Finite Group Databasebeta

← C3×#10601818 #14292514

Subgroups — C3×#10601818 #14292514

Order 1920.

368 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#460C211yesmaximal, characteristic, complemented
2C3×#65362C211yesmaximal, characteristic
3C3×#65316C211yesmaximal, characteristic, complemented
4C3×#65313C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64700C211yesmaximal, characteristic, complemented
8#10601818C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C2×C3×#688—21no—
13C2×C3×#686—21no—
14C2×C3×#686—21no—
15C3×#4020C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×#102—21no—
18C3×#3941—21no—
19C3×C4⋊#168—21no—
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×#3935—21no—
23C3×C4×#168C2211yescharacteristic
24C3×#1688—51nomaximal, Hall
25C5×#460C2×C311yescharacteristic, complemented
26#65362C2×C311yescharacteristic
27#65316C2×C311yescharacteristic, complemented
28#65313C2×C311yescharacteristic, complemented
29#64764C2×C311yescharacteristic, complemented
30#64705C2×C311yescharacteristic, complemented
31#64700C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8D411yescharacteristic
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C3×C5×SD16—42no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C3×#688—42no—
46C3×#686—42no—
47C3×#686—42no—
48C2×C3×#168—21no—
49C2×C3×#168—21no—
50C2×C3×#168D411yescharacteristic
51C2×C3×#168D411yescharacteristic
52C3×#493—51no—
53C3×#460—51no—
54C3×#460D511yescharacteristic, complemented
55C3×#446—51no—
56C3×#334—51no—
57C3×#331—51no—
58C3×#331—51no—
59C2×C5×SD16—21no—
60C5×#127C22×C311yescharacteristic
61C4×C5×Q8C22×C311yescharacteristic
62C2×#688—21no—
63C2×#686—21no—
64C2×#686—21no—
65#4020C22×C311yescharacteristic
66C5×C4⋊C8C22×C311yescharacteristic
67C5×#102—21no—
68#3941—21no—
69C4⋊#168—21no—
70C4⋊#168C22×C311yescharacteristic
71C4⋊#168C22×C311yescharacteristic
72#3935—21no—
73C4×#168C22×C311yescharacteristic
74#1688—51noSylow
75C23×C3×C5—41no—
76C22×C3×D5—41no—
77C3×C5×Q8—21no—
78C3×C5×Q8—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—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C3×D20—41no—
90C3×D20—41no—
91C3×D20—41no—
92C3×D20—41no—
93C3×D20—81no—
94C3×C5×C8—41no—
95C3×#168—21no—
96C3×#168—41no—
97C3×#168—41no—
98C3×#168SD1612yescomplemented
99C2×C3×SD16—21no—
100C2×C3×SD16—101no—
101C2×C3×D8—101no—
102C2×C3×D8—101no—
103C3×#127—51no—
104C3×#127C2×D511yescharacteristic
105C3×C4×Q8C2×D511yescharacteristic
106C3×C4⋊C8—51no—
107C3×C4⋊C8—51no—
108C3×C4⋊C8—101no—
109C3×C4⋊C8C2×D511yescharacteristic
110C3×#102—21no—
111C3×#102—101no—
112C3×#97—101no—
113C3×C4×C8—51no—
114C2×C5×Q8C3×D411yescharacteristic
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×C5×D4—21no—
118C2×D20—21no—
119C2×D20—21no—
120C2×D20—21no—
121C5×SD16—42no—
122C2×C5×C8—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4C3×D411yescharacteristic
125C42×C5—21no—
126C42×C5C23×C311yescharacteristic
127#688—42no—
128#686—42no—
129#686—42no—
130C2×#168—21no—
131C2×#168—21no—
132C2×#168C3×D411yescharacteristic
133C2×#168C3×D411yescharacteristic
134#493—51no—
135#460—51no—
136#460C3×D511yescharacteristic, complemented
137#446—51no—
138#334—51no—
139#331—51no—
140#331—51no—
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5—81no—
144C22×C3×C5#12111yescharacteristic
145C2×C3×D5—81no—
146C2×C3×D5—81no—
147C2×C3×D5—81no—
148C3×C4×C5—21no—
149C3×C4×C5—41no—
150C3×C4×C5—41no—
151C3×C4×C5C2×SD1611yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
154C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
155C2×C3×Q8C22⋊D511yescharacteristic
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—101no—
160C2×C3×D4—101no—
161C2×C3×D4—101no—
162C3×SD16—42no—
163C3×SD16—202no—
164C3×D8—202no—
165C3×D8—202no—
166C2×C3×C8—21no—
167C2×C3×C8—51no—
168C2×C3×C8—51no—
169C2×C3×C8—101no—
170C2×C3×C8—101no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4C22⋊D511yescharacteristic
173C3×C42—21no—
174C3×C42C22×D511yescharacteristic
175C23×C5—41no—
176C22×D5—41no—
177C5×Q8—21no—
178C5×Q8—21no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—41no—
183C5×D4—81no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5C2×C3×D411yescharacteristic
