Finite Group Databasebeta

← #14283195

Subgroups — #14283195

Order 1920.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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#11750820C211yesmaximal, characteristic, complemented
3#11750750C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic
5#11746358C211yesmaximal, characteristic
6#11746288C211yesmaximal, characteristic, complemented
7#11746273C211yesmaximal, characteristic, complemented
8#10599072—31nomaximal, Hall
9C3×C5×#121C2211yescharacteristic
10#91825C411yescharacteristic, complemented
11#91824—21no—
12D4×Dic15—21no—
13D4×Dic15C411yescharacteristic, complemented
14#91813C2211yescharacteristic
15C2×#6712—21no—
16C2×C4×Dic15—21no—
17C2×C4×Dic15C2211yescharacteristic
18#91779C411yescharacteristic, complemented
19#91776C411yescharacteristic, complemented
20#91768—21no—
21#91766—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24#91115C2211yescharacteristic
25#91114C2211yescharacteristic
26#91099—21no—
27#91098—21no—
28#68279—51nomaximal, Hall
29#65934—31no—
30#65008—31no—
31#64938—31no—
32C5×#327D311yescharacteristic
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15—21no—
42C22×Dic15D411yescharacteristic
43C22×Dic15D411yescharacteristic
44C2×Dic30C2×C411yescharacteristic
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C22⋊C4—21no—
48#6719—21no—
49#6719—21no—
50#6719—21no—
51#6719—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15C2×C411yescharacteristic
54#6712—24no—
55#6712—21no—
56#6712—21no—
57#6712—21no—
58C4×Dic15—21no—
59C4×Dic15—42no—
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15C2×C411yescharacteristic
62C4×Dic15D411yescharacteristic
63C4×Dic15D411yescharacteristic
64C2×C3⋊#168—21no—
65#5600—51no—
66#4719—51no—
67#4649—51no—
68C3×#327D511yescharacteristic
69#4537—51no—
70#4467—51no—
71#4452—51no—
72C5×#121C2×D311yescharacteristic
73#4082—31no—
74#4081—61no—
75D4×Dic5—31no—
76D4×Dic5—61no—
77#4070—31no—
78C2×#683—61no—
79C2×C4×Dic5—31no—
80C2×C4×Dic5—61no—
81#4036—31no—
82#4033—31no—
83#4025—61no—
84#4023—61no—
85C5×C22⋊C8C2×D311yescharacteristic
86C5×#95C2×D311yescharacteristic
87#3963—31no—
88C22⋊#168—31no—
89#3947—61no—
90#3946—61no—
91#1509—151noSylow
92C23×C3×C5—21no—
93C23×C3×C5C2×D411yescharacteristic
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—22no—
107C2×Dic15—22no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—42no—
113C2×Dic15C22⋊C411yescharacteristic
114C2×Dic15C22⋊C411yescharacteristic
115C2×Dic15C22⋊C411yescharacteristic
116C2×Dic15C22⋊C411yescharacteristic
117Dic30—41no—
118C3×C5×C8—41no—
119C3⋊#168—41no—
120C3×#121C2×D511yescharacteristic
121#936—51no—
122#935—101no—
123D4×Dic3—51no—
124D4×Dic3—101no—
125#924—51no—
126C2×Dic3⋊C4—101no—
127C2×C4×Dic3—51no—
128C2×C4×Dic3—101no—
129#890—51no—
130#887—51no—
131#879—101no—
132#877—101no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×#95C2×D511yescharacteristic
135C3⋊#95—51no—
136#830—51no—
137#815—101no—
138Dic3⋊C8—101no—
139C2×C5×D4—21no—
140C2×C5×D4C4×D311yescharacteristic
141C22×C4×C5—21no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—31no—
144C22×Dic5—31no—
145C22×Dic5—61no—
146C22×Dic5—61no—
147C2×Dic10—31no—
148C2×C5×C8—21no—
149C5×C4⋊C4C4×D311yescharacteristic
150C5×C22⋊C4—21no—
151C22⋊Dic5—61no—
152C22⋊Dic5—61no—
153C22⋊Dic5—61no—
154C22⋊Dic5—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157#683—61no—
158#683—61no—
159#683—64no—
160#683—61no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166C4×Dic5—122no—
167C2×#168—61no—
168#529—151no—
169#432—151no—
170C4×C4⋊C4—151no—
171#328—151no—
172#328—151no—
173#327—151no—
174#327D1511yescharacteristic
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
182C22×C3×C5#13711yescharacteristic
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—42no—
186C3×C4×C5—41no—
187Dic15—21no—
188Dic15—21no—
189Dic15—21no—
190Dic15—42no—
191Dic15—41no—
192Dic15—41no—
193Dic15#10412yes—
194C2×C3×D4—21no—
195C2×C3×D4C4×D511yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—51no—
199C22×Dic3—51no—
200C22×Dic3—101no—
201C22×Dic3—101no—
202C2×Dic6—51no—
203C2×C3×C8—21no—
204C3×C4⋊C4C4×D511yescharacteristic
205C3×C22⋊C4—21no—
206#217—101no—
207#217—101no—
208#217—101no—
209#217—101no—
210C4⋊Dic3—51no—
211C4⋊Dic3—101no—
212Dic3⋊C4—101no—
213Dic3⋊C4—101no—
214Dic3⋊C4—104no—
215Dic3⋊C4—101no—
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—51no—
