Subgroups — C₂₉×#62759 #20357659

Order 7424.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3551	C₂	1	4	yes	maximal, complemented
2	C₂₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3548	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3547	C₂	1	4	yes	maximal, complemented
6	C₂₉×#3546	C₂	1	4	yes	maximal, complemented
7	C₂₉×#3545	C₂	1	4	yes	maximal, complemented
8	C₂₉×#3544	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3543	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3542	C₂	1	8	yes	maximal, complemented
11	C₂₉×#3529	C₂	1	4	yes	maximal, complemented
12	C₂₉×#3483	C₂	1	2	yes	maximal, complemented
13	C₂₉×#3481	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3475	C₂	1	4	yes	maximal, complemented
15	D₄×#41×C₂₉	C₂	1	4	yes	maximal, complemented
16	C₂₉×#3460	C₂	1	8	yes	maximal, complemented
17	C₂₉×#3449	C₂	1	4	yes	maximal, complemented
18	C₂₉×#3444	C₂	1	2	yes	maximal, complemented
19	C₂×C₂₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₂₉	C₂²	1	2	yes	complemented
21	C₂²×#41×C₂₉	C₂²	1	4	yes	complemented
22	C₂₉×#563	C₂²	1	8	yes	complemented
23	C₂₉×#563	C₂²	1	4	yes	complemented
24	C₂₉×#562	C₂²	1	16	yes	complemented
25	C₂₉×#562	C₂²	1	8	yes	complemented
26	C₂₉×H(3,𝔽₄)	C₂²	1	4	yes	complemented
27	C₂₉×#560	C₂²	1	16	yes	complemented
28	C₂₉×#560	C₂²	1	8	yes	complemented
29	C₂₉×#559	C₂²	1	2	yes	complemented
30	Q₈²×C₂₉	C₂²	1	2	yes	complemented
31	C₂₉×#556	C₂²	1	4	yes	complemented
32	C₂₉×#555	C₂²	1	4	yes	complemented
33	C₂₉×#555	C₂²	1	8	yes	complemented
34	C₂₉×#555	C₂²	1	2	yes	complemented
35	C₂₉×#555	C₂²	1	8	yes	complemented
36	C₂₉×#554	C₂²	1	4	yes	complemented
37	C₂₉×#554	C₂²	1	4	yes	complemented
38	C₂₉×#553	C₂²	1	8	yes	complemented
39	C₂₉×#553	C₂²	1	8	yes	complemented
40	C₂₉×#552	C₂²	1	8	yes	complemented
41	C₂₉×#552	C₂²	1	8	yes	complemented
42	C₂₉×#551	C₂²	1	16	yes	complemented
43	C₂₉×#551	C₂²	1	8	yes	complemented
44	C₂₉×#550	C₂²	1	4	yes	complemented
45	C₂₉×#550	C₂²	1	8	yes	complemented
46	C₂₉×#550	C₂²	1	4	yes	complemented
47	D₄×Q₈×C₂₉	C₂²	1	4	yes	complemented
48	C₂₉×#548	C₂²	1	8	yes	complemented
49	C₂₉×#547	C₂²	1	8	yes	complemented
50	C₂₉×#547	C₂²	1	4	yes	complemented
51	C₂₉×#547	C₂²	1	4	yes	complemented
52	C₂₉×#546	C₂²	1	16	yes	complemented
53	C₂₉×#546	C₂²	1	8	yes	complemented
54	C₂₉×#546	C₂²	1	8	yes	complemented
55	C₂₉×#546	C₂²	1	8	yes	complemented
56	D₄²×C₂₉	C₂²	1	8	yes	complemented
57	D₄²×C₂₉	C₂²	1	4	yes	complemented
58	D₄²×C₂₉	C₂²	1	2	yes	complemented
59	C₂₉×#544	C₂²	1	8	yes	complemented
60	C₂₉×#542	C₂²	1	8	yes	complemented
61	C₂₉×#542	C₂²	1	8	yes	complemented
62	C₂₉×#542	C₂²	1	16	yes	complemented
63	C₂₉×#540	C₂²	1	8	yes	complemented
64	C₂₉×#540	C₂²	1	16	yes	complemented
65	C₂₉×#540	C₂²	1	8	yes	complemented
66	C₂₉×#538	C₂²	1	16	yes	complemented
67	C₂₉×#538	C₂²	1	16	yes	complemented
68	C₂₉×#537	C₂²	1	8	yes	complemented
69	C₂₉×#537	C₂²	1	8	yes	complemented
70	C₂₉×#537	C₂²	1	8	yes	complemented
71	C₂₉×#536	C₂²	1	8	yes	complemented
72	C₂₉×#536	C₂²	1	4	yes	complemented
73	C₂₉×#536	C₂²	1	4	yes	complemented
74	C₂₉×#535	C₂²	1	8	yes	complemented
75	C₂₉×#535	C₂²	1	4	yes	complemented
76	C₂₉×#535	C₂²	1	4	yes	complemented
77	C₂₉×#535	C₂²	1	8	yes	complemented
78	C₂₉×#535	C₂²	1	8	yes	complemented
79	C₂₉×#534	C₂²	1	8	yes	complemented
80	C₂₉×#534	C₂²	1	8	yes	complemented
81	C₂₉×#533	C₂²	1	2	yes	complemented
82	C₂₉×#533	C₂²	1	2	yes	complemented
83	C₂₉×#533	C₂²	1	2	yes	complemented
84	C₂₉×#532	C₂²	1	1	yes	characteristic
85	C₂₉×#532	C₂²	1	1	yes	characteristic
86	C₂₉×#532	C₂²	1	2	yes	—
87	C₂₉×#532	C₂²	1	4	yes	complemented
88	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
89	C₂₉×#532	C₂²	1	2	yes	complemented
90	C₂₉×#532	C₂²	1	4	yes	complemented
91	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
92	C₂₉×#532	C₂²	1	2	yes	complemented
93	C₂₉×#532	C₂²	1	2	yes	complemented
94	C₂₉×#532	C₂²	1	2	yes	complemented
95	C₂₉×#532	C₂²	1	8	yes	complemented
96	C₂₉×#532	C₂²	1	8	yes	complemented
97	C₂₉×#532	C₂²	1	8	yes	complemented
98	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
100	C₂₉×#529	C₂²	1	4	yes	complemented
101	C₂₉×#529	C₂²	1	4	yes	complemented
102	C₂₉×#529	C₂²	1	4	yes	complemented
103	C₂₉×#529	C₂²	1	4	yes	complemented
104	C₂₉×#529	C₂²	1	4	yes	complemented
105	C₂₉×#529	C₂²	1	4	yes	complemented
106	C₂₉×#529	C₂²	1	8	yes	complemented
107	C₂₉×#529	C₂²	1	16	yes	complemented
108	C₂×C₂₉×#124	C₂²	1	2	yes	complemented
109	C₂₉×#525	C₂²	1	4	yes	complemented
110	C₂₉×#525	C₂²	1	4	yes	complemented
111	C₂₉×#525	C₂²	1	4	yes	complemented
112	C₂₉×#525	C₂²	1	8	yes	complemented
113	C₂₉×#525	C₂²	1	8	yes	complemented
114	C₂₉×#525	C₂²	1	8	yes	complemented
115	C₂₉×#525	C₂²	1	16	yes	complemented
116	C₂×C₂₉×#121	C₂²	1	4	yes	complemented
117	C₄×#41×C₂₉	C₂²	1	4	yes	complemented
118	C₄×#41×C₂₉	C₂²	1	4	yes	complemented
119	C₄×#41×C₂₉	C₂²	1	4	yes	complemented
120	C₄×#41×C₂₉	C₂²	1	8	yes	complemented
121	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	complemented
122	C₂×C₄×D₄×C₂₉	C₂²	1	8	yes	complemented
123	C₂×C₂₉×#117	C₂²	1	4	yes	complemented
124	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
125	C₂×#41×C₂₉	—	4	8	no	—
126	C₂×#41×C₂₉	—	4	16	no	—
127	C₂×#41×C₂₉	C₂³	1	4	yes	—
128	C₂×#41×C₂₉	C₂³	1	4	yes	—
129	C₂×#41×C₂₉	C₂³	1	4	yes	—
130	C₂×#41×C₂₉	C₂³	1	8	yes	—
131	C₂×#41×C₂₉	C₂³	1	2	yes	—
132	C₂×#41×C₂₉	C₂³	1	4	yes	—
133	C₂×#41×C₂₉	C₂³	1	8	yes	—
134	C₂×#41×C₂₉	C₂³	1	2	yes	—
135	C₂×#41×C₂₉	C₂³	1	2	yes	—
136	C₂×#41×C₂₉	C₂³	1	4	yes	—
137	C₂×#41×C₂₉	C₂³	1	2	yes	—
138	C₂×#41×C₂₉	C₂³	1	8	yes	—
139	C₂×#41×C₂₉	C₂³	1	8	yes	—
140	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₂₉	C₂³	1	4	yes	—
142	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
143	C₂²×D₄×C₂₉	C₂³	1	8	yes	—
144	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
145	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₂₉	C₂³	1	8	yes	—
147	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
148	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
150	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
151	C₂³×C₄×C₂₉	C₂³	1	8	yes	—
