Finite Group Databasebeta

← C3×#10604282 #14298435

Subgroups — C3×#10604282 #14298435

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C3×#65765C211yesmaximal, characteristic
3C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic
4C3×#64874C214yesmaximal, complemented
5#10604282C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C4×D5—21no—
7C22×C3×C4×D5C2211yescharacteristic
8C2×C3×C22⋊AGL(1,𝔽5)—21no—
9C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
10C2×C3×D5⋊C8C2212yes—
11C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
12C2×C3×C4⋊Dic5C411yescharacteristic, complemented
13C2×C3×#683—21no—
14C3×D5×C4⋊C4—21no—
15C3×D5×C4⋊C4—21no—
16C3×D5×C4⋊C4C412yescomplemented
17C3×D5×C4⋊C4C2212yes—
18C3×C22⋊#170—21no—
19C3×(C2×AGL(1,𝔽5))⋊C4—21no—
20C3×#4003—21no—
21C3×#1823—51nomaximal, Hall
22C2×D5×C4⋊C4C2×C311yescharacteristic
23#65765C2×C311yescharacteristic
24D5⋊(C22⋊C8)C2×C311yescharacteristic
25#64874C2×C314yescomplemented
26C23×C3×D5D411yescharacteristic
27C22×C3×AGL(1,𝔽5)—22no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×Dic5—21no—
31C22×C3×Dic5D411yescharacteristic
32C2×C3×C4×D5—24no—
33C2×C3×C4×D5—22no—
34C2×C3×C4×D5—22no—
35C2×C3×C4×D5—42no—
36C2×C3×C4×D5—42no—
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5C2311yescharacteristic
41C3×C22⋊AGL(1,𝔽5)—42no—
42C2×C3×#170—22no—
43C3×C4⋊AGL(1,𝔽5)—24no—
44C3×D5⋊C8—24no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C412yes—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5C2×C412yes—
49C3×#683—22no—
50C3×#683—22no—
51C22×C3×C4⋊C4—51no—
52C2×C3×C22⋊C8—51no—
53C3×#380—51no—
54C3×#340—54no—
55C22×C4×D5—21no—
56C22×C4×D5C22×C311yescharacteristic
57C2×C22⋊AGL(1,𝔽5)—21no—
58C2×C4⋊AGL(1,𝔽5)C22×C312yes—
59C2×D5⋊C8C22×C312yes—
60C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
61C2×C4⋊Dic5C3×C411yescharacteristic, complemented
62C2×#683—21no—
63D5×C4⋊C4—21no—
64D5×C4⋊C4—21no—
65D5×C4⋊C4C3×C412yescomplemented
66D5×C4⋊C4C22×C312yes—
67C22⋊#170—21no—
68(C2×AGL(1,𝔽5))⋊C4—21no—
69#4003—21no—
70#1823—51noSylow
71C23×C3×C5C22⋊C411yescharacteristic
72C22×C3×D5—22no—
73C22×C3×D5—22no—
74C22×C3×D5C22⋊C411yescharacteristic
75C22×C3×D5D812yes—
76C22×C3×D5SD1612yes—
77C22×C3×D5C2×D411yescharacteristic
78C2×C3×AGL(1,𝔽5)—42no—
79C2×C3×AGL(1,𝔽5)—42no—
80C2×C3×AGL(1,𝔽5)—42no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—42no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×Dic5—22no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—42no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5—22no—
94C3×C4×D5—44no—
95C3×C4×D5—42no—
96C3×C4×D5—42no—
97C3×C4×D5#4114yes—
98C3×#170—42no—
99C23×C3×C4—51no—
100C23×C3×C4—101no—
101C22×C3×C8—52no—
102C2×C3×C4⋊C4—51no—
103C2×C3×C4⋊C4—52no—
104C2×C3×C4⋊C4—52no—
105C2×C3×C4⋊C4—52no—
106C2×C3×C4⋊C4—101no—
107C2×C3×C4⋊C4—101no—
108C2×C3×C4⋊C4—101no—
109C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
110C2×C3×C22⋊C4—101no—
111C3×C22⋊C8—101no—
112C3×C22⋊C8—101no—
113C3×#95—101no—
114C23×D5C3×D411yescharacteristic
115C22×AGL(1,𝔽5)—22no—
116C22×C4×C5—21no—
117C22×C4×C5C2×C3×C411yescharacteristic
118C22×Dic5—21no—
119C22×Dic5C3×D411yescharacteristic
120C2×C4×D5—24no—
121C2×C4×D5—22no—
122C2×C4×D5—22no—
123C2×C4×D5—42no—
124C2×C4×D5—42no—
125C2×C4×D5C2×C3×C411yescharacteristic
