Subgroups — C₂₉×#18044 #20312944

Order 7424.

786 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
3	C₂₉×#1594	C₂	1	2	yes	maximal, complemented
4	C₂₉×#1586	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1580	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1486	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₂₉	C₄	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₉	—	2	2	no	—
11	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
12	C₄×D₈×C₂₉	C₄	1	1	yes	characteristic
13	C₄×D₈×C₂₉	C₄	1	2	yes	—
14	C₄×D₈×C₂₉	C₄	1	1	yes	characteristic
15	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₂₉	C₂²	1	2	yes	—
17	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#436	C₂²	1	4	yes	complemented
19	C₂₉×#435	—	2	4	no	—
20	C₈×D₄×C₂₉	C₂²	1	4	yes	complemented
21	C₂₉×#431	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#107	C₄	1	1	yes	characteristic
23	C₂₉×#423	C₂²	1	2	yes	—
24	C₂×C₂₉×#102	C₄	1	2	yes	—
25	C₂₉×#407	—	2	2	no	—
26	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
28	C₂₉×#334	C₂²	1	2	yes	complemented
29	C₂₉×#334	C₂²	1	2	yes	complemented
30	C₂₉×D₄⋊C₈	C₂²	1	4	yes	complemented
31	C₂₉×D₄⋊C₈	C₂²	1	4	yes	complemented
32	C₂₉×#322	C₂²	1	2	yes	complemented
33	C₂₉×#322	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₂₉	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₂₉	—	2	2	no	—
36	C₂×D₈×C₂₉	—	2	4	no	—
37	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₂₉	—	2	2	no	—
41	C₂×M₁₆×C₂₉	—	2	4	no	—
42	C₂×M₁₆×C₂₉	—	4	8	no	—
43	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
44	C₂²×C₈×C₂₉	—	2	4	no	—
45	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₄×D₄×C₂₉	—	2	2	no	—
48	C₄×D₄×C₂₉	—	2	2	no	—
49	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
50	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₂₉	C₂³	1	2	yes	—
52	C₄×D₄×C₂₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
55	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
56	C₂₉×#107	C₂×C₄	1	2	yes	—
57	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
58	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
59	C₂₉×C₄⋊C₈	—	2	2	no	—
60	C₂₉×C₄⋊C₈	—	2	1	no	—
61	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
62	C₂₉×#102	C₂×C₄	1	2	yes	—
63	C₂₉×#102	C₂×C₄	1	2	yes	—
64	C₂₉×#102	C₂×C₄	1	2	yes	—
65	C₂₉×#102	C₂×C₄	1	2	yes	—
66	C₂₉×C₂²⋊C₈	—	2	1	no	—
67	C₂₉×C₂²⋊C₈	—	2	4	no	—
68	C₂₉×C₂²⋊C₈	—	2	4	no	—
69	C₂₉×#97	D₄	1	2	yes	—
70	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₂₉	C₂³	1	2	yes	—
73	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₂₉	C₂³	1	2	yes	—
76	C₂⁴×C₂₉	—	2	2	no	—
77	C₂×D₄×C₂₉	—	2	4	no	—
78	C₂×D₄×C₂₉	—	2	2	no	—
79	C₂×D₄×C₂₉	—	4	2	no	—
80	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
81	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₂₉	—	2	2	no	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	—	2	2	no	—
85	C₂²×C₄×C₂₉	—	2	2	no	—
86	C₂²×C₄×C₂₉	—	2	2	no	—
87	C₂²×C₄×C₂₉	—	4	4	no	—
88	C₂²×C₄×C₂₉	—	4	4	no	—
89	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
92	D₈×C₂₉	—	2	4	no	—
93	D₈×C₂₉	—	2	2	no	—
94	D₈×C₂₉	M₁₆	1	4	yes	complemented
95	M₁₆×C₂₉	—	2	4	no	—
96	M₁₆×C₂₉	—	4	8	no	—
97	M₁₆×C₂₉	—	4	4	no	—
98	C₂×C₈×C₂₉	—	2	2	no	—
99	C₂×C₈×C₂₉	—	2	4	no	—
100	C₂×C₈×C₂₉	—	2	2	no	—
101	C₂×C₈×C₂₉	—	4	1	no	—
102	C₂×C₈×C₂₉	—	4	8	no	—
103	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
108	C₄⋊C₄×C₂₉	—	2	2	no	—
109	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₂₉	—	2	2	no	—
112	C₂²⋊C₄×C₂₉	—	2	2	no	—
113	C₂²⋊C₄×C₂₉	—	2	2	no	—
114	C₂²⋊C₄×C₂₉	—	2	2	no	—
115	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₂₉	#41	1	1	yes	characteristic
118	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