152	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
155	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
160	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
161	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
162	C₂₉×#127	C₂³	1	1	yes	characteristic
163	C₂₉×#127	C₂³	1	4	yes	—
164	C₂₉×#127	C₂³	1	1	yes	characteristic
165	C₂₉×#127	C₂³	1	2	yes	—
166	C₂₉×#127	C₂³	1	2	yes	—
167	C₂₉×#127	C₂³	1	8	yes	—
168	C₂₉×#127	C₂³	1	8	yes	—
169	C₂₉×#127	C₂³	1	8	yes	—
170	C₂₉×#126	C₂³	1	8	yes	—
171	C₂₉×#126	C₂³	1	8	yes	—
172	C₂₉×#126	C₂³	1	16	yes	—
173	C₂₉×#126	C₂³	1	16	yes	—
174	C₂₉×#126	C₂³	1	16	yes	—
175	C₂₉×#125	C₂³	1	4	yes	—
176	C₂₉×#125	C₂³	1	4	yes	—
177	C₂₉×#125	C₂³	1	4	yes	—
178	C₂₉×#125	C₂³	1	16	yes	—
179	C₂₉×#125	C₂³	1	8	yes	—
180	C₂₉×#124	C₂³	1	2	yes	—
181	C₂₉×#124	C₂³	1	2	yes	—
182	C₂₉×#124	C₂³	1	8	yes	—
183	C₂₉×#124	C₂³	1	2	yes	—
184	C₂₉×#124	C₂³	1	2	yes	—
185	C₂₉×#124	C₂³	1	4	yes	—
186	C₂₉×#124	C₂³	1	4	yes	—
187	C₂₉×#124	C₂³	1	4	yes	—
188	C₂₉×#124	C₂³	1	8	yes	—
189	C₂₉×#124	C₂³	1	16	yes	—
190	C₂₉×#124	C₂³	1	8	yes	—
191	C₂₉×#124	C₂³	1	8	yes	—
192	C₂₉×#124	C₂³	1	8	yes	—
193	C₂₉×#124	C₂³	1	8	yes	—
194	C₂₉×#124	C₂³	1	16	yes	—
195	C₂₉×#123	C₂³	1	8	yes	—
196	C₂₉×#123	C₂³	1	8	yes	—
197	C₂₉×#123	C₂³	1	8	yes	—
198	C₂₉×#123	C₂³	1	8	yes	—
199	C₂₉×#123	C₂³	1	8	yes	—
200	C₂₉×#123	C₂³	1	16	yes	—
201	C₂₉×#123	C₂³	1	8	yes	—
202	C₂₉×#123	C₂³	1	8	yes	—
203	C₂₉×#123	C₂³	1	16	yes	—
204	C₂₉×#123	C₂³	1	16	yes	—
205	C₂₉×#123	C₂³	1	16	yes	—
206	C₂₉×#123	C₂³	1	16	yes	—
207	C₂₉×#123	C₂³	1	16	yes	—
208	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
209	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
210	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
211	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
212	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
213	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
214	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
215	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
216	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
217	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
218	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
219	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
220	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
221	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
222	C₂₉×#121	C₂³	1	4	yes	—
223	C₂₉×#121	C₂³	1	4	yes	—
224	C₂₉×#121	C₂³	1	4	yes	—
225	C₂₉×#121	C₂³	1	8	yes	—
226	C₂₉×#121	C₂³	1	4	yes	—
227	C₂₉×#121	C₂³	1	8	yes	—
228	C₂₉×#121	C₂³	1	4	yes	—
229	C₂₉×#121	C₂³	1	4	yes	—
230	C₂₉×#121	C₂³	1	4	yes	—
231	C₂₉×#121	C₂³	1	4	yes	—
232	C₂₉×#121	C₂³	1	4	yes	—
233	C₂₉×#121	C₂³	1	4	yes	—
234	C₂₉×#121	C₂³	1	16	yes	—
235	C₂₉×#121	C₂³	1	8	yes	—
236	C₂₉×#121	C₂³	1	8	yes	—
237	C₂₉×#121	C₂³	1	16	yes	—
238	C₂₉×#121	C₂³	1	16	yes	—
239	C₂₉×#121	C₂³	1	16	yes	—
240	C₂₉×#121	C₂³	1	8	yes	—
241	C₂₉×#121	C₂³	1	16	yes	—
242	C₂₉×#121	C₂³	1	16	yes	—
243	C₂₉×#121	C₂³	1	16	yes	—
244	C₂₉×#121	C₂³	1	16	yes	—
245	C₂₉×#121	C₂³	1	16	yes	—
246	C₂₉×#121	C₂³	1	8	yes	—
247	C₂₉×#121	C₂³	1	8	yes	—
248	C₂₉×#121	C₂³	1	16	yes	—
249	C₂₉×#120	C₂³	1	8	yes	—
250	C₂₉×#120	C₂³	1	8	yes	—
251	C₂₉×#120	C₂³	1	8	yes	—
252	C₂₉×#120	C₂³	1	16	yes	—
253	C₂₉×#120	C₂³	1	8	yes	—
254	C₂₉×#120	C₂³	1	8	yes	—
255	C₂₉×#120	C₂³	1	16	yes	—
256	C₂₉×#120	C₂³	1	16	yes	—
257	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
258	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
259	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
260	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
261	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
262	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
263	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
264	C₄×D₄×C₂₉	C₂³	1	4	yes	—
265	C₄×D₄×C₂₉	C₂³	1	4	yes	—
266	C₄×D₄×C₂₉	C₂³	1	4	yes	—
267	C₄×D₄×C₂₉	C₂³	1	16	yes	—
268	C₄×D₄×C₂₉	C₂³	1	8	yes	—
269	C₄×D₄×C₂₉	C₂³	1	4	yes	—
270	C₄×D₄×C₂₉	C₂³	1	8	yes	—
271	C₄×D₄×C₂₉	C₂³	1	4	yes	—
272	C₄×D₄×C₂₉	C₂³	1	8	yes	—
273	C₄×D₄×C₂₉	C₂³	1	8	yes	—
274	C₄×D₄×C₂₉	C₂³	1	16	yes	—
275	C₄×D₄×C₂₉	C₂³	1	4	yes	—
276	C₄×D₄×C₂₉	C₂³	1	8	yes	—
277	C₄×D₄×C₂₉	C₂³	1	8	yes	—
278	C₄×D₄×C₂₉	C₂³	1	16	yes	—
279	C₄×D₄×C₂₉	C₂³	1	8	yes	—
280	C₄×D₄×C₂₉	C₂³	1	8	yes	—
281	C₄×D₄×C₂₉	C₂³	1	8	yes	—
282	C₄×D₄×C₂₉	C₂³	1	8	yes	—
283	C₄×D₄×C₂₉	C₂³	1	4	yes	—
284	C₄×D₄×C₂₉	C₂³	1	4	yes	—
285	C₄×D₄×C₂₉	C₂³	1	4	yes	—
286	C₄×D₄×C₂₉	C₂³	1	4	yes	—
287	C₄×D₄×C₂₉	C₂³	1	16	yes	—
288	C₄×D₄×C₂₉	C₂³	1	8	yes	—
289	C₂₉×#117	C₂³	1	4	yes	—
290	C₂₉×#117	C₂³	1	8	yes	—
291	C₂₉×#117	C₂³	1	8	yes	—
292	C₂₉×#117	C₂³	1	4	yes	—
293	C₂₉×#117	C₂³	1	4	yes	—
294	C₂₉×#117	C₂³	1	8	yes	—
295	C₂₉×#117	C₂³	1	4	yes	—
296	C₂₉×#117	C₂³	1	4	yes	—
297	C₂₉×#117	C₂³	1	8	yes	—
298	C₂₉×#117	C₂³	1	8	yes	—
299	C₂₉×#117	C₂³	1	8	yes	—
300	C₂₉×#117	C₂³	1	16	yes	—
301	C₂×C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
302	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
303	C₂×C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
304	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
305	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
306	C₂×C₂²⋊C₄×C₂₉	C₂³	1	16	yes	—
307	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
308	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
310	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
315	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₂₉	C₂³	1	8	yes	—
317	C₂×C₄²×C₂₉	C₂³	1	8	yes	—
318	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
319	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₂₉	C₂⁴	1	8	yes	—
321	#41×C₂₉	—	2	16	no	—
322	#41×C₂₉	—	4	4	no	—
323	#41×C₂₉	—	4	8	no	—
324	#41×C₂₉	—	4	4	no	—
325	#41×C₂₉	—	4	8	no	—
326	#41×C₂₉	—	4	4	no	—
327	#41×C₂₉	—	4	4	no	—
328	#41×C₂₉	—	4	16	no	—
329	#41×C₂₉	—	4	8	no	—
330	#41×C₂₉	—	4	16	no	—
331	#41×C₂₉	—	4	16	no	—
332	#41×C₂₉	—	4	8	no	—
333	#41×C₂₉	—	4	16	no	—
334	C₂×Q₈×C₂₉	—	4	4	no	—
335	C₂×Q₈×C₂₉	—	4	8	no	—
336	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
337	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