126C2×C4×D5C3×D411yescharacteristic
127C2×C4×D5C3×D411yescharacteristic
128C2×C4×D5C23×C311yescharacteristic
129C22⋊AGL(1,𝔽5)—42no—
130C2×#170—22no—
131C4⋊AGL(1,𝔽5)—24no—
132D5⋊C8—24no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4C2×C3×C412yes—
135C4⋊Dic5—21no—
136C4⋊Dic5C2×C3×C412yes—
137#683—22no—
138#683—22no—
139C22×C4⋊C4—51no—
140C2×C22⋊C8—51no—
141#380—51no—
142#340—54no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5#10212yes—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C2×C3×D5—21no—
148C2×C3×D5—21no—
149C2×C3×D5—24no—
150C2×C3×D5—24no—
151C2×C3×D5#10212yes—
152C2×C3×D5#12312yes—
153C2×C3×D5C2×D811yescharacteristic
154C2×C3×D5C2×SD1611yescharacteristic
155C2×C3×D5#13712yes—
156C3×AGL(1,𝔽5)—82no—
157C3×C4×C5—21no—
158C3×C4×C5—42no—
159C3×C4×C5#11712yes—
160C3×Dic5—21no—
161C3×Dic5—42no—
162C3×Dic5#12312yes—
163C24×C3—51no—
164C22×C3×C4—21no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4—104no—
171C22×C3×C4—102no—
172C22×C3×C4—102no—
173C22×C3×C4—101no—
174C22×C3×C4—102no—
175C22×C3×C4—202no—
176C22×C3×C4—202no—
177C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
178C2×C3×C8—102no—
179C2×C3×C8—104no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—52no—
182C3×C4⋊C4—102no—
183C3×C4⋊C4—102no—
184C3×C4⋊C4—104no—
185C3×C4⋊C4—101no—
186C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
187C3×C22⋊C4—202no—
188C23×C5C3×C22⋊C411yescharacteristic
189C22×D5—22no—
190C22×D5—22no—
191C22×D5C3×C22⋊C411yescharacteristic
192C22×D5C3×D812yes—
193C22×D5C3×SD1612yes—
194C22×D5C2×C3×D411yescharacteristic
195C2×AGL(1,𝔽5)—42no—
196C2×AGL(1,𝔽5)—42no—
197C2×AGL(1,𝔽5)—42no—
198C2×C4×C5—22no—
199C2×C4×C5—22no—
200C2×C4×C5—42no—
201C2×C4×C5C3×C22⋊C411yescharacteristic
202C2×C4×C5C22×C3×C411yescharacteristic
203C2×Dic5—22no—
204C2×Dic5—22no—
205C2×Dic5—42no—
206C2×Dic5C3×C22⋊C411yescharacteristic
207C2×Dic5C2×C3×D411yescharacteristic
208C4×D5—22no—
209C4×D5—22no—
210C4×D5—22no—
211C4×D5—44no—
212C4×D5—42no—
213C4×D5—42no—
214C4×D5C3×#4114yes—
215#170—42no—
216C23×C4—51no—
217C23×C4—101no—
218C22×C8—52no—
219C2×C4⋊C4—51no—
220C2×C4⋊C4—52no—
221C2×C4⋊C4—52no—
222C2×C4⋊C4—52no—
223C2×C4⋊C4—101no—
224C2×C4⋊C4—101no—
225C2×C4⋊C4—101no—
226C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
227C2×C22⋊C4—101no—
228C22⋊C8—101no—
229C22⋊C8—101no—
230#95—101no—
231C2×C3×C5—22no—
232C2×C3×C5#38111yescharacteristic
233C2×C3×C5C2×#10211yescharacteristic
234C2×C3×C5#41911yescharacteristic
235C3×D5—22no—
236C3×D5#48012yes—
237C3×D5#48312yes—
238C23×C3—51no—
239C23×C3—51no—
240C23×C3—52no—
241C23×C3—52no—
242C23×C3—102no—
243C23×C3—102no—
244C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—42no—
248C2×C3×C4—51no—
249C2×C3×C4—54no—
250C2×C3×C4—51no—
251C2×C3×C4—102no—
252C2×C3×C4—102no—
253C2×C3×C4—102no—
254C2×C3×C4—102no—
255C2×C3×C4—102no—
256C2×C3×C4—202no—
257C2×C3×C4—202no—
258C2×C3×C4—204no—
259C2×C3×C4—202no—
260C2×C3×C4—202no—
261C2×C3×C4—202no—
262C2×C3×C4—202no—
263C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
264C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
265C3×C8—202no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5C3×#10212yes—
269C22×C5C2×C3×C22⋊C411yescharacteristic
270C2×D5—21no—
271C2×D5—21no—
272C2×D5—24no—
273C2×D5—24no—
