Finite Group Databasebeta

← C3×#10602875 #14316104

Subgroups — C3×#10602875 #14316104

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#135C211yesmaximal, characteristic, complemented
2C2×C3×#3960C211yesmaximal, characteristic, complemented
3C2×C3×#3958C211yesmaximal, characteristic, complemented
4C3×#65404C211yesmaximal, characteristic, complemented
5C3×#64784C211yesmaximal, characteristic, complemented
6C3×#64782C211yesmaximal, characteristic, complemented
7C3×C22⋊#672C211yesmaximal, characteristic, complemented
8#10602875C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#135—22no—
11C3×C5×#135—22no—
12C2×C3×C5×Q16C2211yescharacteristic
13C2×C3×C5×SD16—21no—
14C2×C3×C5×D8C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C3×#4076—21no—
17C2×C3×D40C2211yescharacteristic
18C3×#3960—22no—
19C3×#3958—22no—
20C3×#3953—21no—
21C3×#3950C2211yescharacteristic
22C2×C3×#672C2211yescharacteristic
23C2×C3×#672C2211yescharacteristic
24C3×#2186—51nomaximal, Hall
25C2×C5×#135C2×C311yescharacteristic, complemented
26C2×#3960C2×C311yescharacteristic, complemented
27C2×#3958C2×C311yescharacteristic, complemented
28#65404C2×C311yescharacteristic, complemented
29#64784C2×C311yescharacteristic, complemented
30#64782C2×C311yescharacteristic, complemented
31C22⋊#672C2×C311yescharacteristic, complemented
32C3×C5×#41—24no—
33C3×C5×#41—42no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—41no—
37C22×C3×C4×C5—41no—
38C22×C3×C4×C5D411yescharacteristic
39C2×C3×C22⋊D5—41no—
40C2×C3×D20—21no—
41C3×C5×Q16—21no—
42C3×C5×Q16D412yescomplemented
43C3×C5×SD16—24no—
44C3×C5×D8—21no—
45C3×C5×D8D412yescomplemented
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8D411yescharacteristic
49C2×C3×C5×C8C2311yescharacteristic
50C3×#685—41no—
51C3×C4⋊Dic5—21no—
52C3×D40—21no—
53C3×D40—21no—
54C3×#672—21no—
55C3×#672—21no—
56C2×C3×#135D511yescharacteristic, complemented
57C2×C3×SD32—51no—
58C2×C3×D16—51no—
59C3×#466—51no—
60C3×#358—51no—
61C3×#357—51no—
62C3×C22⋊C16—51no—
63C2×C5×#41—21no—
64C5×#135—22no—
65C5×#135—22no—
66C2×C5×Q16C22×C311yescharacteristic
67C2×C5×SD16—21no—
68C2×C5×D8C22×C311yescharacteristic
69C22×C5×C8C22×C311yescharacteristic
70#4076—21no—
71C2×D40C22×C311yescharacteristic
72#3960—22no—
73#3958—22no—
74#3953—21no—
75#3950C22×C311yescharacteristic
76C2×#672C22×C311yescharacteristic
77C2×#672C22×C311yescharacteristic
78#2186—51noSylow
79C23×C3×C5—41no—
80C23×C3×C5D811yescharacteristic
81C22×C3×D5—41no—
82C3×C5×Q8—22no—
83C3×C5×Q8—41no—
84C3×C5×D4—22no—
85C3×C5×D4—44no—
86C3×C5×D4—41no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—44no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5D811yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C3×C22⋊D5—82no—
94C2×C3×Dic5—41no—
95C3×D20—41no—
96C3×D20—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×C3×#41—21no—
101C3×#135—22no—
102C3×#135—22no—
103C2×C3×Q16C2×D511yescharacteristic
104C2×C3×SD16—21no—
105C2×C3×D8—51no—
106C2×C3×D8C2×D511yescharacteristic
107C22×C3×C8C2×D511yescharacteristic
108C3×#121—101no—
109C3×SD32—102no—
110C3×D16—102no—
111C2×C3×C16—51no—
112C2×C3×C16—51no—
