Finite Group Databasebeta

← #14282776

Subgroups — #14282776

Order 1920.

476 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 94 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#11756359C211yesmaximal, characteristic
2#11748653C211yesmaximal, characteristic, complemented
3#11748331C211yesmaximal, characteristic, complemented
4C5×#4537C211yesmaximal, characteristic
5C3×#64757C211yesmaximal, characteristic
6#11745965C211yesmaximal, characteristic, complemented
7#11745964C211yesmaximal, characteristic, complemented
8#10599069—31nomaximal, Hall
9C3×C5×#121C2211yescharacteristic
10#91825C411yescharacteristic, complemented
11#91824—21no—
12D4×Dic15—21no—
13D4×Dic15C411yescharacteristic, complemented
14#91813C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16#91779C411yescharacteristic, complemented
17#91776C411yescharacteristic, complemented
18#91768—21no—
19#91766—21no—
20C2×Dic3×Dic5—21no—
21C5×C3⋊#95C2211yescharacteristic
22C5×#830C2211yescharacteristic
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25#90994—21no—
26#90983—21no—
27#90951—21no—
28#68276—51nomaximal, Hall
29#65934—31no—
30#65007—31no—
31#64937—31no—
32C5×#327—31no—
33#64757D311yescharacteristic
34#64687—31no—
35#64672—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C22×Dic15D411yescharacteristic
42C2×Dic30C2×C411yescharacteristic
43C22×C5×Dic3—21no—
44C22×C3×Dic5—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47#6719—21no—
48#6719—21no—
49#6719—21no—
50#6719—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15C2×C411yescharacteristic
53#6712—21no—
54#6712—21no—
55#6712—21no—
56C4×Dic15—21no—
57C4×Dic15C2×C411yescharacteristic
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C5×C3⋊C8—21no—
62C2×C3×#168—21no—
63Dic3×Dic5—24no—
64#5600—51no—
65#4718—51no—
66#4648—51no—
67C3×#327—51no—
68#4537D511yescharacteristic
69#4467—51no—
70#4452—51no—
71C5×#121C2×D311yescharacteristic
72#4082—31no—
73#4081—61no—
74D4×Dic5—31no—
75D4×Dic5—61no—
76#4070—31no—
77C2×C4×Dic5—31no—
78C2×C4×Dic5—61no—
79#4036—31no—
80#4033—31no—
81#4025—61no—
82#4023—61no—
83C5×C22⋊C8—31no—
84C5×#95—31no—
85#3963—61no—
86#3963C2×D311yescharacteristic
87C22⋊#168C2×D311yescharacteristic
88#3946—61no—
89C8×Dic5—61no—
90#1500—151noSylow
91C23×C3×C5—21no—
92C23×C3×C5C2×D411yescharacteristic
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—22no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—42no—
106C2×Dic15C22⋊C411yescharacteristic
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C411yescharacteristic
109C2×Dic15C22⋊C411yescharacteristic
110Dic30—41no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3—41no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C3×#168—41no—
118C5×C3⋊C8—41no—
119C3×#121C2×D511yescharacteristic
120#936—51no—
121#935—101no—
122D4×Dic3—51no—
123D4×Dic3—101no—
124#924—51no—
125C2×C4×Dic3—51no—
126C2×C4×Dic3—101no—
127#890—51no—
128#887—51no—
129#879—101no—
130#877—101no—
131C3×C22⋊C8—51no—
132C3×#95—51no—
133C3⋊#95—101no—
134C3⋊#95C2×D511yescharacteristic
135#830C2×D511yescharacteristic
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C2×C5×D4—21no—
139C2×C5×D4C4×D311yescharacteristic
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5—31no—
144C22×Dic5—31no—
145C22×Dic5—61no—
146C2×Dic10—31no—
147C2×C5×C8—61no—
148C5×C4⋊C4C4×D311yescharacteristic
149C5×C22⋊C4—21no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152C22⋊Dic5—61no—
153C22⋊Dic5—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—64no—
164C4×Dic5—61no—
165C2×#168—21no—
166#529—151no—
167#431—151no—
168#376—151no—
169#328—151no—
170#328—151no—
171#327—31no—
172#327—51no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C22×C3×C5#13511yescharacteristic
180C22×C3×C5#13511yescharacteristic
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—41no—
184Dic15—21no—
185Dic15—21no—
186Dic15—21no—
187Dic15—41no—
188Dic15—41no—
189Dic15#10412yes—
190C3×Dic5—42no—
191C5×Dic3—42no—
192C2×C3×D4—21no—
193C2×C3×D4C4×D511yescharacteristic
194C22×C3×C4—101no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—51no—
198C22×Dic3—51no—
199C22×Dic3—101no—
200C2×Dic6—51no—
201C2×C3×C8—101no—
202C3×C4⋊C4C4×D511yescharacteristic
203C3×C22⋊C4—21no—
204#217—101no—
205#217—101no—
206#217—101no—
207#217—101no—
208C4⋊Dic3—51no—
209C4⋊Dic3—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C4×Dic3—51no—
216C4×Dic3—51no—
