Subgroups — C₂₉×#61191 #20356091

Order 7424.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3333	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3322	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3314	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3310	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3309	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3308	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3300	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3294	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#2951	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	C₂×C₂₉×#417	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×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
31	C₂₉×#554	—	2	1	no	—
32	C₂₉×#554	C₂²	1	2	yes	complemented
33	C₂₉×#553	—	2	1	no	—
34	C₂₉×#553	C₂²	1	2	yes	complemented
35	C₂₉×#552	—	2	1	no	—
36	C₂₉×#552	C₂²	1	2	yes	complemented
37	C₂₉×#550	C₂²	1	2	yes	—
38	C₂₉×#548	C₂²	1	2	yes	—
39	C₂₉×#547	—	2	1	no	—
40	C₂₉×#547	C₂²	1	2	yes	complemented
41	C₂₉×#546	—	2	2	no	—
42	C₂₉×#546	C₂²	1	2	yes	—
43	D₄²×C₂₉	—	2	2	no	—
44	D₄²×C₂₉	C₂²	1	2	yes	—
45	C₂₉×#544	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#539	—	2	2	no	—
47	C₂₉×#537	—	2	1	no	—
48	C₂₉×#537	C₂²	1	1	yes	characteristic
49	C₂₉×#537	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#535	—	2	1	no	—
51	C₂₉×#535	C₂²	1	1	yes	characteristic
52	C₂₉×#525	—	2	1	no	—
53	C₂₉×#525	—	2	2	no	—
54	C₂₉×#525	C₂²	1	1	yes	characteristic
55	C₂₉×#525	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂₉×#121	—	2	1	no	—
57	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
58	C₂₉×#520	C₂²	1	1	yes	characteristic
59	C₂₉×#520	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#490	C₂²	1	2	yes	complemented
63	C₂₉×#489	C₂²	1	2	yes	complemented
64	C₂₉×#488	C₂²	1	2	yes	complemented
65	C₂₉×#486	C₂²	1	2	yes	complemented
66	C₂₉×#485	C₂²	1	2	yes	complemented
67	C₂₉×#484	C₂²	1	2	yes	complemented
68	C₂₉×#482	C₂²	1	2	yes	complemented
69	C₂₉×#480	C₂²	1	2	yes	complemented
70	C₂₉×#480	C₂²	1	2	yes	complemented
71	C₂₉×#480	C₂²	1	2	yes	complemented
72	C₂₉×#480	C₂²	1	2	yes	complemented
73	C₂₉×#480	C₂²	1	2	yes	complemented
74	C₂₉×#479	C₂²	1	2	yes	complemented
75	C₂₉×#478	C₂²	1	2	yes	complemented
76	C₂₉×#477	C₂²	1	2	yes	complemented
77	C₂₉×#474	C₂²	1	2	yes	complemented
78	C₂₉×#469	C₂²	1	2	yes	complemented
79	C₂₉×#468	C₂²	1	2	yes	complemented
80	C₂₉×#468	C₂²	1	2	yes	complemented
81	C₂₉×#468	C₂²	1	2	yes	complemented
82	C₂₉×#467	C₂²	1	2	yes	complemented
83	C₂₉×#466	C₂²	1	2	yes	complemented
84	C₂₉×#466	C₂²	1	2	yes	complemented
85	C₂₉×#465	C₂²	1	2	yes	complemented
86	C₂₉×#464	C₂²	1	2	yes	complemented
87	C₂₉×#463	C₂²	1	2	yes	complemented
88	C₂₉×#460	C₂²	1	2	yes	complemented
89	C₂₉×#459	C₂²	1	2	yes	complemented
90	C₂₉×#452	C₂²	1	1	yes	characteristic, complemented
91	C₂₉×#452	C₂²	1	1	yes	characteristic, complemented
92	C₂₉×#452	C₂²	1	2	yes	complemented
93	C₂₉×#451	C₂²	1	1	yes	characteristic, complemented
94	C₂₉×#450	C₂²	1	1	yes	characteristic, complemented
95	C₂₉×#450	C₂²	1	2	yes	complemented
96	C₂₉×#449	C₂²	1	1	yes	characteristic, complemented
97	C₂₉×#449	C₂²	1	1	yes	characteristic, complemented
98	C₂₉×#449	C₂²	1	2	yes	complemented
99	C₂₉×#448	C₂²	1	1	yes	characteristic, complemented
100	C₂₉×#447	C₂²	1	1	yes	characteristic, complemented
101	C₂₉×#447	C₂²	1	2	yes	complemented
102	C₂₉×#440	C₂²	1	2	yes	complemented
103	C₂₉×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
105	C₄×D₈×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	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
114	C₂₉×#418	C₂²	1	2	yes	complemented
115	C₂₉×#418	C₂²	1	1	yes	characteristic, complemented
116	C₂₉×#417	C₂²	1	1	yes	characteristic
117	C₂₉×#417	C₂²	1	1	yes	characteristic
118	C₂₉×#417	C₂²	1	1	yes	characteristic, complemented
119	C₂₉×#417	C₂²	1	1	yes	characteristic, complemented
120	C₂₉×#417	C₂²	1	2	yes	complemented
121	C₂₉×#417	C₂²	1	2	yes	complemented
122	C₂₉×#417	C₂²	1	2	yes	complemented
123	C₂₉×#417	C₂²	1	1	yes	characteristic, complemented
124	C₂₉×#416	C₂²	1	1	yes	characteristic
125	C₂₉×#416	C₂²	1	1	yes	characteristic, complemented
126	C₂₉×#416	C₂²	1	2	yes	complemented
127	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
128	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
130	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
131	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
132	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
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	2	no	—
139	C₂×#41×C₂₉	—	2	1	no	—
140	C₂×#41×C₂₉	—	2	1	no	—
141	C₂×#41×C₂₉	—	2	4	no	—
142	C₂×#41×C₂₉	—	4	2	no	—
143	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
144	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
145	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₉	C₂³	1	2	yes	—
147	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
148	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
149	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
151	C₂²×D₄×C₂₉	—	2	1	no	—
152	C₂²×D₄×C₂₉	—	2	1	no	—
153	C₂²×D₄×C₂₉	—	2	1	no	—
154	C₂²×D₄×C₂₉	—	2	2	no	—
155	C₂²×D₄×C₂₉	—	2	2	no	—
156	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
158	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
