Finite Group Databasebeta

← C3×#10601660 #14292355

Subgroups — C3×#10601660 #14292355

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×#436C211yesmaximal, characteristic, complemented
2C3×#65304C211yesmaximal, characteristic
3C3×#65296C211yesmaximal, characteristic, complemented
4C3×#64982C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6C3×#64702C211yesmaximal, characteristic, complemented
7C3×#64678C211yesmaximal, characteristic, complemented
8#10601660C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×M16—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C2×C3×#686—21no—
12C2×C3×#677—21no—
13C2×C3×#677—21no—
14C3×#4020C2211yescharacteristic
15C3×#4015C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×C22⋊C8—21no—
18C3×C4×C5×C8C2211yescharacteristic
19C3×#3964—21no—
20C3×#3941—21no—
21C3×#3939—21no—
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24C3×#1685—51nomaximal, Hall
25C5×#436C2×C311yescharacteristic, complemented
26#65304C2×C311yescharacteristic
27#65296C2×C311yescharacteristic, complemented
28#64982C2×C311yescharacteristic, complemented
29#64705C2×C311yescharacteristic, complemented
30#64702C2×C311yescharacteristic, complemented
31#64678C2×C311yescharacteristic, complemented
32C2×C3×C5×D4D411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×C3×D20—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×Dic10—21no—
38C3×C5×M16—42no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8D411yescharacteristic
41C2×C3×C5×C8D411yescharacteristic
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45C3×#686—42no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C2×C3×#168—21no—
49C2×C3×#168—21no—
50C3×#677—42no—
51C3×#677—42no—
52C3×#492—51no—
53C3×#474—51no—
54C3×#459—51no—
55C3×#436D511yescharacteristic, complemented
56C3×#335—51no—
57C3×#332—51no—
58C3×#331—51no—
59C2×C5×M16—21no—
60C4×C5×D4C22×C311yescharacteristic
61C2×#686—21no—
62C2×#677—21no—
63C2×#677—21no—
64#4020C22×C311yescharacteristic
65#4015C22×C311yescharacteristic
66C5×C4⋊C8C22×C311yescharacteristic
67C5×C22⋊C8—21no—
68C4×C5×C8C22×C311yescharacteristic
69#3964—21no—
70#3941—21no—
71#3939—21no—
72C4⋊#168C22×C311yescharacteristic
73C4⋊#168C22×C311yescharacteristic
74#1685—51noSylow
75C23×C3×C5—21no—
76C22×C3×D5—41no—
77C3×C5×D4—21no—
78C3×C5×D4—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×Dic5—41no—
86C3×D20—41no—
87C3×D20—41no—
88C3×D20—41no—
89C3×D20—41no—
90C3×D20—81no—
91C3×Dic10—41no—
92C3×Dic10—41no—
93C3×C5×C8—21no—
94C3×C5×C8—41no—
95C3×C5×C8D812yescomplemented
96C3×#168—41no—
97C3×#168—41no—
98C2×C3×SD16—101no—
99C2×C3×SD16—101no—
100C2×C3×D8—101no—
101C2×C3×M16—21no—
102C3×C4⋊Q8—51no—
103C3×#127—51no—
104C3×C4×D4C2×D511yescharacteristic
105C3×#107—101no—
106C3×C4⋊C8—51no—
107C3×C4⋊C8—51no—
108C3×C4⋊C8C2×D511yescharacteristic
109C3×#102—101no—
110C3×#102—101no—
111C3×C22⋊C8—21no—
112C3×C4×C8C2×D511yescharacteristic
113C2×C5×D4C3×D411yescharacteristic
114C22×C4×C5—21no—
115C2×D20—21no—
116C2×D20—21no—
117C2×D20—21no—
118C2×Dic10—21no—
119C5×M16—42no—
120C2×C5×C8—21no—
121C2×C5×C8C3×D411yescharacteristic
122C2×C5×C8C3×D411yescharacteristic
123C5×C4⋊C4C3×D411yescharacteristic
124C5×C22⋊C4—21no—
125C42×C5C23×C311yescharacteristic
126#686—42no—
127C4⋊Dic5—21no—
128C4⋊Dic5—21no—
129C2×#168—21no—
130C2×#168—21no—
131#677—42no—
132#677—42no—
133#492—51no—
134#474—51no—
135#459—51no—
136#436C3×D511yescharacteristic, complemented
137#335—51no—
138#332—51no—
139#331—51no—
140C22×C3×C5—41no—
141C22×C3×C5—41no—
142C22×C3×C5—41no—
143C22×C3×C5#12111yescharacteristic
144C2×C3×D5—81no—
145C2×C3×D5—81no—
146C2×C3×D5—81no—
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—101no—
156C2×C3×D4—101no—
157C2×C3×D4—101no—
158C2×C3×D4D2011yescharacteristic
159C22×C3×C4—21no—
160C3×SD16—202no—
161C3×SD16—202no—
162C3×D8—202no—
163C3×M16—42no—
164C2×C3×C8—21no—
165C2×C3×C8—101no—
166C2×C3×C8—101no—
167C2×C3×C8C22⋊D511yescharacteristic
168C2×C3×C8C22⋊D511yescharacteristic
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4D2011yescharacteristic
172C3×C22⋊C4—21no—
173C3×C42C22×D511yescharacteristic
174C23×C5—21no—
175C22×D5—41no—
176C5×D4—21no—
177C5×D4—21no—
178C2×C4×C5—21no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5C2×C3×D411yescharacteristic
