Subgroups — C₂₉×#60269 #20355169

Order 7424.

1864 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2995	C₂	1	4	yes	maximal, complemented
3	C₂₉×#2992	C₂	1	4	yes	maximal, complemented
4	C₂₉×#2990	C₂	1	4	yes	maximal, complemented
5	C₂₉×#2989	C₂	1	4	yes	maximal, complemented
6	C₂₉×#2961	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2933	C₂	1	4	yes	maximal, complemented
8	C₂₉×#2932	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2925	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2906	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#131	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂₉×#533	C₄	1	1	yes	characteristic
16	C₂₉×#533	C₄	1	1	yes	characteristic
17	C₂₉×#533	C₂²	1	1	yes	characteristic
18	C₂₉×#532	C₄	1	1	yes	characteristic
19	C₂₉×#532	C₄	1	1	yes	characteristic
20	C₂₉×#532	C₂²	1	1	yes	characteristic
21	C₂₉×#529	C₄	1	2	yes	—
22	C₂₉×#529	C₄	1	2	yes	—
23	C₂₉×#529	C₄	1	2	yes	—
24	C₂₉×#529	C₄	1	2	yes	—
25	C₂₉×#529	C₂²	1	2	yes	—
26	C₂₉×#529	C₂²	1	2	yes	—
27	C₂₉×#525	C₄	1	2	yes	—
28	C₂₉×#525	C₄	1	2	yes	—
29	C₂₉×#525	C₂²	1	2	yes	—
30	C₄×#41×C₂₉	C₂²	1	2	yes	—
31	C₄×#41×C₂₉	C₂²	1	2	yes	—
32	C₄×#41×C₂₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#446	C₂²	1	8	yes	complemented
35	C₂₉×#446	C₂²	1	8	yes	complemented
36	C₂₉×#436	C₂²	1	8	yes	—
37	C₂₉×#435	C₂²	1	8	yes	—
38	C₂₉×#435	C₂²	1	8	yes	—
39	C₂₉×#435	C₂²	1	8	yes	complemented
40	C₂₉×#435	C₂²	1	8	yes	complemented
41	C₈×D₄×C₂₉	C₂²	1	8	yes	—
42	C₂₉×#433	C₂²	1	8	yes	complemented
43	C₂₉×#432	C₂²	1	2	yes	—
44	C₂₉×#432	C₂²	1	2	yes	—
45	C₂₉×#432	C₂²	1	2	yes	—
46	C₂₉×#432	C₂²	1	2	yes	—
47	C₂₉×#432	C₂²	1	4	yes	complemented
48	C₂₉×#431	C₂²	1	4	yes	complemented
49	C₂₉×#424	C₂²	1	4	yes	—
50	C₂₉×#424	C₂²	1	8	yes	complemented
51	C₂₉×#423	C₂²	1	2	yes	—
52	C₂₉×#423	C₂²	1	2	yes	—
53	C₂₉×#423	C₂²	1	2	yes	—
54	C₂₉×#423	C₂²	1	2	yes	—
55	C₂₉×#423	C₂²	1	4	yes	complemented
56	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
57	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
58	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₂×C₂₉×C₄⋊C₈	C₂²	1	4	yes	complemented
61	C₂₉×#408	C₂²	1	4	yes	—
62	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
63	C₂₉×#405	C₂²	1	4	yes	—
64	C₂×C₂₉×#97	C₂²	1	2	yes	—
65	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
66	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
67	C₂×#41×C₂₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂₉×#131	—	4	8	no	—
72	C₂×M₁₆×C₂₉	—	4	4	no	—
73	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
74	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
75	C₂×M₁₆×C₂₉	C₂³	1	8	yes	—
76	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
77	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
78	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
79	C₂²×C₈×C₂₉	C₂³	1	8	yes	—
80	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
82	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₂₉×#127	C₂×C₄	1	1	yes	characteristic
84	C₂₉×#126	C₂×C₄	1	4	yes	—
85	C₂₉×#126	C₂×C₄	1	4	yes	—
86	C₂₉×#125	C₂×C₄	1	2	yes	—
87	C₂₉×#125	C₂×C₄	1	2	yes	—
88	C₂₉×#125	C₂×C₄	1	2	yes	—
89	C₂₉×#124	C₂×C₄	1	2	yes	—
90	C₂₉×#124	C₂×C₄	1	2	yes	—
91	C₂₉×#124	C₂×C₄	1	2	yes	—
92	C₂₉×#123	C₂×C₄	1	4	yes	—
93	C₂₉×#123	C₂×C₄	1	4	yes	—
94	C₂₉×#123	C₂×C₄	1	4	yes	—
95	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
96	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
97	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
98	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
99	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
100	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
101	C₂₉×#121	C₂×C₄	1	2	yes	—
102	C₂₉×#121	C₂×C₄	1	2	yes	—
103	C₂₉×#121	C₂×C₄	1	2	yes	—
104	C₂₉×#121	C₂×C₄	1	2	yes	—
105	C₂₉×#121	C₂×C₄	1	2	yes	—
106	C₂₉×#121	C₂×C₄	1	2	yes	—
