Finite Group Databasebeta

← C3×#10604407 #14282292

Subgroups — C3×#10604407 #14282292

Order 1920.

632 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×C4×D4×D5C211yesmaximal, characteristic
2C3×#65683C211yesmaximal, characteristic, complemented
3C3×C4×#700C211yesmaximal, characteristic, complemented
4C3×D4⋊#170C212yesmaximal, complemented
5C3×#64871C212yesmaximal, complemented
6#10604407C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×D4×D5C411yescharacteristic
8C22×C3×C4×D5—21no—
9C2×C3×#700—21no—
10C3×C4×C5×D4C411yescharacteristic
11C3×D4×Dic5C2211yescharacteristic
12C3×C4×C22⋊D5—21no—
13C3×#4039C2211yescharacteristic
14C3×D5×C4⋊C4C411yescharacteristic
15C3×#4027—21no—
16C3×D5×C22⋊C4—21no—
17C3×C4×D20C411yescharacteristic
18C3×C42×D5C2211yescharacteristic
19C3×#4003—21no—
20C3×#4002—21no—
21C3×#4002—21no—
22C3×C4⋊#170C2212yescomplemented
23C3×C4×#170C2212yescomplemented
24C3×#1490—51nomaximal, Hall
25C4×D4×D5C2×C311yescharacteristic
26#65683C2×C311yescharacteristic, complemented
27C4×#700C2×C311yescharacteristic, complemented
28D4⋊#170C2×C312yescomplemented
29#64871C2×C312yescomplemented
30C23×C3×D5—21no—
31C2×C3×C5×D4C2×C411yescharacteristic
32C22×C3×C4×C5—21no—
33C2×C3×C22⋊D5—21no—
34C22×C3×Dic5—21no—
35C3×D4×D5—22no—
36C3×D4×D5—22no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—44no—
42C2×C3×C4×D5C2×C411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×#170—22no—
46C2×C3×#170—22no—
47C3×#700—24no—
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2×C411yescharacteristic
51C3×C22⋊Dic5—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5D411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5C2311yescharacteristic
59C2×C3×C4×D4—51no—
60C3×#432—51no—
61C3×C4×M16—51no—
62C3×D4⋊C8—52no—
63C3×D4⋊C8—52no—
64C2×D4×D5C3×C411yescharacteristic
65C22×C4×D5—21no—
66C2×#700—21no—
67C4×C5×D4C3×C411yescharacteristic
68D4×Dic5C22×C311yescharacteristic
69C4×C22⋊D5—21no—
70#4039C22×C311yescharacteristic
71D5×C4⋊C4C3×C411yescharacteristic
72#4027—21no—
73D5×C22⋊C4—21no—
74C4×D20C3×C411yescharacteristic
75C42×D5C22×C311yescharacteristic
76#4003—21no—
77#4002—21no—
78#4002—21no—
79C4⋊#170C22×C312yescomplemented
80C4×#170C22×C312yescomplemented
81#1490—51noSylow
82C23×C3×C5—21no—
83C22×C3×D5—24no—
84C22×C3×D5—21no—
85C22×C3×D5—42no—
86C22×C3×D5—42no—
87C22×C3×D5C22⋊C411yescharacteristic
88C3×C5×D4—21no—
89C3×C5×D4M1612yescomplemented
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C3×C22⋊D5—24no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—42no—
98C2×C3×Dic5C22⋊C411yescharacteristic
99C2×C3×Dic5C2×D411yescharacteristic
100C2×C3×Dic5C2×D411yescharacteristic
101C3×D20—21no—
102C3×D20M1612yescomplemented
103C3×C4×D5—22no—
104C3×C4×D5—21no—
105C3×C4×D5—21no—
106C3×C4×D5—22no—
107C3×C4×D5—42no—
108C3×C4×D5—42no—
109C3×C4×D5—42no—
110C3×#170—24no—
111C3×#170—42no—
112C22×C3×D4—51no—
113C23×C3×C4—101no—
114C2×C3×M16—101no—
115C3×C4×D4—51no—
116C3×C4×D4—51no—
117C3×C4×D4—51no—
118C3×C4×D4—101no—
119C3×C4×D4—101no—
120C3×C4×D4AGL(1,𝔽5)11yescharacteristic
121C2×C3×C4⋊C4—51no—
122C2×C3×C22⋊C4—101no—
123C2×C3×C42—51no—
124C3×C4⋊C8—52no—
125C3×C22⋊C8—101no—
126C3×#97—101no—
127C3×#97—101no—
128C3×C4×C8—52no—
129C23×D5—21no—
130C2×C5×D4C2×C3×C411yescharacteristic
131C22×C4×C5—21no—
132C2×C22⋊D5—21no—
133C22×Dic5—21no—
134D4×D5—22no—
135D4×D5—22no—
136C2×D20C2×C3×C411yescharacteristic
137C2×C4×D5—21no—
138C2×C4×D5—21no—
139C2×C4×D5—21no—
140C2×C4×D5—44no—
141C2×C4×D5C2×C3×C411yescharacteristic