338	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
339	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
340	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
341	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
342	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
343	C₂×D₄×C₂₉	—	4	8	no	—
344	C₂×D₄×C₂₉	—	4	16	no	—
345	C₂×D₄×C₂₉	—	4	8	no	—
346	C₂×D₄×C₂₉	—	4	4	no	—
347	C₂×D₄×C₂₉	—	4	8	no	—
348	C₂×D₄×C₂₉	—	4	16	no	—
349	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
350	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
351	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
352	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
353	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
354	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
355	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
356	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
357	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
358	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
359	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
360	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
361	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
362	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
363	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
364	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
365	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
366	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
367	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
368	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₂₉	—	2	4	no	—
370	C₂²×C₄×C₂₉	—	2	16	no	—
371	C₂²×C₄×C₂₉	—	4	4	no	—
372	C₂²×C₄×C₂₉	—	4	16	no	—
373	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
380	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
383	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
386	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
387	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
392	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
393	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
394	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
395	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
397	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
398	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
399	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
400	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
401	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
402	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
403	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
404	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
405	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
406	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
407	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
408	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
409	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
410	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
411	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
412	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
413	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
414	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
418	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
419	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
420	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
421	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
422	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
423	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
424	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
425	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
426	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
427	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
428	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
429	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
430	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
431	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
432	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
433	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
434	C₄²×C₂₉	C₂⁴	1	2	yes	—
435	C₄²×C₂₉	C₂⁴	1	2	yes	—
436	C₄²×C₂₉	C₂⁴	1	2	yes	—
437	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
438	C₄²×C₂₉	C₂⁴	1	2	yes	—
439	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
440	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
441	C₄²×C₂₉	C₂⁴	1	8	yes	—
442	C₄²×C₂₉	C₂⁴	1	8	yes	—
443	C₄²×C₂₉	C₂⁴	1	8	yes	—
444	C₄²×C₂₉	C₂⁴	1	8	yes	—
445	C₄²×C₂₉	C₂⁴	1	2	yes	—
446	C₄²×C₂₉	C₂⁴	1	2	yes	—
447	C₄²×C₂₉	C₂⁴	1	8	yes	—
448	#62759	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₉	—	2	2	no	—
450	C₂³×C₂₉	—	2	8	no	—
451	C₂³×C₂₉	—	4	2	no	—
452	C₂³×C₂₉	—	4	8	no	—
453	C₂³×C₂₉	—	4	8	no	—
454	C₂³×C₂₉	—	4	16	no	—
455	C₂³×C₂₉	C₂⁵	1	4	yes	—
456	C₂³×C₂₉	C₂⁵	1	8	yes	—
457	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
458	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
459	C₂³×C₂₉	C₂⁵	1	4	yes	—
460	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
461	Q₈×C₂₉	—	2	8	no	—
462	Q₈×C₂₉	—	2	8	no	—
463	Q₈×C₂₉	—	4	2	no	—
464	Q₈×C₂₉	—	4	4	no	—
465	Q₈×C₂₉	—	4	2	no	—
466	Q₈×C₂₉	—	4	8	no	—
467	Q₈×C₂₉	—	4	4	no	—
468	D₄×C₂₉	—	2	16	no	—
469	D₄×C₂₉	—	2	8	no	—
470	D₄×C₂₉	—	2	8	no	—
471	D₄×C₂₉	—	2	8	no	—
472	D₄×C₂₉	—	2	8	no	—
473	D₄×C₂₉	—	4	8	no	—
474	D₄×C₂₉	—	4	16	no	—
475	D₄×C₂₉	—	4	4	no	—
476	D₄×C₂₉	—	4	4	no	—
477	D₄×C₂₉	—	4	2	no	—
478	D₄×C₂₉	—	4	4	no	—
479	D₄×C₂₉	—	4	4	no	—
480	D₄×C₂₉	—	4	2	no	—
481	D₄×C₂₉	—	4	4	no	—
482	D₄×C₂₉	—	4	8	no	—
483	D₄×C₂₉	—	4	16	no	—
484	D₄×C₂₉	—	4	8	no	—
485	D₄×C₂₉	—	4	4	no	—
486	D₄×C₂₉	—	4	8	no	—
487	D₄×C₂₉	—	4	16	no	—
488	C₂×C₄×C₂₉	—	2	2	no	—
489	C₂×C₄×C₂₉	—	2	8	no	—
490	C₂×C₄×C₂₉	—	2	8	no	—
491	C₂×C₄×C₂₉	—	2	8	no	—
492	C₂×C₄×C₂₉	—	2	8	no	—
493	C₂×C₄×C₂₉	—	2	2	no	—
494	C₂×C₄×C₂₉	—	2	2	no	—
495	C₂×C₄×C₂₉	—	2	8	no	—
496	C₂×C₄×C₂₉	—	2	2	no	—
