Finite Group Databasebeta

← C3×#10604362 #14282230

Subgroups — C3×#10604362 #14282230

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65856C211yesmaximal, characteristic
2C3×#65758C211yesmaximal, characteristic, complemented
3C3×C4×#704C211yesmaximal, characteristic, complemented
4C3×#64872C212yesmaximal, complemented
5C3×#64871C212yesmaximal, complemented
6#10604362C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#709C411yescharacteristic
8C2×C3×#704—21no—
9C2×C3×#704—21no—
10C3×C5×#117C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12C3×#4039C411yescharacteristic
13C3×#4039C2211yescharacteristic
14C3×#4033C411yescharacteristic
15C3×#4033C2211yescharacteristic
16C3×#4027—21no—
17C3×#4027—21no—
18C3×#4018—21no—
19C3×C42×D5—21no—
20C3×#4004—21no—
21C3×#4002—21no—
22C3×C4⋊#170C2212yes—
23C3×C4×#170C2212yes—
24C3×#1489—51nomaximal, Hall
25#65856C2×C311yescharacteristic
26#65758C2×C311yescharacteristic, complemented
27C4×#704C2×C311yescharacteristic, complemented
28#64872C2×C312yescomplemented
29#64871C2×C312yescomplemented
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×C3×C22⋊D5—21no—
32C22×C3×Dic5D411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C3×#709—22no—
35C3×#709—22no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×Dic10C2×C411yescharacteristic
41C3×#704—24no—
42C3×#704—42no—
43C2×C3×#170—22no—
44C2×C3×#170—22no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49C3×#685—21no—
50C3×#685—21no—
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5C2×C411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5C2311yescharacteristic
59C3×C4×#41—51no—
60C3×#423—51no—
61C3×C4×M16—51no—
62C3×Q8⋊C8—52no—
63C3×D4⋊C8—52no—
64C2×#709C3×C411yescharacteristic
65C2×#704—21no—
66C2×#704—21no—
67C5×#117C3×C411yescharacteristic
68C2×C4×Dic5C22×C311yescharacteristic
69#4039C3×C411yescharacteristic
70#4039C22×C311yescharacteristic
71#4033C3×C411yescharacteristic
72#4033C22×C311yescharacteristic
73#4027—21no—
74#4027—21no—
75#4018—21no—
76C42×D5—21no—
77#4004—21no—
78#4002—21no—
79C4⋊#170C22×C312yes—
80C4×#170C22×C312yes—
81#1489—51noSylow
82C23×C3×C5C22⋊C411yescharacteristic
83C22×C3×D5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C3×C22⋊D5—24no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C2×C3×Dic5C2×D411yescharacteristic
99C3×D20—21no—
100C3×D20M1612yescomplemented
101C3×C4×D5—24no—
102C3×C4×D5—42no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105C3×Dic10—21no—
106C3×Dic10M1612yescomplemented
107C3×#170—24no—
108C3×#170—42no—
109C2×C3×#41—51no—
110C2×C3×M16—101no—
111C2×C3×M16—101no—
112C3×C4×Q8—51no—
113C3×C4×Q8—51no—
114C3×C4×D4—51no—
115C3×C4×D4—51no—
116C3×C4×D4—101no—
117C3×C4×D4—101no—
118C3×#117—101no—
119C3×#117AGL(1,𝔽5)11yescharacteristic
120C2×C3×C42—51no—
121C2×C3×C42—101no—
122C3×C4⋊C8—52no—
123C3×C4⋊C8—101no—
124C3×#97—101no—
125C3×C4×C8—52no—
126C22×C4×C5C2×C3×C411yescharacteristic
127C2×C22⋊D5—21no—
128C22×Dic5C3×D411yescharacteristic
129C22×Dic5C3×D411yescharacteristic
130#709—22no—
131#709—22no—
132C2×D20C2×C3×C411yescharacteristic
133C2×C4×D5—21no—
134C2×C4×D5—21no—
135C2×C4×D5—21no—
136C2×Dic10C2×C3×C411yescharacteristic
137#704—24no—
138#704—42no—
139C2×#170—22no—
