Finite Group Databasebeta

← C3×#10598825 #14278080

Subgroups — C3×#10598825 #14278080

Order 1920.

444 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 60 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×#65512C211yesmaximal, characteristic
2C3×#64917C211yesmaximal, characteristic, complemented
3C3×#64915C211yesmaximal, characteristic, complemented
4#10598825C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×D4C411yescharacteristic, complemented
6C22×C3×C22⋊D5—21no—
7C2×C3×C22⋊AGL(1,𝔽5)—21no—
8C2×C3×C22⋊Dic5—21no—
9C2×C3×#685C2211yescharacteristic
10C3×C22⋊#170—21no—
11C3×#3963C411yescharacteristic, complemented
12C3×#1343—51nomaximal, Hall
13#65512C2×C311yescharacteristic
14#64917C2×C311yescharacteristic, complemented
15#64915C2×C311yescharacteristic, complemented
16C24×C3×C5—21no—
17C23×C3×D5D411yescharacteristic
18C22×C3×AGL(1,𝔽5)—41no—
19C2×C3×C5×D4—41no—
20C2×C3×C5×D4—42no—
21C22×C3×C4×C5C2×C411yescharacteristic
22C2×C3×C22⋊D5—42no—
23C2×C3×C22⋊D5—42no—
24C2×C3×C22⋊D5—41no—
25C2×C3×C22⋊D5—41no—
26C22×C3×Dic5—21no—
27C22×C3×Dic5D411yescharacteristic
28C3×C22⋊AGL(1,𝔽5)—22no—
29C3×C22⋊AGL(1,𝔽5)—41no—
30C2×C3×#170—41no—
31C3×C22⋊Dic5—42no—
32C3×#685—41no—
33C3×#392—51no—
34C3×#342—51no—
35C3×#323—51no—
36C22×C5×D4C3×C411yescharacteristic, complemented
37C22×C22⋊D5—21no—
38C2×C22⋊AGL(1,𝔽5)—21no—
39C2×C22⋊Dic5—21no—
40C2×#685C22×C311yescharacteristic
41C22⋊#170—21no—
42#3963C3×C411yescharacteristic, complemented
43#1343—51noSylow
44C23×C3×C5—22no—
45C23×C3×C5—41no—
46C23×C3×C5—41no—
47C23×C3×C5—41no—
48C23×C3×C5—41no—
49C23×C3×C5—41no—
50C23×C3×C5—41no—
51C23×C3×C5C22⋊C411yescharacteristic
52C22×C3×D5—21no—
53C22×C3×D5—21no—
54C22×C3×D5—41no—
55C22×C3×D5—41no—
56C22×C3×D5D811yescharacteristic
57C22×C3×D5SD1611yescharacteristic
58C2×C3×AGL(1,𝔽5)—42no—
59C2×C3×AGL(1,𝔽5)—81no—
60C2×C3×AGL(1,𝔽5)—81no—
61C3×C5×D4—42no—
62C3×C5×D4—42no—
63C2×C3×C4×C5—21no—
64C2×C3×C4×C5—41no—
65C3×C22⋊D5—44no—
66C3×C22⋊D5—44no—
67C2×C3×Dic5—22no—
68C2×C3×Dic5—21no—
69C2×C3×Dic5—41no—
70C2×C3×Dic5—41no—
71C2×C3×Dic5—41no—
72C3×#170—81no—
73C22×C3×D4—101no—
74C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
75C2×C3×C22⋊C4—51no—
76C2×C3×C22⋊C4—101no—
77C2×C3×C22⋊C4—101no—
78C3×C22⋊C8—101no—
79C3×#95—51no—
80C24×C5—21no—
81C23×D5C3×D411yescharacteristic
82C22×AGL(1,𝔽5)—41no—
83C2×C5×D4—41no—
84C2×C5×D4—42no—
85C22×C4×C5C2×C3×C411yescharacteristic
86C2×C22⋊D5—42no—
87C2×C22⋊D5—42no—
88C2×C22⋊D5—41no—
89C2×C22⋊D5—41no—
90C22×Dic5—21no—
91C22×Dic5C3×D411yescharacteristic
92C22⋊AGL(1,𝔽5)—22no—
93C22⋊AGL(1,𝔽5)—41no—
94C2×#170—41no—
95C22⋊Dic5—42no—
96#685—41no—
97#392—51no—
98#342—51no—
99#323—51no—
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5—42no—
105C22×C3×C5—81no—
106C22×C3×C5—81no—
107C22×C3×C5—81no—
108C22×C3×C5—81no—
109C22×C3×C5#9911yescharacteristic
110C22×C3×C5#10211yescharacteristic
111C22×C3×C5#10411yescharacteristic
112C2×C3×D5—21no—
113C2×C3×D5—21no—
114C2×C3×D5—41no—
115C2×C3×D5—41no—
116C2×C3×D5—41no—
117C2×C3×D5—41no—
118C2×C3×D5—81no—
119C3×AGL(1,𝔽5)—82no—
120C3×C4×C5—41no—
121C3×Dic5—42no—
122C3×Dic5—41no—
123C24×C3—21no—
124C24×C3—51no—
125C2×C3×D4—41no—
126C2×C3×D4—42no—
127C2×C3×D4—202no—
128C2×C3×D4—202no—
129C2×C3×D4—201no—
130C2×C3×D4—201no—
131C22×C3×C4—51no—
132C22×C3×C4—101no—
133C22×C3×C4—201no—
134C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
135C2×C3×C8—201no—
136C3×C22⋊C4—102no—
137C3×C22⋊C4—201no—
138C3×C22⋊C4—202no—
139C3×C22⋊C4—201no—
140C23×C5—22no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5C3×C22⋊C411yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—41no—
151C22×D5—41no—
152C22×D5C3×D811yescharacteristic
153C22×D5C3×SD1611yescharacteristic
154C2×AGL(1,𝔽5)—42no—
155C2×AGL(1,𝔽5)—81no—
156C2×AGL(1,𝔽5)—81no—
157C5×D4—42no—
158C5×D4—42no—
159C2×C4×C5—21no—
160C2×C4×C5—41no—
161C22⋊D5—44no—
162C22⋊D5—44no—
163C2×Dic5—22no—
164C2×Dic5—21no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168#170—81no—
169C22×D4—101no—
170C22×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
171C2×C22⋊C4—51no—
172C2×C22⋊C4—101no—