142C2×C4×D5C3×D411yescharacteristic
143C2×C4×D5C3×D411yescharacteristic
144C2×#170—22no—
145C2×#170—22no—
146#700—24no—
147C5×C4⋊C4C2×C3×C411yescharacteristic
148C5×C22⋊C4—21no—
149C42×C5C2×C3×C411yescharacteristic
150C22⋊Dic5—21no—
151#685—21no—
152#685—21no—
153C4⋊Dic5C2×C3×C411yescharacteristic
154#683—21no—
155C4×Dic5C3×D411yescharacteristic
156C4×Dic5C3×D411yescharacteristic
157C4×Dic5C23×C311yescharacteristic
158C2×C4×D4—51no—
159#432—51no—
160C4×M16—51no—
161D4⋊C8—52no—
162D4⋊C8—52no—
163C22×C3×C5—22no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5C2×C22⋊C411yescharacteristic
167C2×C3×D5—21no—
168C2×C3×D5—21no—
169C2×C3×D5—22no—
170C2×C3×D5—48no—
171C2×C3×D5—41no—
172C2×C3×D5—41no—
173C2×C3×D5#10412yes—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—41no—
177C3×C4×C5C2×M1611yescharacteristic
178C3×C4×C5C2×M1611yescharacteristic
179C3×Dic5—21no—
180C3×Dic5—21no—
181C3×Dic5—41no—
182C3×Dic5AGL(1,ℤ/8)12yes—
183C24×C3—101no—
184C2×C3×D4—51no—
185C2×C3×D4—101no—
186C2×C3×D4—102no—
187C2×C3×D4—102no—
188C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—101no—
194C22×C3×C4—101no—
195C22×C3×C4—101no—
196C22×C3×C4—101no—
197C22×C3×C4—204no—
198C3×M16—104no—
199C2×C3×C8—102no—
200C2×C3×C8—102no—
201C3×C4⋊C4—51no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
204C3×C22⋊C4—21no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C42—51no—
209C3×C42—51no—
210C3×C42—51no—
211C3×C42C2×AGL(1,𝔽5)11yescharacteristic
212C23×C5—21no—
213C22×D5—24no—
214C22×D5—21no—
215C22×D5—42no—
216C22×D5—42no—
217C22×D5C3×C22⋊C411yescharacteristic
218C5×D4—21no—
219C5×D4C3×M1612yescomplemented
220C2×C4×C5—21no—
221C2×C4×C5—42no—
222C2×C4×C5C3×C22⋊C411yescharacteristic
223C2×C4×C5C3×C22⋊C411yescharacteristic
224C2×C4×C5C22×C3×C411yescharacteristic
225C22⋊D5—24no—
226C2×Dic5—21no—
227C2×Dic5—42no—
228C2×Dic5C3×C22⋊C411yescharacteristic
229C2×Dic5C2×C3×D411yescharacteristic
230C2×Dic5C2×C3×D411yescharacteristic
231D20—21no—
232D20C3×M1612yescomplemented
233C4×D5—22no—
234C4×D5—21no—
235C4×D5—21no—
236C4×D5—22no—
237C4×D5—42no—
238C4×D5—42no—
239C4×D5—42no—
240#170—24no—
241#170—42no—
242C22×D4—51no—
243C23×C4—101no—
244C2×M16—101no—
245C4×D4—51no—
246C4×D4—51no—
247C4×D4—51no—
248C4×D4—101no—
249C4×D4—101no—
250C4×D4C3×AGL(1,𝔽5)11yescharacteristic
251C2×C4⋊C4—51no—
252C2×C22⋊C4—101no—
253C2×C42—51no—
254C4⋊C8—52no—
255C22⋊C8—101no—
256#97—101no—
257#97—101no—
258C4×C8—52no—
259C2×C3×C5—42no—
260C2×C3×C5#40711yescharacteristic
261C2×C3×C5#41811yescharacteristic
262C2×C3×C5C2×#10411yescharacteristic
263C3×D5—22no—
264C3×D5—42no—
265C23×C3—21no—
266C23×C3—51no—
267C23×C3—104no—
268C23×C3—101no—
269C23×C3—202no—
270C23×C3—202no—
271C3×D4—21no—
272C3×D4—52no—
273C3×D4—104no—
274C3×D4—101no—
275C3×D4#70012yescomplemented
276C2×C3×C4—21no—
277C2×C3×C4—42no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—102no—
282C2×C3×C4—102no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—202no—
287C2×C3×C4—202no—
288C2×C3×C4—202no—
289C2×C3×C4—202no—
290C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
291C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
292C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
293C3×C8—104no—
294C3×C8—202no—
295C22×C5—22no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5C2×C3×C22⋊C411yescharacteristic
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—22no—
302C2×D5—48no—
303C2×D5—41no—
304C2×D5—41no—
305C2×D5C3×#10412yes—
306C4×C5—21no—