119	#18044	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₂₉	—	2	2	no	—
121	C₂³×C₂₉	—	2	2	no	—
122	C₂³×C₂₉	—	4	4	no	—
123	C₂³×C₂₉	—	4	4	no	—
124	C₂³×C₂₉	—	8	2	no	—
125	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
126	D₄×C₂₉	—	2	2	no	—
127	D₄×C₂₉	—	2	2	no	—
128	D₄×C₂₉	—	2	2	no	—
129	D₄×C₂₉	—	4	4	no	—
130	D₄×C₂₉	C₂×M₁₆	1	4	yes	complemented
131	C₂×C₄×C₂₉	—	2	1	no	—
132	C₂×C₄×C₂₉	—	2	1	no	—
133	C₂×C₄×C₂₉	—	2	2	no	—
134	C₂×C₄×C₂₉	—	2	2	no	—
135	C₂×C₄×C₂₉	—	4	1	no	—
136	C₂×C₄×C₂₉	—	4	4	no	—
137	C₂×C₄×C₂₉	—	4	2	no	—
138	C₂×C₄×C₂₉	—	4	2	no	—
139	C₂×C₄×C₂₉	—	4	2	no	—
140	C₂×C₄×C₂₉	—	4	2	no	—
141	C₂×C₄×C₂₉	—	4	4	no	—
142	C₂×C₄×C₂₉	—	4	4	no	—
143	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
147	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
150	C₈×C₂₉	—	2	1	no	—
151	C₈×C₂₉	—	2	1	no	—
152	C₈×C₂₉	—	2	1	no	—
153	C₈×C₂₉	—	2	4	no	—
154	C₈×C₂₉	—	4	2	no	—
155	C₈×C₂₉	—	4	4	no	—
156	C₈×C₂₉	C₂×M₁₆	1	2	yes	complemented
157	C₂×C₄×D₈	C₂×C₂₉	1	1	yes	characteristic
158	D₄×M₁₆	C₂×C₂₉	1	2	yes	complemented
159	#1594	C₂×C₂₉	1	2	yes	complemented
160	#1586	C₂×C₂₉	1	4	yes	complemented
161	#1580	C₂×C₂₉	1	2	yes	complemented
162	#1566	C₂×C₂₉	1	1	yes	characteristic, complemented
163	#1486	C₂×C₂₉	1	2	yes	complemented
164	#1451	C₂×C₂₉	1	1	yes	characteristic, complemented
165	C₂²×C₂₉	—	2	1	no	—
166	C₂²×C₂₉	—	2	1	no	—
167	C₂²×C₂₉	—	2	4	no	—
168	C₂²×C₂₉	—	4	2	no	—
169	C₂²×C₂₉	—	4	2	no	—
170	C₂²×C₂₉	—	4	2	no	—
171	C₂²×C₂₉	—	4	2	no	—
172	C₂²×C₂₉	—	4	2	no	—
173	C₂²×C₂₉	—	8	8	no	—
174	C₂²×C₂₉	#442	1	2	yes	—
175	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
176	C₄×C₂₉	—	2	1	no	—
177	C₄×C₂₉	—	2	1	no	—
178	C₄×C₂₉	—	2	1	no	—
179	C₄×C₂₉	—	4	2	no	—
180	C₄×C₂₉	—	4	2	no	—
181	C₄×C₂₉	#442	1	2	yes	—
182	C₄×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
183	C₄×C₂₉	#568	1	1	yes	characteristic
184	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
185	C₂²×D₈	C₄×C₂₉	1	1	yes	characteristic
186	C₂²×M₁₆	—	2	2	no	—
187	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
188	C₄×D₈	C₄×C₂₉	1	2	yes	—
189	C₄×D₈	C₄×C₂₉	1	1	yes	characteristic
190	C₄×D₈	C₄×C₂₉	1	1	yes	characteristic
191	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
192	C₄×D₈	C₂²×C₂₉	1	2	yes	—
193	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
194	#436	C₂²×C₂₉	1	4	yes	complemented
195	#435	—	2	4	no	—
196	C₈×D₄	C₂²×C₂₉	1	4	yes	complemented
197	#431	C₂²×C₂₉	1	1	yes	characteristic
198	C₂×#107	C₄×C₂₉	1	1	yes	characteristic
199	#423	C₂²×C₂₉	1	2	yes	—
200	C₂×#102	C₄×C₂₉	1	2	yes	—
201	#407	—	2	2	no	—
202	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
204	#334	C₂²×C₂₉	1	2	yes	complemented
205	#334	C₂²×C₂₉	1	2	yes	complemented
206	D₄⋊C₈	C₂²×C₂₉	1	4	yes	complemented
207	D₄⋊C₈	C₂²×C₂₉	1	4	yes	complemented
208	#322	C₂²×C₂₉	1	2	yes	complemented
209	#322	C₂²×C₂₉	1	2	yes	complemented
210	C₂×C₂₉	—	2	2	no	—
211	C₂×C₂₉	—	4	4	no	—
212	C₂×C₂₉	—	8	2	no	—
213	C₂×C₂₉	D₄×M₁₆	1	1	yes	characteristic
214	C₂×C₂₉	C₂×#442	1	1	yes	characteristic
215	C₂×C₂₉	#2957	1	1	yes	characteristic
216	C₂²×D₄	C₂×C₄×C₂₉	1	2	yes	—
217	C₂³×C₄	—	2	2	no	—
218	C₂×D₈	—	2	4	no	—
219	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
220	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic
221	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	4	no	—
224	C₂×M₁₆	—	4	8	no	—
225	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
228	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
232	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
233	C₄×D₄	C₂³×C₂₉	1	2	yes	—
234	C₄×D₄	C₂³×C₂₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
238	#107	C₂×C₄×C₂₉	1	2	yes	—
239	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
240	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
