Finite Group Databasebeta

← #14281235

Subgroups — #14281235

Order 1920.

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

normal subgroups only

This group has 512 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
1C2×#91774C211yesmaximal, characteristic
2#11750820C211yesmaximal, characteristic, complemented
3#11750819C211yesmaximal, characteristic, complemented
4C3×C5×#323C211yesmaximal, characteristic, complemented
5#11746346C211yesmaximal, characteristic, complemented
6#11746289C211yesmaximal, characteristic, complemented
7#11746289C211yesmaximal, characteristic, complemented
8#10598897—31nomaximal, Hall
9C22×#1220C411yescharacteristic
10C22×Dic30C411yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C411yescharacteristic
13C2×#6714C411yescharacteristic
14C2×#6714C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16#91774—21no—
17#91774—21no—
18#91774—21no—
19#91774—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×C5×C22⋊C8C2211yescharacteristic
22#91114C2211yescharacteristic
23#91114C2211yescharacteristic
24#91099—21no—
25#91098—21no—
26#91098—21no—
27C8×Dic15—21no—
28#68104—51nomaximal, Hall
29C2×#4031—31no—
30#65008—31no—
31#65007—31no—
32C5×#323D311yescharacteristic, complemented
33#64745—31no—
34#64688—31no—
35#64688—31no—
36C24×C3×C5C2×C411yescharacteristic
37C23×D15C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—42no—
43C22×Dic15C2×C411yescharacteristic
44C22×Dic15C2×C411yescharacteristic
45C22×Dic15C2×C411yescharacteristic
46C2×Dic30—21no—
47C2×Dic30—21no—
48C2×Dic30—42no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53#6719—21no—
54#6719—21no—
55#6714—21no—
56#6714—21no—
57#6714—21no—
58#6714—21no—
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C4×Dic15D411yescharacteristic
62C4×Dic15D411yescharacteristic
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65C2×#885—51no—
66#4719—51no—
67#4718—51no—
68C3×#323D511yescharacteristic, complemented
69#4525—51no—
70#4468—51no—
71#4468—51no—
72C22×C22⋊D5—31no—
73C22×Dic10—31no—
74C2×C5×C22⋊C4C2×D311yescharacteristic
75C2×C22⋊Dic5—31no—
76C2×#685—31no—
77C2×#685—31no—
78C2×C4×Dic5—31no—
79#4031—61no—
80#4031—61no—
81#4031—61no—
82#4031—61no—
83C5×C22⋊C8C2×D311yescharacteristic
84C5×C22⋊C8C2×D311yescharacteristic
85C22⋊#168—31no—
86C22⋊#168—31no—
87#3947—61no—
88#3946—61no—
89#3946—61no—
90C8×Dic5—61no—
91#1469—151noSylow
92C23×C3×C5—21no—
93C23×C3×C5—21no—
94C23×C3×C5—21no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5C22×C411yescharacteristic
98C22×D15—21no—
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—41no—
102C22×D15—41no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108#1220—42no—
109#1220—42no—
110C2×Dic15—21no—
111C2×Dic15—21no—
112C2×Dic15—22no—
113C2×Dic15—21no—
114C2×Dic15—41no—
115C2×Dic15C22⋊C411yescharacteristic
116C2×Dic15C22⋊C411yescharacteristic
117C2×Dic15C22⋊C411yescharacteristic
118C2×Dic15C22⋊C411yescharacteristic
119Dic30—42no—
120Dic30—42no—
121C3×C5×C8—41no—
122C3×C5×C8—41no—
123C3⋊#168—41no—
124C3⋊#168—41no—
125C22×#67—51no—
126C22×Dic6—51no—
127C2×C3×C22⋊C4C2×D511yescharacteristic
128C2×#217—51no—
129C2×(C2×D3)⋊C4—51no—
130C2×(C2×D3)⋊C4—51no—
131C2×C4×Dic3—51no—
132#885—101no—
133#885—101no—
134#885—101no—
135#885—101no—
136C3×C22⋊C8C2×D511yescharacteristic
137C3×C22⋊C8C2×D511yescharacteristic
138#830—51no—
139#830—51no—
140#815—101no—
141Dic3⋊C8—101no—
142Dic3⋊C8—101no—
143C8×Dic3—101no—
