Finite Group Databasebeta

← #14479148

Subgroups — #14479148

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×#6819C211yesmaximal, characteristic
2C5×#5798C211yesmaximal, characteristic, complemented
3C3×#66132C211yesmaximal, characteristic, complemented
4#11755413C214yesmaximal, complemented
5C2×#91532C214yesmaximal, complemented
6#11754916C218yesmaximal, complemented
7#11754853C218yesmaximal, complemented
8#11754461C212yesmaximal, complemented
9#11754213C212yesmaximal, complemented
10#10617757—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×#1220C2212yes—
13C23×Dic15C2212yes—
14C2×#6819C4116yescomplemented
15C2×#6819C2214yes—
16C2×#6819C2214yes—
17C22×C4×D15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C2×C5×#217C2214yes—
20C5×D4×Dic3C2218yescomplemented
21C5×#926C2212yes—
22C2×C3×C22⋊Dic5C2214yes—
23C3×D4×Dic5C2218yescomplemented
24C3×#4072C2212yes—
25#91561C2214yes—
26#91556C22116yescomplemented
27#91552C22116yescomplemented
28C2×#6669C2218yescomplemented
29#91532C2214yes—
30#91532C2218yes—
31#91532C2218yescomplemented
32#91532C2218yescomplemented
33C2×Dic3×Dic5C2218yescomplemented
34#91437C2214yescomplemented
35C4×#1200C2214yescomplemented
36#91386C2214yescomplemented
37#91347C2214yescomplemented
38#91340C2218yescomplemented
39#91333C2218yescomplemented
40#85856—51nomaximal, Hall
41C22×#711—31no—
42C5×#518—31no—
43#66132D311yescharacteristic, complemented
44#65880—38no—
45C4×#711—38no—
46D5×#117—32no—
47#65850—32no—
48#65820—34no—
49C2×#4023—34no—
50C24×C3×C5C2312yes—
51C23×D15C2311yescharacteristic
52C2×C3×C5×D4C2×C418yescomplemented
53C2×C3×C5×D4C2314yes—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220C2×C4116yescomplemented
56C2×#1220C2318yes—
57C22×Dic15C2×C4116yescomplemented
58C22×Dic15C2314yes—
59C22×Dic15C2312yes—
60C22×Dic15C2311yescharacteristic
61C22×Dic15C2314yes—
62#6819C2×C4132yescomplemented
63#6819C2×C4132yescomplemented
64C2×C4×D15C2×C418yescomplemented
65C2×C4×D15C2312yes—
66C2×C4×D15C2312yes—
67C2×Dic30C2×C418yescomplemented
68C2×Dic30C2314yes—
69C22×C5×Dic3C2318yes—
70C22×C3×Dic5C2318yes—
71C2×#1200C2318yes—
72C5×#217C2314yes—
73C5×#217C2318yes—
74C5×C4⋊Dic3C2314yes—
75C4×C5×Dic3C2314yes—
76C3×C22⋊Dic5C2318yes—
77C3×C22⋊Dic5C2314yes—
78C3×C4⋊Dic5C2314yes—
79C3×C4×Dic5C2314yes—
80#6669C2318yes—
81#6669C23116yes—
82#6667C2318yes—
83Dic3×Dic5C2318yes—
84Dic3×Dic5C23116yes—
85C22×#237—51no—
86C3×#518—51no—
87#5798D511yescharacteristic, complemented
88#5546—58no—
89C4×#237—58no—
90D3×#117—52no—
91#5516—52no—
92#5486—54no—
93C2×#877—54no—
94C22×C5×D4C2×D311yescharacteristic
95C22×C22⋊D5—32no—
96C23×Dic5—32no—
97C2×#711—316no—
98C2×#711—34no—
99C2×#711—34no—
100C22×C4×D5—31no—
101C22×Dic10—31no—
102C4×C5×D4—38no—
