Subgroups — C₂₉×#61188 #20356088

Order 7424.

2056 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3485	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3331	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3323	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3315	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3315	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3314	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3311	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3302	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3296	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
31	C₂₉×#556	C₂²	1	2	yes	complemented
32	C₂₉×#554	C₂²	1	2	yes	complemented
33	C₂₉×#552	—	2	2	no	—
34	C₂₉×#552	C₂²	1	2	yes	complemented
35	C₂₉×#552	C₂²	1	2	yes	complemented
36	C₂₉×#551	—	2	2	no	—
37	C₂₉×#547	—	2	1	no	—
38	C₂₉×#547	—	2	1	no	—
39	C₂₉×#547	C₂²	1	2	yes	—
40	C₂₉×#547	C₂²	1	2	yes	—
41	C₂₉×#546	—	2	1	no	—
42	C₂₉×#546	—	2	1	no	—
43	C₂₉×#546	C₂²	1	2	yes	—
44	C₂₉×#546	C₂²	1	2	yes	—
45	C₂₉×#544	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#542	—	2	1	no	—
47	C₂₉×#541	—	2	1	no	—
48	C₂₉×#536	C₂²	1	1	yes	characteristic
49	C₂₉×#536	C₂²	1	1	yes	characteristic
50	C₂₉×#536	C₂²	1	1	yes	characteristic
51	C₂₉×#534	—	2	2	no	—
52	C₂₉×#533	—	2	1	no	—
53	C₂₉×#529	—	2	1	no	—
54	C₂₉×#525	C₂²	1	1	yes	characteristic
55	C₂₉×#525	C₂²	1	1	yes	characteristic
56	C₂×C₂₉×#123	—	2	2	no	—
57	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×#520	C₂²	1	1	yes	characteristic
59	C₂₉×#519	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#518	C₂²	1	1	yes	characteristic
61	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#491	C₂²	1	2	yes	complemented
63	C₂₉×#489	C₂²	1	2	yes	complemented
64	C₂₉×#488	C₂²	1	2	yes	complemented
65	C₂₉×#487	C₂²	1	2	yes	complemented
66	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#485	C₂²	1	2	yes	complemented
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×#484	C₂²	1	2	yes	complemented
71	C₂₉×#484	C₂²	1	1	yes	characteristic, complemented
72	C₂₉×#483	C₂²	1	2	yes	complemented
73	C₂₉×#483	C₂²	1	1	yes	characteristic, complemented
74	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#481	C₂²	1	1	yes	characteristic, complemented
77	C₂₉×#480	C₂²	1	1	yes	characteristic, complemented
78	C₂₉×#478	C₂²	1	2	yes	complemented
79	C₂₉×#478	C₂²	1	2	yes	complemented
80	C₂₉×#476	C₂²	1	2	yes	complemented
81	C₂₉×#474	C₂²	1	2	yes	complemented
82	C₂₉×#470	C₂²	1	2	yes	complemented
83	C₂₉×#470	C₂²	1	2	yes	complemented
84	C₂₉×#470	C₂²	1	2	yes	complemented
85	C₂₉×#468	C₂²	1	2	yes	complemented
86	C₂₉×#467	C₂²	1	2	yes	complemented
87	C₂₉×#467	C₂²	1	2	yes	complemented
88	C₂₉×#467	C₂²	1	2	yes	complemented
89	C₂₉×#465	C₂²	1	2	yes	complemented
90	C₂₉×#464	C₂²	1	2	yes	complemented
91	C₂₉×#464	C₂²	1	2	yes	complemented
92	C₂₉×#462	C₂²	1	2	yes	complemented
93	C₂₉×#462	C₂²	1	2	yes	complemented
94	C₂₉×#452	C₂²	1	2	yes	complemented
95	C₂₉×#452	C₂²	1	2	yes	complemented
96	C₂₉×#452	C₂²	1	2	yes	complemented
97	C₂₉×#452	C₂²	1	2	yes	complemented
98	C₂₉×#452	C₂²	1	2	yes	complemented
99	C₂₉×#452	C₂²	1	2	yes	complemented
100	C₂₉×#450	C₂²	1	2	yes	complemented
101	C₂₉×#450	C₂²	1	2	yes	complemented
102	C₂₉×#440	C₂²	1	2	yes	complemented
103	C₂₉×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
106	C₂₉×#436	C₂²	1	2	yes	complemented
107	C₂₉×#435	C₂²	1	2	yes	complemented
108	C₂₉×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
110	C₂₉×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂₉×#427	C₂²	1	1	yes	characteristic, complemented
112	C₂₉×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
114	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
115	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
116	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
117	C₂₉×#418	C₂²	1	1	yes	characteristic
118	C₂₉×#418	C₂²	1	1	yes	characteristic
119	C₂₉×#418	C₂²	1	2	yes	complemented
120	C₂₉×#417	C₂²	1	1	yes	characteristic
121	C₂₉×#417	C₂²	1	2	yes	complemented
122	C₂₉×#417	C₂²	1	2	yes	complemented
123	C₂₉×#417	C₂²	1	2	yes	complemented
124	C₂₉×#416	C₂²	1	1	yes	characteristic
125	C₂₉×#416	C₂²	1	1	yes	characteristic
126	C₂₉×#416	C₂²	1	2	yes	complemented
127	C₂₉×#416	C₂²	1	2	yes	complemented
128	C₂₉×#416	C₂²	1	2	yes	complemented
129	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
131	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
132	C₂₉×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
134	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂₉×H(5,𝔽₂)	—	2	4	no	—
136	C₂₉×H(5,𝔽₂)	—	4	2	no	—
137	C₂×#41×C₂₉	—	2	1	no	—
138	C₂×#41×C₂₉	—	2	1	no	—
139	C₂×#41×C₂₉	—	2	1	no	—
