Finite Group Databasebeta

← C3×#10601652 #14287253

Subgroups — C3×#10601652 #14287253

Order 1920.

360 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#436C211yesmaximal, characteristic, complemented
2C3×C4×#686C211yesmaximal, characteristic
3C3×#64977C211yesmaximal, characteristic, complemented
4C3×D4⋊#168C211yesmaximal, characteristic, complemented
5C3×#64703C211yesmaximal, characteristic, complemented
6C3×#64699C211yesmaximal, characteristic, complemented
7C3×C8×#168C211yesmaximal, characteristic, complemented
8#10601652C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×M16—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C2×C3×#686C411yescharacteristic
12C2×C3×#676—21no—
13C3×C4×D20C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C22⋊C8—21no—
16C3×C4×C5×C8C2211yescharacteristic
17C3×#3964C411yescharacteristic
18C3×#3952—21no—
19C3×#3941C411yescharacteristic
20C3×#3939C411yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1589—51nomaximal, Hall
25C5×#436C2×C311yescharacteristic, complemented
26C4×#686C2×C311yescharacteristic
27#64977C2×C311yescharacteristic, complemented
28D4⋊#168C2×C311yescharacteristic, complemented
29#64703C2×C311yescharacteristic, complemented
30#64699C2×C311yescharacteristic, complemented
31C8×#168C2×C311yescharacteristic, complemented
32C2×C3×C5×D4C2×C411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C3×C5×M16—42no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8D411yescharacteristic
40C3×C5×C4⋊C4C2×C411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C3×#686—22no—
44C3×#685—21no—
45C3×C4⋊Dic5C2×C411yescharacteristic
46C2×C3×#168—21no—
47C2×C3×#168—21no—
48C2×C3×#168C2×C411yescharacteristic
49C2×C3×#168C2×C411yescharacteristic
50C3×#676—42no—
51C3×C4×D8—51no—
52C3×#436—51no—
53C3×#436D511yescharacteristic, complemented
54C3×#335—51no—
55C3×D4⋊C8—51no—
56C3×D4⋊C8—51no—
57C3×C82—51no—
58C2×C5×M16—21no—
59C4×C5×D4C22×C311yescharacteristic
60C2×#686C3×C411yescharacteristic
61C2×#676—21no—
62C4×D20C22×C311yescharacteristic
63C5×C4⋊C8C22×C311yescharacteristic
64C5×C22⋊C8—21no—
65C4×C5×C8C22×C311yescharacteristic
66#3964C3×C411yescharacteristic
67#3952—21no—
68#3941C3×C411yescharacteristic
69#3939C3×C411yescharacteristic
70C4⋊#168C22×C311yescharacteristic
71C4×#168C22×C311yescharacteristic
72C4×#168C22×C311yescharacteristic
73#1589—51noSylow
74C23×C3×C5—21no—
75C22×C3×D5—21no—
76C3×C5×D4—21no—
77C3×C5×D4—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×C3×Dic5—21no—
85C3×D20—21no—
86C3×D20—21no—
87C3×C4×D5—41no—
88C3×C4×D5—41no—
89C3×C5×C8—21no—
90C3×C5×C8—41no—
91C3×C5×C8D812yescomplemented
92C3×#168—22no—
93C3×#168—21no—
94C3×#168—41no—
95C3×#168M1612yescomplemented
96C2×C3×D8—51no—
97C2×C3×M16—21no—
98C2×C3×M16—101no—
99C3×C4×D4—51no—
100C3×C4×D4C2×D511yescharacteristic
101C3×#107—51no—
102C3×C4⋊C8—51no—
103C3×C4⋊C8C2×D511yescharacteristic
104C3×#102—51no—
105C3×#102—51no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8—101no—
108C3×C4×C8—51no—
109C3×C4×C8—51no—
110C3×C4×C8C2×D511yescharacteristic