182C2×C4×C5C2×C3×D411yescharacteristic
183C2×C4×C5C3×#4111yescharacteristic
184C2×Dic5—41no—
185D20—41no—
186D20—41no—
187D20—41no—
188D20—41no—
189D20—81no—
190Dic10—41no—
191Dic10—41no—
192C5×C8—21no—
193C5×C8—41no—
194C5×C8C3×D812yescomplemented
195#168—41no—
196#168—41no—
197C2×SD16—101no—
198C2×SD16—101no—
199C2×D8—101no—
200C2×M16—21no—
201C4⋊Q8—51no—
202#127—51no—
203C4×D4C2×C3×D511yescharacteristic
204#107—101no—
205C4⋊C8—51no—
206C4⋊C8—51no—
207C4⋊C8C2×C3×D511yescharacteristic
208#102—101no—
209#102—101no—
210C22⋊C8—21no—
211C4×C8C2×C3×D511yescharacteristic
212C2×C3×C5—81no—
213C2×C3×C5#45911yescharacteristic
214C2×C3×C5#46811yescharacteristic
215C2×C3×C5#47111yescharacteristic
216C3×D5—161no—
217C23×C3—21no—
218C23×C3—201no—
219C3×Q8—201no—
220C3×Q8—201no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4—201no—
224C3×D4—201no—
225C3×D4—201no—
226C3×D4—201no—
227C3×D4—401no—
228C2×C3×C4—21no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—201no—
232C2×C3×C4C2×D2011yescharacteristic
233C2×C3×C4#70911yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C3×C8—21no—
236C3×C8—41no—
237C3×C8—201no—
238C3×C8—201no—
239C3×C8#68612yescomplemented
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5C3×#12111yescharacteristic
244C2×D5—81no—
245C2×D5—81no—
246C2×D5—81no—
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—101no—
256C2×D4—101no—
257C2×D4—101no—
258C2×D4C3×D2011yescharacteristic
259C22×C4—21no—
260SD16—202no—
261SD16—202no—
262D8—202no—
263M16—42no—
264C2×C8—21no—
265C2×C8—101no—
266C2×C8—101no—
267C2×C8C3×C22⋊D511yescharacteristic
268C2×C8C3×C22⋊D511yescharacteristic
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4C3×D2011yescharacteristic
272C22⋊C4—21no—
273C42C22×C3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—401no—
279C22×C3—401no—
280C22×C3—401no—
281C22×C3#407611yescharacteristic
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—401no—
285C3×C4#405411yescharacteristic
286C3×C4#405511yescharacteristic
287C3×C4C2×#68611yescharacteristic
288C3×C4#409511yescharacteristic
289C2×C5—81no—
290C2×C5C3×#45911yescharacteristic
291C2×C5C3×#46811yescharacteristic
292C2×C5C3×#47111yescharacteristic
293D5—161no—
294C23—21no—
295C23—201no—
296Q8—201no—
297Q8—201no—
298D4—21no—
299D4—21no—
300D4—201no—
301D4—201no—
302D4—201no—
303D4—201no—
304D4—401no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—201no—
309C2×C4C2×C3×D2011yescharacteristic
310C2×C4C3×#70911yescharacteristic
311C2×C4C2×C3×C22⋊D511yescharacteristic
312C8—21no—
313C8—41no—
314C8—201no—
315C8—201no—
316C8C3×#68612yescomplemented
317C2×C3—81no—
318C2×C3—801no—
319C2×C3#6530411yescharacteristic
320C2×C3#6542311yescharacteristic
321C2×C3#6543011yescharacteristic
322C5C3×#168511yescharacteristic, complemented, Sylow
323C22—41no—
324C22—41no—
325C22—41no—
326C22—401no—
327C22—401no—
328C22—401no—
329C22C3×#407611yescharacteristic
330C4—21no—
331C4—41no—
332C4—401no—
333C4C3×#405411yescharacteristic
334C4C3×#405511yescharacteristic
335C4C2×C3×#68611yescharacteristic
336C4C3×#409511yescharacteristic
337C3#1060166011yescharacteristic, direct product factor, Sylow
338C2—81no—
339C2—801no—
340C2C3×#6530411yescharacteristic
341C2C3×#6542311yescharacteristic
342C2C3×#6543011yescharacteristic
subgroupG/H
centerC22×C3#4076
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#436C2
socleC22×C3×C5#121
prime radicalC3×#65304C2
hypercenterC3×#436D5
hypocenterC5C3×#1685
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#436

Complements

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

NH ≅ G/Ntype
1. C3×C5×#436C2semidirect
3. C3×#65296C2semidirect
4. C3×#64982C2semidirect
5. C3×#64705C2semidirect
6. C3×#64702C2semidirect
7. C3×#64678C2semidirect
8. #10601660C3direct (N × H)
25. C5×#436C2×C3semidirect
27. #65296C2×C3semidirect
28. #64982C2×C3semidirect
29. #64705C2×C3semidirect
30. #64702C2×C3semidirect
31. #64678C2×C3semidirect
55. C3×#436D5semidirect
95. C3×C5×C8D8semidirect
136. #436C3×D5semidirect
194. C5×C8C3×D8semidirect
239. C3×C8#686semidirect
274. C3×C5#1685semidirect
316. C8C3×#686semidirect
322. C5C3×#1685semidirect
337. C3#10601660direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4362
C3×#653042
C3×#652962
C3×#649822
C3×#647052
C3×#647022
C3×#646782
#106016603
C3×#16855