Finite Group Databasebeta

← C3×#10603918 #14299526

Subgroups — C3×#10603918 #14299526

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5⋊M16C211yesmaximal, characteristic
2C3×#65756C211yesmaximal, characteristic
3C2×C3×#3996C211yesmaximal, characteristic, complemented
4C2×C3×#3995C211yesmaximal, characteristic, complemented
5C3×D5×C22⋊C8C211yesmaximal, characteristic
6C3×#64896C211yesmaximal, characteristic, complemented
7C3×#64896C211yesmaximal, characteristic, complemented
8#10603918C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×#704—21no—
11C3×D5⋊M16—22no—
12C3×D5⋊M16—22no—
13C2×C3×#700C2211yescharacteristic
14C2×C3×#700C2211yescharacteristic
15C2×C3×#700C2211yescharacteristic
16C2×C3×#700C2211yescharacteristic
17C2×C3×D5⋊C8—21no—
18C2×C3×C8×D5C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×C22⋊#170—21no—
21C3×#4003—21no—
22C3×#3996—22no—
23C3×#3995—22no—
24C3×C5×C22⋊C8C411yescharacteristic
25C3×C22⋊#168C411yescharacteristic
26C3×#3952C411yescharacteristic
27C3×#3952C411yescharacteristic
28C3×#1855—51nomaximal, Hall
29C2×D5⋊M16C2×C311yescharacteristic
30#65756C2×C311yescharacteristic
31C2×#3996C2×C311yescharacteristic, complemented
32C2×#3995C2×C311yescharacteristic, complemented
33D5×C22⋊C8C2×C311yescharacteristic
34#64896C2×C311yescharacteristic, complemented
35#64896C2×C311yescharacteristic, complemented
36C23×C3×D5Q811yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5C2×C411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5Q811yescharacteristic
46C2×C3×C4×D5C2311yescharacteristic
47C3×#704—24no—
48C2×C3×#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170—21no—
51C2×C3×#170—21no—
52C3×#700—21no—
53C3×#700—21no—
54C3×#700—21no—
55C3×#700—21no—
56C3×#700—21no—
57C3×#700—21no—
58C3×#700D412yes—
59C3×#700D412yes—
60C3×D5⋊C8—24no—
61C2×C3×C5×C8C2×C411yescharacteristic
62C2×C3×C5×C8C2×C411yescharacteristic
63C2×C3×#168C2×C411yescharacteristic
64C2×C3×#168C2×C411yescharacteristic
65C3×C8×D5—21no—
66C3×C8×D5—21no—
67C3×C8×D5—21no—
68C3×C8×D5—21no—
69C22×C3×M16—51no—
70C2×C3×#108—51no—
71C2×C3×#108—51no—
72C3×#407—51no—
73C2×C3×C22⋊C8—51no—
74C3×#341—51no—
75C3×#341—51no—
76C22×C4×D5C22×C311yescharacteristic
77C2×#704—21no—
78D5⋊M16—22no—
79D5⋊M16—22no—
80C2×#700C22×C311yescharacteristic
81C2×#700C22×C311yescharacteristic
82C2×#700C22×C311yescharacteristic
83C2×#700C22×C311yescharacteristic
84C2×D5⋊C8—21no—
85C2×C8×D5C22×C311yescharacteristic
86C2×C8×D5C22×C311yescharacteristic
87C22⋊#170—21no—
88#4003—21no—
89#3996—22no—
90#3995—22no—
91C5×C22⋊C8C3×C411yescharacteristic
92C22⋊#168C3×C411yescharacteristic
93#3952C3×C411yescharacteristic
94#3952C3×C411yescharacteristic
95#1855—51noSylow
96C23×C3×C5C4⋊C411yescharacteristic
97C22×C3×D5—22no—
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—41no—
101C22×C3×D5C4⋊C411yescharacteristic
102C22×C3×D5C2×Q811yescharacteristic
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5C4⋊C411yescharacteristic
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5C4⋊C411yescharacteristic
110C2×C3×Dic5C2×D411yescharacteristic
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5—21no—
114C3×C4×D5—21no—
115C3×C4×D5—21no—
116C3×C4×D5—21no—
117C3×C4×D5C2×D411yescharacteristic
118C3×C4×D5C2×D411yescharacteristic
119C3×C4×D5#4111yescharacteristic
120C3×C4×D5#4111yescharacteristic
121C3×#170—22no—
122C3×#170—22no—
123C3×#170—41no—
124C3×#170—41no—
125C3×C5×C8—21no—
126C3×C5×C8—21no—
127C3×#168—21no—
128C3×#168—21no—
129C23×C3×C4—51no—
130C2×C3×M16—51no—
131C2×C3×M16—51no—
132C2×C3×M16—51no—
133C2×C3×M16—51no—
134C2×C3×M16—102no—
135C2×C3×M16—102no—
136C2×C3×M16—101no—
137C22×C3×C8—51no—
138C22×C3×C8—51no—
139C22×C3×C8—101no—
140C3×#108—102no—
141C3×#108—102no—
