Finite Group Databasebeta

← C3×#10600850 #14313258

Subgroups — C3×#10600850 #14313258

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 400 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×#65526C211yesmaximal, characteristic, complemented
4C3×#64691C214yesmaximal, complemented
5#10600850C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×D20C411yescharacteristic, complemented
8C3×C5×#117—21no—
9C3×#4093—21no—
10C3×#4086—21no—
11C3×#4083C412yescomplemented
12C3×#4083C2212yes—
13C3×#4076—21no—
14C3×#4076—21no—
15C3×#4072C411yescharacteristic, complemented
16C2×C3×#681—21no—
17C3×C5×#99—21no—
18C3×C5×#99C2212yes—
19C3×#3968—21no—
20C3×#3965C2212yes—
21C3×#2122—51nomaximal, Hall
22#66164C2×C311yescharacteristic
23C5×#410C2×C311yescharacteristic, complemented
24#65526C2×C311yescharacteristic, complemented
25#64691C2×C314yescomplemented
26C23×C3×D5C2×C412yes—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8D411yescharacteristic
30C2×C3×C5×D4C2×C411yescharacteristic
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—21no—
40C2×C3×D20—41no—
41C2×C3×D20—41no—
42C3×C5×C4⋊C4—41no—
43C3×C5×C22⋊C4—22no—
44C3×C42×C5—41no—
45C3×C22⋊Dic5C2×C412yes—
46C3×#685—22no—
47C3×#685—22no—
48C3×C4⋊Dic5—21no—
49C3×C4×Dic5—21no—
50C3×#681—22no—
51C3×#681—41no—
52C2×C3×#168—41no—
53C3×#535—51no—
54C3×#413—51no—
55C3×#410D511yescharacteristic, complemented
56C3×AΣL(1,𝔽16)—54no—
57C2×C5×#41C22×C311yescharacteristic
58C22×D20C3×C411yescharacteristic, complemented
59C5×#117—21no—
60#4093—21no—
61#4086—21no—
62#4083C3×C412yescomplemented
63#4083C22×C312yes—
64#4076—21no—
65#4076—21no—
66#4072C3×C411yescharacteristic, complemented
67C2×#681—21no—
68C5×#99—21no—
69C5×#99C22×C312yes—
70#3968—21no—
71#3965C22×C312yes—
72#2122—51noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22×C411yescharacteristic
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×C5C2×D411yescharacteristic
94C3×C22⋊D5—82no—
95C3×C22⋊D5—82no—
96C2×C3×Dic5—22no—
97C3×D20—42no—
98C3×D20—41no—
99C3×D20—41no—
100C3×#168—42no—
101C2×C3×#41C2×D511yescharacteristic
102C22×C3×D4—51no—
103C2×C3×M16—101no—
104C3×#127—101no—
105C3×#124—101no—
106C3×#121—101no—
107C3×#121—101no—
108C3×#120—52no—
109C3×#120—52no—
110C3×#117—21no—
111C3×#117—51no—
112C3×#101—101no—
113C3×#100—52no—
114C3×#99—21no—
115C3×#99C2×D512yes—
116C23×D5C2×C3×C412yes—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8C3×D411yescharacteristic
120C2×C5×D4C2×C3×C411yescharacteristic
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—21no—
130C2×D20—41no—
131C2×D20—41no—
132C5×C4⋊C4—41no—
133C5×C22⋊C4—22no—
134C42×C5—41no—
135C22⋊Dic5C2×C3×C412yes—
136#685—22no—
137#685—22no—
138C4⋊Dic5—21no—
139C4×Dic5—21no—
140#681—22no—
141#681—41no—
142C2×#168—41no—
143#535—51no—
144#413—51no—
145#410C3×D511yescharacteristic, complemented
146AΣL(1,𝔽16)—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—
165C24×C3—52no—
166C3×#41—41no—
167C3×#41—41no—
168C2×C3×Q8D2011yescharacteristic
169C2×C3×D4—102no—
170C2×C3×D4—102no—
171C2×C3×D4—101no—
172C2×C3×D4—101no—
173C2×C3×D4—201no—
174C2×C3×D4—201no—
175C2×C3×D4C4×D511yescharacteristic
176C2×C3×D4C22⋊D511yescharacteristic
177C2×C3×D4C22×D511yescharacteristic
178C22×C3×C4C4×D511yescharacteristic
179C22×C3×C4D2011yescharacteristic
180C22×C3×C4C22⋊D511yescharacteristic
181C3×M16—102no—
182C3×M16—201no—
183C2×C3×C8—201no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—101no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—52no—
188C3×C22⋊C4—102no—
189C3×C22⋊C4—102no—
190C3×C42—41no—
191C3×C42—101no—
192C23×C5C3×C22⋊C411yescharacteristic
193C23×C5C22×C3×C411yescharacteristic
194C23×C5C2×C3×D411yescharacteristic
195C22×D5—22no—
196C22×D5—42no—
197C22×D5—82no—
198C5×Q8—41no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—42no—
209C2×C4×C5C3×C22⋊C411yescharacteristic
210C2×C4×C5C3×C22⋊C411yescharacteristic
211C2×C4×C5C3×C22⋊C411yescharacteristic
212C2×C4×C5C2×C3×D411yescharacteristic
213C22⋊D5—82no—
214C22⋊D5—82no—
215C2×Dic5—22no—
216D20—42no—
217D20—41no—
