Finite Group Databasebeta

← #14479147

Subgroups — #14479147

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#711C211yesmaximal, characteristic
2#11756557C211yesmaximal, characteristic, complemented
3C5×#5798C211yesmaximal, characteristic, complemented
4#11755406C214yesmaximal, complemented
5C2×#91528C214yesmaximal, complemented
6#11754923C218yesmaximal, complemented
7Dic3×#711C218yesmaximal, complemented
8D5×#926C212yesmaximal, complemented
9#11754188C212yesmaximal, complemented
10#10617757—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C22⋊D5C2212yes—
13C23×C3×Dic5C2212yes—
14C2×C3×#711C4116yescomplemented
15C2×C3×#711C2214yes—
16C2×C3×#711C2214yes—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×#6719C2214yes—
20D4×Dic15C2218yescomplemented
21#91815C2212yes—
22C2×C5×#217C2214yes—
23C5×D4×Dic3C2218yescomplemented
24C5×#926C2212yes—
25#91559C22116yescomplemented
26Dic3×C22⋊D5C22116yescomplemented
27D5×#217C2214yes—
28C2×#6668C2218yescomplemented
29#91528C2214yes—
30#91528C2218yes—
31#91528C2218yescomplemented
32#91528C2218yescomplemented
33C2×Dic3×Dic5C2218yescomplemented
34D5×C4⋊Dic3C2214yescomplemented
35C4×D5×Dic3C2214yescomplemented
36#91358C2214yescomplemented
37#91357C2214yescomplemented
38#91331C2218yescomplemented
39Dic3×Dic10C2218yescomplemented
40#87260—51nomaximal, Hall
41C22×#711D311yescharacteristic
42C5×#518—31no—
43#66132—31no—
44#65880—38no—
45C4×#711—38no—
46D5×#117—32no—
47#65850—32no—
48#65820—34no—
49C2×#4023—34no—
50C24×C3×C5C2312yes—
51C23×C3×D5C2311yescharacteristic
52C2×C3×C5×D4C2×C418yescomplemented
53C2×C3×C5×D4C2314yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2318yes—
56C22×C5×Dic3C2318yes—
57C2×C3×C22⋊D5C2×C4116yescomplemented
58C2×C3×C22⋊D5C2318yes—
59C22×C3×Dic5C2×C4116yescomplemented
60C22×C3×Dic5C2314yes—
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2314yes—
64C3×#711C2×C4132yescomplemented
65C3×#711C2×C4132yescomplemented
66C2×C3×C4×D5C2×C418yescomplemented
67C2×C3×C4×D5C2312yes—
68C2×C3×C4×D5C2312yes—
69C2×C3×Dic10C2×C418yescomplemented
70C2×C3×Dic10C2314yes—
71C2×D5×Dic3C2318yes—
72#6719C2314yes—
73#6719C2318yes—
74C4⋊Dic15C2314yes—
75C4×Dic15C2314yes—
76C5×#217C2314yes—
77C5×#217C2318yes—
78C5×C4⋊Dic3C2314yes—
79C4×C5×Dic3C2314yes—
80#6668C2318yes—
81#6668C23116yes—
82#6665C2318yes—
83Dic3×Dic5C2318yes—
84Dic3×Dic5C23116yes—
85C22×C3×#41—51no—
86#5827—58no—
87Dic3×#41—58no—
88#5812—52no—
89#5798—51no—
90#5798—54no—
91#5798D511yescharacteristic, complemented
92C2×#926—54no—
93C2×#926—52no—
94C22×C5×D4C2×D311yescharacteristic
95C22×C22⋊D5C2×D312yes—
96C23×Dic5C2×D312yes—
97C2×#711Dic3116yescomplemented
98C2×#711C2×D314yes—
99C2×#711C2×D314yes—
100C22×C4×D5C2×D311yescharacteristic
101C22×Dic10C2×D311yescharacteristic
102C4×C5×D4—38no—
103C5×#117—32no—
104C2×C5×C22⋊C4—34no—
105C2×C22⋊Dic5—34no—
106D4×Dic5—38no—
107C4×C22⋊D5—316no—
108#4072—32no—
109C2×#683—38no—
110C2×C4×Dic5—38no—
111#4038—34no—
112D5×C4⋊C4—34no—
113#4033—38no—
114#4027—316no—
