Finite Group Databasebeta

← #14284246

Subgroups — #14284246

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5688C211yesmaximal, characteristic
2D3×#3935C211yesmaximal, characteristic
3#11746878C211yesmaximal, characteristic
4#11746364C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745850C211yesmaximal, characteristic, complemented
8#10602615—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#896—21no—
11C5×#896—21no—
12C5×#892C411yescharacteristic
13C5×#892C411yescharacteristic
14C5×#888C411yescharacteristic
15C5×#888C411yescharacteristic
16C5×#887—21no—
17C5×#887—21no—
18C42×C5×D3C2211yescharacteristic
19C5×#870C2211yescharacteristic
20C2×D3×#168—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25Dic3⋊#168—21no—
26(C2×D3)⋊#168—21no—
27#90953—21no—
28#68365—51nomaximal, Hall
29C5×#533—31no—
30#65215—31no—
31C2×#3935—31no—
32#64763—31no—
33#64763—31no—
34#64763—31no—
35#64763D311yescharacteristic, complemented
36C2×C4×C5×D3C2×C411yescharacteristic
37C2×C4×C5×D3D411yescharacteristic
38C2×C4×C5×D3D411yescharacteristic
39C2×C5×Dic6—21no—
40C2×C5×Dic6—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C5×C4⋊Dic3C2×C411yescharacteristic
52C5×Dic3⋊C4—21no—
53C5×Dic3⋊C4—21no—
54C5×Dic3⋊C4—21no—
55C5×Dic3⋊C4—21no—
56C4×C5×Dic3—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3D411yescharacteristic
60C4×C5×Dic3D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63D3×#168—24no—
64#5688D511yescharacteristic
65#4705—51no—
66D3×#97—51no—
67C3×#330—51no—
68#4543—51no—
69#4465—51no—
70#4465—51no—
71C5×C4⋊Q8—31no—
72C5×C4⋊Q8—31no—
73C5×#125—31no—
74C5×#125C2×D311yescharacteristic
75C5×C22⋊Q8—61no—
76C5×C22⋊Q8—61no—
77C4×C5×Q8—61no—
78C4×C5×Q8—61no—
79C5×#117—31no—
80C5×#117—31no—
81C2×C42×C5—31no—
82C22×#168—61no—
83C22⋊#168—61no—
84C4⋊#168—61no—
85#3935—31no—
86#3935—31no—
87#3935—61no—
88#3935C2×D311yescharacteristic
89#3935C2×D311yescharacteristic
90#1531—151noSylow
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×Dic3—21no—
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C4×C5×D3—22no—
103C4×C5×D3—22no—
104C4×C5×D3—41no—
105C5×Dic6—42no—
106C5×Dic6—42no—
107C3⋊#168—22no—
108C3⋊#168—41no—
109C3×#168—22no—
110C3×#168—41no—
111C3×#125C2×D511yescharacteristic
112C2×D3×C8—101no—
113#896—21no—
114#896—21no—
115#892Dic511yescharacteristic
116#892Dic511yescharacteristic
117#888Dic511yescharacteristic
118#888Dic511yescharacteristic
119#887—21no—
120#887—21no—
121C42×D3C2×D511yescharacteristic
122#870C2×D511yescharacteristic
123C3×#97—51no—
124C3×#97—51no—
125(C2×D3)⋊C8—101no—
126#815—101no—
127Dic3⋊C8—101no—
128#803—51no—
129#803—51no—
130C2×C5×Q8—61no—
131C2×C5×Q8—61no—
132C22×C4×C5—31no—
133C22×C4×C5—31no—
134C22×C4×C5—31no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4C4×D311yescharacteristic
144C5×C4⋊C4C4×D311yescharacteristic
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C42×C5—31no—
148C42×C5—31no—
149C42×C5—31no—
150C42×C5—61no—
151C42×C5—61no—
152C42×C5C22×D311yescharacteristic
153C2×#168—21no—
154C2×#168—21no—
155C2×#168—64no—
156C2×#168—61no—
157C2×#168—61no—
158#533—31no—
159#432—151no—
160C2×#97—151no—
161#330—51no—
162#330—151no—
163#330—151no—
164#330—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C5×D3—21no—
167C2×C5×D3—21no—
168C2×C5×D3#10112yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C5×Dic3—41no—
177C5×Dic3—41no—
178C5×Dic3#10412yes—
179C2×C4×D3C2×Dic511yescharacteristic
180C2×C4×D3C22⋊D511yescharacteristic
181C2×C4×D3C22⋊D511yescharacteristic
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×C3×C8—101no—
185C2×C3×C8—101no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4C2×Dic511yescharacteristic
189C3×C4⋊C4C2×Dic511yescharacteristic
190C3×C42C22×D511yescharacteristic
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3C2×Dic511yescharacteristic
