Subgroups — C₂₉×#3265 #16816979

Order 3712.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₂₉	—	2	1	no	—
19	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×AGL(1,ℤ/8)	—	2	4	no	—
22	C₂×SD₁₆×C₂₉	—	2	4	no	—
23	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₈×C₂₉	C₂²	1	1	yes	characteristic
30	C₂×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
34	C₂₉×#127	C₂²	1	1	yes	characteristic
35	C₂₉×#124	—	2	1	no	—
36	C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×C₂²⋊Q₈	—	2	1	no	—
38	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#121	—	2	1	no	—
40	C₂₉×#121	—	2	1	no	—
41	C₂₉×#121	C₂²	1	1	yes	characteristic
42	C₂₉×#121	C₂²	1	1	yes	characteristic
43	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#120	—	2	1	no	—
45	C₂₉×#120	—	2	1	no	—
46	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄×C₂₉	—	2	1	no	—
48	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
53	C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
54	C₂₉×#102	C₂²	1	1	yes	characteristic
55	C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
56	C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
57	C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₂₉	—	2	1	no	—
62	C₂⁴×C₂₉	—	2	1	no	—
63	#41×C₂₉	—	2	2	no	—
64	#41×C₂₉	—	4	1	no	—
65	C₂×Q₈×C₂₉	—	2	1	no	—
66	C₂×Q₈×C₂₉	—	2	2	no	—
67	C₂×Q₈×C₂₉	—	4	1	no	—
68	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂×D₄×C₂₉	—	2	2	no	—
71	C₂×D₄×C₂₉	—	2	2	no	—
72	C₂×D₄×C₂₉	—	2	1	no	—
73	C₂×D₄×C₂₉	—	2	1	no	—
74	C₂×D₄×C₂₉	—	2	1	no	—
75	C₂×D₄×C₂₉	—	2	1	no	—
76	C₂×D₄×C₂₉	—	2	1	no	—
77	C₂×D₄×C₂₉	—	2	1	no	—
78	C₂×D₄×C₂₉	—	2	1	no	—
79	C₂×D₄×C₂₉	—	2	1	no	—
80	C₂×D₄×C₂₉	—	4	1	no	—
81	C₂×D₄×C₂₉	—	4	1	no	—
82	C₂×D₄×C₂₉	—	4	4	no	—
83	C₂×D₄×C₂₉	D₄	1	1	yes	characteristic
84	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	—	2	1	no	—
89	C₂²×C₄×C₂₉	—	2	1	no	—
90	C₂²×C₄×C₂₉	—	2	1	no	—
91	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
93	SD₁₆×C₂₉	—	2	2	no	—
94	SD₁₆×C₂₉	—	2	2	no	—
95	SD₁₆×C₂₉	—	2	2	no	—
96	SD₁₆×C₂₉	—	2	2	no	—
97	SD₁₆×C₂₉	—	4	1	no	—
98	SD₁₆×C₂₉	D₄	1	4	yes	complemented
99	D₈×C₂₉	—	2	2	no	—
100	D₈×C₂₉	—	2	2	no	—
101	D₈×C₂₉	—	4	1	no	—
102	M₁₆×C₂₉	—	2	2	no	—
103	C₂×C₈×C₂₉	—	2	2	no	—
104	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₂₉	—	2	1	no	—
109	C₄⋊C₄×C₂₉	—	2	1	no	—
110	C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
111	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
113	C₂²⋊C₄×C₂₉	—	2	1	no	—
114	C₂²⋊C₄×C₂₉	—	2	1	no	—
115	C₂²⋊C₄×C₂₉	—	2	1	no	—
116	C₂²⋊C₄×C₂₉	—	2	1	no	—
117	C₂²⋊C₄×C₂₉	—	2	1	no	—
118	C₂²⋊C₄×C₂₉	—	2	1	no	—
119	C₂²⋊C₄×C₂₉	—	2	1	no	—
120	C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
121	C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
122	C₄²×C₂₉	—	2	1	no	—
123	C₄²×C₂₉	C₂³	1	1	yes	characteristic
124	C₂³×C₂₉	—	2	1	no	—
125	C₂³×C₂₉	—	2	1	no	—
126	C₂³×C₂₉	—	2	1	no	—
127	C₂³×C₂₉	—	2	1	no	—
128	C₂³×C₂₉	—	4	2	no	—
129	C₂³×C₂₉	—	4	2	no	—
130	C₂³×C₂₉	—	4	2	no	—
131	C₂³×C₂₉	—	4	2	no	—
132	C₂³×C₂₉	—	8	1	no	—
133	C₂³×C₂₉	—	8	1	no	—
134	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₂₉	—	2	1	no	—
137	Q₈×C₂₉	—	2	1	no	—
138	Q₈×C₂₉	—	2	1	no	—
139	Q₈×C₂₉	—	4	2	no	—
