Finite Group Databasebeta

← C3×D5⋊#359 #14314010

Subgroups — C3×D5⋊#359 #14314010

Order 1920.

448 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#135C211yesmaximal, characteristic
2C3×D5⋊#108C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊C16C211yesmaximal, characteristic, complemented
4C3×#64909C212yesmaximal, complemented
5C3×#64905C212yesmaximal, complemented
6D5⋊#359C311yesmaximal, characteristic, direct product factor, Hall
7C3×D5×#41—21no—
8C3×D5⋊M16—21no—
9C3×C5×#135C411yescharacteristic
10C3×#4096—21no—
11C3×#4065C2211yescharacteristic
12C3×D5×Q16C411yescharacteristic
13C3×#4062—21no—
14C3×D5×SD16—21no—
15C3×#4058C2211yescharacteristic
16C3×D5×D8C411yescharacteristic
17C3×#4050C411yescharacteristic
18C2×C3×C8×D5C2211yescharacteristic
19C2×C3×#674—21no—
20C3×#3996C2212yescomplemented
21C3×#3995—21no—
22C3×D5⋊C16—21no—
23C3×D5⋊C16C2212yescomplemented
24C2×C3×#359—51nomaximal, Hall
25D5×#135C2×C311yescharacteristic
26D5⋊#108C2×C311yescharacteristic, complemented
27C2×D5⋊C16C2×C311yescharacteristic, complemented
28#64909C2×C312yescomplemented
29#64905C2×C312yescomplemented
30C3×C5×#41—21no—
31C3×#713—21no—
32C3×Q8×D5—21no—
33C3×#711—21no—
34C3×#711—41no—
35C3×D4×D5—21no—
36C3×D4×D5—41no—
37C3×#709—21no—
38C3×#709—41no—
39C2×C3×C4×D5—41no—
40C2×C3×C4×D5D411yescharacteristic
41C3×#704—41no—
42C3×#700—22no—
43C3×D5⋊C8—41no—
44C3×C5×Q16C2×C411yescharacteristic
45C3×C5×SD16—21no—
46C3×C5×D8C2×C411yescharacteristic
47C2×C3×C5×C8C2×C411yescharacteristic
48C3×#689—21no—
49C3×#688—21no—
50C3×#687—21no—
51C3×#686—21no—
52C2×C3×#168D411yescharacteristic
53C3×Dic20C2×C411yescharacteristic
54C3×D40C2×C411yescharacteristic
55C3×#677—21no—
56C3×C8×D5C2×C411yescharacteristic
57C3×C8×D5D411yescharacteristic
58C3×C8×D5D411yescharacteristic
59C3×C8×D5C2311yescharacteristic
60C3×#674—22no—
61C2×C3×#135—51no—
62C22×C3×C16—51no—
63C2×C3×#108—51no—
64C3×#359—52no—
65C3×#359—52no—
66D5×#41—21no—
67D5⋊M16—21no—
68C5×#135C3×C411yescharacteristic
69#4096—21no—
70#4065C22×C311yescharacteristic
71D5×Q16C3×C411yescharacteristic
72#4062—21no—
73D5×SD16—21no—
74#4058C22×C311yescharacteristic
75D5×D8C3×C411yescharacteristic
76#4050C3×C411yescharacteristic
77C2×C8×D5C22×C311yescharacteristic
78C2×#674—21no—
79#3996C22×C312yescomplemented
80#3995—21no—
81D5⋊C16—21no—
82D5⋊C16C22×C312yescomplemented
83C2×#359—51noSylow
84C22×C3×D5—41no—
85C22×C3×D5SD1611yescharacteristic
86C3×C5×Q8—21no—
87C3×C5×D4—21no—
88C3×C5×D4—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C3×C22⋊D5—41no—
92C3×C22⋊D5—41no—
93C3×C22⋊D5—41no—
94C2×C3×Dic5—41no—
95C2×C3×Dic5D811yescharacteristic
96C3×D20—21no—
97C3×D20—41no—
98C3×C4×D5—41no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101C3×C4×D5C22⋊C411yescharacteristic
102C3×C4×D5D811yescharacteristic
103C3×C4×D5SD1611yescharacteristic
104C3×C4×D5C2×D411yescharacteristic
105C3×Dic10—21no—
106C3×Dic10—41no—
107C3×#170—42no—
108C3×C5×C8C22⋊C411yescharacteristic
109C3×C5×C8C22×C411yescharacteristic
110C3×#168C22⋊C411yescharacteristic
111C3×#168C2×D411yescharacteristic
112C2×C3×#41—101no—
113C3×#135—51no—
114C3×#135—51no—
115C3×#135—51no—
116C3×#135—101no—
117C3×#135—101no—
118C3×#135AGL(1,𝔽5)11yescharacteristic
119C2×C3×Q16—51no—
120C2×C3×SD16—101no—
121C2×C3×D8—51no—
122C2×C3×M16—101no—
123C22×C3×C8—51no—
124C2×C3×C16—52no—
125C2×C3×C16—101no—
126C2×C3×C16—101no—
