Finite Group Databasebeta

← C3×#10598503 #14276909

Subgroups — C3×#10598503 #14276909

Order 1920.

452 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C3×#65756C211yesmaximal, characteristic
3C3×#64953C211yesmaximal, characteristic
4#10598503C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×C3×C22⋊AGL(1,𝔽5)—21no—
7C2×C3×C4×AGL(1,𝔽5)C412yescomplemented
8C2×C3×#700—21no—
9C2×C3×#685—21no—
10C3×C22⋊#170—21no—
11C3×(C2×AGL(1,𝔽5))⋊C4—21no—
12C3×#4003C412yescomplemented
13C3×C5×#95C411yescharacteristic, complemented
14C3×#3963—21no—
15C3×#3963C411yescharacteristic, complemented
16C3×#1284—51nomaximal, Hall
17C4×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic
18#65756C2×C311yescharacteristic
19#64953C2×C311yescharacteristic
20C23×C3×D5D411yescharacteristic
21C22×C3×AGL(1,𝔽5)—22no—
22C22×C3×C4×C5—21no—
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×C3×Dic5—21no—
25C22×C3×Dic5D411yescharacteristic
26C2×C3×C4×D5—42no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5Q811yescharacteristic
31C3×C22⋊AGL(1,𝔽5)—22no—
32C3×C22⋊AGL(1,𝔽5)—22no—
33C2×C3×#170—22no—
34C3×C4×AGL(1,𝔽5)—42no—
35C3×#700—42no—
36C3×#685—42no—
37C3×#407—51no—
38C3×#381—51no—
39C3×C4×C22⋊C4—51no—
40C22×C4×D5C22×C311yescharacteristic
41C2×C22⋊AGL(1,𝔽5)—21no—
42C2×C4×AGL(1,𝔽5)C3×C412yescomplemented
43C2×#700—21no—
44C2×#685—21no—
45C22⋊#170—21no—
46(C2×AGL(1,𝔽5))⋊C4—21no—
47#4003C3×C412yescomplemented
48C5×#95C3×C411yescharacteristic, complemented
49#3963—21no—
50#3963C3×C411yescharacteristic, complemented
51#1284—51noSylow
52C23×C3×C5C22⋊C411yescharacteristic
53C22×C3×D5—21no—
54C22×C3×D5—21no—
55C22×C3×D5—22no—
56C22×C3×D5—41no—
57C22×C3×D5C22⋊C411yescharacteristic
58C22×C3×D5C4⋊C411yescharacteristic
59C2×C3×AGL(1,𝔽5)—24no—
60C2×C3×AGL(1,𝔽5)—42no—
61C2×C3×AGL(1,𝔽5)—42no—
62C2×C3×C4×C5—41no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5—41no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5C4211yescharacteristic
67C2×C3×C4×C5C4⋊C411yescharacteristic
68C2×C3×Dic5—41no—
69C2×C3×Dic5—41no—
70C2×C3×Dic5—41no—
71C2×C3×Dic5—41no—
72C2×C3×Dic5C22⋊C411yescharacteristic
73C2×C3×Dic5C4⋊C411yescharacteristic
74C3×C4×D5—22no—
75C3×C4×D5—22no—
76C3×C4×D5—41no—
77C3×C4×D5—41no—
78C3×#170—42no—
79C23×C3×C4—51no—
80C2×C3×M16—101no—
81C2×C3×C22⋊C4—101no—
82C2×C3×C22⋊C4—101no—
83C2×C3×C42—52no—
84C3×C22⋊C8—52no—
85C3×C22⋊C8—101no—
86C3×#95—51no—
87C3×#95—101no—
88C3×#95—101no—
89C3×#95AGL(1,𝔽5)11yescharacteristic, complemented
90C23×D5C3×D411yescharacteristic
91C22×AGL(1,𝔽5)—22no—
92C22×C4×C5—21no—
93C22×C4×C5C2×C3×C411yescharacteristic
94C22×Dic5—21no—
95C22×Dic5C3×D411yescharacteristic
96C2×C4×D5—42no—
97C2×C4×D5C2×C3×C411yescharacteristic
98C2×C4×D5C2×C3×C411yescharacteristic
99C2×C4×D5C3×D411yescharacteristic
100C2×C4×D5C3×Q811yescharacteristic
101C22⋊AGL(1,𝔽5)—22no—
102C22⋊AGL(1,𝔽5)—22no—
103C2×#170—22no—
104C4×AGL(1,𝔽5)—42no—
105#700—42no—
106#685—42no—
107#407—51no—
108#381—51no—
109C4×C22⋊C4—51no—
110C22×C3×C5—21no—
111C22×C3×C5—21no—
112C22×C3×C5#9511yescharacteristic
113C22×C3×C5#10411yescharacteristic
114C22×C3×C5#10411yescharacteristic
115C2×C3×D5—21no—
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5—21no—
119C2×C3×D5—21no—
120C2×C3×D5—42no—
121C2×C3×D5—42no—
122C2×C3×D5#9912yes—
123C3×AGL(1,𝔽5)—44no—
124C3×C4×C5—21no—
125C3×C4×C5—21no—
126C3×C4×C5—81no—
127C3×Dic5—21no—
128C3×Dic5—21no—
129C3×Dic5—81no—
130C24×C3—51no—
131C22×C3×C4—21no—
132C22×C3×C4—51no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—102no—
138C22×C3×C4—101no—
139C22×C3×C4—202no—
140C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
141C3×M16—202no—
142C2×C3×C8—102no—
143C3×C22⋊C4—102no—
144C3×C22⋊C4—102no—
145C3×C22⋊C4—202no—
146C3×C42—202no—
147C23×C5C3×C22⋊C411yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—22no—
151C22×D5—41no—
152C22×D5C3×C22⋊C411yescharacteristic
153C22×D5C3×C4⋊C411yescharacteristic
154C2×AGL(1,𝔽5)—24no—
155C2×AGL(1,𝔽5)—42no—
156C2×AGL(1,𝔽5)—42no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5C3×C4211yescharacteristic
162C2×C4×C5C3×C4⋊C411yescharacteristic
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5C3×C22⋊C411yescharacteristic
168C2×Dic5C3×C4⋊C411yescharacteristic
169C4×D5—22no—
170C4×D5—22no—
171C4×D5—41no—
172C4×D5—41no—
