Finite Group Databasebeta

← C5×#10469 #11933189

Subgroups — C5×#10469 #11933189

Order 1280.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3077C211yesmaximal, characteristic
2C5×#1804C211yesmaximal, characteristic
3C5×#1571C211yesmaximal, characteristic, complemented
4C5×#1542C211yesmaximal, characteristic, complemented
5C5×#1518C211yesmaximal, characteristic, complemented
6C5×#1460C211yesmaximal, characteristic
7C5×#1286C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C5×#478—22no—
11C5×#476—21no—
12C5×#474—21no—
13C5×#431C2211yescharacteristic
14C5×#431C2211yescharacteristic
15C5×#428—21no—
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#418—21no—
19C2×C5×#102—21no—
20C5×#382C2211yescharacteristic
21C5×#340—21no—
22C5×#335—22no—
23C5×#333—21no—
24C5×#332—21no—
25C5×#328—22no—
26C5×#323—22no—
27#10469C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×D4D411yescharacteristic
29C23×C4×C5—21no—
30C2×C5×M16—21no—
31C22×C5×C8—21no—
32C5×C4⋊Q8D411yescharacteristic
33C5×C4⋊Q8D411yescharacteristic
34C5×#125—21no—
35C5×C22⋊Q8—21no—
36C5×C22⋊Q8—21no—
37C4×C5×Q8—21no—
38C4×C5×Q8—21no—
39C4×C5×D4—21no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C5×#117—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4D411yescharacteristic
46C2×C5×C22⋊C4—21no—
47C2×C42×C5C2311yescharacteristic
48C5×#107—22no—
49C5×#106—22no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8D412yes—
56C5×#102—22no—
57C5×#102—22no—
58C5×#102—42no—
59C5×C22⋊C8—21no—
60C5×C22⋊C8D412yes—
61C4×C5×C8—21no—
62C4×C5×C8—21no—
63C5×#95—21no—
64C5×#95—21no—
65#3077C2×C511yescharacteristic
66#1804C2×C511yescharacteristic
67#1571C2×C511yescharacteristic, complemented
68#1542C2×C511yescharacteristic, complemented
69#1518C2×C511yescharacteristic, complemented
70#1460C2×C511yescharacteristic
71#1286C2×C511yescharacteristic, complemented
72C24×C5—21no—
73C2×C5×Q8—21no—
74C2×C5×Q8—21no—
75C2×C5×D4—21no—
76C2×C5×D4—21no—
77C2×C5×D4—21no—
78C2×C5×D4—21no—
79C2×C5×D4—21no—
80C2×C5×D4Q1612yes—
81C22×C4×C5—21no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—82no—
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4111yescharacteristic
89C5×M16—41no—
90C5×M16—41no—
91C2×C5×C8—22no—
92C2×C5×C8—22no—
93C2×C5×C8—41no—
94C2×C5×C8—41no—
95C2×C5×C8—41no—
96C2×C5×C8—41no—
97C5×C4⋊C4—21no—
98C5×C4⋊C4—21no—
99C5×C4⋊C4—21no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—41no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4—41no—
107C5×C22⋊C4—41no—
108C5×C22⋊C4—41no—
109C5×C22⋊C4—41no—
110C42×C5—41no—
111C42×C5C2×D411yescharacteristic
112C42×C5C2×D411yescharacteristic
113C42×C5#4111yescharacteristic
114C42×C5#4111yescharacteristic
115#533C22×C511yescharacteristic
116C2×C4×D4C22×C511yescharacteristic
117#478—22no—
118#476—21no—
119#474—21no—
120#431C22×C511yescharacteristic
121#431C22×C511yescharacteristic
122#428—21no—
123#423C22×C511yescharacteristic
124C2×C4⋊C8C22×C511yescharacteristic
125#418—21no—
126C2×#102—21no—
127#382C22×C511yescharacteristic
128#340—21no—
129#335—22no—
130#333—21no—
131#332—21no—
132#328—22no—
133#323—22no—
134C23×C5—22no—
135C23×C5—41no—
136C23×C5—41no—
137C23×C5—81no—
138C23×C5—81no—
139C23×C5#12111yescharacteristic
140C5×Q8—81no—
141C5×Q8—81no—
142C5×D4—22no—
143C5×D4—22no—
144C5×D4—41no—
145C5×D4—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—82no—
152C2×C4×C5—82no—
153C2×C4×C5—81no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5—81no—
157C2×C4×C5#12011yescharacteristic
158C2×C4×C5#12111yescharacteristic
159C2×C4×C5#12111yescharacteristic
160C2×C4×C5#12311yescharacteristic