159	C₂³×C₄×C₂₉	—	2	1	no	—
160	C₂³×C₄×C₂₉	—	2	1	no	—
161	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
162	C₂₉×AGL(1,ℤ/8)	—	4	2	no	—
163	C₂₉×#135	—	2	4	no	—
164	C₂₉×#135	—	4	2	no	—
165	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
166	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
168	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
170	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
171	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
172	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
173	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
174	C₂×D₈×C₂₉	C₂³	1	2	yes	—
175	C₂₉×#131	—	4	2	no	—
176	C₂×M₁₆×C₂₉	—	4	2	no	—
177	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
178	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
179	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
180	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
181	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
182	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
183	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
184	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
185	C₂₉×C₄⋊Q₈	—	2	1	no	—
186	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
187	C₂₉×#127	—	2	2	no	—
188	C₂₉×#127	C₂³	1	2	yes	—
189	C₂₉×#126	—	2	2	no	—
190	C₂₉×#126	—	2	2	no	—
191	C₂₉×#125	—	2	2	no	—
192	C₂₉×#125	—	2	2	no	—
193	C₂₉×#125	—	2	1	no	—
194	C₂₉×#125	C₂³	1	2	yes	—
195	C₂₉×#124	—	2	2	no	—
196	C₂₉×#124	C₂³	1	2	yes	—
197	C₂₉×#123	—	2	2	no	—
198	C₂₉×#123	—	2	1	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	D₄	1	2	yes	—
204	C₂₉×C₂²⋊Q₈	—	2	1	no	—
205	C₂₉×C₂²⋊Q₈	—	2	1	no	—
206	C₂₉×C₂²⋊Q₈	—	2	2	no	—
207	C₂₉×C₂²⋊Q₈	—	2	2	no	—
208	C₂₉×C₂²⋊Q₈	—	2	2	no	—
209	C₂₉×C₂²⋊Q₈	—	2	2	no	—
210	C₂₉×C₂²⋊Q₈	—	2	2	no	—
211	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
213	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₉×#121	—	2	1	no	—
218	C₂₉×#121	—	2	2	no	—
219	C₂₉×#121	—	2	2	no	—
220	C₂₉×#121	—	2	2	no	—
221	C₂₉×#121	—	2	2	no	—
222	C₂₉×#121	—	2	1	no	—
223	C₂₉×#121	—	2	1	no	—
224	C₂₉×#121	—	2	1	no	—
225	C₂₉×#121	—	2	1	no	—
226	C₂₉×#121	—	2	1	no	—
227	C₂₉×#121	—	2	2	no	—
228	C₂₉×#121	—	2	2	no	—
229	C₂₉×#121	—	2	2	no	—
230	C₂₉×#121	—	2	2	no	—
231	C₂₉×#121	D₄	1	1	yes	characteristic
232	C₂₉×#121	D₄	1	1	yes	characteristic
233	C₂₉×#121	C₂³	1	1	yes	characteristic
234	C₂₉×#121	C₂³	1	2	yes	—
235	C₂₉×#121	C₂³	1	1	yes	characteristic
236	C₂₉×#121	C₂³	1	2	yes	—
237	C₂₉×#121	C₂³	1	2	yes	—
238	C₂₉×#121	C₂³	1	2	yes	—
239	C₂₉×#120	—	2	1	no	—
240	C₂₉×#120	—	2	2	no	—
241	C₂₉×#120	—	2	2	no	—
242	C₂₉×#120	—	2	2	no	—
243	C₂₉×#120	—	2	2	no	—
244	C₂₉×#120	D₄	1	2	yes	—
245	C₄×Q₈×C₂₉	—	2	1	no	—
246	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
247	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
248	C₄×D₄×C₂₉	—	2	2	no	—
249	C₄×D₄×C₂₉	—	2	1	no	—
250	C₄×D₄×C₂₉	—	2	2	no	—
251	C₄×D₄×C₂₉	—	2	1	no	—
252	C₄×D₄×C₂₉	—	2	1	no	—
253	C₄×D₄×C₂₉	—	2	2	no	—
254	C₄×D₄×C₂₉	—	2	2	no	—
255	C₄×D₄×C₂₉	—	2	2	no	—
256	C₄×D₄×C₂₉	—	2	2	no	—
257	C₄×D₄×C₂₉	—	2	2	no	—
258	C₄×D₄×C₂₉	C₂³	1	2	yes	—
259	C₄×D₄×C₂₉	C₂³	1	2	yes	—
260	C₄×D₄×C₂₉	C₂³	1	2	yes	—
261	C₄×D₄×C₂₉	C₂³	1	2	yes	—
262	C₂₉×#117	—	2	1	no	—
263	C₂₉×#117	—	2	1	no	—
264	C₂₉×#117	—	2	2	no	—
265	C₂₉×#117	C₂³	1	1	yes	characteristic
266	C₂₉×#117	C₂³	1	2	yes	—
267	C₂₉×#117	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
271	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
272	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
273	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
280	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
281	C₂₉×#107	C₂³	1	2	yes	—
282	C₂₉×#107	C₂³	1	2	yes	—
283	C₂₉×#107	C₂³	1	2	yes	—
284	C₂₉×#107	C₂³	1	2	yes	—
285	C₂₉×#107	C₂³	1	2	yes	—
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	1	yes	characteristic
293	C₂₉×#103	C₂³	1	1	yes	characteristic
294	C₂₉×#103	C₂³	1	1	yes	characteristic
295	C₂₉×#103	C₂³	1	2	yes	—
296	C₂₉×#103	C₂³	1	2	yes	—
297	C₂₉×#103	C₂³	1	2	yes	—
298	C₂₉×#102	C₂³	1	2	yes	—
299	C₂₉×#102	C₂³	1	2	yes	—
300	C₂₉×#102	C₂³	1	2	yes	—
301	C₂₉×#102	C₂³	1	1	yes	characteristic
302	C₂₉×#102	C₂³	1	1	yes	characteristic
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×#102	C₂³	1	1	yes	characteristic
305	C₂₉×#102	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
311	C₂₉×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
316	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
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	—	2	1	no	—
324	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
325	#41×C₂₉	—	2	2	no	—
326	#41×C₂₉	—	2	2	no	—
327	#41×C₂₉	—	2	2	no	—
328	#41×C₂₉	—	2	2	no	—
329	#41×C₂₉	—	2	4	no	—
330	#41×C₂₉	—	2	2	no	—
331	#41×C₂₉	—	2	2	no	—
332	#41×C₂₉	—	2	2	no	—
333	#41×C₂₉	—	2	2	no	—
334	#41×C₂₉	—	2	2	no	—
335	#41×C₂₉	—	4	4	no	—
336	#41×C₂₉	—	4	1	no	—
337	#41×C₂₉	—	4	1	no	—
338	#41×C₂₉	—	4	2	no	—
339	#41×C₂₉	—	4	4	no	—
340	#41×C₂₉	—	4	4	no	—
341	#41×C₂₉	—	8	4	no	—
342	#41×C₂₉	#41	1	4	yes	complemented
343	C₂×Q₈×C₂₉	—	2	1	no	—
344	C₂×Q₈×C₂₉	—	2	2	no	—
345	C₂×Q₈×C₂₉	—	2	2	no	—
346	C₂×Q₈×C₂₉	—	4	1	no	—
347	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₂₉	—	2	1	no	—
352	C₂×D₄×C₂₉	—	2	2	no	—
353	C₂×D₄×C₂₉	—	2	4	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	1	no	—
