Finite Group Databasebeta

← #14285061

Subgroups — #14285061

Order 1920.

504 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#11754572C211yesmaximal, characteristic
2C2×#91233C211yesmaximal, characteristic, complemented
3C3×#65757C211yesmaximal, characteristic, complemented
4#11746511C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10605005—31nomaximal, Hall
7C2×#6817C411yescharacteristic
8C2×C5×#235C411yescharacteristic
9C22×C3⋊#170—21no—
10C2×C3×C4×Dic5C2211yescharacteristic
11#91566—21no—
12#91566—21no—
13#91451C2211yescharacteristic
14C4×#1203—21no—
15C4×#1203—21no—
16#91376C2211yescharacteristic
17#91375C411yescharacteristic
18#91373C411yescharacteristic
19#91233—21no—
20#91233C2212yes—
21C3×C22⋊#170—21no—
22C3×#4004C2212yes—
23C3×#4002—21no—
24#70816—51nomaximal, Hall
25#66166—31no—
26#65757D311yescharacteristic, complemented
27C2×#4004—31no—
28#64931—32no—
29#64925—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32#6817—42no—
33C2×D60C2×C411yescharacteristic
34C2×C4×D15—21no—
35C2×Dic30C2×C411yescharacteristic
36C2×C5×#67—21no—
37C5×#235—42no—
38C2×C5×D12C2×C411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6C2×C411yescharacteristic
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×#1203—21no—
44C2×#1203—21no—
45C2×C3⋊#170—22no—
46C2×C3⋊#170—42no—
47C2×C3×#170—22no—
48C3×C4×Dic5C2×C411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51C3×C4×Dic5C2311yescharacteristic
52#6668—21no—
53#6668—21no—
54#6667—21no—
55#6667—21no—
56(C2×D3)⋊Dic5—21no—
57(C2×D3)⋊Dic5—21no—
58#5477—51no—
59C3×#432—51no—
60C2×C4⋊(C3⋊C8)—51no—
61#4485—52no—
62#4481—52no—
63C2×C5×#41—31no—
64C2×#709—31no—
65C22×#170—61no—
66#4093—31no—
67#4090—31no—
68#4086—31no—
69#4085—61no—
70#4085—61no—
71#4082—31no—
72C4×C22⋊D5—61no—
73C4×C22⋊D5—61no—
74C2×C4×Dic5C2×D311yescharacteristic
75C22⋊#170—21no—
76#4004—32no—
77#4004—61no—
78#4004C2×D312yes—
79#4002—21no—
80#1551—151noSylow
81C23×C3×C5C22⋊C411yescharacteristic
82C22×D15—21no—
83C22×C5×D3—21no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87#1220—42no—
88C2×Dic15—21no—
89D60—41no—
90C4×D15—42no—
91Dic30—41no—
92C5×#67—42no—
93C2×C5×Dic3—21no—
94C5×D12—41no—
95C4×C5×D3—42no—
96C5×Dic6—41no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C2×D411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104#1203—42no—
105#1203—41no—
106#1203—41no—
107C3⋊#170—42no—
108C3×#170—42no—
109C2×#235—51no—
110C2×#235AGL(1,𝔽5)11yescharacteristic
111C2×C3×C42—51no—
112#930—101no—
113#930—101no—
114C22×C3⋊C8—101no—
115#875—51no—
116#875—51no—
117#874—51no—
118C4×D12—101no—
119C4×D12—101no—
120#869—51no—
121C3×C4⋊C8—52no—
122C3×C22⋊C8—101no—
123C3×#97—101no—
124C4⋊(C3⋊C8)—52no—
125C4⋊(C3⋊C8)—101no—
126C5×#41—122no—
127C2×C5×Q8—31no—
128C2×C5×D4—31no—
129C2×C5×D4—61no—
130C22×C4×C5—61no—
131C22×C4×C5C4×D311yescharacteristic
132C2×C22⋊D5—61no—
133C2×C22⋊D5—61no—
134C2×C22⋊D5—61no—
135C22×Dic5D1211yescharacteristic
136C22×Dic5#6711yescharacteristic
137#709—122no—
138C2×D20—31no—
139C2×C4×D5—61no—