161C2×C4×C5#12311yescharacteristic
162C2×C4×C5#12411yescharacteristic
163C2×C4×C5C2×Q1611yescharacteristic
164C2×C4×C5#13511yescharacteristic
165C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C5#13711yescharacteristic
167C5×C8—42no—
168C5×C8—42no—
169C5×C8—81no—
170C5×C8—81no—
171C22×D4C5×D411yescharacteristic
172C23×C4—21no—
173C2×M16—21no—
174C22×C8—21no—
175C4⋊Q8C5×D411yescharacteristic
176C4⋊Q8C5×D411yescharacteristic
177#125—21no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182C4×D4—21no—
183C4×D4—21no—
184C4×D4—21no—
185C4×D4—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C5×D411yescharacteristic
189C2×C22⋊C4—21no—
190C2×C42C23×C511yescharacteristic
191#107—22no—
192#106—22no—
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8C5×D412yes—
199#102—22no—
200#102—22no—
201#102—42no—
202C22⋊C8—21no—
203C22⋊C8C5×D412yes—
204C4×C8—21no—
205C4×C8—21no—
206#95—21no—
207#95—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—42no—
211C22×C5—82no—
212C22×C5—82no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5#39411yescharacteristic
216C22×C5#46711yescharacteristic
217C22×C5#46811yescharacteristic
218C4×C5—21no—
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—81no—
223C4×C5—81no—
224C4×C5—81no—
225C4×C5—161no—
226C4×C5#44911yescharacteristic
227C4×C5#45111yescharacteristic
228C4×C5#48411yescharacteristic
229C4×C5#48511yescharacteristic
230C24—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4C5×Q1612yes—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—82no—
244C22×C4C2×C5×D411yescharacteristic
245C22×C4C2×C5×D411yescharacteristic
246C22×C4C5×#4111yescharacteristic
247M16—41no—
248M16—41no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—41no—
269C42C2×C5×D411yescharacteristic
270C42C2×C5×D411yescharacteristic
271C42C5×#4111yescharacteristic
272C42C5×#4111yescharacteristic
273C2×C5—21no—
274C2×C5—21no—
275C2×C5—82no—
276C2×C5#203611yescharacteristic
277C2×C5#204811yescharacteristic
278C2×C5#205311yescharacteristic
279C23—22no—
280C23—41no—
281C23—41no—
282C23—81no—
283C23—81no—
284C23C5×#12111yescharacteristic
285Q8—81no—
286Q8—81no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4C5×#12011yescharacteristic
303C2×C4C5×#12111yescharacteristic
304C2×C4C5×#12111yescharacteristic
305C2×C4C5×#12311yescharacteristic
306C2×C4C5×#12311yescharacteristic
307C2×C4C5×#12411yescharacteristic
308C2×C4C2×C5×Q1611yescharacteristic
309C2×C4C5×#13511yescharacteristic
310C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C5×#13711yescharacteristic
312C8—42no—
313C8—42no—
314C8—81no—
315C8—81no—
316C5#1046911yescharacteristic, direct product factor, Sylow
317C22—21no—
318C22—21no—
319C22—42no—
320C22—82no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22C5×#39411yescharacteristic
325C22C5×#46711yescharacteristic
326C22C5×#46811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—161no—
335C4C5×#44911yescharacteristic
336C4C5×#45111yescharacteristic
337C4C5×#48411yescharacteristic
338C4C5×#48511yescharacteristic
339C2—21no—
340C2—21no—
341C2—82no—
342C2C5×#203611yescharacteristic
343C2C5×#204811yescharacteristic
344C2C5×#205311yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1571C2semidirect
4. C5×#1542C2semidirect
5. C5×#1518C2semidirect
7. C5×#1286C2semidirect
27. #10469C5direct (N × H)
67. #1571C2×C5semidirect
68. #1542C2×C5semidirect
69. #1518C2×C5semidirect
71. #1286C2×C5semidirect
316. C5#10469direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30772
C5×#18042
C5×#15712
C5×#15422
C5×#15182
C5×#14602
C5×#12862
#104695