Finite Group Databasebeta

← C3×#10601796 #14316872

Subgroups — C3×#10601796 #14316872

Order 1920.

452 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 82 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×#65985C211yesmaximal, characteristic, complemented
2C3×C5×#458C211yesmaximal, characteristic
3C3×#65532C211yesmaximal, characteristic
4C3×#65531C211yesmaximal, characteristic
5C3×#64759C211yesmaximal, characteristic, complemented
6C3×#64693C211yesmaximal, characteristic, complemented
7C3×#64692C211yesmaximal, characteristic, complemented
8#10601796C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×H(5,𝔽2)C2211yescharacteristic
10C3×C5×#123—21no—
11C3×C5×#123C2211yescharacteristic
12C3×#4097—21no—
13C3×#4082C2211yescharacteristic
14C3×#4081—21no—
15C3×#4081C2211yescharacteristic
16C3×#4070—21no—
17C3×#4035—21no—
18C3×#4034—21no—
19C3×#4025—21no—
20C3×#4025—21no—
21C3×#4024—21no—
22C3×C5×#99—21no—
23C3×C5×#99C2211yescharacteristic
24C3×#3969—21no—
25C3×#3966—21no—
26C3×#3966C2211yescharacteristic
27C3×#3965C2211yescharacteristic
28C3×#2201—51nomaximal, Hall
29#65985C2×C311yescharacteristic, complemented
30C5×#458C2×C311yescharacteristic
31#65532C2×C311yescharacteristic
32#65531C2×C311yescharacteristic
33#64759C2×C311yescharacteristic, complemented
34#64693C2×C311yescharacteristic, complemented
35#64692C2×C311yescharacteristic, complemented
36C3×C5×#41—21no—
37C3×C5×#41—41no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—41no—
41C2×C3×C5×D4C2311yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×C3×Dic10—21no—
45C2×C3×Dic10D411yescharacteristic
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—41no—
48C3×C5×C22⋊C4—21no—
49C3×C5×C22⋊C4—21no—
50C3×C5×C22⋊C4—41no—
51C3×C5×C22⋊C4D411yescharacteristic
52C3×C22⋊Dic5—21no—
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—41no—
57C3×C22⋊Dic5D411yescharacteristic
58C3×#689—41no—
59C3×#687—41no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×#683—21no—
66C3×#683—21no—
67C3×#683—41no—
68C3×C4×Dic5—21no—
69C3×C4×Dic5D411yescharacteristic
70C3×#681—21no—
71C3×#563—51no—
72C3×#458—51no—
73C3×#458D511yescharacteristic
74C3×#455—51no—
75C3×#354—51no—
76C3×#352—51no—
77C3×#352—51no—
78C5×H(5,𝔽2)C22×C311yescharacteristic
79C5×#123—21no—
80C5×#123C22×C311yescharacteristic
81#4097—21no—
82#4082C22×C311yescharacteristic
83#4081—21no—
84#4081C22×C311yescharacteristic
85#4070—21no—
86#4035—21no—
87#4034—21no—
88#4025—21no—
89#4025—21no—
90#4024—21no—
91C5×#99—21no—
92C5×#99C22×C311yescharacteristic
93#3969—21no—
94#3966—21no—
95#3966C22×C311yescharacteristic
96#3965C22×C311yescharacteristic
97#2201—51noSylow
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5C2×D411yescharacteristic
101C23×C3×C5C2×D411yescharacteristic
102C3×C5×Q8—21no—
103C3×C5×D4—21no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C3×Dic10—41no—
123C3×Dic10—81no—
124C3×#168—41no—
125C3×H(5,𝔽2)C2×D511yescharacteristic
126C3×#137—101no—
127C3×C4⋊Q8—101no—
128C3×#126—101no—
129C3×#126—101no—
130C3×#125—101no—
131C3×#124—51no—
132C3×#123—21no—
133C3×#123—51no—
134C3×#123—101no—
135C3×#123C2×D511yescharacteristic
