Finite Group Databasebeta

← #14285106

Subgroups — #14285106

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 352 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#11746871C211yesmaximal, characteristic
4#11746368C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599218—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4092—21no—
11C3×Q8×Dic5—21no—
12C3×#4043—21no—
13C3×#4038C412yes—
14C3×#4036C412yes—
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—
25#90952—21no—
26#71831—51nomaximal, Hall
27#66062D311yescharacteristic
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
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⋊C4C2×C412yes—
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#4926—51no—
58C2×C4⋊(C3⋊C8)—51no—
59#4547—51no—
60#4547—51no—
61#4547—51no—
62#4547D511yescharacteristic, complemented
63C5×C4⋊Q8C2×D311yescharacteristic
64#4092—21no—
65Q8×Dic5—21no—
66C2×C8×D5—61no—
67#4043—21no—
68#4038Dic312yes—
69#4036Dic312yes—
70#4033—21no—
71C42×D5C2×D311yescharacteristic
72#4015C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3947—61no—
77#3946—61no—
78C4⋊#168—31no—
79C4⋊#168—31no—
80#1552—151noSylow
81C22×C3×D5C22⋊C411yescharacteristic
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×Dic5—22no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×C4×D5—22no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3⋊#168—41no—
100C3⋊#168—41no—
101C5×C3⋊C8—41no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8—51no—
104C3×C4⋊Q8C2×D511yescharacteristic
105C3×#125—52no—
106C3×C22⋊Q8—101no—
107C3×C22⋊Q8—101no—
108C3×C4×Q8—101no—
109C3×C4×Q8—101no—
110C3×#117—52no—
111C2×C3×C42—51no—
112C22×C3⋊C8—101no—
113#830—101no—
114C4⋊(C3⋊C8)—51no—
115C4⋊(C3⋊C8)—51no—
116C4⋊(C3⋊C8)—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119#803—101no—
120C2×C5×Q8—21no—
121C2×C4×D5C2×Dic311yescharacteristic
122C2×C4×D5#6711yescharacteristic
123C2×C4×D5#6711yescharacteristic
124C2×Dic10—21no—
125C2×C5×C8—61no—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C2×Dic312yes—
129C42×C5C22×D311yescharacteristic
130#685—22no—
131C4⋊Dic5—21no—
132C4⋊Dic5—22no—
133C4⋊Dic5C2×Dic312yes—
134#683—22no—
135C4×Dic5—22no—
136C4×Dic5C2×Dic311yescharacteristic
137C4×Dic5#6711yescharacteristic
138C4×Dic5#6711yescharacteristic
139C2×#168—61no—
140C2×#168—61no—
141C8×D5—122no—
142#533—51no—
143#432—151no—
144C2×C4⋊C8—151no—
145#332—31no—
146#332—151no—
147#332—151no—
148#332—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#10112yes—
153C3×C4×C5—21no—
154C3×C4×C5—42no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—42no—
163C2×C3×Q8—21no—
164C2×C3×Q8—101no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—52no—
170C3×C4⋊C4—102no—
171C3×C4⋊C4—102no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4C4×D512yes—
174C3×C22⋊C4—102no—
175C3×C42—51no—
176C3×C42—51no—
177C3×C42—51no—
178C3×C42—102no—
179C3×C42C22×D511yescharacteristic
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C2×C3⋊C8—202no—
185C22×D5#21711yescharacteristic
186C5×Q8—41no—
187C5×Q8—41no—
188C2×C4×C5—22no—
189C2×C4×C5C22×Dic311yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—22no—
193C2×Dic5#21711yescharacteristic
194C2×Dic5#21711yescharacteristic
195C2×Dic5#21711yescharacteristic
196C4×D5—22no—
197C4×D5—21no—
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—21no—
201Dic10—41no—
