Finite Group Databasebeta

← C3×#10598709 #14279055

Subgroups — C3×#10598709 #14279055

Order 1920.

468 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×C3×#4013C211yesmaximal, characteristic
2C2×C3×#4011C211yesmaximal, characteristic
3C3×#65247C211yesmaximal, characteristic
4#10598709C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C22⋊D5C2211yescharacteristic
6C23×C3×Dic5C411yescharacteristic, complemented
7C2×C3×C22⋊AGL(1,𝔽5)—21no—
8C2×C3×#704—21no—
9C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
10C2×C3×#685—21no—
11C3×#4013—21no—
12C3×#4013C412yescomplemented
13C3×#4011—21no—
14C3×#4011C412yescomplemented
15C3×#3963—21no—
16C3×#1390—51nomaximal, Hall
17C2×#4013C2×C311yescharacteristic
18C2×#4011C2×C311yescharacteristic
19#65247C2×C311yescharacteristic
20C24×C3×C5C2×C411yescharacteristic
21C23×C3×D5D411yescharacteristic
22C22×C3×AGL(1,𝔽5)—41no—
23C22×C3×C4×C5—21no—
24C2×C3×C22⋊D5—41no—
25C2×C3×C22⋊D5—41no—
26C2×C3×C22⋊D5C2×C411yescharacteristic
27C2×C3×C22⋊D5C2×C411yescharacteristic
28C2×C3×C22⋊D5D411yescharacteristic
29C2×C3×C22⋊D5Q811yescharacteristic
30C22×C3×Dic5—21no—
31C22×C3×Dic5—42no—
32C22×C3×Dic5—41no—
33C22×C3×Dic5D411yescharacteristic
34C3×C22⋊AGL(1,𝔽5)—22no—
35C3×C22⋊AGL(1,𝔽5)—41no—
36C3×#704—22no—
37C3×#704—41no—
38C2×C3×#170—41no—
39C3×C5×C22⋊C4—41no—
40C3×#685—42no—
41C2×C3×#100—51no—
42C2×C3×#99—51no—
43C3×#386—51no—
44C22×C22⋊D5C22×C311yescharacteristic
45C23×Dic5C3×C411yescharacteristic, complemented
46C2×C22⋊AGL(1,𝔽5)—21no—
47C2×#704—21no—
48C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
49C2×#685—21no—
50#4013—21no—
51#4013C3×C412yescomplemented
52#4011—21no—
53#4011C3×C412yescomplemented
54#3963—21no—
55#1390—51noSylow
56C23×C3×C5—21no—
57C23×C3×C5—21no—
58C23×C3×C5—41no—
59C23×C3×C5—41no—
60C23×C3×C5C4211yescharacteristic
61C23×C3×C5C22⋊C411yescharacteristic
62C23×C3×C5C4⋊C411yescharacteristic
63C22×C3×D5—21no—
64C22×C3×D5—21no—
65C22×C3×D5—41no—
66C22×C3×D5—41no—
67C22×C3×D5C22⋊C411yescharacteristic
68C22×C3×D5C4⋊C411yescharacteristic
69C2×C3×AGL(1,𝔽5)—42no—
70C2×C3×AGL(1,𝔽5)—81no—
71C2×C3×AGL(1,𝔽5)—81no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C3×C22⋊D5—41no—
76C3×C22⋊D5—41no—
77C3×C22⋊D5—41no—
78C3×C22⋊D5—41no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—22no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—42no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5—42no—
86C2×C3×Dic5C22⋊C411yescharacteristic
87C2×C3×Dic5C4⋊C411yescharacteristic
88C3×#170—42no—
89C22×C3×D4—51no—
90C23×C3×C4—51no—
91C2×C3×M16—101no—
92C2×C3×C22⋊C4—101no—
93C2×C3×C22⋊C4—101no—
94C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
95C3×#100—52no—
96C3×#100—101no—
97C3×#99—52no—
98C3×#99—101no—
99C3×#95—101no—
100C24×C5C2×C3×C411yescharacteristic
101C23×D5C3×D411yescharacteristic
102C22×AGL(1,𝔽5)—41no—
103C22×C4×C5—21no—
104C2×C22⋊D5—41no—
105C2×C22⋊D5—41no—
106C2×C22⋊D5C2×C3×C411yescharacteristic
107C2×C22⋊D5C2×C3×C411yescharacteristic
108C2×C22⋊D5C3×D411yescharacteristic
109C2×C22⋊D5C3×Q811yescharacteristic
110C22×Dic5—21no—
111C22×Dic5—42no—
112C22×Dic5—41no—
113C22×Dic5C3×D411yescharacteristic