358	C₂×D₄×C₂₉	—	2	1	no	—
359	C₂×D₄×C₂₉	—	2	1	no	—
360	C₂×D₄×C₂₉	—	2	2	no	—
361	C₂×D₄×C₂₉	—	2	1	no	—
362	C₂×D₄×C₂₉	—	2	2	no	—
363	C₂×D₄×C₂₉	—	2	2	no	—
364	C₂×D₄×C₂₉	—	2	2	no	—
365	C₂×D₄×C₂₉	—	2	1	no	—
366	C₂×D₄×C₂₉	—	2	2	no	—
367	C₂×D₄×C₂₉	—	2	1	no	—
368	C₂×D₄×C₂₉	—	2	2	no	—
369	C₂×D₄×C₂₉	—	2	2	no	—
370	C₂×D₄×C₂₉	—	2	2	no	—
371	C₂×D₄×C₂₉	—	2	2	no	—
372	C₂×D₄×C₂₉	—	4	1	no	—
373	C₂×D₄×C₂₉	—	4	2	no	—
374	C₂×D₄×C₂₉	—	4	4	no	—
375	C₂×D₄×C₂₉	—	4	8	no	—
376	C₂×D₄×C₂₉	—	4	4	no	—
377	C₂×D₄×C₂₉	—	8	4	no	—
378	C₂×D₄×C₂₉	—	8	2	no	—
379	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
380	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
385	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₂₉	—	2	1	no	—
388	C₂²×C₄×C₂₉	—	2	2	no	—
389	C₂²×C₄×C₂₉	—	2	2	no	—
390	C₂²×C₄×C₂₉	—	2	2	no	—
391	C₂²×C₄×C₂₉	—	2	1	no	—
392	C₂²×C₄×C₂₉	—	2	1	no	—
393	C₂²×C₄×C₂₉	—	2	1	no	—
394	C₂²×C₄×C₂₉	—	2	2	no	—
395	C₂²×C₄×C₂₉	—	2	1	no	—
396	C₂²×C₄×C₂₉	—	2	2	no	—
397	C₂²×C₄×C₂₉	—	2	1	no	—
398	C₂²×C₄×C₂₉	—	2	1	no	—
399	C₂²×C₄×C₂₉	—	2	1	no	—
400	C₂²×C₄×C₂₉	—	2	2	no	—
401	C₂²×C₄×C₂₉	—	2	1	no	—
402	C₂²×C₄×C₂₉	—	2	2	no	—
403	C₂²×C₄×C₂₉	—	2	2	no	—
404	C₂²×C₄×C₂₉	—	4	4	no	—
405	C₂²×C₄×C₂₉	—	8	2	no	—
406	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
413	Q₁₆×C₂₉	—	2	2	no	—
414	Q₁₆×C₂₉	—	4	1	no	—
415	SD₁₆×C₂₉	—	2	2	no	—
416	SD₁₆×C₂₉	—	2	2	no	—
417	SD₁₆×C₂₉	—	4	1	no	—
418	SD₁₆×C₂₉	—	4	1	no	—
419	SD₁₆×C₂₉	—	4	2	no	—
420	D₈×C₂₉	—	2	2	no	—
421	D₈×C₂₉	—	4	1	no	—
422	D₈×C₂₉	—	4	2	no	—
423	M₁₆×C₂₉	—	2	2	no	—
424	M₁₆×C₂₉	—	2	2	no	—
425	M₁₆×C₂₉	—	4	2	no	—
426	M₁₆×C₂₉	—	4	2	no	—
427	C₂×C₈×C₂₉	—	2	2	no	—
428	C₂×C₈×C₂₉	—	2	2	no	—
429	C₂×C₈×C₂₉	—	4	2	no	—
430	C₂×C₈×C₂₉	—	4	2	no	—
431	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
433	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
434	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₉	—	2	1	no	—
438	C₄⋊C₄×C₂₉	—	2	1	no	—
439	C₄⋊C₄×C₂₉	—	2	2	no	—
440	C₄⋊C₄×C₂₉	—	2	2	no	—
441	C₄⋊C₄×C₂₉	—	2	1	no	—
442	C₄⋊C₄×C₂₉	—	2	2	no	—
443	C₄⋊C₄×C₂₉	—	2	2	no	—
444	C₄⋊C₄×C₂₉	—	2	2	no	—
445	C₄⋊C₄×C₂₉	—	2	2	no	—
446	C₄⋊C₄×C₂₉	—	2	2	no	—
447	C₄⋊C₄×C₂₉	—	2	2	no	—
448	C₄⋊C₄×C₂₉	—	2	1	no	—
449	C₄⋊C₄×C₂₉	—	2	2	no	—
450	C₄⋊C₄×C₂₉	—	2	2	no	—
451	C₄⋊C₄×C₂₉	—	2	1	no	—
452	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
454	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
455	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
456	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
457	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
458	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
460	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
461	C₂²⋊C₄×C₂₉	—	2	2	no	—
462	C₂²⋊C₄×C₂₉	—	2	1	no	—
463	C₂²⋊C₄×C₂₉	—	2	1	no	—
464	C₂²⋊C₄×C₂₉	—	2	2	no	—
465	C₂²⋊C₄×C₂₉	—	2	1	no	—
466	C₂²⋊C₄×C₂₉	—	2	2	no	—
467	C₂²⋊C₄×C₂₉	—	2	2	no	—
468	C₂²⋊C₄×C₂₉	—	2	2	no	—
469	C₂²⋊C₄×C₂₉	—	2	2	no	—
470	C₂²⋊C₄×C₂₉	—	2	2	no	—
471	C₂²⋊C₄×C₂₉	—	2	2	no	—
472	C₂²⋊C₄×C₂₉	—	2	2	no	—
473	C₂²⋊C₄×C₂₉	—	2	2	no	—
474	C₂²⋊C₄×C₂₉	—	2	2	no	—
475	C₂²⋊C₄×C₂₉	—	2	1	no	—
476	C₂²⋊C₄×C₂₉	—	2	1	no	—
477	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
478	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
479	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
480	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
481	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
482	C₄²×C₂₉	—	2	2	no	—
483	C₄²×C₂₉	—	2	2	no	—
484	C₄²×C₂₉	—	2	2	no	—
485	C₄²×C₂₉	—	2	1	no	—
486	C₄²×C₂₉	C₂⁴	1	2	yes	—
487	#61191	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
488	C₂³×C₂₉	—	2	2	no	—
489	C₂³×C₂₉	—	2	2	no	—
490	C₂³×C₂₉	—	2	1	no	—
491	C₂³×C₂₉	—	2	1	no	—
492	C₂³×C₂₉	—	2	2	no	—
493	C₂³×C₂₉	—	2	1	no	—
494	C₂³×C₂₉	—	4	1	no	—
495	C₂³×C₂₉	—	4	2	no	—
496	C₂³×C₂₉	—	4	4	no	—
497	C₂³×C₂₉	—	4	2	no	—
498	C₂³×C₂₉	—	4	2	no	—
499	C₂³×C₂₉	—	8	1	no	—
500	C₂³×C₂₉	—	8	1	no	—
501	C₂³×C₂₉	—	8	2	no	—
502	C₂³×C₂₉	—	8	1	no	—
503	C₂³×C₂₉	—	8	2	no	—
504	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
505	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
506	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
507	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
508	Q₈×C₂₉	—	2	2	no	—
509	Q₈×C₂₉	—	2	1	no	—
510	Q₈×C₂₉	—	2	1	no	—
511	Q₈×C₂₉	—	2	1	no	—
512	Q₈×C₂₉	—	2	1	no	—
513	Q₈×C₂₉	—	2	1	no	—
514	Q₈×C₂₉	—	4	2	no	—
515	Q₈×C₂₉	—	8	2	no	—
516	Q₈×C₂₉	C₂×#41	1	2	yes	—
517	D₄×C₂₉	—	2	4	no	—
518	D₄×C₂₉	—	2	4	no	—
519	D₄×C₂₉	—	2	4	no	—
520	D₄×C₂₉	—	2	2	no	—
521	D₄×C₂₉	—	2	1	no	—
522	D₄×C₂₉	—	2	2	no	—
523	D₄×C₂₉	—	2	1	no	—
524	D₄×C₂₉	—	2	1	no	—
525	D₄×C₂₉	—	2	1	no	—
526	D₄×C₂₉	—	2	2	no	—
527	D₄×C₂₉	—	2	1	no	—
528	D₄×C₂₉	—	4	2	no	—
529	D₄×C₂₉	—	4	4	no	—
530	D₄×C₂₉	—	4	2	no	—
531	D₄×C₂₉	—	4	4	no	—
532	D₄×C₂₉	—	4	2	no	—
533	D₄×C₂₉	—	4	2	no	—
534	D₄×C₂₉	—	4	2	no	—
535	D₄×C₂₉	—	4	2	no	—
536	D₄×C₂₉	—	4	2	no	—
537	D₄×C₂₉	—	4	4	no	—
538	D₄×C₂₉	—	4	2	no	—
539	D₄×C₂₉	—	4	2	no	—
540	D₄×C₂₉	—	8	2	no	—
541	D₄×C₂₉	—	8	2	no	—
542	D₄×C₂₉	—	8	2	no	—
543	D₄×C₂₉	—	8	2	no	—
544	D₄×C₂₉	—	8	2	no	—
545	D₄×C₂₉	C₂×#41	1	2	yes	—
546	C₂×C₄×C₂₉	—	2	2	no	—
547	C₂×C₄×C₂₉	—	2	1	no	—
548	C₂×C₄×C₂₉	—	2	2	no	—
549	C₂×C₄×C₂₉	—	2	2	no	—
550	C₂×C₄×C₂₉	—	2	4	no	—
551	C₂×C₄×C₂₉	—	2	1	no	—
552	C₂×C₄×C₂₉	—	2	1	no	—
553	C₂×C₄×C₂₉	—	2	2	no	—