115D5×C22⋊C4—34no—
116#4023—34no—
117#4023—38no—
118#4023—38no—
119#4023—38no—
120#4018—34no—
121C42×D5—34no—
122C4×Dic10—38no—
123#3428—151noSylow
124C23×C3×C5—44no—
125C23×C3×C5C22×C418yes—
126C23×C3×C5C2411yescharacteristic
127C23×C3×C5C2414yes—
128C22×C3×D5—42no—
129C22×C3×D5C22×C414yes—
130C22×C3×D5C2412yes—
131C3×C5×D4C22×C4116yes—
132C2×C3×C4×C5C22×C414yes—
133C2×C3×C4×C5C2412yes—
134C2×Dic15—48no—
135C2×Dic15C2418yes—
136C2×C5×Dic3—48no—
137C2×C5×Dic3C2418yes—
138C3×C22⋊D5C22×C4132yes—
139C2×C3×Dic5C22×C418yes—
140C2×C3×Dic5C22×C414yes—
141C2×C3×Dic5C22×C4116yes—
142C2×C3×Dic5C22×C4116yes—
143C2×C3×Dic5C2411yescharacteristic
144C2×C3×Dic5C2414yes—
145C2×C3×Dic5C2411yescharacteristic
146C3×C4×D5C22×C418yes—
147C3×C4×D5C22×C418yes—
148C3×Dic10C22×C4116yes—
149D5×Dic3—48no—
150C2×C3×#41—516no—
151C2×C3×#41—54no—
152C2×C3×#41—54no—
153C22×C3×Q8—51no—
154C22×C3×D4—52no—
155C22×C3×D4C2×D511yescharacteristic
156C23×C3×C4—52no—
157C23×C3×C4—51no—
158C2×#217—54no—
159C2×#217—54no—
160C2×#217C2×D514yes—
161Q8×Dic3—58no—
162Q8×Dic3—58no—
163D4×Dic3—58no—
164D4×Dic3—516no—
165D4×Dic3—516no—
166D4×Dic3C2×D518yescomplemented
167#926—52no—
168#926—54no—
169#926—58no—
170#926—58no—
171#926—58no—
172#926—54no—
173#926—54no—
174#926C2×D512yes—
175C2×C4⋊Dic3—58no—
176C2×C4⋊Dic3—54no—
177C2×C4×Dic3—58no—
178C2×C4×Dic3—54no—
179C24×C5C22×D312yes—
180C23×D5C22×D311yescharacteristic
181C2×C5×D4C2×Dic318yescomplemented
182C2×C5×D4C22×D314yes—
183C22×C4×C5—38no—
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5C2×Dic3116yescomplemented
186C2×C22⋊D5C22×D318yes—
187C22×Dic5—38no—
188C22×Dic5C2×Dic3116yescomplemented
189C22×Dic5C22×D312yes—
190C22×Dic5C22×D311yescharacteristic
191C22×Dic5C22×D314yes—
192C22×Dic5C22×D314yes—
193#711C2×Dic3132yescomplemented
194#711C2×Dic3132yescomplemented
195C2×C4×D5—38no—
196C2×C4×D5C2×Dic318yescomplemented
197C2×C4×D5C22×D312yes—
198C2×C4×D5C22×D312yes—
199C2×Dic10C2×Dic318yescomplemented
200C2×Dic10C22×D314yes—
201C5×C4⋊C4—34no—
202C5×C22⋊C4—34no—
203C5×C22⋊C4—38no—
204C42×C5—34no—
205C22⋊Dic5—34no—
206C22⋊Dic5—38no—
207#685—38no—
208C4⋊Dic5—34no—
209#683—316no—
210#683—38no—
211C4×Dic5—34no—
212C4×Dic5—316no—
213C4×Dic5—38no—
214C22×#41—51no—
215#520—158no—
216#519—152no—
217#518—31no—
218#518—154no—
219#518—151no—
220C4×#41—158no—
221C2×#117—154no—
222C2×#117—152no—
223C22×C3×C5—28no—
224C22×C3×C5—22no—
225C22×C3×C5—48no—
226C22×C3×C5C23×C412yes—
227C22×C3×C5C23×C418yes—
228C22×C3×C5C2511yescharacteristic
229C2×C3×D5—24no—
230C2×C3×D5—44no—
231C2×C3×D5C23×C414yes—
232C3×C4×C5C23×C414yes—
233Dic15—28no—
234C3×Dic5C23×C418yes—
235C3×Dic5C23×C412yes—
236C3×Dic5C23×C412yes—
237C5×Dic3—28no—
238C24×C3—51no—
239C24×C3C22×D512yes—
240C3×#41—532no—
241C3×#41—532no—
242C2×C3×Q8—58no—
243C2×C3×Q8—54no—
244C2×C3×D4—516no—
245C2×C3×D4—58no—
246C2×C3×D4C4×D518yescomplemented
247C2×C3×D4C22×D514yes—
248C22×C3×C4—516no—
249C22×C3×C4—54no—
250C22×C3×C4—54no—
251C22×C3×C4—51no—
252C22×C3×C4—52no—
253C22×C3×C4—58no—
