Finite Group Databasebeta

← C3×#10602283 #14316509

Subgroups — C3×#10602283 #14316509

Order 1920.

432 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66091C211yesmaximal, characteristic
2C2×C3×C5×SD32C211yesmaximal, characteristic, complemented
3C3×#65481C211yesmaximal, characteristic, complemented
4C3×#65468C211yesmaximal, characteristic, complemented
5C3×#64783C211yesmaximal, characteristic, complemented
6C3×#64730C211yesmaximal, characteristic, complemented
7C3×#64728C211yesmaximal, characteristic, complemented
8#10602283C311yesmaximal, characteristic, direct product factor, Hall
9C3×#4144—21no—
10C2×C3×C5×Q16C2211yescharacteristic, complemented
11C2×C3×C5×D8C2211yescharacteristic
12C3×#4088—21no—
13C3×#4078—21no—
14C3×#4058—21no—
15C3×#4057—22no—
16C3×D5×D8—21no—
17C3×#4050C2211yescharacteristic
18C3×#4047C2211yescharacteristic
19C3×C5×SD32—22no—
20C2×C3×C5×C16C2211yescharacteristic, complemented
21C3×#3968—21no—
22C3×#3961—21no—
23C3×#3960—21no—
24C3×#3951C2211yescharacteristic, complemented
25C3×#3944C2211yescharacteristic, complemented
26C3×#2194—51nomaximal, Hall
27#66091C2×C311yescharacteristic
28C2×C5×SD32C2×C311yescharacteristic, complemented
29#65481C2×C311yescharacteristic, complemented
30#65468C2×C311yescharacteristic, complemented
31#64783C2×C311yescharacteristic, complemented
32#64730C2×C311yescharacteristic, complemented
33#64728C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C22⋊D5—42no—
37C3×#711—22no—
38C3×#711—41no—
39C3×D4×D5—22no—
40C3×D4×D5—41no—
41C3×#709—21no—
42C3×#709D411yescharacteristic
43C3×C5×Q16—21no—
44C3×C5×Q16—21no—
45C3×C5×D8—21no—
46C3×C5×D8D412yes—
47C2×C3×C5×C8C2311yescharacteristic
48C3×#689—41no—
49C3×#688—41no—
50C3×#687—22no—
51C3×#686—22no—
52C3×#681—21no—
53C3×#681D411yescharacteristic
54C3×Dic20D411yescharacteristic
55C3×D40D411yescharacteristic
56C3×#677—21no—
57C3×#676—21no—
58C3×C8×D5—21no—
59C3×C5×C16—21no—
60C3×#672—21no—
61C3×#576—51no—
62C3×#510—51no—
63C2×C3×SD32D511yescharacteristic, complemented
64C3×#473—51no—
65C3×#361—51no—
66C3×#359—51no—
67C3×#350—51no—
68#4144—21no—
69C2×C5×Q16C22×C311yescharacteristic, complemented
70C2×C5×D8C22×C311yescharacteristic
71#4088—21no—
72#4078—21no—
73#4058—21no—
74#4057—22no—
75D5×D8—21no—
76#4050C22×C311yescharacteristic
77#4047C22×C311yescharacteristic
78C5×SD32—22no—
79C2×C5×C16C22×C311yescharacteristic, complemented
80#3968—21no—
81#3961—21no—
82#3960—21no—
83#3951C22×C311yescharacteristic, complemented
84#3944C22×C311yescharacteristic, complemented
85#2194—51noSylow
86C23×C3×C5—41no—
87C22×C3×D5—42no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×D4—22no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C3×C22⋊D5—21no—
95C3×C22⋊D5—42no—
96C3×C22⋊D5—42no—
97C3×C22⋊D5—41no—
98C2×C3×Dic5—42no—
99C3×D20—21no—
100C3×D20D811yescharacteristic
101C3×C4×D5—21no—
102C3×C4×D5—41no—
103C3×Dic10—21no—
104C3×Dic10D811yescharacteristic
105C3×C5×C8C2×D411yescharacteristic
106C3×C5×C8C2×D411yescharacteristic
107C3×#168—21no—
108C3×#168—41no—
109C3×H(5,𝔽2)—101no—
110C3×#137—101no—
111C3×AGL(1,ℤ/8)—101no—
112C3×AGL(1,ℤ/8)—102no—
113C3×#135—51no—
114C3×#135—101no—
115C2×C3×Q16C2×D511yescharacteristic, complemented
116C2×C3×D8—101no—
117C2×C3×D8C2×D511yescharacteristic
118C3×#131—51no—
119C3×Q32—101no—
120C3×SD32—22no—
121C3×SD32—101no—
122C3×M32—51no—
123C2×C3×C16C2×D511yescharacteristic, complemented
124C3×#108—51no—
125C3×#101—101no—
126C2×C5×Q8—21no—
127C2×C5×D4—21no—
128C2×C22⋊D5—42no—
129#711—22no—
130#711—41no—
131D4×D5—22no—
132D4×D5—41no—
133#709—21no—
134#709C3×D411yescharacteristic
135C5×Q16—21no—
136C5×Q16—21no—
137C5×D8—21no—
138C5×D8C3×D412yes—
139C2×C5×C8C23×C311yescharacteristic
140#689—41no—
141#688—41no—
142#687—22no—
143#686—22no—
144#681—21no—
145#681C3×D411yescharacteristic
146Dic20C3×D411yescharacteristic
147D40C3×D411yescharacteristic
148#677—21no—
149#676—21no—
150C8×D5—21no—
151C5×C16—21no—
152#672—21no—
153#576—51no—
154#510—51no—
155C2×SD32C3×D511yescharacteristic, complemented
156#473—51no—
157#361—51no—
158#359—51no—
159#350—51no—
160C22×C3×C5—42no—
161C22×C3×C5—161no—
162C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C3×D5—21no—