140	C₂×#41×C₂₉	—	2	4	no	—
141	C₂×#41×C₂₉	—	4	2	no	—
142	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
143	C₂×#41×C₂₉	C₂³	1	2	yes	—
144	C₂×#41×C₂₉	C₂³	1	2	yes	—
145	C₂×#41×C₂₉	C₂³	1	2	yes	—
146	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₂₉	—	2	1	no	—
150	C₂²×D₄×C₂₉	—	2	2	no	—
151	C₂²×D₄×C₂₉	—	2	1	no	—
152	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
153	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₂₉	—	2	1	no	—
155	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₂₉×#137	—	4	2	no	—
157	C₂×Q₁₆×C₂₉	—	4	2	no	—
158	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₂₉	—	2	4	no	—
162	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
165	C₂₉×#131	—	4	2	no	—
166	C₂×M₁₆×C₂₉	—	4	2	no	—
167	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
170	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
171	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
174	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
175	C₂₉×C₄⋊Q₈	—	2	1	no	—
176	C₂₉×C₄⋊Q₈	—	2	1	no	—
177	C₂₉×C₄⋊Q₈	—	2	1	no	—
178	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
179	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
180	C₂₉×#126	—	2	2	no	—
181	C₂₉×#126	—	2	2	no	—
182	C₂₉×#126	—	2	2	no	—
183	C₂₉×#126	—	2	2	no	—
184	C₂₉×#125	—	2	1	no	—
185	C₂₉×#125	—	2	2	no	—
186	C₂₉×#125	—	2	2	no	—
187	C₂₉×#125	—	2	2	no	—
188	C₂₉×#125	C₂³	1	2	yes	—
189	C₂₉×#124	—	2	1	no	—
190	C₂₉×#124	—	2	1	no	—
191	C₂₉×#124	—	2	2	no	—
192	C₂₉×#124	C₂³	1	2	yes	—
193	C₂₉×#123	—	2	2	no	—
194	C₂₉×#123	—	2	2	no	—
195	C₂₉×#123	—	2	2	no	—
196	C₂₉×#123	—	2	2	no	—
197	C₂₉×#123	—	2	1	no	—
198	C₂₉×#123	—	2	2	no	—
199	C₂₉×#123	—	2	2	no	—
200	C₂₉×#123	—	2	2	no	—
201	C₂₉×#123	—	2	2	no	—
202	C₂₉×#123	—	2	2	no	—
203	C₂₉×#123	—	2	2	no	—
204	C₂₉×#123	—	2	2	no	—
205	C₂₉×#123	D₄	1	2	yes	—
206	C₂₉×C₂²⋊Q₈	—	2	1	no	—
207	C₂₉×C₂²⋊Q₈	—	2	1	no	—
208	C₂₉×C₂²⋊Q₈	—	2	1	no	—
209	C₂₉×C₂²⋊Q₈	—	2	1	no	—
210	C₂₉×C₂²⋊Q₈	—	2	2	no	—
211	C₂₉×C₂²⋊Q₈	—	2	2	no	—
212	C₂₉×C₂²⋊Q₈	—	2	2	no	—
213	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
214	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
215	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂₉×#121	—	2	2	no	—
224	C₂₉×#121	—	2	2	no	—
225	C₂₉×#121	—	2	2	no	—
226	C₂₉×#121	—	2	2	no	—
227	C₂₉×#121	D₄	1	1	yes	characteristic
228	C₂₉×#121	D₄	1	1	yes	characteristic
229	C₂₉×#121	C₂³	1	1	yes	characteristic
230	C₂₉×#121	C₂³	1	1	yes	characteristic
231	C₂₉×#120	—	2	1	no	—
232	C₂₉×#120	—	2	2	no	—
233	C₂₉×#120	—	2	2	no	—
234	C₂₉×#120	D₄	1	2	yes	—
235	C₄×Q₈×C₂₉	—	2	1	no	—
236	C₄×Q₈×C₂₉	—	2	1	no	—
237	C₄×Q₈×C₂₉	—	2	1	no	—
238	C₄×Q₈×C₂₉	—	2	2	no	—
239	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
241	C₄×D₄×C₂₉	—	2	1	no	—
242	C₄×D₄×C₂₉	—	2	2	no	—
243	C₄×D₄×C₂₉	—	2	2	no	—
244	C₄×D₄×C₂₉	—	2	1	no	—
245	C₄×D₄×C₂₉	—	2	1	no	—
246	C₄×D₄×C₂₉	—	2	1	no	—
247	C₄×D₄×C₂₉	—	2	1	no	—
248	C₄×D₄×C₂₉	C₂³	1	2	yes	—
249	C₄×D₄×C₂₉	C₂³	1	2	yes	—
250	C₄×D₄×C₂₉	C₂³	1	2	yes	—
251	C₄×D₄×C₂₉	C₂³	1	2	yes	—
252	C₂₉×#117	—	2	1	no	—
253	C₂₉×#117	—	2	1	no	—
254	C₂₉×#117	—	2	2	no	—
255	C₂₉×#117	—	2	2	no	—
256	C₂₉×#117	—	2	2	no	—
257	C₂₉×#117	C₂³	1	1	yes	characteristic
258	C₂₉×#117	C₂³	1	1	yes	characteristic
259	C₂₉×#117	C₂³	1	1	yes	characteristic
260	C₂₉×#117	C₂³	1	1	yes	characteristic
261	C₂₉×#117	C₂³	1	1	yes	characteristic
262	C₂₉×#117	C₂³	1	2	yes	—
263	C₂₉×#117	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
266	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
267	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
273	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
276	C₂×C₄²×C₂₉	—	2	1	no	—
277	C₂₉×#107	C₂³	1	1	yes	characteristic
278	C₂₉×#107	C₂³	1	1	yes	characteristic
279	C₂₉×#107	C₂³	1	1	yes	characteristic
280	C₂₉×#107	C₂³	1	1	yes	characteristic
281	C₂₉×#107	C₂³	1	2	yes	—
282	C₂₉×#106	C₂³	1	1	yes	characteristic
283	C₂₉×#106	C₂³	1	1	yes	characteristic
284	C₂₉×#106	C₂³	1	1	yes	characteristic
285	C₂₉×#106	C₂³	1	1	yes	characteristic
286	C₂₉×#106	C₂³	1	2	yes	—
287	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
288	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
289	C₂₉×#103	C₂³	1	2	yes	—
290	C₂₉×#103	C₂³	1	2	yes	—
291	C₂₉×#103	C₂³	1	1	yes	characteristic
292	C₂₉×#103	C₂³	1	2	yes	—
293	C₂₉×#103	C₂³	1	2	yes	—
294	C₂₉×#103	C₂³	1	1	yes	characteristic
295	C₂₉×#103	C₂³	1	1	yes	characteristic
296	C₂₉×#103	C₂³	1	1	yes	characteristic
297	C₂₉×#103	C₂³	1	2	yes	—
298	C₂₉×#103	C₂³	1	2	yes	—
299	C₂₉×#103	C₂³	1	2	yes	—
300	C₂₉×#103	C₂³	1	2	yes	—
301	C₂₉×#103	C₂³	1	2	yes	—
302	C₂₉×#102	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×#102	C₂³	1	1	yes	characteristic
