Subgroups — D₂₉×#479 #16829265

Order 3712.

384 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#125×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#14271473	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271472	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271471	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271470	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271469	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271468	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271467	C₂	1	1	yes	maximal, characteristic, complemented
10	#107×D₂₉	C₂	1	1	yes	maximal, characteristic
11	#106×D₂₉	C₂	1	1	yes	maximal, characteristic
12	C₄⋊C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
13	#103×D₂₉	C₂	1	1	yes	maximal, characteristic
14	#103×D₂₉	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#125	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	Q₈×Dic₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×D₂₉	—	2	1	no	—
23	C₄⋊C₄×D₂₉	—	2	1	no	—
24	C₄⋊C₄×D₂₉	—	2	1	no	—
25	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
28	#11745252	C₂²	1	1	yes	characteristic
29	#11745252	C₂²	1	1	yes	characteristic
30	#11745251	—	2	1	no	—
31	#11745251	—	2	1	no	—
32	#11745249	—	2	1	no	—
33	#11745249	C₂²	1	1	yes	characteristic
34	C₄²×D₂₉	—	2	1	no	—
35	C₄²×D₂₉	C₂²	1	1	yes	characteristic
36	#11745232	C₂²	1	1	yes	characteristic
37	C₄×Dic₅₈	—	2	1	no	—
38	C₄×Dic₅₈	C₂²	1	1	yes	characteristic
39	C₂₉×#107	C₂²	1	1	yes	characteristic
40	C₂₉×#106	C₂²	1	1	yes	characteristic
41	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂₉×#103	C₂²	1	1	yes	characteristic
43	C₂₉×#103	C₂²	1	1	yes	characteristic
44	#11745183	C₂²	1	1	yes	characteristic
45	#11745183	C₂²	1	1	yes	characteristic
46	#11745166	C₂²	1	1	yes	characteristic
47	#11745165	C₂²	1	1	yes	characteristic
48	#11745164	C₂²	1	1	yes	characteristic
49	#11745164	C₂²	1	1	yes	characteristic
50	#11745162	C₂²	1	1	yes	characteristic
51	#11745162	C₂²	1	1	yes	characteristic
52	#11745158	C₂²	1	1	yes	characteristic
53	#11745158	C₂²	1	1	yes	characteristic
54	#11745156	C₂²	1	1	yes	characteristic
55	#11745156	C₂²	1	1	yes	characteristic
56	#11745155	C₂²	1	1	yes	characteristic
57	#11745155	C₂²	1	1	yes	characteristic
58	C₄⋊#6597	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
60	Q₈×D₂₉	—	2	2	no	—
61	Q₈×D₂₉	Q₈	1	4	yes	—
62	C₂×C₄×D₂₉	—	2	1	no	—
63	C₂×C₄×D₂₉	—	2	1	no	—
64	C₂×C₄×D₂₉	—	2	1	no	—
65	C₂×C₄×D₂₉	—	2	1	no	—
66	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
67	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
