Subgroups — C₂₉×#60457 #20355357

Order 7424.

2756 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3063	C₂	1	3	yes	maximal, complemented
6	C₂₉×#3062	C₂	1	3	yes	maximal, complemented
7	C₂₉×#3060	C₂	1	3	yes	maximal, complemented
8	C₂₉×#3057	C₂	1	3	yes	maximal, complemented
9	C₂₉×#3056	C₂	1	3	yes	maximal, complemented
10	C₂₉×#3055	C₂	1	3	yes	maximal, complemented
11	C₂₉×#3050	C₂	1	3	yes	maximal, complemented
12	C₂×C₂₉×#465	C₂	1	3	yes	maximal, complemented
13	C₂₉×#2912	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#577	—	2	8	no	—
20	C₂×C₂₉×#137	C₂²	1	3	yes	complemented
21	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
22	C₂×C₂₉×#135	C₂²	1	3	yes	complemented
23	C₂²×SD₁₆×C₂₉	C₂²	1	3	yes	complemented
24	C₂×C₂₉×#131	—	2	8	no	—
25	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#131	C₂²	1	3	yes	complemented
28	C₂×C₂₉×#131	C₂²	1	3	yes	complemented
29	C₂²×M₁₆×C₂₉	C₂²	1	3	yes	complemented
30	C₂³×C₈×C₂₉	C₂²	1	3	yes	complemented
31	C₂₉×#550	—	2	1	no	—
32	D₄×Q₈×C₂₉	—	2	1	no	—
33	C₂₉×#548	—	2	1	no	—
34	C₂₉×#548	—	2	1	no	—
35	C₂₉×#547	—	2	3	no	—
36	C₂₉×#546	—	2	3	no	—
37	C₂₉×#546	—	2	3	no	—
38	D₄²×C₂₉	—	2	3	no	—
39	C₂₉×#537	C₂²	1	3	yes	—
40	C₂₉×#537	C₂²	1	3	yes	complemented
41	C₂₉×#536	C₂²	1	3	yes	complemented
42	C₂₉×#535	C₂²	1	3	yes	—
43	C₂₉×#525	C₂²	1	3	yes	—
44	C₂₉×#525	C₂²	1	3	yes	complemented
45	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	3	yes	complemented
46	C₂×C₂₉×#121	C₂²	1	3	yes	—
47	C₂₉×#520	C₂²	1	1	yes	characteristic
48	C₂₉×#520	C₂²	1	1	yes	characteristic
49	C₂₉×#470	C₂²	1	6	yes	complemented
50	C₂₉×#469	C₂²	1	6	yes	complemented
51	C₂₉×#468	C₂²	1	6	yes	complemented
52	C₂₉×#468	C₂²	1	6	yes	complemented
53	C₂₉×#467	C₂²	1	3	yes	complemented
54	C₂₉×#467	C₂²	1	3	yes	complemented
55	C₂₉×#466	C₂²	1	3	yes	complemented
56	C₂₉×#466	C₂²	1	3	yes	complemented
57	C₂₉×#465	C₂²	1	3	yes	complemented
58	C₂₉×#465	C₂²	1	6	yes	complemented
59	C₂₉×#465	C₂²	1	6	yes	complemented
60	C₂₉×#465	C₂²	1	6	yes	complemented
61	C₂₉×#465	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#465	C₂²	1	3	yes	complemented
63	C₂₉×#465	C₂²	1	3	yes	complemented
64	C₂₉×#428	C₂²	1	3	yes	complemented
65	C₂₉×#428	C₂²	1	3	yes	complemented
66	C₂₉×#427	C₂²	1	3	yes	complemented
67	C₂×C₂₉×#106	C₂²	1	3	yes	complemented
68	C₂₉×#419	C₂²	1	3	yes	complemented
69	C₂₉×#418	C₂²	1	3	yes	complemented
70	C₂₉×#417	C₂²	1	3	yes	complemented
71	C₂₉×#417	C₂²	1	3	yes	complemented
72	C₂₉×#416	C₂²	1	3	yes	complemented
73	C₂₉×#416	C₂²	1	3	yes	complemented
74	C₂×C₂₉×#103	C₂²	1	3	yes	complemented
75	C₂×C₂₉×#102	C₂²	1	3	yes	complemented
76	C₂₉×2₋¹⁺⁴	—	2	4	no	—
77	C₂₉×2₋¹⁺⁴	—	2	4	no	—
78	C₂₉×H(5,𝔽₂)	—	2	4	no	—
79	C₂₉×H(5,𝔽₂)	—	2	4	no	—
80	C₂×#41×C₂₉	—	2	4	no	—
81	C₂×#41×C₂₉	—	2	4	no	—
82	C₂×#41×C₂₉	—	2	1	no	—
83	C₂×#41×C₂₉	—	2	3	no	—
84	C₂×#41×C₂₉	D₄	1	3	yes	—
85	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
86	C₂×#41×C₂₉	C₂³	1	3	yes	—
87	C₂×#41×C₂₉	C₂³	1	3	yes	—
88	C₂×#41×C₂₉	C₂³	1	3	yes	—
89	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₂₉	—	2	1	no	—
91	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₂₉	C₂³	1	3	yes	—
93	C₂²×D₄×C₂₉	—	2	3	no	—
94	C₂²×D₄×C₂₉	—	2	3	no	—
95	C₂²×D₄×C₂₉	D₄	1	3	yes	—
96	C₂²×D₄×C₂₉	C₂³	1	3	yes	—
97	C₂³×C₄×C₂₉	C₂³	1	3	yes	—
98	C₂₉×#137	—	2	12	no	—