114C22⋊AGL(1,𝔽5)—22no—
115C22⋊AGL(1,𝔽5)—41no—
116#704—22no—
117#704—41no—
118C2×#170—41no—
119C5×C22⋊C4—41no—
120#685—42no—
121C2×#100—51no—
122C2×#99—51no—
123#386—51no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—41no—
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5—41no—
133C22×C3×C5#9511yescharacteristic
134C22×C3×C5#9911yescharacteristic
135C22×C3×C5#9911yescharacteristic
136C2×C3×D5—21no—
137C2×C3×D5—21no—
138C2×C3×D5—41no—
139C2×C3×D5—41no—
140C2×C3×D5—41no—
141C2×C3×D5—41no—
142C2×C3×D5—81no—
143C3×AGL(1,𝔽5)—82no—
144C3×C4×C5—81no—
145C3×Dic5—21no—
146C3×Dic5—21no—
147C3×Dic5—42no—
148C24×C3—51no—
149C24×C3C2×AGL(1,𝔽5)11yescharacteristic
150C2×C3×D4—51no—
151C2×C3×D4—51no—
152C2×C3×D4—51no—
153C2×C3×D4—51no—
154C2×C3×D4—201no—
155C2×C3×D4—201no—
156C22×C3×C4—21no—
157C22×C3×C4—51no—
158C22×C3×C4—101no—
159C22×C3×C4—202no—
160C22×C3×C4—201no—
161C22×C3×C4—201no—
162C3×M16—102no—
163C3×M16—201no—
164C2×C3×C8—201no—
165C3×C22⋊C4—41no—
166C3×C22⋊C4—102no—
167C3×C22⋊C4—202no—
168C3×C22⋊C4—201no—
169C23×C5—21no—
170C23×C5—21no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5C3×C4211yescharacteristic
174C23×C5C3×C22⋊C411yescharacteristic
175C23×C5C3×C4⋊C411yescharacteristic
176C22×D5—21no—
177C22×D5—21no—
178C22×D5—41no—
179C22×D5—41no—
180C22×D5C3×C22⋊C411yescharacteristic
181C22×D5C3×C4⋊C411yescharacteristic
182C2×AGL(1,𝔽5)—42no—
183C2×AGL(1,𝔽5)—81no—
184C2×AGL(1,𝔽5)—81no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C22⋊D5—41no—
189C22⋊D5—41no—
190C22⋊D5—41no—
191C22⋊D5—41no—
192C2×Dic5—21no—
193C2×Dic5—21no—
194C2×Dic5—22no—
195C2×Dic5—41no—
196C2×Dic5—42no—
197C2×Dic5—41no—
198C2×Dic5—42no—
199C2×Dic5C3×C22⋊C411yescharacteristic
200C2×Dic5C3×C4⋊C411yescharacteristic
201#170—42no—
202C22×D4—51no—
203C23×C4—51no—
204C2×M16—101no—
205C2×C22⋊C4—101no—
206C2×C22⋊C4—101no—
207C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
208#100—52no—
209#100—101no—
210#99—52no—
211#99—101no—
212#95—101no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—41no—
216C2×C3×C5—41no—
217C2×C3×C5#34211yescharacteristic
218C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
219C2×C3×C5#35211yescharacteristic
220C3×D5—41no—
221C3×D5—41no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—41no—
225C23×C3—41no—
226C23×C3—51no—
227C23×C3—51no—
228C23×C3—101no—
229C23×C3—101no—
230C23×C3—201no—
231C23×C3—201no—
232C23×C3C4×AGL(1,𝔽5)11yescharacteristic
233C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
234C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4—102no—
247C2×C3×C4—201no—
248C2×C3×C4—202no—
249C2×C3×C4—201no—
250C2×C3×C4—202no—
251C2×C3×C4—202no—
252C2×C3×C4—401no—
253C2×C3×C4—401no—
254C3×C8—202no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—42no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5C3×#9511yescharacteristic
265C22×C5C3×#9911yescharacteristic
266C22×C5C3×#9911yescharacteristic
267C2×D5—21no—
268C2×D5—21no—
269C2×D5—41no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—41no—
273C2×D5—81no—
274AGL(1,𝔽5)—82no—
275C4×C5—81no—
276Dic5—21no—
277Dic5—21no—
278Dic5—42no—
279C24—51no—