107	C₂₉×#120	C₂×C₄	1	4	yes	—
108	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
109	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
110	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
111	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
112	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
113	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
114	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
115	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
116	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
117	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
118	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
119	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
120	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
121	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
122	C₄×D₄×C₂₉	C₂³	1	4	yes	—
123	C₄×D₄×C₂₉	C₂³	1	4	yes	—
124	C₄×D₄×C₂₉	C₂³	1	2	yes	—
125	C₄×D₄×C₂₉	C₂³	1	2	yes	—
126	C₂₉×#117	C₂×C₄	1	2	yes	—
127	C₂₉×#117	C₂×C₄	1	2	yes	—
128	C₂₉×#117	C₂×C₄	1	4	yes	—
129	C₂₉×#117	C₂×C₄	1	4	yes	—
130	C₂₉×#117	C₂³	1	4	yes	—
131	C₂₉×#117	C₂³	1	2	yes	—
132	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
139	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
145	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
146	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
147	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
148	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
149	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
150	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
151	C₂₉×C₄⋊C₈	C₂³	1	8	yes	—
152	C₂₉×C₄⋊C₈	C₂³	1	8	yes	—
153	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
154	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
155	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	—
156	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
157	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
158	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	—
159	C₂₉×#97	C₂³	1	4	yes	—
160	C₂₉×#97	C₂³	1	4	yes	—
161	C₂₉×#97	C₂³	1	8	yes	—
162	C₄×C₈×C₂₉	C₂³	1	8	yes	—
163	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
164	#41×C₂₉	—	2	4	no	—
165	#41×C₂₉	—	2	4	no	—
166	#41×C₂₉	—	4	4	no	—
167	#41×C₂₉	—	4	4	no	—
168	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
169	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
170	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
171	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
174	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
175	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₂₉	—	2	2	no	—
178	C₂²×C₄×C₂₉	—	2	2	no	—
179	C₂²×C₄×C₂₉	—	4	2	no	—
180	C₂²×C₄×C₂₉	—	4	2	no	—
181	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
202	M₁₆×C₂₉	—	2	8	no	—
203	M₁₆×C₂₉	—	4	4	no	—
204	M₁₆×C₂₉	—	4	8	no	—
205	C₂×C₈×C₂₉	—	2	4	no	—
206	C₂×C₈×C₂₉	—	2	4	no	—
207	C₂×C₈×C₂₉	—	4	4	no	—
208	C₂×C₈×C₂₉	—	4	8	no	—
209	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
210	C₂×C₈×C₂₉	C₂⁴	1	8	yes	—
211	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
212	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
213	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
214	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
215	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
217	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
221	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
223	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
224	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
225	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
226	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
227	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
228	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