127C3×#108—52no—
128C3×#108—101no—
129C5×#41—21no—
130#713—21no—
131Q8×D5—21no—
132#711—21no—
133#711—41no—
134D4×D5—21no—
135D4×D5—41no—
136#709—21no—
137#709—41no—
138C2×C4×D5—41no—
139C2×C4×D5C3×D411yescharacteristic
140#704—41no—
141#700—22no—
142D5⋊C8—41no—
143C5×Q16C2×C3×C411yescharacteristic
144C5×SD16—21no—
145C5×D8C2×C3×C411yescharacteristic
146C2×C5×C8C2×C3×C411yescharacteristic
147#689—21no—
148#688—21no—
149#687—21no—
150#686—21no—
151C2×#168C3×D411yescharacteristic
152Dic20C2×C3×C411yescharacteristic
153D40C2×C3×C411yescharacteristic
154#677—21no—
155C8×D5C2×C3×C411yescharacteristic
156C8×D5C3×D411yescharacteristic
157C8×D5C3×D411yescharacteristic
158C8×D5C23×C311yescharacteristic
159#674—22no—
160C2×#135—51no—
161C22×C16—51no—
162C2×#108—51no—
163#359—52no—
164#359—52no—
165C22×C3×C5—41no—
166C22×C3×C5#10211yescharacteristic
167C2×C3×D5—22no—
168C2×C3×D5—41no—
169C2×C3×D5—82no—
170C2×C3×D5#10211yescharacteristic
171C2×C3×D5C2×SD1611yescharacteristic
172C3×C4×C5—41no—
173C3×C4×C5#10211yescharacteristic
174C3×C4×C5C2×C22⋊C411yescharacteristic
175C3×Dic5—41no—
176C3×Dic5#10211yescharacteristic
177C3×Dic5C2×D811yescharacteristic
178C3×#41—21no—
179C3×#41—101no—
180C3×#41—101no—
181C3×#41—101no—
182C3×#41—201no—
183C3×#41—201no—
184C2×C3×Q8—101no—
185C2×C3×D4—101no—
186C2×C3×D4—201no—
187C22×C3×C4—51no—
188C22×C3×C4—201no—
189C3×Q16—51no—
190C3×Q16—101no—
191C3×Q16C2×AGL(1,𝔽5)11yescharacteristic
192C3×SD16—21no—
193C3×SD16—101no—
194C3×SD16—101no—
195C3×SD16—101no—
196C3×D8—51no—
197C3×D8—101no—
198C3×D8C2×AGL(1,𝔽5)11yescharacteristic
199C3×M16—102no—
200C3×M16—201no—
201C2×C3×C8—51no—
202C2×C3×C8—51no—
203C2×C3×C8—51no—
204C2×C3×C8—51no—
205C2×C3×C8—51no—
206C2×C3×C8—201no—
207C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
208C3×C16—102no—
209C22×D5—41no—
210C22×D5C3×SD1611yescharacteristic
211C5×Q8—21no—
212C5×D4—21no—
213C5×D4—41no—
214C2×C4×C5—41no—
215C2×C4×C5C3×C22⋊C411yescharacteristic
216C22⋊D5—41no—
217C22⋊D5—41no—
218C22⋊D5—41no—
219C2×Dic5—41no—
220C2×Dic5C3×D811yescharacteristic
221D20—21no—
222D20—41no—
223C4×D5—41no—
224C4×D5—41no—
225C4×D5—41no—
226C4×D5C3×C22⋊C411yescharacteristic
227C4×D5C3×D811yescharacteristic
228C4×D5C3×SD1611yescharacteristic
229C4×D5C2×C3×D411yescharacteristic
230Dic10—21no—
231Dic10—41no—
232#170—42no—
233C5×C8C3×C22⋊C411yescharacteristic
234C5×C8C22×C3×C411yescharacteristic
235#168C3×C22⋊C411yescharacteristic
236#168C2×C3×D411yescharacteristic
237C2×#41—101no—
238#135—51no—
239#135—51no—
240#135—51no—
241#135—101no—
242#135—101no—
243#135C3×AGL(1,𝔽5)11yescharacteristic
244C2×Q16—51no—
245C2×SD16—101no—
246C2×D8—51no—
247C2×M16—101no—
248C22×C8—51no—
249C2×C16—52no—
250C2×C16—101no—
251C2×C16—101no—
252#108—52no—
253#108—101no—
254C2×C3×C5—21no—
255C2×C3×C5—81no—
256C2×C3×C5C2×#10211yescharacteristic
257C3×D5—21no—
258C3×D5—81no—
259C3×D5#35912yescomplemented
260C23×C3—51no—
261C23×C3—201no—
262C3×Q8—21no—
263C3×Q8—101no—
264C3×Q8—201no—
265C3×D4—21no—
266C3×D4—41no—
267C3×D4—101no—
268C3×D4—201no—
269C3×D4—201no—
270C3×D4—201no—
271C3×D4—201no—
272C2×C3×C4—41no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—201no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
283C3×C8—51no—
284C3×C8—51no—
285C3×C8—202no—
286C3×C8C22⋊AGL(1,𝔽5)11yescharacteristic
287C3×C8C22×AGL(1,𝔽5)11yescharacteristic
288C22×C5—41no—