113C3×#107—51no—
114C3×#102—101no—
115C5×#41—24no—
116C5×#41—42no—
117C2×C5×Q8—21no—
118C2×C5×D4—21no—
119C2×C5×D4—41no—
120C22×C4×C5—41no—
121C22×C4×C5C3×D411yescharacteristic
122C2×C22⋊D5—41no—
123C2×D20—21no—
124C5×Q16—21no—
125C5×Q16C3×D412yescomplemented
126C5×SD16—24no—
127C5×D8—21no—
128C5×D8C3×D412yescomplemented
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C2×C5×C8C3×D411yescharacteristic
132C2×C5×C8C23×C311yescharacteristic
133#685—41no—
134C4⋊Dic5—21no—
135D40—21no—
136D40—21no—
137#672—21no—
138#672—21no—
139C2×#135C3×D511yescharacteristic, complemented
140C2×SD32—51no—
141C2×D16—51no—
142#466—51no—
143#358—51no—
144#357—51no—
145C22⋊C16—51no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—42no—
150C22×C3×C5—81no—
151C22×C3×C5—81no—
152C22×C3×C5C2×D811yescharacteristic
153C2×C3×D5—81no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C3×C4×C5—21no—
157C3×C4×C5—42no—
158C3×C4×C5#12011yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×Dic5—81no—
161C3×#41—24no—
162C3×#41—42no—
163C2×C3×Q8—21no—
164C2×C3×D4—21no—
165C2×C3×D4—41no—
166C2×C3×D4—101no—
167C2×C3×D4—201no—
168C22×C3×C4—41no—
169C22×C3×C4C22⋊D511yescharacteristic
170C3×Q16—21no—
171C3×Q16C22⋊D512yescomplemented
172C3×SD16—24no—
173C3×D8—21no—
174C3×D8—101no—
175C3×D8—101no—
176C3×D8C22⋊D512yescomplemented
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8C22⋊D511yescharacteristic
180C2×C3×C8C22×D511yescharacteristic
181C3×C4⋊C4—101no—
182C3×C22⋊C4—201no—
183C3×C16—101no—
184C3×C16—101no—
185C23×C5—41no—
186C23×C5C3×D811yescharacteristic
187C22×D5—41no—
188C5×Q8—22no—
189C5×Q8—41no—
190C5×D4—22no—
191C5×D4—44no—
192C5×D4—41no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—44no—
196C2×C4×C5—41no—
197C2×C4×C5C3×D811yescharacteristic
198C2×C4×C5C2×C3×D411yescharacteristic
199C22⋊D5—82no—
200C2×Dic5—41no—
201D20—41no—
202D20—41no—
203C5×C8—21no—
204C5×C8C2×C3×D411yescharacteristic
205C5×C8C2×C3×D411yescharacteristic
206C2×#41—21no—
207#135—22no—
208#135—22no—
209C2×Q16C2×C3×D511yescharacteristic
210C2×SD16—21no—
211C2×D8—51no—
212C2×D8C2×C3×D511yescharacteristic
213C22×C8C2×C3×D511yescharacteristic
214#121—101no—
215SD32—102no—
216D16—102no—
217C2×C16—51no—
218C2×C16—51no—
219#107—51no—
220#102—101no—
221C2×C3×C5—41no—
222C2×C3×C5—82no—
223C2×C3×C5#44711yescharacteristic
224C2×C3×C5#50811yescharacteristic
225C2×C3×C5#50911yescharacteristic
226C3×D5—161no—
227C23×C3—41no—
228C23×C3—201no—
229C23×C3#68611yescharacteristic
230C3×Q8—22no—
231C3×Q8—41no—
232C3×D4—22no—
233C3×D4—44no—
234C3×D4—41no—
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—402no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—44no—
241C2×C3×C4—41no—
242C2×C3×C4—201no—
243C2×C3×C4#68611yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C3×C8—21no—
246C3×C8C2×C22⋊D511yescharacteristic
247C3×C8C2×C22⋊D511yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—42no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5C2×C3×D811yescharacteristic
255C2×D5—81no—
256C2×D5—81no—
257C2×D5—81no—
258C4×C5—21no—
259C4×C5—42no—
260C4×C5C3×#12011yescharacteristic