305	C₂₉×#102	C₂³	1	1	yes	characteristic
306	C₂₉×#102	C₂³	1	2	yes	—
307	C₂₉×#102	C₂³	1	2	yes	—
308	C₂₉×#102	C₂³	1	2	yes	—
309	C₂₉×#102	C₂³	1	2	yes	—
310	C₂₉×#102	C₂³	1	1	yes	characteristic
311	C₂₉×#102	C₂³	1	1	yes	characteristic
312	C₂₉×#102	C₂³	1	2	yes	—
313	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₂₉×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₂₉	C₂³	1	2	yes	—
321	C₂⁴×C₂₉	—	2	1	no	—
322	C₂⁴×C₂₉	—	2	2	no	—
323	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
324	#41×C₂₉	—	2	2	no	—
325	#41×C₂₉	—	2	2	no	—
326	#41×C₂₉	—	2	4	no	—
327	#41×C₂₉	—	2	4	no	—
328	#41×C₂₉	—	2	4	no	—
329	#41×C₂₉	—	2	2	no	—
330	#41×C₂₉	—	2	2	no	—
331	#41×C₂₉	—	4	2	no	—
332	#41×C₂₉	—	4	2	no	—
333	#41×C₂₉	—	4	2	no	—
334	#41×C₂₉	—	4	4	no	—
335	#41×C₂₉	—	4	4	no	—
336	#41×C₂₉	—	4	4	no	—
337	C₂×Q₈×C₂₉	—	2	1	no	—
338	C₂×Q₈×C₂₉	—	2	1	no	—
339	C₂×Q₈×C₂₉	—	2	2	no	—
340	C₂×Q₈×C₂₉	—	2	2	no	—
341	C₂×Q₈×C₂₉	—	2	2	no	—
342	C₂×Q₈×C₂₉	—	2	2	no	—
343	C₂×Q₈×C₂₉	—	2	2	no	—
344	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
345	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
346	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
347	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₂₉	—	2	4	no	—
349	C₂×D₄×C₂₉	—	2	2	no	—
350	C₂×D₄×C₂₉	—	2	2	no	—
351	C₂×D₄×C₂₉	—	2	1	no	—
352	C₂×D₄×C₂₉	—	2	2	no	—
353	C₂×D₄×C₂₉	—	2	1	no	—
354	C₂×D₄×C₂₉	—	2	1	no	—
355	C₂×D₄×C₂₉	—	2	1	no	—
356	C₂×D₄×C₂₉	—	2	2	no	—
357	C₂×D₄×C₂₉	—	2	2	no	—
358	C₂×D₄×C₂₉	—	4	2	no	—
359	C₂×D₄×C₂₉	—	4	4	no	—
360	C₂×D₄×C₂₉	—	4	8	no	—
361	C₂×D₄×C₂₉	—	4	4	no	—
362	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₂₉	#41	1	4	yes	—
367	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₂₉	—	2	2	no	—
370	C₂²×C₄×C₂₉	—	2	2	no	—
371	C₂²×C₄×C₂₉	—	2	1	no	—
372	C₂²×C₄×C₂₉	—	2	1	no	—
373	C₂²×C₄×C₂₉	—	2	1	no	—
374	C₂²×C₄×C₂₉	—	2	1	no	—
375	C₂²×C₄×C₂₉	—	2	1	no	—
376	C₂²×C₄×C₂₉	—	2	2	no	—
377	C₂²×C₄×C₂₉	—	2	2	no	—
378	C₂²×C₄×C₂₉	—	2	2	no	—
379	C₂²×C₄×C₂₉	—	2	2	no	—
380	C₂²×C₄×C₂₉	—	2	1	no	—
381	C₂²×C₄×C₂₉	—	2	2	no	—
382	C₂²×C₄×C₂₉	—	2	2	no	—
383	C₂²×C₄×C₂₉	—	4	4	no	—
384	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
391	Q₁₆×C₂₉	—	4	2	no	—
392	Q₁₆×C₂₉	—	4	2	no	—
393	Q₁₆×C₂₉	—	4	2	no	—
394	SD₁₆×C₂₉	—	2	4	no	—
395	SD₁₆×C₂₉	—	2	4	no	—
396	SD₁₆×C₂₉	—	4	2	no	—
397	M₁₆×C₂₉	—	2	2	no	—
398	M₁₆×C₂₉	—	2	2	no	—
399	M₁₆×C₂₉	—	4	2	no	—
400	M₁₆×C₂₉	—	4	2	no	—
401	C₂×C₈×C₂₉	—	2	2	no	—
402	C₂×C₈×C₂₉	—	2	2	no	—
403	C₂×C₈×C₂₉	—	4	2	no	—
404	C₂×C₈×C₂₉	—	4	2	no	—
405	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
407	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
408	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₂₉	—	2	1	no	—
412	C₄⋊C₄×C₂₉	—	2	1	no	—
413	C₄⋊C₄×C₂₉	—	2	2	no	—
414	C₄⋊C₄×C₂₉	—	2	2	no	—
415	C₄⋊C₄×C₂₉	—	2	2	no	—
416	C₄⋊C₄×C₂₉	—	2	2	no	—
417	C₄⋊C₄×C₂₉	—	2	2	no	—
418	C₄⋊C₄×C₂₉	—	2	2	no	—
419	C₄⋊C₄×C₂₉	—	2	1	no	—
420	C₄⋊C₄×C₂₉	—	2	1	no	—
421	C₄⋊C₄×C₂₉	—	2	1	no	—
422	C₄⋊C₄×C₂₉	—	2	2	no	—
423	C₄⋊C₄×C₂₉	—	2	2	no	—
424	C₄⋊C₄×C₂₉	—	2	2	no	—
425	C₄⋊C₄×C₂₉	—	2	2	no	—
426	C₄⋊C₄×C₂₉	—	2	2	no	—
427	C₄⋊C₄×C₂₉	—	2	2	no	—
428	C₄⋊C₄×C₂₉	—	2	2	no	—
429	C₄⋊C₄×C₂₉	—	2	2	no	—
430	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
432	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
441	C₂²⋊C₄×C₂₉	—	2	1	no	—
442	C₂²⋊C₄×C₂₉	—	2	1	no	—
443	C₂²⋊C₄×C₂₉	—	2	1	no	—
444	C₂²⋊C₄×C₂₉	—	2	1	no	—
445	C₂²⋊C₄×C₂₉	—	2	1	no	—
446	C₂²⋊C₄×C₂₉	—	2	2	no	—
447	C₂²⋊C₄×C₂₉	—	2	2	no	—
448	C₂²⋊C₄×C₂₉	—	2	2	no	—
449	C₂²⋊C₄×C₂₉	—	2	2	no	—
450	C₂²⋊C₄×C₂₉	—	2	2	no	—
451	C₂²⋊C₄×C₂₉	—	2	2	no	—
452	C₂²⋊C₄×C₂₉	—	2	1	no	—
453	C₂²⋊C₄×C₂₉	—	2	1	no	—
454	C₂²⋊C₄×C₂₉	—	2	2	no	—
455	C₂²⋊C₄×C₂₉	—	2	1	no	—
456	C₂²⋊C₄×C₂₉	—	2	1	no	—
457	C₂²⋊C₄×C₂₉	—	2	2	no	—
458	C₂²⋊C₄×C₂₉	—	2	2	no	—
459	C₂²⋊C₄×C₂₉	—	2	2	no	—
460	C₂²⋊C₄×C₂₉	—	2	2	no	—
461	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
466	C₄²×C₂₉	—	2	1	no	—
467	C₄²×C₂₉	—	2	1	no	—
468	C₄²×C₂₉	—	2	1	no	—
469	C₄²×C₂₉	—	2	1	no	—
470	C₄²×C₂₉	—	2	2	no	—
471	C₄²×C₂₉	—	2	2	no	—
472	C₄²×C₂₉	—	2	2	no	—
473	C₄²×C₂₉	—	2	1	no	—
474	C₄²×C₂₉	C₂⁴	1	2	yes	—
475	#61188	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂³×C₂₉	—	2	2	no	—
477	C₂³×C₂₉	—	2	2	no	—
478	C₂³×C₂₉	—	2	4	no	—
479	C₂³×C₂₉	—	2	1	no	—
480	C₂³×C₂₉	—	4	1	no	—
481	C₂³×C₂₉	—	4	1	no	—
482	C₂³×C₂₉	—	4	4	no	—
483	C₂³×C₂₉	—	8	1	no	—
484	C₂³×C₂₉	—	8	1	no	—
485	C₂³×C₂₉	—	8	2	no	—
486	C₂³×C₂₉	—	8	2	no	—
487	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
488	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
491	Q₈×C₂₉	—	2	2	no	—
492	Q₈×C₂₉	—	2	2	no	—
493	Q₈×C₂₉	—	2	2	no	—
494	Q₈×C₂₉	—	2	1	no	—
495	Q₈×C₂₉	—	2	2	no	—
496	Q₈×C₂₉	—	2	2	no	—
497	Q₈×C₂₉	—	2	1	no	—
498	Q₈×C₂₉	—	4	2	no	—
