Finite Group Databasebeta

← C5×#12962 #11935682

Subgroups — C5×#12962 #11935682

Order 1280.

426 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2977C211yesmaximal, characteristic
2C5×#2120C211yesmaximal, characteristic
3C5×#1891C211yesmaximal, characteristic
4C5×#1868C211yesmaximal, characteristic, complemented
5C5×#1858C211yesmaximal, characteristic, complemented
6C5×#1395C211yesmaximal, characteristic, complemented
7C5×#1392C211yesmaximal, characteristic, complemented
8C5×#568C2211yescharacteristic
9C5×#525C2211yescharacteristic
10C5×#435—21no—
11C5×#435—21no—
12C5×C8×D4—21no—
13C5×C8×D4—21no—
14C5×#433—21no—
15C5×#430—21no—
16C5×#424—21no—
17C5×#413C2211yescharacteristic
18C5×#413C2211yescharacteristic
19C5×#410C2211yescharacteristic
20C5×#408C2211yescharacteristic
21C5×#408C2211yescharacteristic
22C5×#407—21no—
23C2×C5×C22⋊C8—21no—
24C5×#352C412yes—
25C5×AΣL(1,𝔽16)C412yes—
26C5×#344—21no—
27C5×#344—21no—
28C5×#341—21no—
29#12962C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41C2311yescharacteristic
31C23×C4×C5D411yescharacteristic
32C5×#131—42no—
33C2×C5×M16—21no—
34C2×C5×M16—21no—
35C2×C5×M16—21no—
36C2×C5×M16—21no—
37C2×C5×M16—21no—
38C2×C5×M16D411yescharacteristic
39C2×C5×M16D411yescharacteristic
40C22×C5×C8—21no—
41C22×C5×C8—21no—
42C22×C5×C8D411yescharacteristic
43C22×C5×C8D411yescharacteristic
44C5×#123C2×C411yescharacteristic
45C5×#123Q811yescharacteristic
46C5×C22⋊Q8—21no—
47C5×#121—21no—
48C5×#120C2×C411yescharacteristic
49C5×#120Q811yescharacteristic
50C4×C5×D4—21no—
51C4×C5×D4—21no—
52C5×#117—21no—
53C5×#117D411yescharacteristic
54C5×#108—42no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—42no—
58C5×#101—21no—
59C5×#101—21no—
60C5×#100—21no—
61C5×#100C2×C412yes—
62C5×#99—21no—
63C5×#99C2×C412yes—
64C5×C22⋊C8—21no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8—21no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8—42no—
71C5×#97—21no—
72C4×C5×C8—21no—
73#2977C2×C511yescharacteristic
74#2120C2×C511yescharacteristic
75#1891C2×C511yescharacteristic
76#1868C2×C511yescharacteristic, complemented
77#1858C2×C511yescharacteristic, complemented
78#1395C2×C511yescharacteristic, complemented
79#1392C2×C511yescharacteristic, complemented
80C24×C5C4⋊C411yescharacteristic
81C5×#41—41no—
82C5×#41—41no—
83C2×C5×Q8#4111yescharacteristic
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4C22×C411yescharacteristic
87C2×C5×D4C2×Q811yescharacteristic
88C2×C5×D4#4111yescharacteristic
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5C4⋊C411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C5×M16—22no—
98C5×M16—22no—
99C5×M16—41no—
100C5×M16—41no—
101C5×M16—41no—
102C5×M16—41no—
103C5×M16—41no—
104C5×M16—41no—
105C5×M16—41no—
106C5×M16—41no—
107C2×C5×C8—22no—
108C2×C5×C8—22no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C2×C5×C8—21no—
112C2×C5×C8—21no—
113C2×C5×C8—41no—
114C2×C5×C8—41no—
115C2×C5×C8—41no—
116C2×C5×C8—41no—
117C2×C5×C8—41no—
118C2×C5×C8—81no—
119C2×C5×C8—81no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—41no—
124C5×C22⋊C4—21no—
125C5×C22⋊C4—21no—
126C5×C22⋊C4—21no—
127C5×C22⋊C4—21no—
128C5×C22⋊C4—22no—
129C5×C22⋊C4C4⋊C411yescharacteristic
130C5×C22⋊C4C4⋊C411yescharacteristic
131C42×C5—21no—
132C42×C5—41no—
133#568C22×C511yescharacteristic
134#525C22×C511yescharacteristic
135#435—21no—
136#435—21no—
137C8×D4—21no—
138C8×D4—21no—
139#433—21no—
140#430—21no—
141#424—21no—
142#413C22×C511yescharacteristic
143#413C22×C511yescharacteristic
144#410C22×C511yescharacteristic
145#408C22×C511yescharacteristic
146#408C22×C511yescharacteristic
147#407—21no—
148C2×C22⋊C8—21no—
149#352C4×C512yes—
150AΣL(1,𝔽16)C4×C512yes—
151#344—21no—
152#344—21no—
153#341—21no—
154C23×C5—21no—
155C23×C5—41no—
156C23×C5—42no—
157C23×C5C2×C4⋊C411yescharacteristic