140C2×Dic10—31no—
141C2×#170—22no—
142C2×#170—62no—
143C2×#170—122no—
144C22⋊Dic5—61no—
145C22⋊Dic5—61no—
146#685—61no—
147#685—61no—
148#683—61no—
149#683—61no—
150C4×Dic5C4×D311yescharacteristic
151C4×Dic5D1211yescharacteristic
152C4×Dic5#6711yescharacteristic
153C4×Dic5C22×D311yescharacteristic
154#532—151no—
155#432—51no—
156C2×C4⋊C8—151no—
157#333—152no—
158#331—152no—
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5#10012yes—
162C22×C3×C5C2×C22⋊C411yescharacteristic
163C2×D15—41no—
164C2×D15—41no—
165C2×D15—41no—
166C2×C5×D3—41no—
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171Dic15—41no—
172C3×Dic5—21no—
173C3×Dic5—21no—
174C3×Dic5#13512yes—
175C3×Dic5AGL(1,ℤ/8)11yescharacteristic
176C3×Dic5#13711yescharacteristic
177C5×Dic3—41no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
181C2×#67—21no—
182C2×#67—101no—
183#235—42no—
184#235—202no—
185C2×D12—51no—
186C2×D12—101no—
187C2×D12—101no—
188C2×D12C2×AGL(1,𝔽5)11yescharacteristic
189C2×C4×D3—21no—
190C2×C4×D3—101no—
191C2×Dic6—51no—
192C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
193C2×C3×C8—102no—
194C3×C42—51no—
195C3×C42—51no—
196C3×C42—51no—
197C3×C42—51no—
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—101no—
203C4⋊Dic3—101no—
204C2×C3⋊C8—102no—
205C2×C3⋊C8—202no—
206C23×C5—61no—
207C23×C5(C2×D3)⋊C411yescharacteristic
208C22×D5—61no—
209C5×Q8—121no—
210C5×D4—121no—
211C5×D4—122no—
212C2×C4×C5—22no—
213C2×C4×C5—61no—
214C2×C4×C5—122no—
215C2×C4×C5(C2×D3)⋊C411yescharacteristic
216C2×C4×C5C2×C4×D311yescharacteristic
217C22⋊D5—122no—
218C22⋊D5—121no—
219C22⋊D5—121no—
220C22⋊D5—122no—
221C2×Dic5—21no—
222C2×Dic5—21no—
223C2×Dic5—22no—
224C2×Dic5—61no—
225C2×Dic5(C2×D3)⋊C411yescharacteristic
226C2×Dic5(C2×D3)⋊C411yescharacteristic
227C2×Dic5C2×D1211yescharacteristic
228C2×Dic5C2×#6711yescharacteristic
229D20—121no—
230C4×D5—122no—
231Dic10—121no—
232#170—42no—
233#170—122no—
234C2×#41—31no—
235C2×#41—151no—
236C22×C8—301no—
237C4⋊Q8—151no—
238#127—151no—
239#124—151no—
240#124—151no—
241#121—301no—
242#121—301no—
243C4×D4—301no—
244C4×D4—301no—
245C2×C42—51no—
246C4⋊C8—52no—
247C4⋊C8—152no—
248C4⋊C8—301no—
249C22⋊C8—101no—
250#97—101no—
251C2×C3×C5—22no—
252C2×C3×C5C2×#10011yescharacteristic
253C2×C3×C5#41611yescharacteristic
254C2×C3×C5#41711yescharacteristic
255D15—81no—
256C5×D3—81no—
257C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
258C22×D3—21no—
259C22×D3—101no—
260C2×C3×C4—22no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4—102no—
268C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
269C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
270#67—42no—
271#67—202no—
272C2×Dic3—21no—
273C2×Dic3—101no—
274D12—41no—
275D12—201no—
276D12—201no—
277D12—201no—
278D12—202no—
279C4×D3—42no—
280C4×D3—202no—
281Dic6—41no—
282Dic6—201no—
283C3×C8—202no—
284C3⋊C8—202no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—121no—
288C22×C5—121no—
289C22×C5—121no—
290C22×C5#82312yes—
291C22×C5C2×(C2×D3)⋊C411yescharacteristic