99	C₂₉×AGL(1,ℤ/8)	—	2	12	no	—
100	C₂₉×#135	—	2	12	no	—
101	C₂×Q₁₆×C₂₉	C₂³	1	3	yes	—
102	C₂×SD₁₆×C₂₉	—	2	12	no	—
103	C₂×SD₁₆×C₂₉	C₂³	1	3	yes	—
104	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×SD₁₆×C₂₉	C₂³	1	6	yes	—
106	C₂×D₈×C₂₉	C₂³	1	3	yes	—
107	C₂₉×#131	—	2	4	no	—
108	C₂₉×#131	—	2	12	no	—
109	C₂₉×#131	—	2	12	no	—
110	C₂₉×#131	D₄	1	8	yes	complemented
111	C₂×M₁₆×C₂₉	—	2	12	no	—
112	C₂×M₁₆×C₂₉	C₂³	1	6	yes	—
113	C₂×M₁₆×C₂₉	C₂³	1	3	yes	—
114	C₂×M₁₆×C₂₉	C₂³	1	3	yes	—
115	C₂²×C₈×C₂₉	—	2	12	no	—
116	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
118	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
119	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
120	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
121	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
122	C₂₉×C₄⋊Q₈	—	2	3	no	—
123	C₂₉×#127	—	2	3	no	—
124	C₂₉×#124	—	2	3	no	—
125	C₂₉×#124	—	2	3	no	—
126	C₂₉×#123	—	2	6	no	—
127	C₂₉×#123	—	2	3	no	—
128	C₂₉×#123	—	2	3	no	—
129	C₂₉×C₂²⋊Q₈	—	2	3	no	—
130	C₂₉×C₂²⋊Q₈	—	2	3	no	—
131	C₂₉×C₂²⋊Q₈	—	2	3	no	—
132	C₂₉×C₂²⋊Q₈	—	2	3	no	—
133	C₂₉×C₂²⋊Q₈	C₂³	1	3	yes	—
134	C₂₉×C₂²⋊Q₈	C₂³	1	6	yes	—
135	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₂₉×C₂²⋊Q₈	C₂³	1	3	yes	—
137	C₂₉×C₂²⋊Q₈	C₂³	1	3	yes	—
138	C₂₉×#121	—	2	6	no	—
139	C₂₉×#121	—	2	3	no	—
140	C₂₉×#121	—	2	6	no	—
141	C₂₉×#121	—	2	3	no	—
142	C₂₉×#121	—	2	3	no	—
143	C₂₉×#121	—	2	3	no	—
144	C₂₉×#121	C₂³	1	3	yes	—
145	C₂₉×#121	C₂³	1	6	yes	—
146	C₂₉×#121	C₂³	1	1	yes	characteristic
147	C₂₉×#121	C₂³	1	3	yes	—
148	C₂₉×#121	C₂³	1	3	yes	—
149	C₂₉×#120	—	2	3	no	—
150	C₂₉×#120	—	2	3	no	—
151	C₂₉×#120	—	2	6	no	—
152	C₄×Q₈×C₂₉	—	2	1	no	—
153	C₄×Q₈×C₂₉	—	2	1	no	—
154	C₄×D₄×C₂₉	—	2	3	no	—
155	C₄×D₄×C₂₉	—	2	3	no	—
156	C₄×D₄×C₂₉	—	2	3	no	—
157	C₄×D₄×C₂₉	—	2	3	no	—
158	C₄×D₄×C₂₉	—	2	3	no	—
159	C₄×D₄×C₂₉	—	2	3	no	—
160	C₂₉×#117	C₂³	1	3	yes	—
161	C₂₉×#117	C₂³	1	3	yes	—
162	C₂×C₄⋊C₄×C₂₉	—	2	3	no	—
163	C₂×C₄⋊C₄×C₂₉	C₂³	1	3	yes	—
164	C₂×C₄⋊C₄×C₂₉	C₂³	1	3	yes	—
165	C₂×C₂²⋊C₄×C₂₉	—	2	3	no	—
166	C₂×C₂²⋊C₄×C₂₉	—	2	3	no	—
167	C₂₉×#107	C₂³	1	3	yes	—
168	C₂₉×#107	C₂³	1	3	yes	—
169	C₂₉×#106	C₂³	1	3	yes	—
170	C₂₉×#106	C₂³	1	6	yes	—
171	C₂₉×#106	C₂³	1	1	yes	characteristic
172	C₂₉×#103	C₂³	1	3	yes	—
173	C₂₉×#103	C₂³	1	6	yes	—
174	C₂₉×#103	C₂³	1	1	yes	characteristic
175	C₂₉×#103	C₂³	1	3	yes	—
176	C₂₉×#103	C₂³	1	3	yes	—
177	C₂₉×#102	C₂³	1	3	yes	—
178	C₂₉×#102	C₂³	1	6	yes	—
179	C₂₉×#102	C₂³	1	1	yes	characteristic
180	C₂₉×#102	C₂³	1	3	yes	—
181	C₂₉×#102	C₂³	1	3	yes	—
182	C₂⁴×C₂₉	—	2	3	no	—
183	C₂⁴×C₂₉	C₂×D₄	1	3	yes	—
184	#41×C₂₉	—	2	4	no	—
185	#41×C₂₉	—	2	12	no	—
186	#41×C₂₉	—	2	6	no	—
187	#41×C₂₉	—	2	6	no	—
188	#41×C₂₉	—	2	6	no	—
189	#41×C₂₉	—	2	6	no	—
190	#41×C₂₉	—	2	6	no	—
191	#41×C₂₉	—	2	6	no	—
192	#41×C₂₉	—	4	4	no	—
193	#41×C₂₉	—	4	12	no	—
194	#41×C₂₉	C₂×D₄	1	4	yes	—
195	#41×C₂₉	#41	1	4	yes	—
196	C₂×Q₈×C₂₉	—	2	4	no	—
197	C₂×Q₈×C₂₉	—	2	3	no	—
198	C₂×Q₈×C₂₉	—	2	6	no	—
199	C₂×Q₈×C₂₉	—	2	6	no	—
200	C₂×Q₈×C₂₉	—	4	4	no	—
201	C₂×Q₈×C₂₉	C₂×D₄	1	3	yes	—
202	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₂₉	C₂⁴	1	3	yes	—
204	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
205	C₂×D₄×C₂₉	—	2	12	no	—
206	C₂×D₄×C₂₉	—	2	1	no	—
207	C₂×D₄×C₂₉	—	2	3	no	—
208	C₂×D₄×C₂₉	—	2	3	no	—
209	C₂×D₄×C₂₉	—	2	3	no	—
210	C₂×D₄×C₂₉	—	2	3	no	—
