Finite Group Databasebeta

← C3×#10600854 #14313500

Subgroups — C3×#10600854 #14313500

Order 1920.

540 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
1C3×#66164C211yesmaximal, characteristic
2C3×C5×#410C211yesmaximal, characteristic, complemented
3C3×#65529C211yesmaximal, characteristic, complemented
4C3×#64694C214yesmaximal, complemented
5#10600854C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×D20C411yescharacteristic, complemented
8C3×C5×#117—21no—
9C3×#4093C412yescomplemented
10C3×#4086C2212yes—
11C3×#4083—21no—
12C3×#4083—21no—
13C3×#4076—21no—
14C3×#4076—21no—
15C3×#4072—21no—
16C3×#4072C411yescharacteristic, complemented
17C3×C5×#99—21no—
18C3×C5×#99C2212yescomplemented
19C3×#3966—21no—
20C3×#3966C2212yescomplemented
21C3×#2128—51nomaximal, Hall
22#66164C2×C311yescharacteristic
23C5×#410C2×C311yescharacteristic, complemented
24#65529C2×C311yescharacteristic, complemented
25#64694C2×C314yescomplemented
26C23×C3×D5—21no—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8C2×C411yescharacteristic
30C2×C3×C5×D4D411yescharacteristic
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4C2311yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×D20—21no—
39C2×C3×D20—41no—
40C2×C3×D20—41no—
41C2×C3×D20C2×C412yes—
42C3×C5×C4⋊C4—41no—
43C3×C5×C22⋊C4—22no—
44C3×C42×C5—41no—
45C3×C22⋊Dic5—21no—
46C3×C22⋊Dic5—22no—
47C3×#685—22no—
48C3×#685—22no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—41no—
51C3×C4×Dic5—41no—
52C3×C4×Dic5C2×C412yes—
53C3×#535—51no—
54C3×#410—51no—
55C3×#410D511yescharacteristic, complemented
56C3×#353—54no—
57C2×C5×#41C22×C311yescharacteristic
58C22×D20C3×C411yescharacteristic, complemented
59C5×#117—21no—
60#4093C3×C412yescomplemented
61#4086C22×C312yes—
62#4083—21no—
63#4083—21no—
64#4076—21no—
65#4076—21no—
66#4072—21no—
67#4072C3×C411yescharacteristic, complemented
68C5×#99—21no—
69C5×#99C22×C312yescomplemented
70#3966—21no—
71#3966C22×C312yescomplemented
72#2128—51noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—42no—
78C22×C3×D5—82no—
79C3×C5×Q8—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C3×C22⋊D5—82no—
95C3×C22⋊D5—82no—
96C2×C3×Dic5—22no—
97C2×C3×Dic5—42no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C2×C3×#41C2×D511yescharacteristic
102C22×C3×D4—51no—
103C3×#127—52no—
104C3×#124—52no—
105C3×#121—101no—
106C3×#121—101no—
107C3×#120—101no—
108C3×#120—101no—
109C3×#117—21no—
110C3×#117—51no—
111C3×#117—101no—
112C3×#99—21no—
113C3×#99—52no—
114C3×#99—101no—
115C3×#99C2×D512yescomplemented
116C23×D5—21no—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8C2×C3×C411yescharacteristic
120C2×C5×D4C3×D411yescharacteristic
121C2×C5×D4C3×D411yescharacteristic
122C2×C5×D4C23×C311yescharacteristic
123C22×C4×C5C2×C3×C411yescharacteristic
124C22×C4×C5C3×D411yescharacteristic
125C22×C4×C5C3×D411yescharacteristic
126C2×C22⋊D5—22no—
127C2×C22⋊D5—22no—
128C2×D20—21no—
129C2×D20—41no—
130C2×D20—41no—
131C2×D20C2×C3×C412yes—
132C5×C4⋊C4—41no—
133C5×C22⋊C4—22no—
134C42×C5—41no—
135C22⋊Dic5—21no—
136C22⋊Dic5—22no—
137#685—22no—
138#685—22no—
139C4⋊Dic5—21no—
140C4⋊Dic5—41no—
141C4×Dic5—41no—
142C4×Dic5C2×C3×C412yes—
143#535—51no—
144#410—51no—
145#410C3×D511yescharacteristic, complemented
146#353—54no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C2×C3×D5—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—82no—
162C3×C4×C5#9911yescharacteristic
163C3×C4×C5#9911yescharacteristic
164C3×Dic5—42no—
165C3×Dic5—82no—
166C24×C3—101no—
167C3×#41—41no—
168C3×#41—41no—
169C2×C3×Q8C4×D511yescharacteristic
170C2×C3×D4—52no—
171C2×C3×D4—102no—
172C2×C3×D4—102no—
173C2×C3×D4—101no—
174C2×C3×D4—201no—
175C2×C3×D4—201no—
176C2×C3×D4D2011yescharacteristic
177C2×C3×D4C22⋊D511yescharacteristic
178C2×C3×D4C22×D511yescharacteristic
179C22×C3×C4C4×D511yescharacteristic
180C22×C3×C4D2011yescharacteristic
181C22×C3×C4C22⋊D511yescharacteristic
182C3×C4⋊C4—41no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4—201no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—101no—
187C3×C22⋊C4—102no—
188C3×C22⋊C4—102no—
189C3×C22⋊C4—102no—
190C3×C42—41no—
191C3×C42—52no—
192C3×C42—201no—
193C23×C5C3×C22⋊C411yescharacteristic
194C23×C5C2×C3×D411yescharacteristic
195C23×C5C2×C3×D411yescharacteristic
196C22×D5—22no—
197C22×D5—42no—
198C22×D5—82no—
199C5×Q8—41no—
200C5×D4—41no—
201C5×D4—41no—
202C5×D4—41no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—42no—
210C2×C4×C5C3×C22⋊C411yescharacteristic
211C2×C4×C5C3×C22⋊C411yescharacteristic
