Finite Group Databasebeta

← C3×#10604228 #14297476

Subgroups — C3×#10604228 #14297476

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4023C211yesmaximal, characteristic
2C2×C3×C22⋊#170C212yesmaximal
3C2×C3×#4004C211yesmaximal, characteristic, complemented
4C2×C3×C4⋊#170C211yesmaximal, characteristic, complemented
5C3×#64918C212yesmaximal, complemented
6#10604228C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×Dic5C2211yescharacteristic
8C22×C3×#170C2212yes—
9C22×C3×#170C2212yes—
10C2×C3×C5×C22⋊C4C411yescharacteristic
11C2×C3×C22⋊Dic5C411yescharacteristic
12C2×C3×#683C411yescharacteristic
13C2×C3×#683C411yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4023—22no—
17C3×#4023—22no—
18C3×C22⋊#170—24no—
19C3×#4004—22no—
20C3×C4⋊#170—22no—
21C3×#1798—51nomaximal, Hall
22C2×#4023C2×C311yescharacteristic
23C2×C22⋊#170C2×C312yes—
24C2×#4004C2×C311yescharacteristic, complemented
25C2×C4⋊#170C2×C311yescharacteristic, complemented
26#64918C2×C312yescomplemented
27C24×C3×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×Dic5—21no—
31C22×C3×Dic5—21no—
32C22×C3×Dic5—21no—
33C22×C3×Dic5—21no—
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2×C411yescharacteristic
37C22×C3×Dic5D412yes—
38C22×C3×Dic5Q812yes—
39C22×C3×Dic5C2311yescharacteristic
40C2×C3×#170—22no—
41C2×C3×#170—22no—
42C2×C3×#170—22no—
43C2×C3×#170—22no—
44C2×C3×#170—22no—
45C2×C3×#170—22no—
46C3×C5×C22⋊C4—22no—
47C3×C22⋊Dic5—22no—
48C3×#683—22no—
49C3×#683—22no—
50C3×C4×Dic5—21no—
51C3×C4×Dic5—21no—
52C3×C4×Dic5D412yes—
53C3×C4×Dic5D412yes—
54C2×C3×#117—51no—
55C2×C3×C4⋊C8—51no—
56C2×C3×C4⋊C8—51no—
57C2×C3×C22⋊C8—52no—
58C3×#336—52no—
59C23×Dic5C22×C311yescharacteristic
60C22×#170C22×C312yes—
61C22×#170C22×C312yes—
62C2×C5×C22⋊C4C3×C411yescharacteristic
63C2×C22⋊Dic5C3×C411yescharacteristic
64C2×#683C3×C411yescharacteristic
65C2×#683C3×C411yescharacteristic
66C2×C4×Dic5C22×C311yescharacteristic
67C2×C4×Dic5C22×C311yescharacteristic
68#4023—22no—
69#4023—22no—
70C22⋊#170—24no—
71#4004—22no—
72C4⋊#170—22no—
73#1798—51noSylow
74C23×C3×C5—21no—
75C23×C3×C5—21no—
76C23×C3×C5—22no—
77C23×C3×C5—22no—
78C23×C3×C5C4⋊C412yes—
79C23×C3×C5C22×C411yescharacteristic
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C22⋊C412yes—
84C2×C3×Dic5—21no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—22no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5C22⋊C412yes—
94C2×C3×Dic5C4⋊C412yes—
95C2×C3×Dic5C2×D411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C2×C3×Dic5C2×Q811yescharacteristic
99C2×C3×Dic5#4111yescharacteristic
100C2×C3×Dic5#4111yescharacteristic
101C3×#170—42no—
102C3×#170—42no—
103C23×C3×C4—51no—
104C22×C3×C8—52no—
105C22×C3×C8—52no—
106C3×#117—102no—
107C3×#117—102no—
108C2×C3×C4⋊C4—51no—
109C2×C3×C4⋊C4—51no—
110C2×C3×C22⋊C4—51no—
111C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
112C2×C3×C42—51no—
113C2×C3×C42—51no—
114C3×C4⋊C8—102no—
115C3×C4⋊C8—102no—
116C3×C22⋊C8—104no—
117C24×C5C2×C3×C411yescharacteristic
118C22×C4×C5C2×C3×C411yescharacteristic
119C22×C4×C5C2×C3×C411yescharacteristic
120C22×Dic5—21no—
121C22×Dic5—21no—
122C22×Dic5—21no—
123C22×Dic5—21no—
124C22×Dic5C2×C3×C411yescharacteristic
125C22×Dic5C2×C3×C411yescharacteristic
126C22×Dic5C2×C3×C411yescharacteristic