68	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
69	C₂×Dic₅₈	—	2	1	no	—
70	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₄⋊C₄×C₂₉	—	2	1	no	—
74	C₄⋊C₄×C₂₉	—	2	1	no	—
75	C₄⋊C₄×C₂₉	—	2	1	no	—
76	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
79	C₄²×C₂₉	—	2	1	no	—
80	C₄²×C₂₉	C₂³	1	1	yes	characteristic
81	C₄⋊Dic₂₉	—	2	1	no	—
82	C₄⋊Dic₂₉	—	2	1	no	—
83	C₄⋊Dic₂₉	—	2	1	no	—
84	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
85	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
87	#90779	—	2	1	no	—
88	#90779	—	2	1	no	—
89	#90779	—	2	1	no	—
90	#90779	—	2	1	no	—
91	#90779	—	2	1	no	—
92	#90779	—	2	1	no	—
93	#90779	—	2	1	no	—
94	#90779	—	2	1	no	—
95	#90779	—	2	1	no	—
96	C₄×Dic₂₉	—	2	1	no	—
97	C₄×Dic₂₉	—	2	1	no	—
98	C₄×Dic₂₉	—	2	1	no	—
99	C₄×Dic₂₉	D₄	1	1	yes	characteristic
100	C₄×Dic₂₉	D₄	1	1	yes	characteristic
101	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
102	C₂×#6597	C₂³	1	1	yes	characteristic
103	C₂×#6597	C₂³	1	1	yes	characteristic
104	C₈×D₂₉	—	2	2	no	—
105	C₈×D₂₉	—	2	2	no	—
106	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
107	Q₈×C₂₉	—	2	1	no	—
108	Q₈×C₂₉	C₂×Q₈	1	2	yes	—
109	C₂×C₄×C₂₉	—	2	1	no	—
110	C₂×C₄×C₂₉	—	2	1	no	—
111	C₂×C₄×C₂₉	—	2	1	no	—
112	C₂×C₄×C₂₉	—	2	1	no	—
113	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
116	C₂×Dic₂₉	—	2	1	no	—
117	C₂×Dic₂₉	—	2	1	no	—
118	C₂×Dic₂₉	—	2	1	no	—
119	C₂×Dic₂₉	—	2	1	no	—
120	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
123	C₄×D₂₉	—	2	4	no	—
124	C₄×D₂₉	—	2	2	no	—
125	C₄×D₂₉	—	2	2	no	—
126	C₄×D₂₉	—	4	2	no	—
127	C₄×D₂₉	—	4	2	no	—
128	C₄×D₂₉	—	4	2	no	—
129	C₄×D₂₉	C₂×Q₈	1	2	yes	—
130	C₄×D₂₉	#41	1	2	yes	—
131	Dic₅₈	—	2	1	no	—
132	Dic₅₈	—	2	4	no	—
133	Dic₅₈	C₂×Q₈	1	2	yes	—
134	C₈×C₂₉	—	2	1	no	—
135	C₈×C₂₉	—	2	1	no	—
136	#6597	—	2	1	no	—
137	#6597	—	2	1	no	—
138	C₂×#479	—	29	1	no	maximal, Sylow
139	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
140	C₂×D₂₉	C₂²⋊Q₈	1	2	yes	—
141	C₂×D₂₉	#135	1	2	yes	—
142	C₂×D₂₉	#137	1	2	yes	—
143	C₄×C₂₉	—	2	2	no	—
144	C₄×C₂₉	—	2	1	no	—
145	C₄×C₂₉	—	2	1	no	—
146	C₄×C₂₉	—	4	1	no	—
147	C₄×C₂₉	—	4	1	no	—
148	C₄×C₂₉	—	4	1	no	—
149	C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
150	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
151	Dic₂₉	—	2	2	no	—
152	Dic₂₉	—	2	1	no	—
153	Dic₂₉	—	2	1	no	—
154	Dic₂₉	—	4	1	no	—
155	Dic₂₉	—	4	1	no	—
156	Dic₂₉	—	4	1	no	—
157	Dic₂₉	C₂²⋊Q₈	1	2	yes	—
158	C₂×#125	—	29	1	no	—
159	C₂×C₄×Q₈	—	29	1	no	—
160	#479	—	29	1	no	—
161	#479	—	29	1	no	—
162	#479	—	29	1	no	—
163	#479	—	29	1	no	—
164	#479	—	29	1	no	—
165	#479	—	29	1	no	—
166	#479	—	29	1	no	—
