Finite Group Databasebeta

← C5×#12193 #11934913

Subgroups — C5×#12193 #11934913

Order 1280.

442 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2764C211yesmaximal, characteristic, complemented
2C5×#2022C211yesmaximal, characteristic
3C5×#1607C211yesmaximal, characteristic
4C5×#1601C211yesmaximal, characteristic
5C5×#1351C211yesmaximal, characteristic, complemented
6C5×#1344C211yesmaximal, characteristic, complemented
7C5×#1317C211yesmaximal, characteristic, complemented
8C5×#534C2211yescharacteristic
9C2×C5×#123—21no—
10C5×#480—21no—
11C5×#448—21no—
12C2×C5×#99—21no—
13C5×#400—21no—
14C5×#398—21no—
15C5×#397C2211yescharacteristic
16C5×#393C2211yescharacteristic
17C5×#391—21no—
18C5×#388—21no—
19C5×#385—21no—
20C5×#383—21no—
21C5×#381C2211yescharacteristic
22C5×#342C2211yescharacteristic
23C5×#327—21no—
24C5×#327—21no—
25C5×#323C2211yescharacteristic
26C5×#323C2211yescharacteristic
27#12193C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8D411yescharacteristic
29C22×C5×D4—21no—
30C23×C4×C5D411yescharacteristic
31C2×C5×SD16—41no—
32C5×#123—42no—
33C5×#123—41no—
34C5×#123—42no—
35C5×#121—21no—
36C5×#121—21no—
37C5×#120—41no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—41no—
42C2×C5×C4⋊C4D411yescharacteristic
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—41no—
47C2×C5×C22⋊C4D411yescharacteristic
48C2×C5×C22⋊C4C2311yescharacteristic
49C2×C42×C5—21no—
50C5×#107—41no—
51C5×#103—41no—
52C5×#102—41no—
53C5×#99—42no—
54C5×C22⋊C8—21no—
55C5×C22⋊C8—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95—21no—
60C5×#95—21no—
61C5×#95—21no—
62C5×#95—21no—
63C5×#95—21no—
64C5×#95D411yescharacteristic
65C5×#95D411yescharacteristic
66#2764C2×C511yescharacteristic, complemented
67#2022C2×C511yescharacteristic
68#1607C2×C511yescharacteristic
69#1601C2×C511yescharacteristic
70#1351C2×C511yescharacteristic, complemented
71#1344C2×C511yescharacteristic, complemented
72#1317C2×C511yescharacteristic, complemented
73C24×C5—21no—
74C24×C5C2×D411yescharacteristic
75C2×C5×Q8—42no—
76C2×C5×Q8—41no—
77C2×C5×D4—21no—
78C2×C5×D4—21no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—41no—
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5C2×D411yescharacteristic
99C5×SD16—82no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—44no—
106C5×C4⋊C4—81no—
107C5×C4⋊C4—81no—
108C5×C4⋊C4—81no—
109C5×C22⋊C4—22no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—42no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C5×C22⋊C4—44no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—41no—
118C5×C22⋊C4—41no—
119C42×C5—42no—
120#534C22×C511yescharacteristic
121C2×#123—21no—
122#480—21no—
123#448—21no—
124C2×#99—21no—
125#400—21no—
126#398—21no—
127#397C22×C511yescharacteristic
128#393C22×C511yescharacteristic
129#391—21no—
130#388—21no—
131#385—21no—
132#383—21no—
133#381C22×C511yescharacteristic
134#342C22×C511yescharacteristic
135#327—21no—
136#327—21no—
137#323C22×C511yescharacteristic
138#323C22×C511yescharacteristic
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—81no—
147C23×C5—81no—
148C23×C5#12011yescharacteristic
149C23×C5#13511yescharacteristic
150C23×C5AGL(1,ℤ/8)11yescharacteristic
151C5×Q8—42no—
152C5×Q8—81no—
153C5×D4—81no—
154C5×D4—81no—
155C5×D4—81no—
156C5×D4—81no—
157C5×D4—81no—
158C5×D4—81no—
159C2×C4×C5—22no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—42no—
169C2×C4×C5—42no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—81no—
187C2×C4×C5—81no—
188C2×C4×C5—81no—
189C5×C8—81no—
190C5×C8—81no—
191C22×Q8C5×D411yescharacteristic
192C22×D4—21no—
193C23×C4C5×D411yescharacteristic
194C2×SD16—41no—
195#123—42no—
196#123—41no—
197#123—42no—
198#121—21no—
199#121—21no—
200#120—41no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4C5×D411yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—41no—
210C2×C22⋊C4C5×D411yescharacteristic
211C2×C22⋊C4C23×C511yescharacteristic
212C2×C42—21no—
213#107—41no—
214#103—41no—
215#102—41no—
216#99—42no—
217C22⋊C8—21no—
218C22⋊C8—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C5×D411yescharacteristic
228#95C5×D411yescharacteristic
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—41no—
234C22×C5—41no—
235C22×C5—41no—
236C22×C5—41no—
237C22×C5—81no—
238C22×C5—82no—
239C22×C5—81no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5—161no—
243C22×C5#44911yescharacteristic
244C22×C5#45311yescharacteristic
245C22×C5B(4,𝔽2)11yescharacteristic
246C4×C5—41no—
247C4×C5—42no—
248C4×C5—41no—
249C4×C5—81no—
250C4×C5—81no—
251C4×C5—81no—
252C4×C5—82no—
253C4×C5—81no—
254C4×C5—81no—
255C4×C5—81no—
256C24—21no—
257C24C2×C5×D411yescharacteristic
258C2×Q8—42no—
259C2×Q8—41no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C2×C5×D411yescharacteristic
281C22×C4C2×C5×D411yescharacteristic
282SD16—82no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—44no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C22⋊C4—22no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—44no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42—42no—
303C2×C5—21no—
304C2×C5—21no—
305C2×C5—41no—
306C2×C5—41no—
307C2×C5—161no—
308C2×C5#160011yescharacteristic
309C2×C5#219711yescharacteristic
310C2×C5#220111yescharacteristic
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23C5×#12011yescharacteristic
321C23C5×#13511yescharacteristic
322C23C5×AGL(1,ℤ/8)11yescharacteristic
323Q8—42no—
324Q8—81no—
325D4—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C8—81no—
362C8—81no—
363C5#1219311yescharacteristic, direct product factor, Sylow
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—161no—
378C22C5×#44911yescharacteristic
379C22C5×#45311yescharacteristic
380C22C5×B(4,𝔽2)11yescharacteristic
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2C5×#160011yescharacteristic
397C2C5×#219711yescharacteristic
398C2C5×#220111yescharacteristic
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC5×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C2×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2764C2semidirect
5. C5×#1351C2semidirect
6. C5×#1344C2semidirect
7. C5×#1317C2semidirect
27. #12193C5direct (N × H)
66. #2764C2×C5semidirect
70. #1351C2×C5semidirect
71. #1344C2×C5semidirect
72. #1317C2×C5semidirect
363. C5#12193direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#27642
C5×#20222
C5×#16072
C5×#16012
C5×#13512
C5×#13442
C5×#13172
#121935