Finite Group Databasebeta

← C5×#19287 #11942007

Subgroups — C5×#19287 #11942007

Order 1280.

582 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3170C211yesmaximal, characteristic
2C5×#3078C212yesmaximal
3C2×C5×#446C211yesmaximal, characteristic
4C5×#1704C214yesmaximal, complemented
5C5×#1696C212yesmaximal, complemented
6C5×#1690C212yesmaximal, complemented
7C5×#1566C211yesmaximal, characteristic
8C5×#1550C212yesmaximal
9C5×#533C2212yes—
10C2×C4×C5×Q8C2211yescharacteristic
11C5×#500C2211yescharacteristic
12C5×#494C2211yescharacteristic
13C5×#487C2212yes—
14C5×#479—24no—
15C5×#477C2214yes—
16C5×#475C2214yes—
17C5×#467—21no—
18C5×#467—21no—
19C5×#446—21no—
20C5×#446—21no—
21C5×#446C2212yes—
22C5×#446C2212yes—
23C4×C5×Q16—21no—
24C4×C5×Q16—21no—
25C5×#428—22no—
26C5×#423C2212yes—
27C2×C5×C4⋊C8—21no—
28C2×C5×C4⋊C8C2211yescharacteristic
29C5×#419—22no—
30C2×C5×#97—21no—
31C2×C4×C5×C8C2211yescharacteristic
32C5×#334C2212yes—
33C5×#334C2212yes—
34C5×#333C2214yes—
35C5×#332C2214yes—
36#19287C511yesmaximal, characteristic, direct product factor, Sylow
37C22×C5×Q8D411yescharacteristic
38C2×C5×Q16—21no—
39C2×C5×Q16—21no—
40C2×C5×M16—22no—
41C22×C5×C8—21no—
42C22×C5×C8D411yescharacteristic
43C22×C5×C8D411yescharacteristic
44C5×C4⋊Q8C2312yes—
45C5×C4⋊Q8C2312yes—
46C5×#125—22no—
47C5×C22⋊Q8—22no—
48C5×C22⋊Q8—22no—
49C4×C5×Q8—21no—
50C4×C5×Q8—21no—
51C4×C5×Q8—22no—
52C4×C5×Q8—22no—
53C4×C5×Q8D412yes—
54C4×C5×Q8C2312yes—
55C5×#117—22no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4D411yescharacteristic
58C2×C42×C5—21no—
59C2×C42×C5C2311yescharacteristic
60C5×#107—21no—
61C5×#107—21no—
62C5×#107—24no—
63C5×#106—24no—
64C5×C4⋊C8—22no—
65C5×C4⋊C8—22no—
66C5×C4⋊C8—21no—
67C5×C4⋊C8—22no—
68C5×C4⋊C8C2312yes—
69C5×C4⋊C8C2314yes—
70C5×#103—24no—
71C5×#103—24no—
72C5×#103—22no—
73C5×#103—22no—
74C5×#97—22no—
75C5×#97—22no—
76C4×C5×C8D411yescharacteristic
77C4×C5×C8D411yescharacteristic
78C4×C5×C8C2311yescharacteristic
79C4×C5×C8C2311yescharacteristic
80#3170C2×C511yescharacteristic
81#3078C2×C512yes—
82C2×#446C2×C511yescharacteristic
83#1704C2×C514yescomplemented
84#1696C2×C512yescomplemented
85#1690C2×C512yescomplemented
86#1566C2×C511yescharacteristic
87#1550C2×C512yes—
88C2×C5×Q8—21no—
89C2×C5×Q8—24no—
90C2×C5×Q8—22no—
91C2×C5×Q8—22no—
92C2×C5×Q8C2×D412yes—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5#4111yescharacteristic
98C5×Q16—42no—
99C5×Q16—42no—
100C5×M16—44no—
101C2×C5×C8—22no—
102C2×C5×C8—22no—
103C2×C5×C8—24no—
104C2×C5×C8—41no—
105C2×C5×C8—42no—
106C2×C5×C8C2×D411yescharacteristic
107C2×C5×C8C2×D411yescharacteristic
108C2×C5×C8C2×D411yescharacteristic
109C2×C5×C8C2×D411yescharacteristic
110C5×C4⋊C4—22no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4—22no—
115C5×C4⋊C4—22no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—42no—
118C5×C4⋊C4—42no—
119C5×C4⋊C4C2×D412yes—
120C5×C22⋊C4—42no—
121C42×C5—22no—
122C42×C5—22no—
123C42×C5—42no—
124C42×C5C2×D411yescharacteristic
125C42×C5C2×D411yescharacteristic
126C42×C5#4111yescharacteristic
127C42×C5C2411yescharacteristic
128#533C22×C512yes—
129C2×C4×Q8C22×C511yescharacteristic
130#500C22×C511yescharacteristic
131#494C22×C511yescharacteristic
132#487C22×C512yes—
133#479—24no—
134#477C22×C514yes—
135#475C22×C514yes—
136#467—21no—
137#467—21no—
138#446—21no—
139#446—21no—
140#446C22×C512yes—
141#446C22×C512yes—
142C4×Q16—21no—
143C4×Q16—21no—
144#428—22no—
145#423C22×C512yes—
146C2×C4⋊C8—21no—
147C2×C4⋊C8C22×C511yescharacteristic
148#419—22no—
149C2×#97—21no—
150C2×C4×C8C22×C511yescharacteristic
151#334C22×C512yes—
152#334C22×C512yes—
153#333C22×C514yes—
154#332C22×C514yes—
155C23×C5#12111yescharacteristic
156C5×Q8—24no—
157C5×Q8—42no—
158C5×Q8—42no—
159C5×Q8—42no—
160C5×Q8—82no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—41no—
