Finite Group Databasebeta

← C3×#10600046 #14316347

Subgroups — C3×#10600046 #14316347

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×#66102C211yesmaximal, characteristic
2C3×#65484C211yesmaximal, characteristic, complemented
3C3×#65198C211yesmaximal, characteristic, complemented
4C3×#65157C211yesmaximal, characteristic, complemented
5C3×C5×#360C211yesmaximal, characteristic, complemented
6C3×#64734C211yesmaximal, characteristic, complemented
7C3×#64708C211yesmaximal, characteristic, complemented
8#10600046C311yesmaximal, characteristic, direct product factor, Hall
9C3×D5×#41—21no—
10C3×C5×#135C2211yescharacteristic
11C3×#4096—21no—
12C3×#4064—21no—
13C3×#4061—21no—
14C3×#4060—21no—
15C3×#4057—21no—
16C2×C3×Dic20C2211yescharacteristic, complemented
17C3×#4050C2211yescharacteristic
18C2×C3×#676C2211yescharacteristic
19C3×#4043—21no—
20C3×C5×M32C2211yescharacteristic, complemented
21C3×C5×#106C2211yescharacteristic, complemented
22C3×#3961—21no—
23C3×#3959—21no—
24C3×#3944C2211yescharacteristic, complemented
25C3×#3942—21no—
26C3×Dic40—21no—
27C3×#3932—21no—
28C3×#2191—51nomaximal, Hall
29#66102C2×C311yescharacteristic
30#65484C2×C311yescharacteristic, complemented
31#65198C2×C311yescharacteristic, complemented
32#65157C2×C311yescharacteristic, complemented
33C5×#360C2×C311yescharacteristic, complemented
34#64734C2×C311yescharacteristic, complemented
35#64708C2×C311yescharacteristic, complemented
36C3×C5×#41—21no—
37C3×#713—21no—
38C3×Q8×D5—21no—
39C3×#711—21no—
40C3×#711—41no—
41C3×D4×D5—21no—
42C3×D4×D5—41no—
43C3×#709—21no—
44C3×#709—41no—
45C2×C3×C4×D5—41no—
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×Dic10—21no—
48C3×C5×Q16D411yescharacteristic
49C3×C5×SD16—21no—
50C3×C5×D8D411yescharacteristic
51C2×C3×C5×C8C2311yescharacteristic
52C3×C5×C4⋊C4—21no—
53C3×#689—21no—
54C3×#688—21no—
55C3×#687—21no—
56C3×#686—21no—
57C3×#685—41no—
58C3×C4⋊Dic5—41no—
59C2×C3×#168D411yescharacteristic
60C3×Dic20—21no—
61C3×Dic20—21no—
62C3×Dic20D411yescharacteristic
63C3×D40D411yescharacteristic
64C3×#677—21no—
65C3×#676—21no—
66C3×#676—21no—
67C3×C5×C16—21no—
68C3×#672—21no—
69C3×#575—51no—
70C3×#510—51no—
71C3×#510—51no—
72C3×#470—51no—
73C3×#360—51no—
74C3×#360D511yescharacteristic, complemented
75C3×#349—51no—
76D5×#41—21no—
77C5×#135C22×C311yescharacteristic
78#4096—21no—
79#4064—21no—
80#4061—21no—
81#4060—21no—
82#4057—21no—
83C2×Dic20C22×C311yescharacteristic, complemented
84#4050C22×C311yescharacteristic
85C2×#676C22×C311yescharacteristic
86#4043—21no—
87C5×M32C22×C311yescharacteristic, complemented
88C5×#106C22×C311yescharacteristic, complemented
89#3961—21no—
90#3959—21no—
91#3944C22×C311yescharacteristic, complemented
92#3942—21no—
93Dic40—21no—
94#3932—21no—
95#2191—51noSylow
96C22×C3×D5—41no—
97C22×C3×D5D811yescharacteristic
98C3×C5×Q8—21no—
99C3×C5×D4—21no—
100C3×C5×D4—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—41no—
105C3×C22⋊D5—41no—
106C3×C22⋊D5—41no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5D811yescharacteristic
110C3×D20—21no—
111C3×D20—41no—
112C3×C4×D5—21no—
113C3×C4×D5—21no—
114C3×C4×D5—41no—
115C3×C4×D5—41no—
116C3×C4×D5—41no—
117C3×Dic10—21no—
118C3×Dic10—41no—
119C3×Dic10—41no—
120C3×Dic10—41no—
121C3×C5×C8C2×D411yescharacteristic
122C3×C5×C8C2×D411yescharacteristic
123C3×#168—21no—
124C2×C3×#41—101no—
125C3×#137—101no—
126C3×#137—101no—
127C3×AGL(1,ℤ/8)—101no—
128C3×AGL(1,ℤ/8)—101no—
129C3×#135—51no—
130C3×#135—101no—
131C3×#135C2×D511yescharacteristic
132C2×C3×Q16—51no—
133C2×C3×M16—51no—
134C3×C22⋊Q8—101no—
135C3×Q32—101no—
136C3×Q32—101no—
137C3×SD32—101no—
138C3×SD32—101no—
139C3×M32—51no—
140C3×M32C2×D511yescharacteristic, complemented
141C3×#106C2×D511yescharacteristic, complemented
142C3×#103—101no—
143C5×#41—21no—
144#713—21no—
145Q8×D5—21no—
146#711—21no—
147#711—41no—
148D4×D5—21no—
149D4×D5—41no—
150#709—21no—
151#709—41no—
152C2×C4×D5—41no—
153C2×C4×D5C3×D411yescharacteristic
154C2×Dic10—21no—
155C5×Q16C3×D411yescharacteristic
156C5×SD16—21no—
157C5×D8C3×D411yescharacteristic
158C2×C5×C8C23×C311yescharacteristic
159C5×C4⋊C4—21no—
160#689—21no—
161#688—21no—
162#687—21no—
163#686—21no—
164#685—41no—
165C4⋊Dic5—41no—
166C2×#168C3×D411yescharacteristic
167Dic20—21no—
168Dic20—21no—
169Dic20C3×D411yescharacteristic
170D40C3×D411yescharacteristic
171#677—21no—
172#676—21no—
173#676—21no—
174C5×C16—21no—
175#672—21no—
176#575—51no—
177#510—51no—
178#510—51no—
179#470—51no—
180#360—51no—
181#360C3×D511yescharacteristic, complemented
182#349—51no—
183C22×C3×C5—41no—
184C22×C3×C5C2×D811yescharacteristic
185C2×C3×D5—21no—
186C2×C3×D5—41no—
187C2×C3×D5—41no—
188C2×C3×D5—82no—
189C3×C4×C5—41no—
190C3×C4×C5—81no—
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