554	C₂×C₄×C₂₉	—	2	1	no	—
555	C₂×C₄×C₂₉	—	2	2	no	—
556	C₂×C₄×C₂₉	—	2	1	no	—
557	C₂×C₄×C₂₉	—	2	1	no	—
558	C₂×C₄×C₂₉	—	2	1	no	—
559	C₂×C₄×C₂₉	—	2	2	no	—
560	C₂×C₄×C₂₉	—	2	2	no	—
561	C₂×C₄×C₂₉	—	2	1	no	—
562	C₂×C₄×C₂₉	—	2	1	no	—
563	C₂×C₄×C₂₉	—	2	2	no	—
564	C₂×C₄×C₂₉	—	4	2	no	—
565	C₂×C₄×C₂₉	—	4	4	no	—
566	C₂×C₄×C₂₉	—	4	2	no	—
567	C₂×C₄×C₂₉	—	4	2	no	—
568	C₂×C₄×C₂₉	—	4	4	no	—
569	C₂×C₄×C₂₉	—	4	2	no	—
570	C₂×C₄×C₂₉	—	4	2	no	—
571	C₂×C₄×C₂₉	—	8	2	no	—
572	C₂×C₄×C₂₉	—	8	2	no	—
573	C₂×C₄×C₂₉	—	8	1	no	—
574	C₂×C₄×C₂₉	—	8	2	no	—
575	C₂×C₄×C₂₉	—	8	1	no	—
576	C₂×C₄×C₂₉	—	8	1	no	—
577	C₂×C₄×C₂₉	—	8	2	no	—
578	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
580	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
585	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
587	C₈×C₂₉	—	2	1	no	—
588	C₈×C₂₉	—	2	1	no	—
589	C₈×C₂₉	—	2	1	no	—
590	C₈×C₂₉	—	2	1	no	—
591	C₈×C₂₉	—	2	2	no	—
592	C₈×C₂₉	—	2	2	no	—
593	#3492	C₂×C₂₉	1	1	yes	characteristic, complemented
594	#3488	C₂×C₂₉	1	1	yes	characteristic, complemented
595	#3333	C₂×C₂₉	1	2	yes	complemented
596	#3322	C₂×C₂₉	1	2	yes	complemented
597	#3314	C₂×C₂₉	1	2	yes	complemented
598	#3310	C₂×C₂₉	1	2	yes	complemented
599	#3309	C₂×C₂₉	1	2	yes	complemented
600	#3308	C₂×C₂₉	1	2	yes	complemented
601	#3300	C₂×C₂₉	1	2	yes	complemented
602	#3294	C₂×C₂₉	1	2	yes	complemented
603	#3136	C₂×C₂₉	1	1	yes	characteristic, complemented
604	#3098	C₂×C₂₉	1	1	yes	characteristic, complemented
605	C₂×#480	C₂×C₂₉	1	1	yes	characteristic, complemented
606	#3083	C₂×C₂₉	1	1	yes	characteristic, complemented
607	#3061	C₂×C₂₉	1	1	yes	characteristic, complemented
608	#3055	C₂×C₂₉	1	1	yes	characteristic, complemented
609	#3045	C₂×C₂₉	1	1	yes	characteristic, complemented
610	#3012	C₂×C₂₉	1	1	yes	characteristic, complemented
611	#3002	C₂×C₂₉	1	1	yes	characteristic, complemented
612	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
613	#2933	C₂×C₂₉	1	1	yes	characteristic, complemented
614	#2897	C₂×C₂₉	1	1	yes	characteristic, complemented
615	C₂×#417	C₂×C₂₉	1	1	yes	characteristic, complemented
616	C₂²×C₂₉	—	2	1	no	—
617	C₂²×C₂₉	—	2	1	no	—
618	C₂²×C₂₉	—	2	1	no	—
619	C₂²×C₂₉	—	2	1	no	—
620	C₂²×C₂₉	—	2	1	no	—
621	C₂²×C₂₉	—	2	2	no	—
622	C₂²×C₂₉	—	2	1	no	—
623	C₂²×C₂₉	—	2	2	no	—
624	C₂²×C₂₉	—	2	2	no	—
625	C₂²×C₂₉	—	2	1	no	—
626	C₂²×C₂₉	—	2	2	no	—
627	C₂²×C₂₉	—	4	4	no	—
628	C₂²×C₂₉	—	4	1	no	—
629	C₂²×C₂₉	—	4	1	no	—
630	C₂²×C₂₉	—	4	1	no	—
631	C₂²×C₂₉	—	4	1	no	—
632	C₂²×C₂₉	—	4	2	no	—
633	C₂²×C₂₉	—	4	1	no	—
634	C₂²×C₂₉	—	4	2	no	—
635	C₂²×C₂₉	—	4	1	no	—
636	C₂²×C₂₉	—	4	1	no	—
637	C₂²×C₂₉	—	4	2	no	—
638	C₂²×C₂₉	—	4	1	no	—
639	C₂²×C₂₉	—	8	4	no	—
640	C₂²×C₂₉	—	16	2	no	—
641	C₂²×C₂₉	—	16	4	no	—
642	C₂²×C₂₉	#546	1	2	yes	—
643	C₂²×C₂₉	#576	1	2	yes	—
644	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
645	C₄×C₂₉	—	2	2	no	—
646	C₄×C₂₉	—	2	1	no	—
647	C₄×C₂₉	—	2	1	no	—
648	C₄×C₂₉	—	2	2	no	—
649	C₄×C₂₉	—	2	2	no	—
650	C₄×C₂₉	—	2	2	no	—
651	C₄×C₂₉	—	4	1	no	—
652	C₄×C₂₉	—	4	1	no	—
653	C₄×C₂₉	—	4	1	no	—
654	C₄×C₂₉	—	4	2	no	—
655	C₄×C₂₉	—	4	2	no	—
656	C₄×C₂₉	—	4	2	no	—
657	C₄×C₂₉	—	4	1	no	—
658	C₄×C₂₉	#546	1	2	yes	—
659	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
660	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic
662	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
663	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic, complemented
664	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
665	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
668	#554	—	2	1	no	—
669	#554	C₂²×C₂₉	1	2	yes	complemented
670	#553	—	2	1	no	—
671	#553	C₂²×C₂₉	1	2	yes	complemented
672	#552	—	2	1	no	—
673	#552	C₂²×C₂₉	1	2	yes	complemented
674	#550	C₂²×C₂₉	1	2	yes	—
675	#548	C₂²×C₂₉	1	2	yes	—
676	#547	—	2	1	no	—
677	#547	C₂²×C₂₉	1	2	yes	complemented
678	#546	—	2	2	no	—
679	#546	C₂²×C₂₉	1	2	yes	—
680	D₄²	—	2	2	no	—
681	D₄²	C₂²×C₂₉	1	2	yes	—
682	#544	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#539	—	2	2	no	—
684	#537	—	2	1	no	—
685	#537	C₂²×C₂₉	1	1	yes	characteristic
686	#537	C₂²×C₂₉	1	1	yes	characteristic, complemented
687	#535	—	2	1	no	—
688	#535	C₂²×C₂₉	1	1	yes	characteristic
689	#525	—	2	1	no	—
690	#525	—	2	2	no	—
691	#525	C₂²×C₂₉	1	1	yes	characteristic
692	#525	C₂²×C₂₉	1	1	yes	characteristic, complemented
693	C₂×#121	—	2	1	no	—
694	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
695	#520	C₂²×C₂₉	1	1	yes	characteristic
696	#520	C₂²×C₂₉	1	1	yes	characteristic, complemented
697	#520	C₂²×C₂₉	1	1	yes	characteristic, complemented
698	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
699	#490	C₂²×C₂₉	1	2	yes	complemented
700	#489	C₂²×C₂₉	1	2	yes	complemented
701	#488	C₂²×C₂₉	1	2	yes	complemented
702	#486	C₂²×C₂₉	1	2	yes	complemented
703	#485	C₂²×C₂₉	1	2	yes	complemented
704	#484	C₂²×C₂₉	1	2	yes	complemented
705	#482	C₂²×C₂₉	1	2	yes	complemented
706	#480	C₂²×C₂₉	1	2	yes	complemented
707	#480	C₂²×C₂₉	1	2	yes	complemented
708	#480	C₂²×C₂₉	1	2	yes	complemented
709	#480	C₂²×C₂₉	1	2	yes	complemented
710	#480	C₂²×C₂₉	1	2	yes	complemented
711	#479	C₂²×C₂₉	1	2	yes	complemented
712	#478	C₂²×C₂₉	1	2	yes	complemented
713	#477	C₂²×C₂₉	1	2	yes	complemented
714	#474	C₂²×C₂₉	1	2	yes	complemented
715	#469	C₂²×C₂₉	1	2	yes	complemented
716	#468	C₂²×C₂₉	1	2	yes	complemented
717	#468	C₂²×C₂₉	1	2	yes	complemented