164C2×C3×D5—41no—
165C2×C3×D5—162no—
166C3×C4×C5—81no—
167C3×C4×C5#12011yescharacteristic
168C3×C4×C5C2×D811yescharacteristic
169C3×Dic5—21no—
170C3×Dic5—41no—
171C3×#41—51no—
172C3×#41—102no—
173C3×#41—101no—
174C3×#41—201no—
175C2×C3×Q8—21no—
176C2×C3×D4—21no—
177C2×C3×D4—102no—
178C2×C3×D4—201no—
179C2×C3×D4—202no—
180C3×Q16—21no—
181C3×Q16—21no—
182C3×Q16—51no—
183C3×Q16—201no—
184C3×SD16—102no—
185C3×SD16—101no—
186C3×SD16—201no—
187C3×D8—21no—
188C3×D8—51no—
189C3×D8—102no—
190C3×D8C22⋊D512yes—
191C3×M16—51no—
192C3×M16—101no—
193C3×M16—101no—
194C2×C3×C8—101no—
195C2×C3×C8C22×D511yescharacteristic
196C3×C16—21no—
197C3×C16—101no—
198C23×C5—41no—
199C22×D5—42no—
200C5×Q8—41no—
201C5×Q8—41no—
202C5×D4—22no—
203C5×D4—41no—
204C2×C4×C5—41no—
205C2×C4×C5C2×C3×D411yescharacteristic
206C22⋊D5—21no—
207C22⋊D5—42no—
208C22⋊D5—42no—
209C22⋊D5—41no—
210C2×Dic5—42no—
211D20—21no—
212D20C3×D811yescharacteristic
213C4×D5—21no—
214C4×D5—41no—
215Dic10—21no—
216Dic10C3×D811yescharacteristic
217C5×C8C2×C3×D411yescharacteristic
218C5×C8C2×C3×D411yescharacteristic
219#168—21no—
220#168—41no—
221H(5,𝔽2)—101no—
222#137—101no—
223AGL(1,ℤ/8)—101no—
224AGL(1,ℤ/8)—102no—
225#135—51no—
226#135—101no—
227C2×Q16C2×C3×D511yescharacteristic, complemented
228C2×D8—101no—
229C2×D8C2×C3×D511yescharacteristic
230#131—51no—
231Q32—101no—
232SD32—22no—
233SD32—101no—
234M32—51no—
235C2×C16C2×C3×D511yescharacteristic, complemented
236#108—51no—
237#101—101no—
238C2×C3×C5—21no—
239C2×C3×C5—82no—
240C2×C3×C5#44711yescharacteristic
241C3×D5—41no—
242C3×D5—81no—
243C23×C3—41no—
244C23×C3—202no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—51no—
248C3×Q8—101no—
249C3×D4—22no—
250C3×D4—41no—
251C3×D4—51no—
252C3×D4—101no—
253C3×D4—101no—
254C3×D4—202no—
255C3×D4—202no—
256C3×D4—201no—
257C2×C3×C4—41no—
258C2×C3×C4—101no—
259C2×C3×C4—202no—
260C2×C3×C4—201no—
261C2×C3×C4D4×D511yescharacteristic
262C3×C8—101no—
263C3×C8—201no—
264C3×C8D4×D511yescharacteristic
265C3×C8C2×C22⋊D511yescharacteristic
266C22×C5—42no—
267C22×C5—161no—
268C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
269C2×D5—21no—
270C2×D5—41no—
271C2×D5—162no—
272C4×C5—81no—
273C4×C5C3×#12011yescharacteristic
274C4×C5C2×C3×D811yescharacteristic
275Dic5—21no—
276Dic5—41no—
277#41—51no—
278#41—102no—
279#41—101no—
280#41—201no—
281C2×Q8—21no—
282C2×D4—21no—
283C2×D4—102no—
284C2×D4—201no—
285C2×D4—202no—
286Q16—21no—
287Q16—21no—
288Q16—51no—
289Q16—201no—
290SD16—102no—
291SD16—101no—
292SD16—201no—
293D8—21no—
294D8—51no—
295D8—102no—
296D8C3×C22⋊D512yes—
297M16—51no—
298M16—101no—
299M16—101no—
300C2×C8—101no—
301C2×C8C22×C3×D511yescharacteristic
302C16—21no—
303C16—101no—
304C3×C5#219411yescharacteristic, complemented, Hall
305C22×C3—42no—
306C22×C3—101no—
307C22×C3—161no—
308C22×C3—201no—
309C22×C3—802no—
310C22×C3#405711yescharacteristic
311C3×C4—81no—
312C3×C4—101no—
313C3×C4—201no—
314C3×C4D5×D811yescharacteristic
315C3×C4#408311yescharacteristic
316C2×C5—21no—
317C2×C5—82no—
318C2×C5C3×#44711yescharacteristic
319D5—41no—
320D5—81no—
321C23—41no—
322C23—202no—
323Q8—41no—
324Q8—41no—
325Q8—51no—
326Q8—101no—
327D4—22no—
328D4—41no—
329D4—51no—
330D4—101no—
331D4—101no—
332D4—202no—
333D4—202no—
334D4—201no—
335C2×C4—41no—
336C2×C4—101no—
337C2×C4—202no—
338C2×C4—201no—
339C2×C4C3×D4×D511yescharacteristic
340C8—101no—
341C8—201no—
342C8C3×D4×D511yescharacteristic
343C8C2×C3×C22⋊D511yescharacteristic
344C2×C3—21no—
345C2×C3—82no—
346C2×C3—201no—
347C2×C3—401no—
348C2×C3#6544511yescharacteristic
349C5C3×#219411yescharacteristic, complemented, Sylow
350C22—42no—
351C22—101no—
352C22—161no—
353C22—201no—
354C22—802no—
355C22C3×#405711yescharacteristic
356C4—81no—
357C4—101no—
358C4—201no—
359C4C3×D5×D811yescharacteristic
360C4C3×#408311yescharacteristic
361C3#1060228311yescharacteristic, direct product factor, Sylow
362C2—21no—
363C2—82no—
364C2—201no—
365C2—401no—
366C2C3×#6544511yescharacteristic
subgroupG/H
centerC2×C3#65445
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×SD32C2
socleC2×C3×C5#447
prime radicalC3×#66091C2
hypercenterC2×C3×SD32D5
hypocenterC5C3×#2194
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×SD32