217C4×Dic3—104no—
218C4×Dic3—101no—
219C2×C3⋊C8—21no—
220C23×C5—21no—
221C23×C5D3×D411yescharacteristic
222C5×D4—41no—
223C5×D4—41no—
224C5×D4—41no—
225C2×C4×C5—21no—
226C2×C4×C5—41no—
227C2×C4×C5—62no—
228C2×C4×C5—121no—
229C2×C4×C5—121no—
230C2×C4×C5C2×C4×D311yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C2×Dic5—22no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—62no—
240C2×Dic5—61no—
241C2×Dic5—61no—
242C2×Dic5—61no—
243C2×Dic5—61no—
244C2×Dic5—122no—
245Dic10—121no—
246C5×C8—121no—
247#168—41no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—151no—
253#121D3×D511yescharacteristic
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C42—151no—
259C2×C42—301no—
260C4⋊C8—301no—
261C22⋊C8—31no—
262C22⋊C8—51no—
263C4×C8—301no—
264#95—31no—
265#95—51no—
266#95—301no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5—81no—
270C2×C3×C5#41011yescharacteristic
271C2×C3×C5#41611yescharacteristic
272C2×C3×C5C2×#10411yescharacteristic
273C23×C3—21no—
274C23×C3D4×D511yescharacteristic
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C2×C3×C4—21no—
279C2×C3×C4—41no—
280C2×C3×C4—102no—
281C2×C3×C4—201no—
282C2×C3×C4—201no—
283C2×C3×C4C2×C4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×Dic3—22no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—51no—
289C2×Dic3—51no—
290C2×Dic3—51no—
291C2×Dic3—51no—
292C2×Dic3—102no—
293C2×Dic3—101no—
294C2×Dic3—101no—
295C2×Dic3—101no—
296C2×Dic3—101no—
297C2×Dic3—202no—
298Dic6—201no—
299C3×C8—201no—
300C3⋊C8—41no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—41no—
306C22×C5D3×C22⋊C411yescharacteristic
307C22×C5#91211yescharacteristic
308C22×C5#91611yescharacteristic
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—41no—
312C4×C5—122no—
313Dic5—32no—
314Dic5—42no—
315Dic5—61no—
316Dic5—61no—
317Dic5—61no—
318Dic5—121no—
319Dic5—121no—
320C2×Q8—151no—
321C2×D4—21no—
322C2×D4#120011yescharacteristic
323C22×C4—61no—
324C22×C4—101no—
325C22×C4—151no—
326C22×C4—151no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—61no—
330C2×C8—101no—
331C4⋊C4—151no—
332C4⋊C4—301no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4#120011yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C42—151no—
343C42—151no—
344C42—151no—
345C42—151no—
346C42—301no—
347C42—304no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3D5×C22⋊C411yescharacteristic
355C22×C3#405811yescharacteristic
356C22×C3#406211yescharacteristic
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4—202no—
361Dic3—42no—
362Dic3—52no—
363Dic3—101no—
364Dic3—101no—
365Dic3—101no—
366Dic3—201no—
367Dic3—201no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5—81no—
371C2×C5#474011yescharacteristic
372C2×C5#477211yescharacteristic
373C2×C5D3×#10411yescharacteristic
374C23—21no—
375C23#679011yescharacteristic
376Q8—601no—
377D4—41no—
378D4—41no—
379D4—41no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—62no—
383C2×C4—102no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—151no—
387C2×C4—151no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—201no—
391C2×C4—201no—
392C2×C4—302no—
393C2×C4—301no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—301no—
397C2×C4—602no—
398C2×C4C2×#120011yescharacteristic
399C2×C4#679011yescharacteristic
400C8—121no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—81no—
405C2×C3#6502911yescharacteristic
406C2×C3#6506111yescharacteristic
407C2×C3D5×#10411yescharacteristic
408C5#6827611yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22#9149711yescharacteristic
415C22#9149911yescharacteristic
416C22#9156111yescharacteristic
417C4—21no—
418C4—21no—
419C4—41no—
420C4—122no—
421C4—152no—
422C4—202no—
423C4—301no—
424C4—301no—
425C4—301no—
426C4—601no—
427C4—601no—
428C3#1059906911yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—81no—
432C2#1174896911yescharacteristic
433C2#1174917411yescharacteristic
434C2#1174943011yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11748653C2semidirect
3. #11748331C2semidirect
6. #11745965C2semidirect
7. #11745964C2semidirect
10. #91825C4semidirect
13. D4×Dic15C4semidirect
16. #91779C4semidirect
17. #91776C4semidirect
348. C3×C5#1500semidirect
408. C5#68276semidirect
428. C3#10599069semidirect

Maximal subgroups

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

subgroupindex
#117563592
#117486532
#117483312
C5×#45372
C3×#647572
#117459652
#117459642
#105990693
#682765