718	#468	C₂²×C₂₉	1	2	yes	complemented
719	#467	C₂²×C₂₉	1	2	yes	complemented
720	#466	C₂²×C₂₉	1	2	yes	complemented
721	#466	C₂²×C₂₉	1	2	yes	complemented
722	#465	C₂²×C₂₉	1	2	yes	complemented
723	#464	C₂²×C₂₉	1	2	yes	complemented
724	#463	C₂²×C₂₉	1	2	yes	complemented
725	#460	C₂²×C₂₉	1	2	yes	complemented
726	#459	C₂²×C₂₉	1	2	yes	complemented
727	#452	C₂²×C₂₉	1	1	yes	characteristic, complemented
728	#452	C₂²×C₂₉	1	2	yes	complemented
729	#452	C₂²×C₂₉	1	1	yes	characteristic, complemented
730	#451	C₂²×C₂₉	1	1	yes	characteristic, complemented
731	#450	C₂²×C₂₉	1	1	yes	characteristic, complemented
732	#450	C₂²×C₂₉	1	2	yes	complemented
733	#449	C₂²×C₂₉	1	1	yes	characteristic, complemented
734	#449	C₂²×C₂₉	1	1	yes	characteristic, complemented
735	#449	C₂²×C₂₉	1	2	yes	complemented
736	#448	C₂²×C₂₉	1	1	yes	characteristic, complemented
737	#447	C₂²×C₂₉	1	1	yes	characteristic, complemented
738	#447	C₂²×C₂₉	1	2	yes	complemented
739	#440	C₂²×C₂₉	1	2	yes	complemented
740	#440	C₂²×C₂₉	1	2	yes	complemented
741	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
742	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
743	#436	C₂²×C₂₉	1	2	yes	complemented
744	#435	C₂²×C₂₉	1	2	yes	complemented
745	#435	C₂²×C₂₉	1	2	yes	complemented
746	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
747	#428	C₂²×C₂₉	1	1	yes	characteristic, complemented
748	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
749	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
750	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
751	#418	C₂²×C₂₉	1	1	yes	characteristic, complemented
752	#418	C₂²×C₂₉	1	2	yes	complemented
753	#417	C₂²×C₂₉	1	1	yes	characteristic
754	#417	C₂²×C₂₉	1	1	yes	characteristic
755	#417	C₂²×C₂₉	1	2	yes	complemented
756	#417	C₂²×C₂₉	1	2	yes	complemented
757	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
758	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
759	#417	C₂²×C₂₉	1	2	yes	complemented
760	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
761	#416	C₂²×C₂₉	1	1	yes	characteristic
762	#416	C₂²×C₂₉	1	1	yes	characteristic, complemented
763	#416	C₂²×C₂₉	1	2	yes	complemented
764	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
765	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
766	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
767	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
768	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
769	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
770	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
771	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
772	C₂×C₂₉	—	2	2	no	—
773	C₂×C₂₉	—	2	2	no	—
774	C₂×C₂₉	—	4	1	no	—
775	C₂×C₂₉	—	4	2	no	—
776	C₂×C₂₉	—	4	2	no	—
777	C₂×C₂₉	—	8	1	no	—
778	C₂×C₂₉	—	8	1	no	—
779	C₂×C₂₉	—	8	2	no	—
780	C₂×C₂₉	C₂×#546	1	1	yes	characteristic
781	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
782	C₂×C₂₉	#3586	1	1	yes	characteristic
783	H(5,𝔽₂)	—	2	4	no	—
784	H(5,𝔽₂)	—	4	2	no	—
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	2	2	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	—	2	1	no	—
789	C₂×#41	—	2	4	no	—
790	C₂×#41	—	4	2	no	—
791	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
792	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
793	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
794	C₂×#41	C₂³×C₂₉	1	2	yes	—
795	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
796	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
797	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
798	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	—	2	1	no	—
802	C₂²×D₄	—	2	2	no	—
803	C₂²×D₄	—	2	2	no	—
804	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
805	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
806	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
807	C₂³×C₄	—	2	1	no	—
808	C₂³×C₄	—	2	1	no	—
809	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
810	AGL(1,ℤ/8)	—	4	2	no	—
811	#135	—	2	4	no	—
812	#135	—	4	2	no	—
813	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
814	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
815	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
816	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
817	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
818	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
819	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
820	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
821	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
822	C₂×D₈	C₂³×C₂₉	1	2	yes	—
823	#131	—	4	2	no	—
824	C₂×M₁₆	—	4	2	no	—
825	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
826	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
827	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
828	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
829	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
830	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
831	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
832	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
833	C₄⋊Q₈	—	2	1	no	—
834	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
835	#127	—	2	2	no	—
836	#127	C₂³×C₂₉	1	2	yes	—
837	#126	—	2	2	no	—
838	#126	—	2	2	no	—
839	#125	—	2	2	no	—
