Finite Group Databasebeta

← C3×#10601603 #14284400

Subgroups — C3×#10601603 #14284400

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2C3×C5×#432C211yesmaximal, characteristic, complemented
3C3×#65215C211yesmaximal, characteristic, complemented
4C3×#64685C212yesmaximal, complemented
5C3×#64684C212yesmaximal, complemented
6#10601603C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C3×#4076C411yescharacteristic
9C3×#4075—21no—
10C3×C4×C22⋊D5—21no—
11C3×#4070C411yescharacteristic
12C3×#4022—21no—
13C3×#4021C2211yescharacteristic
14C3×C4×D20C411yescharacteristic
15C3×#4018—21no—
16C3×#4016C2211yescharacteristic
17C3×C4×Dic10C411yescharacteristic
18C3×C5×C4⋊C8—21no—
19C3×C5×C22⋊C8—21no—
20C3×C5×#97C2212yes—
21C3×C22⋊#168—21no—
22C3×C4⋊#168—21no—
23C3×#3935C2212yes—
24C3×#1535—51nomaximal, Hall
25#65813C2×C311yescharacteristic
26C5×#432C2×C311yescharacteristic, complemented
27#65215C2×C311yescharacteristic, complemented
28#64685C2×C312yescomplemented
29#64684C2×C312yescomplemented
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×C3×C22⋊D5—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×Dic10C2×C411yescharacteristic
37C2×C3×C5×C8—22no—
38C3×C42×C5C2×C411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5C2311yescharacteristic
42C3×C22⋊Dic5—21no—
43C3×#685—21no—
44C3×#685—21no—
45C3×#685—21no—
46C3×#685—21no—
47C3×C4⋊Dic5C2×C411yescharacteristic
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×#683—21no—
50C3×#683—21no—
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5—21no—
54C2×C3×#168—22no—
55C3×#529—51no—
56C3×#432—51no—
57C3×#432D511yescharacteristic, complemented
58C3×#330—52no—
59C3×#329—52no—
60C2×C42×C5C22×C311yescharacteristic
61#4076C3×C411yescharacteristic
62#4075—21no—
63C4×C22⋊D5—21no—
64#4070C3×C411yescharacteristic
65#4022—21no—
66#4021C22×C311yescharacteristic
67C4×D20C3×C411yescharacteristic
68#4018—21no—
69#4016C22×C311yescharacteristic
70C4×Dic10C3×C411yescharacteristic
71C5×C4⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×#97C22×C312yes—
74C22⋊#168—21no—
75C4⋊#168—21no—
76#3935C22×C312yes—
77#1535—51noSylow
78C23×C3×C5C22⋊C411yescharacteristic
79C22×C3×D5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C3×C22⋊D5—42no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×D20—41no—
94C3×C4×D5—42no—
95C3×Dic10—41no—
96C3×C5×C8—42no—
97C3×#168—42no—
98C3×#126—101no—
99C3×#125—51no—
100C3×#124—51no—
101C3×#123—101no—
102C3×C22⋊Q8—51no—
103C3×#121—51no—
104C3×C4×Q8—51no—
105C3×C4×D4—51no—
106C3×C4×D4—101no—
107C3×#117—101no—
108C2×C3×C42C2×D511yescharacteristic
109C3×C4⋊C8—21no—
110C3×C4⋊C8—101no—
111C3×C22⋊C8—21no—
112C3×C22⋊C8—101no—
113C3×#97—52no—
114C3×#97C2×D512yes—
115C22×C4×C5C2×C3×C411yescharacteristic
116C22×C4×C5C3×D411yescharacteristic
117C22×C4×C5C3×D411yescharacteristic
118C2×C22⋊D5—21no—
119C2×D20C2×C3×C411yescharacteristic
120C2×C4×D5—21no—
121C2×Dic10C2×C3×C411yescharacteristic
122C2×C5×C8—22no—
123C42×C5C2×C3×C411yescharacteristic
124C42×C5C3×D411yescharacteristic
125C42×C5C3×D411yescharacteristic
126C42×C5C23×C311yescharacteristic
127C22⋊Dic5—21no—
128#685—21no—
129#685—21no—
130#685—21no—
131#685—21no—
132C4⋊Dic5C2×C3×C411yescharacteristic
133C4⋊Dic5C2×C3×C411yescharacteristic
134#683—21no—
135#683—21no—
136#683—21no—
137#683—21no—
138C4×Dic5—21no—
139C2×#168—22no—
140#529—51no—
141#432—51no—
142#432C3×D511yescharacteristic, complemented
143#330—52no—
144#329—52no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×Dic5—41no—
159C3×Dic5—41no—
160C3×Dic5—41no—
161C2×C3×Q8—51no—
162C2×C3×D4—51no—
163C2×C3×D4—101no—
164C22×C3×C4—101no—
165C22×C3×C4C4×D511yescharacteristic
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C2×C3×C8—22no—
169C2×C3×C8—102no—
170C3×C4⋊C4—51no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C22⋊C4—101no—
177C3×C22⋊C4—101no—
178C3×C22⋊C4—101no—
179C3×C22⋊C4—101no—
180C3×C22⋊C4—101no—
181C3×C42—101no—
182C3×C42C4×D511yescharacteristic
183C3×C42D2011yescharacteristic
184C3×C42C22⋊D511yescharacteristic
185C3×C42C22×D511yescharacteristic