211	C₂×D₄×C₂₉	—	2	3	no	—
212	C₂×D₄×C₂₉	—	2	6	no	—
213	C₂×D₄×C₂₉	—	2	6	no	—
214	C₂×D₄×C₂₉	—	2	3	no	—
215	C₂×D₄×C₂₉	—	2	6	no	—
216	C₂×D₄×C₂₉	—	4	12	no	—
217	C₂×D₄×C₂₉	—	8	6	no	—
218	C₂×D₄×C₂₉	C₂×D₄	1	6	yes	—
219	C₂×D₄×C₂₉	C₂×D₄	1	3	yes	—
220	C₂×D₄×C₂₉	C₂×D₄	1	3	yes	—
221	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
222	C₂×D₄×C₂₉	C₂⁴	1	3	yes	—
223	C₂²×C₄×C₂₉	—	2	6	no	—
224	C₂²×C₄×C₂₉	—	2	6	no	—
225	C₂²×C₄×C₂₉	—	2	3	no	—
226	C₂²×C₄×C₂₉	—	2	3	no	—
227	C₂²×C₄×C₂₉	—	2	3	no	—
228	C₂²×C₄×C₂₉	—	2	3	no	—
229	C₂²×C₄×C₂₉	—	2	3	no	—
230	C₂²×C₄×C₂₉	C₂×D₄	1	3	yes	—
231	C₂²×C₄×C₂₉	C₂×D₄	1	3	yes	—
232	C₂²×C₄×C₂₉	C₂×D₄	1	3	yes	—
233	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₂₉	C₂⁴	1	3	yes	—
235	C₂²×C₄×C₂₉	C₂⁴	1	3	yes	—
236	Q₁₆×C₂₉	—	2	6	no	—
237	SD₁₆×C₂₉	—	2	6	no	—
238	SD₁₆×C₂₉	—	2	12	no	—
239	SD₁₆×C₂₉	—	2	2	no	—
240	D₈×C₂₉	—	2	6	no	—
241	M₁₆×C₂₉	—	2	6	no	—
242	M₁₆×C₂₉	—	2	12	no	—
243	M₁₆×C₂₉	C₂×D₄	1	12	yes	complemented
244	C₂×C₈×C₂₉	—	2	6	no	—
245	C₂×C₈×C₂₉	—	2	2	no	—
246	C₂×C₈×C₂₉	—	2	6	no	—
247	C₂×C₈×C₂₉	—	2	6	no	—
248	C₂×C₈×C₂₉	—	2	6	no	—
249	C₂×C₈×C₂₉	C₂×D₄	1	12	yes	complemented
250	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₂₉	C₂⁴	1	3	yes	—
252	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₂₉	C₂⁴	1	3	yes	—
254	C₄⋊C₄×C₂₉	—	2	3	no	—
255	C₄⋊C₄×C₂₉	—	2	6	no	—
256	C₄⋊C₄×C₂₉	—	2	3	no	—
257	C₄⋊C₄×C₂₉	—	2	3	no	—
258	C₄⋊C₄×C₂₉	—	2	1	no	—
259	C₄⋊C₄×C₂₉	—	2	3	no	—
260	C₄⋊C₄×C₂₉	—	2	3	no	—
261	C₄⋊C₄×C₂₉	C₂⁴	1	3	yes	—
262	C₄⋊C₄×C₂₉	C₂⁴	1	3	yes	—
263	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
265	C₂²⋊C₄×C₂₉	—	2	3	no	—
266	C₂²⋊C₄×C₂₉	—	2	6	no	—
267	C₂²⋊C₄×C₂₉	—	2	3	no	—
268	C₂²⋊C₄×C₂₉	—	2	3	no	—
269	C₂²⋊C₄×C₂₉	—	2	1	no	—
270	C₂²⋊C₄×C₂₉	—	2	3	no	—
271	C₂²⋊C₄×C₂₉	—	2	3	no	—
272	C₂²⋊C₄×C₂₉	—	2	3	no	—
273	C₂²⋊C₄×C₂₉	—	2	6	no	—
274	C₂²⋊C₄×C₂₉	—	2	1	no	—
275	C₂²⋊C₄×C₂₉	—	2	3	no	—
276	C₂²⋊C₄×C₂₉	—	2	3	no	—
277	C₄²×C₂₉	—	2	3	no	—
278	C₄²×C₂₉	—	2	3	no	—
279	#60457	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂³×C₂₉	—	2	6	no	—
281	C₂³×C₂₉	—	2	6	no	—
282	C₂³×C₂₉	—	2	1	no	—
283	C₂³×C₂₉	—	2	3	no	—
284	C₂³×C₂₉	—	4	3	no	—
285	C₂³×C₂₉	—	4	6	no	—
286	C₂³×C₂₉	—	8	3	no	—
287	C₂³×C₂₉	—	8	3	no	—
288	C₂³×C₂₉	C₂²×D₄	1	3	yes	—
289	C₂³×C₂₉	C₂²×D₄	1	3	yes	—
290	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
291	Q₈×C₂₉	—	2	6	no	—
292	Q₈×C₂₉	—	2	3	no	—
293	Q₈×C₂₉	—	2	1	no	—
294	Q₈×C₂₉	—	2	3	no	—
295	Q₈×C₂₉	—	2	1	no	—
296	Q₈×C₂₉	—	4	6	no	—
297	Q₈×C₂₉	#121	1	4	yes	—
298	D₄×C₂₉	—	2	12	no	—
299	D₄×C₂₉	—	2	6	no	—
300	D₄×C₂₉	—	2	1	no	—
301	D₄×C₂₉	—	2	3	no	—
302	D₄×C₂₉	—	2	3	no	—
303	D₄×C₂₉	—	2	1	no	—
304	D₄×C₂₉	—	4	6	no	—
305	D₄×C₂₉	—	4	6	no	—
306	D₄×C₂₉	—	4	2	no	—
307	D₄×C₂₉	—	4	6	no	—
308	D₄×C₂₉	—	4	6	no	—
309	D₄×C₂₉	—	8	3	no	—
310	D₄×C₂₉	—	8	3	no	—
311	D₄×C₂₉	—	8	6	no	—
312	D₄×C₂₉	#121	1	12	yes	—
313	C₂×C₄×C₂₉	—	2	6	no	—
314	C₂×C₄×C₂₉	—	2	6	no	—
315	C₂×C₄×C₂₉	—	2	6	no	—
316	C₂×C₄×C₂₉	—	2	1	no	—
317	C₂×C₄×C₂₉	—	2	3	no	—
318	C₂×C₄×C₂₉	—	2	1	no	—
319	C₂×C₄×C₂₉	—	2	3	no	—
320	C₂×C₄×C₂₉	—	2	1	no	—
321	C₂×C₄×C₂₉	—	2	1	no	—
322	C₂×C₄×C₂₉	—	2	3	no	—
323	C₂×C₄×C₂₉	—	2	3	no	—
324	C₂×C₄×C₂₉	—	2	1	no	—
325	C₂×C₄×C₂₉	—	2	3	no	—
326	C₂×C₄×C₂₉	—	4	6	no	—
327	C₂×C₄×C₂₉	—	4	6	no	—
328	C₂×C₄×C₂₉	—	4	6	no	—
329	C₂×C₄×C₂₉	—	8	3	no	—
330	C₂×C₄×C₂₉	—	8	3	no	—
