Finite Group Databasebeta

← C3×#10600014 #14313892

Subgroups — C3×#10600014 #14313892

Order 1920.

464 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4065C211yesmaximal, characteristic
2C2×C3×#3930C211yesmaximal, characteristic, complemented
3C3×D5×#107C211yesmaximal, characteristic, complemented
4C3×C5×#358C211yesmaximal, characteristic, complemented
5C3×#64784C211yesmaximal, characteristic, complemented
6C3×#64729C211yesmaximal, characteristic, complemented
7C3×#64711C211yesmaximal, characteristic, complemented
8#10600014C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×C3×#688—21no—
12C3×#4065—22no—
13C3×#4065C414yescomplemented
14C2×C3×D40C2211yescharacteristic
15C2×C3×C8×D5C2211yescharacteristic
16C3×D5×C4⋊C4—21no—
17C2×C3×C5×C16C2211yescharacteristic
18C3×C5×#107C2211yescharacteristic
19C3×#3950C2211yescharacteristic
20C2×C3×#672C2211yescharacteristic
21C3×#3939—21no—
22C3×#3930—22no—
23C3×#2139—51nomaximal, Hall
24C2×#4065C2×C311yescharacteristic
25C2×#3930C2×C311yescharacteristic, complemented
26D5×#107C2×C311yescharacteristic, complemented
27C5×#358C2×C311yescharacteristic, complemented
28#64784C2×C311yescharacteristic, complemented
29#64729C2×C311yescharacteristic, complemented
30#64711C2×C311yescharacteristic, complemented
31C2×C3×C5×Q8—21no—
32C3×#713—24no—
33C3×#713—42no—
34C2×C3×D20—21no—
35C2×C3×D20—41no—
36C2×C3×C4×D5—41no—
37C2×C3×C4×D5—41no—
38C2×C3×C4×D5D411yescharacteristic
39C3×C5×Q16—21no—
40C3×C5×Q16C2×C412yescomplemented
41C2×C3×C5×C8C2311yescharacteristic
42C3×C5×C4⋊C4—21no—
43C3×#688—24no—
44C3×C4⋊Dic5—21no—
45C3×#683—41no—
46C2×C3×#168D411yescharacteristic
47C3×D40—21no—
48C3×D40C2×C412yescomplemented
49C3×C8×D5C2×C412yes—
50C3×C8×D5D412yes—
51C3×C5×C16—21no—
52C3×#672—21no—
53C2×C3×#135—51no—
54C2×C3×M32—51no—
55C2×C3×#107—51no—
56C3×#358—51no—
57C3×#358D511yescharacteristic, complemented
58C3×#357—51no—
59C3×#357—51no—
60C2×#713—21no—
61C2×C5×Q16C22×C311yescharacteristic
62C2×#688—21no—
63#4065—22no—
64#4065C3×C414yescomplemented
65C2×D40C22×C311yescharacteristic
66C2×C8×D5C22×C311yescharacteristic
67D5×C4⋊C4—21no—
68C2×C5×C16C22×C311yescharacteristic
69C5×#107C22×C311yescharacteristic
70#3950C22×C311yescharacteristic
71C2×#672C22×C311yescharacteristic
72#3939—21no—
73#3930—22no—
74#2139—51noSylow
75C22×C3×D5—41no—
76C22×C3×D5D811yescharacteristic
77C3×C5×Q8—22no—
78C3×C5×Q8—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×Dic5—41no—
83C2×C3×Dic5D811yescharacteristic
84C3×D20—22no—
85C3×D20—44no—
86C3×D20—41no—
87C3×C4×D5—44no—
88C3×C4×D5—82no—
89C3×C4×D5C22⋊C412yes—
90C3×C4×D5SD1612yes—
91C3×C5×C8C22×C411yescharacteristic
92C3×C5×C8C2×D411yescharacteristic
93C3×#168C22⋊C412yes—
94C2×C3×#41—101no—
95C3×#135—54no—
96C3×#135—102no—
97C2×C3×Q16C2×D511yescharacteristic
98C2×C3×SD16—101no—
99C2×C3×D8—51no—
100C22×C3×C8—51no—
101C2×C3×C4⋊C4—101no—
102C3×M32—102no—
103C2×C3×C16—51no—
104C2×C3×C16C2×D511yescharacteristic