136C3×C22⋊Q8—101no—
137C3×C22⋊Q8—101no—
138C3×#104—101no—
139C3×#100—51no—
140C3×#99—21no—
141C3×#99—51no—
142C3×#99—101no—
143C3×#99C2×D511yescharacteristic
144C5×#41—21no—
145C5×#41—41no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—41no—
149C2×C5×D4C23×C311yescharacteristic
150C22×C4×C5C3×D411yescharacteristic
151C22×Dic5C3×D411yescharacteristic
152C2×Dic10—21no—
153C2×Dic10C3×D411yescharacteristic
154C5×C4⋊C4—21no—
155C5×C4⋊C4—41no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4—41no—
159C5×C22⋊C4C3×D411yescharacteristic
160C22⋊Dic5—21no—
161C22⋊Dic5—21no—
162C22⋊Dic5—21no—
163C22⋊Dic5—21no—
164C22⋊Dic5—41no—
165C22⋊Dic5C3×D411yescharacteristic
166#689—41no—
167#687—41no—
168C4⋊Dic5—21no—
169C4⋊Dic5—21no—
170#683—21no—
171#683—21no—
172#683—21no—
173#683—21no—
174#683—21no—
175#683—41no—
176C4×Dic5—21no—
177C4×Dic5C3×D411yescharacteristic
178#681—21no—
179#563—51no—
180#458—51no—
181#458C3×D511yescharacteristic
182#455—51no—
183#354—51no—
184#352—51no—
185#352—51no—
186C22×C3×C5—21no—
187C22×C3×C5—21no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—81no—
192C22×C3×C5—81no—
193C22×C3×C5#12011yescharacteristic
194C3×C4×C5—21no—
195C3×C4×C5—41no—
196C3×C4×C5—41no—
197C3×C4×C5—41no—
198C3×C4×C5—81no—
199C3×Dic5—41no—
200C3×Dic5—41no—
201C3×Dic5—41no—
202C3×Dic5—41no—
203C3×Dic5—81no—
204C3×#41—21no—
205C3×#41—41no—
206C2×C3×Q8—51no—
207C2×C3×Q8—101no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—41no—
211C2×C3×D4C22×D511yescharacteristic
212C22×C3×C4—51no—
213C22×C3×C4C22⋊D511yescharacteristic
214C3×Q16—201no—
215C3×SD16—201no—
216C3×M16—101no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C4⋊C4—201no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—41no—
230C3×C22⋊C4—51no—
231C3×C22⋊C4—101no—
232C3×C22⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—101no—
235C3×C22⋊C4—201no—
236C3×C22⋊C4C22⋊D511yescharacteristic
237C3×C42—51no—
238C3×C42—101no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5C2×C3×D411yescharacteristic
242C23×C5C2×C3×D411yescharacteristic
243C5×Q8—21no—
244C5×D4—21no—
245C5×D4—41no—
246C5×D4—41no—
247C5×D4—41no—
248C5×D4—41no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5C2×C3×D411yescharacteristic
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—21no—
260C2×Dic5—21no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263Dic10—41no—
264Dic10—81no—
265#168—41no—
266H(5,𝔽2)C2×C3×D511yescharacteristic
267#137—101no—
268C4⋊Q8—101no—
269#126—101no—
270#126—101no—
271#125—101no—
272#124—51no—
273#123—21no—
274#123—51no—
275#123—101no—
276#123C2×C3×D511yescharacteristic
277C22⋊Q8—101no—
278C22⋊Q8—101no—
279#104—101no—
280#100—51no—
281#99—21no—
282#99—51no—
283#99—101no—
284#99C2×C3×D511yescharacteristic
285C2×C3×C5—21no—
286C2×C3×C5—41no—
287C2×C3×C5—41no—
288C2×C3×C5—81no—
289C2×C3×C5B(4,𝔽2)11yescharacteristic
290C23×C3—21no—
291C23×C3—21no—
292C23×C3D4×D511yescharacteristic
293C23×C3C2×C22⋊D511yescharacteristic
294C3×Q8—21no—
295C3×Q8—201no—
296C3×Q8—401no—
297C3×D4—21no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—101no—
310C2×C3×C4—101no—