187C2×C4×C5C2×C3×D411yescharacteristic
188C2×C4×C5C3×#4111yescharacteristic
189D20—41no—
190D20—41no—
191D20—41no—
192D20—41no—
193D20—81no—
194C5×C8—41no—
195#168—21no—
196#168—41no—
197#168—41no—
198#168C3×SD1612yescomplemented
199C2×SD16—21no—
200C2×SD16—101no—
201C2×D8—101no—
202C2×D8—101no—
203#127—51no—
204#127C2×C3×D511yescharacteristic
205C4×Q8C2×C3×D511yescharacteristic
206C4⋊C8—51no—
207C4⋊C8—51no—
208C4⋊C8—101no—
209C4⋊C8C2×C3×D511yescharacteristic
210#102—21no—
211#102—101no—
212#97—101no—
213C4×C8—51no—
214C2×C3×C5—161no—
215C2×C3×C5#46011yescharacteristic
216C2×C3×C5#46911yescharacteristic
217C2×C3×C5#47211yescharacteristic
218C3×D5—161no—
219C23×C3—41no—
220C23×C3—201no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—81no—
228C3×D4—201no—
229C3×D4—201no—
230C3×D4—201no—
231C3×D4—201no—
232C3×D4—401no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4#71111yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C3×C8—41no—
239C3×C8—52no—
240C3×C8—101no—
241C3×C8—201no—
242C3×C8—201no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5C3×#12111yescharacteristic
247C2×D5—81no—
248C2×D5—81no—
249C2×D5—81no—
250C4×C5—21no—
251C4×C5—41no—
252C4×C5—41no—
253C4×C5C2×C3×SD1611yescharacteristic
254C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
255C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
256C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
257C2×Q8C3×C22⋊D511yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—101no—
262C2×D4—101no—
263C2×D4—101no—
264SD16—42no—
265SD16—202no—
266D8—202no—
267D8—202no—
268C2×C8—21no—
269C2×C8—51no—
270C2×C8—51no—
271C2×C8—101no—
272C2×C8—101no—
273C4⋊C4—21no—
274C4⋊C4C3×C22⋊D511yescharacteristic
275C42—21no—
276C42C22×C3×D511yescharacteristic
277C3×C5#168811yescharacteristic, complemented, Hall
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3—401no—
282C22×C3—401no—
283C22×C3—401no—
284C22×C3#408511yescharacteristic
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4D5×SD1611yescharacteristic
289C3×C4#406011yescharacteristic
290C3×C4#407811yescharacteristic
291C3×C4#409511yescharacteristic
292C2×C5—161no—
293C2×C5C3×#46011yescharacteristic
294C2×C5C3×#46911yescharacteristic
295C2×C5C3×#47211yescharacteristic
296D5—161no—
297C23—41no—
298C23—201no—
299Q8—21no—
300Q8—21no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—201no—
307D4—201no—
308D4—201no—
309D4—201no—
310D4—401no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4C3×D4×D511yescharacteristic
314C2×C4C3×#71111yescharacteristic
315C2×C4C2×C3×C22⋊D511yescharacteristic
316C8—41no—
317C8—52no—
318C8—101no—
319C8—201no—
320C8—201no—
321C2×C3—161no—
322C2×C3—801no—
323C2×C3#6532811yescharacteristic
324C2×C3#6545211yescharacteristic
325C2×C3#6548811yescharacteristic
326C5C3×#168811yescharacteristic, complemented, Sylow
327C22—81no—
328C22—81no—
329C22—81no—
330C22—401no—
331C22—401no—
332C22—401no—
333C22C3×#408511yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4C3×D5×SD1611yescharacteristic
338C4C3×#406011yescharacteristic
339C4C3×#407811yescharacteristic
340C4C3×#409511yescharacteristic
341C3#1060181811yescharacteristic, direct product factor, Sylow
342C2—161no—
343C2—801no—
344C2C3×#6532811yescharacteristic
345C2C3×#6545211yescharacteristic
346C2C3×#6548811yescharacteristic
subgroupG/H
centerC22×C3#4085
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#460C2
socleC22×C3×C5#121
prime radicalC3×#65362C2
hypercenterC3×#460D5
hypocenterC5C3×#1688
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C3×C5×#460C2semidirect
3. C3×#65316C2semidirect
4. C3×#65313C2semidirect
5. C3×#64764C2semidirect
6. C3×#64705C2semidirect
7. C3×#64700C2semidirect
8. #10601818C3direct (N × H)
25. C5×#460C2×C3semidirect
27. #65316C2×C3semidirect
28. #65313C2×C3semidirect
29. #64764C2×C3semidirect
30. #64705C2×C3semidirect
31. #64700C2×C3semidirect
54. C3×#460D5semidirect
98. C3×#168SD16semidirect
136. #460C3×D5semidirect
198. #168C3×SD16semidirect
277. C3×C5#1688semidirect
326. C5C3×#1688semidirect
341. C3#10601818direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4602
C3×#653622
C3×#653162
C3×#653132
C3×#647642
C3×#647052
C3×#647002
#106018183
C3×#16885