202Dic10—41no—
203C5×C8—121no—
204C5×C8—121no—
205#168—121no—
206#168—121no—
207C22×C8—301no—
208C4⋊Q8—51no—
209C4⋊Q8D3×D511yescharacteristic
210#125—52no—
211C22⋊Q8—101no—
212C22⋊Q8—101no—
213C4×Q8—101no—
214C4×Q8—101no—
215#117—52no—
216C2×C42—51no—
217C4⋊C8—31no—
218C4⋊C8—31no—
219C4⋊C8—151no—
220C4⋊C8—151no—
221C4⋊C8—301no—
222C22⋊C8—301no—
223#97—301no—
224C2×C3×C5C2×#10111yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#41711yescharacteristic
227C3×D5—22no—
228C23×C3—51no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—201no—
232C3×Q8—201no—
233C2×C3×C4—22no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—102no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—102no—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C3⋊C8—41no—
247C3⋊C8—41no—
248C3⋊C8—201no—
249C3⋊C8—201no—
250C22×C5C2×#21711yescharacteristic
251C2×D5—21no—
252C2×D5—21no—
253C2×D5#83612yes—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5#94911yescharacteristic
257C4×C5#95011yescharacteristic
258C4×C5#95011yescharacteristic
259C4×C5#95111yescharacteristic
260Dic5—21no—
261Dic5—21no—
262Dic5—21no—
263Dic5—42no—
264C2×Q8—21no—
265C2×Q8—101no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—301no—
272C2×C8—301no—
273C2×C8—602no—
274C4⋊C4—21no—
275C4⋊C4—52no—
276C4⋊C4—102no—
277C4⋊C4—102no—
278C4⋊C4—101no—
279C4⋊C4D5×Dic312yes—
280C22⋊C4—102no—
281C42—51no—
282C42—51no—
283C42—51no—
284C42—102no—
285C42C2×D3×D511yescharacteristic
286C3×C5#155211yescharacteristic, complemented, Hall
287C22×C3—52no—
288C22×C3—101no—
289C22×C3—101no—
290C22×C3D5×C22⋊C411yescharacteristic
291C3×C4—21no—
292C3×C4—42no—
293C3×C4—101no—
294C3×C4—101no—
295C3×C4—101no—
296C3×C4—202no—
297C3×C4#405711yescharacteristic
298C3×C4#406111yescharacteristic
299C3×C4#406211yescharacteristic
300C3×C4#406511yescharacteristic
301C2×C5C2×#83611yescharacteristic
302C2×C5#523211yescharacteristic
303C2×C5#523311yescharacteristic
304D5—22no—
305C23—51no—
306Q8—41no—
307Q8—41no—
308Q8—201no—
309Q8—201no—
310C2×C4—22no—
311C2×C4—51no—
312C2×C4—51no—
313C2×C4—51no—
314C2×C4—102no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—102no—
320C2×C4C2×D5×Dic311yescharacteristic
321C2×C4D5×#6711yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C8—121no—
324C8—121no—
325C8—601no—
326C8—601no—
327C2×C3—102no—
328C2×C3D5×#10111yescharacteristic
329C2×C3#6506011yescharacteristic
330C2×C3#6509311yescharacteristic
331C5#7183111yescharacteristic, complemented, Sylow
332C22—52no—
333C22—101no—
334C22—101no—
335C22D5×#21711yescharacteristic
336C4—21no—
337C4—42no—
338C4—101no—
339C4—101no—
340C4—101no—
341C4—202no—
342C4#9147811yescharacteristic
343C4#9148411yescharacteristic
344C4#9151411yescharacteristic
345C4#9151611yescharacteristic
346C3#1059921811yescharacteristic, complemented, Sylow
347C2—102no—
348C2#1174895111yescharacteristic
349C2#1174920711yescharacteristic
350C2D5×#83611yescharacteristic
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#1552
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. #11746368C2semidirect
5. C5×#4547C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
62. #4547D5semidirect
286. C3×C5#1552semidirect
331. C5#71831semidirect
346. C3#10599218semidirect

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
#117468712
#117463682
C5×#45472
#117458562
#117458552
#105992183
#718315