261C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
262Dic5—81no—
263#41—24no—
264#41—42no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—101no—
269C2×D4—201no—
270C22×C4—41no—
271C22×C4C3×C22⋊D511yescharacteristic
272Q16—21no—
273Q16C3×C22⋊D512yescomplemented
274SD16—24no—
275D8—21no—
276D8—101no—
277D8—101no—
278D8C3×C22⋊D512yescomplemented
279C2×C8—21no—
280C2×C8—21no—
281C2×C8C3×C22⋊D511yescharacteristic
282C2×C8C22×C3×D511yescharacteristic
283C4⋊C4—101no—
284C22⋊C4—201no—
285C16—101no—
286C16—101no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—81no—
293C22×C3—81no—
294C22×C3—401no—
295C22×C3—401no—
296C22×C3—401no—
297C22×C3C2×#68611yescharacteristic
298C3×C4—21no—
299C3×C4—42no—
300C3×C4—401no—
301C3×C4#407811yescharacteristic
302C3×C4#409911yescharacteristic
303C2×C5—41no—
304C2×C5—82no—
305C2×C5C3×#44711yescharacteristic
306C2×C5C3×#50811yescharacteristic
307C2×C5C3×#50911yescharacteristic
308D5—161no—
309C23—41no—
310C23—201no—
311C23C3×#68611yescharacteristic
312Q8—22no—
313Q8—41no—
314D4—22no—
315D4—44no—
316D4—41no—
317D4—201no—
318D4—201no—
319D4—402no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—44no—
323C2×C4—41no—
324C2×C4—201no—
325C2×C4C3×#68611yescharacteristic
326C2×C4C2×C3×C22⋊D511yescharacteristic
327C8—21no—
328C8C2×C3×C22⋊D511yescharacteristic
329C8C2×C3×C22⋊D511yescharacteristic
330C2×C3—41no—
331C2×C3—82no—
332C2×C3—801no—
333C2×C3#6548211yescharacteristic
334C2×C3#6548311yescharacteristic
335C2×C3#6550611yescharacteristic
336C5C3×#218611yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—401no—
344C22—401no—
345C22—401no—
346C22C2×C3×#68611yescharacteristic
347C4—21no—
348C4—42no—
349C4—401no—
350C4C3×#407811yescharacteristic
351C4C3×#409911yescharacteristic
352C3#1060287511yescharacteristic, direct product factor, Sylow
353C2—41no—
354C2—82no—
355C2—801no—
356C2C3×#6548211yescharacteristic
357C2C3×#6548311yescharacteristic
358C2C3×#6550611yescharacteristic
subgroupG/H
centerC22×C3C2×#686
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×#135C2
socleC22×C3×C5C2×D8
hypercenterC2×C3×#135D5
hypocenterC5C3×#2186
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#135

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#135C2semidirect
2. C2×C3×#3960C2semidirect
3. C2×C3×#3958C2semidirect
4. C3×#65404C2semidirect
5. C3×#64784C2semidirect
6. C3×#64782C2semidirect
7. C3×C22⋊#672C2semidirect
8. #10602875C3direct (N × H)
25. C2×C5×#135C2×C3semidirect
26. C2×#3960C2×C3semidirect
27. C2×#3958C2×C3semidirect
28. #65404C2×C3semidirect
29. #64784C2×C3semidirect
30. #64782C2×C3semidirect
31. C22⋊#672C2×C3semidirect
42. C3×C5×Q16D4semidirect
45. C3×C5×D8D4semidirect
56. C2×C3×#135D5semidirect
125. C5×Q16C3×D4semidirect
128. C5×D8C3×D4semidirect
139. C2×#135C3×D5semidirect
171. C3×Q16C22⋊D5semidirect
176. C3×D8C22⋊D5semidirect
273. Q16C3×C22⋊D5semidirect
278. D8C3×C22⋊D5semidirect
287. C3×C5#2186semidirect
336. C5C3×#2186semidirect
352. C3#10602875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1352
C2×C3×#39602
C2×C3×#39582
C3×#654042
C3×#647842
C3×#647822
C3×C22⋊#6722
#106028753
C3×#21865