311C2×C3×C4—101no—
312C2×C3×C4—101no—
313C2×C3×C4—201no—
314C2×C3×C4—201no—
315C2×C3×C4D4×D511yescharacteristic
316C3×C8—201no—
317C22×C5—21no—
318C22×C5—21no—
319C22×C5—41no—
320C22×C5—41no—
321C22×C5—41no—
322C22×C5—81no—
323C22×C5—81no—
324C22×C5C3×#12011yescharacteristic
325C4×C5—21no—
326C4×C5—41no—
327C4×C5—41no—
328C4×C5—41no—
329C4×C5—81no—
330Dic5—41no—
331Dic5—41no—
332Dic5—41no—
333Dic5—41no—
334Dic5—81no—
335#41—21no—
336#41—41no—
337C2×Q8—51no—
338C2×Q8—101no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4C22×C3×D511yescharacteristic
343C22×C4—51no—
344C22×C4C3×C22⋊D511yescharacteristic
345Q16—201no—
346SD16—201no—
347M16—101no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—101no—
351C4⋊C4—101no—
352C4⋊C4—101no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C4⋊C4—101no—
357C4⋊C4—201no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—41no—
361C22⋊C4—51no—
362C22⋊C4—101no—
363C22⋊C4—101no—
364C22⋊C4—101no—
365C22⋊C4—101no—
366C22⋊C4—201no—
367C22⋊C4C3×C22⋊D511yescharacteristic
368C42—51no—
369C42—101no—
370C3×C5#220111yescharacteristic, complemented, Hall
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—81no—
377C22×C3—81no—
378C22×C3#408311yescharacteristic
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—81no—
384C3×C4—201no—
385C3×C4—201no—
386C3×C4—201no—
387C3×C4—201no—
388C3×C4—401no—
389C2×C5—21no—
390C2×C5—41no—
391C2×C5—41no—
392C2×C5—81no—
393C2×C5C3×B(4,𝔽2)11yescharacteristic
394C23—21no—
395C23—21no—
396C23C3×D4×D511yescharacteristic
397C23C2×C3×C22⋊D511yescharacteristic
398Q8—21no—
399Q8—201no—
400Q8—401no—
401D4—21no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—101no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—101no—
417C2×C4—201no—
418C2×C4—201no—
419C2×C4C3×D4×D511yescharacteristic
420C8—201no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—81no—
425C2×C3#6532111yescharacteristic
426C5C3×#220111yescharacteristic, complemented, Sylow
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22C3×#408311yescharacteristic
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—81no—
440C4—201no—
441C4—201no—
442C4—201no—
443C4—201no—
444C4—401no—
445C3#1060179611yescharacteristic, direct product factor, Sylow
446C2—21no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2C3×#6532111yescharacteristic
subgroupG/H
centerC2×C3#65321
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#458C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×C5×H(5,𝔽2)C22
hypercenterC3×#458D5
hypocenterC5C3×#2201
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#458

Complements

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

NH ≅ G/Ntype
1. C3×#65985C2semidirect
5. C3×#64759C2semidirect
6. C3×#64693C2semidirect
7. C3×#64692C2semidirect
8. #10601796C3direct (N × H)
29. #65985C2×C3semidirect
33. #64759C2×C3semidirect
34. #64693C2×C3semidirect
35. #64692C2×C3semidirect
370. C3×C5#2201semidirect
426. C5C3×#2201semidirect
445. C3#10601796direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659852
C3×C5×#4582
C3×#655322
C3×#655312
C3×#647592
C3×#646932
C3×#646922
#106017963
C3×#22015