254C22×C3×C4—52no—
255C22×C3×C4—52no—
256C22×C3×C4C22×D511yescharacteristic
257C22×Dic3—58no—
258C22×Dic3—58no—
259C22×Dic3C22×D518yes—
260#217—54no—
261#217—58no—
262#217—58no—
263#217C22×D514yes—
264#217C22×D518yes—
265C4⋊Dic3—54no—
266C4⋊Dic3—58no—
267C4⋊Dic3—516no—
268C4⋊Dic3C22×D514yes—
269C4×Dic3—54no—
270C4×Dic3—58no—
271C4×Dic3—516no—
272C4×Dic3C22×D514yes—
273C23×C5—44no—
274C23×C5C22×Dic318yes—
275C23×C5C23×D311yescharacteristic
276C23×C5C23×D314yes—
277C22×D5—42no—
278C22×D5C22×Dic314yes—
279C22×D5C23×D312yes—
280C5×D4C22×Dic3116yes—
281C2×C4×C5—38no—
282C2×C4×C5—128no—
283C2×C4×C5C22×Dic314yes—
284C2×C4×C5C23×D312yes—
285C22⋊D5C22×Dic3132yes—
286C2×Dic5—38no—
287C2×Dic5—128no—
288C2×Dic5C22×Dic318yes—
289C2×Dic5C22×Dic314yes—
290C2×Dic5C22×Dic3116yes—
291C2×Dic5C22×Dic3116yes—
292C2×Dic5C23×D311yescharacteristic
293C2×Dic5C23×D314yes—
294C2×Dic5C23×D311yescharacteristic
295C4×D5—128no—
296C4×D5C22×Dic318yes—
297C4×D5C22×Dic318yes—
298Dic10C22×Dic3116yes—
299C2×#41—516no—
300C2×#41—54no—
301C2×#41—54no—
302C22×Q8—51no—
303C22×D4—52no—
304C22×D4D3×D511yescharacteristic
305C23×C4—52no—
306C23×C4—51no—
307C4×Q8—158no—
308C4×Q8—158no—
309C4×D4—38no—
310C4×D4—1516no—
311C4×D4—1516no—
312C4×D4—158no—
313#117—32no—
314#117—154no—
315#117—154no—
316#117—158no—
317#117—158no—
318#117—158no—
319#117—154no—
320#117—152no—
321C2×C4⋊C4—154no—
322C2×C4⋊C4—158no—
323C2×C22⋊C4—34no—
324C2×C22⋊C4—154no—
325C2×C22⋊C4—154no—
326C2×C42—154no—
327C2×C42—158no—
328C2×C3×C5—22no—
329C2×C3×C5—28no—
330C2×C3×C5C24×C411yescharacteristic
331C2×C3×C5#58512yes—
332C3×D5—24no—
333C23×C3—44no—
334C23×C3—52no—
335C23×C3—54no—
336C23×C3—202no—
337C23×C3C2×C4×D518yes—
338C23×C3C23×D511yescharacteristic
339C23×C3C23×D514yes—
340C3×Q8—516no—
341C3×D4—532no—
342C3×D4C2×C4×D5116yes—
343C2×C3×C4—54no—
344C2×C3×C4—58no—
345C2×C3×C4—516no—
346C2×C3×C4—516no—
347C2×C3×C4—51no—
348C2×C3×C4—54no—
349C2×C3×C4—51no—
350C2×C3×C4—58no—
351C2×C3×C4—58no—
352C2×C3×C4C2×C4×D514yes—
353C2×C3×C4C23×D512yes—
354C2×Dic3—48no—
355C2×Dic3—58no—
356C2×Dic3—208no—
357C2×Dic3—208no—
358C2×Dic3C23×D518yes—
359C22×C5—28no—
360C22×C5—22no—
361C22×C5—48no—
362C22×C5C23×Dic312yes—
363C22×C5C23×Dic318yes—
364C22×C5C24×D311yescharacteristic
365C2×D5—24no—
366C2×D5—44no—
367C2×D5C23×Dic314yes—
368C4×C5—68no—
369C4×C5C23×Dic314yes—
370Dic5—68no—
371Dic5C23×Dic318yes—
372Dic5C23×Dic312yes—
373Dic5C23×Dic312yes—
374C24—51no—
375C24C2×D3×D512yes—
376#41—532no—
377#41—532no—
378C2×Q8—58no—
379C2×Q8—54no—
380C2×D4—516no—
381C2×D4—58no—
382C2×D4D5×Dic318yescomplemented
383C2×D4C2×D3×D514yes—
384C22×C4—38no—
385C22×C4—516no—
386C22×C4—54no—
387C22×C4—54no—
388C22×C4—51no—
389C22×C4—52no—
390C22×C4—58no—
391C22×C4—52no—
392C22×C4—52no—
393C22×C4—158no—
394C22×C4—158no—
395C22×C4C2×D3×D511yescharacteristic
396C4⋊C4—34no—
397C4⋊C4—158no—
398C4⋊C4—1516no—
399C4⋊C4—154no—
400C22⋊C4—34no—
401C22⋊C4—38no—
402C22⋊C4—158no—
403C22⋊C4—154no—
404C22⋊C4—158no—
405C42—34no—
406C42—158no—
407C42—1516no—