167	#479	D₂₉	1	1	yes	characteristic, direct product factor
168	C₂×#107	—	29	1	no	—
169	C₂×#106	—	29	1	no	—
170	C₂×C₄⋊C₈	—	29	1	no	—
171	C₂×#103	—	29	1	no	—
172	C₂×#103	—	29	1	no	—
173	C₂×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₂₉	C₂×#135	1	1	yes	characteristic
175	C₂×C₂₉	C₂×#137	1	1	yes	characteristic
176	D₂₉	#479	1	4	yes	direct product factor
177	C₂²×Q₈	—	29	1	no	—
178	C₂²×C₈	—	29	1	no	—
179	C₂²×C₈	—	29	1	no	—
180	#125	—	29	1	no	—
181	#125	—	29	1	no	—
182	#125	—	29	1	no	—
183	#125	—	58	1	no	—
184	#125	—	58	1	no	—
185	#125	C₂×D₂₉	1	1	yes	characteristic
186	C₄×Q₈	—	29	1	no	—
187	C₄×Q₈	—	29	1	no	—
188	C₄×Q₈	—	29	1	no	—
189	C₄×Q₈	—	58	1	no	—
190	C₄×Q₈	—	58	1	no	—
191	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic
192	C₂×C₄⋊C₄	—	29	1	no	—
193	C₂×C₄⋊C₄	—	29	1	no	—
194	C₂×C₄⋊C₄	—	29	1	no	—
195	C₂×C₄⋊C₄	—	58	1	no	—
196	C₂×C₄⋊C₄	—	58	1	no	—
197	C₂×C₄⋊C₄	—	58	1	no	—
198	C₂×C₄²	—	29	1	no	—
199	C₂×C₄²	—	58	1	no	—
200	#107	—	29	1	no	—
201	#107	—	29	1	no	—
202	#107	—	29	1	no	—
203	#107	C₂×D₂₉	1	1	yes	characteristic
204	#106	—	29	1	no	—
205	#106	—	29	1	no	—
206	#106	—	29	1	no	—
207	#106	C₂×D₂₉	1	1	yes	characteristic
208	C₄⋊C₈	—	29	1	no	—
209	C₄⋊C₈	—	29	1	no	—
210	C₄⋊C₈	—	29	1	no	—
211	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic
212	#103	—	29	1	no	—
213	#103	—	29	1	no	—
214	#103	—	29	1	no	—
215	#103	—	29	1	no	—
216	#103	—	29	1	no	—
217	#103	—	29	1	no	—
218	#103	C₂×D₂₉	1	1	yes	characteristic
219	#103	C₂×D₂₉	1	1	yes	characteristic
220	C₂₉	C₂×#479	1	1	yes	characteristic, complemented, Sylow
221	C₂×Q₈	—	29	4	no	—
222	C₂×Q₈	—	29	1	no	—
223	C₂×Q₈	—	58	1	no	—
224	C₂×Q₈	—	58	2	no	—
225	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
226	C₂²×C₄	—	29	1	no	—
227	C₂²×C₄	—	29	1	no	—
228	C₂²×C₄	—	29	1	no	—
229	C₂²×C₄	—	58	1	no	—
230	C₂²×C₄	—	58	1	no	—
231	C₂²×C₄	—	58	1	no	—
232	C₂²×C₄	—	58	1	no	—
233	C₂×C₈	—	29	1	no	—
234	C₂×C₈	—	29	1	no	—
235	C₂×C₈	—	58	2	no	—
236	C₂×C₈	—	58	2	no	—
237	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
238	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
239	C₄⋊C₄	—	2	1	no	—
240	C₄⋊C₄	—	2	1	no	—
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	—	29	1	no	—
243	C₄⋊C₄	—	29	1	no	—
244	C₄⋊C₄	—	29	1	no	—
245	C₄⋊C₄	—	58	1	no	—
246	C₄⋊C₄	—	58	1	no	—
247	C₄⋊C₄	—	58	1	no	—
248	C₄⋊C₄	—	58	1	no	—
249	C₄⋊C₄	—	58	1	no	—
250	C₄⋊C₄	—	58	1	no	—
251	C₄⋊C₄	—	58	1	no	—
252	C₄⋊C₄	—	58	1	no	—
253	C₄⋊C₄	—	58	1	no	—
254	C₄⋊C₄	—	58	1	no	—
255	C₄⋊C₄	—	58	1	no	—
256	C₄⋊C₄	—	58	1	no	—
257	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