220C4×Dic3—101no—
221C4×Dic3—202no—
222C2×C3⋊C8—101no—
223C23×C5—21no—
224C23×C5D3×D411yescharacteristic
225C5×D4—41no—
226C5×D4—41no—
227C5×D4—41no—
228C2×C4×C5—22no—
229C2×C4×C5—21no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—62no—
240C2×Dic5—61no—
241C2×Dic5—61no—
242C2×Dic5—62no—
243C2×Dic5—61no—
244C2×Dic5—61no—
245C2×Dic5—122no—
246C2×Dic5—121no—
247C2×Dic5—121no—
248Dic10—121no—
249C5×C8—41no—
250#168—121no—
251#126—301no—
252#125—151no—
253#124—151no—
254#123—301no—
255C22⋊Q8—151no—
256#121C2×D1511yescharacteristic
257C4×Q8—151no—
258C4×D4—151no—
259C4×D4—301no—
260#117—301no—
261C2×C4⋊C4—301no—
262C2×C42—151no—
263C2×C42—301no—
264C4⋊C8—301no—
265C22⋊C8—151no—
266C22⋊C8C2×D1511yescharacteristic
267#97—301no—
268#95—151no—
269#95C2×D1511yescharacteristic
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—81no—
273C2×C3×C5#41011yescharacteristic
274C2×C3×C5#41711yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C23×C3—21no—
277C23×C3D4×D511yescharacteristic
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—41no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×Dic3—51no—
289C2×Dic3—51no—
290C2×Dic3—51no—
291C2×Dic3—51no—
292C2×Dic3—102no—
293C2×Dic3—101no—
294C2×Dic3—101no—
295C2×Dic3—102no—
296C2×Dic3—101no—
297C2×Dic3—101no—
298C2×Dic3—202no—
299C2×Dic3—201no—
300C2×Dic3—201no—
301Dic6—201no—
302C3×C8—41no—
303C3⋊C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5D3×C22⋊C411yescharacteristic
310C22×C5#91111yescharacteristic
311C22×C5#91511yescharacteristic
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—42no—
315C4×C5—41no—
316Dic5—32no—
317Dic5—61no—
318Dic5—61no—
319Dic5—61no—
320Dic5—122no—
321Dic5—121no—
322Dic5—121no—
323C2×Q8—151no—
324C2×D4—21no—
325C2×D4C4×D1511yescharacteristic
326C22×C4—21no—
327C22×C4—151no—
328C22×C4—151no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4C22×D1511yescharacteristic
332C2×C8—21no—
333C2×C8—301no—
334C4⋊C4—151no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C4⋊C4—301no—
338C4⋊C4—304no—
339C4⋊C4—301no—
340C4⋊C4C4×D1511yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C42—151no—
347C42—151no—
348C42—151no—
349C42—151no—
350C42—301no—
351C42—602no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3D5×C22⋊C411yescharacteristic
359C22×C3#405711yescharacteristic
360C22×C3#406111yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—41no—
365Dic3—52no—
366Dic3—101no—
367Dic3—101no—
368Dic3—101no—
369Dic3—202no—
370Dic3—201no—
371Dic3—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—81no—
375C2×C5#474011yescharacteristic
376C2×C5#477111yescharacteristic
377C2×C5D3×#10411yescharacteristic
378C23—21no—
379C23D4×D1511yescharacteristic
380Q8—601no—
381D4—41no—
382D4—41no—
383D4—41no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—151no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—302no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—302no—
397C2×C4—301no—
398C2×C4—301no—
399C2×C4—602no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C2×C4×D1511yescharacteristic
403C2×C4D4×D1511yescharacteristic
404C8—41no—
405C8—601no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—81no—
409C2×C3#6502911yescharacteristic
410C2×C3#6506011yescharacteristic
411C2×C3D5×#10411yescharacteristic
412C5#6827911yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22C22⋊C4×D1511yescharacteristic
419C22#9180011yescharacteristic
420C22#9180411yescharacteristic
421C4—21no—
422C4—21no—
423C4—42no—
424C4—41no—
425C4—152no—
426C4—301no—
427C4—301no—
428C4—301no—
429C4—602no—
430C4—601no—
431C4—601no—
432C3#1059907211yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—81no—
436C2#1175084111yescharacteristic
437C2#1175087211yescharacteristic
438C2D15×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×C5×#121C22
cosocleC22×C3×C4×C5C23
hypercenter#327D15
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #11750820C2semidirect
3. #11750750C2semidirect
6. #11746288C2semidirect
7. #11746273C2semidirect
10. #91825C4semidirect
13. D4×Dic15C4semidirect
18. #91779C4semidirect
19. #91776C4semidirect
352. C3×C5#1509semidirect
412. C5#68279semidirect
432. C3#10599072semidirect

Maximal subgroups

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

subgroupindex
#117563592
#117508202
#117507502
C3×C5×#3272
#117463582
#117462882
#117462732
#105990723
#682795