteristic
240#124—31no—
241#123—61no—
242C22⋊Q8—31no—
243#121—31no—
244C4×Q8—31no—
245C4×D4—31no—
246C4×D4—61no—
247#117—61no—
248C2×C42—31no—
249#97—51no—
250#97—51no—
251#97—151no—
252#97—151no—
253#97—301no—
254C4×C8—301no—
255C2×C3×C5#41311yescharacteristic
256C2×C3×C5C2×#10411yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258C5×D3—22no—
259C5×D3—81no—
260C22×D3—21no—
261C22×D3C22⋊Dic511yescharacteristic
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4C22×Dic511yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C2×C3×C4C2×C22⋊D511yescharacteristic
267C2×Dic3—21no—
268C2×Dic3C22⋊Dic511yescharacteristic
269C2×Dic3C22⋊Dic511yescharacteristic
270C2×Dic3C22⋊Dic511yescharacteristic
271D12—41no—
272D12—42no—
273C4×D3—22no—
274C4×D3—22no—
275C4×D3—41no—
276C4×D3—42no—
277Dic6—41no—
278C3×C8—102no—
279C3×C8—102no—
280C3⋊C8—102no—
281C3⋊C8—102no—
282C22×C5—32no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5—121no—
286C22×C5—121no—
287C22×C5—121no—
288C22×C5D3×C22⋊C411yescharacteristic
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—32no—
293C4×C5—41no—
294C4×C5—41no—
295C4×C5—61no—
296C4×C5—61no—
297C4×C5—121no—
298C2×Q8—31no—
299C2×D4—31no—
300C2×D4—61no—
301C22×C4—31no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—61no—
305M16—304no—
306C2×C8—101no—
307C2×C8—101no—
308C2×C8—304no—
309C2×C8—301no—
310C2×C8—301no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4D3×Dic511yescharacteristic
316C4⋊C4D3×Dic511yescharacteristic
317C22⋊C4—61no—
318C22⋊C4—61no—
319C22⋊C4—61no—
320C22⋊C4—61no—
321C22⋊C4—61no—
322C42—31no—
323C42—31no—
324C42—31no—
325C42—61no—
326C42C2×D3×D511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3C2×C22⋊Dic511yescharacteristic
329C2×D3—21no—
330C2×D3—21no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3#396912yes—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—41no—
340Dic3—21no—
341Dic3—21no—
342Dic3—41no—
343Dic3#396912yes—
344C2×C5—62no—
345C2×C5—241no—
346C2×C5#475111yescharacteristic
347C2×C5D3×#10411yescharacteristic
348C2×C5D3×#10411yescharacteristic
349C23—31no—
350C23—61no—
351Q8—121no—
352D4—121no—
353D4—122no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—61no—
362C2×C4—121no—
363C2×C4—122no—
364C2×C4C2×D3×Dic511yescharacteristic
365C2×C4D3×C22⋊D511yescharacteristic
366C2×C4D3×C22⋊D511yescharacteristic
367C8—102no—
368C8—102no—
369C8—302no—
370C8—302no—
371C2×C3C2×#396911yescharacteristic
372C2×C3C2×#396911yescharacteristic
373C2×C3#6552611yescharacteristic
374D3—22no—
375D3—81no—
376C5#6836111yescharacteristic, complemented, Sylow
377C22—32no—
378C22—61no—
379C22—61no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22D3×C22⋊Dic511yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—32no—
388C4—41no—
389C4—41no—
390C4—61no—
391C4—61no—
392C4—121no—
393C3#1060253911yescharacteristic, complemented, Sylow
394C2—62no—
395C2—241no—
396C2#1174937211yescharacteristic
397C2D3×#396911yescharacteristic
398C2D3×#396911yescharacteristic
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#1524
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. #11747005C2semidirect
3. D3×#3935C2semidirect
4. #11746364C2semidirect
5. C3×#64763C2semidirect
6. #11745847C2semidirect
7. #11745847C2semidirect
33. #64763D3semidirect
327. C3×C5#1524semidirect
376. C5#68361semidirect
393. C3#10602539semidirect

Maximal subgroups

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

subgroupindex
C5×#56912
#117470052
D3×#39352
#117463642
C3×#647632
#117458472
#106025393
#683615