292C2×D5—121no—
293C2×D5—121no—
294C2×D5—121no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—121no—
298Dic5—21no—
299Dic5—21no—
300Dic5—121no—
301Dic5#90811yescharacteristic
302Dic5#90911yescharacteristic
303Dic5#95012yes—
304#41—122no—
305#41—602no—
306C2×Q8—31no—
307C2×Q8—151no—
308C2×D4—31no—
309C2×D4—61no—
310C2×D4—151no—
311C2×D4—301no—
312C2×D4—301no—
313C2×D4—301no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—61no—
317C22×C4—301no—
318C22×C4D3×AGL(1,𝔽5)11yescharacteristic
319C2×C8—102no—
320C2×C8—302no—
321C2×C8—602no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C22⋊C4—301no—
325C22⋊C4—301no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C42—51no—
329C42—51no—
330C42—51no—
331C42—51no—
332C3×C5#155111yescharacteristic, complemented, Hall
333C22×C3—21no—
334C22×C3—21no—
335C22×C3#401312yes—
336C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—201no—
341C2×D3—201no—
342C2×D3—201no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—51no—
346C3×C4—51no—
347C3×C4—52no—
348C3×C4—101no—
349C3×C4—101no—
350Dic3—41no—
351Dic3—201no—
352C2×C5—22no—
353C2×C5—241no—
354C2×C5#500211yescharacteristic
355C2×C5C2×#82311yescharacteristic
356C2×C5#513311yescharacteristic
357D5—241no—
358C23—61no—
359C23—301no—
360C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
361Q8—121no—
362Q8—601no—
363D4—121no—
364D4—122no—
365D4—601no—
366D4—602no—
367D4—601no—
368D4—601no—
369D4—602no—
370C2×C4—22no—
371C2×C4—51no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—51no—
375C2×C4—61no—
376C2×C4—101no—
377C2×C4—102no—
378C2×C4—101no—
379C2×C4—122no—
380C2×C4—301no—
381C2×C4—602no—
382C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
383C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
384C8—202no—
385C8—602no—
386C2×C3—22no—
387C2×C3#6579311yescharacteristic
388C2×C3#6579411yescharacteristic
389C2×C3C2×#401311yescharacteristic
390D3—81no—
391D3—401no—
392C5#7081611yescharacteristic, complemented, Sylow
393C22—21no—
394C22—21no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—601no—
399C22—601no—
400C22—601no—
401C22#9117412yes—
402C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
403C4—21no—
404C4—21no—
405C4—52no—
406C4—51no—
407C4—51no—
408C4—101no—
409C4—101no—
410C4—121no—
411C4—601no—
412C3#1060500511yescharacteristic, complemented, Sylow
413C2—22no—
414C2—241no—
415C2—1201no—
416C2#1175170311yescharacteristic
417C2#1175170811yescharacteristic
418C2C2×#9117411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11754572C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1551
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91233C2semidirect
3. C3×#65757C2semidirect
4. #11746511C2semidirect
5. #11746508C2semidirect
26. #65757D3semidirect
332. C3×C5#1551semidirect
392. C5#70816semidirect
412. C3#10605005semidirect

Maximal subgroups

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

subgroupindex
#117545722
C2×#912332
C3×#657572
#117465112
#117465082
#106050053
#708165