Finite Group Databasebeta

← #14284821

Subgroups — #14284821

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 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#11746368C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599213—31nomaximal, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4090—21no—
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C412yes—
14C3×#4034—21no—
15C3×#4034C412yes—
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#71773—51nomaximal, Hall
27D5×C4⋊Q8D311yescharacteristic
28#65126—31no—
29#65122—31no—
30C5×#332—31no—
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C3×Q8×D5—42no—
36C3×Q8×D5—42no—
37C2×C3×C4×D5—22no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×Dic10—21no—
42C2×C3×Dic10—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C412yes—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5C2×C412yes—
52C3×#683—22no—
53C3×#683—22no—
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57#6649—42no—
58C2×C3×C4⋊Q8—51no—
59#4925—51no—
60#4924—51no—
61#4547—51no—
62#4547—51no—
63#4547—51no—
64#4547D511yescharacteristic, complemented
65C2×Q8×D5—21no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4090—21no—
68C2×#676—61no—
69D5×C4⋊C4—21no—
70D5×C4⋊C4Dic312yes—
71#4034—21no—
72#4034Dic312yes—
73C42×D5C2×D311yescharacteristic
74#4015C2×D311yescharacteristic
75C5×C4⋊C8—31no—
76C5×C4⋊C8—31no—
77#3952—61no—
78#3946—61no—
79C8×Dic5—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82#1546—151noSylow
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—22no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—22no—
97C3×C4×D5—44no—
98C3×C4×D5D812yes—
99C3×C4×D5SD1612yes—
100C3×Dic10—41no—
101C3×Dic10—41no—
102C3×Dic10—44no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C5×C3⋊C8—41no—
107C22×C3×Q8—101no—
108C3×C4⋊Q8—52no—
109C3×C4⋊Q8—51no—
110C3×C4⋊Q8—101no—
111C3×C4⋊Q8—101no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C2×C3×C4⋊C4—52no—
114C2×C3×C4⋊C4—101no—
115C2×C3×C42—51no—
116C2×#208—101no—
117#830—101no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4×C3⋊C8—101no—
124C2×C5×Q8—21no—
125Q8×D5—42no—
126Q8×D5—42no—
127C2×C4×D5—22no—
128C2×C4×D5C2×Dic311yescharacteristic
129C2×C4×D5#6711yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×Dic10—21no—
132C2×Dic10—22no—
133C2×C5×C8—61no—
134C2×C5×C8—61no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4C2×Dic312yes—
137C42×C5C22×D311yescharacteristic
138C4⋊Dic5—21no—
139C4⋊Dic5C2×Dic312yes—
140#683—22no—
141#683—22no—
142C4×Dic5C2×Dic311yescharacteristic
143C4×Dic5#6711yescharacteristic
144C4×Dic5#6711yescharacteristic
145C2×#168—61no—
146C2×#168—61no—
147#676—122no—
148C2×C4⋊Q8—51no—
149#431—151no—
150#423—151no—
151#332—31no—
152#332—151no—
153#332—151no—
154#332—151no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5#10212yes—
159C3×C4×C5—21no—
160C3×C4×C5—42no—
161C3×C4×C5C2×D811yescharacteristic
162C3×C4×C5C2×SD1611yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—21no—
166C3×Dic5—42no—
167C3×Dic5#10112yes—
168C3×Dic5#10212yes—
169C2×C3×Q8—21no—
170C2×C3×Q8—102no—
171C2×C3×Q8—101no—
172C2×C3×Q8—202no—
173C2×C3×Q8—202no—
174C22×C3×C4—51no—
175C22×C3×C4—51no—
176C22×C3×C4—51no—
177C22×C3×C4—102no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—52no—
180C3×C4⋊C4—102no—
181C3×C4⋊C4—102no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4C4×D512yes—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42C22×D511yescharacteristic
188#208—202no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C2×C3⋊C8—101no—
193C22×D5#21711yescharacteristic
194C5×Q8—41no—
195C5×Q8—41no—
196C2×C4×C5—22no—
197C2×C4×C5C22×Dic311yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—22no—