408C42—154no—
409C3×C5#342811yescharacteristic, complemented, Hall
410C22×C3—28no—
411C22×C3—22no—
412C22×C3—48no—
413C22×C3—54no—
414C22×C3—104no—
415C22×C3—204no—
416C22×C3C22×C4×D512yes—
417C22×C3C22×C4×D518yes—
418C22×C3C24×D511yescharacteristic
419C3×C4—52no—
420C3×C4—52no—
421C3×C4—58no—
422C3×C4C22×C4×D514yes—
423Dic3—28no—
424Dic3—108no—
425C2×C5—22no—
426C2×C5—28no—
427C2×C5#596412yes—
428C2×C5C24×Dic311yescharacteristic
429D5—24no—
430C23—44no—
431C23—52no—
432C23—54no—
433C23—202no—
434C23C2×D5×Dic318yes—
435C23C22×D3×D511yescharacteristic
436C23C22×D3×D514yes—
437Q8—516no—
438D4—532no—
439D4C2×D5×Dic3116yes—
440C2×C4—38no—
441C2×C4—54no—
442C2×C4—58no—
443C2×C4—516no—
444C2×C4—516no—
445C2×C4—51no—
446C2×C4—54no—
447C2×C4—51no—
448C2×C4—58no—
449C2×C4—58no—
450C2×C4—128no—
451C2×C4—158no—
452C2×C4—608no—
453C2×C4—608no—
454C2×C4C2×D5×Dic314yes—
455C2×C4C22×D3×D512yes—
456C2×C3—22no—
457C2×C3—28no—
458C2×C3—104no—
459C2×C3C23×C4×D511yescharacteristic
460C2×C3#6628512yes—
461C5#8726011yescharacteristic, complemented, Sylow
462C22—28no—
463C22—22no—
464C22—48no—
465C22—54no—
466C22—104no—
467C22—204no—
468C22C22×D5×Dic312yes—
469C22C22×D5×Dic318yes—
470C22C23×D3×D511yescharacteristic
471C4—52no—
472C4—52no—
473C4—58no—
474C4—68no—
475C4—308no—
476C4C22×D5×Dic314yes—
477C3#1061775711yescharacteristic, complemented, Sylow
478C2—22no—
479C2—28no—
480C2—104no—
481C2#1175703412yes—
482C2C23×D5×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC22×C3×C5×D4C22
socle, cosocleC22×C3×C5C25
prime radicalC22×C3×#711C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11756557C2semidirect
3. C5×#5798C2semidirect
4. #11755406C2semidirect
5. C2×#91528C2semidirect
6. #11754923C2semidirect
7. Dic3×#711C2semidirect
8. D5×#926C2semidirect
9. #11754188C2semidirect
14. C2×C3×#711C4semidirect
20. D4×Dic15C22semidirect
23. C5×D4×Dic3C22semidirect
25. #91559C22semidirect
26. Dic3×C22⋊D5C22semidirect
28. C2×#6668C22semidirect
31. #91528C22semidirect
32. #91528C22semidirect
33. C2×Dic3×Dic5C22semidirect
34. D5×C4⋊Dic3C22semidirect
35. C4×D5×Dic3C22semidirect
36. #91358C22semidirect
37. #91357C22semidirect
38. #91331C22semidirect
39. Dic3×Dic10C22semidirect
52. C2×C3×C5×D4C2×C4semidirect
57. C2×C3×C22⋊D5C2×C4semidirect
59. C22×C3×Dic5C2×C4semidirect
64. C3×#711C2×C4semidirect
65. C3×#711C2×C4semidirect
66. C2×C3×C4×D5C2×C4semidirect
69. C2×C3×Dic10C2×C4semidirect
91. #5798D5semidirect
97. C2×#711Dic3semidirect
166. D4×Dic3C2×D5semidirect
181. C2×C5×D4C2×Dic3semidirect
185. C2×C22⋊D5C2×Dic3semidirect
188. C22×Dic5C2×Dic3semidirect
193. #711C2×Dic3semidirect
194. #711C2×Dic3semidirect
196. C2×C4×D5C2×Dic3semidirect
199. C2×Dic10C2×Dic3semidirect
246. C2×C3×D4C4×D5semidirect
382. C2×D4D5×Dic3semidirect
409. C3×C5#3428semidirect
461. C5#87260semidirect
477. C3#10617757semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7112
#117565572
C5×#57982
#117554062
C2×#915282
#117549232
Dic3×#7112
D5×#9262
#117541882
#106177573
#872605