144C24×C5C4×D311yescharacteristic
145C23×D5—31no—
146C22×C4×C5C4×D311yescharacteristic
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—61no—
149C2×C22⋊D5—61no—
150C2×C22⋊D5—122no—
151C22×Dic5—31no—
152C22×Dic5—31no—
153C22×Dic5—31no—
154C2×Dic10—61no—
155C2×Dic10—61no—
156C2×Dic10—122no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C5×C22⋊C4—21no—
160C5×C22⋊C4—21no—
161C22⋊Dic5—61no—
162C22⋊Dic5—61no—
163#685—61no—
164#685—61no—
165#685—61no—
166#685—61no—
167C4×Dic5—31no—
168C4×Dic5—31no—
169C4×Dic5—31no—
170C4×Dic5—31no—
171C2×#168—61no—
172C2×#168—61no—
173C2×#124—151no—
174#432—151no—
175#431—151no—
176#323—151no—
177#323—151no—
178#323—151no—
179#323D1511yescharacteristic, complemented
180C22×C3×C5—21no—
181C22×C3×C5—21no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—81no—
186C22×C3×C5—81no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5#13111yescharacteristic
189C22×C3×C5#13111yescharacteristic
190C2×D15—41no—
191C2×D15—41no—
192C2×D15—41no—
193C2×D15—81no—
194C2×D15—81no—
195C3×C4×C5—21no—
196C3×C4×C5—21no—
197C3×C4×C5—41no—
198Dic15—21no—
199Dic15—21no—
200Dic15—21no—
201Dic15—41no—
202Dic15#10012yes—
203C24×C3C4×D511yescharacteristic
204C23×D3—51no—
205C22×C3×C4C4×D511yescharacteristic
206C22×C3×C4C22×D511yescharacteristic
207C2×#67—101no—
208C2×#67—101no—
209C2×#67—202no—
210C22×Dic3—51no—
211C22×Dic3—51no—
212C22×Dic3—51no—
213C2×Dic6—101no—
214C2×Dic6—101no—
215C2×Dic6—202no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220#217—101no—
221#217—101no—
222(C2×D3)⋊C4—101no—
223(C2×D3)⋊C4—101no—
224(C2×D3)⋊C4—101no—
225(C2×D3)⋊C4—101no—
226C4×Dic3—51no—
227C4×Dic3—51no—
228C4×Dic3—51no—
229C4×Dic3—51no—
230C2×C3⋊C8—101no—
231C2×C3⋊C8—101no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5—21no—
235C23×C5—41no—
236C23×C5—41no—
237C23×C5C2×C4×D311yescharacteristic
238C22×D5—61no—
239C22×D5—61no—
240C22×D5—61no—
241C22×D5—121no—
242C22×D5—121no—
243C2×C4×C5—21no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C22⋊D5—122no—
249C22⋊D5—122no—
250C2×Dic5—31no—
251C2×Dic5—31no—
252C2×Dic5—31no—
253C2×Dic5—31no—
254C2×Dic5—62no—
255C2×Dic5—61no—
256C2×Dic5—61no—
257C2×Dic5—61no—
258C2×Dic5—121no—
259Dic10—122no—
260Dic10—122no—
261C5×C8—41no—
262C5×C8—41no—
263#168—121no—
264#168—121no—
265C22×Q8—151no—
266C22×D4—151no—
267#124—301no—
268#124—301no—
269#124—301no—
270#124—301no—
271C2×C22⋊C4—151no—
272C2×C22⋊C4—151no—
273C2×C22⋊C4—151no—
274C2×C22⋊C4C2×D1511yescharacteristic
275C2×C42—151no—
276C4⋊C8—301no—
277C4⋊C8—301no—
278C22⋊C8—151no—
279C22⋊C8—151no—
280C22⋊C8C2×D1511yescharacteristic
281C22⋊C8C2×D1511yescharacteristic
282#97—301no—
283C4×C8—301no—
284C2×C3×C5—21no—
285C2×C3×C5—21no—
286C2×C3×C5—81no—
287C2×C3×C5#40811yescharacteristic
288C2×C3×C5#41011yescharacteristic
289C2×C3×C5C2×#10011yescharacteristic
290D15—81no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3C2×C4×D511yescharacteristic
297C22×D3—101no—
298C22×D3—101no—
299C22×D3—101no—
300C22×D3—201no—
301C22×D3—201no—
302C2×C3×C4—21no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307#67—202no—
308#67—202no—
309C2×Dic3—51no—
310C2×Dic3—51no—
311C2×Dic3—51no—
312C2×Dic3—51no—
313C2×Dic3—102no—
314C2×Dic3—101no—
315C2×Dic3—101no—
316C2×Dic3—101no—
317C2×Dic3—201no—
318Dic6—202no—
319Dic6—202no—
320C3×C8—41no—
321C3×C8—41no—
322C3⋊C8—201no—
323C3⋊C8—201no—
324C22×C5—21no—
325C22×C5—21no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5—81no—
330C22×C5—81no—