229	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
230	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
233	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
235	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
236	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
238	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
246	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
247	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
248	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
249	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
250	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
251	C₄²×C₂₉	C₂⁴	1	4	yes	—
252	#60269	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂³×C₂₉	—	2	2	no	—
254	C₂³×C₂₉	—	2	2	no	—
255	C₂³×C₂₉	—	4	1	no	—
256	C₂³×C₂₉	C₂³×C₄	1	4	yes	—
257	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
258	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
259	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
260	Q₈×C₂₉	—	2	4	no	—
261	Q₈×C₂₉	—	4	2	no	—
262	Q₈×C₂₉	—	4	2	no	—
263	D₄×C₂₉	—	2	8	no	—
264	D₄×C₂₉	—	2	8	no	—
265	D₄×C₂₉	—	2	4	no	—
266	D₄×C₂₉	—	4	2	no	—
267	D₄×C₂₉	—	4	2	no	—
268	D₄×C₂₉	—	4	4	no	—
269	C₂×C₄×C₂₉	—	2	2	no	—
270	C₂×C₄×C₂₉	—	2	2	no	—
271	C₂×C₄×C₂₉	—	2	2	no	—
272	C₂×C₄×C₂₉	—	2	2	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	2	no	—
276	C₂×C₄×C₂₉	—	2	2	no	—
277	C₂×C₄×C₂₉	—	2	8	no	—
278	C₂×C₄×C₂₉	—	2	1	no	—
279	C₂×C₄×C₂₉	—	2	4	no	—
280	C₂×C₄×C₂₉	—	2	1	no	—
281	C₂×C₄×C₂₉	—	2	1	no	—
282	C₂×C₄×C₂₉	—	2	1	no	—
283	C₂×C₄×C₂₉	—	2	4	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	4	1	no	—
286	C₂×C₄×C₂₉	—	4	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	4	1	no	—
289	C₂×C₄×C₂₉	—	4	1	no	—
290	C₂×C₄×C₂₉	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	4	no	—
292	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
307	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
308	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
309	C₈×C₂₉	—	2	4	no	—
310	C₈×C₂₉	—	2	8	no	—
311	C₈×C₂₉	—	2	4	no	—
312	#3444	C₂×C₂₉	1	1	yes	characteristic
313	#2995	C₂×C₂₉	1	4	yes	complemented
314	#2992	C₂×C₂₉	1	4	yes	complemented
315	#2990	C₂×C₂₉	1	4	yes	complemented
316	#2989	C₂×C₂₉	1	4	yes	complemented
317	#2961	C₂×C₂₉	1	2	yes	complemented
318	#2933	C₂×C₂₉	1	4	yes	complemented
319	#2932	C₂×C₂₉	1	2	yes	complemented
320	#2925	C₂×C₂₉	1	2	yes	complemented
321	C₂×#432	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#2906	C₂×C₂₉	1	2	yes	complemented
323	C₂×#423	C₂×C₂₉	1	1	yes	characteristic, complemented
324	C₂²×C₂₉	—	2	1	no	—
325	C₂²×C₂₉	—	2	1	no	—
326	C₂²×C₂₉	—	2	1	no	—
327	C₂²×C₂₉	—	2	1	no	—
328	C₂²×C₂₉	—	2	1	no	—
329	C₂²×C₂₉	—	2	4	no	—
330	C₂²×C₂₉	—	2	1	no	—
331	C₂²×C₂₉	—	2	4	no	—
332	C₂²×C₂₉	—	2	1	no	—
333	C₂²×C₂₉	—	2	4	no	—
334	C₂²×C₂₉	—	4	4	no	—
335	C₂²×C₂₉	#520	1	2	yes	—
336	C₂²×C₂₉	#568	1	2	yes	—
337	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
338	C₄×C₂₉	—	2	1	no	—
339	C₄×C₂₉	—	2	1	no	—
340	C₄×C₂₉	—	2	4	no	—
341	C₄×C₂₉	—	2	1	no	—
342	C₄×C₂₉	—	2	1	no	—
343	C₄×C₂₉	—	2	1	no	—
344	C₄×C₂₉	—	2	1	no	—
345	C₄×C₂₉	—	2	1	no	—
346	C₄×C₂₉	—	2	1	no	—
347	C₄×C₂₉	—	2	1	no	—
348	C₄×C₂₉	—	2	4	no	—
349	C₄×C₂₉	—	2	4	no	—
350	C₄×C₂₉	#520	1	2	yes	—
351	C₄×C₂₉	#568	1	2	yes	—
352	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₄×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
354	C₂×#131	C₂²×C₂₉	1	4	yes	—
355	C₂²×M₁₆	C₂²×C₂₉	1	2	yes	—
356	#533	C₄×C₂₉	1	1	yes	characteristic
357	#533	C₄×C₂₉	1	1	yes	characteristic
358	#533	C₂²×C₂₉	1	1	yes	characteristic
359	#532	C₄×C₂₉	1	1	yes	characteristic
360	#532	C₄×C₂₉	1	1	yes	characteristic
361	#532	C₂²×C₂₉	1	1	yes	characteristic
362	#529	C₄×C₂₉	1	2	yes	—
363	#529	C₄×C₂₉	1	2	yes	—
364	#529	C₄×C₂₉	1	2	yes	—
365	#529	C₄×C₂₉	1	2	yes	—