193C3×Dic5—21no—
194C3×Dic5—41no—
195C3×Dic5—81no—
196C3×#41—21no—
197C3×#41—101no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—201no—
201C3×#41—201no—
202C2×C3×Q8—101no—
203C2×C3×Q8—101no—
204C2×C3×D4—101no—
205C2×C3×D4—201no—
206C22×C3×C4—51no—
207C22×C3×C4—201no—
208C3×Q16—51no—
209C3×Q16—101no—
210C3×Q16—101no—
211C3×Q16—101no—
212C3×Q16D2011yescharacteristic
213C3×SD16—21no—
214C3×SD16—101no—
215C3×SD16—101no—
216C3×SD16—101no—
217C3×D8—51no—
218C3×D8—101no—
219C3×D8D2011yescharacteristic
220C3×M16—101no—
221C3×M16—101no—
222C2×C3×C8—51no—
223C2×C3×C8C22×D511yescharacteristic
224C3×C4⋊C4—21no—
225C3×C4⋊C4—201no—
226C3×C22⋊C4—201no—
227C3×C16—21no—
228C3×C16—101no—
229C22×D5—41no—
230C22×D5C3×D811yescharacteristic
231C5×Q8—21no—
232C5×D4—21no—
233C5×D4—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5C2×C3×D411yescharacteristic
237C22⋊D5—41no—
238C22⋊D5—41no—
239C22⋊D5—41no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5C3×D811yescharacteristic
243D20—21no—
244D20—41no—
245C4×D5—21no—
246C4×D5—21no—
247C4×D5—41no—
248C4×D5—41no—
249C4×D5—41no—
250Dic10—21no—
251Dic10—41no—
252Dic10—41no—
253Dic10—41no—
254C5×C8C2×C3×D411yescharacteristic
255C5×C8C2×C3×D411yescharacteristic
256#168—21no—
257C2×#41—101no—
258#137—101no—
259#137—101no—
260AGL(1,ℤ/8)—101no—
261AGL(1,ℤ/8)—101no—
262#135—51no—
263#135—101no—
264#135C2×C3×D511yescharacteristic
265C2×Q16—51no—
266C2×M16—51no—
267C22⋊Q8—101no—
268Q32—101no—
269Q32—101no—
270SD32—101no—
271SD32—101no—
272M32—51no—
273M32C2×C3×D511yescharacteristic, complemented
274#106C2×C3×D511yescharacteristic, complemented
275#103—101no—
276C2×C3×C5—21no—
277C2×C3×C5—81no—
278C2×C3×C5#44711yescharacteristic
279C3×D5—41no—
280C3×D5—81no—
281C23×C3—51no—
282C23×C3—201no—
283C3×Q8—21no—
284C3×Q8—101no—
285C3×Q8—201no—
286C3×Q8—201no—
287C3×Q8—201no—
288C3×D4—21no—
289C3×D4—41no—
290C3×D4—101no—
291C3×D4—201no—
292C3×D4—201no—
293C3×D4—201no—
294C3×D4—201no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—51no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4—201no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4D4×D511yescharacteristic
306C3×C8—101no—
307C3×C8C2×D2011yescharacteristic
308C3×C8D4×D511yescharacteristic
309C22×C5—41no—
310C22×C5C2×C3×D811yescharacteristic
311C2×D5—21no—
312C2×D5—41no—
313C2×D5—41no—
314C2×D5—82no—
315C4×C5—41no—
316C4×C5—81no—
317C4×C5C3×#12011yescharacteristic
318C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
319Dic5—21no—
320Dic5—41no—
321Dic5—81no—
322#41—21no—
323#41—101no—
324#41—101no—
325#41—101no—
326#41—201no—
327#41—201no—
328C2×Q8—101no—
329C2×Q8—101no—
330C2×D4—101no—
331C2×D4—201no—
332C22×C4—51no—
333C22×C4—201no—
334Q16—51no—
335Q16—101no—
336Q16—101no—
337Q16—101no—
338Q16C3×D2011yescharacteristic
339SD16—21no—
340SD16—101no—
341SD16—101no—
342SD16—101no—
343D8—51no—
344D8—101no—
345D8C3×D2011yescharacteristic
346M16—101no—
347M16—101no—
348C2×C8—51no—
349C2×C8C22×C3×D511yescharacteristic
350C4⋊C4—21no—
351C4⋊C4—201no—
352C22⋊C4—201no—
353C16—21no—
354C16—101no—
355C3×C5#219111yescharacteristic, complemented, Hall
356C22×C3—41no—
357C22×C3—101no—
358C22×C3—201no—
359C22×C3—201no—
360C22×C3—402no—
361C22×C3D5×D811yescharacteristic
362C3×C4—41no—
363C3×C4—81no—
364C3×C4—101no—
365C3×C4—201no—
366C3×C4—401no—
367C3×C4#402811yescharacteristic
368C3×C4#406011yescharacteristic
369C2×C5—21no—
370C2×C5—81no—
371C2×C5C3×#44711yescharacteristic
372D5—41no—
373D5—81no—
374C23—51no—
375C23—201no—
376Q8—21no—
377Q8—101no—
378Q8—201no—
379Q8—201no—
380Q8—201no—
381D4—21no—
382D4—41no—
383D4—101no—
384D4—201no—
385D4—201no—
386D4—201no—
387D4—201no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—51no—
391C2×C4—101no—
392C2×C4—101no—
393C2×C4—201no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4—201no—
397C2×C4—201no—
398C2×C4C3×D4×D511yescharacteristic
399C8—101no—
400C8C2×C3×D2011yescharacteristic
401C8C3×D4×D511yescharacteristic
402C2×C3—21no—
403C2×C3—81no—
404C2×C3—201no—
405C2×C3—401no—
406C2×C3#6506211yescharacteristic
407C5C3×#219111yescharacteristic, complemented, Sylow
408C22—41no—
409C22—101no—
410C22—201no—
411C22—201no—
412C22—402no—
413C22C3×D5×D811yescharacteristic
414C4—41no—
415C4—81no—
416C4—101no—
417C4—201no—
418C4—401no—
419C4C3×#402811yescharacteristic
420C4C3×#406011yescharacteristic
421C3#1060004611yescharacteristic, direct product factor, Sylow
422C2—21no—
423C2—81no—
424C2—201no—
425C2—401no—
426C2C3×#6506211yescharacteristic
subgroupG/H
centerC2×C3#65062
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#360C2
socleC2×C3×C5#447
prime radicalC3×#66102C2
hypercenterC3×#360D5
hypocenterC5C3×#2191
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#360