201C2×Dic5#21711yescharacteristic
202C2×Dic5#21711yescharacteristic
203C2×Dic5#21711yescharacteristic
204C4×D5—21no—
205C4×D5—21no—
206C4×D5—22no—
207C4×D5—44no—
208C4×D5#21312yes—
209C4×D5#21412yes—
210Dic10—41no—
211Dic10—41no—
212Dic10—44no—
213C5×C8—121no—
214C5×C8—121no—
215#168—121no—
216#168—121no—
217C22×Q8—101no—
218C2×M16—301no—
219C4⋊Q8—52no—
220C4⋊Q8—51no—
221C4⋊Q8—101no—
222C4⋊Q8—101no—
223C4⋊Q8D3×D511yescharacteristic
224C2×C4⋊C4—52no—
225C2×C4⋊C4—101no—
226C2×C42—51no—
227C4⋊C8—31no—
228C4⋊C8—31no—
229C4⋊C8—151no—
230C4⋊C8—151no—
231C4⋊C8—301no—
232C22⋊C8—301no—
233C4×C8—301no—
234C2×C3×C5C2×#10111yescharacteristic
235C2×C3×C5C2×#10211yescharacteristic
236C2×C3×C5#41911yescharacteristic
237C3×D5—22no—
238C23×C3—51no—
239C3×Q8—41no—
240C3×Q8—41no—
241C3×Q8—204no—
242C3×Q8—201no—
243C3×Q8—201no—
244C2×C3×C4—22no—
245C2×C3×C4—51no—
246C2×C3×C4—51no—
247C2×C3×C4—52no—
248C2×C3×C4—52no—
249C2×C3×C4—51no—
250C2×C3×C4—102no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—102no—
254C2×C3×C4—204no—
255C2×C3×C4C2×C4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C3⋊C8—41no—
259C3⋊C8—41no—
260C3⋊C8—201no—
261C3⋊C8—201no—
262C22×C5C2×#21711yescharacteristic
263C2×D5—21no—
264C2×D5—21no—
265C2×D5#83212yes—
266C4×C5—21no—
267C4×C5—42no—
268C4×C5C2×#21311yescharacteristic
269C4×C5C2×#21411yescharacteristic
270C4×C5#94211yescharacteristic
271C4×C5#94211yescharacteristic
272Dic5—21no—
273Dic5—42no—
274Dic5#83212yes—
275Dic5#83612yes—
276C2×Q8—21no—
277C2×Q8—102no—
278C2×Q8—101no—
279C2×Q8—202no—
280C2×Q8—202no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4—102no—
285M16—602no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4—21no—
291C4⋊C4—52no—
292C4⋊C4—102no—
293C4⋊C4—102no—
294C4⋊C4—101no—
295C4⋊C4D5×Dic312yes—
296C42—51no—
297C42—51no—
298C42—51no—
299C42C2×D3×D511yescharacteristic
300C3×C5#154611yescharacteristic, complemented, Hall
301C22×C3—52no—
302C22×C3—101no—
303C22×C3—101no—
304C22×C3D5×C22⋊C411yescharacteristic
305C3×C4—21no—
306C3×C4—42no—
307C3×C4—52no—
308C3×C4—52no—
309C3×C4—101no—
310C3×C4—202no—
311C3×C4D5×D811yescharacteristic
312C3×C4D5×SD1611yescharacteristic
313C3×C4#406111yescharacteristic
314C3×C4#406411yescharacteristic
315C2×C5C2×#83211yescharacteristic
316C2×C5#522511yescharacteristic
317C2×C5C2×#83611yescharacteristic
318D5—22no—
319C23—51no—
320Q8—41no—
321Q8—41no—
322Q8—204no—
323Q8—201no—
324Q8—201no—
325C2×C4—22no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—52no—
329C2×C4—52no—
330C2×C4—51no—
331C2×C4—102no—
332C2×C4—101no—
333C2×C4—101no—
334C2×C4—102no—
335C2×C4—204no—
336C2×C4C2×D5×Dic311yescharacteristic
337C2×C4D5×#6711yescharacteristic
338C2×C4D5×#6711yescharacteristic
339C8—121no—
340C8—121no—
341C8—601no—
342C8—601no—
343C2×C3—102no—
344C2×C3D5×#10111yescharacteristic
345C2×C3D5×#10211yescharacteristic
346C2×C3#6509111yescharacteristic
347C5#7177311yescharacteristic, complemented, Sylow
348C22—52no—
349C22—101no—
350C22—101no—
351C22D5×#21711yescharacteristic
352C4—21no—
353C4—42no—
354C4—52no—
355C4—52no—
356C4—101no—
357C4—202no—
358C4D5×#21311yescharacteristic
359C4D5×#21411yescharacteristic
360C4#9151311yescharacteristic
361C4#9151511yescharacteristic
362C3#1059921311yescharacteristic, complemented, Sylow
363C2—102no—
364C2D5×#83211yescharacteristic
365C2#1174920811yescharacteristic
366C2D5×#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#1546
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
64. #4547D5semidirect
300. C3×C5#1546semidirect
347. C5#71773semidirect
362. C3#10599213semidirect

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
#117463682
C5×#45472
#117458562
#117458552
#105992133
#717735