366	#529	C₂²×C₂₉	1	2	yes	—
367	#529	C₂²×C₂₉	1	2	yes	—
368	#525	C₄×C₂₉	1	2	yes	—
369	#525	C₄×C₂₉	1	2	yes	—
370	#525	C₂²×C₂₉	1	2	yes	—
371	C₄×#41	C₂²×C₂₉	1	2	yes	—
372	C₄×#41	C₂²×C₂₉	1	2	yes	—
373	C₄×#41	C₂²×C₂₉	1	2	yes	—
374	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
375	#446	C₂²×C₂₉	1	8	yes	complemented
376	#446	C₂²×C₂₉	1	8	yes	complemented
377	#436	C₂²×C₂₉	1	8	yes	—
378	#435	C₂²×C₂₉	1	8	yes	—
379	#435	C₂²×C₂₉	1	8	yes	—
380	#435	C₂²×C₂₉	1	8	yes	complemented
381	#435	C₂²×C₂₉	1	8	yes	complemented
382	C₈×D₄	C₂²×C₂₉	1	8	yes	—
383	#433	C₂²×C₂₉	1	8	yes	complemented
384	#432	C₂²×C₂₉	1	2	yes	—
385	#432	C₂²×C₂₉	1	2	yes	—
386	#432	C₂²×C₂₉	1	2	yes	—
387	#432	C₂²×C₂₉	1	2	yes	—
388	#432	C₂²×C₂₉	1	4	yes	complemented
389	#431	C₂²×C₂₉	1	4	yes	complemented
390	#424	C₂²×C₂₉	1	4	yes	—
391	#424	C₂²×C₂₉	1	8	yes	complemented
392	#423	C₂²×C₂₉	1	2	yes	—
393	#423	C₂²×C₂₉	1	2	yes	—
394	#423	C₂²×C₂₉	1	2	yes	—
395	#423	C₂²×C₂₉	1	2	yes	—
396	#423	C₂²×C₂₉	1	4	yes	complemented
397	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
398	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
399	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
400	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×C₄⋊C₈	C₂²×C₂₉	1	4	yes	complemented
402	#408	C₂²×C₂₉	1	4	yes	—
403	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
404	#405	C₂²×C₂₉	1	4	yes	—
405	C₂×#97	C₂²×C₂₉	1	2	yes	—
406	C₂×C₂₉	—	2	2	no	—
407	C₂×C₂₉	—	2	2	no	—
408	C₂×C₂₉	—	4	4	no	—
409	C₂×C₂₉	—	4	1	no	—
410	C₂×C₂₉	C₂×#520	1	1	yes	characteristic
411	C₂×C₂₉	C₂×#568	1	1	yes	characteristic
412	C₂×C₂₉	C₂×#568	1	1	yes	characteristic
413	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
414	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
415	C₂×#41	C₂³×C₂₉	1	2	yes	—
416	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
417	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
419	#131	—	4	8	no	—
420	C₂×M₁₆	—	4	4	no	—
421	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
422	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
423	C₂×M₁₆	C₂³×C₂₉	1	8	yes	—
424	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
425	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
426	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
427	C₂²×C₈	C₂³×C₂₉	1	8	yes	—
428	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
429	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
430	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
431	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
432	#126	C₂×C₄×C₂₉	1	4	yes	—
433	#126	C₂×C₄×C₂₉	1	4	yes	—
434	#125	C₂×C₄×C₂₉	1	2	yes	—
435	#125	C₂×C₄×C₂₉	1	2	yes	—
436	#125	C₂×C₄×C₂₉	1	2	yes	—
437	#124	C₂×C₄×C₂₉	1	2	yes	—
438	#124	C₂×C₄×C₂₉	1	2	yes	—
439	#124	C₂×C₄×C₂₉	1	2	yes	—
440	#123	C₂×C₄×C₂₉	1	4	yes	—
441	#123	C₂×C₄×C₂₉	1	4	yes	—
442	#123	C₂×C₄×C₂₉	1	4	yes	—
443	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
444	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
445	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
446	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
447	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
448	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
449	#121	C₂×C₄×C₂₉	1	2	yes	—
450	#121	C₂×C₄×C₂₉	1	2	yes	—
451	#121	C₂×C₄×C₂₉	1	2	yes	—
452	#121	C₂×C₄×C₂₉	1	2	yes	—
453	#121	C₂×C₄×C₂₉	1	2	yes	—
454	#121	C₂×C₄×C₂₉	1	2	yes	—
455	#120	C₂×C₄×C₂₉	1	4	yes	—
456	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
457	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
458	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
459	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
460	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
461	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
462	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