166C2×C4×C5—42no—
167C2×C4×C5—42no—
168C2×C4×C5—42no—
169C2×C4×C5—42no—
170C2×C4×C5#12111yescharacteristic
171C2×C4×C5#12111yescharacteristic
172C2×C4×C5#12111yescharacteristic
173C2×C4×C5#13714yes—
174C2×C4×C5C22×D411yescharacteristic
175C2×C4×C5C22×D411yescharacteristic
176C2×C4×C5C2×#4111yescharacteristic
177C5×C8—21no—
178C5×C8—21no—
179C5×C8—21no—
180C5×C8—44no—
181C5×C8—42no—
182C5×C8#13712yes—
183C22×Q8C5×D411yescharacteristic
184C2×Q16—21no—
185C2×Q16—21no—
186C2×M16—22no—
187C22×C8—21no—
188C22×C8C5×D411yescharacteristic
189C22×C8C5×D411yescharacteristic
190C4⋊Q8C23×C512yes—
191C4⋊Q8C23×C512yes—
192#125—22no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C4×Q8—21no—
196C4×Q8—21no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×Q8C5×D412yes—
200C4×Q8C23×C512yes—
201#117—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C5×D411yescharacteristic
204C2×C42—21no—
205C2×C42C23×C511yescharacteristic
206#107—21no—
207#107—21no—
208#107—24no—
209#106—24no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—21no—
213C4⋊C8—22no—
214C4⋊C8C23×C512yes—
215C4⋊C8C23×C514yes—
216#103—24no—
217#103—24no—
218#103—22no—
219#103—22no—
220#97—22no—
221#97—22no—
222C4×C8C5×D411yescharacteristic
223C4×C8C5×D411yescharacteristic
224C4×C8C23×C511yescharacteristic
225C4×C8C23×C511yescharacteristic
226C22×C5—21no—
227C22×C5—21no—
228C22×C5#47012yes—
229C22×C5C2×#12111yescharacteristic
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—42no—
234C4×C5—42no—
235C4×C5—82no—
236C4×C5—82no—
237C4×C5#47012yes—
238C4×C5C2×#13711yescharacteristic
239C4×C5C2×#13712yes—
240C4×C5#57511yescharacteristic
241C2×Q8—21no—
242C2×Q8—24no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8C2×C5×D412yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C2×C5×D411yescharacteristic
249C22×C4C2×C5×D411yescharacteristic
250C22×C4C5×#4111yescharacteristic
251Q16—42no—
252Q16—42no—
253M16—44no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—24no—
257C2×C8—41no—
258C2×C8—42no—
259C2×C8C2×C5×D411yescharacteristic
260C2×C8C2×C5×D411yescharacteristic
261C2×C8C2×C5×D411yescharacteristic
262C2×C8C2×C5×D411yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4C2×C5×D412yes—
273C22⋊C4—42no—
274C42—22no—
275C42—22no—
276C42—42no—
277C42C2×C5×D411yescharacteristic
278C42C2×C5×D411yescharacteristic
279C42C5×#4111yescharacteristic
280C42C24×C511yescharacteristic
281C2×C5—22no—
282C2×C5#303711yescharacteristic
283C2×C5C2×#47011yescharacteristic
284C2×C5#306711yescharacteristic
285C23C5×#12111yescharacteristic
286Q8—24no—
287Q8—42no—
288Q8—42no—
289Q8—42no—
290Q8—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4C5×#12111yescharacteristic
301C2×C4C5×#12111yescharacteristic
302C2×C4C5×#12111yescharacteristic
303C2×C4C5×#13714yes—
304C2×C4C22×C5×D411yescharacteristic
305C2×C4C22×C5×D411yescharacteristic
306C2×C4C2×C5×#4111yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—44no—
311C8—42no—
312C8C5×#13712yes—
313C5#1928711yescharacteristic, direct product factor, Sylow
314C22—21no—
315C22—21no—
316C22C5×#47012yes—
317C22C2×C5×#12111yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—82no—
324C4—82no—
325C4C5×#47012yes—
326C4C2×C5×#13711yescharacteristic
327C4C2×C5×#13712yes—
328C4C5×#57511yescharacteristic
329C2—22no—
330C2C5×#303711yescharacteristic
331C2C2×C5×#47011yescharacteristic
332C2C5×#306711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC23×C5#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1704C2semidirect
5. C5×#1696C2semidirect
6. C5×#1690C2semidirect
36. #19287C5direct (N × H)
83. #1704C2×C5semidirect
84. #1696C2×C5semidirect
85. #1690C2×C5semidirect
313. C5#19287direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31702
C5×#30782
C2×C5×#4462
C5×#17042
C5×#16962
C5×#16902
C5×#15662
C5×#15502
#192875