111C2×C5×D4C2×C3×C411yescharacteristic
112C22×C4×C5—21no—
113C2×D20C2×C3×C411yescharacteristic
114C2×C4×D5—21no—
115C5×M16—42no—
116C2×C5×C8—21no—
117C2×C5×C8C3×D411yescharacteristic
118C2×C5×C8C3×D411yescharacteristic
119C5×C4⋊C4C2×C3×C411yescharacteristic
120C5×C22⋊C4—21no—
121C42×C5C23×C311yescharacteristic
122#686—22no—
123#685—21no—
124C4⋊Dic5C2×C3×C411yescharacteristic
125C2×#168—21no—
126C2×#168—21no—
127C2×#168C2×C3×C411yescharacteristic
128C2×#168C2×C3×C411yescharacteristic
129#676—42no—
130C4×D8—51no—
131#436—51no—
132#436C3×D511yescharacteristic, complemented
133#335—51no—
134D4⋊C8—51no—
135D4⋊C8—51no—
136C82—51no—
137C22×C3×C5—41no—
138C22×C3×C5—41no—
139C22×C3×C5—41no—
140C22×C3×C5C4×D411yescharacteristic
141C2×C3×D5—41no—
142C2×C3×D5—41no—
143C2×C3×D5—41no—
144C3×C4×C5—21no—
145C3×C4×C5—41no—
146C3×C4×C5C2×M1611yescharacteristic
147C3×C4×C5#13111yescharacteristic
148C3×C4×C5C2×D811yescharacteristic
149C3×C4×C5#13511yescharacteristic
150C3×Dic5—41no—
151C2×C3×D4—51no—
152C2×C3×D4C4×D511yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—101no—
155C3×D8—102no—
156C3×M16—42no—
157C3×M16—202no—
158C2×C3×C8—21no—
159C2×C3×C8—51no—
160C2×C3×C8—51no—
161C2×C3×C8—101no—
162C2×C3×C8—101no—
163C2×C3×C8C22⋊D511yescharacteristic
164C2×C3×C8C22⋊D511yescharacteristic
165C3×C4⋊C4—51no—
166C3×C4⋊C4C4×D511yescharacteristic
167C3×C22⋊C4—21no—
168C3×C22⋊C4—101no—
169C3×C42C22×D511yescharacteristic
170C23×C5—21no—
171C22×D5—21no—
172C5×D4—21no—
173C5×D4—21no—
174C2×C4×C5—21no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5C22×C3×C411yescharacteristic
178C2×C4×C5C2×C3×D411yescharacteristic
179C2×C4×C5C3×#4111yescharacteristic
180C2×Dic5—21no—
181D20—21no—
182D20—21no—
183C4×D5—41no—
184C4×D5—41no—
185C5×C8—21no—
186C5×C8—41no—
187C5×C8C3×D812yescomplemented
188#168—22no—
189#168—21no—
190#168—41no—
191#168C3×M1612yescomplemented
192C2×D8—51no—
193C2×M16—21no—
194C2×M16—101no—
195C4×D4—51no—
196C4×D4C2×C3×D511yescharacteristic
197#107—51no—
198C4⋊C8—51no—
199C4⋊C8C2×C3×D511yescharacteristic
200#102—51no—
201#102—51no—
202C22⋊C8—21no—
203C22⋊C8—101no—
204C4×C8—51no—
205C4×C8—51no—
206C4×C8C2×C3×D511yescharacteristic
207C2×C3×C5—81no—
208C2×C3×C5#43611yescharacteristic
209C2×C3×C5C4×D811yescharacteristic
210C2×C3×C5#44311yescharacteristic
211C3×D5—81no—
212C23×C3—21no—
213C23×C3—101no—
214C3×D4—21no—
215C3×D4—21no—
216C3×D4—101no—
217C3×D4—101no—
218C2×C3×C4—21no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—101no—
222C2×C3×C4—201no—
223C2×C3×C4—201no—
224C2×C3×C4C2×C4×D511yescharacteristic
225C2×C3×C4#70911yescharacteristic
226C2×C3×C4C2×C22⋊D511yescharacteristic
227C3×C8—21no—
228C3×C8—41no—
229C3×C8—52no—
230C3×C8—102no—
231C3×C8—101no—
232C3×C8—201no—
233C3×C8#68612yescomplemented
234C22×C5—41no—
235C22×C5—41no—
236C22×C5—41no—
237C22×C5C3×C4×D411yescharacteristic
238C2×D5—41no—
239C2×D5—41no—
240C2×D5—41no—
241C4×C5—21no—
242C4×C5—41no—
243C4×C5C2×C3×M1611yescharacteristic
244C4×C5C3×#13111yescharacteristic
245C4×C5C2×C3×D811yescharacteristic
246C4×C5C3×#13511yescharacteristic
247Dic5—41no—
