Finite Group Databasebeta

← #14284673

Subgroups — #14284673

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66062C211yesmaximal, characteristic
2D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
3#11746869C211yesmaximal, characteristic
4#11746367C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599274—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4092C412yes—
11C3×Q8×Dic5C412yes—
12C3×#4043—21no—
13C3×#4038—21no—
14C3×#4036—21no—
15C3×#4033—21no—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×D5×C3⋊C8—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90982—21no—
24#90955—21no—
25Dic5×C3⋊C8—21no—
26#71828—51nomaximal, Hall
27#66062D311yescharacteristic
28#65122—31no—
29D5×C4⋊C8—31no—
30C5×#333—31no—
31#64766—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8C2×C412yes—
35C2×C3×C4×D5C2×C411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C2×C5×C3⋊C8—21no—
45C2×C5×C3⋊C8—21no—
46C3×#685—22no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—22no—
49C3×C4⋊Dic5C2×C412yes—
50C3×#683—22no—
51C3×C4×Dic5—22no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55D5×C3⋊C8—42no—
56C3×#533—51no—
57#4925—51no—
58C2×C4⋊(C3⋊C8)—51no—
59#4547—51no—
60#4547—51no—
61#4546—51no—
62#4546D511yescharacteristic, complemented
63C5×C4⋊Q8C2×D311yescharacteristic
64#4092Dic312yes—
65Q8×Dic5Dic312yes—
66C2×C8×D5—61no—
67#4043—21no—
68#4038—21no—
69#4036—21no—
70#4033—21no—
71C42×D5C2×D311yescharacteristic
72#4015C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3946—61no—
77C8×Dic5—61no—
78C4⋊#168—31no—
79C4⋊#168—31no—
80#1542—151noSylow
81C22×C3×D5C22⋊C411yescharacteristic
82C3×C5×Q8—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×Dic5—22no—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C3×C4×D5—21no—
92C3×C4×D5—21no—
93C3×C4×D5—41no—
94C3×C4×D5SD1612yes—
95C3×C4×D5Q1612yes—
96C3×Dic10—41no—
97C3×Dic10—41no—
98C3⋊#168—41no—
99C3⋊#168—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×C4⋊Q8C2×D511yescharacteristic
104C3×#125—101no—
105C3×C22⋊Q8—52no—
106C3×C22⋊Q8—101no—
107C3×C4×Q8—52no—
108C3×C4×Q8—101no—
109C3×#117—101no—
110C2×C3×C42—51no—
111C22×C3⋊C8—101no—
112#830—101no—
113C4⋊(C3⋊C8)—51no—
114C4⋊(C3⋊C8)—51no—
115C4⋊(C3⋊C8)—101no—
116C4⋊(C3⋊C8)C2×D511yescharacteristic
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—101no—
119C2×C5×Q8C2×Dic312yes—
120C2×C4×D5C2×Dic311yescharacteristic
121C2×C4×D5#6711yescharacteristic
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—21no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C42×C5C22×D311yescharacteristic
129#685—22no—
130C4⋊Dic5—21no—
131C4⋊Dic5—22no—
132C4⋊Dic5C2×Dic312yes—
133#683—22no—
134C4×Dic5—22no—
135C4×Dic5C2×Dic311yescharacteristic
136C4×Dic5#6711yescharacteristic
137C4×Dic5#6711yescharacteristic
138C2×#168—61no—
139C2×#168—61no—
140C8×D5—122no—
141#533—51no—
142#431—151no—
143C2×C4⋊C8—151no—
144#333—31no—
145#333—151no—
146#332—151no—
147#332—151no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C3×D5—21no—
150C2×C3×D5—21no—
151C2×C3×D5#10312yes—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5C2×SD1611yescharacteristic
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5—42no—
161C3×Dic5#10312yes—
162C2×C3×Q8—101no—
163C2×C3×Q8C4×D512yes—
164C22×C3×C4—51no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—52no—
170C3×C4⋊C4—102no—
171C3×C4⋊C4—102no—
172C3×C4⋊C4—101no—
173C3×C22⋊C4—102no—
174C3×C42—51no—
175C3×C42—51no—
176C3×C42—51no—
177C3×C42—102no—
178C3×C42C22×D511yescharacteristic
179C2×C3⋊C8—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—101no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—202no—
184C22×D5#21711yescharacteristic
185C5×Q8—42no—
186C2×C4×C5—22no—
187C2×C4×C5C22×Dic311yescharacteristic