840	#125	—	2	2	no	—
841	#125	—	2	1	no	—
842	#125	C₂³×C₂₉	1	2	yes	—
843	#124	—	2	2	no	—
844	#124	C₂³×C₂₉	1	2	yes	—
845	#123	—	2	2	no	—
846	#123	—	2	1	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	D₄×C₂₉	1	2	yes	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	—	2	2	no	—
856	C₂²⋊Q₈	—	2	2	no	—
857	C₂²⋊Q₈	—	2	2	no	—
858	C₂²⋊Q₈	—	2	2	no	—
859	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
860	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
864	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
865	#121	—	2	1	no	—
866	#121	—	2	2	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	2	no	—
876	#121	—	2	2	no	—
877	#121	—	2	2	no	—
878	#121	—	2	2	no	—
879	#121	D₄×C₂₉	1	1	yes	characteristic
880	#121	D₄×C₂₉	1	1	yes	characteristic
881	#121	C₂³×C₂₉	1	2	yes	—
882	#121	C₂³×C₂₉	1	2	yes	—
883	#121	C₂³×C₂₉	1	1	yes	characteristic
884	#121	C₂³×C₂₉	1	1	yes	characteristic
885	#121	C₂³×C₂₉	1	2	yes	—
886	#121	C₂³×C₂₉	1	2	yes	—
887	#120	—	2	1	no	—
888	#120	—	2	2	no	—
889	#120	—	2	2	no	—
890	#120	—	2	2	no	—
891	#120	—	2	2	no	—
892	#120	D₄×C₂₉	1	2	yes	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
895	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	2	no	—
902	C₄×D₄	—	2	2	no	—
903	C₄×D₄	—	2	2	no	—
904	C₄×D₄	—	2	2	no	—
905	C₄×D₄	—	2	2	no	—
906	C₄×D₄	C₂³×C₂₉	1	2	yes	—
907	C₄×D₄	C₂³×C₂₉	1	2	yes	—
908	C₄×D₄	C₂³×C₂₉	1	2	yes	—
909	C₄×D₄	C₂³×C₂₉	1	2	yes	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	2	no	—
913	#117	C₂³×C₂₉	1	1	yes	characteristic
914	#117	C₂³×C₂₉	1	2	yes	—
915	#117	C₂³×C₂₉	1	1	yes	characteristic
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	—	2	1	no	—
918	C₂×C₄⋊C₄	—	2	1	no	—
919	C₂×C₄⋊C₄	—	2	1	no	—
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
924	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
925	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
926	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	2	no	—
929	#107	C₂³×C₂₉	1	2	yes	—
930	#107	C₂³×C₂₉	1	2	yes	—
931	#107	C₂³×C₂₉	1	2	yes	—
932	#107	C₂³×C₂₉	1	2	yes	—
933	#107	C₂³×C₂₉	1	2	yes	—
934	#106	C₂³×C₂₉	1	2	yes	—
935	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
936	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
937	#103	C₂³×C₂₉	1	2	yes	—
938	#103	C₂³×C₂₉	1	2	yes	—
939	#103	C₂³×C₂₉	1	2	yes	—
940	#103	C₂³×C₂₉	1	2	yes	—
941	#103	C₂³×C₂₉	1	1	yes	characteristic
942	#103	C₂³×C₂₉	1	1	yes	characteristic
943	#103	C₂³×C₂₉	1	1	yes	characteristic
944	#103	C₂³×C₂₉	1	1	yes	characteristic
945	#103	C₂³×C₂₉	1	2	yes	—
946	#102	C₂³×C₂₉	1	1	yes	characteristic
947	#102	C₂³×C₂₉	1	2	yes	—
948	#102	C₂³×C₂₉	1	2	yes	—
949	#102	C₂³×C₂₉	1	2	yes	—
950	#102	C₂³×C₂₉	1	2	yes	—
951	#102	C₂³×C₂₉	1	2	yes	—
952	#102	C₂³×C₂₉	1	2	yes	—
953	#102	C₂³×C₂₉	1	2	yes	—
954	#102	C₂³×C₂₉	1	2	yes	—
955	#102	C₂³×C₂₉	1	2	yes	—
956	#102	C₂³×C₂₉	1	1	yes	characteristic
957	#102	C₂³×C₂₉	1	2	yes	—
958	#102	C₂³×C₂₉	1	1	yes	characteristic
959	#102	C₂³×C₂₉	1	1	yes	characteristic
960	#102	C₂³×C₂₉	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
963	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
964	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
965	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
967	#97	C₂³×C₂₉	1	2	yes	—
968	C₄×C₈	C₂³×C₂₉	1	2	yes	—
969	C₂₉	#61191	1	1	yes	characteristic, direct product factor, Sylow
970	C₂⁴	—	2	1	no	—
971	C₂⁴	—	2	2	no	—
972	C₂⁴	—	2	1	no	—
973	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	4	no	—
979	#41	—	2	2	no	—
980	#41	—	2	2	no	—
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	4	4	no	—
985	#41	—	4	1	no	—
986	#41	—	4	1	no	—
987	#41	—	4	2	no	—
988	#41	—	4	4	no	—
989	#41	—	4	4	no	—
990	#41	—	8	4	no	—
991	#41	#41×C₂₉	1	4	yes	complemented
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	2	2	no	—
995	C₂×Q₈	—	4	1	no	—
996	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
999	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	4	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	1	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	4	1	no	—
1022	C₂×D₄	—	4	2	no	—
1023	C₂×D₄	—	4	4	no	—
1024	C₂×D₄	—	4	8	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	8	4	no	—
1027	C₂×D₄	—	8	2	no	—
1028	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
1029	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1030	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
1031	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
1033	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1034	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1035	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	2	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	4	4	no	—
1054	C₂²×C₄	—	8	2	no	—
1055	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1058	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
1061	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1062	Q₁₆	—	2	2	no	—
1063	Q₁₆	—	4	1	no	—
1064	SD₁₆	—	2	2	no	—
1065	SD₁₆	—	2	2	no	—
1066	SD₁₆	—	4	1	no	—
1067	SD₁₆	—	4	1	no	—
1068	SD₁₆	—	4	2	no	—
1069	D₈	—	2	2	no	—
1070	D₈	—	4	1	no	—
1071	D₈	—	4	2	no	—
1072	M₁₆	—	2	2	no	—
1073	M₁₆	—	2	2	no	—
1074	M₁₆	—	4	2	no	—
1075	M₁₆	—	4	2	no	—
1076	C₂×C₈	—	2	2	no	—
1077	C₂×C₈	—	2	2	no	—
1078	C₂×C₈	—	4	2	no	—
1079	C₂×C₈	—	4	2	no	—