142C3×C22⋊C8—51no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8—51no—
145C3×C22⋊C8—101no—
146C3×C22⋊C8—101no—
147C3×C22⋊C8AGL(1,𝔽5)11yescharacteristic
148C23×D5C3×Q811yescharacteristic
149C22×C4×C5C2×C3×C411yescharacteristic
150C22×Dic5C3×D411yescharacteristic
151C2×C4×D5—21no—
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×C4×D5C2×C3×C411yescharacteristic
156C2×C4×D5C3×D411yescharacteristic
157C2×C4×D5C3×Q811yescharacteristic
158C2×C4×D5C23×C311yescharacteristic
159#704—24no—
160C2×#170—21no—
161C2×#170—21no—
162C2×#170—21no—
163C2×#170—21no—
164#700—21no—
165#700—21no—
166#700—21no—
167#700—21no—
168#700—21no—
169#700—21no—
170#700C3×D412yes—
171#700C3×D412yes—
172D5⋊C8—24no—
173C2×C5×C8C2×C3×C411yescharacteristic
174C2×C5×C8C2×C3×C411yescharacteristic
175C2×#168C2×C3×C411yescharacteristic
176C2×#168C2×C3×C411yescharacteristic
177C8×D5—21no—
178C8×D5—21no—
179C8×D5—21no—
180C8×D5—21no—
181C22×M16—51no—
182C2×#108—51no—
183C2×#108—51no—
184#407—51no—
185C2×C22⋊C8—51no—
186#341—51no—
187#341—51no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5C2×C4⋊C411yescharacteristic
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—21no—
195C2×C3×D5—21no—
196C2×C3×D5—42no—
197C2×C3×D5—42no—
198C2×C3×D5#10812yescomplemented
199C2×C3×D5C22⋊Q811yescharacteristic
200C2×C3×D5C22⋊Q811yescharacteristic
201C3×C4×C5—21no—
202C3×C4×C5C4×D411yescharacteristic
203C3×C4×C5C4×D411yescharacteristic
204C3×Dic5—21no—
205C3×Dic5#12011yescharacteristic
206C3×Dic5#12311yescharacteristic
207C24×C3—51no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—101no—
214C22×C3×C4—101no—
215C22×C3×C4—101no—
216C22×C3×C4—101no—
217C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
218C3×M16—52no—
219C3×M16—52no—
220C3×M16—101no—
221C3×M16—101no—
222C3×M16—104no—
223C3×M16—101no—
224C3×M16—101no—
225C3×M16—101no—
226C3×M16—101no—
227C2×C3×C8—51no—
228C2×C3×C8—51no—
229C2×C3×C8—101no—
230C2×C3×C8—101no—
231C2×C3×C8—101no—
232C2×C3×C8—101no—
233C2×C3×C8—101no—
234C2×C3×C8—101no—
235C2×C3×C8—104no—
236C2×C3×C8—101no—
237C2×C3×C8—101no—
238C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
239C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
240C23×C5C3×C4⋊C411yescharacteristic
241C22×D5—22no—
242C22×D5—21no—
243C22×D5—21no—
244C22×D5—41no—
245C22×D5C3×C4⋊C411yescharacteristic
246C22×D5C2×C3×Q811yescharacteristic
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5C3×C4⋊C411yescharacteristic
250C2×C4×C5C22×C3×C411yescharacteristic
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5C3×C4⋊C411yescharacteristic
254C2×Dic5C2×C3×D411yescharacteristic
255C4×D5—21no—
256C4×D5—21no—
257C4×D5—21no—
258C4×D5—21no—
259C4×D5—21no—
260C4×D5—21no—
261C4×D5C2×C3×D411yescharacteristic
262C4×D5C2×C3×D411yescharacteristic
263C4×D5C3×#4111yescharacteristic
264C4×D5C3×#4111yescharacteristic
265#170—22no—
266#170—22no—
267#170—41no—
268#170—41no—
269C5×C8—21no—
270C5×C8—21no—
271#168—21no—
272#168—21no—
273C23×C4—51no—
274C2×M16—51no—
275C2×M16—51no—
276C2×M16—51no—
277C2×M16—51no—
278C2×M16—102no—
279C2×M16—102no—
280C2×M16—101no—
281C22×C8—51no—
282C22×C8—51no—
283C22×C8—101no—
284#108—102no—
285#108—102no—
286C22⋊C8—51no—
287C22⋊C8—51no—
288C22⋊C8—51no—
289C22⋊C8—101no—
290C22⋊C8—101no—
291C22⋊C8C3×AGL(1,𝔽5)11yescharacteristic
292C2×C3×C5—41no—
293C2×C3×C5#38511yescharacteristic
294C2×C3×C5C2×#10811yescharacteristic
295C2×C3×C5#43011yescharacteristic
296C3×D5—22no—
297C3×D5—21no—
298C3×D5—21no—
299C23×C3—51no—
300C23×C3—51no—
301C23×C3—101no—
302C23×C3—101no—
303C23×C3—102no—
304C23×C3—201no—
305C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—51no—
309C2×C3×C4—51no—
310C2×C3×C4—51no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
323C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
