Finite Group Databasebeta

← C3×#10599918 #14313000

Subgroups — C3×#10599918 #14313000

Order 1920.

440 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#131C211yesmaximal, characteristic
2C3×D5×M32C211yesmaximal, characteristic, complemented
3C2×C3×#3930C211yesmaximal, characteristic, complemented
4C3×C5×#350C211yesmaximal, characteristic, complemented
5C3×#64781C211yesmaximal, characteristic, complemented
6C3×#64735C211yesmaximal, characteristic, complemented
7C3×#64728C211yesmaximal, characteristic, complemented
8#10599918C311yesmaximal, characteristic, direct product factor, Hall
9C3×D5×#41C411yescharacteristic
10C3×C5×#131C2211yescharacteristic
11C3×#4094C411yescharacteristic
12C3×#4053—21no—
13C3×#4053C411yescharacteristic
14C3×D5×M16—21no—
15C3×D5×M16C411yescharacteristic
16C3×#4047—21no—
17C3×#4047C2211yescharacteristic
18C2×C3×C8×D5—21no—
19C2×C3×C8×D5C2211yescharacteristic
20C3×C5×M32C2211yescharacteristic, complemented
21C2×C3×C5×C16C2211yescharacteristic, complemented
22C3×#3944C2211yescharacteristic, complemented
23C2×C3×#672C2211yescharacteristic, complemented
24C3×#3930—21no—
25C3×#3930—21no—
26C3×#3930—21no—
27C3×D5×C16—21no—
28C3×#2117—51nomaximal, Hall
29D5×#131C2×C311yescharacteristic
30D5×M32C2×C311yescharacteristic, complemented
31C2×#3930C2×C311yescharacteristic, complemented
32C5×#350C2×C311yescharacteristic, complemented
33#64781C2×C311yescharacteristic, complemented
34#64735C2×C311yescharacteristic, complemented
35#64728C2×C311yescharacteristic, complemented
36C3×C5×#41C2×C411yescharacteristic
37C3×#713C811yescharacteristic
38C3×Q8×D5C811yescharacteristic
39C3×#711—21no—
40C3×#711C811yescharacteristic
41C3×D4×D5—21no—
42C3×D4×D5C811yescharacteristic
43C3×#709—21no—
44C3×#709C2×C411yescharacteristic
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5C2×C411yescharacteristic
47C3×C5×M16—21no—
48C3×C5×M16C2×C411yescharacteristic
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8C2311yescharacteristic
51C3×#681—21no—
52C3×#681C2×C411yescharacteristic
53C2×C3×#168—21no—
54C2×C3×#168C2×C411yescharacteristic
55C3×#676—21no—
56C3×#676—21no—
57C3×#676—21no—
58C3×C8×D5—21no—
59C3×C8×D5—21no—
60C3×C8×D5—21no—
61C3×C8×D5D411yescharacteristic
62C3×C8×D5D411yescharacteristic
63C3×C8×D5D411yescharacteristic
64C3×C8×D5D411yescharacteristic
65C3×C5×C16—21no—
66C3×C5×C16—21no—
67C3×#672—21no—
68C3×#672—21no—
69C2×C3×#131—51no—
70C2×C3×M32—51no—
71C2×C3×M32—51no—
72C3×#350—51no—
73C3×#350—51no—
74C3×#350—51no—
75C3×#350D511yescharacteristic, complemented
76D5×#41C3×C411yescharacteristic
77C5×#131C22×C311yescharacteristic
78#4094C3×C411yescharacteristic
79#4053—21no—
80#4053C3×C411yescharacteristic
81D5×M16—21no—
82D5×M16C3×C411yescharacteristic
83#4047—21no—
84#4047C22×C311yescharacteristic
85C2×C8×D5—21no—
86C2×C8×D5C22×C311yescharacteristic
87C5×M32C22×C311yescharacteristic, complemented
88C2×C5×C16C22×C311yescharacteristic, complemented
89#3944C22×C311yescharacteristic, complemented
90C2×#672C22×C311yescharacteristic, complemented
91#3930—21no—
92#3930—21no—
93#3930—21no—
94D5×C16—21no—
95#2117—51noSylow
96C22×C3×D5—21no—
97C22×C3×D5M1611yescharacteristic
98C3×C5×Q8C2×C811yescharacteristic
99C3×C5×D4—21no—
100C3×C5×D4C2×C811yescharacteristic
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C3×C22⋊D5—21no—
104C3×C22⋊D5—21no—
105C3×C22⋊D5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5M1611yescharacteristic
108C3×D20—21no—
109C3×D20C2×C811yescharacteristic
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5C22⋊C411yescharacteristic
114C3×C4×D5C22⋊C411yescharacteristic