331C22×C5D3×C22⋊C411yescharacteristic
332C22×C5#90111yescharacteristic
333C22×C5#90711yescharacteristic
334C2×D5—121no—
335C2×D5—121no—
336C2×D5—121no—
337C2×D5—241no—
338C2×D5—241no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—41no—
342Dic5—32no—
343Dic5—61no—
344Dic5—61no—
345Dic5—61no—
346Dic5—121no—
347C24—151no—
348C24C4×D1511yescharacteristic
349C2×Q8—301no—
350C2×Q8—301no—
351C2×Q8—602no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—602no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4—151no—
358C22×C4C4×D1511yescharacteristic
359C22×C4C22×D1511yescharacteristic
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—301no—
363C2×C8—301no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C22⋊C4—301no—
370C22⋊C4—301no—
371C22⋊C4—301no—
372C42—151no—
373C42—151no—
374C42—151no—
375C42—151no—
376C3×C5#146911yescharacteristic, complemented, Hall
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—81no—
383C22×C3—81no—
384C22×C3D5×C22⋊C411yescharacteristic
385C22×C3#404711yescharacteristic
386C22×C3#405311yescharacteristic
387C2×D3—201no—
388C2×D3—201no—
389C2×D3—201no—
390C2×D3—401no—
391C2×D3—401no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—41no—
395Dic3—52no—
396Dic3—101no—
397Dic3—101no—
398Dic3—101no—
399Dic3—201no—
400C2×C5—21no—
401C2×C5—21no—
402C2×C5—81no—
403C2×C5#472711yescharacteristic
404C2×C5#474011yescharacteristic
405C2×C5D3×#10011yescharacteristic
406D5—241no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—301no—
413C23—301no—
414C23—301no—
415C23—601no—
416C23—601no—
417C23C2×C4×D1511yescharacteristic
418Q8—602no—
419Q8—602no—
420D4—602no—
421D4—602no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—151no—
426C2×C4—151no—
427C2×C4—151no—
428C2×C4—151no—
429C2×C4—302no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4—301no—
433C2×C4—601no—
434C2×C4D4×D1511yescharacteristic
435C2×C4D4×D1511yescharacteristic
436C8—41no—
437C8—41no—
438C8—601no—
439C8—601no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—81no—
443C2×C3#6501611yescharacteristic
444C2×C3#6502911yescharacteristic
445C2×C3D5×#10011yescharacteristic
446D3—401no—
447C5#6810411yescharacteristic, complemented, Sylow
448C22—21no—
449C22—21no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—601no—
456C22—601no—
457C22—601no—
458C22—1201no—
459C22—1201no—
460C22C22⋊C4×D1511yescharacteristic
461C22#9179011yescharacteristic
462C22#9179611yescharacteristic
463C4—21no—
464C4—21no—
465C4—41no—
466C4—152no—
467C4—301no—
468C4—301no—
469C4—301no—
470C4—601no—
471C3#1059889711yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—81no—
475C2—1201no—
476C2#1175082811yescharacteristic
477C2#1175084111yescharacteristic
478C2D15×#10011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#323C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1220C4
cosocleC22×C3×C4×C5C23
hypercenter#323D15
hypocenterC3×C5#1469
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #11750820C2semidirect
3. #11750819C2semidirect
4. C3×C5×#323C2semidirect
5. #11746346C2semidirect
6. #11746289C2semidirect
7. #11746289C2semidirect
32. C5×#323D3semidirect
68. C3×#323D5semidirect
179. #323D15semidirect
376. C3×C5#1469semidirect
447. C5#68104semidirect
471. C3#10598897semidirect

Maximal subgroups

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

subgroupindex
C2×#917742
#117508202
#117508192
C3×C5×#3232
#117463462
#117462892
#105988973
#681045