173#170—42no—
174C23×C4—51no—
175C2×M16—101no—
176C2×C22⋊C4—101no—
177C2×C22⋊C4—101no—
178C2×C42—52no—
179C22⋊C8—52no—
180C22⋊C8—101no—
181#95—51no—
182#95—101no—
183#95—101no—
184#95C3×AGL(1,𝔽5)11yescharacteristic, complemented
185C2×C3×C5—21no—
186C2×C3×C5—21no—
187C2×C3×C5H(3,ℤ/4)11yescharacteristic
188C2×C3×C5#33911yescharacteristic
189C2×C3×C5#34211yescharacteristic
190C3×D5—22no—
191C3×D5—41no—
192C23×C3—51no—
193C23×C3—51no—
194C23×C3—102no—
195C23×C3—101no—
196C23×C3—101no—
197C23×C3—201no—
198C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—51no—
204C2×C3×C4—51no—
205C2×C3×C4—102no—
206C2×C3×C4—102no—
207C2×C3×C4—104no—
208C2×C3×C4—201no—
209C2×C3×C4—201no—
210C2×C3×C4—201no—
211C2×C3×C4—202no—
212C2×C3×C4—202no—
213C2×C3×C4—201no—
214C2×C3×C4—201no—
215C2×C3×C4—201no—
216C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
217C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
218C3×C8—202no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5C3×#9511yescharacteristic
222C22×C5C3×#10411yescharacteristic
223C22×C5C3×#10411yescharacteristic
224C2×D5—21no—
225C2×D5—21no—
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—21no—
229C2×D5—42no—
230C2×D5—42no—
231C2×D5C3×#9912yes—
232AGL(1,𝔽5)—44no—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—81no—
236Dic5—21no—
237Dic5—21no—
238Dic5—81no—
239C24—51no—
240C22×C4—21no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—51no—
246C22×C4—102no—
247C22×C4—101no—
248C22×C4—202no—
249C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
250M16—202no—
251C2×C8—102no—
252C22⋊C4—102no—
253C22⋊C4—102no—
254C22⋊C4—202no—
255C42—202no—
256C3×C5#128411yescharacteristic, complemented, Hall
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—52no—
260C22×C3—101no—
261C22×C3—101no—
262C22×C3—101no—
263C22×C3—101no—
264C22×C3—101no—
265C22×C3—202no—
266C22×C3—202no—
267C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
268C22×C3#400811yescharacteristic
269C22×C3#401011yescharacteristic
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—81no—
273C3×C4—101no—
274C3×C4—101no—
275C3×C4—204no—
276C3×C4—401no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5C3×H(3,ℤ/4)11yescharacteristic
280C2×C5C3×#33911yescharacteristic
281C2×C5C3×#34211yescharacteristic
282D5—22no—
283D5—41no—
284C23—51no—
285C23—51no—
286C23—102no—
287C23—101no—
288C23—101no—
289C23—201no—
290C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—102no—
298C2×C4—102no—
299C2×C4—104no—
300C2×C4—201no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4—202no—
304C2×C4—202no—
305C2×C4—201no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
309C2×C4C3×C4⋊AGL(1,𝔽5)11yescharacteristic
310C8—202no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—102no—
314C2×C3—201no—
315C2×C3#6486311yescharacteristic
316C2×C3#6486611yescharacteristic
317C2×C3#6487511yescharacteristic
318C5C3×#128411yescharacteristic, complemented, Sylow
319C22—21no—
320C22—21no—
321C22—52no—
322C22—101no—
323C22—101no—
324C22—101no—
325C22—101no—
326C22—101no—
327C22—202no—
328C22—202no—
329C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
330C22C3×#400811yescharacteristic
331C22C3×#401011yescharacteristic
332C4—21no—
333C4—21no—
334C4—81no—
335C4—101no—
336C4—101no—
337C4—204no—
338C4—401no—
339C3#1059850311yescharacteristic, direct product factor, Sylow
340C2—21no—
341C2—21no—
342C2—102no—
343C2—201no—
344C2C3×#6486311yescharacteristic
345C2C3×#6486611yescharacteristic
346C2C3×#6487511yescharacteristic
subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC3×C5×#95C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC22×C4×D5C22×C3
hypercenterC3×#95AGL(1,𝔽5)
hypocenterC5C3×#1284
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
4. #10598503C3direct (N × H)
7. C2×C3×C4×AGL(1,𝔽5)C4semidirect
12. C3×#4003C4semidirect
13. C3×C5×#95C4semidirect
15. C3×#3963C4semidirect
42. C2×C4×AGL(1,𝔽5)C3×C4semidirect
47. #4003C3×C4semidirect
48. C5×#95C3×C4semidirect
50. #3963C3×C4semidirect
89. C3×#95AGL(1,𝔽5)semidirect
184. #95C3×AGL(1,𝔽5)semidirect
256. C3×C5#1284semidirect
318. C5C3×#1284semidirect
339. C3#10598503direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C22⋊AGL(1,𝔽5)2
C3×#657562
C3×#649532
#105985033
C3×#12845