324C3×C8—21no—
325C3×C8—21no—
326C3×C8—102no—
327C3×C8—102no—
328C3×C8—101no—
329C3×C8—101no—
330C3×C8—201no—
331C3×C8—201no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5C2×C3×C4⋊C411yescharacteristic
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—21no—
339C2×D5—21no—
340C2×D5—42no—
341C2×D5—42no—
342C2×D5C3×#10812yescomplemented
343C2×D5C3×C22⋊Q811yescharacteristic
344C2×D5C3×C22⋊Q811yescharacteristic
345C4×C5—21no—
346C4×C5C3×C4×D411yescharacteristic
347C4×C5C3×C4×D411yescharacteristic
348Dic5—21no—
349Dic5C3×#12011yescharacteristic
350Dic5C3×#12311yescharacteristic
351C24—51no—
352C22×C4—51no—
353C22×C4—51no—
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—101no—
358C22×C4—101no—
359C22×C4—101no—
360C22×C4—101no—
361C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
362M16—52no—
363M16—52no—
364M16—101no—
365M16—101no—
366M16—104no—
367M16—101no—
368M16—101no—
369M16—101no—
370M16—101no—
371C2×C8—51no—
372C2×C8—51no—
373C2×C8—101no—
374C2×C8—101no—
375C2×C8—101no—
376C2×C8—101no—
377C2×C8—101no—
378C2×C8—101no—
379C2×C8—104no—
380C2×C8—101no—
381C2×C8—101no—
382C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
383C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
384C3×C5#185511yescharacteristic, complemented, Hall
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—51no—
389C22×C3—51no—
390C22×C3—52no—
391C22×C3—101no—
392C22×C3—101no—
393C22×C3—101no—
394C22×C3—101no—
395C22×C3—202no—
396C22×C3—202no—
397C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
398C3×C4—21no—
399C3×C4—51no—
400C3×C4—51no—
401C3×C4—101no—
402C3×C4D4×AGL(1,𝔽5)11yescharacteristic
403C3×C4D4×AGL(1,𝔽5)11yescharacteristic
404C2×C5—41no—
405C2×C5C3×#38511yescharacteristic
406C2×C5C2×C3×#10811yescharacteristic
407C2×C5C3×#43011yescharacteristic
408D5—22no—
409D5—21no—
410D5—21no—
411C23—51no—
412C23—51no—
413C23—101no—
414C23—101no—
415C23—102no—
416C23—201no—
417C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—51no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4C3×C4⋊AGL(1,𝔽5)11yescharacteristic
435C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
436C8—21no—
437C8—21no—
438C8—102no—
439C8—102no—
440C8—101no—
441C8—101no—
442C8—201no—
443C8—201no—
444C2×C3—41no—
445C2×C3—101no—
446C2×C3—101no—
447C2×C3—102no—
448C2×C3#6569911yescharacteristic
449C2×C3D5⋊#10811yescharacteristic
450C2×C3#6572911yescharacteristic
451C5C3×#185511yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—51no—
456C22—51no—
457C22—52no—
458C22—101no—
459C22—101no—
460C22—101no—
461C22—101no—
462C22—202no—
463C22—202no—
464C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
465C4—21no—
466C4—51no—
467C4—51no—
468C4—101no—
469C4C3×D4×AGL(1,𝔽5)11yescharacteristic
470C4C3×D4×AGL(1,𝔽5)11yescharacteristic
471C3#1060391811yescharacteristic, direct product factor, Sylow
472C2—41no—
473C2—101no—
474C2—101no—
475C2—102no—
476C2C3×#6569911yescharacteristic
477C2C3×D5⋊#10811yescharacteristic
478C2C3×#6572911yescharacteristic
subgroupG/H
centerC22×C3C2×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×D5Q8
cosocleC2×C4×D5C23×C3
hypercenterC3×C22⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1855
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#3996C2semidirect
4. C2×C3×#3995C2semidirect
6. C3×#64896C2semidirect
7. C3×#64896C2semidirect
8. #10603918C3direct (N × H)
31. C2×#3996C2×C3semidirect
32. C2×#3995C2×C3semidirect
34. #64896C2×C3semidirect
35. #64896C2×C3semidirect
198. C2×C3×D5#108semidirect
342. C2×D5C3×#108semidirect
384. C3×C5#1855semidirect
451. C5C3×#1855semidirect
471. C3#10603918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5⋊M162
C3×#657562
C2×C3×#39962
C2×C3×#39952
C3×D5×C22⋊C82
C3×#648962
#106039183
C3×#18555