497	C₂×C₄×C₂₉	—	2	2	no	—
498	C₂×C₄×C₂₉	—	2	16	no	—
499	C₂×C₄×C₂₉	—	2	4	no	—
500	C₂×C₄×C₂₉	—	2	4	no	—
501	C₂×C₄×C₂₉	—	2	4	no	—
502	C₂×C₄×C₂₉	—	2	16	no	—
503	C₂×C₄×C₂₉	—	4	2	no	—
504	C₂×C₄×C₂₉	—	4	2	no	—
505	C₂×C₄×C₂₉	—	4	2	no	—
506	C₂×C₄×C₂₉	—	4	8	no	—
507	C₂×C₄×C₂₉	—	4	16	no	—
508	C₂×C₄×C₂₉	—	4	8	no	—
509	C₂×C₄×C₂₉	—	4	16	no	—
510	C₂×C₄×C₂₉	H(5,𝔽₂)	1	4	yes	—
511	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
512	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
513	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
514	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
515	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
516	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
517	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
518	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
519	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
520	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
521	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
522	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
523	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
524	#3551	C₂×C₂₉	1	4	yes	complemented
525	#3550	C₂×C₂₉	1	1	yes	characteristic, complemented
526	#3549	C₂×C₂₉	1	1	yes	characteristic, complemented
527	#3548	C₂×C₂₉	1	2	yes	complemented
528	#3547	C₂×C₂₉	1	4	yes	complemented
529	#3546	C₂×C₂₉	1	4	yes	complemented
530	#3545	C₂×C₂₉	1	4	yes	complemented
531	#3544	C₂×C₂₉	1	2	yes	complemented
532	#3543	C₂×C₂₉	1	2	yes	complemented
533	#3542	C₂×C₂₉	1	8	yes	complemented
534	#3529	C₂×C₂₉	1	4	yes	complemented
535	#3483	C₂×C₂₉	1	2	yes	complemented
536	#3481	C₂×C₂₉	1	2	yes	complemented
537	#3475	C₂×C₂₉	1	4	yes	complemented
538	D₄×#41	C₂×C₂₉	1	4	yes	complemented
539	#3460	C₂×C₂₉	1	8	yes	complemented
540	#3449	C₂×C₂₉	1	4	yes	complemented
541	#3444	C₂×C₂₉	1	2	yes	complemented
542	C₂×#532	C₂×C₂₉	1	1	yes	characteristic, complemented
543	C₂²×C₂₉	—	2	2	no	—
544	C₂²×C₂₉	—	2	4	no	—
545	C₂²×C₂₉	—	2	1	no	—
546	C₂²×C₂₉	—	2	1	no	—
547	C₂²×C₂₉	—	2	4	no	—
548	C₂²×C₂₉	—	2	8	no	—
549	C₂²×C₂₉	—	2	2	no	—
550	C₂²×C₂₉	—	2	2	no	—
551	C₂²×C₂₉	—	2	8	no	—
552	C₂²×C₂₉	—	2	8	no	—
553	C₂²×C₂₉	—	2	8	no	—
554	C₂²×C₂₉	—	2	8	no	—
555	C₂²×C₂₉	—	4	4	no	—
556	C₂²×C₂₉	—	8	8	no	—
557	C₂²×C₂₉	—	8	16	no	—
558	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
559	C₂²×C₂₉	C₂⁶	1	1	yes	characteristic
560	C₄×C₂₉	—	2	4	no	—
561	C₄×C₂₉	—	2	1	no	—
562	C₄×C₂₉	—	2	1	no	—
563	C₄×C₂₉	—	2	4	no	—
564	C₄×C₂₉	—	2	8	no	—
565	C₄×C₂₉	—	2	2	no	—
566	C₄×C₂₉	—	2	2	no	—
567	C₄×C₂₉	—	2	8	no	—
568	C₄×C₂₉	—	2	2	no	—
569	C₄×C₂₉	—	2	8	no	—
570	C₄×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
571	C₄×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
572	C₄×C₂₉	#585	1	4	yes	—
573	C₂²×#41	C₂²×C₂₉	1	2	yes	complemented
574	C₂²×#41	C₂²×C₂₉	1	4	yes	complemented
575	#563	C₂²×C₂₉	1	8	yes	complemented
576	#563	C₂²×C₂₉	1	4	yes	complemented
577	#562	C₂²×C₂₉	1	16	yes	complemented
578	#562	C₂²×C₂₉	1	8	yes	complemented
579	H(3,𝔽₄)	C₂²×C₂₉	1	4	yes	complemented
580	#560	C₂²×C₂₉	1	16	yes	complemented
581	#560	C₂²×C₂₉	1	8	yes	complemented
582	#559	C₂²×C₂₉	1	2	yes	complemented
583	Q₈²	C₂²×C₂₉	1	2	yes	complemented
584	#556	C₂²×C₂₉	1	4	yes	complemented
585	#555	C₂²×C₂₉	1	4	yes	complemented
586	#555	C₂²×C₂₉	1	8	yes	complemented
587	#555	C₂²×C₂₉	1	2	yes	complemented
588	#555	C₂²×C₂₉	1	8	yes	complemented
589	#554	C₂²×C₂₉	1	4	yes	complemented
590	#554	C₂²×C₂₉	1	4	yes	complemented
591	#553	C₂²×C₂₉	1	8	yes	complemented
592	#553	C₂²×C₂₉	1	8	yes	complemented
593	#552	C₂²×C₂₉	1	8	yes	complemented
594	#552	C₂²×C₂₉	1	8	yes	complemented
595	#551	C₂²×C₂₉	1	16	yes	complemented
596	#551	C₂²×C₂₉	1	8	yes	complemented
597	#550	C₂²×C₂₉	1	4	yes	complemented
598	#550	C₂²×C₂₉	1	8	yes	complemented
599	#550	C₂²×C₂₉	1	4	yes	complemented
600	D₄×Q₈	C₂²×C₂₉	1	4	yes	complemented
601	#548	C₂²×C₂₉	1	8	yes	complemented
602	#547	C₂²×C₂₉	1	8	yes	complemented
603	#547	C₂²×C₂₉	1	4	yes	complemented
604	#547	C₂²×C₂₉	1	4	yes	complemented
605	#546	C₂²×C₂₉	1	16	yes	complemented
606	#546	C₂²×C₂₉	1	8	yes	complemented
607	#546	C₂²×C₂₉	1	8	yes	complemented
608	#546	C₂²×C₂₉	1	8	yes	complemented
609	D₄²	C₂²×C₂₉	1	8	yes	complemented
610	D₄²	C₂²×C₂₉	1	4	yes	complemented
611	D₄²	C₂²×C₂₉	1	2	yes	complemented
612	#544	C₂²×C₂₉	1	8	yes	complemented
613	#542	C₂²×C₂₉	1	8	yes	complemented
614	#542	C₂²×C₂₉	1	8	yes	complemented
615	#542	C₂²×C₂₉	1	16	yes	complemented
616	#540	C₂²×C₂₉	1	8	yes	complemented
617	#540	C₂²×C₂₉	1	16	yes	complemented
618	#540	C₂²×C₂₉	1	8	yes	complemented
619	#538	C₂²×C₂₉	1	16	yes	complemented
620	#538	C₂²×C₂₉	1	16	yes	complemented
621	#537	C₂²×C₂₉	1	8	yes	complemented
622	#537	C₂²×C₂₉	1	8	yes	complemented
623	#537	C₂²×C₂₉	1	8	yes	complemented
624	#536	C₂²×C₂₉	1	8	yes	complemented
625	#536	C₂²×C₂₉	1	4	yes	complemented
626	#536	C₂²×C₂₉	1	4	yes	complemented
627	#535	C₂²×C₂₉	1	8	yes	complemented
628	#535	C₂²×C₂₉	1	4	yes	complemented
629	#535	C₂²×C₂₉	1	4	yes	complemented
630	#535	C₂²×C₂₉	1	8	yes	complemented
631	#535	C₂²×C₂₉	1	8	yes	complemented
632	#534	C₂²×C₂₉	1	8	yes	complemented
633	#534	C₂²×C₂₉	1	8	yes	complemented
634	#533	C₂²×C₂₉	1	2	yes	complemented
635	#533	C₂²×C₂₉	1	2	yes	complemented
636	#533	C₂²×C₂₉	1	2	yes	complemented
637	#532	C₂²×C₂₉	1	1	yes	characteristic
638	#532	C₂²×C₂₉	1	1	yes	characteristic
639	#532	C₂²×C₂₉	1	2	yes	—
640	#532	C₂²×C₂₉	1	4	yes	complemented
641	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
642	#532	C₂²×C₂₉	1	2	yes	complemented
643	#532	C₂²×C₂₉	1	4	yes	complemented
644	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
645	#532	C₂²×C₂₉	1	2	yes	complemented
646	#532	C₂²×C₂₉	1	2	yes	complemented
647	#532	C₂²×C₂₉	1	2	yes	complemented
648	#532	C₂²×C₂₉	1	8	yes	complemented
649	#532	C₂²×C₂₉	1	8	yes	complemented
650	#532	C₂²×C₂₉	1	8	yes	complemented
651	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
652	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
653	#529	C₂²×C₂₉	1	4	yes	complemented
654	#529	C₂²×C₂₉	1	4	yes	complemented