140	Q₈×C₂₉	C₂×D₄	1	2	yes	complemented
141	D₄×C₂₉	—	2	2	no	—
142	D₄×C₂₉	—	2	1	no	—
143	D₄×C₂₉	—	2	1	no	—
144	D₄×C₂₉	—	2	1	no	—
145	D₄×C₂₉	—	2	1	no	—
146	D₄×C₂₉	—	2	1	no	—
147	D₄×C₂₉	—	2	1	no	—
148	D₄×C₂₉	—	2	1	no	—
149	D₄×C₂₉	—	4	2	no	—
150	D₄×C₂₉	—	4	2	no	—
151	D₄×C₂₉	—	4	2	no	—
152	D₄×C₂₉	—	4	2	no	—
153	D₄×C₂₉	—	4	2	no	—
154	D₄×C₂₉	—	4	2	no	—
155	D₄×C₂₉	—	4	2	no	—
156	D₄×C₂₉	—	8	1	no	—
157	D₄×C₂₉	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₂₉	—	2	1	no	—
159	C₂×C₄×C₂₉	—	2	1	no	—
160	C₂×C₄×C₂₉	—	2	1	no	—
161	C₂×C₄×C₂₉	—	2	1	no	—
162	C₂×C₄×C₂₉	—	2	1	no	—
163	C₂×C₄×C₂₉	—	2	1	no	—
164	C₂×C₄×C₂₉	—	2	1	no	—
165	C₂×C₄×C₂₉	—	2	1	no	—
166	C₂×C₄×C₂₉	—	4	2	no	—
167	C₂×C₄×C₂₉	—	4	2	no	—
168	C₂×C₄×C₂₉	—	4	2	no	—
169	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
174	C₈×C₂₉	—	2	1	no	—
175	C₈×C₂₉	—	2	1	no	—
176	C₈×C₂₉	—	2	1	no	—
177	C₈×C₂₉	C₂×D₄	1	2	yes	complemented
178	#3265	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₂₉	—	2	1	no	—
180	C₂²×C₂₉	—	2	1	no	—
181	C₂²×C₂₉	—	2	1	no	—
182	C₂²×C₂₉	—	2	2	no	—
183	C₂²×C₂₉	—	2	1	no	—
184	C₂²×C₂₉	—	2	1	no	—
185	C₂²×C₂₉	—	4	1	no	—
186	C₂²×C₂₉	—	4	1	no	—
187	C₂²×C₂₉	—	4	1	no	—
188	C₂²×C₂₉	—	4	1	no	—
189	C₂²×C₂₉	—	4	1	no	—
190	C₂²×C₂₉	—	4	1	no	—
191	C₂²×C₂₉	—	4	1	no	—
192	C₂²×C₂₉	—	4	1	no	—
193	C₂²×C₂₉	—	4	1	no	—
194	C₂²×C₂₉	—	4	1	no	—
195	C₂²×C₂₉	—	4	1	no	—
196	C₂²×C₂₉	—	8	4	no	—
197	C₂²×C₂₉	—	8	4	no	—
198	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
200	C₄×C₂₉	—	2	1	no	—
201	C₄×C₂₉	—	2	1	no	—
202	C₄×C₂₉	—	2	2	no	—
203	C₄×C₂₉	—	2	1	no	—
204	C₄×C₂₉	—	2	1	no	—
205	C₄×C₂₉	—	4	1	no	—
206	C₄×C₂₉	—	4	1	no	—
207	C₄×C₂₉	—	4	1	no	—
208	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×AGL(1,ℤ/8)	C₂×C₂₉	1	1	yes	characteristic, complemented
211	C₂²×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
212	#548	C₂×C₂₉	1	1	yes	characteristic, complemented
213	D₄²	C₂×C₂₉	1	1	yes	characteristic, complemented
214	#496	C₂×C₂₉	1	1	yes	characteristic, complemented
215	#468	C₂×C₂₉	1	1	yes	characteristic, complemented
216	#466	C₂×C₂₉	1	1	yes	characteristic, complemented
217	#463	C₂×C₂₉	1	1	yes	characteristic, complemented
218	#460	C₂×C₂₉	1	1	yes	characteristic, complemented
219	#450	C₂×C₂₉	1	1	yes	characteristic, complemented
220	#449	C₂×C₂₉	1	1	yes	characteristic, complemented
221	#448	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#447	C₂×C₂₉	1	1	yes	characteristic, complemented
223	#440	C₂×C₂₉	1	1	yes	characteristic, complemented
224	#435	C₂×C₂₉	1	1	yes	characteristic, complemented
225	C₂×C₂₉	—	2	2	no	—
226	C₂×C₂₉	—	4	1	no	—
227	C₂×C₂₉	—	4	2	no	—
228	C₂×C₂₉	—	8	1	no	—
229	C₂×C₂₉	—	8	1	no	—
230	C₂×C₂₉	—	8	1	no	—
231	C₂×C₂₉	D₄²	1	1	yes	characteristic
232	C₂×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₂₉	#577	1	1	yes	characteristic
234	C₂×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
235	C₂²×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
238	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
239	AGL(1,ℤ/8)	—	2	4	no	—
240	C₂×SD₁₆	—	2	4	no	—
241	C₂×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
242	C₂×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