212C2×C4×C5C3×C22⋊C411yescharacteristic
213C2×C4×C5C22×C3×C411yescharacteristic
214C22⋊D5—82no—
215C22⋊D5—82no—
216C2×Dic5—22no—
217C2×Dic5—42no—
218D20—42no—
219D20—41no—
220D20—41no—
221C2×#41C2×C3×D511yescharacteristic
222C22×D4—51no—
223#127—52no—
224#124—52no—
225#121—101no—
226#121—101no—
227#120—101no—
228#120—101no—
229#117—21no—
230#117—51no—
231#117—101no—
232#99—21no—
233#99—52no—
234#99—101no—
235#99C2×C3×D512yescomplemented
236C2×C3×C5—21no—
237C2×C3×C5—41no—
238C2×C3×C5—41no—
239C2×C3×C5—41no—
240C2×C3×C5C2×#9911yescharacteristic
241C3×D5—82no—
242C23×C3—102no—
243C23×C3—202no—
244C23×C3—402no—
245C23×C3#68511yescharacteristic
246C23×C3C2×D2011yescharacteristic
247C23×C3C2×C22⋊D511yescharacteristic
248C3×Q8—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—202no—
253C3×D4—201no—
254C3×D4—201no—
255C3×D4—402no—
256C3×D4—402no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—42no—
264C2×C3×C4—102no—
265C2×C3×C4—202no—
266C2×C3×C4#68511yescharacteristic
267C2×C3×C4#68511yescharacteristic
268C2×C3×C4#68511yescharacteristic
269C2×C3×C4C2×C4×D511yescharacteristic
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5—41no—
276C22×C5C2×C3×C22⋊C411yescharacteristic
277C2×D5—42no—
278C2×D5—42no—
279C2×D5—42no—
280C2×D5—84no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—82no—
285C4×C5C3×#9911yescharacteristic
286C4×C5C3×#9911yescharacteristic
287Dic5—42no—
288Dic5—82no—
289C24—101no—
290#41—41no—
291#41—41no—
292C2×Q8C3×C4×D511yescharacteristic
293C2×D4—52no—
294C2×D4—102no—
295C2×D4—102no—
296C2×D4—101no—
297C2×D4—201no—
298C2×D4—201no—
299C2×D4C3×D2011yescharacteristic
300C2×D4C3×C22⋊D511yescharacteristic
301C2×D4C22×C3×D511yescharacteristic
302C22×C4C3×C4×D511yescharacteristic
303C22×C4C3×D2011yescharacteristic
304C22×C4C3×C22⋊D511yescharacteristic
305C4⋊C4—41no—
306C4⋊C4—101no—
307C4⋊C4—201no—
308C22⋊C4—22no—
309C22⋊C4—101no—
310C22⋊C4—102no—
311C22⋊C4—102no—
312C22⋊C4—102no—
313C42—41no—
314C42—52no—
315C42—201no—
316C3×C5#212811yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3—202no—
326C22×C3—404no—
327C22×C3C2×#68511yescharacteristic
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—82no—
332C3×C4—202no—
333C3×C4—402no—
334C3×C4#393811yescharacteristic
335C3×C4#393811yescharacteristic
336C2×C5—21no—
337C2×C5—41no—
338C2×C5—41no—
339C2×C5—41no—
340C2×C5C2×C3×#9911yescharacteristic
341D5—82no—
342C23—102no—
343C23—202no—
344C23—402no—
345C23C3×#68511yescharacteristic
346C23C2×C3×D2011yescharacteristic
347C23C2×C3×C22⋊D511yescharacteristic
348Q8—41no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—202no—
353D4—201no—
354D4—201no—
355D4—402no—
356D4—402no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—102no—
365C2×C4—202no—
366C2×C4C3×#68511yescharacteristic
367C2×C4C3×#68511yescharacteristic
368C2×C4C3×#68511yescharacteristic
369C2×C4C2×C3×C4×D511yescharacteristic
370C2×C3—21no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—41no—
374C2×C3—402no—
375C2×C3C2×#393811yescharacteristic
376C5C3×#212811yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—202no—
384C22—202no—
385C22—202no—
386C22—404no—
387C22C2×C3×#68511yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—202no—
393C4—402no—
394C4C3×#393811yescharacteristic
395C4C3×#393811yescharacteristic
396C3#1060085411yescharacteristic, direct product factor, Sylow
397C2—21no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—402no—
402C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC2×C3C2×#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#410C2
socleC2×C3×C5C2×#99
prime radicalC3×#66164C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#410D5
hypocenterC5C3×#2128
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
2. C3×C5×#410C2semidirect
3. C3×#65529C2semidirect
4. C3×#64694C2semidirect
5. #10600854C3direct (N × H)
7. C22×C3×D20C4semidirect
9. C3×#4093C4semidirect
16. C3×#4072C4semidirect
18. C3×C5×#99C22semidirect
20. C3×#3966C22semidirect
23. C5×#410C2×C3semidirect
24. #65529C2×C3semidirect
25. #64694C2×C3semidirect
55. C3×#410D5semidirect
58. C22×D20C3×C4semidirect
60. #4093C3×C4semidirect
67. #4072C3×C4semidirect
69. C5×#99C22×C3semidirect
71. #3966C22×C3semidirect
115. C3×#99C2×D5semidirect
145. #410C3×D5semidirect
235. #99C2×C3×D5semidirect
316. C3×C5#2128semidirect
376. C5C3×#2128semidirect
396. C3#10600854direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661642
C3×C5×#4102
C3×#655292
C3×#646942
#106008543
C3×#21285