274C2×D5C3×#10212yes—
275C2×D5C3×#12312yes—
276C2×D5C2×C3×D811yescharacteristic
277C2×D5C2×C3×SD1611yescharacteristic
278C2×D5C3×#13712yes—
279AGL(1,𝔽5)—82no—
280C4×C5—21no—
281C4×C5—42no—
282C4×C5C3×#11712yes—
283Dic5—21no—
284Dic5—42no—
285Dic5C3×#12312yes—
286C24—51no—
287C22×C4—21no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—104no—
294C22×C4—102no—
295C22×C4—102no—
296C22×C4—101no—
297C22×C4—102no—
298C22×C4—202no—
299C22×C4—202no—
300C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
301C2×C8—102no—
302C2×C8—104no—
303C4⋊C4—21no—
304C4⋊C4—52no—
305C4⋊C4—102no—
306C4⋊C4—102no—
307C4⋊C4—104no—
308C4⋊C4—101no—
309C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
310C22⋊C4—202no—
311C3×C5#182311yescharacteristic, complemented, Hall
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—52no—
315C22×C3—51no—
316C22×C3—51no—
317C22×C3—52no—
318C22×C3—52no—
319C22×C3—104no—
320C22×C3—104no—
321C22×C3—101no—
322C22×C3—101no—
323C22×C3#400712yes—
324C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
325C3×C4—21no—
326C3×C4—42no—
327C3×C4—52no—
328C3×C4—101no—
329C3×C4—202no—
330C3×C4—402no—
331C3×C4#413012yes—
332C2×C5—22no—
333C2×C5C3×#38111yescharacteristic
334C2×C5C2×C3×#10211yescharacteristic
335C2×C5C3×#41911yescharacteristic
336D5—22no—
337D5C3×#48012yes—
338D5C3×#48312yes—
339C23—51no—
340C23—52no—
341C23—52no—
342C23—51no—
343C23—102no—
344C23—102no—
345C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—51no—
350C2×C4—54no—
351C2×C4—51no—
352C2×C4—102no—
353C2×C4—102no—
354C2×C4—102no—
355C2×C4—102no—
356C2×C4—102no—
357C2×C4—202no—
358C2×C4—202no—
359C2×C4—204no—
360C2×C4—202no—
361C2×C4—202no—
362C2×C4—202no—
363C2×C4—202no—
364C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
365C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
366C8—202no—
367C2×C3—22no—
368C2×C3—52no—
369C2×C3—52no—
370C2×C3—102no—
371C2×C3#6576411yescharacteristic
372C2×C3C2×#400711yescharacteristic
373C2×C3#6578211yescharacteristic
374C5C3×#182311yescharacteristic, complemented, Sylow
375C22—21no—
376C22—21no—
377C22—52no—
378C22—51no—
379C22—51no—
380C22—52no—
381C22—52no—
382C22—104no—
383C22—104no—
384C22—101no—
385C22—101no—
386C22C3×#400712yes—
387C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
388C4—21no—
389C4—42no—
390C4—52no—
391C4—101no—
392C4—202no—
393C4—402no—
394C4C3×#413012yes—
395C3#1060428211yescharacteristic, direct product factor, Sylow
396C2—22no—
397C2—52no—
398C2—52no—
399C2—102no—
400C2C3×#6576411yescharacteristic
401C2C2×C3×#400711yescharacteristic
402C2C3×#6578211yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C4×D5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1823
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#64874C2semidirect
5. #10604282C3direct (N × H)
11. C2×C3×C5×C4⋊C4C4semidirect
12. C2×C3×C4⋊Dic5C4semidirect
16. C3×D5×C4⋊C4C4semidirect
25. #64874C2×C3semidirect
60. C2×C5×C4⋊C4C3×C4semidirect
61. C2×C4⋊Dic5C3×C4semidirect
65. D5×C4⋊C4C3×C4semidirect
109. C2×C3×C4⋊C4AGL(1,𝔽5)semidirect
226. C2×C4⋊C4C3×AGL(1,𝔽5)semidirect
311. C3×C5#1823semidirect
374. C5C3×#1823semidirect
395. C3#10604282direct (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×C4⋊C42
C3×#657652
C3×D5⋊(C22⋊C8)2
C3×#648742
#106042823
C3×#18235