Finite Group Databasebeta

← C5×#9354 #11932074

Subgroups — C5×#9354 #11932074

Order 1280.

470 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3039C211yesmaximal, characteristic
2C5×#2991C211yesmaximal, characteristic
3C5×#1997C211yesmaximal, characteristic, complemented
4C5×#1548C211yesmaximal, characteristic, complemented
5C5×#1489C211yesmaximal, characteristic
6C5×#1309C211yesmaximal, characteristic, complemented
7C5×#1299C211yesmaximal, characteristic, complemented
8C2×C5×#137C412yes—
9C2×C5×C4⋊Q8C2211yescharacteristic
10C4×C5×#41C2211yescharacteristic
11C5×#462—21no—
12C5×#462—21no—
13C5×#461—21no—
14C5×#461—21no—
15C5×C8×Q8—21no—
16C5×#436—22no—
17C5×#436—21no—
18C5×#431—21no—
19C5×#431C2211yescharacteristic
20C5×#423—21no—
21C5×#423C2211yescharacteristic
22C5×#423C2211yescharacteristic
23C5×#423C2211yescharacteristic
24C5×#419C412yes—
25C4×C5×M16C2211yescharacteristic
26C5×#343—22no—
27C5×#333—21no—
28C5×#333—21no—
29C5×Q8⋊C8—21no—
30C5×D4⋊C8—21no—
31#9354C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41C2×C411yescharacteristic
33C22×C5×Q8C2×C412yes—
34C5×#137—44no—
35C2×C5×Q16—22no—
36C2×C5×SD16—22no—
37C2×C5×M16—22no—
38C2×C5×M16—21no—
39C2×C5×M16—21no—
40C2×C5×M16C2×C412yes—
41C2×C5×M16D412yes—
42C5×C4⋊Q8—21no—
43C5×C4⋊Q8—21no—
44C5×C4⋊Q8—21no—
45C5×C4⋊Q8—21no—
46C4×C5×Q8D411yescharacteristic
47C4×C5×Q8D411yescharacteristic
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C4×C5×D4D411yescharacteristic
51C4×C5×D4D411yescharacteristic
52C5×#117—21no—
53C5×#117C2×C411yescharacteristic
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C42×C5—21no—
57C2×C42×C5C2311yescharacteristic
58C5×C4⋊C8—22no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8D411yescharacteristic
66C5×C4⋊C8D411yescharacteristic
67C5×#103—22no—
68C5×#103—22no—
69C5×C22⋊C8—22no—
70C5×C22⋊C8—21no—
71C5×#97—21no—
72C4×C5×C8—22no—
73C4×C5×C8—21no—
74C4×C5×C8—21no—
75#3039C2×C511yescharacteristic
76#2991C2×C511yescharacteristic
77#1997C2×C511yescharacteristic, complemented
78#1548C2×C511yescharacteristic, complemented
79#1489C2×C511yescharacteristic
80#1309C2×C511yescharacteristic, complemented
81#1299C2×C511yescharacteristic, complemented
82C5×#41—22no—
83C5×#41—41no—
84C2×C5×Q8—22no—
85C2×C5×Q8—22no—
86C2×C5×Q8—42no—
87C2×C5×Q8—42no—
88C2×C5×Q8C22⋊C411yescharacteristic
89C2×C5×D4—21no—
90C2×C5×D4C22⋊C411yescharacteristic
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—22no—
95C22×C4×C5C22×C411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5#4111yescharacteristic
98C5×Q16—44no—
99C5×SD16—44no—
100C5×M16—22no—
101C5×M16—41no—
102C5×M16—42no—
103C5×M16—42no—
104C5×M16—82no—
105C5×M16—81no—
106C2×C5×C8—22no—
107C2×C5×C8—21no—
108C2×C5×C8—22no—
109C2×C5×C8—21no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4—41no—
116C5×C4⋊C4—41no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4C22⋊C411yescharacteristic
119C5×C4⋊C4C22⋊C411yescharacteristic
120C5×C22⋊C4—21no—
121C5×C22⋊C4—21no—
122C5×C22⋊C4—21no—
123C42×C5—21no—
124C42×C5—21no—
125C42×C5—21no—
126C42×C5C2×D411yescharacteristic
127C42×C5C2×D411yescharacteristic
128C42×C5C2×D411yescharacteristic
129C42×C5#4111yescharacteristic
130C2×#137C4×C512yes—
131C2×C4⋊Q8C22×C511yescharacteristic
132C4×#41C22×C511yescharacteristic
133#462—21no—
134#462—21no—
135#461—21no—
136#461—21no—
137C8×Q8—21no—
138#436—22no—
139#436—21no—
140#431—21no—
141#431C22×C511yescharacteristic
142#423—21no—
143#423C22×C511yescharacteristic
144#423C22×C511yescharacteristic
145#423C22×C511yescharacteristic
146#419C4×C512yes—
147C4×M16C22×C511yescharacteristic
148#343—22no—
149#333—21no—
150#333—21no—
151Q8⋊C8—21no—
152D4⋊C8—21no—
153C23×C5—21no—
154C23×C5C4×D411yescharacteristic
155C5×Q8—21no—
156C5×Q8—42no—
157C5×Q8—42no—
158C5×Q8—82no—
159C5×Q8#10012yes—
160C5×D4—21no—
161C5×D4—21no—
162C5×D4—42no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
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—42no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—42no—
