Finite Group Databasebeta

← #14281967

Subgroups — #14281967

Order 1920.

468 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 106 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#11754415C211yesmaximal, characteristic
2C2×C4⋊(C3⋊#170)C211yesmaximal, characteristic, complemented
3C3×C4×#704C211yesmaximal, characteristic, complemented
4#11746493C212yesmaximal, complemented
5#11746491C212yesmaximal, complemented
6#10604511—31nomaximal, Hall
7C22×C3⋊#170—21no—
8C2×C3×#704—21no—
9#91819C411yescharacteristic
10C5×#924C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91552—21no—
13#91546—21no—
14#91418C2211yescharacteristic
15#91402—21no—
16#91388C411yescharacteristic
17#91387—21no—
18#91375C411yescharacteristic
19Dic5×Dic6C2211yescharacteristic
20C4⋊(C3⋊#170)—21no—
21C4⋊(C3⋊#170)C2212yes—
22C3×#4002—21no—
23C3×C4×#170C2212yes—
24#69852—51nomaximal, Hall
25#65958—31no—
26C4×#704D311yescharacteristic, complemented
27C2×C4⋊#170—31no—
28Q8⋊#170—32no—
29#64871—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32C2×D60C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×#1200—21no—
37C2×C3⋊#170—22no—
38C2×C3⋊#170—42no—
39C3×#704—24no—
40C2×C3×#170—22no—
41#6714—21no—
42C4⋊Dic15C2×C411yescharacteristic
43C5×#217—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×Dic3⋊C4—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51Dic3⋊Dic5—21no—
52#6669—21no—
53#6667—21no—
54#6667—21no—
55#6667—21no—
56Dic3×Dic5—21no—
57#5479—51no—
58C3×C4×M16—51no—
59C2×C4⋊(C3⋊C8)—51no—
60#4459—52no—
61#4456—52no—
62C2×#704—21no—
63C22×#170—61no—
64C5×C22⋊Q8—31no—
65#4093—31no—
66Q8×Dic5—31no—
67#4076—31no—
68C2×C4×Dic5C2×D311yescharacteristic
69#4044—61no—
70#4039—31no—
71#4038—61no—
72#4036—31no—
73#4032—61no—
74#4027—61no—
75#4002—21no—
76C4⋊#170—32no—
77C4⋊#170—61no—
78C4×#170C2×D312yes—
79#1483—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85#1220—42no—
86C2×Dic15—21no—
87D60—22no—
88C2×C5×Dic3—21no—
89C2×C5×Dic3—21no—
90C5×Dic6—22no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98#1200—41no—
99#1200—41no—
100C3⋊#170—42no—
101C3×#170—24no—
102C2×C3×M16—101no—
103C2×C3×C42—51no—
104#930—51no—
105#929—101no—
106C4×#67—101no—
107#924AGL(1,𝔽5)11yescharacteristic
108C22×C3⋊C8—101no—
109#876—101no—
110#875—51no—
111C4×D12—51no—
112#872—101no—
113#870—51no—
114C4×Dic6—51no—
115C3×#97—101no—
116C3×C4×C8—52no—
117C4⋊(C3⋊C8)—52no—
118C4⋊(C3⋊C8)—101no—
119C2×C5×Q8—31no—
120C22×C4×C5C4×D311yescharacteristic
121C2×C22⋊D5—61no—
122C22×Dic5D1211yescharacteristic
123C22×Dic5#6711yescharacteristic
124C2×D20—31no—
125C2×C4×D5—61no—
126#704—24no—
127C2×#170—22no—
128C2×#170—62no—
129C2×#170—122no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—61no—
132C5×C22⋊C4—61no—
133#685—61no—
134#685—61no—
135#685—61no—
136#685—61no—
137C4⋊Dic5—31no—
138C4⋊Dic5—61no—
139C4⋊Dic5—61no—
140#683—61no—
141C4×Dic5—61no—
142C4×Dic5C4×D311yescharacteristic
143C4×Dic5D1211yescharacteristic
144C4×Dic5#6711yescharacteristic
145C4×Dic5C22×D311yescharacteristic
146#529—151no—
147C2×C4⋊C8—151no—
148C4×M16—51no—
149Q8⋊C8—152no—
150D4⋊C8—152no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5#10412yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C2×D15—41no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—21no—
159C3×C4×C5#13112yes—
160Dic15—41no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C3×Dic5AGL(1,ℤ/8)11yescharacteristic
165C3×Dic5#13711yescharacteristic
166C5×Dic3—41no—
167C5×Dic3—41no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
171C2×#67—101no—
172C2×D12—51no—
173C2×C4×D3—101no—
174C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
175C3×M16—104no—
176C2×C3×C8—102no—
177C3×C42—51no—
178C3×C42—51no—
179C3×C42—51no—
180C3×C42—51no—
181#217—21no—
182(C2×D3)⋊C4—101no—
183(C2×D3)⋊C4—101no—
184(C2×D3)⋊C4—101no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—51no—
187C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—101no—
190Dic3⋊C4—101no—
191Dic3⋊C4—101no—
192C4×Dic3—101no—
193C2×C3⋊C8—102no—
194C2×C3⋊C8—202no—
195C23×C5(C2×D3)⋊C411yescharacteristic
196C22×D5—61no—
197C5×Q8—62no—
198C2×C4×C5—22no—