499	Q₈×C₂₉	—	4	2	no	—
500	Q₈×C₂₉	—	8	2	no	—
501	D₄×C₂₉	—	2	4	no	—
502	D₄×C₂₉	—	2	4	no	—
503	D₄×C₂₉	—	2	2	no	—
504	D₄×C₂₉	—	2	1	no	—
505	D₄×C₂₉	—	2	2	no	—
506	D₄×C₂₉	—	2	1	no	—
507	D₄×C₂₉	—	4	2	no	—
508	D₄×C₂₉	—	4	2	no	—
509	D₄×C₂₉	—	4	4	no	—
510	D₄×C₂₉	—	4	4	no	—
511	D₄×C₂₉	—	4	4	no	—
512	D₄×C₂₉	—	4	4	no	—
513	D₄×C₂₉	—	4	2	no	—
514	D₄×C₂₉	—	8	1	no	—
515	D₄×C₂₉	—	8	1	no	—
516	D₄×C₂₉	C₂×#41	1	4	yes	—
517	C₂×C₄×C₂₉	—	2	2	no	—
518	C₂×C₄×C₂₉	—	2	2	no	—
519	C₂×C₄×C₂₉	—	2	2	no	—
520	C₂×C₄×C₂₉	—	2	1	no	—
521	C₂×C₄×C₂₉	—	2	1	no	—
522	C₂×C₄×C₂₉	—	2	2	no	—
523	C₂×C₄×C₂₉	—	2	1	no	—
524	C₂×C₄×C₂₉	—	2	2	no	—
525	C₂×C₄×C₂₉	—	2	1	no	—
526	C₂×C₄×C₂₉	—	2	1	no	—
527	C₂×C₄×C₂₉	—	2	1	no	—
528	C₂×C₄×C₂₉	—	2	1	no	—
529	C₂×C₄×C₂₉	—	2	2	no	—
530	C₂×C₄×C₂₉	—	2	1	no	—
531	C₂×C₄×C₂₉	—	2	1	no	—
532	C₂×C₄×C₂₉	—	2	1	no	—
533	C₂×C₄×C₂₉	—	2	2	no	—
534	C₂×C₄×C₂₉	—	2	2	no	—
535	C₂×C₄×C₂₉	—	2	1	no	—
536	C₂×C₄×C₂₉	—	4	4	no	—
537	C₂×C₄×C₂₉	—	4	4	no	—
538	C₂×C₄×C₂₉	—	4	4	no	—
539	C₂×C₄×C₂₉	—	4	2	no	—
540	C₂×C₄×C₂₉	—	4	2	no	—
541	C₂×C₄×C₂₉	—	4	2	no	—
542	C₂×C₄×C₂₉	—	4	2	no	—
543	C₂×C₄×C₂₉	—	8	2	no	—
544	C₂×C₄×C₂₉	—	8	2	no	—
545	C₂×C₄×C₂₉	—	8	2	no	—
546	C₂×C₄×C₂₉	—	8	1	no	—
547	C₂×C₄×C₂₉	—	8	1	no	—
548	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
555	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
556	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
557	C₈×C₂₉	—	2	1	no	—
558	C₈×C₂₉	—	2	1	no	—
559	C₈×C₂₉	—	2	1	no	—
560	C₈×C₂₉	—	2	1	no	—
561	C₈×C₂₉	—	2	2	no	—
562	C₈×C₂₉	—	2	2	no	—
563	#3495	C₂×C₂₉	1	1	yes	characteristic, complemented
564	#3485	C₂×C₂₉	1	1	yes	characteristic
565	#3331	C₂×C₂₉	1	2	yes	complemented
566	#3323	C₂×C₂₉	1	2	yes	complemented
567	#3315	C₂×C₂₉	1	2	yes	complemented
568	#3315	C₂×C₂₉	1	2	yes	complemented
569	#3314	C₂×C₂₉	1	2	yes	complemented
570	#3311	C₂×C₂₉	1	2	yes	complemented
571	#3302	C₂×C₂₉	1	2	yes	complemented
572	#3296	C₂×C₂₉	1	2	yes	complemented
573	#3137	C₂×C₂₉	1	1	yes	characteristic, complemented
574	#3097	C₂×C₂₉	1	1	yes	characteristic, complemented
575	#3091	C₂×C₂₉	1	1	yes	characteristic, complemented
576	#3081	C₂×C₂₉	1	1	yes	characteristic, complemented
577	#3059	C₂×C₂₉	1	1	yes	characteristic, complemented
578	#3056	C₂×C₂₉	1	1	yes	characteristic, complemented
579	#3044	C₂×C₂₉	1	1	yes	characteristic, complemented
580	#3009	C₂×C₂₉	1	1	yes	characteristic, complemented
581	C₂×#452	C₂×C₂₉	1	1	yes	characteristic, complemented
582	#2949	C₂×C₂₉	1	1	yes	characteristic, complemented
583	#2933	C₂×C₂₉	1	1	yes	characteristic, complemented
584	#2897	C₂×C₂₉	1	1	yes	characteristic, complemented
585	#2896	C₂×C₂₉	1	1	yes	characteristic, complemented
586	C₂²×C₂₉	—	2	1	no	—
587	C₂²×C₂₉	—	2	1	no	—
588	C₂²×C₂₉	—	2	2	no	—
589	C₂²×C₂₉	—	2	1	no	—
590	C₂²×C₂₉	—	2	1	no	—
591	C₂²×C₂₉	—	2	1	no	—
592	C₂²×C₂₉	—	2	2	no	—
593	C₂²×C₂₉	—	2	1	no	—
594	C₂²×C₂₉	—	2	1	no	—
595	C₂²×C₂₉	—	2	1	no	—
596	C₂²×C₂₉	—	2	2	no	—
597	C₂²×C₂₉	—	2	4	no	—
598	C₂²×C₂₉	—	4	2	no	—
599	C₂²×C₂₉	—	4	2	no	—
600	C₂²×C₂₉	—	4	1	no	—
601	C₂²×C₂₉	—	4	1	no	—
602	C₂²×C₂₉	—	4	1	no	—
603	C₂²×C₂₉	—	8	2	no	—
604	C₂²×C₂₉	—	8	4	no	—
605	C₂²×C₂₉	—	16	4	no	—
606	C₂²×C₂₉	#546	1	2	yes	—
607	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₂₉	—	2	2	no	—
609	C₄×C₂₉	—	2	2	no	—
610	C₄×C₂₉	—	2	1	no	—
611	C₄×C₂₉	—	2	1	no	—
612	C₄×C₂₉	—	2	2	no	—
613	C₄×C₂₉	—	4	1	no	—
614	C₄×C₂₉	—	4	1	no	—
615	C₄×C₂₉	—	4	2	no	—
616	C₄×C₂₉	—	4	1	no	—
617	C₄×C₂₉	—	4	1	no	—
618	C₄×C₂₉	—	4	1	no	—
619	C₄×C₂₉	—	4	1	no	—
620	C₄×C₂₉	—	4	1	no	—
621	C₄×C₂₉	—	4	2	no	—
622	C₄×C₂₉	—	4	2	no	—
623	C₄×C₂₉	#546	1	2	yes	—
624	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
625	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic
627	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
628	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
629	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
630	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
631	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
632	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
633	#556	C₂²×C₂₉	1	2	yes	complemented
634	#554	C₂²×C₂₉	1	2	yes	complemented
635	#552	—	2	2	no	—
636	#552	C₂²×C₂₉	1	2	yes	complemented
637	#552	C₂²×C₂₉	1	2	yes	complemented
638	#551	—	2	2	no	—
639	#547	—	2	1	no	—
640	#547	—	2	1	no	—
641	#547	C₂²×C₂₉	1	2	yes	—
642	#547	C₂²×C₂₉	1	2	yes	—
643	#546	—	2	1	no	—
644	#546	—	2	1	no	—
645	#546	C₂²×C₂₉	1	2	yes	—
646	#546	C₂²×C₂₉	1	2	yes	—
647	#544	C₂²×C₂₉	1	1	yes	characteristic, complemented
648	#542	—	2	1	no	—
649	#541	—	2	1	no	—
650	#536	C₂²×C₂₉	1	1	yes	characteristic
651	#536	C₂²×C₂₉	1	1	yes	characteristic
652	#536	C₂²×C₂₉	1	1	yes	characteristic
653	#534	—	2	2	no	—