194C4⋊Dic3C2×Dic511yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199C4×Dic3—21no—
200C4×Dic3—21no—
201C4×Dic3C2×Dic511yescharacteristic
202C4×Dic3C22⋊D511yescharacteristic
203C4×Dic3C22⋊D511yescharacteristic
204C2×C3⋊C8—101no—
205C2×C3⋊C8—101no—
206D3×C8—104no—
207C23×C5—31no—
208C5×Q8—122no—
209C5×Q8—122no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5—31no—
215C2×C4×C5—62no—
216C2×C4×C5—62no—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5—121no—
220C2×C4×C5C2×C4×D311yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223#168—22no—
224#168—41no—
225#168—62no—
226#168—121no—
227C22×C8—301no—
228C4⋊Q8—31no—
229C4⋊Q8—31no—
230#125—31no—
231#125D3×D511yescharacteristic
232C22⋊Q8—61no—
233C22⋊Q8—61no—
234C4×Q8—61no—
235C4×Q8—61no—
236#117—31no—
237#117—31no—
238C2×C42—31no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—51no—
242#97—51no—
243#97—151no—
244#97—151no—
245#97—301no—
246C2×C3×C5C2×#10111yescharacteristic
247C2×C3×C5C2×#10411yescharacteristic
248C2×C3×C5#42111yescharacteristic
249C5×D3—22no—
250C22×D3C22⋊Dic511yescharacteristic
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4C22×Dic511yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3C22⋊Dic511yescharacteristic
259C2×Dic3C22⋊Dic511yescharacteristic
260C2×Dic3C22⋊Dic511yescharacteristic
261C4×D3—22no—
262C4×D3—22no—
263C4×D3—41no—
264Dic6—42no—
265Dic6—42no—
266C3×C8—102no—
267C3×C8—201no—
268C3⋊C8—102no—
269C3⋊C8—201no—
270C22×C5—32no—
271C22×C5—61no—
272C22×C5—61no—
273C22×C5D3×C22⋊C411yescharacteristic
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—32no—
278C4×C5—41no—
279C4×C5—41no—
280C4×C5—61no—
281C4×C5—61no—
282C4×C5—121no—
283C4×C5—121no—
284C2×Q8—61no—
285C2×Q8—61no—
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—31no—
289C2×C8—101no—
290C2×C8—101no—
291C2×C8—304no—
292C2×C8—301no—
293C2×C8—301no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4D3×Dic511yescharacteristic
303C4⋊C4D3×Dic511yescharacteristic
304C22⋊C4—61no—
305C22⋊C4—61no—
306C42—31no—
307C42—31no—
308C42—31no—
309C42—61no—
310C42—61no—
311C42C2×D3×D511yescharacteristic
312C3×C5#153111yescharacteristic, complemented, Hall
313C22×C3C2×C22⋊Dic511yescharacteristic
314C2×D3—21no—
315C2×D3—21no—
316C2×D3#396812yes—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322Dic3—21no—
323Dic3—21no—
324Dic3—41no—
325Dic3—41no—
326Dic3#396912yes—
327C2×C5—62no—
328C2×C5D3×#10111yescharacteristic
329C2×C5D3×#10411yescharacteristic
330C2×C5#482111yescharacteristic
331C23—31no—
332Q8—122no—
333Q8—122no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—31no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—121no—
344C2×C4C2×D3×Dic511yescharacteristic
345C2×C4D3×C22⋊D511yescharacteristic
346C2×C4D3×C22⋊D511yescharacteristic
347C8—102no—
348C8—201no—
349C8—302no—
350C8—601no—
351C2×C3C2×#396811yescharacteristic
352C2×C3C2×#396911yescharacteristic
353C2×C3#6552511yescharacteristic
354D3—22no—
355C5#6836511yescharacteristic, complemented, Sylow
356C22—32no—
357C22—61no—
358C22—61no—
359C22D3×C22⋊Dic511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—32no—
364C4—41no—
365C4—41no—
366C4—61no—
367C4—61no—
368C4—121no—
369C4—121no—
370C3#1060261511yescharacteristic, complemented, Sylow
371C2—62no—
372C2D3×#396811yescharacteristic
373C2D3×#396911yescharacteristic
374C2#1174942911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1531
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
4. #11746364C2semidirect
5. C3×#64763C2semidirect
6. #11745850C2semidirect
7. #11745850C2semidirect
35. #64763D3semidirect
312. C3×C5#1531semidirect
355. C5#68365semidirect
370. C3#10602615semidirect

Maximal subgroups

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

subgroupindex
C5×#56882
D3×#39352
#117468782
#117463642
C3×#647632
#117458502
#106026153
#683655