186C23×C5C3×C22⋊C411yescharacteristic
187C22×D5—21no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5C3×C22⋊C411yescharacteristic
192C2×C4×C5C3×C22⋊C411yescharacteristic
193C2×C4×C5C3×C22⋊C411yescharacteristic
194C2×C4×C5C22×C3×C411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C22⋊D5—42no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—21no—
201D20—41no—
202C4×D5—42no—
203Dic10—41no—
204C5×C8—42no—
205#168—42no—
206#126—101no—
207#125—51no—
208#124—51no—
209#123—101no—
210C22⋊Q8—51no—
211#121—51no—
212C4×Q8—51no—
213C4×D4—51no—
214C4×D4—101no—
215#117—101no—
216C2×C42C2×C3×D511yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—101no—
219C22⋊C8—21no—
220C22⋊C8—101no—
221#97—52no—
222#97C2×C3×D512yes—
223C2×C3×C5—41no—
224C2×C3×C5#41311yescharacteristic
225C2×C3×C5#42111yescharacteristic
226C2×C3×C5#42111yescharacteristic
227C3×D5—81no—
228C23×C3—101no—
229C23×C3#68511yescharacteristic
230C3×Q8—201no—
231C3×D4—201no—
232C3×D4—202no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—202no—
240C2×C3×C4#68511yescharacteristic
241C2×C3×C4#68511yescharacteristic
242C2×C3×C4#68511yescharacteristic
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C3×C8—42no—
247C3×C8—202no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C2×C3×C22⋊C411yescharacteristic
252C2×D5—41no—
253C2×D5—41no—
254C2×D5—41no—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261Dic5—41no—
262Dic5—41no—
263Dic5—41no—
264C2×Q8—51no—
265C2×D4—51no—
266C2×D4—101no—
267C22×C4—101no—
268C22×C4C3×C4×D511yescharacteristic
269C22×C4C3×D2011yescharacteristic
270C22×C4C3×C22⋊D511yescharacteristic
271C2×C8—22no—
272C2×C8—102no—
273C4⋊C4—51no—
274C4⋊C4—51no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C22⋊C4—101no—
280C22⋊C4—101no—
281C22⋊C4—101no—
282C22⋊C4—101no—
283C22⋊C4—101no—
284C42—101no—
285C42C3×C4×D511yescharacteristic
286C42C3×D2011yescharacteristic
287C42C3×C22⋊D511yescharacteristic
288C42C22×C3×D511yescharacteristic
289C3×C5#153511yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—201no—
294C22×C3—201no—
295C22×C3—201no—
296C22×C3C2×#68511yescharacteristic
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—201no—
304C3×C4—201no—
305C3×C4—201no—
306C2×C5—41no—
307C2×C5C3×#41311yescharacteristic
308C2×C5C3×#42111yescharacteristic
309C2×C5C3×#42111yescharacteristic
310D5—81no—
311C23—101no—
312C23C3×#68511yescharacteristic
313Q8—201no—
314D4—201no—
315D4—202no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—202no—
323C2×C4C3×#68511yescharacteristic
324C2×C4C3×#68511yescharacteristic
325C2×C4C3×#68511yescharacteristic
326C2×C4C2×C3×C4×D511yescharacteristic
327C2×C4C2×C3×D2011yescharacteristic
328C2×C4C2×C3×C22⋊D511yescharacteristic
329C8—42no—
330C8—202no—
331C2×C3—41no—
332C2×C3—401no—
333C2×C3#6529411yescharacteristic
334C2×C3#6542111yescharacteristic
335C2×C3#6542811yescharacteristic
336C5C3×#153511yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—201no—
341C22—201no—
342C22—201no—
343C22C2×C3×#68511yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—201no—
351C4—201no—
352C4—201no—
353C3#1060160311yescharacteristic, direct product factor, Sylow
354C2—41no—
355C2—401no—
356C2C3×#6529411yescharacteristic
357C2C3×#6542111yescharacteristic
358C2C3×#6542811yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#432C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C4
cosocleC42×C5C23×C3
hypercenterC3×#432D5
hypocenterC5C3×#1535
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#432

Complements

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

NH ≅ G/Ntype
2. C3×C5×#432C2semidirect
3. C3×#65215C2semidirect
4. C3×#64685C2semidirect
5. C3×#64684C2semidirect
6. #10601603C3direct (N × H)
26. C5×#432C2×C3semidirect
27. #65215C2×C3semidirect
28. #64685C2×C3semidirect
29. #64684C2×C3semidirect
57. C3×#432D5semidirect
142. #432C3×D5semidirect
289. C3×C5#1535semidirect
336. C5C3×#1535semidirect
353. C3#10601603direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658132
C3×C5×#4322
C3×#652152
C3×#646852
C3×#646842
#106016033
C3×#15355