173C2×C22⋊C4—101no—
174C22⋊C8—101no—
175#95—51no—
176C2×C3×C5—21no—
177C2×C3×C5—21no—
178C2×C3×C5—82no—
179C2×C3×C5#32711yescharacteristic
180C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
181C2×C3×C5#35311yescharacteristic
182C3×D5—41no—
183C3×D5—41no—
184C23×C3—22no—
185C23×C3—41no—
186C23×C3—41no—
187C23×C3—41no—
188C23×C3—41no—
189C23×C3—41no—
190C23×C3—41no—
191C23×C3—51no—
192C23×C3—51no—
193C23×C3—101no—
194C23×C3—101no—
195C23×C3—201no—
196C23×C3—201no—
197C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—204no—
201C3×D4—204no—
202C2×C3×C4—21no—
203C2×C3×C4—41no—
204C2×C3×C4—102no—
205C2×C3×C4—101no—
206C2×C3×C4—201no—
207C2×C3×C4—201no—
208C2×C3×C4—201no—
209C2×C3×C4—202no—
210C2×C3×C4—401no—
211C2×C3×C4—401no—
212C3×C8—401no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—42no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—81no—
219C22×C5—81no—
220C22×C5—81no—
221C22×C5—81no—
222C22×C5C3×#9911yescharacteristic
223C22×C5C3×#10211yescharacteristic
224C22×C5C3×#10411yescharacteristic
225C2×D5—21no—
226C2×D5—21no—
227C2×D5—41no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—81no—
232AGL(1,𝔽5)—82no—
233C4×C5—41no—
234Dic5—42no—
235Dic5—41no—
236C24—21no—
237C24—51no—
238C2×D4—41no—
239C2×D4—42no—
240C2×D4—202no—
241C2×D4—202no—
242C2×D4—201no—
243C2×D4—201no—
244C22×C4—51no—
245C22×C4—101no—
246C22×C4—201no—
247C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
248C2×C8—201no—
249C22⋊C4—102no—
250C22⋊C4—201no—
251C22⋊C4—202no—
252C22⋊C4—201no—
253C3×C5#134311yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—42no—
257C22×C3—42no—
258C22×C3—42no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—101no—
264C22×C3—101no—
265C22×C3—201no—
266C22×C3—201no—
267C22×C3—201no—
268C22×C3—201no—
269C22×C3—401no—
270C22×C3#400711yescharacteristic
271C22×C3#400811yescharacteristic
272C22×C3#401111yescharacteristic
273C3×C4—41no—
274C3×C4—202no—
275C3×C4—201no—
276C3×C4—402no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—82no—
280C2×C5C3×#32711yescharacteristic
281C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
282C2×C5C3×#35311yescharacteristic
283D5—41no—
284D5—41no—
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—51no—
293C23—51no—
294C23—101no—
295C23—101no—
296C23—201no—
297C23—201no—
298C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
299D4—42no—
300D4—42no—
301D4—204no—
302D4—204no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—102no—
306C2×C4—101no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—202no—
311C2×C4—401no—
312C2×C4—401no—
313C8—401no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—82no—
317C2×C3—201no—
318C2×C3—201no—
319C2×C3#6492011yescharacteristic
320C2×C3#6492211yescharacteristic
321C2×C3#6493411yescharacteristic
322C5C3×#134311yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—101no—
333C22—101no—
334C22—201no—
335C22—201no—
336C22—201no—
337C22—201no—
338C22—401no—
339C22C3×#400711yescharacteristic
340C22C3×#400811yescharacteristic
341C22C3×#401111yescharacteristic
342C4—41no—
343C4—202no—
344C4—201no—
345C4—402no—
346C3#1059882511yescharacteristic, direct product factor, Sylow
347C2—21no—
348C2—21no—
349C2—82no—
350C2—201no—
351C2—201no—
352C2C3×#6492011yescharacteristic
353C2C3×#6492211yescharacteristic
354C2C3×#6493411yescharacteristic
subgroupG/H
centerC22×C3#4011
commutatorC22×C4×C5C2×C3×C4
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5#99
prime radicalC3×#65512C2
cosocleC2×#685C22×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#1343
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64917C2semidirect
3. C3×#64915C2semidirect
4. #10598825C3direct (N × H)
5. C22×C3×C5×D4C4semidirect
11. C3×#3963C4semidirect
14. #64917C2×C3semidirect
15. #64915C2×C3semidirect
36. C22×C5×D4C3×C4semidirect
42. #3963C3×C4semidirect
74. C22×C3×D4AGL(1,𝔽5)semidirect
170. C22×D4C3×AGL(1,𝔽5)semidirect
253. C3×C5#1343semidirect
322. C5C3×#1343semidirect
346. C3#10598825direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#655122
C3×#649172
C3×#649152
#105988253
C3×#13435