Finite Group Databasebeta

← C3×#10601801 #14292349

Subgroups — C3×#10601801 #14292349

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#459C211yesmaximal, characteristic
2C3×#65365C211yesmaximal, characteristic, complemented
3C3×#65301C211yesmaximal, characteristic, complemented
4C3×#65296C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64699C211yesmaximal, characteristic, complemented
8#10601801C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×D8—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C2×C3×#687—21no—
13C2×C3×#687—21no—
14C2×C3×#681—21no—
15C3×#4015C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×#102—21no—
18C3×#3964—21no—
19C3×C22⋊#168—21no—
20C3×#3939—21no—
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1685—51nomaximal, Hall
25C5×#459C2×C311yescharacteristic
26#65365C2×C311yescharacteristic, complemented
27#65301C2×C311yescharacteristic, complemented
28#65296C2×C311yescharacteristic, complemented
29#64764C2×C311yescharacteristic, complemented
30#64706C2×C311yescharacteristic, complemented
31#64699C2×C311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C3×Dic10—21no—
38C3×C5×D8—42no—
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C3×#687—42no—
44C3×#687—42no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×#681—42no—
48C2×C3×#168—21no—
49C2×C3×#168—21no—
50C2×C3×#168D411yescharacteristic
51C2×C3×#168D411yescharacteristic
52C3×#492—51no—
53C3×#474—51no—
54C3×#459D511yescharacteristic
55C3×#436—51no—
56C3×#335—51no—
57C3×#332—51no—
58C3×#331—51no—
59C2×C5×D8—21no—
60C5×#127C22×C311yescharacteristic
61C4×C5×D4C22×C311yescharacteristic
62C2×#687—21no—
63C2×#687—21no—
64C2×#681—21no—
65#4015C22×C311yescharacteristic
66C5×C4⋊C8C22×C311yescharacteristic
67C5×#102—21no—
68#3964—21no—
69C22⋊#168—21no—
70#3939—21no—
71C4⋊#168C22×C311yescharacteristic
72C4⋊#168C22×C311yescharacteristic
73C4×#168C22×C311yescharacteristic
74#1685—51noSylow
75C23×C3×C5—21no—
76C23×C3×C5—41no—
77C3×C5×D4—21no—
78C3×C5×D4—21no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C3×Dic5—41no—
91C3×Dic10—41no—
92C3×Dic10—41no—
93C3×C5×C8—41no—
94C3×#168—21no—
95C3×#168—41no—
96C3×#168—41no—
97C3×#168D812yescomplemented
98C2×C3×SD16—101no—
99C2×C3×SD16—101no—
100C2×C3×D8—21no—
101C2×C3×M16—101no—
102C3×C4⋊Q8—51no—
103C3×#127C2×D511yescharacteristic
104C3×C4×D4C2×D511yescharacteristic
105C3×#107—101no—
106C3×C4⋊C8—51no—
107C3×C4⋊C8—51no—
108C3×C4⋊C8C2×D511yescharacteristic
109C3×#102—21no—
110C3×#102—101no—
111C3×C22⋊C8—101no—
112C3×C4×C8—51no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4C3×D411yescharacteristic
117C22×C4×C5—21no—
118C2×Dic10—21no—
119C5×D8—42no—
120C2×C5×C8—21no—
121C5×C4⋊C4C3×D411yescharacteristic
122C5×C22⋊C4—21no—
123C42×C5C23×C311yescharacteristic
124#687—42no—
125#687—42no—
126C4⋊Dic5—21no—
127C4⋊Dic5—21no—
128#681—42no—
129C2×#168—21no—
130C2×#168—21no—
131C2×#168C3×D411yescharacteristic
132C2×#168C3×D411yescharacteristic
133#492—51no—
134#474—51no—
135#459C3×D511yescharacteristic
136#436—51no—
137#335—51no—
138#332—51no—
139#331—51no—
140C22×C3×C5—41no—
141C22×C3×C5—41no—
142C22×C3×C5—41no—
143C22×C3×C5—81no—
144C22×C3×C5—81no—
145C22×C3×C5—81no—
146C22×C3×C5#12111yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×Dic5—81no—
154C2×C3×Q8—101no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4C22⋊D511yescharacteristic
159C22×C3×C4—21no—
160C3×SD16—202no—
161C3×SD16—202no—
162C3×D8—42no—
163C3×M16—202no—
164C2×C3×C8—21no—
165C2×C3×C8—51no—
166C2×C3×C8—51no—
167C2×C3×C8—101no—
168C2×C3×C8—101no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4C22⋊D511yescharacteristic
172C3×C22⋊C4—21no—
173C3×C42C22×D511yescharacteristic
174C23×C5—21no—
175C23×C5—41no—
176C5×D4—21no—
177C5×D4—21no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—81no—
183C2×C4×C5—21no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5C2×C3×D411yescharacteristic
187C2×C4×C5C2×C3×D411yescharacteristic