115C3×C4×D5C2×C811yescharacteristic
116C3×C4×D5C2×C811yescharacteristic
117C3×Dic10—21no—
118C3×Dic10C2×C811yescharacteristic
119C3×C5×C8—21no—
120C3×C5×C8C2×D411yescharacteristic
121C3×C5×C8C2×D411yescharacteristic
122C3×#168—21no—
123C3×#168C22⋊C411yescharacteristic
124C3×#168C22⋊C411yescharacteristic
125C2×C3×#41—51no—
126C3×#131—51no—
127C3×#131—51no—
128C3×#131—51no—
129C3×#131—101no—
130C3×#131—101no—
131C3×#131C2×D511yescharacteristic
132C2×C3×M16—51no—
133C2×C3×M16—101no—
134C22×C3×C8—51no—
135C22×C3×C8—101no—
136C3×M32—51no—
137C3×M32—101no—
138C3×M32—101no—
139C3×M32—101no—
140C3×M32C2×D511yescharacteristic, complemented
141C2×C3×C16—51no—
142C2×C3×C16—101no—
143C2×C3×C16C2×D511yescharacteristic, complemented
144C5×#41C2×C3×C411yescharacteristic
145#713C3×C811yescharacteristic
146Q8×D5C3×C811yescharacteristic
147#711—21no—
148#711C3×C811yescharacteristic
149D4×D5—21no—
150D4×D5C3×C811yescharacteristic
151#709—21no—
152#709C2×C3×C411yescharacteristic
153C2×C4×D5—21no—
154C2×C4×D5C2×C3×C411yescharacteristic
155C5×M16—21no—
156C5×M16C2×C3×C411yescharacteristic
157C2×C5×C8—21no—
158C2×C5×C8C23×C311yescharacteristic
159#681—21no—
160#681C2×C3×C411yescharacteristic
161C2×#168—21no—
162C2×#168C2×C3×C411yescharacteristic
163#676—21no—
164#676—21no—
165#676—21no—
166C8×D5—21no—
167C8×D5—21no—
168C8×D5—21no—
169C8×D5C3×D411yescharacteristic
170C8×D5C3×D411yescharacteristic
171C8×D5C3×D411yescharacteristic
172C8×D5C3×D411yescharacteristic
173C5×C16—21no—
174C5×C16—21no—
175#672—21no—
176#672—21no—
177C2×#131—51no—
178C2×M32—51no—
179C2×M32—51no—
180#350—51no—
181#350—51no—
182#350—51no—
183#350C3×D511yescharacteristic, complemented
184C22×C3×C5—21no—
185C22×C3×C5C2×M1611yescharacteristic
186C2×C3×D5—21no—
187C2×C3×D5—41no—
188C2×C3×D5—42no—
189C2×C3×D5C22⋊C811yescharacteristic
190C2×C3×D5C22⋊C811yescharacteristic
191C3×C4×C5—21no—
192C3×C4×C5C2×C22⋊C411yescharacteristic
193C3×C4×C5C22×C811yescharacteristic
194C3×Dic5—21no—
195C3×Dic5C22⋊C811yescharacteristic
196C3×Dic5C22⋊C811yescharacteristic
197C3×#41—51no—
198C3×#41—51no—
199C3×#41—51no—
200C3×#41—101no—
201C3×#41—101no—
202C3×#41C4×D511yescharacteristic
203C2×C3×Q8—51no—
204C2×C3×D4—51no—
205C2×C3×D4—101no—
206C22×C3×C4—51no—
207C22×C3×C4—101no—
208C3×M16—21no—
209C3×M16—51no—
210C3×M16—101no—
211C3×M16—101no—
212C3×M16—101no—
213C3×M16—101no—
214C3×M16C4×D511yescharacteristic
215C2×C3×C8—21no—
216C2×C3×C8—51no—
217C2×C3×C8—51no—
218C2×C3×C8—51no—
219C2×C3×C8—51no—
220C2×C3×C8—51no—
221C2×C3×C8—101no—
222C2×C3×C8—101no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C2×C3×C8C22×D511yescharacteristic
226C3×C16—21no—
227C3×C16—21no—
228C3×C16—101no—
229C3×C16—101no—
230C22×D5—21no—
231C22×D5C3×M1611yescharacteristic
232C5×Q8C2×C3×C811yescharacteristic
233C5×D4—21no—
234C5×D4C2×C3×C811yescharacteristic
235C2×C4×C5—21no—
236C2×C4×C5C22×C3×C411yescharacteristic
237C22⋊D5—21no—
238C22⋊D5—21no—
239C22⋊D5—21no—
240C2×Dic5—21no—
241C2×Dic5C3×M1611yescharacteristic
242D20—21no—
243D20C2×C3×C811yescharacteristic
244C4×D5—21no—
245C4×D5—21no—
246C4×D5—21no—
247C4×D5C3×C22⋊C411yescharacteristic
248C4×D5C3×C22⋊C411yescharacteristic
249C4×D5C2×C3×C811yescharacteristic
250C4×D5C2×C3×C811yescharacteristic
251Dic10—21no—
252Dic10C2×C3×C811yescharacteristic
253C5×C8—21no—
254C5×C8C2×C3×D411yescharacteristic
255C5×C8C2×C3×D411yescharacteristic
256#168—21no—
257#168C3×C22⋊C411yescharacteristic
258#168C3×C22⋊C411yescharacteristic
259C2×#41—51no—
260#131—51no—
261#131—51no—
262#131—51no—
263#131—101no—
264#131—101no—
265#131C2×C3×D511yescharacteristic
266C2×M16—51no—
267C2×M16—101no—
