Finite Group Databasebeta

← #14284909

Subgroups — #14284909

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2#11747007C211yesmaximal, characteristic
3#11746869C211yesmaximal, characteristic
4#11746367C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10599276—31nomaximal, Hall
9C2×C3×Q8×D5C412yes—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4090C412yes—
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4—21no—
14C3×#4034—21no—
15C3×#4034—21no—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6649—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#71774—51nomaximal, Hall
27D5×C4⋊Q8D311yescharacteristic
28#65126—31no—
29#65122—31no—
30C5×#333—31no—
31#64766—31no—
32#64701—31no—
33#64701—31no—
34C2×C3×C5×Q8C2×C412yes—
35C3×Q8×D5—44no—
36C2×C3×C4×D5—22no—
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×Dic10—22no—
41C2×C3×Dic10C2×C412yes—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×#683—22no—
52C3×#683—22no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56#6649—42no—
57C2×C3×C4⋊Q8—51no—
58#4925—51no—
59#4924—51no—
60#4546—51no—
61#4546—51no—
62#4546—51no—
63#4546D511yescharacteristic, complemented
64C2×Q8×D5Dic312yes—
65C5×C4⋊Q8C2×D311yescharacteristic
66#4090Dic312yes—
67C2×#676—61no—
68D5×C4⋊C4—21no—
69D5×C4⋊C4—21no—
70#4034—21no—
71#4034—21no—
72C42×D5C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76#3952—61no—
77#3946—61no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1548—151noSylow
82C22×C3×D5C22⋊C411yescharacteristic
83C3×C5×Q8—42no—
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—21no—
93C3×C4×D5—21no—
94C3×C4×D5—22no—
95C3×C4×D5—44no—
96C3×C4×D5SD1612yes—
97C3×C4×D5Q1612yes—
98C3×Dic10—44no—
99C3×Dic10—42no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C5×C3⋊C8—41no—
103C5×C3⋊C8—41no—
104C22×C3×Q8—52no—
105C3×C4⋊Q8—52no—
106C3×C4⋊Q8—51no—
107C3×C4⋊Q8—101no—
108C3×C4⋊Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C2×C3×C4⋊C4—101no—
111C2×C3×C4⋊C4—101no—
112C2×C3×C42—51no—
113C2×#208—101no—
114#830—101no—
115C4⋊(C3⋊C8)—51no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C4×C3⋊C8—101no—
121C2×C5×Q8C2×Dic312yes—
122Q8×D5—44no—
123C2×C4×D5—22no—
124C2×C4×D5C2×Dic311yescharacteristic
125C2×C4×D5#6711yescharacteristic
126C2×C4×D5#6711yescharacteristic
127C2×Dic10—22no—
128C2×Dic10C2×Dic312yes—
129C2×C5×C8—61no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C42×C5C22×D311yescharacteristic
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136#683—22no—
137#683—22no—
138C4×Dic5C2×Dic311yescharacteristic
139C4×Dic5#6711yescharacteristic
140C4×Dic5#6711yescharacteristic
141C2×#168—61no—
142C2×#168—61no—
143#676—122no—
144C2×C4⋊Q8—51no—
145#431—151no—
146#423—151no—
147#333—31no—
148#333—151no—
149#333—151no—
150#333—151no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×C3×D5—21no—
153C2×C3×D5—21no—
154C2×C3×D5#10312yes—
155C3×C4×C5—21no—
156C3×C4×C5—42no—
157C3×C4×C5C2×SD1611yescharacteristic
158C3×C4×C5C2×Q1611yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—21no—
162C3×Dic5—42no—
163C3×Dic5#10012yes—
164C3×Dic5#10312yes—
165C2×C3×Q8—52no—
166C2×C3×Q8—102no—
167C2×C3×Q8—204no—
168C2×C3×Q8C4×D512yes—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—102no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—102no—
176C3×C4⋊C4—102no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C42—51no—
180C3×C42—51no—
181C3×C42—51no—
182C3×C42C22×D511yescharacteristic
183#208—202no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C22×D5#21711yescharacteristic
189C5×Q8—42no—
190C2×C4×C5—22no—
191C2×C4×C5C22×Dic311yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×Dic5—22no—
195C2×Dic5#21711yescharacteristic
196C2×Dic5#21711yescharacteristic