188C2×C4×C5C3×#4111yescharacteristic
189C2×Dic5—41no—
190Dic10—41no—
191Dic10—41no—
192C5×C8—41no—
193#168—21no—
194#168—41no—
195#168—41no—
196#168C3×D812yescomplemented
197C2×SD16—101no—
198C2×SD16—101no—
199C2×D8—21no—
200C2×M16—101no—
201C4⋊Q8—51no—
202#127C2×C3×D511yescharacteristic
203C4×D4C2×C3×D511yescharacteristic
204#107—101no—
205C4⋊C8—51no—
206C4⋊C8—51no—
207C4⋊C8C2×C3×D511yescharacteristic
208#102—21no—
209#102—101no—
210C22⋊C8—101no—
211C4×C8—51no—
212C2×C3×C5—81no—
213C2×C3×C5—161no—
214C2×C3×C5#45911yescharacteristic
215C2×C3×C5#46811yescharacteristic
216C2×C3×C5#47111yescharacteristic
217C23×C3—21no—
218C23×C3—41no—
219C3×Q8—201no—
220C3×Q8—201no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—81no—
228C2×C3×C4—21no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—201no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4#71111yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C3×C8—41no—
236C3×C8—52no—
237C3×C8—101no—
238C3×C8—201no—
239C3×C8—201no—
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5C3×#12111yescharacteristic
247C4×C5—21no—
248C4×C5—41no—
249C4×C5C2×C3×D811yescharacteristic
250C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
251C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
252C4×C5C3×#13711yescharacteristic
253Dic5—81no—
254C2×Q8—101no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4C3×C22⋊D511yescharacteristic
259C22×C4—21no—
260SD16—202no—
261SD16—202no—
262D8—42no—
263M16—202no—
264C2×C8—21no—
265C2×C8—51no—
266C2×C8—51no—
267C2×C8—101no—
268C2×C8—101no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4C3×C22⋊D511yescharacteristic
272C22⋊C4—21no—
273C42C22×C3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3#408511yescharacteristic
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—401no—
285C3×C4D5×D811yescharacteristic
286C3×C4#405711yescharacteristic
287C3×C4#407811yescharacteristic
288C3×C4#409711yescharacteristic
289C2×C5—81no—
290C2×C5—161no—
291C2×C5C3×#45911yescharacteristic
292C2×C5C3×#46811yescharacteristic
293C2×C5C3×#47111yescharacteristic
294C23—21no—
295C23—41no—
296Q8—201no—
297Q8—201no—
298D4—21no—
299D4—21no—
300D4—41no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—81no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—201no—
309C2×C4C3×D4×D511yescharacteristic
310C2×C4C3×#71111yescharacteristic
311C2×C4C2×C3×C22⋊D511yescharacteristic
312C8—41no—
313C8—52no—
314C8—101no—
315C8—201no—
316C8—201no—
317C2×C3—81no—
318C2×C3—161no—
319C2×C3#6533111yescharacteristic
320C2×C3#6543911yescharacteristic
321C2×C3#6548911yescharacteristic
322C5C3×#168511yescharacteristic, complemented, Sylow
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C3×#408511yescharacteristic
330C4—21no—
331C4—41no—
332C4—401no—
333C4C3×D5×D811yescharacteristic
334C4C3×#405711yescharacteristic
335C4C3×#407811yescharacteristic
336C4C3×#409711yescharacteristic
337C3#1060180111yescharacteristic, direct product factor, Sylow
338C2—81no—
339C2—161no—
340C2C3×#6533111yescharacteristic
341C2C3×#6543911yescharacteristic
342C2C3×#6548911yescharacteristic
subgroupG/H
centerC22×C3#4085
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
Fitting, prime radicalC3×C5×#459C2
socleC22×C3×C5#121
hypercenterC3×#459D5
hypocenterC5C3×#1685
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
2. C3×#65365C2semidirect
3. C3×#65301C2semidirect
4. C3×#65296C2semidirect
5. C3×#64764C2semidirect
6. C3×#64706C2semidirect
7. C3×#64699C2semidirect
8. #10601801C3direct (N × H)
26. #65365C2×C3semidirect
27. #65301C2×C3semidirect
28. #65296C2×C3semidirect
29. #64764C2×C3semidirect
30. #64706C2×C3semidirect
31. #64699C2×C3semidirect
97. C3×#168D8semidirect
196. #168C3×D8semidirect
274. C3×C5#1685semidirect
322. C5C3×#1685semidirect
337. C3#10601801direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4592
C3×#653652
C3×#653012
C3×#652962
C3×#647642
C3×#647062
C3×#646992
#106018013
C3×#16855