280C24C2×C3×AGL(1,𝔽5)11yescharacteristic
281C2×D4—51no—
282C2×D4—51no—
283C2×D4—51no—
284C2×D4—51no—
285C2×D4—201no—
286C2×D4—201no—
287C22×C4—21no—
288C22×C4—51no—
289C22×C4—101no—
290C22×C4—202no—
291C22×C4—201no—
292C22×C4—201no—
293M16—102no—
294M16—201no—
295C2×C8—201no—
296C22⋊C4—41no—
297C22⋊C4—102no—
298C22⋊C4—202no—
299C22⋊C4—201no—
300C3×C5#139011yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—101no—
311C22×C3—101no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3—201no—
316C22×C3—401no—
317C22×C3#399911yescharacteristic
318C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
319C22×C3#401111yescharacteristic
320C3×C4—81no—
321C3×C4—101no—
322C3×C4—101no—
323C3×C4—202no—
324C3×C4—402no—
325C2×C5—21no—
326C2×C5—21no—
327C2×C5—41no—
328C2×C5—41no—
329C2×C5C3×#34211yescharacteristic
330C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
331C2×C5C3×#35211yescharacteristic
332D5—41no—
333D5—41no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—51no—
339C23—51no—
340C23—101no—
341C23—101no—
342C23—201no—
343C23—201no—
344C23C3×C4×AGL(1,𝔽5)11yescharacteristic
345C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
346C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
347D4—201no—
348D4—201no—
349D4—201no—
350D4—201no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—101no—
357C2×C4—101no—
358C2×C4—102no—
359C2×C4—201no—
360C2×C4—202no—
361C2×C4—201no—
362C2×C4—202no—
363C2×C4—202no—
364C2×C4—401no—
365C2×C4—401no—
366C8—202no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—201no—
372C2×C3—201no—
373C2×C3#6486411yescharacteristic
374C2×C3#6486511yescharacteristic
375C2×C3#6491711yescharacteristic
376C5C3×#139011yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—41no—
385C22—41no—
386C22—101no—
387C22—101no—
388C22—201no—
389C22—201no—
390C22—201no—
391C22—201no—
392C22—401no—
393C22C3×#399911yescharacteristic
394C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
395C22C3×#401111yescharacteristic
396C4—81no—
397C4—101no—
398C4—101no—
399C4—202no—
400C4—402no—
401C3#1059870911yescharacteristic, direct product factor, Sylow
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—201no—
407C2—201no—
408C2C3×#6486411yescharacteristic
409C2C3×#6486511yescharacteristic
410C2C3×#6491711yescharacteristic
subgroupG/H
centerC22×C3#3999
commutatorC23×C5C3×C42
FrattiniC24C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5#99
prime radicalC22×C3×C22⋊D5C22
cosocleC22×C22⋊D5C22×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1390
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C24×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10598709C3direct (N × H)
6. C23×C3×Dic5C4semidirect
9. C2×C3×C5×C22⋊C4C4semidirect
12. C3×#4013C4semidirect
14. C3×#4011C4semidirect
45. C23×Dic5C3×C4semidirect
48. C2×C5×C22⋊C4C3×C4semidirect
51. #4013C3×C4semidirect
53. #4011C3×C4semidirect
94. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
207. C2×C22⋊C4C3×AGL(1,𝔽5)semidirect
300. C3×C5#1390semidirect
376. C5C3×#1390semidirect
401. C3#10598709direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40132
C2×C3×#40112
C3×#652472
#105987093
C3×#13905