197C2×Dic5#21711yescharacteristic
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—22no—
201C4×D5—44no—
202C4×D5#21512yes—
203C4×D5#21612yes—
204Dic10—44no—
205Dic10—42no—
206C5×C8—121no—
207C5×C8—121no—
208#168—121no—
209#168—121no—
210C22×Q8—52no—
211C2×M16—301no—
212C4⋊Q8—52no—
213C4⋊Q8—51no—
214C4⋊Q8—101no—
215C4⋊Q8—101no—
216C4⋊Q8D3×D511yescharacteristic
217C2×C4⋊C4—101no—
218C2×C4⋊C4—101no—
219C2×C42—51no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222C4⋊C8—151no—
223C4⋊C8—151no—
224C4⋊C8—301no—
225C22⋊C8—301no—
226C4×C8—301no—
227C2×C3×C5C2×#10011yescharacteristic
228C2×C3×C5C2×#10311yescharacteristic
229C2×C3×C5#41911yescharacteristic
230C3×D5—22no—
231C23×C3—51no—
232C3×Q8—42no—
233C3×Q8—202no—
234C3×Q8—204no—
235C2×C3×C4—22no—
236C2×C3×C4—51no—
237C2×C3×C4—51no—
238C2×C3×C4—52no—
239C2×C3×C4—52no—
240C2×C3×C4—51no—
241C2×C3×C4—102no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4—102no—
245C2×C3×C4—204no—
246C2×C3×C4C2×C4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C3⋊C8—41no—
250C3⋊C8—41no—
251C3⋊C8—201no—
252C3⋊C8—201no—
253C22×C5C2×#21711yescharacteristic
254C2×D5—21no—
255C2×D5—21no—
256C2×D5#83512yes—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5C2×#21511yescharacteristic
260C4×C5#94211yescharacteristic
261C4×C5#94211yescharacteristic
262C4×C5C2×#21611yescharacteristic
263Dic5—21no—
264Dic5—42no—
265Dic5#83312yes—
266Dic5#83512yes—
267C2×Q8—52no—
268C2×Q8—102no—
269C2×Q8—204no—
270C2×Q8D5×Dic312yes—
271C22×C4—51no—
272C22×C4—51no—
273C22×C4—51no—
274C22×C4—102no—
275M16—602no—
276C2×C8—61no—
277C2×C8—61no—
278C2×C8—301no—
279C2×C8—301no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—102no—
283C4⋊C4—102no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C42—51no—
287C42—51no—
288C42—51no—
289C42C2×D3×D511yescharacteristic
290C3×C5#154811yescharacteristic, complemented, Hall
291C22×C3—52no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3D5×C22⋊C411yescharacteristic
295C3×C4—21no—
296C3×C4—42no—
297C3×C4—52no—
298C3×C4—52no—
299C3×C4—101no—
300C3×C4—202no—
301C3×C4D5×SD1611yescharacteristic
302C3×C4#406111yescharacteristic
303C3×C4D5×Q1611yescharacteristic
304C3×C4#406411yescharacteristic
305C2×C5C2×#83311yescharacteristic
306C2×C5C2×#83511yescharacteristic
307C2×C5#522511yescharacteristic
308D5—22no—
309C23—51no—
310Q8—42no—
311Q8—202no—
312Q8—204no—
313C2×C4—22no—
314C2×C4—51no—
315C2×C4—51no—
316C2×C4—52no—
317C2×C4—52no—
318C2×C4—51no—
319C2×C4—102no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—102no—
323C2×C4—204no—
324C2×C4C2×D5×Dic311yescharacteristic
325C2×C4D5×#6711yescharacteristic
326C2×C4D5×#6711yescharacteristic
327C8—121no—
328C8—121no—
329C8—601no—
330C8—601no—
331C2×C3—102no—
332C2×C3D5×#10011yescharacteristic
333C2×C3D5×#10311yescharacteristic
334C2×C3#6509111yescharacteristic
335C5#7177411yescharacteristic, complemented, Sylow
336C22—52no—
337C22—101no—
338C22—101no—
339C22D5×#21711yescharacteristic
340C4—21no—
341C4—42no—
342C4—52no—
343C4—52no—
344C4—101no—
345C4—202no—
346C4D5×#21511yescharacteristic
347C4D5×#21611yescharacteristic
348C4#9151311yescharacteristic
349C4#9151511yescharacteristic
350C3#1059927611yescharacteristic, complemented, Sylow
351C2—102no—
352C2D5×#83311yescharacteristic
353C2D5×#83511yescharacteristic
354C2#1174920811yescharacteristic
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#1548
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. #11745861C2semidirect
7. #11745861C2semidirect
63. #4546D5semidirect
290. C3×C5#1548semidirect
335. C5#71774semidirect
350. C3#10599276semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
#117470072
#117468692
#117463672
C5×#45462
#117458612
#105992763
#717745