331	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₉	C₂²×D₄	1	3	yes	—
333	C₂×C₄×C₂₉	C₂²×D₄	1	3	yes	—
334	C₂×C₄×C₂₉	C₂²×D₄	1	6	yes	—
335	C₂×C₄×C₂₉	C₂×#41	1	6	yes	—
336	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
337	C₈×C₂₉	—	2	1	no	—
338	C₈×C₂₉	—	2	3	no	—
339	C₈×C₂₉	C₂²×D₄	1	2	yes	—
340	C₈×C₂₉	C₂²×D₄	1	6	yes	—
341	C₂×#577	C₂×C₂₉	1	1	yes	characteristic, complemented
342	C₂²×#131	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#3489	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#3488	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#3063	C₂×C₂₉	1	3	yes	complemented
346	#3062	C₂×C₂₉	1	3	yes	complemented
347	#3060	C₂×C₂₉	1	3	yes	complemented
348	#3057	C₂×C₂₉	1	3	yes	complemented
349	#3056	C₂×C₂₉	1	3	yes	complemented
350	#3055	C₂×C₂₉	1	3	yes	complemented
351	#3050	C₂×C₂₉	1	3	yes	complemented
352	C₂×#465	C₂×C₂₉	1	3	yes	complemented
353	#2912	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#2898	C₂×C₂₉	1	1	yes	characteristic, complemented
355	#2897	C₂×C₂₉	1	1	yes	characteristic, complemented
356	C₂²×C₂₉	—	2	3	no	—
357	C₂²×C₂₉	—	2	1	no	—
358	C₂²×C₂₉	—	2	1	no	—
359	C₂²×C₂₉	—	2	3	no	—
360	C₂²×C₂₉	—	2	3	no	—
361	C₂²×C₂₉	—	2	3	no	—
362	C₂²×C₂₉	—	2	3	no	—
363	C₂²×C₂₉	—	4	12	no	—
364	C₂²×C₂₉	—	4	1	no	—
365	C₂²×C₂₉	—	4	3	no	—
366	C₂²×C₂₉	—	4	1	no	—
367	C₂²×C₂₉	—	4	3	no	—
368	C₂²×C₂₉	—	4	3	no	—
369	C₂²×C₂₉	—	4	1	no	—
370	C₂²×C₂₉	—	16	6	no	—
371	C₂²×C₂₉	C₂×#121	1	6	yes	—
372	C₂²×C₂₉	#577	1	2	yes	complemented
373	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₂₉	—	2	1	no	—
375	C₄×C₂₉	—	2	3	no	—
376	C₄×C₂₉	—	4	3	no	—
377	C₄×C₂₉	—	4	1	no	—
378	C₄×C₂₉	—	4	1	no	—
379	C₄×C₂₉	—	4	3	no	—
380	C₄×C₂₉	—	4	3	no	—
381	C₄×C₂₉	—	4	1	no	—
382	C₄×C₂₉	C₂×#121	1	6	yes	—
383	C₄×C₂₉	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
385	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic
387	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
388	#577	—	2	8	no	—
389	C₂×#137	C₂²×C₂₉	1	3	yes	complemented
390	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	3	yes	complemented
391	C₂×#135	C₂²×C₂₉	1	3	yes	complemented
392	C₂²×SD₁₆	C₂²×C₂₉	1	3	yes	complemented
393	C₂×#131	—	2	8	no	—
394	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
395	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×#131	C₂²×C₂₉	1	3	yes	complemented
397	C₂×#131	C₂²×C₂₉	1	3	yes	complemented
398	C₂²×M₁₆	C₂²×C₂₉	1	3	yes	complemented
399	C₂³×C₈	C₂²×C₂₉	1	3	yes	complemented
400	#550	—	2	1	no	—
401	D₄×Q₈	—	2	1	no	—
402	#548	—	2	1	no	—
403	#548	—	2	1	no	—
404	#547	—	2	3	no	—
405	#546	—	2	3	no	—
406	#546	—	2	3	no	—
407	D₄²	—	2	3	no	—
408	#537	C₂²×C₂₉	1	3	yes	—
409	#537	C₂²×C₂₉	1	3	yes	complemented
410	#536	C₂²×C₂₉	1	3	yes	complemented
411	#535	C₂²×C₂₉	1	3	yes	—
412	#525	C₂²×C₂₉	1	3	yes	—
413	#525	C₂²×C₂₉	1	3	yes	complemented
414	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	3	yes	complemented
415	C₂×#121	C₂²×C₂₉	1	3	yes	—
416	#520	C₂²×C₂₉	1	1	yes	characteristic
417	#520	C₂²×C₂₉	1	1	yes	characteristic
418	#470	C₂²×C₂₉	1	6	yes	complemented
419	#469	C₂²×C₂₉	1	6	yes	complemented
420	#468	C₂²×C₂₉	1	6	yes	complemented
421	#468	C₂²×C₂₉	1	6	yes	complemented
422	#467	C₂²×C₂₉	1	3	yes	complemented
423	#467	C₂²×C₂₉	1	3	yes	complemented
424	#466	C₂²×C₂₉	1	3	yes	complemented