654	#533	—	2	1	no	—
655	#529	—	2	1	no	—
656	#525	C₂²×C₂₉	1	1	yes	characteristic
657	#525	C₂²×C₂₉	1	1	yes	characteristic
658	C₂×#123	—	2	2	no	—
659	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
660	#520	C₂²×C₂₉	1	1	yes	characteristic
661	#519	C₂²×C₂₉	1	1	yes	characteristic, complemented
662	#518	C₂²×C₂₉	1	1	yes	characteristic
663	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic, complemented
664	#491	C₂²×C₂₉	1	2	yes	complemented
665	#489	C₂²×C₂₉	1	2	yes	complemented
666	#488	C₂²×C₂₉	1	2	yes	complemented
667	#487	C₂²×C₂₉	1	2	yes	complemented
668	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
669	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
670	#485	C₂²×C₂₉	1	2	yes	complemented
671	#485	C₂²×C₂₉	1	2	yes	complemented
672	#484	C₂²×C₂₉	1	1	yes	characteristic, complemented
673	#484	C₂²×C₂₉	1	2	yes	complemented
674	#483	C₂²×C₂₉	1	1	yes	characteristic, complemented
675	#483	C₂²×C₂₉	1	2	yes	complemented
676	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
677	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	#481	C₂²×C₂₉	1	1	yes	characteristic, complemented
679	#480	C₂²×C₂₉	1	1	yes	characteristic, complemented
680	#478	C₂²×C₂₉	1	2	yes	complemented
681	#478	C₂²×C₂₉	1	2	yes	complemented
682	#476	C₂²×C₂₉	1	2	yes	complemented
683	#474	C₂²×C₂₉	1	2	yes	complemented
684	#470	C₂²×C₂₉	1	2	yes	complemented
685	#470	C₂²×C₂₉	1	2	yes	complemented
686	#470	C₂²×C₂₉	1	2	yes	complemented
687	#468	C₂²×C₂₉	1	2	yes	complemented
688	#467	C₂²×C₂₉	1	2	yes	complemented
689	#467	C₂²×C₂₉	1	2	yes	complemented
690	#467	C₂²×C₂₉	1	2	yes	complemented
691	#465	C₂²×C₂₉	1	2	yes	complemented
692	#464	C₂²×C₂₉	1	2	yes	complemented
693	#464	C₂²×C₂₉	1	2	yes	complemented
694	#462	C₂²×C₂₉	1	2	yes	complemented
695	#462	C₂²×C₂₉	1	2	yes	complemented
696	#452	C₂²×C₂₉	1	2	yes	complemented
697	#452	C₂²×C₂₉	1	2	yes	complemented
698	#452	C₂²×C₂₉	1	2	yes	complemented
699	#452	C₂²×C₂₉	1	2	yes	complemented
700	#452	C₂²×C₂₉	1	2	yes	complemented
701	#452	C₂²×C₂₉	1	2	yes	complemented
702	#450	C₂²×C₂₉	1	2	yes	complemented
703	#450	C₂²×C₂₉	1	2	yes	complemented
704	#440	C₂²×C₂₉	1	2	yes	complemented
705	#440	C₂²×C₂₉	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
707	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
708	#436	C₂²×C₂₉	1	2	yes	complemented
709	#435	C₂²×C₂₉	1	2	yes	complemented
710	#435	C₂²×C₂₉	1	2	yes	complemented
711	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
712	#428	C₂²×C₂₉	1	1	yes	characteristic, complemented
713	#427	C₂²×C₂₉	1	1	yes	characteristic, complemented
714	#427	C₂²×C₂₉	1	1	yes	characteristic, complemented
715	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
716	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
717	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
718	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
719	#418	C₂²×C₂₉	1	1	yes	characteristic
720	#418	C₂²×C₂₉	1	1	yes	characteristic
721	#418	C₂²×C₂₉	1	2	yes	complemented
722	#417	C₂²×C₂₉	1	1	yes	characteristic
723	#417	C₂²×C₂₉	1	2	yes	complemented
724	#417	C₂²×C₂₉	1	2	yes	complemented
725	#417	C₂²×C₂₉	1	2	yes	complemented
726	#416	C₂²×C₂₉	1	1	yes	characteristic
727	#416	C₂²×C₂₉	1	1	yes	characteristic
728	#416	C₂²×C₂₉	1	2	yes	complemented
729	#416	C₂²×C₂₉	1	2	yes	complemented
730	#416	C₂²×C₂₉	1	2	yes	complemented
731	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
732	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
733	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
734	#408	C₂²×C₂₉	1	1	yes	characteristic
735	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
736	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
737	C₂×C₂₉	—	2	2	no	—
738	C₂×C₂₉	—	4	1	no	—
739	C₂×C₂₉	—	4	1	no	—
740	C₂×C₂₉	—	4	2	no	—
741	C₂×C₂₉	—	4	4	no	—
742	C₂×C₂₉	—	8	1	no	—
743	C₂×C₂₉	C₂×#546	1	1	yes	characteristic
744	C₂×C₂₉	#3584	1	1	yes	characteristic
745	C₂×C₂₉	#3586	1	1	yes	characteristic
746	H(5,𝔽₂)	—	2	4	no	—
747	H(5,𝔽₂)	—	4	2	no	—
748	C₂×#41	—	2	1	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	4	no	—
752	C₂×#41	—	4	2	no	—
753	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
754	C₂×#41	C₂³×C₂₉	1	2	yes	—
755	C₂×#41	C₂³×C₂₉	1	2	yes	—
756	C₂×#41	C₂³×C₂₉	1	2	yes	—
757	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
758	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
759	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	—	2	2	no	—
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
764	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
765	C₂³×C₄	—	2	1	no	—
766	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
767	#137	—	4	2	no	—