127C22×Dic5C3×D412yes—
128C22×Dic5C3×Q812yes—
129C22×Dic5C23×C311yescharacteristic
130C2×#170—22no—
131C2×#170—22no—
132C2×#170—22no—
133C2×#170—22no—
134C2×#170—22no—
135C2×#170—22no—
136C5×C22⋊C4—22no—
137C22⋊Dic5—22no—
138#683—22no—
139#683—22no—
140C4×Dic5—21no—
141C4×Dic5—21no—
142C4×Dic5C3×D412yes—
143C4×Dic5C3×D412yes—
144C2×#117—51no—
145C2×C4⋊C8—51no—
146C2×C4⋊C8—51no—
147C2×C22⋊C8—52no—
148#336—52no—
149C22×C3×C5—22no—
150C22×C3×C5—24no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—42no—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C22×C3×C5C2×C4⋊C411yescharacteristic
156C22×C3×C5#11711yescharacteristic
157C22×C3×C5#13112yes—
158C22×C3×C5#13112yes—
159C3×C4×C5—22no—
160C3×C4×C5—41no—
161C3×Dic5—22no—
162C3×Dic5—22no—
163C3×Dic5—41no—
164C3×Dic5#12111yescharacteristic
165C3×Dic5#12111yescharacteristic
166C3×Dic5C22⋊Q811yescharacteristic
167C3×Dic5C22⋊Q811yescharacteristic
168C24×C3C2×AGL(1,𝔽5)11yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—52no—
171C22×C3×C4—52no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4—101no—
176C22×C3×C4—101no—
177C22×C3×C4—101no—
178C22×C3×C4—101no—
179C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
180C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
181C2×C3×C8—102no—
182C2×C3×C8—102no—
183C2×C3×C8—102no—
184C2×C3×C8—102no—
185C2×C3×C8—102no—
186C2×C3×C8—102no—
187C3×C4⋊C4—102no—
188C3×C4⋊C4—102no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—102no—
191C3×C42—52no—
192C3×C42—52no—
193C3×C42—101no—
194C3×C42—101no—
195C23×C5—21no—
196C23×C5—21no—
197C23×C5—22no—
198C23×C5—22no—
199C23×C5C3×C4⋊C412yes—
200C23×C5C22×C3×C411yescharacteristic
201C2×C4×C5—22no—
202C2×C4×C5—21no—
203C2×C4×C5—22no—
204C2×C4×C5C3×C22⋊C412yes—
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—22no—
208C2×Dic5—22no—
209C2×Dic5—22no—
210C2×Dic5—22no—
211C2×Dic5—22no—
212C2×Dic5—21no—
213C2×Dic5—22no—
214C2×Dic5C3×C22⋊C412yes—
215C2×Dic5C3×C4⋊C412yes—
216C2×Dic5C2×C3×D411yescharacteristic
217C2×Dic5C2×C3×D411yescharacteristic
218C2×Dic5C2×C3×D411yescharacteristic
219C2×Dic5C2×C3×Q811yescharacteristic
220C2×Dic5C3×#4111yescharacteristic
221C2×Dic5C3×#4111yescharacteristic
222#170—42no—
223#170—42no—
224C23×C4—51no—
225C22×C8—52no—
226C22×C8—52no—
227#117—102no—
228#117—102no—
229C2×C4⋊C4—51no—
230C2×C4⋊C4—51no—
231C2×C22⋊C4—51no—
232C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic
233C2×C42—51no—
234C2×C42—51no—
235C4⋊C8—102no—
236C4⋊C8—102no—
237C22⋊C8—104no—
238C2×C3×C5—42no—
239C2×C3×C5#38011yescharacteristic
240C2×C3×C5#40811yescharacteristic
241C2×C3×C5#40811yescharacteristic
242C2×C3×C5#42412yes—
243C2×C3×C5#43312yes—
244C23×C3—21no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—21no—
248C23×C3C4⋊AGL(1,𝔽5)12yes—
249C23×C3C22×AGL(1,𝔽5)11yescharacteristic
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—52no—
260C2×C3×C4—52no—
261C2×C3×C4—102no—
262C2×C3×C4—102no—
263C2×C3×C4—102no—
264C2×C3×C4—102no—
265C2×C3×C4—101no—
266C2×C3×C4—102no—
267C2×C3×C4—101no—
268C2×C3×C4—102no—
269C2×C3×C4—101no—
270C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
271C3×C8—202no—
272C3×C8—202no—
273C22×C5—22no—
274C22×C5—24no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5—42no—