243	C₂×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
244	C₂×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
245	C₂×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
246	C₂×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
247	C₂×D₈	C₂²×C₂₉	1	1	yes	characteristic
248	C₂×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
249	C₂×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
250	C₂×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
251	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
252	#127	C₂²×C₂₉	1	1	yes	characteristic
253	#124	—	2	1	no	—
254	#124	C₂²×C₂₉	1	1	yes	characteristic, complemented
255	C₂²⋊Q₈	—	2	1	no	—
256	C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	C₂²×C₂₉	1	1	yes	characteristic
260	#121	C₂²×C₂₉	1	1	yes	characteristic
261	#121	C₂²×C₂₉	1	1	yes	characteristic, complemented
262	#120	—	2	1	no	—
263	#120	—	2	1	no	—
264	C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
267	C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
268	#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
269	C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
270	#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
271	#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
272	#102	C₂²×C₂₉	1	1	yes	characteristic
273	#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
274	#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
275	#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
276	C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
278	#97	C₂²×C₂₉	1	1	yes	characteristic, complemented
279	C₂₉	#3265	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	2	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₂³×C₂₉	1	1	yes	characteristic
288	C₂×Q₈	C₂³×C₂₉	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	D₄×C₂₉	1	1	yes	characteristic
303	C₂×D₄	C₂³×C₂₉	1	1	yes	characteristic
304	C₂×D₄	C₂³×C₂₉	1	1	yes	characteristic
305	C₂×D₄	C₂³×C₂₉	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₂₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	2	2	no	—
315	SD₁₆	—	2	2	no	—
316	SD₁₆	—	4	1	no	—
317	SD₁₆	D₄×C₂₉	1	4	yes	complemented
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	4	1	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
324	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
325	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
326	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
330	C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
340	C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
341	C₄²	—	2	1	no	—
342	C₄²	C₂³×C₂₉	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
354	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	C₂×D₄×C₂₉	1	2	yes	complemented
360	D₄	—	2	2	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	1	no	—
376	D₄	C₂×D₄×C₂₉	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
392	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	C₂×D₄×C₂₉	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	8	4	no	—
415	C₂²	—	8	4	no	—
416	C₂²	C₂₉×AGL(1,ℤ/8)	1	2	yes	complemented
417	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