768	C₂×Q₁₆	—	4	2	no	—
769	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
770	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
772	C₂×SD₁₆	—	2	4	no	—
773	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
776	#131	—	4	2	no	—
777	C₂×M₁₆	—	4	2	no	—
778	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
779	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
780	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
781	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
782	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
783	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
784	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
785	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
790	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
791	#126	—	2	2	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#125	—	2	1	no	—
796	#125	—	2	2	no	—
797	#125	—	2	2	no	—
798	#125	—	2	2	no	—
799	#125	C₂³×C₂₉	1	2	yes	—
800	#124	—	2	1	no	—
801	#124	—	2	1	no	—
802	#124	—	2	2	no	—
803	#124	C₂³×C₂₉	1	2	yes	—
804	#123	—	2	2	no	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	1	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	D₄×C₂₉	1	2	yes	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
825	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
826	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
828	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
829	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	D₄×C₂₉	1	1	yes	characteristic
839	#121	D₄×C₂₉	1	1	yes	characteristic
840	#121	C₂³×C₂₉	1	1	yes	characteristic
841	#121	C₂³×C₂₉	1	1	yes	characteristic
842	#120	—	2	1	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	D₄×C₂₉	1	2	yes	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	2	no	—
850	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
851	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	C₂³×C₂₉	1	2	yes	—
860	C₄×D₄	C₂³×C₂₉	1	2	yes	—
861	C₄×D₄	C₂³×C₂₉	1	2	yes	—
862	C₄×D₄	C₂³×C₂₉	1	2	yes	—
863	#117	—	2	1	no	—
864	#117	—	2	1	no	—
865	#117	—	2	2	no	—
866	#117	—	2	2	no	—
867	#117	—	2	2	no	—
868	#117	C₂³×C₂₉	1	1	yes	characteristic
869	#117	C₂³×C₂₉	1	1	yes	characteristic
870	#117	C₂³×C₂₉	1	1	yes	characteristic
871	#117	C₂³×C₂₉	1	1	yes	characteristic
872	#117	C₂³×C₂₉	1	1	yes	characteristic
873	#117	C₂³×C₂₉	1	2	yes	—
874	#117	C₂³×C₂₉	1	1	yes	characteristic
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	2	no	—
877	C₂×C₄⋊C₄	—	2	2	no	—
878	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
882	C₂×C₂²⋊C₄	—	2	1	no	—
883	C₂×C₂²⋊C₄	—	2	1	no	—
884	C₂×C₂²⋊C₄	—	2	2	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₄²	—	2	1	no	—
888	#107	C₂³×C₂₉	1	1	yes	characteristic
889	#107	C₂³×C₂₉	1	1	yes	characteristic
890	#107	C₂³×C₂₉	1	1	yes	characteristic
891	#107	C₂³×C₂₉	1	1	yes	characteristic
892	#107	C₂³×C₂₉	1	2	yes	—
893	#106	C₂³×C₂₉	1	1	yes	characteristic
894	#106	C₂³×C₂₉	1	1	yes	characteristic
895	#106	C₂³×C₂₉	1	1	yes	characteristic
896	#106	C₂³×C₂₉	1	1	yes	characteristic
897	#106	C₂³×C₂₉	1	2	yes	—
898	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
899	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
900	#103	C₂³×C₂₉	1	2	yes	—
901	#103	C₂³×C₂₉	1	2	yes	—
902	#103	C₂³×C₂₉	1	1	yes	characteristic
903	#103	C₂³×C₂₉	1	1	yes	characteristic
904	#103	C₂³×C₂₉	1	1	yes	characteristic
905	#103	C₂³×C₂₉	1	1	yes	characteristic
906	#103	C₂³×C₂₉	1	2	yes	—
907	#103	C₂³×C₂₉	1	2	yes	—
908	#103	C₂³×C₂₉	1	2	yes	—
909	#103	C₂³×C₂₉	1	2	yes	—
910	#103	C₂³×C₂₉	1	2	yes	—
911	#103	C₂³×C₂₉	1	2	yes	—
912	#103	C₂³×C₂₉	1	2	yes	—
913	#102	C₂³×C₂₉	1	2	yes	—
914	#102	C₂³×C₂₉	1	2	yes	—
915	#102	C₂³×C₂₉	1	1	yes	characteristic
916	#102	C₂³×C₂₉	1	2	yes	—
917	#102	C₂³×C₂₉	1	2	yes	—
918	#102	C₂³×C₂₉	1	1	yes	characteristic
919	#102	C₂³×C₂₉	1	1	yes	characteristic
920	#102	C₂³×C₂₉	1	1	yes	characteristic
921	#102	C₂³×C₂₉	1	2	yes	—
922	#102	C₂³×C₂₉	1	2	yes	—
923	#102	C₂³×C₂₉	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
925	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
926	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
930	#97	C₂³×C₂₉	1	2	yes	—
931	C₄×C₈	C₂³×C₂₉	1	2	yes	—
932	C₂₉	#61188	1	1	yes	characteristic, direct product factor, Sylow
933	C₂⁴	—	2	1	no	—
934	C₂⁴	—	2	2	no	—
935	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	2	4	no	—
939	#41	—	2	4	no	—
940	#41	—	2	4	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	4	2	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	4	no	—
947	#41	—	4	4	no	—
948	#41	—	4	4	no	—
949	C₂×Q₈	—	2	1	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
959	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
