Finite Group Databasebeta

← C3×#10600942 #14313718

Subgroups — C3×#10600942 #14313718

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66164C211yesmaximal, characteristic
2C3×C5×#413C211yesmaximal, characteristic, complemented
3C3×#65526C211yesmaximal, characteristic, complemented
4C3×#64697C214yesmaximal, complemented
5#10600942C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×D20C411yescharacteristic
8C2×C3×C5×M16—21no—
9C3×#4093C2212yes—
10C3×#4086C412yes—
11C3×#4083—21no—
12C3×#4083—21no—
13C3×#4076—21no—
14C3×#4076—21no—
15C3×#4072C411yescharacteristic
16C2×C3×#681—21no—
17C3×C5×#101C2212yescomplemented
18C3×C5×#100—21no—
19C3×#3968C2212yescomplemented
20C3×#3965—21no—
21C3×#2134—51nomaximal, Hall
22#66164C2×C311yescharacteristic
23C5×#413C2×C311yescharacteristic, complemented
24#65526C2×C311yescharacteristic, complemented
25#64697C2×C314yescomplemented
26C23×C3×D5—21no—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8C2311yescharacteristic
30C2×C3×C5×D4C2×C411yescharacteristic
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4D411yescharacteristic
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×M16—22no—
43C3×C5×M16—41no—
44C2×C3×C5×C8—41no—
45C3×C22⋊Dic5—21no—
46C3×#685—22no—
47C3×#685—22no—
48C3×C4⋊Dic5—21no—
49C3×C4×Dic5C2×C412yes—
50C3×#681—22no—
51C3×#681—41no—
52C2×C3×#168—41no—
53C3×#535—51no—
54C3×#413—51no—
55C3×#413D511yescharacteristic, complemented
56C3×#355—54no—
57C2×C5×#41C22×C311yescharacteristic
58C22×D20C3×C411yescharacteristic
59C2×C5×M16—21no—
60#4093C22×C312yes—
61#4086C3×C412yes—
62#4083—21no—
63#4083—21no—
64#4076—21no—
65#4076—21no—
66#4072C3×C411yescharacteristic
67C2×#681—21no—
68C5×#101C22×C312yescomplemented
69C5×#100—21no—
70#3968C22×C312yescomplemented
71#3965—21no—
72#2134—51noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22⋊C411yescharacteristic
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×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C3×C22⋊D5—82no—
94C3×C22⋊D5—82no—
95C2×C3×Dic5—22no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×C5×C8—42no—
100C3×#168—42no—
101C2×C3×#41C2×D511yescharacteristic
102C22×C3×D4—51no—
103C2×C3×M16—21no—
104C2×C3×M16—101no—
105C3×#127—52no—
106C3×#124—52no—
107C3×#121—101no—
108C3×#121—101no—
109C3×#120—101no—
110C3×#120—101no—
111C3×#117—51no—
112C3×#101—52no—
113C3×#101C2×D512yescomplemented
114C3×#100—21no—
115C3×#100—101no—
116C23×D5—21no—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8C23×C311yescharacteristic
120C2×C5×D4C2×C3×C411yescharacteristic
121C2×C5×D4C3×D411yescharacteristic
122C2×C5×D4C3×D411yescharacteristic
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×M16—22no—
133C5×M16—41no—
134C2×C5×C8—41no—
135C22⋊Dic5—21no—
136#685—22no—
137#685—22no—
138C4⋊Dic5—21no—
139C4×Dic5C2×C3×C412yes—
140#681—22no—
141#681—41no—
142C2×#168—41no—
143#535—51no—
144#413—51no—
145#413C3×D511yescharacteristic, complemented
146#355—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#9911yescharacteristic
162C3×C4×C5#9911yescharacteristic
163C3×Dic5—42no—
164C24×C3—101no—
165C3×#41—41no—
166C3×#41—41no—
167C2×C3×Q8C22×D511yescharacteristic
168C2×C3×D4—52no—
169C2×C3×D4—102no—
170C2×C3×D4—102no—
171C2×C3×D4—101no—
172C2×C3×D4—201no—
173C2×C3×D4—201no—
174C2×C3×D4C4×D511yescharacteristic
175C2×C3×D4D2011yescharacteristic
176C2×C3×D4C22⋊D511yescharacteristic
177C22×C3×C4C4×D511yescharacteristic
178C22×C3×C4D2011yescharacteristic
179C22×C3×C4C22⋊D511yescharacteristic
180C3×M16—22no—
181C3×M16—41no—
182C3×M16—102no—
183C3×M16—201no—
184C2×C3×C8—41no—
185C2×C3×C8—201no—
186C3×C4⋊C4—101no—
187C3×C22⋊C4—101no—
188C3×C22⋊C4—102no—
189C3×C22⋊C4—102no—
190C3×C42—52no—
191C23×C5C3×C22⋊C411yescharacteristic
192C23×C5C3×C22⋊C411yescharacteristic
193C23×C5C3×C22⋊C411yescharacteristic
194C22×D5—22no—
195C22×D5—42no—
196C22×D5—82no—
197C5×Q8—41no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5C3×C22⋊C411yescharacteristic
208C2×C4×C5C22×C3×C411yescharacteristic
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C22⋊D5—82no—
212C22⋊D5—82no—
213C2×Dic5—22no—
214D20—42no—
