Finite Group Databasebeta

← #14284245

Subgroups — #14284245

Order 1920.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 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
1#11756447C211yesmaximal, characteristic
2#11746983C211yesmaximal, characteristic
3#11746940C211yesmaximal, characteristic
4C5×#4543C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745851C211yesmaximal, characteristic, complemented
8#10599158—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10#91785—21no—
11#91785—21no—
12#91781C411yescharacteristic
13#91781C411yescharacteristic
14#91777C411yescharacteristic
15#91777C411yescharacteristic
16#91776—21no—
17#91776—21no—
18C42×D15C2211yescharacteristic
19#91759C2211yescharacteristic
20C2×#6648—21no—
21C5×#803C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25#90983—21no—
26#90957—21no—
27#90954—21no—
28#68365—51nomaximal, Hall
29#66022—31no—
30#64994—31no—
31D5×#97—31no—
32C5×#330—31no—
33#64763D311yescharacteristic, complemented
34#64685—31no—
35#64685—31no—
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×Dic30—21no—
40C2×Dic30—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46#6714—21no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C4⋊Dic15C2×C411yescharacteristic
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54C4×Dic15—21no—
55C4×Dic15—21no—
56C4×Dic15C2×C411yescharacteristic
57C4×Dic15D411yescharacteristic
58C4×Dic15D411yescharacteristic
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63#6648—24no—
64#5688—51no—
65#4705—51no—
66D3×#97—51no—
67C3×#330—51no—
68#4543D511yescharacteristic, complemented
69#4465—51no—
70#4465—51no—
71C5×#125C2×D311yescharacteristic
72C2×C8×D5—61no—
73#4042—61no—
74#4042—61no—
75#4038—31no—
76#4038—31no—
77#4034—31no—
78#4034—31no—
79#4033—61no—
80#4033—61no—
81C42×D5—31no—
82#4016—31no—
83C5×#97—31no—
84C5×#97—31no—
85#3952—61no—
86#3947—61no—
87#3946—61no—
88#3935C2×D311yescharacteristic
89#3935C2×D311yescharacteristic
90#1531—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15C22⋊C411yescharacteristic
100C2×Dic15C22⋊C411yescharacteristic
101C2×Dic15C22⋊C411yescharacteristic
102C4×D15—22no—
103C4×D15—22no—
104C4×D15—41no—
105Dic30—42no—
106Dic30—42no—
107C3×#168—22no—
108C3×#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C3×#125C2×D511yescharacteristic
112C2×D3×C8—101no—
113#896—101no—
114#896—101no—
115#892—51no—
116#892—51no—
117#888—51no—
118#888—51no—
119#887—101no—
120#887—101no—
121C42×D3—51no—
122#870—51no—
123C3×#97—51no—
124C3×#97—51no—
125(C2×D3)⋊C8—101no—
126#815—101no—
127Dic3⋊C8—101no—
128#803C2×D511yescharacteristic
129#803C2×D511yescharacteristic
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×Dic10—61no—
134C2×Dic10—61no—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4C4×D311yescharacteristic
140C5×C4⋊C4C4×D311yescharacteristic
141C42×C5C22×D311yescharacteristic
142#685—61no—
143#685—61no—
144C4⋊Dic5—31no—
145C4⋊Dic5—31no—
146#683—61no—
147#683—61no—
148#683—61no—
149#683—61no—
150C4×Dic5—31no—
151C4×Dic5—31no—
152C4×Dic5—31no—
153C4×Dic5—61no—
154C4×Dic5—61no—
155C2×#168—21no—
156C2×#168—21no—
157C8×D5—64no—
158#533—151no—
159#432—151no—
160C2×#97—151no—
161#330—31no—
162#330—51no—
163#330—151no—
164#330—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×D15—21no—
167C2×D15—21no—
168C2×D15#10112yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174Dic15—21no—
175Dic15—21no—
176Dic15—41no—
177Dic15—41no—
178Dic15#10412yes—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×Dic6—101no—
183C2×Dic6—101no—
184C2×C3×C8—101no—
185C2×C3×C8—101no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4C4×D511yescharacteristic
189C3×C4⋊C4C4×D511yescharacteristic
190C3×C42C22×D511yescharacteristic