268C22×C8—51no—
269C22×C8—101no—
270M32—51no—
271M32—101no—
272M32—101no—
273M32—101no—
274M32C2×C3×D511yescharacteristic, complemented
275C2×C16—51no—
276C2×C16—101no—
277C2×C16C2×C3×D511yescharacteristic, complemented
278C2×C3×C5—21no—
279C2×C3×C5—41no—
280C2×C3×C5C2×C22⋊C811yescharacteristic
281C3×D5—21no—
282C3×D5—21no—
283C3×D5—41no—
284C23×C3—51no—
285C23×C3—101no—
286C3×Q8—51no—
287C3×Q8—101no—
288C3×Q8C8×D511yescharacteristic
289C3×D4—21no—
290C3×D4—51no—
291C3×D4—101no—
292C3×D4—101no—
293C3×D4—101no—
294C3×D4—101no—
295C3×D4C8×D511yescharacteristic
296C2×C3×C4—21no—
297C2×C3×C4—51no—
298C2×C3×C4—51no—
299C2×C3×C4—51no—
300C2×C3×C4—51no—
301C2×C3×C4—51no—
302C2×C3×C4—101no—
303C2×C3×C4—101no—
304C2×C3×C4—101no—
305C2×C3×C4—101no—
306C2×C3×C4C2×C4×D511yescharacteristic
307C3×C8—21no—
308C3×C8—51no—
309C3×C8—51no—
310C3×C8—101no—
311C3×C8D4×D511yescharacteristic
312C3×C8D4×D511yescharacteristic
313C22×C5—21no—
314C22×C5C2×C3×M1611yescharacteristic
315C2×D5—21no—
316C2×D5—41no—
317C2×D5—42no—
318C2×D5C3×C22⋊C811yescharacteristic
319C2×D5C3×C22⋊C811yescharacteristic
320C4×C5—21no—
321C4×C5C2×C3×C22⋊C411yescharacteristic
322C4×C5C22×C3×C811yescharacteristic
323Dic5—21no—
324Dic5C3×C22⋊C811yescharacteristic
325Dic5C3×C22⋊C811yescharacteristic
326#41—51no—
327#41—51no—
328#41—51no—
329#41—101no—
330#41—101no—
331#41C3×C4×D511yescharacteristic
332C2×Q8—51no—
333C2×D4—51no—
334C2×D4—101no—
335C22×C4—51no—
336C22×C4—101no—
337M16—21no—
338M16—51no—
339M16—101no—
340M16—101no—
341M16—101no—
342M16—101no—
343M16C3×C4×D511yescharacteristic
344C2×C8—21no—
345C2×C8—51no—
346C2×C8—51no—
347C2×C8—51no—
348C2×C8—51no—
349C2×C8—51no—
350C2×C8—101no—
351C2×C8—101no—
352C2×C8—101no—
353C2×C8—101no—
354C2×C8C22×C3×D511yescharacteristic
355C16—21no—
356C16—21no—
357C16—101no—
358C16—101no—
359C3×C5#211711yescharacteristic, complemented, Hall
360C22×C3—21no—
361C22×C3—51no—
362C22×C3—51no—
363C22×C3—101no—
364C22×C3—201no—
365C22×C3—202no—
366C22×C3D5×M1611yescharacteristic
367C3×C4—21no—
368C3×C4—51no—
369C3×C4—51no—
370C3×C4—101no—
371C3×C4D5×C22⋊C411yescharacteristic
372C3×C4C2×C8×D511yescharacteristic
373C2×C5—21no—
374C2×C5—41no—
375C2×C5C2×C3×C22⋊C811yescharacteristic
376D5—21no—
377D5—21no—
378D5—41no—
379C23—51no—
380C23—101no—
381Q8—51no—
382Q8—101no—
383Q8C3×C8×D511yescharacteristic
384D4—21no—
385D4—51no—
386D4—101no—
387D4—101no—
388D4—101no—
389D4—101no—
390D4C3×C8×D511yescharacteristic
391C2×C4—21no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—101no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4C2×C3×C4×D511yescharacteristic
402C8—21no—
403C8—51no—
404C8—51no—
405C8—101no—
406C8C3×D4×D511yescharacteristic
407C8C3×D4×D511yescharacteristic
408C2×C3—21no—
409C2×C3—41no—
410C2×C3—101no—
411C2×C3—101no—
412C2×C3—201no—
413C2×C3D5×C22⋊C811yescharacteristic
414C5C3×#211711yescharacteristic, complemented, Sylow
415C22—21no—
416C22—51no—
417C22—51no—
418C22—101no—
419C22—201no—
420C22—202no—
421C22C3×D5×M1611yescharacteristic
422C4—21no—
423C4—51no—
424C4—51no—
425C4—101no—
426C4C3×D5×C22⋊C411yescharacteristic
427C4C2×C3×C8×D511yescharacteristic
428C3#1059991811yescharacteristic, direct product factor, Sylow
429C2—21no—
430C2—41no—
431C2—101no—
432C2—101no—
433C2—201no—
434C2C3×D5×C22⋊C811yescharacteristic
subgroupG/H
centerC3×C8D4×D5
commutatorC4×C5C22×C3×C8
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#350C2
socleC2×C3×C5C2×C22⋊C8
prime radicalC3×D5×#41C4
cosocleC2×C5×C8C23×C3
hypercenterC3×#350D5
hypocenterC5C3×#2117
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×C8 ◁ C3×#350