1080	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1083	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1084	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1085	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	2	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1102	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1103	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1104	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1105	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1106	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1107	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1108	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1109	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1127	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1128	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1129	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1130	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1131	C₄²	—	2	2	no	—
1132	C₄²	—	2	2	no	—
1133	C₄²	—	2	2	no	—
1134	C₄²	—	2	1	no	—
1135	C₄²	C₂⁴×C₂₉	1	2	yes	—
1136	C₂³	—	2	2	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	2	1	no	—
1140	C₂³	—	2	2	no	—
1141	C₂³	—	2	1	no	—
1142	C₂³	—	4	1	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	4	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	4	2	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	—	8	1	no	—
1149	C₂³	—	8	2	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	2	no	—
1152	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1153	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1154	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	2	1	no	—
1162	Q₈	—	4	2	no	—
1163	Q₈	—	8	2	no	—
1164	Q₈	C₂×#41×C₂₉	1	2	yes	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	4	no	—
1167	D₄	—	2	4	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	2	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	2	1	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	4	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	C₂×#41×C₂₉	1	2	yes	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	4	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	4	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	2	no	—
1223	C₂×C₄	—	8	1	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	—	8	2	no	—
1226	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1227	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1229	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1232	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
1233	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1234	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	1	no	—
1238	C₈	—	2	1	no	—
1239	C₈	—	2	2	no	—
1240	C₈	—	2	2	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	2	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	2	2	no	—
1252	C₂²	—	4	4	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	4	1	no	—
1263	C₂²	—	4	2	no	—
1264	C₂²	—	8	4	no	—
1265	C₂²	—	16	2	no	—
1266	C₂²	—	16	4	no	—
1267	C₂²	C₂₉×#546	1	2	yes	—
1268	C₂²	C₂₉×#576	1	2	yes	—
1269	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	2	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	C₂₉×#546	1	2	yes	—
1284	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1285	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1286	C₂	—	2	2	no	—
1287	C₂	—	2	2	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	—	8	2	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₂×C₂₉×#546	1	1	yes	characteristic
1295	C₂	C₂×C₂₉×#576	1	1	yes	characteristic
1296	C₂	C₂₉×#3586	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 ◁ C₂₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3492	C₂	semidirect
2. C₂₉×#3488	C₂	semidirect
3. C₂₉×#3333	C₂	semidirect
4. C₂₉×#3322	C₂	semidirect
5. C₂₉×#3314	C₂	semidirect
6. C₂₉×#3310	C₂	semidirect
7. C₂₉×#3309	C₂	semidirect
8. C₂₉×#3308	C₂	semidirect
9. C₂₉×#3300	C₂	semidirect
10. C₂₉×#3294	C₂	semidirect
11. C₂₉×#3136	C₂	semidirect
12. C₂₉×#3098	C₂	semidirect
13. C₂×C₂₉×#480	C₂	semidirect
14. C₂₉×#3083	C₂	semidirect
15. C₂₉×#3061	C₂	semidirect
16. C₂₉×#3055	C₂	semidirect
17. C₂₉×#3045	C₂	semidirect
18. C₂₉×#3012	C₂	semidirect
19. C₂₉×#3002	C₂	semidirect
20. C₂₉×#2951	C₂	semidirect
21. C₂₉×#2933	C₂	semidirect
22. C₂₉×#2897	C₂	semidirect
23. C₂×C₂₉×#417	C₂	semidirect
26. C₂×C₂₉×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₂₉×#135	C₂²	semidirect
29. C₂×C₂₉×#131	C₂²	semidirect
30. C₂²×M₁₆×C₂₉	C₂²	semidirect
32. C₂₉×#554	C₂²	semidirect
34. C₂₉×#553	C₂²	semidirect
36. C₂₉×#552	C₂²	semidirect
40. C₂₉×#547	C₂²	semidirect
45. C₂₉×#544	C₂²	semidirect
49. C₂₉×#537	C₂²	semidirect
55. C₂₉×#525	C₂²	semidirect
59. C₂₉×#520	C₂²	semidirect
60. C₂₉×#520	C₂²	semidirect
61. C₂²×C₄⋊C₄×C₂₉	C₂²	semidirect
62. C₂₉×#490	C₂²	semidirect
63. C₂₉×#489	C₂²	semidirect
64. C₂₉×#488	C₂²	semidirect
65. C₂₉×#486	C₂²	semidirect
66. C₂₉×#485	C₂²	semidirect
67. C₂₉×#484	C₂²	semidirect
68. C₂₉×#482	C₂²	semidirect
69. C₂₉×#480	C₂²	semidirect
70. C₂₉×#480	C₂²	semidirect
71. C₂₉×#480	C₂²	semidirect
72. C₂₉×#480	C₂²	semidirect
73. C₂₉×#480	C₂²	semidirect
74. C₂₉×#479	C₂²	semidirect
75. C₂₉×#478	C₂²	semidirect
76. C₂₉×#477	C₂²	semidirect
77. C₂₉×#474	C₂²	semidirect
78. C₂₉×#469	C₂²	semidirect