463	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
464	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
465	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
466	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
467	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
468	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
469	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
470	C₄×D₄	C₂³×C₂₉	1	4	yes	—
471	C₄×D₄	C₂³×C₂₉	1	4	yes	—
472	C₄×D₄	C₂³×C₂₉	1	2	yes	—
473	C₄×D₄	C₂³×C₂₉	1	2	yes	—
474	#117	C₂×C₄×C₂₉	1	2	yes	—
475	#117	C₂×C₄×C₂₉	1	2	yes	—
476	#117	C₂×C₄×C₂₉	1	4	yes	—
477	#117	C₂×C₄×C₂₉	1	4	yes	—
478	#117	C₂³×C₂₉	1	2	yes	—
479	#117	C₂³×C₂₉	1	4	yes	—
480	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
481	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
482	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
483	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
484	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
485	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
487	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
493	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
494	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
495	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
496	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
497	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
498	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
499	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
500	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
501	C₄⋊C₈	C₂³×C₂₉	1	8	yes	—
502	C₄⋊C₈	C₂³×C₂₉	1	8	yes	—
503	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
504	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
505	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	—
506	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	—
507	#97	C₂³×C₂₉	1	4	yes	—
508	#97	C₂³×C₂₉	1	4	yes	—
509	#97	C₂³×C₂₉	1	8	yes	—
510	C₄×C₈	C₂³×C₂₉	1	8	yes	—
511	C₂₉	#60269	1	1	yes	characteristic, direct product factor, Sylow
512	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
513	#41	—	2	4	no	—
514	#41	—	2	4	no	—
515	#41	—	4	4	no	—
516	#41	—	4	4	no	—
517	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
518	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
519	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
521	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
522	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
523	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
524	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
525	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
539	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
551	M₁₆	—	2	8	no	—
552	M₁₆	—	4	4	no	—
553	M₁₆	—	4	8	no	—
554	C₂×C₈	—	2	4	no	—
555	C₂×C₈	—	2	4	no	—
556	C₂×C₈	—	4	4	no	—
557	C₂×C₈	—	4	8	no	—
558	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
559	C₂×C₈	C₂⁴×C₂₉	1	8	yes	—
560	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
562	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
563	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
566	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
567	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
571	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
582	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
583	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
584	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
585	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
586	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
587	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
588	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
589	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