Complements

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

NH ≅ G/Ntype
2. C3×D5×M32C2semidirect
3. C2×C3×#3930C2semidirect
4. C3×C5×#350C2semidirect
5. C3×#64781C2semidirect
6. C3×#64735C2semidirect
7. C3×#64728C2semidirect
8. #10599918C3direct (N × H)
20. C3×C5×M32C22semidirect
21. C2×C3×C5×C16C22semidirect
22. C3×#3944C22semidirect
23. C2×C3×#672C22semidirect
30. D5×M32C2×C3semidirect
31. C2×#3930C2×C3semidirect
32. C5×#350C2×C3semidirect
33. #64781C2×C3semidirect
34. #64735C2×C3semidirect
35. #64728C2×C3semidirect
75. C3×#350D5semidirect
87. C5×M32C22×C3semidirect
88. C2×C5×C16C22×C3semidirect
89. #3944C22×C3semidirect
90. C2×#672C22×C3semidirect
140. C3×M32C2×D5semidirect
143. C2×C3×C16C2×D5semidirect
183. #350C3×D5semidirect
274. M32C2×C3×D5semidirect
277. C2×C16C2×C3×D5semidirect
359. C3×C5#2117semidirect
414. C5C3×#2117semidirect
428. C3#10599918direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1312
C3×D5×M322
C2×C3×#39302
C3×C5×#3502
C3×#647812
C3×#647352
C3×#647282
#105999183
C3×#21175