Finite Group Databasebeta

← C3×#10599252 #14289758

Subgroups — C3×#10599252 #14289758

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66061C211yesmaximal, characteristic
2C3×#65382C211yesmaximal, characteristic, complemented
3C3×#65139C211yesmaximal, characteristic, complemented
4C3×#65131C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic
8#10599252C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4092—21no—
12C3×#4042—22no—
13C3×#4039—21no—
14C3×#4034—21no—
15C3×C4×D20C2211yescharacteristic
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×#3953—21no—
21C3×#3950—21no—
22C3×#3949—21no—
23C3×#3948—21no—
24C3×#3942—22no—
25C3×C4×#168C2211yescharacteristic
26C3×#1637—51nomaximal, Hall
27#66061C2×C311yescharacteristic
28#65382C2×C311yescharacteristic, complemented
29#65139C2×C311yescharacteristic, complemented
30#65131C2×C311yescharacteristic
31C5×#332C2×C311yescharacteristic, complemented
32#64704C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic
34C2×C3×C5×Q8—21no—
35C3×Q8×D5—42no—
36C3×Q8×D5—42no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—22no—
39C2×C3×C4×D5—21no—
40C2×C3×Dic10—22no—
41C2×C3×Dic10—21no—
42C2×C3×Dic10D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D412yes—
47C3×C42×C5C2311yescharacteristic
48C3×#685—22no—
49C3×#685—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C3×D4×Q8—51no—
59C3×#487—51no—
60C3×#477—51no—
61C3×#476—51no—
62C3×#332D511yescharacteristic, complemented
63C3×Q8⋊C8—51no—
64C3×D4⋊C8—51no—
65C2×Q8×D5—21no—
66C5×C4⋊Q8C22×C311yescharacteristic
67#4092—21no—
68#4042—22no—
69#4039—21no—
70#4034—21no—
71C4×D20C22×C311yescharacteristic
72#4015C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C5×C4⋊C8C22×C311yescharacteristic
76#3953—21no—
77#3950—21no—
78#3949—21no—
79#3948—21no—
80#3942—22no—
81C4×#168C22×C311yescharacteristic
82#1637—51noSylow
83C22×C3×D5—21no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—41no—
94C3×D20—21no—
95C3×D20Q1612yes—
96C3×C4×D5—44no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×Dic10—21no—
100C3×Dic10—44no—
101C3×Dic10—42no—
102C3×Dic10SD1612yes—
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3×#168—41no—
106C22×C3×Q8—101no—
107C3×C4⋊Q8—51no—
108C3×C4⋊Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×C22⋊Q8—101no—
111C3×C22⋊Q8—102no—
112C3×C4×Q8—51no—
113C3×C4×D4—51no—
114C3×C4×D4—101no—
115C3×#107—101no—
116C3×#106—101no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#103—101no—
120C3×#103—102no—
121C3×#102—101no—
122C3×C4×C8—51no—
123C2×C5×Q8—21no—
124Q8×D5—42no—
125Q8×D5—42no—
126C2×D20C3×D411yescharacteristic
127C2×C4×D5—22no—
128C2×C4×D5—21no—
129C2×Dic10—22no—
130C2×Dic10—21no—
131C2×Dic10C3×D411yescharacteristic
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C3×D412yes—
136C42×C5C23×C311yescharacteristic
137#685—22no—
138#685—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5C3×D411yescharacteristic
142C4⋊Dic5C3×D411yescharacteristic
143#683—22no—
144#683—21no—
145C4×Dic5—21no—
146C2×#168—21no—
147D4×Q8—51no—
148#487—51no—
149#477—51no—
150#476—51no—
151#332C3×D511yescharacteristic, complemented
152Q8⋊C8—51no—
153D4⋊C8—51no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—22no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—21no—
159C3×C4×C5—42no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—22no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C3×Dic5—81no—
168C2×C3×Q8—21no—
169C2×C3×Q8—51no—
170C2×C3×Q8—102no—
171C2×C3×Q8—101no—
172C2×C3×Q8—202no—
173C2×C3×Q8—202no—
174C2×C3×D4—51no—
175C22×C3×C4—102no—
176C22×C3×C4—101no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—101no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—102no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4—101no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4D2012yes—
188C3×C22⋊C4—102no—
189C3×C22⋊C4—101no—
190C3×C42—101no—
191C3×C42C22×D511yescharacteristic