244	#102	C₂×C₄×C₂₉	1	2	yes	—
245	#102	C₂×C₄×C₂₉	1	2	yes	—
246	#102	C₂×C₄×C₂₉	1	2	yes	—
247	#102	C₂×C₄×C₂₉	1	2	yes	—
248	C₂²⋊C₈	—	2	1	no	—
249	C₂²⋊C₈	—	2	4	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	#97	D₄×C₂₉	1	2	yes	—
252	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
253	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₂₉	1	2	yes	—
255	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
256	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₂₉	1	2	yes	—
258	C₂₉	#18044	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	—	2	2	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
264	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
275	D₈	—	2	4	no	—
276	D₈	—	2	2	no	—
277	D₈	M₁₆×C₂₉	1	4	yes	complemented
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	8	no	—
280	M₁₆	—	4	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	8	no	—
286	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
293	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
300	C₄²	#41×C₂₉	1	1	yes	characteristic
301	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	8	2	no	—
307	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
308	D₄	—	2	2	no	—
309	D₄	—	2	2	no	—
310	D₄	—	2	2	no	—
311	D₄	—	4	4	no	—
312	D₄	C₂×M₁₆×C₂₉	1	4	yes	complemented
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
326	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
327	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
328	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	4	yes	—
329	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	2	4	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	4	no	—
338	C₈	C₂×M₁₆×C₂₉	1	2	yes	complemented
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	8	no	—
348	C₂²	C₂₉×#442	1	2	yes	—
349	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	C₂₉×#442	1	2	yes	—
356	C₄	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
357	C₄	C₂₉×#568	1	1	yes	characteristic
358	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	4	4	no	—
361	C₂	—	8	2	no	—
362	C₂	D₄×M₁₆×C₂₉	1	1	yes	characteristic
363	C₂	C₂×C₂₉×#442	1	1	yes	characteristic
364	C₂	C₂₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂²×D₈×C₂₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₄×M₁₆×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₂₉	C₂	semidirect
3. C₂₉×#1594	C₂	semidirect
4. C₂₉×#1586	C₂	semidirect
5. C₂₉×#1580	C₂	semidirect
6. C₂₉×#1566	C₂	semidirect
7. C₂₉×#1486	C₂	semidirect
8. C₂₉×#1451	C₂	semidirect
18. C₂₉×#436	C₂²	semidirect
20. C₈×D₄×C₂₉	C₂²	semidirect
28. C₂₉×#334	C₂²	semidirect
29. C₂₉×#334	C₂²	semidirect
30. C₂₉×D₄⋊C₈	C₂²	semidirect
31. C₂₉×D₄⋊C₈	C₂²	semidirect
32. C₂₉×#322	C₂²	semidirect
33. C₂₉×#322	C₂²	semidirect
94. D₈×C₂₉	M₁₆	semidirect
119. #18044	C₂₉	direct (N × H)
130. D₄×C₂₉	C₂×M₁₆	semidirect
156. C₈×C₂₉	C₂×M₁₆	semidirect
158. D₄×M₁₆	C₂×C₂₉	semidirect
159. #1594	C₂×C₂₉	semidirect
160. #1586	C₂×C₂₉	semidirect
161. #1580	C₂×C₂₉	semidirect
162. #1566	C₂×C₂₉	semidirect
163. #1486	C₂×C₂₉	semidirect
164. #1451	C₂×C₂₉	semidirect
194. #436	C₂²×C₂₉	semidirect
196. C₈×D₄	C₂²×C₂₉	semidirect
204. #334	C₂²×C₂₉	semidirect
205. #334	C₂²×C₂₉	semidirect
206. D₄⋊C₈	C₂²×C₂₉	semidirect
207. D₄⋊C₈	C₂²×C₂₉	semidirect
208. #322	C₂²×C₂₉	semidirect
209. #322	C₂²×C₂₉	semidirect
258. C₂₉	#18044	direct (N × H)
277. D₈	M₁₆×C₂₉	semidirect
312. D₄	C₂×M₁₆×C₂₉	semidirect
338. C₈	C₂×M₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₂₉	2
D₄×M₁₆×C₂₉	2
C₂₉×#1594	2
C₂₉×#1586	2
C₂₉×#1580	2
C₂₉×#1566	2
C₂₉×#1486	2
C₂₉×#1451	2
#18044	29

Subgroups — C29×#18044 #20312944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18044 #20312944