140C2×#170—22no—
141C5×C4⋊C4C2×C3×C411yescharacteristic
142C5×C4⋊C4C2×C3×C411yescharacteristic
143C5×C22⋊C4—21no—
144C42×C5—21no—
145#685—21no—
146#685—21no—
147#683—21no—
148#683—21no—
149C4×Dic5—21no—
150C4×Dic5—21no—
151C4×Dic5C2×C3×C411yescharacteristic
152C4×Dic5C3×D411yescharacteristic
153C4×Dic5C3×D411yescharacteristic
154C4×Dic5C23×C311yescharacteristic
155C4×#41—51no—
156#423—51no—
157C4×M16—51no—
158Q8⋊C8—52no—
159D4⋊C8—52no—
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5C2×C22⋊C411yescharacteristic
164C2×C3×D5—22no—
165C2×C3×D5—41no—
166C2×C3×D5—41no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170C3×C4×C5C2×M1611yescharacteristic
171C3×C4×C5C2×M1611yescharacteristic
172C3×Dic5—22no—
173C3×Dic5—21no—
174C3×Dic5—21no—
175C3×Dic5#10412yes—
176C3×Dic5AGL(1,ℤ/8)11yescharacteristic
177C3×Dic5#13711yescharacteristic
178C3×#41—102no—
179C3×#41—102no—
180C2×C3×Q8—51no—
181C2×C3×D4—51no—
182C2×C3×D4—101no—
183C22×C3×C4—51no—
184C22×C3×C4—51no—
185C22×C3×C4—101no—
186C22×C3×C4—101no—
187C22×C3×C4—101no—
188C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
189C3×M16—104no—
190C3×M16—202no—
191C2×C3×C8—102no—
192C2×C3×C8—102no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
196C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
197C3×C22⋊C4—21no—
198C3×C22⋊C4—101no—
199C3×C22⋊C4—101no—
200C3×C42—21no—
201C3×C42—51no—
202C3×C42—51no—
203C3×C42—51no—
204C3×C42—51no—
205C3×C42—101no—
206C3×C42—101no—
207C23×C5C3×C22⋊C411yescharacteristic
208C22×D5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5C3×C22⋊C411yescharacteristic
214C2×C4×C5C22×C3×C411yescharacteristic
215C22⋊D5—24no—
216C2×Dic5—21no—
217C2×Dic5—22no—
218C2×Dic5—21no—
219C2×Dic5—21no—
220C2×Dic5C3×C22⋊C411yescharacteristic
221C2×Dic5C3×C22⋊C411yescharacteristic
222C2×Dic5C2×C3×D411yescharacteristic
223C2×Dic5C2×C3×D411yescharacteristic
224D20—21no—
225D20C3×M1612yescomplemented
226C4×D5—24no—
227C4×D5—42no—
228C4×D5—41no—
229C4×D5—41no—
230Dic10—21no—
231Dic10C3×M1612yescomplemented
232#170—24no—
233#170—42no—
234C2×#41—51no—
235C2×M16—101no—
236C2×M16—101no—
237C4×Q8—51no—
238C4×Q8—51no—
239C4×D4—51no—
240C4×D4—51no—
241C4×D4—101no—
242C4×D4—101no—
243#117—101no—
244#117C3×AGL(1,𝔽5)11yescharacteristic
245C2×C42—51no—
246C2×C42—101no—
247C4⋊C8—52no—
248C4⋊C8—101no—
249#97—101no—
250C4×C8—52no—
251C2×C3×C5—41no—
252C2×C3×C5#40711yescharacteristic
253C2×C3×C5#41711yescharacteristic
254C2×C3×C5C2×#10411yescharacteristic
255C3×D5—42no—
256C23×C3—101no—
257C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
258C3×Q8—52no—
259C3×Q8—101no—
260C3×D4—52no—
261C3×D4—104no—
262C3×D4—101no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—51no—
268C2×C3×C4—51no—
269C2×C3×C4—51no—
270C2×C3×C4—51no—
271C2×C3×C4—104no—
272C2×C3×C4—102no—
273C2×C3×C4—101no—
274C2×C3×C4—101no—
275C2×C3×C4—101no—
276C2×C3×C4—202no—
277C2×C3×C4—201no—
278C2×C3×C4—201no—
279C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
280C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
281C3×C8—104no—
282C3×C8—202no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5C2×C3×C22⋊C411yescharacteristic
287C2×D5—22no—
288C2×D5—41no—
289C2×D5—41no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5—41no—