158C23×C5C4×D411yescharacteristic
159C23×C5C22⋊Q811yescharacteristic
160C5×Q8—41no—
161C5×D4—41no—
162C5×D4—41no—
163C5×D4—41no—
164C5×D4—42no—
165C5×D4—42no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—42no—
179C2×C4×C5—81no—
180C2×C4×C5C4×D411yescharacteristic
181C2×C4×C5#12011yescharacteristic
182C2×C4×C5C22⋊Q811yescharacteristic
183C2×C4×C5#12311yescharacteristic
184C5×C8—42no—
185C5×C8—42no—
186C5×C8—41no—
187C5×C8—41no—
188C5×C8—41no—
189C5×C8—41no—
190C5×C8—81no—
191C2×#41C23×C511yescharacteristic
192C23×C4C5×D411yescharacteristic
193#131—42no—
194C2×M16—21no—
195C2×M16—21no—
196C2×M16—21no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16C5×D411yescharacteristic
200C2×M16C5×D411yescharacteristic
201C22×C8—21no—
202C22×C8—21no—
203C22×C8C5×D411yescharacteristic
204C22×C8C5×D411yescharacteristic
205#123C2×C4×C511yescharacteristic
206#123C5×Q811yescharacteristic
207C22⋊Q8—21no—
208#121—21no—
209#120C2×C4×C511yescharacteristic
210#120C5×Q811yescharacteristic
211C4×D4—21no—
212C4×D4—21no—
213#117—21no—
214#117C5×D411yescharacteristic
215#108—42no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—42no—
219#101—21no—
220#101—21no—
221#100—21no—
222#100C2×C4×C512yes—
223#99—21no—
224#99C2×C4×C512yes—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—42no—
232#97—21no—
233C4×C8—21no—
234C22×C5—22no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—42no—
243C22×C5—41no—
244C22×C5—81no—
245C22×C5#38511yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—41no—
250C4×C5—41no—
251C4×C5—41no—
252C4×C5—82no—
253C4×C5B(4,𝔽2)11yescharacteristic
254C4×C5#45811yescharacteristic
255C24C5×C4⋊C411yescharacteristic
256#41—41no—
257#41—41no—
258C2×Q8C5×#4111yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4C22×C4×C511yescharacteristic
262C2×D4C2×C5×Q811yescharacteristic
263C2×D4C5×#4111yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C5×C4⋊C411yescharacteristic
269C22×C4C2×C5×D411yescharacteristic
270C22×C4C2×C5×D411yescharacteristic
271C22×C4C2×C5×D411yescharacteristic
272M16—22no—
273M16—22no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—81no—
294C2×C8—81no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—22no—
304C22⋊C4C5×C4⋊C411yescharacteristic
305C22⋊C4C5×C4⋊C411yescharacteristic
306C42—21no—
307C42—41no—
308C2×C5—21no—
309C2×C5—41no—
310C2×C5—41no—
311C2×C5—42no—
312C2×C5—41no—
313C2×C5#186711yescharacteristic
314C23—21no—
315C23—41no—
316C23—42no—
317C23C2×C5×C4⋊C411yescharacteristic
318C23C4×C5×D411yescharacteristic
319C23C5×C22⋊Q811yescharacteristic
320Q8—41no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—42no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4C4×C5×D411yescharacteristic
341C2×C4C5×#12011yescharacteristic
342C2×C4C5×C22⋊Q811yescharacteristic
343C2×C4C5×#12311yescharacteristic
344C8—42no—
345C8—42no—
346C8—41no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—81no—
351C5#1296211yescharacteristic, direct product factor, Sylow
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—41no—
362C22—81no—
363C22C5×#38511yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—82no—
371C4C5×B(4,𝔽2)11yescharacteristic
372C4C5×#45811yescharacteristic
373C2—21no—
374C2—41no—
375C2—42no—
376C2—41no—
377C2—41no—
378C2C5×#186711yescharacteristic
subgroupG/H
centerC4×C5B(4,𝔽2)
commutatorC2×D4C22×C4×C5
Frattini, cosocleC2×#41C23×C5
socleC2×C5#1867
prime radicalC5×#525C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1868C2semidirect
5. C5×#1858C2semidirect
6. C5×#1395C2semidirect
7. C5×#1392C2semidirect
29. #12962C5direct (N × H)
76. #1868C2×C5semidirect
77. #1858C2×C5semidirect
78. #1395C2×C5semidirect
79. #1392C2×C5semidirect
351. C5#12962direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29772
C5×#21202
C5×#18912
C5×#18682
C5×#18582
C5×#13952
C5×#13922
#129625