191(C2×D3)⋊C4—101no—
192(C2×D3)⋊C4—101no—
193C4⋊Dic3—51no—
194C4⋊Dic3—51no—
195Dic3⋊C4—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199C4×Dic3—51no—
200C4×Dic3—51no—
201C4×Dic3—51no—
202C4×Dic3—101no—
203C4×Dic3—101no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206D3×C8—104no—
207C22×D5—31no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5C2×C4×D311yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—31no—
216C2×Dic5—61no—
217C2×Dic5—61no—
218C4×D5—62no—
219C4×D5—62no—
220C4×D5—121no—
221Dic10—122no—
222Dic10—122no—
223C5×C8—62no—
224C5×C8—121no—
225#168—22no—
226#168—41no—
227C22×C8—301no—
228C4⋊Q8—151no—
229C4⋊Q8—151no—
230#125—151no—
231#125D3×D511yescharacteristic
232C22⋊Q8—301no—
233C22⋊Q8—301no—
234C4×Q8—301no—
235C4×Q8—301no—
236#117—151no—
237#117—151no—
238C2×C42—151no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—31no—
242#97—31no—
243#97—51no—
244#97—51no—
245#97—301no—
246C2×C3×C5C2×#10111yescharacteristic
247C2×C3×C5C2×#10411yescharacteristic
248C2×C3×C5#42111yescharacteristic
249D15—22no—
250C22×D3—51no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4C2×C4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261C4×D3—102no—
262C4×D3—102no—
263C4×D3—201no—
264Dic6—202no—
265Dic6—202no—
266C3×C8—102no—
267C3×C8—201no—
268C3⋊C8—22no—
269C3⋊C8—41no—
270C22×C5D3×C22⋊C411yescharacteristic
271C2×D5—32no—
272C2×D5—61no—
273C2×D5—61no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—41no—
278C4×C5—41no—
279Dic5—32no—
280Dic5—61no—
281Dic5—61no—
282Dic5—121no—
283Dic5—121no—
284C2×Q8—301no—
285C2×Q8—301no—
286C22×C4—151no—
287C22×C4—151no—
288C22×C4—151no—
289C2×C8—61no—
290C2×C8—61no—
291C2×C8—101no—
292C2×C8—101no—
293C2×C8—304no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4#120011yescharacteristic
303C4⋊C4#120011yescharacteristic
304C22⋊C4—301no—
305C22⋊C4—301no—
306C42—151no—
307C42—151no—
308C42—151no—
309C42—301no—
310C42—301no—
311C42C2×D3×D511yescharacteristic
312C3×C5#153111yescharacteristic, complemented, Hall
313C22×C3D5×C22⋊C411yescharacteristic
314C2×D3—52no—
315C2×D3—101no—
316C2×D3—101no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322Dic3—52no—
323Dic3—101no—
324Dic3—101no—
325Dic3—201no—
326Dic3—201no—
327C2×C5D3×#10111yescharacteristic
328C2×C5D3×#10411yescharacteristic
329C2×C5#482111yescharacteristic
330D5—62no—
331C23—151no—
332Q8—602no—
333Q8—602no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—151no—
337C2×C4—151no—
338C2×C4—151no—
339C2×C4—302no—
340C2×C4—302no—
341C2×C4—301no—
342C2×C4—301no—
343C2×C4—601no—
344C2×C4C2×#120011yescharacteristic
345C2×C4#679011yescharacteristic
346C2×C4#679011yescharacteristic
347C8—62no—
348C8—102no—
349C8—121no—
350C8—201no—
351C2×C3D5×#10111yescharacteristic
352C2×C3D5×#10411yescharacteristic
353C2×C3#6511011yescharacteristic
354D3—102no—
355C5#6836511yescharacteristic, complemented, Sylow
356C22—152no—
357C22—301no—
358C22—301no—
359C22#9156111yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—152no—
366C4—301no—
367C4—301no—
368C4—601no—
369C4—601no—
370C3#1059915811yescharacteristic, complemented, Sylow
371C2—302no—
372C2#1174937311yescharacteristic
373C2#1174943011yescharacteristic
374C2#1174943111yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1531
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
4. C5×#4543C2semidirect
5. C3×#64763C2semidirect
6. #11745851C2semidirect
7. #11745851C2semidirect
33. #64763D3semidirect
68. #4543D5semidirect
312. C3×C5#1531semidirect
355. C5#68365semidirect
370. C3#10599158semidirect

Maximal subgroups

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

subgroupindex
#117564472
#117469832
#117469402
C5×#45432
C3×#647632
#117458512
#105991583
#683655