258	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
259	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
260	C₄²	—	2	1	no	—
261	C₄²	—	29	1	no	—
262	C₄²	—	29	1	no	—
263	C₄²	—	29	1	no	—
264	C₄²	—	58	1	no	—
265	C₄²	—	58	1	no	—
266	C₄²	—	58	1	no	—
267	C₄²	C₂²×D₂₉	1	1	yes	characteristic
268	C₂³	—	29	1	no	—
269	Q₈	—	2	1	no	—
270	Q₈	—	29	2	no	—
271	Q₈	—	58	4	no	—
272	Q₈	—	58	1	no	—
273	Q₈	Q₈×D₂₉	1	2	yes	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	29	1	no	—
279	C₂×C₄	—	29	2	no	—
280	C₂×C₄	—	29	2	no	—
281	C₂×C₄	—	29	1	no	—
282	C₂×C₄	—	29	1	no	—
283	C₂×C₄	—	58	2	no	—
284	C₂×C₄	—	58	2	no	—
285	C₂×C₄	—	58	4	no	—
286	C₂×C₄	—	58	1	no	—
287	C₂×C₄	—	58	1	no	—
288	C₂×C₄	—	58	1	no	—
289	C₂×C₄	—	58	1	no	—
290	C₂×C₄	—	116	2	no	—
291	C₂×C₄	—	116	2	no	—
292	C₂×C₄	—	116	2	no	—
293	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
294	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
295	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
296	C₈	—	2	1	no	—
297	C₈	—	2	1	no	—
298	C₈	—	58	1	no	—
299	C₈	—	58	1	no	—
300	C₂²	—	29	2	no	—
301	C₂²	—	29	2	no	—
302	C₂²	—	29	2	no	—
303	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
304	C₄	—	2	2	no	—
305	C₄	—	2	1	no	—
306	C₄	—	2	1	no	—
307	C₄	—	4	1	no	—
308	C₄	—	4	1	no	—
309	C₄	—	4	1	no	—
310	C₄	—	29	2	no	—
311	C₄	—	58	2	no	—
312	C₄	—	58	1	no	—
313	C₄	—	58	1	no	—
314	C₄	—	116	1	no	—
315	C₄	—	116	1	no	—
316	C₄	—	116	1	no	—
317	C₄	C₂×Q₈×D₂₉	1	1	yes	characteristic
318	C₄	#41×D₂₉	1	1	yes	characteristic
319	C₂	—	29	4	no	—
320	C₂	C₂²⋊Q₈×D₂₉	1	1	yes	characteristic
321	C₂	#135×D₂₉	1	1	yes	characteristic
322	C₂	#137×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂₉×#479	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂²×D₂₉	C₂×D₄
hypercenter	#479	D₂₉
hypocenter	C₂₉	C₂×#479
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #479

Complements

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

N	H ≅ G/N	type
3. #14271473	C₂	semidirect
4. #14271472	C₂	semidirect
5. #14271471	C₂	semidirect
6. #14271470	C₂	semidirect
7. #14271469	C₂	semidirect
8. #14271468	C₂	semidirect
9. #14271467	C₂	semidirect
15. C₂₉×#479	C₂	semidirect
167. #479	D₂₉	direct (N × H)
176. D₂₉	#479	direct (N × H)
220. C₂₉	C₂×#479	semidirect

Maximal subgroups

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

subgroup	index
#125×D₂₉	2
C₄×Q₈×D₂₉	2
#14271473	2
#14271472	2
#14271471	2
#14271470	2
#14271469	2
#14271468	2
#14271467	2
#107×D₂₉	2
#106×D₂₉	2
C₄⋊C₈×D₂₉	2
#103×D₂₉	2
C₂₉×#479	2
C₂×#479	29

Subgroups — D29×#479 #16829265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×#479 #16829265