103C5×#117—32no—
104C2×C5×C22⋊C4—34no—
105C2×C22⋊Dic5C2×D314yes—
106D4×Dic5C2×D318yescomplemented
107C4×C22⋊D5—316no—
108#4072C2×D312yes—
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×D15—42no—
129C22×D15C22×C414yes—
130C22×D15C2412yes—
131C3×C5×D4C22×C4116yes—
132C2×C3×C4×C5C22×C414yes—
133C2×C3×C4×C5C2412yes—
134#1220C22×C4132yes—
135C2×Dic15C22×C418yes—
136C2×Dic15C22×C414yes—
137C2×Dic15C22×C4116yes—
138C2×Dic15C22×C4116yes—
139C2×Dic15C2411yescharacteristic
140C2×Dic15C2414yes—
141C2×Dic15C2411yescharacteristic
142C4×D15C22×C418yes—
143C4×D15C22×C418yes—
144Dic30C22×C4116yes—
145C2×C5×Dic3—48no—
146C2×C5×Dic3C2418yes—
147C2×C3×Dic5—48no—
148C2×C3×Dic5C2418yes—
149#1200—48no—
150C22×C3×D4C2×D511yescharacteristic
151C22×#67—52no—
152C23×Dic3—52no—
153C2×#237—516no—
154C2×#237—54no—
155C2×#237—54no—
156C22×C4×D3—51no—
157C22×Dic6—51no—
158C3×C4×D4—58no—
159C3×#117—52no—
160C2×C3×C22⋊C4—54no—
161C2×#217C2×D514yes—
162D4×Dic3C2×D518yescomplemented
163C4×#67—516no—
164#926C2×D512yes—
165C2×Dic3⋊C4—58no—
166C2×C4×Dic3—58no—
167#892—54no—
168D3×C4⋊C4—54no—
169#887—58no—
170#67⋊C4—516no—
171D3×C22⋊C4—54no—
172#877—54no—
173#877—58no—
174#877—58no—
175#877—58no—
176#872—54no—
177C42×D3—54no—
178C4×Dic6—58no—
179C24×C5C22×D312yes—
180C23×D5—31no—
181C2×C5×D4C4×D318yescomplemented
182C2×C5×D4C22×D314yes—
183C22×C4×C5—38no—
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—316no—
186C2×C22⋊D5—38no—
187C22×Dic5—316no—
188C22×Dic5—32no—
189C22×Dic5—31no—
190C22×Dic5—34no—
191C22×Dic5—34no—
192C22×Dic5C22×D318yes—
193#711—332no—
194#711—332no—
195C2×C4×D5—38no—
196C2×C4×D5—32no—
197C2×C4×D5—32no—
198C2×C4×D5—38no—
199C2×Dic10—38no—
200C2×Dic10—34no—
201C5×C4⋊C4—34no—
202C5×C22⋊C4—34no—
203C5×C22⋊C4—38no—
204C42×C5—34no—
205C22⋊Dic5C22×D314yes—
206C22⋊Dic5C22×D318yes—
207#685—38no—
208C4⋊Dic5C22×D314yes—
209#683—316no—
210#683—38no—
211C4×Dic5—316no—
212C4×Dic5—38no—
213C4×Dic5C22×D314yes—
214C22×#41—151no—
215#520—158no—
216#519—152no—
217#518—31no—
218#518—51no—
219#518—154no—
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×D15—24no—
230C2×D15—44no—
231C2×D15C23×C414yes—
232C3×C4×C5C23×C414yes—
233Dic15C23×C418yes—
234Dic15C23×C412yes—
235Dic15C23×C412yes—
236C3×Dic5—28no—
237C5×Dic3—28no—
238C24×C3C22×D512yes—
239C23×D3—51no—
240C2×C3×D4C4×D518yescomplemented
241C2×C3×D4C22×D514yes—
242C22×C3×C4—58no—
243C22×C3×C4C22×D511yescharacteristic
244C2×#67—516no—
245C2×#67—58no—
246C22×Dic3—516no—
247C22×Dic3—52no—
248C22×Dic3—51no—
249C22×Dic3—54no—
250C22×Dic3—54no—
251C22×Dic3C22×D518yes—
252#237—532no—
253#237—532no—
254C2×C4×D3—58no—
255C2×C4×D3—52no—
256C2×C4×D3—52no—
257C2×C4×D3—58no—
258C2×Dic6—58no—
259C2×Dic6—54no—
260C3×C4⋊C4—54no—
261C3×C22⋊C4—54no—
