Finite Group Databasebeta

← C29×#13030 #20307930

Subgroups — C29×#13030 #20307930

Order 7424.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3414C211yesmaximal, characteristic
2C29×#2952C211yesmaximal, characteristic, complemented
3C29×#2145C211yesmaximal, characteristic, complemented
4C2×C29×#360C211yesmaximal, characteristic, complemented
5C29×#1976C211yesmaximal, characteristic, complemented
6C29×#1386C211yesmaximal, characteristic, complemented
7C29×#1378C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C2×C29×#135C2211yescharacteristic
10C29×#520—21no—
11C29×#510—21no—
12C29×#510C412yescomplemented
13C29×#509—21no—
14C29×#509C412yescomplemented
15C29×#508—22no—
16C2×C29×M32C2211yescharacteristic
17C2×C29×M32C2211yescharacteristic
18C29×#442—21no—
19C29×#441—21no—
20C4×SD16×C29—22no—
21C29×#427C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C29×#421—21no—
24C29×#417—21no—
25C29×#410—21no—
26C29×#405C2211yescharacteristic
27C29×#360—22no—
28C29×#360—22no—
29C2×#41×C29—21no—
30C2×#41×C29—21no—
31C29×#135—21no—
32C29×#135—21no—
33C29×#135—21no—
34C29×#135—21no—
35C29×#135—21no—
36C29×#135—21no—
37C29×#135C2×C412yes—
38C29×#135D412yes—
39C2×Q16×C29C2×C411yescharacteristic, complemented
40C2×Q16×C29D411yescharacteristic
41C2×SD16×C29—21no—
42C2×SD16×C29—21no—
43C2×D8×C29C2×C411yescharacteristic, complemented
44C2×D8×C29D411yescharacteristic
45C2×M16×C29D411yescharacteristic
46C22×C8×C29C2311yescharacteristic
47C4×Q8×C29—22no—
48C4×D4×C29—22no—
49C4×D4×C29—42no—
50C29×#117—21no—
51C29×#117—41no—
52C29×#117D411yescharacteristic
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—41no—
55C29×Q32—22no—
56C29×SD32—22no—
57C29×SD32—22no—
58C29×D16—22no—
59C29×M32—21no—
60C29×M32—21no—
61C29×M32—21no—
62C29×M32C2×C412yescomplemented
63C2×C16×C29—21no—
64C2×C16×C29—21no—
65C29×#107—21no—
66C29×#106—21no—
67C29×#106—21no—
68C29×#106D412yes—
69C29×#104—42no—
70C29×#103—22no—
71C29×#102—22no—
72C29×#99—42no—
73C29×#97—21no—
74C4×C8×C29—21no—
75#41×C29—22no—
76#41×C29—22no—
77#41×C29—41no—
78#41×C29—41no—
79#41×C29—41no—
80#41×C29—41no—
81#41×C29—41no—
82#41×C29—41no—
83C2×Q8×C29—21no—
84C2×Q8×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—21no—
87C2×D4×C29—41no—
88C2×D4×C29—41no—
89C22×C4×C29—42no—
90C22×C4×C29—41no—
91C22×C4×C29—41no—
92C22×C4×C29—41no—
93C22×C4×C29C2×D411yescharacteristic
94Q16×C29—21no—
95Q16×C29—21no—
96Q16×C29—21no—
97Q16×C29C22⋊C412yes—
98SD16×C29—22no—
99SD16×C29—22no—
100SD16×C29—41no—
101SD16×C29—41no—
102D8×C29—21no—
103D8×C29—21no—
104D8×C29—21no—
105D8×C29C22⋊C412yes—
106M16×C29—21no—
107M16×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29C22×C411yescharacteristic
110C2×C8×C29C2×D411yescharacteristic
111C2×C8×C29C2×D411yescharacteristic
112C2×C8×C29C2×D411yescharacteristic
113C2×C8×C29#4111yescharacteristic
114C2×C8×C29#4111yescharacteristic
115C4⋊C4×C29—21no—
116C4⋊C4×C29—22no—
