Finite Group Databasebeta

← C3×#10602061 #14292346

Subgroups — C3×#10602061 #14292346

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×#492C211yesmaximal, characteristic, complemented
2C3×#65376C211yesmaximal, characteristic, complemented
3C3×#65361C211yesmaximal, characteristic
4C3×#64977C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64764C211yesmaximal, characteristic, complemented
7C3×#64678C211yesmaximal, characteristic, complemented
8#10602061C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C2×C3×C5×SD16—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#127C2211yescharacteristic
13C2×C3×#686—21no—
14C2×C3×#676—21no—
15C3×C4×D20C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17C3×#3964—21no—
18C3×#3952—21no—
19C3×#3941—21no—
20C3×#3939—21no—
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24C3×#1685—51nomaximal, Hall
25C5×#492C2×C311yescharacteristic, complemented
26#65376C2×C311yescharacteristic, complemented
27#65361C2×C311yescharacteristic
28#64977C2×C311yescharacteristic, complemented
29#64767C2×C311yescharacteristic, complemented
30#64764C2×C311yescharacteristic, complemented
31#64678C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C3×C5×SD16—42no—
39C3×C5×SD16—42no—
40C2×C3×C5×C8D411yescharacteristic
41C2×C3×C5×C8D411yescharacteristic
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45C3×#686—42no—
46C3×#685—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C2×C3×#168—21no—
49C2×C3×#168—21no—
50C2×C3×#168—21no—
51C3×#676—42no—
52C3×#492D511yescharacteristic, complemented
53C3×#474—51no—
54C3×#459—51no—
55C3×#436—51no—
56C3×#335—51no—
57C3×#332—51no—
58C3×#331—51no—
59C2×C5×SD16—21no—
60C2×C5×SD16—21no—
61C5×C4⋊Q8C22×C311yescharacteristic
62C5×#127C22×C311yescharacteristic
63C2×#686—21no—
64C2×#676—21no—
65C4×D20C22×C311yescharacteristic
66C4×C5×C8C22×C311yescharacteristic
67#3964—21no—
68#3952—21no—
69#3941—21no—
70#3939—21no—
71C4⋊#168C22×C311yescharacteristic
72C4⋊#168C22×C311yescharacteristic
73C4⋊#168C22×C311yescharacteristic
74#1685—51noSylow
75C23×C3×C5—41no—
76C22×C3×D5—21no—
77C3×C5×Q8—41no—
78C3×C5×Q8—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C2×C3×Dic5—21no—
89C3×D20—21no—
90C3×D20—21no—
91C3×C4×D5—41no—
92C3×C4×D5—41no—
93C3×C5×C8—21no—
94C3×C5×C8D812yescomplemented
95C3×#168—41no—
96C3×#168—41no—
97C3×#168—41no—
98C2×C3×SD16—21no—
99C2×C3×SD16—21no—
100C2×C3×D8—101no—
101C2×C3×M16—101no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×#127C2×D511yescharacteristic
104C3×C4×D4—51no—
105C3×#107—101no—
106C3×C4⋊C8—51no—
107C3×C4⋊C8—51no—
108C3×C4⋊C8—51no—
109C3×#102—101no—
110C3×#102—101no—
111C3×C22⋊C8—101no—
112C3×C4×C8C2×D511yescharacteristic
113C2×C5×Q8—21no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×D20C3×D411yescharacteristic
118C2×C4×D5—21no—
119C5×SD16—42no—
120C5×SD16—42no—
121C2×C5×C8C3×D411yescharacteristic
122C2×C5×C8C3×D411yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C42×C5C23×C311yescharacteristic
126#686—42no—
127#685—21no—
128C4⋊Dic5C3×D411yescharacteristic
129C2×#168—21no—
130C2×#168—21no—
131C2×#168—21no—
132#676—42no—
133#492C3×D511yescharacteristic, complemented
134#474—51no—
135#459—51no—
136#436—51no—
137#335—51no—
138#332—51no—
139#331—51no—
140C22×C3×C5—81no—
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5#12111yescharacteristic
144C2×C3×D5—41no—
145C2×C3×D5—41no—
146C2×C3×D5—41no—
147C3×C4×C5—21no—
148C3×C4×C5—81no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×Dic5—41no—
154C2×C3×Q8—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—51no—
159C22×C3×C4—101no—
160C3×SD16—42no—
161C3×SD16—42no—
162C3×D8—202no—
163C3×M16—202no—
164C2×C3×C8—101no—
165C2×C3×C8—101no—
166C2×C3×C8—101no—
167C2×C3×C8C22⋊D511yescharacteristic
168C2×C3×C8C22⋊D511yescharacteristic
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—51no—
172C3×C22⋊C4—101no—
173C3×C42C22×D511yescharacteristic
174C23×C5—41no—
175C22×D5—21no—
176C5×Q8—41no—
177C5×Q8—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—81no—
183C2×C4×C5—41no—
184C2×C4×C5C2×C3×D411yescharacteristic
185C2×C4×C5C2×C3×D411yescharacteristic
186C2×C4×C5C3×#4111yescharacteristic
187C2×Dic5—21no—
188D20—21no—