655	#529	C₂²×C₂₉	1	4	yes	complemented
656	#529	C₂²×C₂₉	1	4	yes	complemented
657	#529	C₂²×C₂₉	1	4	yes	complemented
658	#529	C₂²×C₂₉	1	4	yes	complemented
659	#529	C₂²×C₂₉	1	8	yes	complemented
660	#529	C₂²×C₂₉	1	16	yes	complemented
661	C₂×#124	C₂²×C₂₉	1	2	yes	complemented
662	#525	C₂²×C₂₉	1	4	yes	complemented
663	#525	C₂²×C₂₉	1	4	yes	complemented
664	#525	C₂²×C₂₉	1	4	yes	complemented
665	#525	C₂²×C₂₉	1	8	yes	complemented
666	#525	C₂²×C₂₉	1	8	yes	complemented
667	#525	C₂²×C₂₉	1	8	yes	complemented
668	#525	C₂²×C₂₉	1	16	yes	complemented
669	C₂×#121	C₂²×C₂₉	1	4	yes	complemented
670	C₄×#41	C₂²×C₂₉	1	4	yes	complemented
671	C₄×#41	C₂²×C₂₉	1	4	yes	complemented
672	C₄×#41	C₂²×C₂₉	1	4	yes	complemented
673	C₄×#41	C₂²×C₂₉	1	8	yes	complemented
674	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	complemented
675	C₂×C₄×D₄	C₂²×C₂₉	1	8	yes	complemented
676	C₂×#117	C₂²×C₂₉	1	4	yes	complemented
677	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	C₂×C₂₉	—	2	2	no	—
679	C₂×C₂₉	—	4	1	no	—
680	C₂×C₂₉	—	4	1	no	—
681	C₂×C₂₉	—	4	4	no	—
682	C₂×C₂₉	—	4	8	no	—
683	C₂×C₂₉	—	4	4	no	—
684	C₂×C₂₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂×C₂₉	C₂×#585	1	2	yes	—
686	C₂×#41	—	4	8	no	—
687	C₂×#41	—	4	16	no	—
688	C₂×#41	C₂³×C₂₉	1	4	yes	—
689	C₂×#41	C₂³×C₂₉	1	4	yes	—
690	C₂×#41	C₂³×C₂₉	1	4	yes	—
691	C₂×#41	C₂³×C₂₉	1	8	yes	—
692	C₂×#41	C₂³×C₂₉	1	2	yes	—
693	C₂×#41	C₂³×C₂₉	1	4	yes	—
694	C₂×#41	C₂³×C₂₉	1	8	yes	—
695	C₂×#41	C₂³×C₂₉	1	2	yes	—
696	C₂×#41	C₂³×C₂₉	1	2	yes	—
697	C₂×#41	C₂³×C₂₉	1	4	yes	—
698	C₂×#41	C₂³×C₂₉	1	2	yes	—
699	C₂×#41	C₂³×C₂₉	1	8	yes	—
700	C₂×#41	C₂³×C₂₉	1	8	yes	—
701	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
702	C₂²×Q₈	C₂³×C₂₉	1	4	yes	—
703	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
704	C₂²×D₄	C₂³×C₂₉	1	8	yes	—
705	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
706	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
707	C₂²×D₄	C₂³×C₂₉	1	8	yes	—
708	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
709	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
710	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
711	C₂³×C₄	C₂³×C₂₉	1	8	yes	—
712	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
716	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
721	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
722	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
723	#127	C₂³×C₂₉	1	1	yes	characteristic
724	#127	C₂³×C₂₉	1	4	yes	—
725	#127	C₂³×C₂₉	1	1	yes	characteristic
726	#127	C₂³×C₂₉	1	2	yes	—
727	#127	C₂³×C₂₉	1	2	yes	—
728	#127	C₂³×C₂₉	1	8	yes	—
729	#127	C₂³×C₂₉	1	8	yes	—
730	#127	C₂³×C₂₉	1	8	yes	—
731	#126	C₂³×C₂₉	1	8	yes	—
732	#126	C₂³×C₂₉	1	8	yes	—
733	#126	C₂³×C₂₉	1	16	yes	—
734	#126	C₂³×C₂₉	1	16	yes	—
735	#126	C₂³×C₂₉	1	16	yes	—
736	#125	C₂³×C₂₉	1	4	yes	—
737	#125	C₂³×C₂₉	1	4	yes	—
738	#125	C₂³×C₂₉	1	4	yes	—
739	#125	C₂³×C₂₉	1	16	yes	—
740	#125	C₂³×C₂₉	1	8	yes	—
741	#124	C₂³×C₂₉	1	2	yes	—
742	#124	C₂³×C₂₉	1	2	yes	—
743	#124	C₂³×C₂₉	1	8	yes	—
744	#124	C₂³×C₂₉	1	2	yes	—
745	#124	C₂³×C₂₉	1	2	yes	—
746	#124	C₂³×C₂₉	1	4	yes	—
747	#124	C₂³×C₂₉	1	4	yes	—
748	#124	C₂³×C₂₉	1	4	yes	—
749	#124	C₂³×C₂₉	1	8	yes	—
750	#124	C₂³×C₂₉	1	16	yes	—
751	#124	C₂³×C₂₉	1	8	yes	—
752	#124	C₂³×C₂₉	1	8	yes	—
753	#124	C₂³×C₂₉	1	8	yes	—
754	#124	C₂³×C₂₉	1	8	yes	—
755	#124	C₂³×C₂₉	1	16	yes	—
756	#123	C₂³×C₂₉	1	8	yes	—
757	#123	C₂³×C₂₉	1	8	yes	—
758	#123	C₂³×C₂₉	1	8	yes	—
759	#123	C₂³×C₂₉	1	8	yes	—
760	#123	C₂³×C₂₉	1	8	yes	—
761	#123	C₂³×C₂₉	1	16	yes	—
762	#123	C₂³×C₂₉	1	8	yes	—
763	#123	C₂³×C₂₉	1	8	yes	—
764	#123	C₂³×C₂₉	1	16	yes	—
765	#123	C₂³×C₂₉	1	16	yes	—
766	#123	C₂³×C₂₉	1	16	yes	—
767	#123	C₂³×C₂₉	1	16	yes	—
768	#123	C₂³×C₂₉	1	16	yes	—
769	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
770	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
771	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
772	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
773	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
774	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
775	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
776	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
777	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
778	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
779	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
780	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
781	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
782	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
783	#121	C₂³×C₂₉	1	4	yes	—
784	#121	C₂³×C₂₉	1	4	yes	—
785	#121	C₂³×C₂₉	1	4	yes	—
786	#121	C₂³×C₂₉	1	8	yes	—
787	#121	C₂³×C₂₉	1	4	yes	—
788	#121	C₂³×C₂₉	1	8	yes	—
789	#121	C₂³×C₂₉	1	4	yes	—
790	#121	C₂³×C₂₉	1	4	yes	—
791	#121	C₂³×C₂₉	1	4	yes	—
792	#121	C₂³×C₂₉	1	4	yes	—
793	#121	C₂³×C₂₉	1	4	yes	—
794	#121	C₂³×C₂₉	1	4	yes	—
795	#121	C₂³×C₂₉	1	16	yes	—
796	#121	C₂³×C₂₉	1	8	yes	—
797	#121	C₂³×C₂₉	1	8	yes	—
798	#121	C₂³×C₂₉	1	16	yes	—
799	#121	C₂³×C₂₉	1	16	yes	—
800	#121	C₂³×C₂₉	1	16	yes	—
801	#121	C₂³×C₂₉	1	8	yes	—
802	#121	C₂³×C₂₉	1	16	yes	—
803	#121	C₂³×C₂₉	1	16	yes	—
804	#121	C₂³×C₂₉	1	16	yes	—
805	#121	C₂³×C₂₉	1	16	yes	—
806	#121	C₂³×C₂₉	1	16	yes	—
807	#121	C₂³×C₂₉	1	8	yes	—
808	#121	C₂³×C₂₉	1	8	yes	—
809	#121	C₂³×C₂₉	1	16	yes	—
810	#120	C₂³×C₂₉	1	8	yes	—
811	#120	C₂³×C₂₉	1	8	yes	—
812	#120	C₂³×C₂₉	1	8	yes	—
813	#120	C₂³×C₂₉	1	16	yes	—
814	#120	C₂³×C₂₉	1	8	yes	—
815	#120	C₂³×C₂₉	1	8	yes	—
816	#120	C₂³×C₂₉	1	16	yes	—
817	#120	C₂³×C₂₉	1	16	yes	—
818	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
819	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
820	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
821	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
822	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
823	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
824	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
825	C₄×D₄	C₂³×C₂₉	1	4	yes	—
826	C₄×D₄	C₂³×C₂₉	1	4	yes	—
827	C₄×D₄	C₂³×C₂₉	1	4	yes	—
828	C₄×D₄	C₂³×C₂₉	1	16	yes	—
829	C₄×D₄	C₂³×C₂₉	1	8	yes	—