262C3×C22⋊C4—58no—
263C3×C42—54no—
264#217C22×D514yes—
265#217C22×D518yes—
266(C2×D3)⋊C4—58no—
267C4⋊Dic3C22×D514yes—
268Dic3⋊C4—516no—
269Dic3⋊C4—58no—
270C4×Dic3—516no—
271C4×Dic3—58no—
272C4×Dic3C22×D514yes—
273C23×C5—44no—
274C23×C5C2×C4×D318yes—
275C23×C5C23×D311yescharacteristic
276C23×C5C23×D314yes—
277C22×D5—32no—
278C22×D5—34no—
279C22×D5—122no—
280C5×D4C2×C4×D3116yes—
281C2×C4×C5—38no—
282C2×C4×C5—128no—
283C2×C4×C5C2×C4×D314yes—
284C2×C4×C5C23×D312yes—
285C22⋊D5—332no—
286C2×Dic5—38no—
287C2×Dic5—34no—
288C2×Dic5—316no—
289C2×Dic5—316no—
290C2×Dic5—31no—
291C2×Dic5—34no—
292C2×Dic5—31no—
293C2×Dic5—48no—
294C2×Dic5C23×D318yes—
295C4×D5—38no—
296C4×D5—38no—
297C4×D5—128no—
298Dic10—316no—
299C2×#41—1516no—
300C2×#41—154no—
301C2×#41—154no—
302C22×Q8—151no—
303C22×D4—152no—
304C22×D4D3×D511yescharacteristic
305C23×C4—152no—
306C23×C4—151no—
307C4×Q8—158no—
308C4×Q8—158no—
309C4×D4—38no—
310C4×D4—58no—
311C4×D4—1516no—
312C4×D4—1516no—
313#117—32no—
314#117—52no—
315#117—154no—
316#117—154no—
317#117—158no—
318#117—158no—
319#117—158no—
320#117—154no—
321C2×C4⋊C4—154no—
322C2×C4⋊C4—158no—
323C2×C22⋊C4—34no—
324C2×C22⋊C4—54no—
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—
332D15—24no—
333C23×C3—44no—
334C23×C3C2×C4×D518yes—
335C23×C3C23×D511yescharacteristic
336C23×C3C23×D514yes—
337C22×D3—52no—
338C22×D3—54no—
339C22×D3—202no—
340C3×D4C2×C4×D5116yes—
341C2×C3×C4—58no—
342C2×C3×C4—208no—
343C2×C3×C4C2×C4×D514yes—
344C2×C3×C4C23×D512yes—
345#67—532no—
346C2×Dic3—48no—
347C2×Dic3—58no—
348C2×Dic3—54no—
349C2×Dic3—516no—
350C2×Dic3—516no—
351C2×Dic3—51no—
352C2×Dic3—54no—
353C2×Dic3—51no—
354C2×Dic3C23×D518yes—
355C4×D3—58no—
356C4×D3—58no—
357C4×D3—208no—
358Dic6—516no—
359C22×C5—28no—
360C22×C5—22no—
361C22×C5—48no—
362C22×C5C22×C4×D312yes—
363C22×C5C22×C4×D318yes—
364C22×C5C24×D311yescharacteristic
365C2×D5—34no—
366C2×D5—64no—
367C2×D5—124no—
368C4×C5—68no—
369C4×C5C22×C4×D314yes—
370Dic5—28no—
371Dic5—38no—
372Dic5—32no—
373Dic5—32no—
374C24—151no—
375C24C2×D3×D512yes—
376#41—1532no—
377#41—1532no—
378C2×Q8—158no—
379C2×Q8—154no—
380C2×D4—1516no—
381C2×D4—158no—
382C2×D4#120018yescomplemented
383C2×D4C2×D3×D514yes—
384C22×C4—38no—
385C22×C4—58no—
386C22×C4—158no—
387C22×C4—1516no—
388C22×C4—154no—
389C22×C4—154no—
390C22×C4—151no—
391C22×C4—152no—
392C22×C4—158no—
393C22×C4—152no—
394C22×C4—152no—
395C22×C4C2×D3×D511yescharacteristic
396C4⋊C4—34no—
397C4⋊C4—54no—
398C4⋊C4—158no—
399C4⋊C4—1516no—
400C22⋊C4—34no—
401C22⋊C4—38no—
402C22⋊C4—54no—
403C22⋊C4—58no—
404C22⋊C4—158no—
405C42—34no—
406C42—54no—
407C42—158no—
408C42—1516no—
409C3×C5#342811yescharacteristic, complemented, Hall
410C22×C3—28no—
411C22×C3—22no—
412C22×C3—48no—