189D20—21no—
190C4×D5—41no—
191C4×D5—41no—
192C5×C8—21no—
193C5×C8C3×D812yescomplemented
194#168—41no—
195#168—41no—
196#168—41no—
197C2×SD16—21no—
198C2×SD16—21no—
199C2×D8—101no—
200C2×M16—101no—
201C4⋊Q8C2×C3×D511yescharacteristic
202#127C2×C3×D511yescharacteristic
203C4×D4—51no—
204#107—101no—
205C4⋊C8—51no—
206C4⋊C8—51no—
207C4⋊C8—51no—
208#102—101no—
209#102—101no—
210C22⋊C8—101no—
211C4×C8C2×C3×D511yescharacteristic
212C2×C3×C5—161no—
213C2×C3×C5#45911yescharacteristic
214C2×C3×C5#46811yescharacteristic
215C2×C3×C5#47111yescharacteristic
216C3×D5—81no—
217C23×C3—41no—
218C23×C3—101no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—81no—
226C3×D4—101no—
227C3×D4—101no—
228C2×C3×C4—41no—
229C2×C3×C4—101no—
230C2×C3×C4—201no—
231C2×C3×C4—201no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4#71111yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C3×C8—21no—
236C3×C8—201no—
237C3×C8—201no—
238C3×C8—201no—
239C3×C8#68612yescomplemented
240C22×C5—81no—
241C22×C5—81no—
242C22×C5—81no—
243C22×C5C3×#12111yescharacteristic
244C2×D5—41no—
245C2×D5—41no—
246C2×D5—41no—
247C4×C5—21no—
248C4×C5—81no—
249C4×C5C2×C3×D811yescharacteristic
250C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
251C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
252C4×C5C3×#13711yescharacteristic
253Dic5—41no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—51no—
259C22×C4—101no—
260SD16—42no—
261SD16—42no—
262D8—202no—
263M16—202no—
264C2×C8—101no—
265C2×C8—101no—
266C2×C8—101no—
267C2×C8C3×C22⋊D511yescharacteristic
268C2×C8C3×C22⋊D511yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—51no—
272C22⋊C4—101no—
273C42C22×C3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—81no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3—201no—
279C22×C3—201no—
280C22×C3—201no—
281C22×C3#408411yescharacteristic
282C3×C4—21no—
283C3×C4—81no—
284C3×C4—201no—
285C3×C4#406011yescharacteristic
286C3×C4#406111yescharacteristic
287C3×C4C2×#68611yescharacteristic
288C3×C4#407811yescharacteristic
289C2×C5—161no—
290C2×C5C3×#45911yescharacteristic
291C2×C5C3×#46811yescharacteristic
292C2×C5C3×#47111yescharacteristic
293D5—81no—
294C23—41no—
295C23—101no—
296Q8—41no—
297Q8—41no—
298D4—41no—
299D4—41no—
300D4—41no—
301D4—41no—
302D4—81no—
303D4—101no—
304D4—101no—
305C2×C4—41no—
306C2×C4—101no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4C3×D4×D511yescharacteristic
310C2×C4C3×#71111yescharacteristic
311C2×C4C2×C3×C22⋊D511yescharacteristic
312C8—21no—
313C8—201no—
314C8—201no—
315C8—201no—
316C8C3×#68612yescomplemented
317C2×C3—161no—
318C2×C3—401no—
319C2×C3#6536111yescharacteristic
320C2×C3#6546311yescharacteristic
321C2×C3#6546611yescharacteristic
322C5C3×#168511yescharacteristic, complemented, Sylow
323C22—81no—
324C22—81no—
325C22—81no—
326C22—201no—
327C22—201no—
328C22—201no—
329C22C3×#408411yescharacteristic
330C4—21no—
331C4—81no—
332C4—201no—
333C4C3×#406011yescharacteristic
334C4C3×#406111yescharacteristic
335C4C2×C3×#68611yescharacteristic
336C4C3×#407811yescharacteristic
337C3#1060206111yescharacteristic, direct product factor, Sylow
338C2—161no—
339C2—401no—
340C2C3×#6536111yescharacteristic
341C2C3×#6546311yescharacteristic
342C2C3×#6546611yescharacteristic
subgroupG/H
centerC22×C3#4084
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#492C2
socleC22×C3×C5#121
prime radicalC3×#65361C2
hypercenterC3×#492D5
hypocenterC5C3×#1685
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C3×C5×#492C2semidirect
2. C3×#65376C2semidirect
4. C3×#64977C2semidirect
5. C3×#64767C2semidirect
6. C3×#64764C2semidirect
7. C3×#64678C2semidirect
8. #10602061C3direct (N × H)
25. C5×#492C2×C3semidirect
26. #65376C2×C3semidirect
28. #64977C2×C3semidirect
29. #64767C2×C3semidirect
30. #64764C2×C3semidirect
31. #64678C2×C3semidirect
52. C3×#492D5semidirect
94. C3×C5×C8D8semidirect
133. #492C3×D5semidirect
193. C5×C8C3×D8semidirect
239. C3×C8#686semidirect
274. C3×C5#1685semidirect
316. C8C3×#686semidirect
322. C5C3×#1685semidirect
337. C3#10602061direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4922
C3×#653762
C3×#653612
C3×#649772
C3×#647672
C3×#647642
C3×#646782
#106020613
C3×#16855