425	#466	C₂²×C₂₉	1	3	yes	complemented
426	#465	C₂²×C₂₉	1	3	yes	complemented
427	#465	C₂²×C₂₉	1	6	yes	complemented
428	#465	C₂²×C₂₉	1	6	yes	complemented
429	#465	C₂²×C₂₉	1	6	yes	complemented
430	#465	C₂²×C₂₉	1	1	yes	characteristic, complemented
431	#465	C₂²×C₂₉	1	3	yes	complemented
432	#465	C₂²×C₂₉	1	3	yes	complemented
433	#428	C₂²×C₂₉	1	3	yes	complemented
434	#428	C₂²×C₂₉	1	3	yes	complemented
435	#427	C₂²×C₂₉	1	3	yes	complemented
436	C₂×#106	C₂²×C₂₉	1	3	yes	complemented
437	#419	C₂²×C₂₉	1	3	yes	complemented
438	#418	C₂²×C₂₉	1	3	yes	complemented
439	#417	C₂²×C₂₉	1	3	yes	complemented
440	#417	C₂²×C₂₉	1	3	yes	complemented
441	#416	C₂²×C₂₉	1	3	yes	complemented
442	#416	C₂²×C₂₉	1	3	yes	complemented
443	C₂×#103	C₂²×C₂₉	1	3	yes	complemented
444	C₂×#102	C₂²×C₂₉	1	3	yes	complemented
445	C₂×C₂₉	—	2	2	no	—
446	C₂×C₂₉	—	2	6	no	—
447	C₂×C₂₉	—	4	3	no	—
448	C₂×C₂₉	—	8	1	no	—
449	C₂×C₂₉	—	8	3	no	—
450	C₂×C₂₉	C₂²×#121	1	1	yes	characteristic
451	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
452	C₂×C₂₉	#3584	1	1	yes	characteristic
453	2₋¹⁺⁴	—	2	4	no	—
454	2₋¹⁺⁴	—	2	4	no	—
455	H(5,𝔽₂)	—	2	4	no	—
456	H(5,𝔽₂)	—	2	4	no	—
457	C₂×#41	—	2	4	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	3	no	—
461	C₂×#41	D₄×C₂₉	1	3	yes	—
462	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
463	C₂×#41	C₂³×C₂₉	1	3	yes	—
464	C₂×#41	C₂³×C₂₉	1	3	yes	—
465	C₂×#41	C₂³×C₂₉	1	3	yes	—
466	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
467	C₂²×Q₈	—	2	1	no	—
468	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₂₉	1	3	yes	—
470	C₂²×D₄	—	2	3	no	—
471	C₂²×D₄	—	2	3	no	—
472	C₂²×D₄	D₄×C₂₉	1	3	yes	—
473	C₂²×D₄	C₂³×C₂₉	1	3	yes	—
474	C₂³×C₄	C₂³×C₂₉	1	3	yes	—
475	#137	—	2	12	no	—
476	AGL(1,ℤ/8)	—	2	12	no	—
477	#135	—	2	12	no	—
478	C₂×Q₁₆	C₂³×C₂₉	1	3	yes	—
479	C₂×SD₁₆	—	2	12	no	—
480	C₂×SD₁₆	C₂³×C₂₉	1	3	yes	—
481	C₂×SD₁₆	C₂³×C₂₉	1	6	yes	—
482	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
483	C₂×D₈	C₂³×C₂₉	1	3	yes	—
484	#131	—	2	4	no	—
485	#131	—	2	12	no	—
486	#131	—	2	12	no	—
487	#131	D₄×C₂₉	1	8	yes	complemented
488	C₂×M₁₆	—	2	12	no	—
489	C₂×M₁₆	C₂³×C₂₉	1	3	yes	—
490	C₂×M₁₆	C₂³×C₂₉	1	6	yes	—
491	C₂×M₁₆	C₂³×C₂₉	1	3	yes	—
492	C₂²×C₈	—	2	12	no	—
493	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
495	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
496	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
497	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
498	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
499	C₄⋊Q₈	—	2	3	no	—
500	#127	—	2	3	no	—
501	#124	—	2	3	no	—
502	#124	—	2	3	no	—
503	#123	—	2	6	no	—
504	#123	—	2	3	no	—
505	#123	—	2	3	no	—
506	C₂²⋊Q₈	—	2	3	no	—
507	C₂²⋊Q₈	—	2	3	no	—
508	C₂²⋊Q₈	—	2	3	no	—
509	C₂²⋊Q₈	—	2	3	no	—
510	C₂²⋊Q₈	C₂³×C₂₉	1	3	yes	—
511	C₂²⋊Q₈	C₂³×C₂₉	1	6	yes	—
512	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
513	C₂²⋊Q₈	C₂³×C₂₉	1	3	yes	—
514	C₂²⋊Q₈	C₂³×C₂₉	1	3	yes	—
515	#121	—	2	6	no	—
516	#121	—	2	3	no	—
517	#121	—	2	6	no	—
518	#121	—	2	3	no	—
519	#121	—	2	3	no	—
520	#121	—	2	3	no	—
521	#121	C₂³×C₂₉	1	3	yes	—
522	#121	C₂³×C₂₉	1	6	yes	—
523	#121	C₂³×C₂₉	1	3	yes	—
524	#121	C₂³×C₂₉	1	1	yes	characteristic
525	#121	C₂³×C₂₉	1	3	yes	—
526	#120	—	2	3	no	—
527	#120	—	2	3	no	—
528	#120	—	2	6	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×D₄	—	2	3	no	—