105C3×#107—51no—
106C3×#107—101no—
107C3×#107C2×D511yescharacteristic
108C2×C5×Q8—21no—
109#713—24no—
110#713—42no—
111C2×D20—21no—
112C2×D20—41no—
113C2×C4×D5—41no—
114C2×C4×D5—41no—
115C2×C4×D5C3×D411yescharacteristic
116C5×Q16—21no—
117C5×Q16C2×C3×C412yescomplemented
118C2×C5×C8C23×C311yescharacteristic
119C5×C4⋊C4—21no—
120#688—24no—
121C4⋊Dic5—21no—
122#683—41no—
123C2×#168C3×D411yescharacteristic
124D40—21no—
125D40C2×C3×C412yescomplemented
126C8×D5C2×C3×C412yes—
127C8×D5C3×D412yes—
128C5×C16—21no—
129#672—21no—
130C2×#135—51no—
131C2×M32—51no—
132C2×#107—51no—
133#358—51no—
134#358C3×D511yescharacteristic, complemented
135#357—51no—
136#357—51no—
137C22×C3×C5C2×D811yescharacteristic
138C2×C3×D5—21no—
139C2×C3×D5—21no—
140C2×C3×D5—42no—
141C2×C3×D5—81no—
142C2×C3×D5—81no—
143C2×C3×D5#10212yes—
144C3×C4×C5—42no—
145C3×C4×C5—81no—
146C3×C4×C5C2×C22⋊C411yescharacteristic
147C3×C4×C5C2×SD1611yescharacteristic
148C3×Dic5—81no—
149C3×Dic5#10212yes—
150C3×#41—104no—
151C3×#41—202no—
152C2×C3×Q8—21no—
153C2×C3×D4—101no—
154C2×C3×D4—201no—
155C22×C3×C4—51no—
156C22×C3×C4—201no—
157C22×C3×C4—201no—
158C3×Q16—21no—
159C3×Q16C4×D512yescomplemented
160C3×SD16—104no—
161C3×D8—52no—
162C3×D8—101no—
163C2×C3×C8—51no—
164C2×C3×C8—52no—
165C2×C3×C8—52no—
166C2×C3×C8C22×D511yescharacteristic
167C3×C4⋊C4—21no—
168C3×C4⋊C4—101no—
169C3×C4⋊C4—201no—
170C3×C16—21no—
171C3×C16—101no—
172C22×D5—41no—
173C22×D5C3×D811yescharacteristic
174C5×Q8—22no—
175C5×Q8—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5C2×C3×D411yescharacteristic
179C2×Dic5—41no—
180C2×Dic5C3×D811yescharacteristic
181D20—22no—
182D20—44no—
183D20—41no—
184C4×D5—44no—
185C4×D5—82no—
186C4×D5C3×C22⋊C412yes—
187C4×D5C3×SD1612yes—
188C5×C8C22×C3×C411yescharacteristic
189C5×C8C2×C3×D411yescharacteristic
190#168C3×C22⋊C412yes—
191C2×#41—101no—
192#135—54no—
193#135—102no—
194C2×Q16C2×C3×D511yescharacteristic
195C2×SD16—101no—
196C2×D8—51no—
197C22×C8—51no—
198C2×C4⋊C4—101no—
199M32—102no—
200C2×C16—51no—
201C2×C16C2×C3×D511yescharacteristic
202#107—51no—
203#107—101no—
204#107C2×C3×D511yescharacteristic
205C2×C3×C5C2×#10211yescharacteristic
206C2×C3×C5#50911yescharacteristic
207C2×C3×C5#51011yescharacteristic
208C3×D5—22no—
209C3×D5—82no—
210C23×C3—51no—
211C23×C3—201no—
212C3×Q8—22no—
213C3×Q8—41no—
214C3×D4—102no—
215C3×D4—204no—
216C3×D4—201no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—51no—
220C2×C3×C4—52no—
221C2×C3×C4—52no—
222C2×C3×C4—204no—
223C2×C3×C4—201no—
224C2×C3×C4—402no—
225C2×C3×C4D4×D511yescharacteristic
226C3×C8—52no—
227C3×C8C2×C4×D511yescharacteristic
228C3×C8D4×D511yescharacteristic
229C22×C5C2×C3×D811yescharacteristic
230C2×D5—21no—
231C2×D5—21no—
232C2×D5—42no—
233C2×D5—81no—
234C2×D5—81no—
235C2×D5C3×#10212yes—
236C4×C5—42no—
237C4×C5—81no—
238C4×C5C2×C3×C22⋊C411yescharacteristic
239C4×C5C2×C3×SD1611yescharacteristic
240Dic5—81no—
241Dic5C3×#10212yes—
242#41—104no—
243#41—202no—