289C22×C5C3×#10211yescharacteristic
290C2×D5—22no—
291C2×D5—41no—
292C2×D5—82no—
293C2×D5C3×#10211yescharacteristic
294C2×D5C2×C3×SD1611yescharacteristic
295C4×C5—41no—
296C4×C5C3×#10211yescharacteristic
297C4×C5C2×C3×C22⋊C411yescharacteristic
298Dic5—41no—
299Dic5C3×#10211yescharacteristic
300Dic5C2×C3×D811yescharacteristic
301#41—21no—
302#41—101no—
303#41—101no—
304#41—101no—
305#41—201no—
306#41—201no—
307C2×Q8—101no—
308C2×D4—101no—
309C2×D4—201no—
310C22×C4—51no—
311C22×C4—201no—
312Q16—51no—
313Q16—101no—
314Q16C2×C3×AGL(1,𝔽5)11yescharacteristic
315SD16—21no—
316SD16—101no—
317SD16—101no—
318SD16—101no—
319D8—51no—
320D8—101no—
321D8C2×C3×AGL(1,𝔽5)11yescharacteristic
322M16—102no—
323M16—201no—
324C2×C8—51no—
325C2×C8—51no—
326C2×C8—51no—
327C2×C8—51no—
328C2×C8—51no—
329C2×C8—201no—
330C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
331C16—102no—
332C3×C5C2×#35911yescharacteristic, complemented, Hall
333C22×C3—41no—
334C22×C3—51no—
335C22×C3—51no—
336C22×C3—102no—
337C22×C3—201no—
338C22×C3—402no—
339C22×C3#400711yescharacteristic
340C3×C4—41no—
341C3×C4—51no—
342C3×C4—51no—
343C3×C4—201no—
344C3×C4#400711yescharacteristic
345C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
346C2×C5—21no—
347C2×C5—81no—
348C2×C5C2×C3×#10211yescharacteristic
349D5—21no—
350D5—81no—
351D5C3×#35912yescomplemented
352C23—51no—
353C23—201no—
354Q8—21no—
355Q8—101no—
356Q8—201no—
357D4—21no—
358D4—41no—
359D4—101no—
360D4—201no—
361D4—201no—
362D4—201no—
363D4—201no—
364C2×C4—41no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—51no—
369C2×C4—51no—
370C2×C4—201no—
371C2×C4—201no—
372C2×C4—201no—
373C2×C4—201no—
374C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
375C8—51no—
376C8—51no—
377C8—202no—
378C8C3×C22⋊AGL(1,𝔽5)11yescharacteristic
379C8C22×C3×AGL(1,𝔽5)11yescharacteristic
380C2×C3—21no—
381C2×C3—52no—
382C2×C3—81no—
383C2×C3—101no—
384C2×C3—401no—
385C2×C3C2×#400711yescharacteristic
386C5C2×C3×#35911yescharacteristic, complemented, Sylow
387C22—41no—
388C22—51no—
389C22—51no—
390C22—102no—
391C22—201no—
392C22—402no—
393C22C3×#400711yescharacteristic
394C4—41no—
395C4—51no—
396C4—51no—
397C4—201no—
398C4C3×#400711yescharacteristic
399C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
400C3D5⋊#35911yescharacteristic, direct product factor, Sylow
401C2—21no—
402C2—52no—
403C2—81no—
404C2—101no—
405C2—401no—
406C2C2×C3×#400711yescharacteristic
subgroupG/H
centerC3×C4#4007
commutatorC5×C8C22×C3×C4
FrattiniC8C22×C3×AGL(1,𝔽5)
FittingC3×C5×#135C4
socleC2×C3×C5C2×#102
prime radicalC3×D5×#135C2
cosocleC8×D5C23×C3
hypercenterC3×#135AGL(1,𝔽5)
hypocenterC5C2×C3×#359
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#135

Complements

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

NH ≅ G/Ntype
2. C3×D5⋊#108C2semidirect
3. C2×C3×D5⋊C16C2semidirect
4. C3×#64909C2semidirect
5. C3×#64905C2semidirect
6. D5⋊#359C3direct (N × H)
20. C3×#3996C22semidirect
23. C3×D5⋊C16C22semidirect
26. D5⋊#108C2×C3semidirect
27. C2×D5⋊C16C2×C3semidirect
28. #64909C2×C3semidirect
29. #64905C2×C3semidirect
79. #3996C22×C3semidirect
82. D5⋊C16C22×C3semidirect
259. C3×D5#359semidirect
332. C3×C5C2×#359semidirect
351. D5C3×#359semidirect
386. C5C2×C3×#359semidirect
400. C3D5⋊#359direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1352
C3×D5⋊#1082
C2×C3×D5⋊C162
C3×#649092
C3×#649052
D5⋊#3593
C2×C3×#3595