Finite Group Databasebeta

← #14290046

Subgroups — #14290046

Order 1920.

500 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752554C211yesmaximal, characteristic
2#11750950C211yesmaximal, characteristic, complemented
3#11746964C211yesmaximal, characteristic, complemented
4#11746890C211yesmaximal, characteristic, complemented
5C5×#4483C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7#11745844C211yesmaximal, characteristic, complemented
8#10598983—31nomaximal, Hall
9C2×#6765—21no—
10C2×Dic60—21no—
11#91758C2211yescharacteristic
12C4×Dic30C2211yescharacteristic
13C4×C5×D12C2211yescharacteristic
14C3×#4020C2211yescharacteristic
15#91463—21no—
16#91456—21no—
17#91434—21no—
18#91408—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91100—21no—
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90988—21no—
24#90967—21no—
25#90965—22no—
26#68407—51nomaximal, Hall
27#65887—31no—
28#65296—31no—
29#65138—31no—
30#64983—31no—
31C5×D4⋊C8—31no—
32#64705D311yescharacteristic, complemented
33#64676—31no—
34C2×Dic30—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D412yes—
41C2×#1201—22no—
42C2×#1201—22no—
43C2×D5×Dic3—22no—
44#6765—42no—
45#6765—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C4×Dic15—21no—
53Dic60—42no—
54C5×(C2×D3)⋊C4—21no—
55C5×C4⋊Dic3D411yescharacteristic
56C2×C5×C3⋊C8—21no—
57C2×C3×#168—21no—
58#6665—22no—
59#5718—51no—
60#5070—51no—
61#4849—51no—
62#4846—51no—
63C3×#331—51no—
64#4484—51no—
65#4483D511yescharacteristic, complemented
66C2×#709—61no—
67C4×C5×D4—31no—
68#4086—61no—
69#4076—61no—
70C2×Dic20—61no—
71#4039—61no—
72#4030—62no—
73#4020C2×D311yescharacteristic
74#4015—31no—
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C4×C5×C8—31no—
78#3964—61no—
79#3953—62no—
80#3948—61no—
81#3939—61no—
82C4⋊#168C2×D311yescharacteristic
83#1641—151noSylow
84C22×C5×D3—21no—
85C22×C3×D5—22no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—41no—
92Dic30—21no—
93Dic30—41no—
94Dic30—41no—
95Dic30D812yes—
96C2×C5×Dic3—21no—
97C5×D12—21no—
98C5×D12—21no—
99C4×C5×D3—41no—
100C4×C5×D3—41no—
101C3×D20—42no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106#1201—44no—
107#1201—82no—
108D5×Dic3—44no—
109C3×C5×C8—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C2×#237—101no—
113C3×#127—51no—
114#940—101no—
115#939—102no—
116#938—101no—
117D4×Dic3—101no—
118C2×Dic12—101no—
119C4×D12C2×D511yescharacteristic
120#869—51no—
121C4×Dic6—51no—
122C3×C4⋊C8—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124#832—102no—
125#821—101no—
126#818—101no—
127#816—101no—
128C4×C3⋊C8C2×D511yescharacteristic
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133#709—122no—
134#709—122no—
135C2×D20—21no—
136C2×D20—21no—
137C2×D20D1212yes—
138C2×C4×D5—62no—
139C2×Dic10—31no—
140C2×Dic10—61no—
141C2×C5×C8—21no—
142C2×C5×C8—61no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#685—62no—
147C4⋊Dic5—31no—
148C4⋊Dic5—61no—
149C4⋊Dic5—61no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—21no—
153Dic20—122no—
154#550—151no—
155#486—151no—
156#474—151no—
157#462—151no—
158#331—51no—
159Q8⋊C8—151no—
160D4⋊C8—31no—
161C22×C3×C5#12011yescharacteristic
162C2×C5×D3—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C2×C3×D5—42no—
168C3×C4×C5—21no—
169C3×C4×C5C2×D811yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—22no—
174Dic15—41no—
175Dic15—81no—
176C5×Dic3—41no—
177C2×C3×D4—52no—
178C2×C3×D4—101no—
179C2×C3×D4—101no—
180C2×#67—102no—
181C2×#67—102no—
182C22×Dic3—102no—
183#237—202no—
184#237—202no—
185C2×D12D2011yescharacteristic
186C2×C4×D3—21no—
187C2×Dic6—51no—
188C2×Dic6—101no—
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C3×C42C22×D511yescharacteristic
192#217—102no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3—51no—
195C4⋊Dic3—101no—
196C4⋊Dic3—101no—
197C4⋊Dic3D2011yescharacteristic
198Dic3⋊C4—101no—
199C4×Dic3—101no—
200C2×C3⋊C8—21no—
201Dic12—202no—
202C23×C5—61no—
203C22×D5—22no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—61no—
207C2×C4×C5—121no—
208C2×C4×C5—121no—
209C2×C4×C5C2×D1211yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C22⋊D5—124no—