218D20—41no—
219#168—42no—
220C2×#41C2×C3×D511yescharacteristic
221C22×D4—51no—
222C2×M16—101no—
223#127—101no—
224#124—101no—
225#121—101no—
226#121—101no—
227#120—52no—
228#120—52no—
229#117—21no—
230#117—51no—
231#101—101no—
232#100—52no—
233#99—21no—
234#99C2×C3×D512yes—
235C2×C3×C5—21no—
236C2×C3×C5—41no—
237C2×C3×C5—41no—
238C2×C3×C5—41no—
239C2×C3×C5C2×#9911yescharacteristic
240C3×D5—82no—
241C23×C3—102no—
242C23×C3—202no—
243C23×C3—402no—
244C23×C3#68511yescharacteristic
245C23×C3C2×C4×D511yescharacteristic
246C23×C3C2×C22⋊D511yescharacteristic
247C3×Q8—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—202no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4—402no—
255C3×D4—402no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—102no—
264C2×C3×C4#68511yescharacteristic
265C2×C3×C4#68511yescharacteristic
266C2×C3×C4#68511yescharacteristic
267C2×C3×C4C2×D2011yescharacteristic
268C3×C8—202no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5C2×C3×C22⋊C411yescharacteristic
276C2×D5—42no—
277C2×D5—42no—
278C2×D5—42no—
279C2×D5—84no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—82no—
284C4×C5C3×#9911yescharacteristic
285C4×C5C3×#9911yescharacteristic
286Dic5—42no—
287C24—52no—
288#41—41no—
289#41—41no—
290C2×Q8C3×D2011yescharacteristic
291C2×D4—102no—
292C2×D4—102no—
293C2×D4—101no—
294C2×D4—101no—
295C2×D4—201no—
296C2×D4—201no—
297C2×D4C3×C4×D511yescharacteristic
298C2×D4C3×C22⋊D511yescharacteristic
299C2×D4C22×C3×D511yescharacteristic
300C22×C4C3×C4×D511yescharacteristic
301C22×C4C3×D2011yescharacteristic
302C22×C4C3×C22⋊D511yescharacteristic
303M16—102no—
304M16—201no—
305C2×C8—201no—
306C4⋊C4—41no—
307C4⋊C4—101no—
308C22⋊C4—22no—
309C22⋊C4—52no—
310C22⋊C4—102no—
311C22⋊C4—102no—
312C42—41no—
313C42—101no—
314C3×C5#212211yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—202no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—404no—
325C22×C3C2×#68511yescharacteristic
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—82no—
330C3×C4—202no—
331C3×C4#393811yescharacteristic
332C3×C4#393811yescharacteristic
333C2×C5—21no—
334C2×C5—41no—
335C2×C5—41no—
336C2×C5—41no—
337C2×C5C2×C3×#9911yescharacteristic
338D5—82no—
339C23—102no—
340C23—202no—
341C23—402no—
342C23C3×#68511yescharacteristic
343C23C2×C3×C4×D511yescharacteristic
344C23C2×C3×C22⋊D511yescharacteristic
345Q8—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—202no—
350D4—201no—
351D4—201no—
352D4—402no—
353D4—402no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—102no—
362C2×C4C3×#68511yescharacteristic
363C2×C4C3×#68511yescharacteristic
364C2×C4C3×#68511yescharacteristic
365C2×C4C2×C3×D2011yescharacteristic
366C8—202no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—402no—
372C2×C3C2×#393811yescharacteristic
373C5C3×#212211yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—202no—
381C22—202no—
382C22—202no—
383C22—404no—
384C22C2×C3×#68511yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—82no—
389C4—202no—
390C4C3×#393811yescharacteristic
391C4C3×#393811yescharacteristic
392C3#1060085011yescharacteristic, direct product factor, Sylow
393C2—21no—
394C2—41no—
395C2—41no—
396C2—41no—
397C2—402no—
398C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC2×C3C2×#3938
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#410C2
socleC2×C3×C5C2×#99
prime radicalC3×#66164C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#410D5
hypocenterC5C3×#2122
LCSG ▷ C23×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×#65526C2semidirect
4. C3×#64691C2semidirect
5. #10600850C3direct (N × H)
7. C22×C3×D20C4semidirect
11. C3×#4083C4semidirect
15. C3×#4072C4semidirect
23. C5×#410C2×C3semidirect
24. #65526C2×C3semidirect
25. #64691C2×C3semidirect
55. C3×#410D5semidirect
58. C22×D20C3×C4semidirect
62. #4083C3×C4semidirect
66. #4072C3×C4semidirect
145. #410C3×D5semidirect
314. C3×C5#2122semidirect
373. C5C3×#2122semidirect
392. C3#10600850direct (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×#655262
C3×#646912
#106008503
C3×#21225