960	C₂×D₄	—	2	4	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	4	no	—
972	C₂×D₄	—	4	8	no	—
973	C₂×D₄	—	4	4	no	—
974	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
975	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
976	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
977	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
978	C₂×D₄	#41×C₂₉	1	4	yes	—
979	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	4	4	no	—
996	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
1001	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	Q₁₆	—	4	2	no	—
1006	SD₁₆	—	2	4	no	—
1007	SD₁₆	—	2	4	no	—
1008	SD₁₆	—	4	2	no	—
1009	M₁₆	—	2	2	no	—
1010	M₁₆	—	2	2	no	—
1011	M₁₆	—	4	2	no	—
1012	M₁₆	—	4	2	no	—
1013	C₂×C₈	—	2	2	no	—
1014	C₂×C₈	—	2	2	no	—
1015	C₂×C₈	—	4	2	no	—
1016	C₂×C₈	—	4	2	no	—
1017	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1043	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1044	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1047	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	C₂⁴×C₂₉	1	2	yes	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	4	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	4	1	no	—
1092	C₂³	—	4	1	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	8	1	no	—
1095	C₂³	—	8	1	no	—
1096	C₂³	—	8	2	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1099	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1100	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1101	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	2	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	4	2	no	—
1110	Q₈	—	4	2	no	—
1111	Q₈	—	8	2	no	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	8	1	no	—
1126	D₄	—	8	1	no	—
1127	D₄	C₂×#41×C₂₉	1	4	yes	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1160	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1162	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1165	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
1166	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1167	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	1	no	—
1171	C₈	—	2	1	no	—
1172	C₈	—	2	2	no	—
1173	C₈	—	2	2	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	4	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	8	2	no	—
1192	C₂²	—	8	4	no	—
1193	C₂²	—	16	4	no	—
1194	C₂²	C₂₉×#546	1	2	yes	—
1195	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	C₂₉×#546	1	2	yes	—
1212	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1213	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1214	C₂	—	2	2	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	1	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	4	no	—
1219	C₂	—	8	1	no	—
1220	C₂	C₂×C₂₉×#546	1	1	yes	characteristic
1221	C₂	C₂₉×#3584	1	1	yes	characteristic
1222	C₂	C₂₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3485	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3495	C₂	semidirect
3. C₂₉×#3331	C₂	semidirect
4. C₂₉×#3323	C₂	semidirect
5. C₂₉×#3315	C₂	semidirect
6. C₂₉×#3315	C₂	semidirect
7. C₂₉×#3314	C₂	semidirect
8. C₂₉×#3311	C₂	semidirect
9. C₂₉×#3302	C₂	semidirect
10. C₂₉×#3296	C₂	semidirect
11. C₂₉×#3137	C₂	semidirect
12. C₂₉×#3097	C₂	semidirect
13. C₂₉×#3091	C₂	semidirect
14. C₂₉×#3081	C₂	semidirect
15. C₂₉×#3059	C₂	semidirect
16. C₂₉×#3056	C₂	semidirect
17. C₂₉×#3044	C₂	semidirect
18. C₂₉×#3009	C₂	semidirect
19. C₂×C₂₉×#452	C₂	semidirect
20. C₂₉×#2949	C₂	semidirect
21. C₂₉×#2933	C₂	semidirect
22. C₂₉×#2897	C₂	semidirect
23. C₂₉×#2896	C₂	semidirect
27. C₂²×Q₁₆×C₂₉	C₂²	semidirect
30. C₂²×M₁₆×C₂₉	C₂²	semidirect
31. C₂₉×#556	C₂²	semidirect
32. C₂₉×#554	C₂²	semidirect
34. C₂₉×#552	C₂²	semidirect
35. C₂₉×#552	C₂²	semidirect
45. C₂₉×#544	C₂²	semidirect
57. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
59. C₂₉×#519	C₂²	semidirect
61. C₂×C₂₉×#117	C₂²	semidirect
62. C₂₉×#491	C₂²	semidirect
63. C₂₉×#489	C₂²	semidirect
64. C₂₉×#488	C₂²	semidirect
65. C₂₉×#487	C₂²	semidirect
66. C₂₉×#485	C₂²	semidirect
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
69. C₂₉×#485	C₂²	semidirect
70. C₂₉×#484	C₂²	semidirect
71. C₂₉×#484	C₂²	semidirect
72. C₂₉×#483	C₂²	semidirect
73. C₂₉×#483	C₂²	semidirect
74. C₂₉×#482	C₂²	semidirect
75. C₂₉×#482	C₂²	semidirect
76. C₂₉×#481	C₂²	semidirect
77. C₂₉×#480	C₂²	semidirect
78. C₂₉×#478	C₂²	semidirect
79. C₂₉×#478	C₂²	semidirect
80. C₂₉×#476	C₂²	semidirect
81. C₂₉×#474	C₂²	semidirect
82. C₂₉×#470	C₂²	semidirect
83. C₂₉×#470	C₂²	semidirect
84. C₂₉×#470	C₂²	semidirect
85. C₂₉×#468	C₂²	semidirect
86. C₂₉×#467	C₂²	semidirect
87. C₂₉×#467	C₂²	semidirect
88. C₂₉×#467	C₂²	semidirect