248C2×D4—51no—
249C2×D4C3×C4×D511yescharacteristic
250C22×C4—21no—
251C22×C4—101no—
252D8—102no—
253M16—42no—
254M16—202no—
255C2×C8—21no—
256C2×C8—51no—
257C2×C8—51no—
258C2×C8—101no—
259C2×C8—101no—
260C2×C8C3×C22⋊D511yescharacteristic
261C2×C8C3×C22⋊D511yescharacteristic
262C4⋊C4—51no—
263C4⋊C4C3×C4×D511yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—101no—
266C42C22×C3×D511yescharacteristic
267C3×C5#158911yescharacteristic, complemented, Hall
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—201no—
272C22×C3—201no—
273C22×C3—201no—
274C22×C3C4×C22⋊D511yescharacteristic
275C3×C4—21no—
276C3×C4—41no—
277C3×C4—201no—
278C3×C4D5×M1611yescharacteristic
279C3×C4#405311yescharacteristic
280C3×C4C2×#68611yescharacteristic
281C3×C4#409611yescharacteristic
282C2×C5—81no—
283C2×C5C3×#43611yescharacteristic
284C2×C5C3×C4×D811yescharacteristic
285C2×C5C3×#44311yescharacteristic
286D5—81no—
287C23—21no—
288C23—101no—
289D4—21no—
290D4—21no—
291D4—101no—
292D4—101no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—101no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4C2×C3×C4×D511yescharacteristic
300C2×C4C3×#70911yescharacteristic
301C2×C4C2×C3×C22⋊D511yescharacteristic
302C8—21no—
303C8—41no—
304C8—52no—
305C8—102no—
306C8—101no—
307C8—201no—
308C8C3×#68612yescomplemented
309C2×C3—81no—
310C2×C3—401no—
311C2×C3C4×#68611yescharacteristic
312C2×C3#6541711yescharacteristic
313C2×C3#6543311yescharacteristic
314C5C3×#158911yescharacteristic, complemented, Sylow
315C22—41no—
316C22—41no—
317C22—41no—
318C22—201no—
319C22—201no—
320C22—201no—
321C22C3×C4×C22⋊D511yescharacteristic
322C4—21no—
323C4—41no—
324C4—201no—
325C4C3×D5×M1611yescharacteristic
326C4C3×#405311yescharacteristic
327C4C2×C3×#68611yescharacteristic
328C4C3×#409611yescharacteristic
329C3#1060165211yescharacteristic, direct product factor, Sylow
330C2—81no—
331C2—401no—
332C2C3×C4×#68611yescharacteristic
333C2C3×#6541711yescharacteristic
334C2C3×#6543311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#436C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×#686C4
cosocleC42×C5C23×C3
hypercenterC3×#436D5
hypocenterC5C3×#1589
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×#436

Complements

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

NH ≅ G/Ntype
1. C3×C5×#436C2semidirect
3. C3×#64977C2semidirect
4. C3×D4⋊#168C2semidirect
5. C3×#64703C2semidirect
6. C3×#64699C2semidirect
7. C3×C8×#168C2semidirect
8. #10601652C3direct (N × H)
25. C5×#436C2×C3semidirect
27. #64977C2×C3semidirect
28. D4⋊#168C2×C3semidirect
29. #64703C2×C3semidirect
30. #64699C2×C3semidirect
31. C8×#168C2×C3semidirect
53. C3×#436D5semidirect
91. C3×C5×C8D8semidirect
95. C3×#168M16semidirect
132. #436C3×D5semidirect
187. C5×C8C3×D8semidirect
191. #168C3×M16semidirect
233. C3×C8#686semidirect
267. C3×C5#1589semidirect
308. C8C3×#686semidirect
314. C5C3×#1589semidirect
329. C3#10601652direct (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×C4×#6862
C3×#649772
C3×D4⋊#1682
C3×#647032
C3×#646992
C3×C8×#1682
#106016523
C3×#15895