117C4⋊C4×C29—42no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C22⋊C4×C29—42no—
121C22⋊C4×C29—41no—
122C22⋊C4×C29D812yes—
123C42×C29—21no—
124C42×C29—42no—
125C42×C29—41no—
126C16×C29—22no—
127C16×C29—41no—
128#13030C2911yesmaximal, characteristic, direct product factor, Sylow
129C23×C29—41no—
130C23×C29—41no—
131C23×C29C2×D811yescharacteristic
132Q8×C29—22no—
133Q8×C29—41no—
134Q8×C29—41no—
135Q8×C29—41no—
136D4×C29—22no—
137D4×C29—42no—
138D4×C29—42no—
139D4×C29—41no—
140D4×C29—41no—
141D4×C29—41no—
142D4×C29—81no—
143D4×C29—81no—
144C2×C4×C29—22no—
145C2×C4×C29—41no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29—41no—
149C2×C4×C29—42no—
150C2×C4×C29—81no—
151C2×C4×C29—81no—
152C2×C4×C29—81no—
153C2×C4×C29—162no—
154C2×C4×C29—161no—
155C2×C4×C29C4×D411yescharacteristic
156C2×C4×C29#12011yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#13511yescharacteristic
159C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
161C8×C29—41no—
162C8×C29C2×C22⋊C411yescharacteristic
163C8×C29C4×D411yescharacteristic
164C8×C29#12111yescharacteristic
165C8×C29#12311yescharacteristic
166#3414C2×C2911yescharacteristic
167#2952C2×C2911yescharacteristic, complemented
168#2145C2×C2911yescharacteristic, complemented
169C2×#360C2×C2911yescharacteristic, complemented
170#1976C2×C2911yescharacteristic, complemented
171#1386C2×C2911yescharacteristic, complemented
172#1378C2×C2911yescharacteristic, complemented
173C22×C29—41no—
174C22×C29—42no—
175C22×C29—81no—
176C22×C29—81no—
177C22×C29—81no—
178C22×C29—161no—
179C22×C29C4×D811yescharacteristic
180C22×C29#44711yescharacteristic
181C22×C29#45911yescharacteristic
182C4×C29—42no—
183C4×C29—42no—
184C4×C29—82no—
185C4×C29—81no—
186C4×C29—161no—
187C4×C29#38611yescharacteristic
188C4×C29#44211yescharacteristic
189C4×C29#44911yescharacteristic
190C4×C29#46311yescharacteristic
191C2×#135C22×C2911yescharacteristic
192C2×#135C22×C2911yescharacteristic
193#520—21no—
194#510—21no—
195#510C4×C2912yescomplemented
196#509—21no—
197#509C4×C2912yescomplemented
198#508—22no—
199C2×M32C22×C2911yescharacteristic
200C2×M32C22×C2911yescharacteristic
201#442—21no—
202#441—21no—
203C4×SD16—22no—
204#427C22×C2911yescharacteristic
205C2×#106C22×C2911yescharacteristic
206#421—21no—
207#417—21no—
208#410—21no—
209#405C22×C2911yescharacteristic
210#360—22no—
211#360—22no—
212C2×C29—21no—
213C2×C29—21no—
214C2×C29—21no—
215C2×C29—82no—
216C2×C29—161no—
217C2×C29#187911yescharacteristic
218C2×#41—21no—
219C2×#41—21no—
220#135—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135C2×C4×C2912yes—
227#135D4×C2912yes—
228C2×Q16C2×C4×C2911yescharacteristic, complemented
229C2×Q16D4×C2911yescharacteristic
230C2×SD16—21no—
231C2×SD16—21no—
232C2×D8C2×C4×C2911yescharacteristic, complemented
233C2×D8D4×C2911yescharacteristic
234C2×M16D4×C2911yescharacteristic
235C22×C8C23×C2911yescharacteristic
236C4×Q8—22no—
237C4×D4—22no—
