Finite Group Databasebeta

← #14285247

Subgroups — #14285247

Order 1920.

456 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×C4⋊Q8C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic
3#11750936C211yesmaximal, characteristic
4C3×C5×#332C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10599221—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91833—21no—
12C4⋊C4×D15—21no—
13C4⋊C4×D15C412yes—
14#91777—21no—
15#91777C412yes—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21#91104—21no—
22#91099—21no—
23#91099—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68428—51nomaximal, Hall
27D5×C4⋊Q8—31no—
28#65124—31no—
29#65124—31no—
30C5×#332D311yescharacteristic, complemented
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35Q8×D15—42no—
36Q8×D15—42no—
37C2×C4×D15—22no—
38C2×C4×D15C2×C411yescharacteristic
39C2×C4×D15D411yescharacteristic
40C2×C4×D15D411yescharacteristic
41C2×Dic30—21no—
42C2×Dic30—22no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C412yes—
47C3×C42×C5C2311yescharacteristic
48C4⋊Dic15—21no—
49C4⋊Dic15C2×C412yes—
50#6712—22no—
51#6712—22no—
52C4×Dic15C2×C411yescharacteristic
53C4×Dic15D411yescharacteristic
54C4×Dic15D411yescharacteristic
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57D3×C4⋊Q8—51no—
58#4835—51no—
59#4835—51no—
60C3×#332D511yescharacteristic, complemented
61#4547—51no—
62#4486—51no—
63#4482—51no—
64C2×Q8×D5—61no—
65C5×C4⋊Q8C2×D311yescharacteristic
66#4090—61no—
67D5×C4⋊C4—32no—
68D5×C4⋊C4—61no—
69#4034—32no—
70#4034—61no—
71C42×D5—31no—
72#4015—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—61no—
76#3952—61no—
77#3947—61no—
78#3947—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1556—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92C2×Dic15C22⋊C411yescharacteristic
93C4×D15—22no—
94C4×D15—21no—
95C4×D15—21no—
96C4×D15—21no—
97C4×D15—21no—
98C4×D15—44no—
99Dic30—44no—
100Dic30—41no—
101Dic30—41no—
102C3×C5×C8—41no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3⋊#168—41no—
106C2×D3×Q8—101no—
107C3×C4⋊Q8C2×D511yescharacteristic
108#944—101no—
109D3×C4⋊C4—52no—
110D3×C4⋊C4—101no—
111#888—52no—
112#888—101no—
113C42×D3—51no—
114#869—51no—
115C3×C4⋊C8C2×D511yescharacteristic
116C3×C4⋊C8C2×D511yescharacteristic
117(C2×D3)⋊C8—101no—
118(C2×D3)⋊C8—101no—
119#815—101no—
120#815—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—21no—
124Q8×D5—122no—
125Q8×D5—122no—
126C2×C4×D5—31no—
127C2×C4×D5—31no—
128C2×C4×D5—31no—
129C2×C4×D5—62no—
130C2×Dic10—62no—
131C2×Dic10—61no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C4×D312yes—
136C42×C5C22×D311yescharacteristic
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141C4×Dic5—31no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C2×#168—61no—
145C2×#168—61no—
146C2×C4⋊Q8—151no—
147#432—151no—
148#432—151no—
149#332—151no—
150#332—151no—
151#332—151no—
152#332D1511yescharacteristic, complemented
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×D15—21no—
155C2×D15—21no—
156C2×D15#10112yes—
157C3×C4×C5—21no—
158C3×C4×C5—42no—
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—21no—
164Dic15—21no—
165Dic15—21no—
166Dic15—42no—
167C2×C3×Q8—21no—
168D3×Q8—202no—
169D3×Q8—202no—
170C2×C4×D3—51no—
171C2×C4×D3—51no—
172C2×C4×D3—51no—
173C2×C4×D3—102no—
174C2×Dic6—102no—
175C2×Dic6—101no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4C4×D512yes—
180C3×C42C22×D511yescharacteristic
181C4⋊Dic3—52no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C4×Dic3—51no—
186C4×Dic3—51no—
187C4×Dic3—51no—
188C2×C3⋊C8—101no—
189C2×C3⋊C8—101no—
190C22×D5—31no—
191C5×Q8—41no—
192C5×Q8—41no—
193C2×C4×C5—22no—
194C2×C4×C5C2×C4×D311yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—31no—
198C2×Dic5—31no—
199C2×Dic5—31no—
200C2×Dic5—62no—
201C4×D5—62no—
202C4×D5—61no—
203C4×D5—61no—
