Finite Group Databasebeta

← #14282937

Subgroups — #14282937

Order 1920.

480 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 102 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#11756381C211yesmaximal, characteristic
2#11748663C211yesmaximal, characteristic
3#11748331C211yesmaximal, characteristic
4C5×#4538C211yesmaximal, characteristic
5C3×#64758C211yesmaximal, characteristic
6#11745965C211yesmaximal, characteristic
7#11745964C211yesmaximal, characteristic
8#10599102—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10Q8×Dic15C411yescharacteristic, complemented
11#91833C411yescharacteristic, complemented
12#91813C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14#91778—21no—
15#91777C411yescharacteristic, complemented
16#91776—21no—
17#91776C411yescharacteristic, complemented
18#91767—21no—
19#91766—21no—
20C2×#6669—21no—
21C2×Dic3×Dic5—21no—
22C5×C3⋊#95C2211yescharacteristic
23C5×#830C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90983—21no—
27#90951—21no—
28#68309—51nomaximal, Hall
29#65956—31no—
30#65007—31no—
31#64938—31no—
32C5×#328—31no—
33#64758D311yescharacteristic
34#64687—31no—
35#64672—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15D411yescharacteristic
39C22×Dic15D411yescharacteristic
40C2×Dic30—21no—
41C2×Dic30C2×C411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C3×Dic5—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47#6719—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15C2×C411yescharacteristic
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54#6712—21no—
55C4×Dic15—21no—
56C4×Dic15—21no—
57C4×Dic15C2×C411yescharacteristic
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C5×C3⋊C8—21no—
62C2×C3×#168—21no—
63#6669—24no—
64Dic3×Dic5—42no—
65#5622—51no—
66#4718—51no—
67#4649—51no—
68C3×#328—51no—
69#4538D511yescharacteristic
70#4467—51no—
71#4452—51no—
72C5×C22⋊Q8C2×D311yescharacteristic
73Q8×Dic5—31no—
74#4090—31no—
75#4070—31no—
76C2×#683—61no—
77C2×C4×Dic5—31no—
78C2×C4×Dic5—61no—
79#4035—61no—
80#4034—31no—
81#4033—31no—
82#4033—61no—
83#4024—61no—
84#4023—61no—
85C5×C22⋊C8—31no—
86C5×#95—31no—
87#3963C2×D311yescharacteristic
88C22⋊#168C2×D311yescharacteristic
89#3946—61no—
90C8×Dic5—61no—
91#1503—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C3×C5×Q8—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—22no—
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C2×Dic15C22⋊C411yescharacteristic
106C2×Dic15SD1612yes—
107C2×Dic15Q1612yes—
108Dic30—42no—
109Dic30—41no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C3×#168—41no—
117C5×C3⋊C8—41no—
118C3×C22⋊Q8C2×D511yescharacteristic
119Q8×Dic3—51no—
120#944—51no—
121#924—51no—
122C2×Dic3⋊C4—101no—
123C2×C4×Dic3—51no—
124C2×C4×Dic3—101no—
125#889—101no—
126#888—51no—
127#887—51no—
128#887—101no—
129#878—101no—
130#877—101no—
131C3×C22⋊C8—51no—
132C3×#95—51no—
133C3⋊#95C2×D511yescharacteristic
134#830C2×D511yescharacteristic
135Dic3⋊C8—101no—
136C8×Dic3—101no—
137C2×C5×Q8C4×D311yescharacteristic
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—21no—
141C22×Dic5—31no—
142C22×Dic5—31no—
143C2×Dic10—31no—
144C2×Dic10—61no—
145C2×C5×C8—61no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4C4×D311yescharacteristic
148C5×C22⋊C4—21no—
149C22⋊Dic5—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—61no—
152#683—64no—
153#683—61no—
154#683—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—31no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164C4×Dic5—122no—
165C2×#168—21no—
166#533—151no—
167#431—151no—
168C4×C4⋊C4—151no—
169#328—31no—
170#328—51no—
171#328—151no—
172#328—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5C2×Q1611yescharacteristic
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182Dic15—21no—
183Dic15—41no—
184Dic15—41no—
185Dic15#10312yes—
186Dic15#10312yes—
187Dic15#10412yes—
188C3×Dic5—42no—
189C5×Dic3—42no—
190C2×C3×Q8C4×D511yescharacteristic
191C22×C3×C4—101no—
192C22×C3×C4C22×D511yescharacteristic
193C22×Dic3—21no—
194C22×Dic3—51no—
195C22×Dic3—51no—
196C2×Dic6—51no—
197C2×Dic6—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4C4×D511yescharacteristic
201C3×C22⋊C4—21no—
202#217—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—101no—
205Dic3⋊C4—104no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211C4×Dic3—51no—
212C4×Dic3—51no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C4×Dic3—101no—
216C4×Dic3—101no—