238C4×D4—42no—
239#117—21no—
240#117—41no—
241#117D4×C2911yescharacteristic
242C2×C4⋊C4—21no—
243C2×C4⋊C4—41no—
244Q32—22no—
245SD32—22no—
246SD32—22no—
247D16—22no—
248M32—21no—
249M32—21no—
250M32—21no—
251M32C2×C4×C2912yescomplemented
252C2×C16—21no—
253C2×C16—21no—
254#107—21no—
255#106—21no—
256#106—21no—
257#106D4×C2912yes—
258#104—42no—
259#103—22no—
260#102—22no—
261#99—42no—
262#97—21no—
263C4×C8—21no—
264C29#1303011yescharacteristic, direct product factor, Sylow
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C2×D4×C2911yescharacteristic
284Q16—21no—
285Q16—21no—
286Q16—21no—
287Q16C22⋊C4×C2912yes—
288SD16—22no—
289SD16—22no—
290SD16—41no—
291SD16—41no—
292D8—21no—
293D8—21no—
294D8—21no—
295D8C22⋊C4×C2912yes—
296M16—21no—
297M16—21no—
298C2×C8—21no—
299C2×C8C22×C4×C2911yescharacteristic
300C2×C8C2×D4×C2911yescharacteristic
301C2×C8C2×D4×C2911yescharacteristic
302C2×C8C2×D4×C2911yescharacteristic
303C2×C8#41×C2911yescharacteristic
304C2×C8#41×C2911yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4D8×C2912yes—
313C42—21no—
314C42—42no—
315C42—41no—
316C16—22no—
317C16—41no—
318C23—41no—
319C23—41no—
320C23C2×D8×C2911yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—162no—
343C2×C4—161no—
344C2×C4C4×D4×C2911yescharacteristic
345C2×C4C29×#12011yescharacteristic
346C2×C4C29×#12111yescharacteristic
347C2×C4C29×#13511yescharacteristic
348C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
349C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
350C8—41no—
351C8C2×C22⋊C4×C2911yescharacteristic
352C8C4×D4×C2911yescharacteristic
353C8C29×#12111yescharacteristic
354C8C29×#12311yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22C4×D8×C2911yescharacteristic
362C22C29×#44711yescharacteristic
363C22C29×#45911yescharacteristic
364C4—42no—
365C4—42no—
366C4—82no—
367C4—81no—
368C4—161no—
369C4C29×#38611yescharacteristic
370C4C29×#44211yescharacteristic
371C4C29×#44911yescharacteristic
372C4C29×#46311yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2C29×#187911yescharacteristic
subgroupG/H
center, socleC2×C29#1879
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2952C2semidirect
3. C29×#2145C2semidirect
4. C2×C29×#360C2semidirect
5. C29×#1976C2semidirect
6. C29×#1386C2semidirect
7. C29×#1378C2semidirect
12. C29×#510C4semidirect
14. C29×#509C4semidirect
39. C2×Q16×C29C2×C4semidirect
43. C2×D8×C29C2×C4semidirect
62. C29×M32C2×C4semidirect
128. #13030C29direct (N × H)
167. #2952C2×C29semidirect
168. #2145C2×C29semidirect
169. C2×#360C2×C29semidirect
170. #1976C2×C29semidirect
171. #1386C2×C29semidirect
172. #1378C2×C29semidirect
195. #510C4×C29semidirect
197. #509C4×C29semidirect
228. C2×Q16C2×C4×C29semidirect
232. C2×D8C2×C4×C29semidirect
251. M32C2×C4×C29semidirect
264. C29#13030direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34142
C29×#29522
C29×#21452
C2×C29×#3602
C29×#19762
C29×#13862
C29×#13782
#1303029