413C22×C3C22×C4×D512yes—
414C22×C3C22×C4×D518yes—
415C22×C3C24×D511yescharacteristic
416C2×D3—54no—
417C2×D3—104no—
418C2×D3—204no—
419C3×C4—108no—
420C3×C4C22×C4×D514yes—
421Dic3—28no—
422Dic3—58no—
423Dic3—52no—
424Dic3—52no—
425C2×C5—22no—
426C2×C5—28no—
427C2×C5C23×C4×D311yescharacteristic
428C2×C5#596612yes—
429D5—64no—
430C23—44no—
431C23—152no—
432C23—154no—
433C23—602no—
434C23C2×#120018yes—
435C23C22×D3×D511yescharacteristic
436C23C22×D3×D514yes—
437Q8—1516no—
438D4—1532no—
439D4C2×#1200116yes—
440C2×C4—38no—
441C2×C4—58no—
442C2×C4—128no—
443C2×C4—154no—
444C2×C4—158no—
445C2×C4—1516no—
446C2×C4—1516no—
447C2×C4—151no—
448C2×C4—154no—
449C2×C4—151no—
450C2×C4—158no—
451C2×C4—158no—
452C2×C4—208no—
453C2×C4—608no—
454C2×C4C2×#120014yes—
455C2×C4C22×D3×D512yes—
456C2×C3—22no—
457C2×C3—28no—
458C2×C3C23×C4×D511yescharacteristic
459C2×C3#6628512yes—
460D3—104no—
461C5#8585611yescharacteristic, complemented, Sylow
462C22—28no—
463C22—22no—
464C22—48no—
465C22—154no—
466C22—304no—
467C22—604no—
468C22C22×#120012yes—
469C22C22×#120018yes—
470C22C23×D3×D511yescharacteristic
471C4—68no—
472C4—108no—
473C4—152no—
474C4—152no—
475C4—158no—
476C4C22×#120014yes—
477C3#1061775711yescharacteristic, complemented, Sylow
478C2—22no—
479C2—28no—
480C2—304no—
481C2#1175703612yes—
482C2C23×#120011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC22×C3×C5×D4C22
socle, cosocleC22×C3×C5C25
prime radicalC22×#6819C2
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. C5×#5798C2semidirect
3. C3×#66132C2semidirect
4. #11755413C2semidirect
5. C2×#91532C2semidirect
6. #11754916C2semidirect
7. #11754853C2semidirect
8. #11754461C2semidirect
9. #11754213C2semidirect
14. C2×#6819C4semidirect
20. C5×D4×Dic3C22semidirect
23. C3×D4×Dic5C22semidirect
26. #91556C22semidirect
27. #91552C22semidirect
28. C2×#6669C22semidirect
31. #91532C22semidirect
32. #91532C22semidirect
33. C2×Dic3×Dic5C22semidirect
34. #91437C22semidirect
35. C4×#1200C22semidirect
36. #91386C22semidirect
37. #91347C22semidirect
38. #91340C22semidirect
39. #91333C22semidirect
43. #66132D3semidirect
52. C2×C3×C5×D4C2×C4semidirect
55. C2×#1220C2×C4semidirect
57. C22×Dic15C2×C4semidirect
62. #6819C2×C4semidirect
63. #6819C2×C4semidirect
64. C2×C4×D15C2×C4semidirect
67. C2×Dic30C2×C4semidirect
87. #5798D5semidirect
106. D4×Dic5C2×D3semidirect
162. D4×Dic3C2×D5semidirect
181. C2×C5×D4C4×D3semidirect
240. C2×C3×D4C4×D5semidirect
382. C2×D4#1200semidirect
409. C3×C5#3428semidirect
461. C5#85856semidirect
477. C3#10617757semidirect

Maximal subgroups

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

subgroupindex
C22×#68192
C5×#57982
C3×#661322
#117554132
C2×#915322
#117549162
#117548532
#117544612
#117542132
#106177573
#858565