79. C₂₉×#468	C₂²	semidirect
80. C₂₉×#468	C₂²	semidirect
81. C₂₉×#468	C₂²	semidirect
82. C₂₉×#467	C₂²	semidirect
83. C₂₉×#466	C₂²	semidirect
84. C₂₉×#466	C₂²	semidirect
85. C₂₉×#465	C₂²	semidirect
86. C₂₉×#464	C₂²	semidirect
87. C₂₉×#463	C₂²	semidirect
88. C₂₉×#460	C₂²	semidirect
89. C₂₉×#459	C₂²	semidirect
90. C₂₉×#452	C₂²	semidirect
91. C₂₉×#452	C₂²	semidirect
92. C₂₉×#452	C₂²	semidirect
93. C₂₉×#451	C₂²	semidirect
94. C₂₉×#450	C₂²	semidirect
95. C₂₉×#450	C₂²	semidirect
96. C₂₉×#449	C₂²	semidirect
97. C₂₉×#449	C₂²	semidirect
98. C₂₉×#449	C₂²	semidirect
99. C₂₉×#448	C₂²	semidirect
100. C₂₉×#447	C₂²	semidirect
101. C₂₉×#447	C₂²	semidirect
102. C₂₉×#440	C₂²	semidirect
103. C₂₉×#440	C₂²	semidirect
104. C₄×Q₁₆×C₂₉	C₂²	semidirect
105. C₄×D₈×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. C₂×C₂₉×#107	C₂²	semidirect
112. C₂×C₂₉×#107	C₂²	semidirect
113. C₂₉×#424	C₂²	semidirect
114. C₂₉×#418	C₂²	semidirect
115. C₂₉×#418	C₂²	semidirect
118. C₂₉×#417	C₂²	semidirect
119. C₂₉×#417	C₂²	semidirect
120. C₂₉×#417	C₂²	semidirect
121. C₂₉×#417	C₂²	semidirect
122. C₂₉×#417	C₂²	semidirect
123. C₂₉×#417	C₂²	semidirect
125. C₂₉×#416	C₂²	semidirect
126. C₂₉×#416	C₂²	semidirect
127. C₂×C₂₉×#103	C₂²	semidirect
128. C₂×C₂₉×#102	C₂²	semidirect
129. C₂×C₂₉×#102	C₂²	semidirect
130. C₂×C₂₉×#102	C₂²	semidirect
131. C₂×C₂₉×#102	C₂²	semidirect
132. C₂₉×#408	C₂²	semidirect
133. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
134. C₂₉×#405	C₂²	semidirect
342. #41×C₂₉	#41	semidirect
487. #61191	C₂₉	direct (N × H)
593. #3492	C₂×C₂₉	semidirect
594. #3488	C₂×C₂₉	semidirect
595. #3333	C₂×C₂₉	semidirect
596. #3322	C₂×C₂₉	semidirect
597. #3314	C₂×C₂₉	semidirect
598. #3310	C₂×C₂₉	semidirect
599. #3309	C₂×C₂₉	semidirect
600. #3308	C₂×C₂₉	semidirect
601. #3300	C₂×C₂₉	semidirect
602. #3294	C₂×C₂₉	semidirect
603. #3136	C₂×C₂₉	semidirect
604. #3098	C₂×C₂₉	semidirect
605. C₂×#480	C₂×C₂₉	semidirect
606. #3083	C₂×C₂₉	semidirect
607. #3061	C₂×C₂₉	semidirect
608. #3055	C₂×C₂₉	semidirect
609. #3045	C₂×C₂₉	semidirect
610. #3012	C₂×C₂₉	semidirect
611. #3002	C₂×C₂₉	semidirect
612. #2951	C₂×C₂₉	semidirect
613. #2933	C₂×C₂₉	semidirect
614. #2897	C₂×C₂₉	semidirect
615. C₂×#417	C₂×C₂₉	semidirect
663. C₂×AGL(1,ℤ/8)	C₂²×C₂₉	semidirect
665. C₂×#135	C₂²×C₂₉	semidirect
666. C₂×#131	C₂²×C₂₉	semidirect
667. C₂²×M₁₆	C₂²×C₂₉	semidirect
669. #554	C₂²×C₂₉	semidirect
671. #553	C₂²×C₂₉	semidirect
673. #552	C₂²×C₂₉	semidirect
677. #547	C₂²×C₂₉	semidirect
682. #544	C₂²×C₂₉	semidirect
686. #537	C₂²×C₂₉	semidirect
692. #525	C₂²×C₂₉	semidirect
696. #520	C₂²×C₂₉	semidirect
697. #520	C₂²×C₂₉	semidirect
698. C₂²×C₄⋊C₄	C₂²×C₂₉	semidirect
699. #490	C₂²×C₂₉	semidirect
700. #489	C₂²×C₂₉	semidirect
701. #488	C₂²×C₂₉	semidirect
702. #486	C₂²×C₂₉	semidirect
703. #485	C₂²×C₂₉	semidirect
704. #484	C₂²×C₂₉	semidirect
705. #482	C₂²×C₂₉	semidirect
706. #480	C₂²×C₂₉	semidirect
707. #480	C₂²×C₂₉	semidirect
708. #480	C₂²×C₂₉	semidirect
709. #480	C₂²×C₂₉	semidirect
710. #480	C₂²×C₂₉	semidirect
711. #479	C₂²×C₂₉	semidirect
712. #478	C₂²×C₂₉	semidirect
713. #477	C₂²×C₂₉	semidirect
714. #474	C₂²×C₂₉	semidirect
715. #469	C₂²×C₂₉	semidirect
716. #468	C₂²×C₂₉	semidirect
717. #468	C₂²×C₂₉	semidirect
718. #468	C₂²×C₂₉	semidirect
719. #467	C₂²×C₂₉	semidirect
720. #466	C₂²×C₂₉	semidirect
721. #466	C₂²×C₂₉	semidirect
722. #465	C₂²×C₂₉	semidirect
723. #464	C₂²×C₂₉	semidirect
724. #463	C₂²×C₂₉	semidirect
725. #460	C₂²×C₂₉	semidirect
726. #459	C₂²×C₂₉	semidirect
727. #452	C₂²×C₂₉	semidirect
728. #452	C₂²×C₂₉	semidirect
729. #452	C₂²×C₂₉	semidirect
730. #451	C₂²×C₂₉	semidirect
731. #450	C₂²×C₂₉	semidirect
732. #450	C₂²×C₂₉	semidirect
733. #449	C₂²×C₂₉	semidirect
734. #449	C₂²×C₂₉	semidirect
735. #449	C₂²×C₂₉	semidirect
736. #448	C₂²×C₂₉	semidirect
737. #447	C₂²×C₂₉	semidirect
738. #447	C₂²×C₂₉	semidirect
739. #440	C₂²×C₂₉	semidirect
740. #440	C₂²×C₂₉	semidirect
741. C₄×Q₁₆	C₂²×C₂₉	semidirect
742. C₄×D₈	C₂²×C₂₉	semidirect
743. #436	C₂²×C₂₉	semidirect
744. #435	C₂²×C₂₉	semidirect
745. #435	C₂²×C₂₉	semidirect
746. C₈×D₄	C₂²×C₂₉	semidirect
747. #428	C₂²×C₂₉	semidirect
748. C₂×#107	C₂²×C₂₉	semidirect
749. C₂×#107	C₂²×C₂₉	semidirect
750. #424	C₂²×C₂₉	semidirect
751. #418	C₂²×C₂₉	semidirect
752. #418	C₂²×C₂₉	semidirect
755. #417	C₂²×C₂₉	semidirect
756. #417	C₂²×C₂₉	semidirect
757. #417	C₂²×C₂₉	semidirect
758. #417	C₂²×C₂₉	semidirect
759. #417	C₂²×C₂₉	semidirect
760. #417	C₂²×C₂₉	semidirect
762. #416	C₂²×C₂₉	semidirect
763. #416	C₂²×C₂₉	semidirect
764. C₂×#103	C₂²×C₂₉	semidirect
765. C₂×#102	C₂²×C₂₉	semidirect
766. C₂×#102	C₂²×C₂₉	semidirect
767. C₂×#102	C₂²×C₂₉	semidirect
768. C₂×#102	C₂²×C₂₉	semidirect
769. #408	C₂²×C₂₉	semidirect
770. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
771. #405	C₂²×C₂₉	semidirect
969. C₂₉	#61191	direct (N × H)
991. #41	#41×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3492	2
C₂₉×#3488	2
C₂₉×#3333	2
C₂₉×#3322	2
C₂₉×#3314	2
C₂₉×#3310	2
C₂₉×#3309	2
C₂₉×#3308	2
C₂₉×#3300	2
C₂₉×#3294	2
C₂₉×#3136	2
C₂₉×#3098	2
C₂×C₂₉×#480	2
C₂₉×#3083	2
C₂₉×#3061	2
C₂₉×#3055	2
C₂₉×#3045	2
C₂₉×#3012	2
C₂₉×#3002	2
C₂₉×#2951	2
C₂₉×#2933	2
C₂₉×#2897	2
C₂×C₂₉×#417	2
#61191	29

Subgroups — C29×#61191 #20356091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61191 #20356091