244C2×Q8—21no—
245C2×D4—101no—
246C2×D4—201no—
247C22×C4—51no—
248C22×C4—201no—
249C22×C4—201no—
250Q16—21no—
251Q16C3×C4×D512yescomplemented
252SD16—104no—
253D8—52no—
254D8—101no—
255C2×C8—51no—
256C2×C8—52no—
257C2×C8—52no—
258C2×C8C22×C3×D511yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—101no—
261C4⋊C4—201no—
262C16—21no—
263C16—101no—
264C3×C5#213911yescharacteristic, complemented, Hall
265C22×C3—52no—
266C22×C3—101no—
267C22×C3—101no—
268C22×C3—202no—
269C22×C3—401no—
270C22×C3—401no—
271C22×C3D5×D811yescharacteristic
272C3×C4—42no—
273C3×C4—52no—
274C3×C4—81no—
275C3×C4—401no—
276C3×C4D5×C22⋊C411yescharacteristic
277C3×C4D5×SD1611yescharacteristic
278C2×C5C2×C3×#10211yescharacteristic
279C2×C5C3×#50911yescharacteristic
280C2×C5C3×#51011yescharacteristic
281D5—22no—
282D5—82no—
283C23—51no—
284C23—201no—
285Q8—22no—
286Q8—41no—
287D4—102no—
288D4—204no—
289D4—201no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—51no—
293C2×C4—52no—
294C2×C4—52no—
295C2×C4—204no—
296C2×C4—201no—
297C2×C4—402no—
298C2×C4C3×D4×D511yescharacteristic
299C8—52no—
300C8C2×C3×C4×D511yescharacteristic
301C8C3×D4×D511yescharacteristic
302C2×C3—102no—
303C2×C3—402no—
304C2×C3D5×#10211yescharacteristic
305C2×C3#6520311yescharacteristic
306C2×C3#6520711yescharacteristic
307C5C3×#213911yescharacteristic, complemented, Sylow
308C22—52no—
309C22—101no—
310C22—101no—
311C22—202no—
312C22—401no—
313C22—401no—
314C22C3×D5×D811yescharacteristic
315C4—42no—
316C4—52no—
317C4—81no—
318C4—401no—
319C4C3×D5×C22⋊C411yescharacteristic
320C4C3×D5×SD1611yescharacteristic
321C3#1060001411yescharacteristic, direct product factor, Sylow
322C2—102no—
323C2—402no—
324C2C3×D5×#10211yescharacteristic
325C2C3×#6520311yescharacteristic
326C2C3×#6520711yescharacteristic
subgroupG/H
centerC22×C3D5×D8
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#358C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×#4065C2
cosocleC2×C5×C8C23×C3
hypercenterC3×#358D5
hypocenterC5C3×#2139
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#358

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3930C2semidirect
3. C3×D5×#107C2semidirect
4. C3×C5×#358C2semidirect
5. C3×#64784C2semidirect
6. C3×#64729C2semidirect
7. C3×#64711C2semidirect
8. #10600014C3direct (N × H)
13. C3×#4065C4semidirect
25. C2×#3930C2×C3semidirect
26. D5×#107C2×C3semidirect
27. C5×#358C2×C3semidirect
28. #64784C2×C3semidirect
29. #64729C2×C3semidirect
30. #64711C2×C3semidirect
40. C3×C5×Q16C2×C4semidirect
48. C3×D40C2×C4semidirect
57. C3×#358D5semidirect
64. #4065C3×C4semidirect
117. C5×Q16C2×C3×C4semidirect
125. D40C2×C3×C4semidirect
134. #358C3×D5semidirect
159. C3×Q16C4×D5semidirect
251. Q16C3×C4×D5semidirect
264. C3×C5#2139semidirect
307. C5C3×#2139semidirect
321. C3#10600014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40652
C2×C3×#39302
C3×D5×#1072
C3×C5×#3582
C3×#647842
C3×#647292
C3×#647112
#106000143
C3×#21395