213C22⋊D5—242no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216C2×Dic5—121no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—124no—
223Dic10—32no—
224Dic10—61no—
225Dic10—121no—
226Dic10—121no—
227C5×C8—41no—
228C5×C8—121no—
229#168—41no—
230C2×#41—301no—
231C2×Q16—301no—
232C4⋊Q8—151no—
233#127—51no—
234#127—301no—
235#121—302no—
236#121—301no—
237C4×Q8—151no—
238C4×D4—31no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8—51no—
242C4⋊C8D3×D511yescharacteristic
243#103—301no—
244#102—302no—
245#102—301no—
246C4×C8—31no—
247C2×C3×C5#44711yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45511yescharacteristic
250C3×D5—82no—
251C5×D3—81no—
252C23×C3—102no—
253C22×D3—21no—
254C3×D4—202no—
255C3×D4—201no—
256C3×D4—201no—
257C3×D4—201no—
258C3×D4—201no—
259C2×C3×C4C2×D2011yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—21no—
265C2×Dic3—101no—
266C2×Dic3—101no—
267C2×Dic3—204no—
268C2×Dic3—201no—
269D12—21no—
270D12—21no—
271C4×D3—41no—
272C4×D3—41no—
273Dic6—52no—
274Dic6—101no—
275Dic6—201no—
276Dic6—201no—
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—41no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5#88211yescharacteristic
284C2×D5—42no—
285C2×D5—42no—
286C2×D5—42no—
287C4×C5—21no—
288C4×C5—121no—
289C4×C5D3×D811yescharacteristic
290C4×C5#91211yescharacteristic
291C4×C5#91411yescharacteristic
292C4×C5#91511yescharacteristic
293Dic5—62no—
294Dic5—121no—
295Dic5—241no—
296#41—602no—
297#41—602no—
298C2×Q8—151no—
299C2×Q8—301no—
300C2×D4—31no—
301C2×D4—52no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4—302no—
305C2×D4—302no—
306C22×C4—61no—
307C22×C4—302no—
308Q16—602no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—101no—
312C4⋊C4—31no—
313C4⋊C4—151no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—61no—
318C22⋊C4—302no—
319C42—301no—
320C42C2×D3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3#402811yescharacteristic
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C3×C4—21no—
330C3×C4#405011yescharacteristic
331C3×C4#405511yescharacteristic
332C3×C4D5×D811yescharacteristic
333C3×C4#406011yescharacteristic
334Dic3—41no—
335Dic3—102no—
336Dic3—201no—
337Dic3—401no—
338C2×C5—241no—
339C2×C5#474611yescharacteristic
340C2×C5#477311yescharacteristic
341C2×C5#478311yescharacteristic
342D5—82no—
343C23—61no—
344C23—102no—
345Q8—152no—
346Q8—301no—
347Q8—601no—
348Q8—601no—
349D4—61no—
350D4—61no—
351D4—202no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356D4—604no—
357D4—1202no—
358C2×C4—61no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—301no—
362C2×C4—301no—
363C2×C4—604no—
364C2×C4—601no—
365C2×C4D5×D1211yescharacteristic
366C2×C4D3×D2011yescharacteristic
367C2×C4#679011yescharacteristic
368C8—41no—
369C8—121no—
370C8—201no—
371C2×C3—402no—
372C2×C3#6502211yescharacteristic
373C2×C3#6506211yescharacteristic
374C2×C3#6511411yescharacteristic
375D3—81no—
376C5#6840711yescharacteristic, complemented, Sylow
377C22—121no—
378C22—121no—
379C22—121no—
380C22—202no—
381C22—202no—
382C22—202no—
383C22#9147611yescharacteristic
384C4—21no—
385C4—121no—
386C4—302no—
387C4—601no—
388C4—1201no—
389C4#9127311yescharacteristic
390C4#9127411yescharacteristic
391C4#9148111yescharacteristic
392C4#9150611yescharacteristic
393C3#1059898311yescharacteristic, complemented, Sylow
394C2—241no—
395C2—402no—
396C2#1174748511yescharacteristic
397C2#1174816211yescharacteristic
398C2#1174825011yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752554C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1641
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750950C2semidirect
3. #11746964C2semidirect
4. #11746890C2semidirect
5. C5×#4483C2semidirect
6. C3×#64705C2semidirect
7. #11745844C2semidirect
32. #64705D3semidirect
65. #4483D5semidirect
321. C3×C5#1641semidirect
376. C5#68407semidirect
393. C3#10598983semidirect

Maximal subgroups

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

subgroupindex
#117525542
#117509502
#117469642
#117468902
C5×#44832
C3×#647052
#117458442
#105989833
#684075