830	C₄×D₄	C₂³×C₂₉	1	4	yes	—
831	C₄×D₄	C₂³×C₂₉	1	8	yes	—
832	C₄×D₄	C₂³×C₂₉	1	4	yes	—
833	C₄×D₄	C₂³×C₂₉	1	8	yes	—
834	C₄×D₄	C₂³×C₂₉	1	8	yes	—
835	C₄×D₄	C₂³×C₂₉	1	16	yes	—
836	C₄×D₄	C₂³×C₂₉	1	4	yes	—
837	C₄×D₄	C₂³×C₂₉	1	8	yes	—
838	C₄×D₄	C₂³×C₂₉	1	8	yes	—
839	C₄×D₄	C₂³×C₂₉	1	16	yes	—
840	C₄×D₄	C₂³×C₂₉	1	8	yes	—
841	C₄×D₄	C₂³×C₂₉	1	8	yes	—
842	C₄×D₄	C₂³×C₂₉	1	8	yes	—
843	C₄×D₄	C₂³×C₂₉	1	8	yes	—
844	C₄×D₄	C₂³×C₂₉	1	4	yes	—
845	C₄×D₄	C₂³×C₂₉	1	4	yes	—
846	C₄×D₄	C₂³×C₂₉	1	4	yes	—
847	C₄×D₄	C₂³×C₂₉	1	4	yes	—
848	C₄×D₄	C₂³×C₂₉	1	16	yes	—
849	C₄×D₄	C₂³×C₂₉	1	8	yes	—
850	#117	C₂³×C₂₉	1	4	yes	—
851	#117	C₂³×C₂₉	1	8	yes	—
852	#117	C₂³×C₂₉	1	8	yes	—
853	#117	C₂³×C₂₉	1	4	yes	—
854	#117	C₂³×C₂₉	1	4	yes	—
855	#117	C₂³×C₂₉	1	8	yes	—
856	#117	C₂³×C₂₉	1	4	yes	—
857	#117	C₂³×C₂₉	1	4	yes	—
858	#117	C₂³×C₂₉	1	8	yes	—
859	#117	C₂³×C₂₉	1	8	yes	—
860	#117	C₂³×C₂₉	1	8	yes	—
861	#117	C₂³×C₂₉	1	16	yes	—
862	C₂×C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
863	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
864	C₂×C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
865	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
867	C₂×C₂²⋊C₄	C₂³×C₂₉	1	16	yes	—
868	C₂×C₄²	C₂³×C₂₉	1	8	yes	—
869	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
870	C₂×C₄²	C₂³×C₂₉	1	8	yes	—
871	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
872	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
873	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
874	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
875	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
876	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
877	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
878	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
879	C₂₉	#62759	1	1	yes	characteristic, direct product factor, Sylow
880	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
881	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
882	C₂⁴	C₂⁴×C₂₉	1	8	yes	—
883	#41	—	2	16	no	—
884	#41	—	4	4	no	—
885	#41	—	4	8	no	—
886	#41	—	4	4	no	—
887	#41	—	4	8	no	—
888	#41	—	4	4	no	—
889	#41	—	4	4	no	—
890	#41	—	4	16	no	—
891	#41	—	4	8	no	—
892	#41	—	4	16	no	—
893	#41	—	4	16	no	—
894	#41	—	4	8	no	—
895	#41	—	4	16	no	—
896	C₂×Q₈	—	4	4	no	—
897	C₂×Q₈	—	4	8	no	—
898	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
899	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
900	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
901	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
903	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
904	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
905	C₂×D₄	—	4	8	no	—
906	C₂×D₄	—	4	8	no	—
907	C₂×D₄	—	4	16	no	—
908	C₂×D₄	—	4	4	no	—
909	C₂×D₄	—	4	8	no	—
910	C₂×D₄	—	4	16	no	—
911	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
912	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
913	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
914	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
915	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
916	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
917	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
918	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
919	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
920	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
921	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
922	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
923	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
924	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
925	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
926	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
927	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
928	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
929	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
930	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
931	C₂²×C₄	—	2	4	no	—
932	C₂²×C₄	—	2	16	no	—
933	C₂²×C₄	—	4	16	no	—
934	C₂²×C₄	—	4	4	no	—
935	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
936	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
939	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
945	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
946	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
947	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
948	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
949	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
950	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
954	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
955	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
956	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
957	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
959	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
960	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
961	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
962	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
963	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
964	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
965	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
966	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
967	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
968	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
969	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
970	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
971	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
972	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
973	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
974	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
975	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
976	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
977	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
978	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