278C22×C5C2×C3×C22⋊C411yescharacteristic
279C22×C5C2×C3×C4⋊C411yescharacteristic
280C22×C5C3×#11711yescharacteristic
281C22×C5C3×#13112yes—
282C22×C5C3×#13112yes—
283C4×C5—22no—
284C4×C5—41no—
285Dic5—22no—
286Dic5—22no—
287Dic5—41no—
288Dic5C3×#12111yescharacteristic
289Dic5C3×#12111yescharacteristic
290Dic5C3×C22⋊Q811yescharacteristic
291Dic5C3×C22⋊Q811yescharacteristic
292C24C2×C3×AGL(1,𝔽5)11yescharacteristic
293C22×C4—51no—
294C22×C4—52no—
295C22×C4—52no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—101no—
300C22×C4—101no—
301C22×C4—101no—
302C22×C4—101no—
303C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
304C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
305C2×C8—102no—
306C2×C8—102no—
307C2×C8—102no—
308C2×C8—102no—
309C2×C8—102no—
310C2×C8—102no—
311C4⋊C4—102no—
312C4⋊C4—102no—
313C22⋊C4—22no—
314C22⋊C4—102no—
315C42—52no—
316C42—52no—
317C42—101no—
318C42—101no—
319C3×C5#179811yescharacteristic, complemented, Hall
320C22×C3—24no—
321C22×C3—22no—
322C22×C3—42no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
326C22×C3#413011yescharacteristic
327C22×C3#413112yes—
328C22×C3#413112yes—
329C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
330C3×C4—22no—
331C3×C4—41no—
332C3×C4—51no—
333C3×C4—51no—
334C3×C4—51no—
335C3×C4—51no—
336C3×C4—102no—
337C3×C4—102no—
338C3×C4—201no—
339C2×C5—42no—
340C2×C5C3×#38011yescharacteristic
341C2×C5C3×#40811yescharacteristic
342C2×C5C3×#40811yescharacteristic
343C2×C5C3×#42412yes—
344C2×C5C3×#43312yes—
345C23—21no—
346C23—22no—
347C23—22no—
348C23—21no—
349C23C3×C4⋊AGL(1,𝔽5)12yes—
350C23C22×C3×AGL(1,𝔽5)11yescharacteristic
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—51no—
360C2×C4—52no—
361C2×C4—52no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4—102no—
365C2×C4—102no—
366C2×C4—101no—
367C2×C4—102no—
368C2×C4—101no—
369C2×C4—102no—
370C2×C4—101no—
371C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
372C8—202no—
373C8—202no—
374C2×C3—42no—
375C2×C3#6569612yes—
376C2×C3#6569712yes—
377C2×C3#6576511yescharacteristic
378C2×C3#6577511yescharacteristic
379C2×C3#6577611yescharacteristic
380C5C3×#179811yescharacteristic, complemented, Sylow
381C22—24no—
382C22—22no—
383C22—42no—
384C22—41no—
385C22—41no—
386C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
387C22C3×#413011yescharacteristic
388C22C3×#413112yes—
389C22C3×#413112yes—
390C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
391C4—22no—
392C4—41no—
393C4—51no—
394C4—51no—
395C4—51no—
396C4—51no—
397C4—102no—
398C4—102no—
399C4—201no—
400C3#1060422811yescharacteristic, direct product factor, Sylow
401C2—42no—
402C2C3×#6569612yes—
403C2C3×#6569712yes—
404C2C3×#6576511yescharacteristic
405C2C3×#6577511yescharacteristic
406C2C3×#6577611yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1798
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#4004C2semidirect
4. C2×C3×C4⋊#170C2semidirect
5. C3×#64918C2semidirect
6. #10604228C3direct (N × H)
24. C2×#4004C2×C3semidirect
25. C2×C4⋊#170C2×C3semidirect
26. #64918C2×C3semidirect
319. C3×C5#1798semidirect
380. C5C3×#1798semidirect
400. C3#10604228direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40232
C2×C3×C22⋊#1702
C2×C3×#40042
C2×C3×C4⋊#1702
C3×#649182
#106042283
C3×#17985