532	C₄×D₄	—	2	3	no	—
533	C₄×D₄	—	2	3	no	—
534	C₄×D₄	—	2	3	no	—
535	C₄×D₄	—	2	3	no	—
536	C₄×D₄	—	2	3	no	—
537	#117	C₂³×C₂₉	1	3	yes	—
538	#117	C₂³×C₂₉	1	3	yes	—
539	C₂×C₄⋊C₄	—	2	3	no	—
540	C₂×C₄⋊C₄	C₂³×C₂₉	1	3	yes	—
541	C₂×C₄⋊C₄	C₂³×C₂₉	1	3	yes	—
542	C₂×C₂²⋊C₄	—	2	3	no	—
543	C₂×C₂²⋊C₄	—	2	3	no	—
544	#107	C₂³×C₂₉	1	3	yes	—
545	#107	C₂³×C₂₉	1	3	yes	—
546	#106	C₂³×C₂₉	1	3	yes	—
547	#106	C₂³×C₂₉	1	6	yes	—
548	#106	C₂³×C₂₉	1	1	yes	characteristic
549	#103	C₂³×C₂₉	1	3	yes	—
550	#103	C₂³×C₂₉	1	6	yes	—
551	#103	C₂³×C₂₉	1	1	yes	characteristic
552	#103	C₂³×C₂₉	1	3	yes	—
553	#103	C₂³×C₂₉	1	3	yes	—
554	#102	C₂³×C₂₉	1	3	yes	—
555	#102	C₂³×C₂₉	1	6	yes	—
556	#102	C₂³×C₂₉	1	1	yes	characteristic
557	#102	C₂³×C₂₉	1	3	yes	—
558	#102	C₂³×C₂₉	1	3	yes	—
559	C₂₉	#60457	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	—	2	3	no	—
561	C₂⁴	C₂×D₄×C₂₉	1	3	yes	—
562	#41	—	2	4	no	—
563	#41	—	2	12	no	—
564	#41	—	2	6	no	—
565	#41	—	2	6	no	—
566	#41	—	2	6	no	—
567	#41	—	2	6	no	—
568	#41	—	2	6	no	—
569	#41	—	2	6	no	—
570	#41	—	4	4	no	—
571	#41	—	4	12	no	—
572	#41	C₂×D₄×C₂₉	1	4	yes	—
573	#41	#41×C₂₉	1	4	yes	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	3	no	—
576	C₂×Q₈	—	2	6	no	—
577	C₂×Q₈	—	2	6	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	C₂×D₄×C₂₉	1	3	yes	—
580	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
581	C₂×Q₈	C₂⁴×C₂₉	1	3	yes	—
582	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
583	C₂×D₄	—	2	12	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	3	no	—
586	C₂×D₄	—	2	3	no	—
587	C₂×D₄	—	2	3	no	—
588	C₂×D₄	—	2	3	no	—
589	C₂×D₄	—	2	3	no	—
590	C₂×D₄	—	2	6	no	—
591	C₂×D₄	—	2	6	no	—
592	C₂×D₄	—	2	3	no	—
593	C₂×D₄	—	2	6	no	—
594	C₂×D₄	—	4	12	no	—
595	C₂×D₄	—	8	6	no	—
596	C₂×D₄	C₂×D₄×C₂₉	1	6	yes	—
597	C₂×D₄	C₂×D₄×C₂₉	1	3	yes	—
598	C₂×D₄	C₂×D₄×C₂₉	1	3	yes	—
599	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
600	C₂×D₄	C₂⁴×C₂₉	1	3	yes	—
601	C₂²×C₄	—	2	6	no	—
602	C₂²×C₄	—	2	6	no	—
603	C₂²×C₄	—	2	3	no	—
604	C₂²×C₄	—	2	3	no	—
605	C₂²×C₄	—	2	3	no	—
606	C₂²×C₄	—	2	3	no	—
607	C₂²×C₄	—	2	3	no	—
608	C₂²×C₄	C₂×D₄×C₂₉	1	3	yes	—
609	C₂²×C₄	C₂×D₄×C₂₉	1	3	yes	—
610	C₂²×C₄	C₂×D₄×C₂₉	1	3	yes	—
611	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₂₉	1	3	yes	—
613	C₂²×C₄	C₂⁴×C₂₉	1	3	yes	—
614	Q₁₆	—	2	6	no	—
615	SD₁₆	—	2	6	no	—
616	SD₁₆	—	2	12	no	—
617	SD₁₆	—	2	2	no	—
618	D₈	—	2	6	no	—
619	M₁₆	—	2	6	no	—
620	M₁₆	—	2	12	no	—
621	M₁₆	C₂×D₄×C₂₉	1	12	yes	complemented
622	C₂×C₈	—	2	6	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	6	no	—
625	C₂×C₈	—	2	6	no	—
626	C₂×C₈	—	2	6	no	—
627	C₂×C₈	C₂×D₄×C₂₉	1	12	yes	complemented
628	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₂₉	1	3	yes	—
630	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₂₉	1	3	yes	—
632	C₄⋊C₄	—	2	3	no	—
633	C₄⋊C₄	—	2	6	no	—
634	C₄⋊C₄	—	2	3	no	—
635	C₄⋊C₄	—	2	3	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	3	no	—
638	C₄⋊C₄	—	2	3	no	—
639	C₄⋊C₄	C₂⁴×C₂₉	1	3	yes	—
640	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
641	C₄⋊C₄	C₂⁴×C₂₉	1	3	yes	—
642	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
643	C₂²⋊C₄	—	2	3	no	—
644	C₂²⋊C₄	—	2	6	no	—
645	C₂²⋊C₄	—	2	3	no	—
646	C₂²⋊C₄	—	2	3	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	3	no	—
649	C₂²⋊C₄	—	2	3	no	—