979	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
980	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
981	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
982	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
983	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
984	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
985	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
986	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
987	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
988	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
989	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
990	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
991	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
992	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
993	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
994	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
995	C₄²	C₂⁴×C₂₉	1	2	yes	—
996	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
997	C₄²	C₂⁴×C₂₉	1	2	yes	—
998	C₄²	C₂⁴×C₂₉	1	8	yes	—
999	C₄²	C₂⁴×C₂₉	1	2	yes	—
1000	C₄²	C₂⁴×C₂₉	1	2	yes	—
1001	C₄²	C₂⁴×C₂₉	1	2	yes	—
1002	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₂₉	1	2	yes	—
1004	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₂₉	1	8	yes	—
1007	C₄²	C₂⁴×C₂₉	1	8	yes	—
1008	C₄²	C₂⁴×C₂₉	1	8	yes	—
1009	C₄²	C₂⁴×C₂₉	1	8	yes	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	8	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	4	8	no	—
1014	C₂³	—	4	8	no	—
1015	C₂³	—	4	16	no	—
1016	C₂³	C₂⁵×C₂₉	1	4	yes	—
1017	C₂³	C₂⁵×C₂₉	1	8	yes	—
1018	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
1019	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
1020	C₂³	C₂⁵×C₂₉	1	4	yes	—
1021	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
1022	Q₈	—	2	8	no	—
1023	Q₈	—	2	8	no	—
1024	Q₈	—	4	2	no	—
1025	Q₈	—	4	4	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	8	no	—
1028	Q₈	—	4	4	no	—
1029	D₄	—	2	16	no	—
1030	D₄	—	2	8	no	—
1031	D₄	—	2	8	no	—
1032	D₄	—	2	8	no	—
1033	D₄	—	2	8	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	4	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	8	no	—
1042	D₄	—	4	16	no	—
1043	D₄	—	4	8	no	—
1044	D₄	—	4	16	no	—
1045	D₄	—	4	8	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	8	no	—
1048	D₄	—	4	16	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	8	no	—
1051	C₂×C₄	—	2	8	no	—
1052	C₂×C₄	—	2	8	no	—
1053	C₂×C₄	—	2	8	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	8	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	16	no	—
1060	C₂×C₄	—	2	4	no	—
1061	C₂×C₄	—	2	4	no	—
1062	C₂×C₄	—	2	4	no	—
1063	C₂×C₄	—	2	16	no	—
1064	C₂×C₄	—	4	8	no	—
1065	C₂×C₄	—	4	16	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	8	no	—
1070	C₂×C₄	—	4	16	no	—
1071	C₂×C₄	C₂₉×H(5,𝔽₂)	1	4	yes	—
1072	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1074	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1075	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1076	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1077	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1079	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
1080	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1081	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
1082	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1083	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1084	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	4	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	8	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	8	no	—
1094	C₂²	—	2	8	no	—
1095	C₂²	—	2	8	no	—
1096	C₂²	—	2	8	no	—
1097	C₂²	—	4	4	no	—
1098	C₂²	—	8	8	no	—
1099	C₂²	—	8	16	no	—
1100	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
1101	C₂²	C₂⁶×C₂₉	1	1	yes	characteristic
1102	C₄	—	2	4	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	4	no	—
1106	C₄	—	2	8	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	8	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	8	no	—
1112	C₄	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
1113	C₄	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
1114	C₄	C₂₉×#585	1	4	yes	—
1115	C₂	—	2	2	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	4	4	no	—
1119	C₂	—	4	8	no	—
1120	C₂	—	4	4	no	—
1121	C₂	C₂²×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1122	C₂	C₂×C₂₉×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₉
socle	C₂²×C₂₉	C₂⁶
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
1. C₂₉×#3551	C₂	semidirect
2. C₂₉×#3550	C₂	semidirect
3. C₂₉×#3549	C₂	semidirect
4. C₂₉×#3548	C₂	semidirect
5. C₂₉×#3547	C₂	semidirect
6. C₂₉×#3546	C₂	semidirect
7. C₂₉×#3545	C₂	semidirect
8. C₂₉×#3544	C₂	semidirect
9. C₂₉×#3543	C₂	semidirect
10. C₂₉×#3542	C₂	semidirect
11. C₂₉×#3529	C₂	semidirect
12. C₂₉×#3483	C₂	semidirect
13. C₂₉×#3481	C₂	semidirect
14. C₂₉×#3475	C₂	semidirect
15. D₄×#41×C₂₉	C₂	semidirect
16. C₂₉×#3460	C₂	semidirect
17. C₂₉×#3449	C₂	semidirect
18. C₂₉×#3444	C₂	semidirect
19. C₂×C₂₉×#532	C₂	semidirect
20. C₂²×#41×C₂₉	C₂²	semidirect
21. C₂²×#41×C₂₉	C₂²	semidirect
22. C₂₉×#563	C₂²	semidirect
23. C₂₉×#563	C₂²	semidirect
24. C₂₉×#562	C₂²	semidirect
25. C₂₉×#562	C₂²	semidirect
26. C₂₉×H(3,𝔽₄)	C₂²	semidirect
27. C₂₉×#560	C₂²	semidirect
28. C₂₉×#560	C₂²	semidirect
29. C₂₉×#559	C₂²	semidirect
30. Q₈²×C₂₉	C₂²	semidirect
31. C₂₉×#556	C₂²	semidirect
32. C₂₉×#555	C₂²	semidirect
33. C₂₉×#555	C₂²	semidirect
34. C₂₉×#555	C₂²	semidirect
35. C₂₉×#555	C₂²	semidirect
36. C₂₉×#554	C₂²	semidirect
37. C₂₉×#554	C₂²	semidirect
38. C₂₉×#553	C₂²	semidirect
39. C₂₉×#553	C₂²	semidirect
40. C₂₉×#552	C₂²	semidirect
41. C₂₉×#552	C₂²	semidirect
42. C₂₉×#551	C₂²	semidirect
43. C₂₉×#551	C₂²	semidirect
44. C₂₉×#550	C₂²	semidirect
45. C₂₉×#550	C₂²	semidirect
46. C₂₉×#550	C₂²	semidirect
47. D₄×Q₈×C₂₉	C₂²	semidirect
48. C₂₉×#548	C₂²	semidirect
49. C₂₉×#547	C₂²	semidirect
50. C₂₉×#547	C₂²	semidirect
51. C₂₉×#547	C₂²	semidirect
52. C₂₉×#546	C₂²	semidirect
53. C₂₉×#546	C₂²	semidirect
54. C₂₉×#546	C₂²	semidirect