188C2×C4×C5C2×#6711yescharacteristic
189C2×C4×C5C2×#6711yescharacteristic
190C2×Dic5—22no—
191C2×Dic5#21711yescharacteristic
192C2×Dic5#21711yescharacteristic
193C2×Dic5#21711yescharacteristic
194C4×D5—21no—
195C4×D5—21no—
196C4×D5—41no—
197C4×D5#21512yes—
198C4×D5#21612yes—
199Dic10—41no—
200Dic10—41no—
201C5×C8—121no—
202C5×C8—121no—
203#168—121no—
204#168—121no—
205C22×C8—301no—
206C4⋊Q8—51no—
207C4⋊Q8D3×D511yescharacteristic
208#125—101no—
209C22⋊Q8—52no—
210C22⋊Q8—101no—
211C4×Q8—52no—
212C4×Q8—101no—
213#117—101no—
214C2×C42—51no—
215C4⋊C8—31no—
216C4⋊C8—31no—
217C4⋊C8—151no—
218C4⋊C8—151no—
219C4⋊C8—301no—
220C22⋊C8—301no—
221C4×C8—301no—
222C2×C3×C5#41311yescharacteristic
223C2×C3×C5C2×#10311yescharacteristic
224C2×C3×C5#41611yescharacteristic
225C3×D5—22no—
226C23×C3—51no—
227C3×Q8—42no—
228C3×Q8—201no—
229C3×Q8—201no—
230C2×C3×C4—22no—
231C2×C3×C4—51no—
232C2×C3×C4—52no—
233C2×C3×C4—52no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—102no—
239C2×C3×C4—201no—
240C2×C3×C4C2×C4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C3⋊C8—41no—
244C3⋊C8—41no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5C2×#21711yescharacteristic
248C2×D5—21no—
249C2×D5—21no—
250C2×D5#83512yes—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5C2×#21511yescharacteristic
254C4×C5C2×#21611yescharacteristic
255C4×C5#95011yescharacteristic
256C4×C5#95011yescharacteristic
257Dic5—21no—
258Dic5—21no—
259Dic5—42no—
260Dic5#83512yes—
261C2×Q8—101no—
262C2×Q8D5×Dic312yes—
263C22×C4—51no—
264C22×C4—51no—
265C22×C4—51no—
266C2×C8—61no—
267C2×C8—61no—
268C2×C8—301no—
269C2×C8—301no—
270C2×C8—602no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—52no—
274C4⋊C4—102no—
275C4⋊C4—102no—
276C4⋊C4—101no—
277C22⋊C4—102no—
278C42—51no—
279C42—51no—
280C42—51no—
281C42—102no—
282C42C2×D3×D511yescharacteristic
283C3×C5#154211yescharacteristic, complemented, Hall
284C22×C3—52no—
285C22×C3—101no—
286C22×C3—101no—
287C22×C3D5×C22⋊C411yescharacteristic
288C3×C4—21no—
289C3×C4—42no—
290C3×C4—52no—
291C3×C4—101no—
292C3×C4—101no—
293C3×C4—202no—
294C3×C4D5×SD1611yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4D5×Q1611yescharacteristic
297C3×C4#406511yescharacteristic
298C2×C5C2×#83511yescharacteristic
299C2×C5#523311yescharacteristic
300C2×C5#523711yescharacteristic
301D5—22no—
302C23—51no—
303Q8—42no—
304Q8—201no—
305Q8—201no—
306C2×C4—22no—
307C2×C4—51no—
308C2×C4—52no—
309C2×C4—52no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—102no—
315C2×C4—201no—
316C2×C4C2×D5×Dic311yescharacteristic
317C2×C4D5×#6711yescharacteristic
318C2×C4D5×#6711yescharacteristic
319C8—121no—
320C8—121no—
321C8—601no—
322C8—601no—
323C2×C3—102no—
324C2×C3#6503411yescharacteristic
325C2×C3D5×#10311yescharacteristic
326C2×C3#6509311yescharacteristic
327C5#7182811yescharacteristic, complemented, Sylow
328C22—52no—
329C22—101no—
330C22—101no—
331C22D5×#21711yescharacteristic
332C4—21no—
333C4—42no—
334C4—52no—
335C4—101no—
336C4—101no—
337C4—202no—
338C4D5×#21511yescharacteristic
339C4D5×#21611yescharacteristic
340C4#9151411yescharacteristic
341C4#9151611yescharacteristic
342C3#1059927411yescharacteristic, complemented, Sylow
343C2—102no—
344C2#1174912311yescharacteristic
345C2D5×#83511yescharacteristic
346C2#1174920711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1542
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746367C2semidirect
5. C5×#4546C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
62. #4546D5semidirect
283. C3×C5#1542semidirect
327. C5#71828semidirect
342. C3#10599274semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
D5×C4⋊(C3⋊C8)2
#117468692
#117463672
C5×#45462
#117458562
#117458552
#105992743
#718285