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×SD32C2semidirect
3. C3×#65481C2semidirect
4. C3×#65468C2semidirect
5. C3×#64783C2semidirect
6. C3×#64730C2semidirect
7. C3×#64728C2semidirect
8. #10602283C3direct (N × H)
10. C2×C3×C5×Q16C22semidirect
20. C2×C3×C5×C16C22semidirect
24. C3×#3951C22semidirect
25. C3×#3944C22semidirect
28. C2×C5×SD32C2×C3semidirect
29. #65481C2×C3semidirect
30. #65468C2×C3semidirect
31. #64783C2×C3semidirect
32. #64730C2×C3semidirect
33. #64728C2×C3semidirect
63. C2×C3×SD32D5semidirect
69. C2×C5×Q16C22×C3semidirect
79. C2×C5×C16C22×C3semidirect
83. #3951C22×C3semidirect
84. #3944C22×C3semidirect
115. C2×C3×Q16C2×D5semidirect
123. C2×C3×C16C2×D5semidirect
155. C2×SD32C3×D5semidirect
227. C2×Q16C2×C3×D5semidirect
235. C2×C16C2×C3×D5semidirect
304. C3×C5#2194semidirect
349. C5C3×#2194semidirect
361. C3#10602283direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660912
C2×C3×C5×SD322
C3×#654812
C3×#654682
C3×#647832
C3×#647302
C3×#647282
#106022833
C3×#21945