217C4×Dic3—202no—
218C2×C3⋊C8—21no—
219C23×C5D3×D411yescharacteristic
220C5×Q8—41no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—41no—
224C2×C4×C5—62no—
225C2×C4×C5—121no—
226C2×C4×C5—121no—
227C2×C4×C5C2×C4×D311yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229C2×Dic5—22no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5—32no—
234C2×Dic5—32no—
235C2×Dic5—31no—
236C2×Dic5—41no—
237C2×Dic5—41no—
238C2×Dic5—62no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241Dic10—122no—
242Dic10—121no—
243C5×C8—121no—
244#168—41no—
245C4⋊Q8—151no—
246C4⋊Q8—151no—
247#125—301no—
248C22⋊Q8—151no—
249C22⋊Q8—301no—
250C22⋊Q8D3×D511yescharacteristic
251C4×Q8—151no—
252C4×Q8—151no—
253C4×Q8—301no—
254#117—301no—
255C2×C4⋊C4—301no—
256C2×C42—151no—
257C2×C42—301no—
258C4⋊C8—301no—
259C22⋊C8—31no—
260C22⋊C8—51no—
261C4×C8—301no—
262#95—31no—
263#95—51no—
264C2×C3×C5—21no—
265C2×C3×C5—21no—
266C2×C3×C5#41011yescharacteristic
267C2×C3×C5C2×#10311yescharacteristic
268C2×C3×C5C2×#10411yescharacteristic
269C23×C3D4×D511yescharacteristic
270C3×Q8—41no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—102no—
275C2×C3×C4—201no—
276C2×C3×C4—201no—
277C2×C3×C4C2×C4×D511yescharacteristic
278C2×C3×C4D4×D511yescharacteristic
279C2×Dic3—22no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—51no—
283C2×Dic3—51no—
284C2×Dic3—51no—
285C2×Dic3—52no—
286C2×Dic3—52no—
287C2×Dic3—51no—
288C2×Dic3—102no—
289C2×Dic3—101no—
290C2×Dic3—101no—
291Dic6—202no—
292Dic6—201no—
293C3×C8—201no—
294C3⋊C8—41no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5D3×C22⋊C411yescharacteristic
298C22×C5D3×SD1611yescharacteristic
299C22×C5D3×Q1611yescharacteristic
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—41no—
303C4×C5—41no—
304C4×C5—122no—
305Dic5—32no—
306Dic5—32no—
307Dic5—32no—
308Dic5—42no—
309Dic5—61no—
310Dic5—121no—
311Dic5—121no—
312C2×Q8—151no—
313C2×Q8—301no—
314C2×Q8#120011yescharacteristic
315C22×C4—61no—
316C22×C4—101no—
317C22×C4—151no—
318C22×C4—151no—
319C22×C4C2×D3×D511yescharacteristic
320C2×C8—61no—
321C2×C8—101no—
322C4⋊C4—21no—
323C4⋊C4—151no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—304no—
330C4⋊C4—301no—
331C4⋊C4#120011yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—301no—
334C42—151no—
335C42—151no—
336C42—151no—
337C42—151no—
338C42—301no—
339C42—301no—
340C42—602no—
341C3×C5#150311yescharacteristic, complemented, Hall
342C22×C3—21no—
343C22×C3—21no—
344C22×C3D5×C22⋊C411yescharacteristic
345C22×C3D5×SD1611yescharacteristic
346C22×C3D5×Q1611yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—202no—
352Dic3—42no—
353Dic3—52no—
354Dic3—52no—
355Dic3—52no—
356Dic3—101no—
357Dic3—201no—
358Dic3—201no—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5#474011yescharacteristic
362C2×C5D3×#10311yescharacteristic
363C2×C5D3×#10411yescharacteristic
364C23#679011yescharacteristic
365Q8—41no—
366Q8—601no—
367Q8—602no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—62no—
372C2×C4—102no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4—152no—
376C2×C4—152no—
377C2×C4—151no—
378C2×C4—151no—
379C2×C4—151no—
380C2×C4—151no—
381C2×C4—201no—
382C2×C4—201no—
383C2×C4—302no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4C2×#120011yescharacteristic
387C2×C4#679011yescharacteristic
388C8—121no—
389C8—201no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3#6502911yescharacteristic
393C2×C3D5×#10311yescharacteristic
394C2×C3D5×#10411yescharacteristic
395C5#6830911yescharacteristic, complemented, Sylow
396C22—21no—
397C22—21no—
398C22#9150511yescharacteristic
399C22#9151111yescharacteristic
400C22#9156111yescharacteristic
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—122no—
406C4—152no—
407C4—152no—
408C4—152no—
409C4—202no—
410C4—301no—
411C4—601no—
412C4—601no—
413C3#1059910211yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2#1174917411yescharacteristic
417C2#1174920311yescharacteristic
418C2#1174943011yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1503
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
10. Q8×Dic15C4semidirect
11. #91833C4semidirect
15. #91777C4semidirect
17. #91776C4semidirect
341. C3×C5#1503semidirect
395. C5#68309semidirect
413. C3#10599102semidirect

Maximal subgroups

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

subgroupindex
#117563812
#117486632
#117483312
C5×#45382
C3×#647582
#117459652
#117459642
#105991023
#683095