204C4×D5—61no—
205C4×D5—61no—
206C4×D5—124no—
207Dic10—124no—
208Dic10—121no—
209Dic10—121no—
210C5×C8—41no—
211C5×C8—41no—
212#168—121no—
213#168—121no—
214C22×Q8—301no—
215C4⋊Q8—152no—
216C4⋊Q8—151no—
217C4⋊Q8—301no—
218C4⋊Q8—301no—
219C4⋊Q8C2×D1511yescharacteristic
220C2×C4⋊C4—152no—
221C2×C4⋊C4—301no—
222C2×C42—151no—
223C4⋊C8—151no—
224C4⋊C8—151no—
225C4⋊C8C2×D1511yescharacteristic
226C4⋊C8C2×D1511yescharacteristic
227C22⋊C8—301no—
228C22⋊C8—301no—
229#97—301no—
230#97—301no—
231C2×C3×C5C2×#10111yescharacteristic
232C2×C3×C5#41811yescharacteristic
233C2×C3×C5#41911yescharacteristic
234D15—22no—
235C22×D3—51no—
236C3×Q8—41no—
237C3×Q8—41no—
238C2×C3×C4—22no—
239C2×C3×C4C2×C4×D511yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×Dic3—51no—
243C2×Dic3—51no—
244C2×Dic3—51no—
245C2×Dic3—102no—
246C4×D3—102no—
247C4×D3—101no—
248C4×D3—101no—
249C4×D3—101no—
250C4×D3—101no—
251C4×D3—204no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255C3×C8—41no—
256C3×C8—41no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5D3×C22⋊C411yescharacteristic
260C2×D5—32no—
261C2×D5—61no—
262C2×D5—61no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5#91111yescharacteristic
266C4×C5#91411yescharacteristic
267C4×C5#91511yescharacteristic
268C4×C5#91811yescharacteristic
269Dic5—61no—
270Dic5—61no—
271Dic5—61no—
272Dic5—122no—
273C2×Q8—21no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—602no—
277C2×Q8—602no—
278C22×C4—151no—
279C22×C4—151no—
280C22×C4—151no—
281C22×C4—302no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—301no—
285C2×C8—301no—
286C4⋊C4—21no—
287C4⋊C4—152no—
288C4⋊C4—302no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4C4×D1512yes—
292C42—151no—
293C42—151no—
294C42—151no—
295C42C22×D1511yescharacteristic
296C3×C5#155611yescharacteristic, complemented, Hall
297C22×C3D5×C22⋊C411yescharacteristic
298C2×D3—52no—
299C2×D3—101no—
300C2×D3—101no—
301C3×C4—21no—
302C3×C4—42no—
303C3×C4#405711yescharacteristic
304C3×C4#406011yescharacteristic
305C3×C4#406111yescharacteristic
306C3×C4#406411yescharacteristic
307Dic3—101no—
308Dic3—101no—
309Dic3—101no—
310Dic3—202no—
311C2×C5D3×#10111yescharacteristic
312C2×C5#477011yescharacteristic
313C2×C5#480211yescharacteristic
314D5—62no—
315C23—151no—
316Q8—41no—
317Q8—41no—
318Q8—604no—
319Q8—601no—
320Q8—601no—
321C2×C4—22no—
322C2×C4—151no—
323C2×C4—151no—
324C2×C4—151no—
325C2×C4—302no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—302no—
331C2×C4—604no—
332C2×C4C2×C4×D1511yescharacteristic
333C2×C4D4×D1511yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C8—41no—
336C8—41no—
337C8—601no—
338C8—601no—
339C2×C3D5×#10111yescharacteristic
340C2×C3#6505911yescharacteristic
341C2×C3#6509111yescharacteristic
342D3—102no—
343C5#6842811yescharacteristic, complemented, Sylow
344C22—152no—
345C22—301no—
346C22—301no—
347C22C22⋊C4×D1511yescharacteristic
348C4—21no—
349C4—42no—
350C4—301no—
351C4—301no—
352C4—301no—
353C4—602no—
354C4#9180011yescharacteristic
355C4#9180311yescharacteristic
356C4#9180411yescharacteristic
357C4#9180711yescharacteristic
358C3#1059922111yescharacteristic, complemented, Sylow
359C2—302no—
360C2D15×#10111yescharacteristic
361C2#1175087111yescharacteristic
362C2#1175090311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#332D15
hypocenterC3×C5#1556
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. C3×C5×#332C2semidirect
5. #11746368C2semidirect
6. #11746307C2semidirect
7. #11746303C2semidirect
30. C5×#332D3semidirect
60. C3×#332D5semidirect
152. #332D15semidirect
296. C3×C5#1556semidirect
343. C5#68428semidirect
358. C3#10599221semidirect

Maximal subgroups

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

subgroupindex
D15×C4⋊Q82
#117509362
C3×C5×#3322
#117463682
#117463072
#117463032
#105992213
#684285