Complements

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

NH ≅ G/Ntype
2. C3×#65484C2semidirect
3. C3×#65198C2semidirect
4. C3×#65157C2semidirect
5. C3×C5×#360C2semidirect
6. C3×#64734C2semidirect
7. C3×#64708C2semidirect
8. #10600046C3direct (N × H)
16. C2×C3×Dic20C22semidirect
20. C3×C5×M32C22semidirect
21. C3×C5×#106C22semidirect
24. C3×#3944C22semidirect
30. #65484C2×C3semidirect
31. #65198C2×C3semidirect
32. #65157C2×C3semidirect
33. C5×#360C2×C3semidirect
34. #64734C2×C3semidirect
35. #64708C2×C3semidirect
74. C3×#360D5semidirect
83. C2×Dic20C22×C3semidirect
87. C5×M32C22×C3semidirect
88. C5×#106C22×C3semidirect
91. #3944C22×C3semidirect
140. C3×M32C2×D5semidirect
141. C3×#106C2×D5semidirect
181. #360C3×D5semidirect
273. M32C2×C3×D5semidirect
274. #106C2×C3×D5semidirect
355. C3×C5#2191semidirect
407. C5C3×#2191semidirect
421. C3#10600046direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661022
C3×#654842
C3×#651982
C3×#651572
C3×C5×#3602
C3×#647342
C3×#647082
#106000463
C3×#21915