293C4×C5C2×C3×M1611yescharacteristic
294C4×C5C2×C3×M1611yescharacteristic
295Dic5—22no—
296Dic5—21no—
297Dic5—21no—
298Dic5C3×#10412yes—
299Dic5C3×AGL(1,ℤ/8)11yescharacteristic
300Dic5C3×#13711yescharacteristic
301#41—102no—
302#41—102no—
303C2×Q8—51no—
304C2×D4—51no—
305C2×D4—101no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—101no—
309C22×C4—101no—
310C22×C4—101no—
311C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
312M16—104no—
313M16—202no—
314C2×C8—102no—
315C2×C8—102no—
316C4⋊C4—101no—
317C4⋊C4—101no—
318C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
319C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—101no—
322C22⋊C4—101no—
323C42—21no—
324C42—51no—
325C42—51no—
326C42—51no—
327C42—51no—
328C42—101no—
329C42—101no—
330C3×C5#148911yescharacteristic, complemented, Hall
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—102no—
335C22×C3—201no—
336C22×C3—201no—
337C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—52no—
342C3×C4—51no—
343C3×C4—51no—
344C3×C4—101no—
345C3×C4—101no—
346C3×C4—102no—
347C3×C4D5⋊M1611yescharacteristic
348C3×C4D5⋊M1611yescharacteristic
349C2×C5—41no—
350C2×C5C3×#40711yescharacteristic
351C2×C5C3×#41711yescharacteristic
352C2×C5C2×C3×#10411yescharacteristic
353D5—42no—
354C23—101no—
355C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
356Q8—52no—
357Q8—101no—
358D4—52no—
359D4—104no—
360D4—101no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—51no—
369C2×C4—104no—
370C2×C4—102no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—202no—
375C2×C4—201no—
376C2×C4—201no—
377C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
378C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
379C8—104no—
380C8—202no—
381C2×C3—41no—
382C2×C3—202no—
383C2×C3#6575511yescharacteristic
384C2×C3D5⋊#10411yescharacteristic
385C2×C3#6579311yescharacteristic
386C5C3×#148911yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—21no—
390C22—102no—
391C22—201no—
392C22—201no—
393C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
394C4—21no—
395C4—41no—
396C4—41no—
397C4—52no—
398C4—51no—
399C4—51no—
400C4—102no—
401C4—101no—
402C4—101no—
403C4C3×D5⋊M1611yescharacteristic
404C4C3×D5⋊M1611yescharacteristic
405C3#1060436211yescharacteristic, direct product factor, Sylow
406C2—41no—
407C2—202no—
408C2C3×#6575511yescharacteristic
409C2C3×D5⋊#10411yescharacteristic
410C2C3×#6579311yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#117C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#709C4
cosocleC4×Dic5C23×C3
hypercenterC3×#117AGL(1,𝔽5)
hypocenterC5C3×#1489
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
2. C3×#65758C2semidirect
3. C3×C4×#704C2semidirect
4. C3×#64872C2semidirect
5. C3×#64871C2semidirect
6. #10604362C3direct (N × H)
26. #65758C2×C3semidirect
27. C4×#704C2×C3semidirect
28. #64872C2×C3semidirect
29. #64871C2×C3semidirect
100. C3×D20M16semidirect
106. C3×Dic10M16semidirect
225. D20C3×M16semidirect
231. Dic10C3×M16semidirect
330. C3×C5#1489semidirect
386. C5C3×#1489semidirect
405. C3#10604362direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658562
C3×#657582
C3×C4×#7042
C3×#648722
C3×#648712
#106043623
C3×#14895