178C2×C4×C5—82no—
179C2×C4×C5C2×C22⋊C411yescharacteristic
180C2×C4×C5C4×D411yescharacteristic
181C2×C4×C5#12011yescharacteristic
182C2×C4×C5#12111yescharacteristic
183C2×C4×C5#12111yescharacteristic
184C2×C4×C5#12311yescharacteristic
185C5×C8—42no—
186C5×C8—42no—
187C5×C8—42no—
188C5×C8—41no—
189C5×C8—41no—
190C5×C8—81no—
191C2×#41C2×C4×C511yescharacteristic
192C22×Q8C2×C4×C512yes—
193#137—44no—
194C2×Q16—22no—
195C2×SD16—22no—
196C2×M16—22no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16C2×C4×C512yes—
200C2×M16C5×D412yes—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4×Q8C5×D411yescharacteristic
206C4×Q8C5×D411yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4C5×D411yescharacteristic
210C4×D4C5×D411yescharacteristic
211#117—21no—
212#117C2×C4×C511yescharacteristic
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C42—21no—
216C2×C42C23×C511yescharacteristic
217C4⋊C8—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8C5×D411yescharacteristic
225C4⋊C8C5×D411yescharacteristic
226#103—22no—
227#103—22no—
228C22⋊C8—22no—
229C22⋊C8—21no—
230#97—21no—
231C4×C8—22no—
232C4×C8—21no—
233C4×C8—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—41no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5#38611yescharacteristic
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—22no—
244C4×C5—21no—
245C4×C5—41no—
246C4×C5—41no—
247C4×C5—82no—
248C4×C5C2×#10011yescharacteristic
249C4×C5#41311yescharacteristic
250C4×C5#45511yescharacteristic
251C4×C5#45611yescharacteristic
252C4×C5#47111yescharacteristic
253C4×C5#47311yescharacteristic
254#41—22no—
255#41—41no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8C5×C22⋊C411yescharacteristic
261C2×D4—21no—
262C2×D4C5×C22⋊C411yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4C22×C4×C511yescharacteristic
268C22×C4C2×C5×D411yescharacteristic
269C22×C4C5×#4111yescharacteristic
270Q16—44no—
271SD16—44no—
272M16—22no—
273M16—41no—
274M16—42no—
275M16—42no—
276M16—82no—
277M16—81no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C5×C22⋊C411yescharacteristic
291C4⋊C4C5×C22⋊C411yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42C2×C5×D411yescharacteristic
299C42C2×C5×D411yescharacteristic
300C42C2×C5×D411yescharacteristic
301C42C5×#4111yescharacteristic
302C2×C5—41no—
303C2×C5—81no—
304C2×C5#188211yescharacteristic
305C2×C5#190011yescharacteristic
306C2×C5#190811yescharacteristic
307C23—21no—
308C23C4×C5×D411yescharacteristic
309Q8—21no—
310Q8—42no—
311Q8—42no—
312Q8—82no—
313Q8C5×#10012yes—
314D4—21no—
315D4—21no—
316D4—42no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4C2×C5×C22⋊C411yescharacteristic
334C2×C4C4×C5×D411yescharacteristic
335C2×C4C5×#12011yescharacteristic
336C2×C4C5×#12111yescharacteristic
337C2×C4C5×#12111yescharacteristic
338C2×C4C5×#12311yescharacteristic
339C8—42no—
340C8—42no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—81no—
345C5#935411yescharacteristic, direct product factor, Sylow
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22C5×#38611yescharacteristic
353C4—21no—
354C4—21no—
355C4—22no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—82no—
360C4C2×C5×#10011yescharacteristic
361C4C5×#41311yescharacteristic
362C4C5×#45511yescharacteristic
363C4C5×#45611yescharacteristic
364C4C5×#47111yescharacteristic
365C4C5×#47311yescharacteristic
366C2—41no—
367C2—81no—
368C2C5×#188211yescharacteristic
369C2C5×#190011yescharacteristic
370C2C5×#190811yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#41C2×C4
LCSG ▷ C22×C4 ▷ 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×#1997C2semidirect
4. C5×#1548C2semidirect
6. C5×#1309C2semidirect
7. C5×#1299C2semidirect
31. #9354C5direct (N × H)
77. #1997C2×C5semidirect
78. #1548C2×C5semidirect
80. #1309C2×C5semidirect
81. #1299C2×C5semidirect
345. C5#9354direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30392
C5×#29912
C5×#19972
C5×#15482
C5×#14892
C5×#13092
C5×#12992
#93545