89. C₂₉×#465	C₂²	semidirect
90. C₂₉×#464	C₂²	semidirect
91. C₂₉×#464	C₂²	semidirect
92. C₂₉×#462	C₂²	semidirect
93. C₂₉×#462	C₂²	semidirect
94. C₂₉×#452	C₂²	semidirect
95. C₂₉×#452	C₂²	semidirect
96. C₂₉×#452	C₂²	semidirect
97. C₂₉×#452	C₂²	semidirect
98. C₂₉×#452	C₂²	semidirect
99. C₂₉×#452	C₂²	semidirect
100. C₂₉×#450	C₂²	semidirect
101. C₂₉×#450	C₂²	semidirect
102. C₂₉×#440	C₂²	semidirect
103. C₂₉×#440	C₂²	semidirect
104. C₄×SD₁₆×C₂₉	C₂²	semidirect
105. C₄×SD₁₆×C₂₉	C₂²	semidirect
106. C₂₉×#436	C₂²	semidirect
107. C₂₉×#435	C₂²	semidirect
108. C₂₉×#435	C₂²	semidirect
109. C₈×D₄×C₂₉	C₂²	semidirect
110. C₂₉×#428	C₂²	semidirect
111. C₂₉×#427	C₂²	semidirect
112. C₂₉×#427	C₂²	semidirect
113. C₂₉×#424	C₂²	semidirect
114. C₂₉×#419	C₂²	semidirect
115. C₂₉×#419	C₂²	semidirect
116. C₂₉×#419	C₂²	semidirect
119. C₂₉×#418	C₂²	semidirect
121. C₂₉×#417	C₂²	semidirect
122. C₂₉×#417	C₂²	semidirect
123. C₂₉×#417	C₂²	semidirect
126. C₂₉×#416	C₂²	semidirect
127. C₂₉×#416	C₂²	semidirect
128. C₂₉×#416	C₂²	semidirect
129. C₂×C₂₉×#103	C₂²	semidirect
131. C₂×C₂₉×#102	C₂²	semidirect
133. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
134. C₂₉×#405	C₂²	semidirect
475. #61188	C₂₉	direct (N × H)
563. #3495	C₂×C₂₉	semidirect
565. #3331	C₂×C₂₉	semidirect
566. #3323	C₂×C₂₉	semidirect
567. #3315	C₂×C₂₉	semidirect
568. #3315	C₂×C₂₉	semidirect
569. #3314	C₂×C₂₉	semidirect
570. #3311	C₂×C₂₉	semidirect
571. #3302	C₂×C₂₉	semidirect
572. #3296	C₂×C₂₉	semidirect
573. #3137	C₂×C₂₉	semidirect
574. #3097	C₂×C₂₉	semidirect
575. #3091	C₂×C₂₉	semidirect
576. #3081	C₂×C₂₉	semidirect
577. #3059	C₂×C₂₉	semidirect
578. #3056	C₂×C₂₉	semidirect
579. #3044	C₂×C₂₉	semidirect
580. #3009	C₂×C₂₉	semidirect
581. C₂×#452	C₂×C₂₉	semidirect
582. #2949	C₂×C₂₉	semidirect
583. #2933	C₂×C₂₉	semidirect
584. #2897	C₂×C₂₉	semidirect
585. #2896	C₂×C₂₉	semidirect
629. C₂²×Q₁₆	C₂²×C₂₉	semidirect
632. C₂²×M₁₆	C₂²×C₂₉	semidirect
633. #556	C₂²×C₂₉	semidirect
634. #554	C₂²×C₂₉	semidirect
636. #552	C₂²×C₂₉	semidirect
637. #552	C₂²×C₂₉	semidirect
647. #544	C₂²×C₂₉	semidirect
659. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
661. #519	C₂²×C₂₉	semidirect
663. C₂×#117	C₂²×C₂₉	semidirect
664. #491	C₂²×C₂₉	semidirect
665. #489	C₂²×C₂₉	semidirect
666. #488	C₂²×C₂₉	semidirect
667. #487	C₂²×C₂₉	semidirect
668. #485	C₂²×C₂₉	semidirect
669. #485	C₂²×C₂₉	semidirect
670. #485	C₂²×C₂₉	semidirect
671. #485	C₂²×C₂₉	semidirect
672. #484	C₂²×C₂₉	semidirect
673. #484	C₂²×C₂₉	semidirect
674. #483	C₂²×C₂₉	semidirect
675. #483	C₂²×C₂₉	semidirect
676. #482	C₂²×C₂₉	semidirect
677. #482	C₂²×C₂₉	semidirect
678. #481	C₂²×C₂₉	semidirect
679. #480	C₂²×C₂₉	semidirect
680. #478	C₂²×C₂₉	semidirect
681. #478	C₂²×C₂₉	semidirect
682. #476	C₂²×C₂₉	semidirect
683. #474	C₂²×C₂₉	semidirect
684. #470	C₂²×C₂₉	semidirect
685. #470	C₂²×C₂₉	semidirect
686. #470	C₂²×C₂₉	semidirect
687. #468	C₂²×C₂₉	semidirect
688. #467	C₂²×C₂₉	semidirect
689. #467	C₂²×C₂₉	semidirect
690. #467	C₂²×C₂₉	semidirect
691. #465	C₂²×C₂₉	semidirect
692. #464	C₂²×C₂₉	semidirect
693. #464	C₂²×C₂₉	semidirect
694. #462	C₂²×C₂₉	semidirect
695. #462	C₂²×C₂₉	semidirect
696. #452	C₂²×C₂₉	semidirect
697. #452	C₂²×C₂₉	semidirect
698. #452	C₂²×C₂₉	semidirect
699. #452	C₂²×C₂₉	semidirect
700. #452	C₂²×C₂₉	semidirect
701. #452	C₂²×C₂₉	semidirect
702. #450	C₂²×C₂₉	semidirect
703. #450	C₂²×C₂₉	semidirect
704. #440	C₂²×C₂₉	semidirect
705. #440	C₂²×C₂₉	semidirect
706. C₄×SD₁₆	C₂²×C₂₉	semidirect
707. C₄×SD₁₆	C₂²×C₂₉	semidirect
708. #436	C₂²×C₂₉	semidirect
709. #435	C₂²×C₂₉	semidirect
710. #435	C₂²×C₂₉	semidirect
711. C₈×D₄	C₂²×C₂₉	semidirect
712. #428	C₂²×C₂₉	semidirect
713. #427	C₂²×C₂₉	semidirect
714. #427	C₂²×C₂₉	semidirect
715. #424	C₂²×C₂₉	semidirect
716. #419	C₂²×C₂₉	semidirect
717. #419	C₂²×C₂₉	semidirect
718. #419	C₂²×C₂₉	semidirect
721. #418	C₂²×C₂₉	semidirect
723. #417	C₂²×C₂₉	semidirect
724. #417	C₂²×C₂₉	semidirect
725. #417	C₂²×C₂₉	semidirect
728. #416	C₂²×C₂₉	semidirect
729. #416	C₂²×C₂₉	semidirect
730. #416	C₂²×C₂₉	semidirect
731. C₂×#103	C₂²×C₂₉	semidirect
733. C₂×#102	C₂²×C₂₉	semidirect
735. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
736. #405	C₂²×C₂₉	semidirect
932. C₂₉	#61188	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×#3495	2
C₂₉×#3485	2
C₂₉×#3331	2
C₂₉×#3323	2
C₂₉×#3315	2
C₂₉×#3314	2
C₂₉×#3311	2
C₂₉×#3302	2
C₂₉×#3296	2
C₂₉×#3137	2
C₂₉×#3097	2
C₂₉×#3091	2
C₂₉×#3081	2
C₂₉×#3059	2
C₂₉×#3056	2
C₂₉×#3044	2
C₂₉×#3009	2
C₂×C₂₉×#452	2
C₂₉×#2949	2
C₂₉×#2933	2
C₂₉×#2897	2
C₂₉×#2896	2
#61188	29

Subgroups — C29×#61188 #20356088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61188 #20356088