192C22×D5—21no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—22no—
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—41no—
203D20—21no—
204D20C3×Q1612yes—
205C4×D5—44no—
206C4×D5—41no—
207C4×D5—41no—
208Dic10—21no—
209Dic10—44no—
210Dic10—42no—
211Dic10C3×SD1612yes—
212C5×C8—41no—
213C5×C8—41no—
214#168—41no—
215C22×Q8—101no—
216C4⋊Q8—51no—
217C4⋊Q8—101no—
218C4⋊Q8C2×C3×D511yescharacteristic
219C22⋊Q8—101no—
220C22⋊Q8—102no—
221C4×Q8—51no—
222C4×D4—51no—
223C4×D4—101no—
224#107—101no—
225#106—101no—
226C4⋊C8C2×C3×D511yescharacteristic
227C4⋊C8C2×C3×D511yescharacteristic
228#103—101no—
229#103—102no—
230#102—101no—
231C4×C8—51no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—42no—
236C23×C3—101no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—52no—
240C3×Q8—101no—
241C3×Q8—202no—
242C3×Q8—204no—
243C3×D4—52no—
244C3×D4—101no—
245C2×C3×C4—22no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—204no—
250C2×C3×C4—201no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C3×C8—41no—
257C3×C8—41no—
258C3×C8—201no—
259C22×C5C3×#12011yescharacteristic
260C2×D5—22no—
261C2×D5—41no—
262C2×D5—41no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5C2×C3×SD1611yescharacteristic
266C4×C5C2×C3×Q1611yescharacteristic
267C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
268C4×C5C3×#13711yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—41no—
272Dic5—81no—
273C2×Q8—21no—
274C2×Q8—51no—
275C2×Q8—102no—
276C2×Q8—101no—
277C2×Q8—202no—
278C2×Q8—202no—
279C2×D4—51no—
280C22×C4—102no—
281C22×C4—101no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—101no—
285C4⋊C4—21no—
286C4⋊C4—51no—
287C4⋊C4—51no—
288C4⋊C4—102no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4C3×D2012yes—
293C22⋊C4—102no—
294C22⋊C4—101no—
295C42—101no—
296C42C22×C3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—102no—
299C22×C3—201no—
300C22×C3—201no—
301C22×C3#402811yescharacteristic
302C3×C4—21no—
303C3×C4—42no—
304C3×C4—102no—
305C3×C4—201no—
306C3×C4—201no—
307C3×C4—401no—
308C3×C4#405711yescharacteristic
309C3×C4D5×SD1611yescharacteristic
310C3×C4#406111yescharacteristic
311C3×C4D5×Q1611yescharacteristic
312C2×C5C3×#45011yescharacteristic
313C2×C5C3×#45111yescharacteristic
314C2×C5C3×#45411yescharacteristic
315D5—42no—
316C23—101no—
317Q8—41no—
318Q8—41no—
319Q8—52no—
320Q8—101no—
321Q8—202no—
322Q8—204no—
323D4—52no—
324D4—101no—
325C2×C4—22no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—204no—
330C2×C4—201no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4C2×C3×D2011yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C3×D4×D511yescharacteristic
336C8—41no—
337C8—41no—
338C8—201no—
339C2×C3—202no—
340C2×C3#6504211yescharacteristic
341C2×C3#6506511yescharacteristic
342C2×C3#6509711yescharacteristic
343C5C3×#163711yescharacteristic, complemented, Sylow
344C22—102no—
345C22—201no—
346C22—201no—
347C22C3×#402811yescharacteristic
348C4—21no—
349C4—42no—
350C4—102no—
351C4—201no—
352C4—201no—
353C4—401no—
354C4C3×#405711yescharacteristic
355C4C3×D5×SD1611yescharacteristic
356C4C3×#406111yescharacteristic
357C4C3×D5×Q1611yescharacteristic
358C3#1059925211yescharacteristic, direct product factor, Sylow
359C2—202no—
360C2C3×#6504211yescharacteristic
361C2C3×#6506511yescharacteristic
362C2C3×#6509711yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#332D5
hypocenterC5C3×#1637
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
2. C3×#65382C2semidirect
3. C3×#65139C2semidirect
5. C3×C5×#332C2semidirect
6. C3×#64704C2semidirect
8. #10599252C3direct (N × H)
28. #65382C2×C3semidirect
29. #65139C2×C3semidirect
31. C5×#332C2×C3semidirect
32. #64704C2×C3semidirect
62. C3×#332D5semidirect
151. #332C3×D5semidirect
297. C3×C5#1637semidirect
343. C5C3×#1637semidirect
358. C3#10599252direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660612
C3×#653822
C3×#651392
C3×#651312
C3×C5×#3322
C3×#647042
C3×#647032
#105992523
C3×#16375