199C2×C4×C5—61no—
200C2×C4×C5—61no—
201C2×C4×C5(C2×D3)⋊C411yescharacteristic
202C2×C4×C5C2×C4×D311yescharacteristic
203C22⋊D5—122no—
204C2×Dic5—22no—
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—61no—
208C2×Dic5(C2×D3)⋊C411yescharacteristic
209C2×Dic5(C2×D3)⋊C411yescharacteristic
210C2×Dic5C2×D1211yescharacteristic
211C2×Dic5C2×#6711yescharacteristic
212D20—62no—
213C4×D5—121no—
214C4×D5—121no—
215#170—24no—
216#170—122no—
217C2×M16—101no—
218C22×C8—301no—
219#126—301no—
220#125—151no—
221#124—151no—
222#123—301no—
223C22⋊Q8—31no—
224#121—151no—
225C4×Q8—151no—
226C4×D4—151no—
227C4×D4—301no—
228#117—301no—
229C2×C42—51no—
230C4⋊C8—152no—
231C4⋊C8—301no—
232#97—101no—
233C4×C8—52no—
234C2×C3×C5—22no—
235C2×C3×C5#40811yescharacteristic
236C2×C3×C5#41711yescharacteristic
237C2×C3×C5C2×#10411yescharacteristic
238D15—81no—
239C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
240C22×D3—101no—
241C2×C3×C4—22no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—102no—
249C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
250C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
251#67—202no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—101no—
255D12—102no—
256C4×D3—201no—
257C4×D3—201no—
258Dic6—22no—
259C3×C8—104no—
260C3⋊C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5#80512yes—
264C22×C5C2×(C2×D3)⋊C411yescharacteristic
265C2×D5—121no—
266C2×D5—121no—
267C2×D5—121no—
268C4×C5—21no—
269C4×C5—121no—
270C4×C5—121no—
271C4×C5#90712yes—
272Dic5—21no—
273Dic5—21no—
274Dic5—21no—
275Dic5—121no—
276Dic5#90811yescharacteristic
277Dic5#90911yescharacteristic
278C2×Q8—31no—
279C2×D4—151no—
280C2×D4—301no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—301no—
284C22×C4D3×AGL(1,𝔽5)11yescharacteristic
285M16—104no—
286C2×C8—102no—
287C2×C8—302no—
288C2×C8—602no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—151no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—61no—
296C22⋊C4—301no—
297C22⋊C4—301no—
298C22⋊C4—301no—
299C22⋊C4—301no—
300C42—51no—
301C42—51no—
302C42—51no—
303C42—51no—
304C42—301no—
305C3×C5#148311yescharacteristic, complemented, Hall
306C22×C3—21no—
307C22×C3—21no—
308C22×C3#401012yes—
309C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C2×D3—201no—
311C2×D3—201no—
312C2×D3—201no—
313C3×C4—21no—
314C3×C4—51no—
315C3×C4—51no—
316C3×C4—101no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4#413112yes—
320Dic3—41no—
321Dic3—41no—
322Dic3—201no—
323C2×C5—22no—
324C2×C5C2×#80511yescharacteristic
325C2×C5#512911yescharacteristic
326C2×C5#513311yescharacteristic
327D5—241no—
328C23—301no—
329C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
330Q8—62no—
331D4—302no—
332D4—602no—
333C2×C4—22no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—101no—
341C2×C4—101no—
342C2×C4—102no—
343C2×C4—301no—
344C2×C4—601no—
345C2×C4—601no—
346C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
347C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
348C8—104no—
349C8—602no—
350C2×C3—22no—
351C2×C3#6577511yescharacteristic
352C2×C3C2×#401011yescharacteristic
353C2×C3#6579311yescharacteristic
354D3—401no—
355C5#6985211yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—601no—
359C22—601no—
360C22—601no—
361C22#9115812yes—
362C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
363C4—21no—
364C4—51no—
365C4—51no—
366C4—101no—
367C4—101no—
368C4—101no—
369C4—121no—
370C4—121no—
371C4—601no—
372C4#9192912yes—
373C3#1060451111yescharacteristic, complemented, Sylow
374C2—22no—
375C2—1201no—
376C2#1175170811yescharacteristic
377C2C2×#9115811yescharacteristic
378C2#1175200111yescharacteristic
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#91819C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C3⋊#170)C2semidirect
3. C3×C4×#704C2semidirect
4. #11746493C2semidirect
5. #11746491C2semidirect
26. C4×#704D3semidirect
305. C3×C5#1483semidirect
355. C5#69852semidirect
373. C3#10604511semidirect

Maximal subgroups

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

subgroupindex
#117544152
C2×C4⋊(C3⋊#170)2
C3×C4×#7042
#117464932
#117464912
#106045113
#698525