215D20—41no—
216D20—41no—
217C5×C8—42no—
218#168—42no—
219C2×#41C2×C3×D511yescharacteristic
220C22×D4—51no—
221C2×M16—21no—
222C2×M16—101no—
223#127—52no—
224#124—52no—
225#121—101no—
226#121—101no—
227#120—101no—
228#120—101no—
229#117—51no—
230#101—52no—
231#101C2×C3×D512yescomplemented
232#100—21no—
233#100—101no—
234C2×C3×C5—21no—
235C2×C3×C5—41no—
236C2×C3×C5—41no—
237C2×C3×C5—41no—
238C2×C3×C5C2×#9911yescharacteristic
239C3×D5—82no—
240C23×C3—102no—
241C23×C3—202no—
242C23×C3—402no—
243C23×C3#68511yescharacteristic
244C23×C3#68511yescharacteristic
245C23×C3#68511yescharacteristic
246C3×Q8—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—202no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—402no—
254C3×D4—402no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—102no—
262C2×C3×C4#68511yescharacteristic
263C2×C3×C4C2×C4×D511yescharacteristic
264C2×C3×C4C2×D2011yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C3×C8—42no—
267C3×C8—202no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5C2×C3×C22⋊C411yescharacteristic
275C2×D5—42no—
276C2×D5—42no—
277C2×D5—42no—
278C2×D5—84no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5C3×#9911yescharacteristic
283C4×C5C3×#9911yescharacteristic
284Dic5—42no—
285C24—101no—
286#41—41no—
287#41—41no—
288C2×Q8C22×C3×D511yescharacteristic
289C2×D4—52no—
290C2×D4—102no—
291C2×D4—102no—
292C2×D4—101no—
293C2×D4—201no—
294C2×D4—201no—
295C2×D4C3×C4×D511yescharacteristic
296C2×D4C3×D2011yescharacteristic
297C2×D4C3×C22⋊D511yescharacteristic
298C22×C4C3×C4×D511yescharacteristic
299C22×C4C3×D2011yescharacteristic
300C22×C4C3×C22⋊D511yescharacteristic
301M16—22no—
302M16—41no—
303M16—102no—
304M16—201no—
305C2×C8—41no—
306C2×C8—201no—
307C4⋊C4—101no—
308C22⋊C4—101no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C42—52no—
312C3×C5#213411yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3—404no—
323C22×C3C2×#68511yescharacteristic
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—202no—
328C3×C4#393811yescharacteristic
329C3×C4#393811yescharacteristic
330C2×C5—21no—
331C2×C5—41no—
332C2×C5—41no—
333C2×C5—41no—
334C2×C5C2×C3×#9911yescharacteristic
335D5—82no—
336C23—102no—
337C23—202no—
338C23—402no—
339C23C3×#68511yescharacteristic
340C23C3×#68511yescharacteristic
341C23C3×#68511yescharacteristic
342Q8—41no—
343D4—41no—
344D4—41no—
345D4—41no—
346D4—202no—
347D4—201no—
348D4—201no—
349D4—402no—
350D4—402no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—102no—
358C2×C4C3×#68511yescharacteristic
359C2×C4C2×C3×C4×D511yescharacteristic
360C2×C4C2×C3×D2011yescharacteristic
361C2×C4C2×C3×C22⋊D511yescharacteristic
362C8—42no—
363C8—202no—
364C2×C3—21no—
365C2×C3—41no—
366C2×C3—41no—
367C2×C3—41no—
368C2×C3—402no—
369C2×C3C2×#393811yescharacteristic
370C5C3×#213411yescharacteristic, complemented, Sylow
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—202no—
378C22—202no—
379C22—202no—
380C22—404no—
381C22C2×C3×#68511yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—202no—
386C4C3×#393811yescharacteristic
387C4C3×#393811yescharacteristic
388C3#1060094211yescharacteristic, direct product factor, Sylow
389C2—21no—
390C2—41no—
391C2—41no—
392C2—41no—
393C2—402no—
394C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC2×C3C2×#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#413C2
socleC2×C3×C5C2×#99
prime radicalC3×#66164C2
cosocleC2×C5×Q8C23×C3
hypercenterC3×#413D5
hypocenterC5C3×#2134
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
2. C3×C5×#413C2semidirect
3. C3×#65526C2semidirect
4. C3×#64697C2semidirect
5. #10600942C3direct (N × H)
17. C3×C5×#101C22semidirect
19. C3×#3968C22semidirect
23. C5×#413C2×C3semidirect
24. #65526C2×C3semidirect
25. #64697C2×C3semidirect
55. C3×#413D5semidirect
68. C5×#101C22×C3semidirect
70. #3968C22×C3semidirect
113. C3×#101C2×D5semidirect
145. #413C3×D5semidirect
231. #101C2×C3×D5semidirect
312. C3×C5#2134semidirect
370. C5C3×#2134semidirect
388. C3#10600942direct (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×#4132
C3×#655262
C3×#646972
#106009423
C3×#21345