650	C₂²⋊C₄	—	2	3	no	—
651	C₂²⋊C₄	—	2	6	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	3	no	—
654	C₂²⋊C₄	—	2	3	no	—
655	C₄²	—	2	3	no	—
656	C₄²	—	2	3	no	—
657	C₂³	—	2	6	no	—
658	C₂³	—	2	6	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	3	no	—
661	C₂³	—	4	3	no	—
662	C₂³	—	4	6	no	—
663	C₂³	—	8	3	no	—
664	C₂³	—	8	3	no	—
665	C₂³	C₂²×D₄×C₂₉	1	3	yes	—
666	C₂³	C₂²×D₄×C₂₉	1	3	yes	—
667	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
668	Q₈	—	2	6	no	—
669	Q₈	—	2	3	no	—
670	Q₈	—	2	1	no	—
671	Q₈	—	2	3	no	—
672	Q₈	—	2	1	no	—
673	Q₈	—	4	6	no	—
674	Q₈	C₂₉×#121	1	4	yes	—
675	D₄	—	2	12	no	—
676	D₄	—	2	6	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	3	no	—
679	D₄	—	2	3	no	—
680	D₄	—	2	1	no	—
681	D₄	—	4	6	no	—
682	D₄	—	4	6	no	—
683	D₄	—	4	6	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	6	no	—
686	D₄	—	8	6	no	—
687	D₄	—	8	3	no	—
688	D₄	—	8	3	no	—
689	D₄	C₂₉×#121	1	12	yes	—
690	C₂×C₄	—	2	6	no	—
691	C₂×C₄	—	2	6	no	—
692	C₂×C₄	—	2	6	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	3	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	3	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	3	no	—
700	C₂×C₄	—	2	3	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	3	no	—
703	C₂×C₄	—	4	6	no	—
704	C₂×C₄	—	4	6	no	—
705	C₂×C₄	—	4	6	no	—
706	C₂×C₄	—	8	3	no	—
707	C₂×C₄	—	8	3	no	—
708	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₂₉	1	3	yes	—
710	C₂×C₄	C₂²×D₄×C₂₉	1	3	yes	—
711	C₂×C₄	C₂²×D₄×C₂₉	1	6	yes	—
712	C₂×C₄	C₂×#41×C₂₉	1	6	yes	—
713	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	3	no	—
716	C₈	C₂²×D₄×C₂₉	1	2	yes	—
717	C₈	C₂²×D₄×C₂₉	1	6	yes	—
718	C₂²	—	2	3	no	—
719	C₂²	—	2	3	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	3	no	—
723	C₂²	—	2	3	no	—
724	C₂²	—	2	3	no	—
725	C₂²	—	4	12	no	—
726	C₂²	—	4	3	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	3	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	3	no	—
732	C₂²	—	16	6	no	—
733	C₂²	C₂×C₂₉×#121	1	6	yes	—
734	C₂²	C₂₉×#577	1	2	yes	complemented
735	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
736	C₄	—	2	1	no	—
737	C₄	—	2	3	no	—
738	C₄	—	4	3	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	3	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	3	no	—
744	C₄	C₂×C₂₉×#121	1	6	yes	—
745	C₄	C₂³×D₄×C₂₉	1	1	yes	characteristic
746	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
747	C₂	—	2	2	no	—
748	C₂	—	2	6	no	—
749	C₂	—	4	3	no	—
750	C₂	—	8	3	no	—
751	C₂	—	8	1	no	—
752	C₂	C₂²×C₂₉×#121	1	1	yes	characteristic
753	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
754	C₂	C₂₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#577	C₂	semidirect
2. C₂²×C₂₉×#131	C₂	semidirect
3. C₂₉×#3489	C₂	semidirect
4. C₂₉×#3488	C₂	semidirect
5. C₂₉×#3063	C₂	semidirect
6. C₂₉×#3062	C₂	semidirect
7. C₂₉×#3060	C₂	semidirect
8. C₂₉×#3057	C₂	semidirect
9. C₂₉×#3056	C₂	semidirect
10. C₂₉×#3055	C₂	semidirect
11. C₂₉×#3050	C₂	semidirect
12. C₂×C₂₉×#465	C₂	semidirect
13. C₂₉×#2912	C₂	semidirect
14. C₂₉×#2898	C₂	semidirect
15. C₂₉×#2897	C₂	semidirect
20. C₂×C₂₉×#137	C₂²	semidirect
21. C₂×C₂₉×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₂₉×#135	C₂²	semidirect
23. C₂²×SD₁₆×C₂₉	C₂²	semidirect
27. C₂×C₂₉×#131	C₂²	semidirect
28. C₂×C₂₉×#131	C₂²	semidirect
29. C₂²×M₁₆×C₂₉	C₂²	semidirect