55. C₂₉×#546	C₂²	semidirect
56. D₄²×C₂₉	C₂²	semidirect
57. D₄²×C₂₉	C₂²	semidirect
58. D₄²×C₂₉	C₂²	semidirect
59. C₂₉×#544	C₂²	semidirect
60. C₂₉×#542	C₂²	semidirect
61. C₂₉×#542	C₂²	semidirect
62. C₂₉×#542	C₂²	semidirect
63. C₂₉×#540	C₂²	semidirect
64. C₂₉×#540	C₂²	semidirect
65. C₂₉×#540	C₂²	semidirect
66. C₂₉×#538	C₂²	semidirect
67. C₂₉×#538	C₂²	semidirect
68. C₂₉×#537	C₂²	semidirect
69. C₂₉×#537	C₂²	semidirect
70. C₂₉×#537	C₂²	semidirect
71. C₂₉×#536	C₂²	semidirect
72. C₂₉×#536	C₂²	semidirect
73. C₂₉×#536	C₂²	semidirect
74. C₂₉×#535	C₂²	semidirect
75. C₂₉×#535	C₂²	semidirect
76. C₂₉×#535	C₂²	semidirect
77. C₂₉×#535	C₂²	semidirect
78. C₂₉×#535	C₂²	semidirect
79. C₂₉×#534	C₂²	semidirect
80. C₂₉×#534	C₂²	semidirect
81. C₂₉×#533	C₂²	semidirect
82. C₂₉×#533	C₂²	semidirect
83. C₂₉×#533	C₂²	semidirect
87. C₂₉×#532	C₂²	semidirect
88. C₂₉×#532	C₂²	semidirect
89. C₂₉×#532	C₂²	semidirect
90. C₂₉×#532	C₂²	semidirect
91. C₂₉×#532	C₂²	semidirect
92. C₂₉×#532	C₂²	semidirect
93. C₂₉×#532	C₂²	semidirect
94. C₂₉×#532	C₂²	semidirect
95. C₂₉×#532	C₂²	semidirect
96. C₂₉×#532	C₂²	semidirect
97. C₂₉×#532	C₂²	semidirect
98. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
100. C₂₉×#529	C₂²	semidirect
101. C₂₉×#529	C₂²	semidirect
102. C₂₉×#529	C₂²	semidirect
103. C₂₉×#529	C₂²	semidirect
104. C₂₉×#529	C₂²	semidirect
105. C₂₉×#529	C₂²	semidirect
106. C₂₉×#529	C₂²	semidirect
107. C₂₉×#529	C₂²	semidirect
108. C₂×C₂₉×#124	C₂²	semidirect
109. C₂₉×#525	C₂²	semidirect
110. C₂₉×#525	C₂²	semidirect
111. C₂₉×#525	C₂²	semidirect
112. C₂₉×#525	C₂²	semidirect
113. C₂₉×#525	C₂²	semidirect
114. C₂₉×#525	C₂²	semidirect
115. C₂₉×#525	C₂²	semidirect
116. C₂×C₂₉×#121	C₂²	semidirect
117. C₄×#41×C₂₉	C₂²	semidirect
118. C₄×#41×C₂₉	C₂²	semidirect
119. C₄×#41×C₂₉	C₂²	semidirect
120. C₄×#41×C₂₉	C₂²	semidirect
121. C₂×C₄×D₄×C₂₉	C₂²	semidirect
122. C₂×C₄×D₄×C₂₉	C₂²	semidirect
123. C₂×C₂₉×#117	C₂²	semidirect
124. C₂²×C₄²×C₂₉	C₂²	semidirect
448. #62759	C₂₉	direct (N × H)
524. #3551	C₂×C₂₉	semidirect
525. #3550	C₂×C₂₉	semidirect
526. #3549	C₂×C₂₉	semidirect
527. #3548	C₂×C₂₉	semidirect
528. #3547	C₂×C₂₉	semidirect
529. #3546	C₂×C₂₉	semidirect
530. #3545	C₂×C₂₉	semidirect
531. #3544	C₂×C₂₉	semidirect
532. #3543	C₂×C₂₉	semidirect
533. #3542	C₂×C₂₉	semidirect
534. #3529	C₂×C₂₉	semidirect
535. #3483	C₂×C₂₉	semidirect
536. #3481	C₂×C₂₉	semidirect
537. #3475	C₂×C₂₉	semidirect
538. D₄×#41	C₂×C₂₉	semidirect
539. #3460	C₂×C₂₉	semidirect
540. #3449	C₂×C₂₉	semidirect
541. #3444	C₂×C₂₉	semidirect
542. C₂×#532	C₂×C₂₉	semidirect
573. C₂²×#41	C₂²×C₂₉	semidirect
574. C₂²×#41	C₂²×C₂₉	semidirect
575. #563	C₂²×C₂₉	semidirect
576. #563	C₂²×C₂₉	semidirect
577. #562	C₂²×C₂₉	semidirect
578. #562	C₂²×C₂₉	semidirect
579. H(3,𝔽₄)	C₂²×C₂₉	semidirect
580. #560	C₂²×C₂₉	semidirect
581. #560	C₂²×C₂₉	semidirect
582. #559	C₂²×C₂₉	semidirect
583. Q₈²	C₂²×C₂₉	semidirect
584. #556	C₂²×C₂₉	semidirect
585. #555	C₂²×C₂₉	semidirect
586. #555	C₂²×C₂₉	semidirect
587. #555	C₂²×C₂₉	semidirect
588. #555	C₂²×C₂₉	semidirect
589. #554	C₂²×C₂₉	semidirect
590. #554	C₂²×C₂₉	semidirect
591. #553	C₂²×C₂₉	semidirect
592. #553	C₂²×C₂₉	semidirect
593. #552	C₂²×C₂₉	semidirect
594. #552	C₂²×C₂₉	semidirect
595. #551	C₂²×C₂₉	semidirect
596. #551	C₂²×C₂₉	semidirect
597. #550	C₂²×C₂₉	semidirect
598. #550	C₂²×C₂₉	semidirect
599. #550	C₂²×C₂₉	semidirect
600. D₄×Q₈	C₂²×C₂₉	semidirect
601. #548	C₂²×C₂₉	semidirect
602. #547	C₂²×C₂₉	semidirect
603. #547	C₂²×C₂₉	semidirect
604. #547	C₂²×C₂₉	semidirect
605. #546	C₂²×C₂₉	semidirect
606. #546	C₂²×C₂₉	semidirect
607. #546	C₂²×C₂₉	semidirect
608. #546	C₂²×C₂₉	semidirect
609. D₄²	C₂²×C₂₉	semidirect
610. D₄²	C₂²×C₂₉	semidirect
611. D₄²	C₂²×C₂₉	semidirect
612. #544	C₂²×C₂₉	semidirect
613. #542	C₂²×C₂₉	semidirect
614. #542	C₂²×C₂₉	semidirect
615. #542	C₂²×C₂₉	semidirect
616. #540	C₂²×C₂₉	semidirect
617. #540	C₂²×C₂₉	semidirect
618. #540	C₂²×C₂₉	semidirect
619. #538	C₂²×C₂₉	semidirect
620. #538	C₂²×C₂₉	semidirect
621. #537	C₂²×C₂₉	semidirect
622. #537	C₂²×C₂₉	semidirect
623. #537	C₂²×C₂₉	semidirect
624. #536	C₂²×C₂₉	semidirect
625. #536	C₂²×C₂₉	semidirect
626. #536	C₂²×C₂₉	semidirect
627. #535	C₂²×C₂₉	semidirect
628. #535	C₂²×C₂₉	semidirect
629. #535	C₂²×C₂₉	semidirect
630. #535	C₂²×C₂₉	semidirect
631. #535	C₂²×C₂₉	semidirect
632. #534	C₂²×C₂₉	semidirect
633. #534	C₂²×C₂₉	semidirect
634. #533	C₂²×C₂₉	semidirect
635. #533	C₂²×C₂₉	semidirect
636. #533	C₂²×C₂₉	semidirect
640. #532	C₂²×C₂₉	semidirect
641. #532	C₂²×C₂₉	semidirect
642. #532	C₂²×C₂₉	semidirect
643. #532	C₂²×C₂₉	semidirect
644. #532	C₂²×C₂₉	semidirect
645. #532	C₂²×C₂₉	semidirect
646. #532	C₂²×C₂₉	semidirect
647. #532	C₂²×C₂₉	semidirect
648. #532	C₂²×C₂₉	semidirect
649. #532	C₂²×C₂₉	semidirect
650. #532	C₂²×C₂₉	semidirect
651. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
653. #529	C₂²×C₂₉	semidirect
654. #529	C₂²×C₂₉	semidirect
655. #529	C₂²×C₂₉	semidirect
656. #529	C₂²×C₂₉	semidirect
657. #529	C₂²×C₂₉	semidirect
658. #529	C₂²×C₂₉	semidirect
659. #529	C₂²×C₂₉	semidirect
660. #529	C₂²×C₂₉	semidirect
661. C₂×#124	C₂²×C₂₉	semidirect
662. #525	C₂²×C₂₉	semidirect
663. #525	C₂²×C₂₉	semidirect
664. #525	C₂²×C₂₉	semidirect
665. #525	C₂²×C₂₉	semidirect
666. #525	C₂²×C₂₉	semidirect
667. #525	C₂²×C₂₉	semidirect
668. #525	C₂²×C₂₉	semidirect
669. C₂×#121	C₂²×C₂₉	semidirect
670. C₄×#41	C₂²×C₂₉	semidirect
671. C₄×#41	C₂²×C₂₉	semidirect
672. C₄×#41	C₂²×C₂₉	semidirect
673. C₄×#41	C₂²×C₂₉	semidirect
674. C₂×C₄×D₄	C₂²×C₂₉	semidirect
675. C₂×C₄×D₄	C₂²×C₂₉	semidirect
676. C₂×#117	C₂²×C₂₉	semidirect
677. C₂²×C₄²	C₂²×C₂₉	semidirect
879. C₂₉	#62759	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×#3551	2
C₂₉×#3550	2
C₂₉×#3549	2
C₂₉×#3548	2
C₂₉×#3547	2
C₂₉×#3546	2
C₂₉×#3545	2
C₂₉×#3544	2
C₂₉×#3543	2
C₂₉×#3542	2
C₂₉×#3529	2
C₂₉×#3483	2
C₂₉×#3481	2
C₂₉×#3475	2
D₄×#41×C₂₉	2
C₂₉×#3460	2
C₂₉×#3449	2
C₂₉×#3444	2
C₂×C₂₉×#532	2
#62759	29

Subgroups — C29×#62759 #20357659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62759 #20357659