590	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
593	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
595	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
596	C₄²	C₂⁴×C₂₉	1	4	yes	—
597	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
598	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
599	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
600	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	4	1	no	—
604	C₂³	C₂³×C₄×C₂₉	1	4	yes	—
605	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
606	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
607	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
608	Q₈	—	2	4	no	—
609	Q₈	—	4	2	no	—
610	Q₈	—	4	2	no	—
611	D₄	—	2	8	no	—
612	D₄	—	2	8	no	—
613	D₄	—	2	4	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
641	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
642	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
643	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
646	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
650	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
651	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
652	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
653	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
654	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
655	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
656	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
657	C₈	—	2	4	no	—
658	C₈	—	2	8	no	—
659	C₈	—	2	4	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	4	4	no	—
671	C₂²	C₂₉×#520	1	2	yes	—
672	C₂²	C₂₉×#568	1	2	yes	—
673	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	4	no	—
686	C₄	C₂₉×#520	1	2	yes	—
687	C₄	C₂₉×#568	1	2	yes	—
688	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
689	C₄	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂	—	2	2	no	—
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	4	no	—
694	C₂	C₂×C₂₉×#520	1	1	yes	characteristic
695	C₂	C₂×C₂₉×#568	1	1	yes	characteristic
696	C₂	C₂×C₂₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁴×C₄
prime radical	C₂₉×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2995	C₂	semidirect
3. C₂₉×#2992	C₂	semidirect
4. C₂₉×#2990	C₂	semidirect
5. C₂₉×#2989	C₂	semidirect
6. C₂₉×#2961	C₂	semidirect
7. C₂₉×#2933	C₂	semidirect
8. C₂₉×#2932	C₂	semidirect
9. C₂₉×#2925	C₂	semidirect
10. C₂×C₂₉×#432	C₂	semidirect
11. C₂₉×#2906	C₂	semidirect
12. C₂×C₂₉×#423	C₂	semidirect
34. C₂₉×#446	C₂²	semidirect
35. C₂₉×#446	C₂²	semidirect
39. C₂₉×#435	C₂²	semidirect
40. C₂₉×#435	C₂²	semidirect
42. C₂₉×#433	C₂²	semidirect
47. C₂₉×#432	C₂²	semidirect
48. C₂₉×#431	C₂²	semidirect
50. C₂₉×#424	C₂²	semidirect
55. C₂₉×#423	C₂²	semidirect
60. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
252. #60269	C₂₉	direct (N × H)
313. #2995	C₂×C₂₉	semidirect
314. #2992	C₂×C₂₉	semidirect
315. #2990	C₂×C₂₉	semidirect
316. #2989	C₂×C₂₉	semidirect
317. #2961	C₂×C₂₉	semidirect
318. #2933	C₂×C₂₉	semidirect
319. #2932	C₂×C₂₉	semidirect
320. #2925	C₂×C₂₉	semidirect
321. C₂×#432	C₂×C₂₉	semidirect
322. #2906	C₂×C₂₉	semidirect
323. C₂×#423	C₂×C₂₉	semidirect
375. #446	C₂²×C₂₉	semidirect
376. #446	C₂²×C₂₉	semidirect
380. #435	C₂²×C₂₉	semidirect
381. #435	C₂²×C₂₉	semidirect
383. #433	C₂²×C₂₉	semidirect
388. #432	C₂²×C₂₉	semidirect
389. #431	C₂²×C₂₉	semidirect
391. #424	C₂²×C₂₉	semidirect
396. #423	C₂²×C₂₉	semidirect
401. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
511. C₂₉	#60269	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#3444	2
C₂₉×#2995	2
C₂₉×#2992	2
C₂₉×#2990	2
C₂₉×#2989	2
C₂₉×#2961	2
C₂₉×#2933	2
C₂₉×#2932	2
C₂₉×#2925	2
C₂×C₂₉×#432	2
C₂₉×#2906	2
C₂×C₂₉×#423	2
#60269	29

Subgroups — C29×#60269 #20355169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60269 #20355169