307C4×C5—21no—
308C4×C5—41no—
309C4×C5C2×C3×M1611yescharacteristic
310C4×C5C2×C3×M1611yescharacteristic
311Dic5—21no—
312Dic5—21no—
313Dic5—41no—
314Dic5C3×AGL(1,ℤ/8)12yes—
315C24—101no—
316C2×D4—51no—
317C2×D4—101no—
318C2×D4—102no—
319C2×D4—102no—
320C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
321C22×C4—21no—
322C22×C4—51no—
323C22×C4—51no—
324C22×C4—51no—
325C22×C4—101no—
326C22×C4—101no—
327C22×C4—101no—
328C22×C4—101no—
329C22×C4—204no—
330M16—104no—
331C2×C8—102no—
332C2×C8—102no—
333C4⋊C4—51no—
334C4⋊C4—101no—
335C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
336C22⋊C4—21no—
337C22⋊C4—101no—
338C22⋊C4—101no—
339C22⋊C4—101no—
340C42—51no—
341C42—51no—
342C42—51no—
343C42C2×C3×AGL(1,𝔽5)11yescharacteristic
344C3×C5#149011yescharacteristic, complemented, Hall
345C22×C3—22no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—52no—
349C22×C3—101no—
350C22×C3—101no—
351C22×C3—102no—
352C22×C3—208no—
353C22×C3—201no—
354C22×C3—201no—
355C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—52no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—201no—
363C3×C4C2×#70011yescharacteristic
364C3×C4D5⋊M1611yescharacteristic
365C2×C5—42no—
366C2×C5C3×#40711yescharacteristic
367C2×C5C3×#41811yescharacteristic
368C2×C5C2×C3×#10411yescharacteristic
369D5—22no—
370D5—42no—
371C23—21no—
372C23—51no—
373C23—104no—
374C23—101no—
375C23—202no—
376C23—202no—
377D4—21no—
378D4—52no—
379D4—104no—
380D4—101no—
381D4C3×#70012yescomplemented
382C2×C4—21no—
383C2×C4—42no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—102no—
388C2×C4—102no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—202no—
393C2×C4—202no—
394C2×C4—202no—
395C2×C4—202no—
396C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
397C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
398C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
399C8—104no—
400C8—202no—
401C2×C3—42no—
402C2×C3—102no—
403C2×C3—202no—
404C2×C3#6575611yescharacteristic
405C2×C3#6576711yescharacteristic
406C2×C3D5⋊#10411yescharacteristic
407C5C3×#149011yescharacteristic, complemented, Sylow
408C22—22no—
409C22—41no—
410C22—41no—
411C22—52no—
412C22—101no—
413C22—101no—
414C22—102no—
415C22—208no—
416C22—201no—
417C22—201no—
418C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
419C4—21no—
420C4—21no—
421C4—41no—
422C4—52no—
423C4—101no—
424C4—101no—
425C4—201no—
426C4C2×C3×#70011yescharacteristic
427C4C3×D5⋊M1611yescharacteristic
428C3#1060440711yescharacteristic, direct product factor, Sylow
429C2—42no—
430C2—102no—
431C2—202no—
432C2C3×#6575611yescharacteristic
433C2C3×#6576711yescharacteristic
434C2C3×D5⋊#10411yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4×D4AGL(1,𝔽5)
hypocenterC5C3×#1490
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65683C2semidirect
3. C3×C4×#700C2semidirect
4. C3×D4⋊#170C2semidirect
5. C3×#64871C2semidirect
6. #10604407C3direct (N × H)
22. C3×C4⋊#170C22semidirect
23. C3×C4×#170C22semidirect
26. #65683C2×C3semidirect
27. C4×#700C2×C3semidirect
28. D4⋊#170C2×C3semidirect
29. #64871C2×C3semidirect
79. C4⋊#170C22×C3semidirect
80. C4×#170C22×C3semidirect
89. C3×C5×D4M16semidirect
102. C3×D20M16semidirect
219. C5×D4C3×M16semidirect
232. D20C3×M16semidirect
275. C3×D4#700semidirect
344. C3×C5#1490semidirect
381. D4C3×#700semidirect
407. C5C3×#1490semidirect
428. C3#10604407direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×D4×D52
C3×#656832
C3×C4×#7002
C3×D4⋊#1702
C3×#648712
#106044073
C3×#14905