30. C₂³×C₈×C₂₉	C₂²	semidirect
40. C₂₉×#537	C₂²	semidirect
41. C₂₉×#536	C₂²	semidirect
44. C₂₉×#525	C₂²	semidirect
45. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
49. C₂₉×#470	C₂²	semidirect
50. C₂₉×#469	C₂²	semidirect
51. C₂₉×#468	C₂²	semidirect
52. C₂₉×#468	C₂²	semidirect
53. C₂₉×#467	C₂²	semidirect
54. C₂₉×#467	C₂²	semidirect
55. C₂₉×#466	C₂²	semidirect
56. C₂₉×#466	C₂²	semidirect
57. C₂₉×#465	C₂²	semidirect
58. C₂₉×#465	C₂²	semidirect
59. C₂₉×#465	C₂²	semidirect
60. C₂₉×#465	C₂²	semidirect
61. C₂₉×#465	C₂²	semidirect
62. C₂₉×#465	C₂²	semidirect
63. C₂₉×#465	C₂²	semidirect
64. C₂₉×#428	C₂²	semidirect
65. C₂₉×#428	C₂²	semidirect
66. C₂₉×#427	C₂²	semidirect
67. C₂×C₂₉×#106	C₂²	semidirect
68. C₂₉×#419	C₂²	semidirect
69. C₂₉×#418	C₂²	semidirect
70. C₂₉×#417	C₂²	semidirect
71. C₂₉×#417	C₂²	semidirect
72. C₂₉×#416	C₂²	semidirect
73. C₂₉×#416	C₂²	semidirect
74. C₂×C₂₉×#103	C₂²	semidirect
75. C₂×C₂₉×#102	C₂²	semidirect
110. C₂₉×#131	D₄	semidirect
243. M₁₆×C₂₉	C₂×D₄	semidirect
249. C₂×C₈×C₂₉	C₂×D₄	semidirect
279. #60457	C₂₉	direct (N × H)
341. C₂×#577	C₂×C₂₉	semidirect
342. C₂²×#131	C₂×C₂₉	semidirect
343. #3489	C₂×C₂₉	semidirect
344. #3488	C₂×C₂₉	semidirect
345. #3063	C₂×C₂₉	semidirect
346. #3062	C₂×C₂₉	semidirect
347. #3060	C₂×C₂₉	semidirect
348. #3057	C₂×C₂₉	semidirect
349. #3056	C₂×C₂₉	semidirect
350. #3055	C₂×C₂₉	semidirect
351. #3050	C₂×C₂₉	semidirect
352. C₂×#465	C₂×C₂₉	semidirect
353. #2912	C₂×C₂₉	semidirect
354. #2898	C₂×C₂₉	semidirect
355. #2897	C₂×C₂₉	semidirect
372. C₂²×C₂₉	#577	semidirect
389. C₂×#137	C₂²×C₂₉	semidirect
390. C₂×AGL(1,ℤ/8)	C₂²×C₂₉	semidirect
391. C₂×#135	C₂²×C₂₉	semidirect
392. C₂²×SD₁₆	C₂²×C₂₉	semidirect
396. C₂×#131	C₂²×C₂₉	semidirect
397. C₂×#131	C₂²×C₂₉	semidirect
398. C₂²×M₁₆	C₂²×C₂₉	semidirect
399. C₂³×C₈	C₂²×C₂₉	semidirect
409. #537	C₂²×C₂₉	semidirect
410. #536	C₂²×C₂₉	semidirect
413. #525	C₂²×C₂₉	semidirect
414. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
418. #470	C₂²×C₂₉	semidirect
419. #469	C₂²×C₂₉	semidirect
420. #468	C₂²×C₂₉	semidirect
421. #468	C₂²×C₂₉	semidirect
422. #467	C₂²×C₂₉	semidirect
423. #467	C₂²×C₂₉	semidirect
424. #466	C₂²×C₂₉	semidirect
425. #466	C₂²×C₂₉	semidirect
426. #465	C₂²×C₂₉	semidirect
427. #465	C₂²×C₂₉	semidirect
428. #465	C₂²×C₂₉	semidirect
429. #465	C₂²×C₂₉	semidirect
430. #465	C₂²×C₂₉	semidirect
431. #465	C₂²×C₂₉	semidirect
432. #465	C₂²×C₂₉	semidirect
433. #428	C₂²×C₂₉	semidirect
434. #428	C₂²×C₂₉	semidirect
435. #427	C₂²×C₂₉	semidirect
436. C₂×#106	C₂²×C₂₉	semidirect
437. #419	C₂²×C₂₉	semidirect
438. #418	C₂²×C₂₉	semidirect
439. #417	C₂²×C₂₉	semidirect
440. #417	C₂²×C₂₉	semidirect
441. #416	C₂²×C₂₉	semidirect
442. #416	C₂²×C₂₉	semidirect
443. C₂×#103	C₂²×C₂₉	semidirect
444. C₂×#102	C₂²×C₂₉	semidirect
487. #131	D₄×C₂₉	semidirect
559. C₂₉	#60457	direct (N × H)
621. M₁₆	C₂×D₄×C₂₉	semidirect
627. C₂×C₈	C₂×D₄×C₂₉	semidirect
734. C₂²	C₂₉×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#577	2
C₂²×C₂₉×#131	2
C₂₉×#3489	2
C₂₉×#3488	2
C₂₉×#3063	2
C₂₉×#3062	2
C₂₉×#3060	2
C₂₉×#3057	2
C₂₉×#3056	2
C₂₉×#3055	2
C₂₉×#3050	2
C₂×C₂₉×#465	2
C₂₉×#2912	2
C₂₉×#2898	2
C₂₉×#2897	2
#60457	29

Subgroups — C29×#60457 #20355357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60457 #20355357