427	C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	1	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	1	no	—
432	C₂	—	8	1	no	—
433	C₂	—	8	1	no	—
434	C₂	D₄²×C₂₉	1	1	yes	characteristic
435	C₂	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
436	C₂	C₂₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×SD₁₆×C₂₉	C₂	semidirect
3. C₂₉×#548	C₂	semidirect
4. D₄²×C₂₉	C₂	semidirect
5. C₂₉×#496	C₂	semidirect
6. C₂₉×#468	C₂	semidirect
7. C₂₉×#466	C₂	semidirect
8. C₂₉×#463	C₂	semidirect
9. C₂₉×#460	C₂	semidirect
10. C₂₉×#450	C₂	semidirect
11. C₂₉×#449	C₂	semidirect
12. C₂₉×#448	C₂	semidirect
13. C₂₉×#447	C₂	semidirect
14. C₂₉×#440	C₂	semidirect
15. C₂₉×#435	C₂	semidirect
16. C₂×#41×C₂₉	C₂²	semidirect
17. C₂²×Q₈×C₂₉	C₂²	semidirect
25. C₂×SD₁₆×C₂₉	C₂²	semidirect
26. C₂×SD₁₆×C₂₉	C₂²	semidirect
27. C₂×SD₁₆×C₂₉	C₂²	semidirect
28. C₂×SD₁₆×C₂₉	C₂²	semidirect
30. C₂×D₈×C₂₉	C₂²	semidirect
31. C₂×D₈×C₂₉	C₂²	semidirect
32. C₂×M₁₆×C₂₉	C₂²	semidirect
33. C₂²×C₈×C₂₉	C₂²	semidirect
36. C₂₉×#124	C₂²	semidirect
38. C₂₉×C₂²⋊Q₈	C₂²	semidirect
43. C₂₉×#121	C₂²	semidirect
46. C₄×Q₈×C₂₉	C₂²	semidirect
50. C₂₉×#107	C₂²	semidirect
51. C₂₉×C₄⋊C₈	C₂²	semidirect
52. C₂₉×#103	C₂²	semidirect
53. C₂₉×#103	C₂²	semidirect
55. C₂₉×#102	C₂²	semidirect
56. C₂₉×#102	C₂²	semidirect
57. C₂₉×#102	C₂²	semidirect
58. C₂₉×C₂²⋊C₈	C₂²	semidirect
59. C₂₉×C₂²⋊C₈	C₂²	semidirect
60. C₂₉×#97	C₂²	semidirect
98. SD₁₆×C₂₉	D₄	semidirect
140. Q₈×C₂₉	C₂×D₄	semidirect
177. C₈×C₂₉	C₂×D₄	semidirect
178. #3265	C₂₉	direct (N × H)
198. C₂²×C₂₉	AGL(1,ℤ/8)	semidirect
210. C₂×AGL(1,ℤ/8)	C₂×C₂₉	semidirect
211. C₂²×SD₁₆	C₂×C₂₉	semidirect
212. #548	C₂×C₂₉	semidirect
213. D₄²	C₂×C₂₉	semidirect
214. #496	C₂×C₂₉	semidirect
215. #468	C₂×C₂₉	semidirect
216. #466	C₂×C₂₉	semidirect
217. #463	C₂×C₂₉	semidirect
218. #460	C₂×C₂₉	semidirect
219. #450	C₂×C₂₉	semidirect
220. #449	C₂×C₂₉	semidirect
221. #448	C₂×C₂₉	semidirect
222. #447	C₂×C₂₉	semidirect
223. #440	C₂×C₂₉	semidirect
224. #435	C₂×C₂₉	semidirect
234. C₂×#41	C₂²×C₂₉	semidirect
235. C₂²×Q₈	C₂²×C₂₉	semidirect
243. C₂×SD₁₆	C₂²×C₂₉	semidirect
244. C₂×SD₁₆	C₂²×C₂₉	semidirect
245. C₂×SD₁₆	C₂²×C₂₉	semidirect
246. C₂×SD₁₆	C₂²×C₂₉	semidirect
248. C₂×D₈	C₂²×C₂₉	semidirect
249. C₂×D₈	C₂²×C₂₉	semidirect
250. C₂×M₁₆	C₂²×C₂₉	semidirect
251. C₂²×C₈	C₂²×C₂₉	semidirect
254. #124	C₂²×C₂₉	semidirect
256. C₂²⋊Q₈	C₂²×C₂₉	semidirect
261. #121	C₂²×C₂₉	semidirect
264. C₄×Q₈	C₂²×C₂₉	semidirect
268. #107	C₂²×C₂₉	semidirect
269. C₄⋊C₈	C₂²×C₂₉	semidirect
270. #103	C₂²×C₂₉	semidirect
271. #103	C₂²×C₂₉	semidirect
273. #102	C₂²×C₂₉	semidirect
274. #102	C₂²×C₂₉	semidirect
275. #102	C₂²×C₂₉	semidirect
276. C₂²⋊C₈	C₂²×C₂₉	semidirect
277. C₂²⋊C₈	C₂²×C₂₉	semidirect
278. #97	C₂²×C₂₉	semidirect
279. C₂₉	#3265	direct (N × H)
317. SD₁₆	D₄×C₂₉	semidirect
359. Q₈	C₂×D₄×C₂₉	semidirect
396. C₈	C₂×D₄×C₂₉	semidirect
416. C₂²	C₂₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×AGL(1,ℤ/8)	2
C₂²×SD₁₆×C₂₉	2
C₂₉×#548	2
D₄²×C₂₉	2
C₂₉×#496	2
C₂₉×#468	2
C₂₉×#466	2
C₂₉×#463	2
C₂₉×#460	2
C₂₉×#450	2
C₂₉×#449	2
C₂₉×#448	2
C₂₉×#447	2
C₂₉×#440	2
C₂₉×#435	2
#3265	29

Subgroups — C29×#3265 #16816979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#3265 #16816979