Subgroups — C₂₉×#62127 #20357027

Order 7424.

1810 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3481	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3385	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3375	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3346	C₂	1	4	yes	maximal, complemented
6	C₂₉×#3338	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3314	C₂	1	4	yes	maximal, complemented
8	C₂₉×#3295	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#3248	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3239	C₂	1	2	yes	maximal, complemented
12	C₂₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3110	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#474	C₂	1	2	yes	maximal, complemented
17	C₂₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#559	C₂²	1	1	yes	characteristic
19	Q₈²×C₂₉	C₂²	1	2	yes	complemented
20	C₂₉×#557	—	2	1	no	—
21	C₂₉×#554	C₂²	1	1	yes	characteristic
22	C₂₉×#554	C₂²	1	1	yes	characteristic
23	C₂₉×#554	C₂²	1	2	yes	—
24	C₂₉×#554	C₂²	1	4	yes	complemented
25	C₂₉×#553	—	2	1	no	—
26	C₂₉×#553	C₂²	1	2	yes	—
27	C₂₉×#551	—	2	2	no	—
28	D₄×Q₈×C₂₉	—	2	1	no	—
29	D₄×Q₈×C₂₉	—	2	2	no	—
30	C₂₉×#546	—	2	1	no	—
31	C₂₉×#546	C₂²	1	2	yes	—
32	D₄²×C₂₉	C₂²	1	1	yes	characteristic
33	C₂₉×#544	—	2	2	no	—
34	C₂₉×#544	—	2	1	no	—
35	C₂₉×#533	C₂²	1	2	yes	complemented
36	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#532	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
40	C₂₉×#529	—	2	1	no	—
41	C₂₉×#529	C₂²	1	2	yes	—
42	C₂₉×#525	—	2	2	no	—
43	C₂₉×#520	—	2	1	no	—
44	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
45	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₉	—	2	1	no	—
47	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
48	C₂₉×#501	C₂²	1	4	yes	complemented
49	C₂₉×#500	C₂²	1	2	yes	complemented
50	C₂₉×#489	C₂²	1	4	yes	complemented
51	C₂₉×#486	C₂²	1	2	yes	—
52	C₂₉×#485	C₂²	1	2	yes	complemented
53	C₂₉×#484	C₂²	1	4	yes	complemented
54	C₂₉×#484	C₂²	1	4	yes	complemented
55	C₂₉×#481	C₂²	1	4	yes	—
56	C₂₉×#480	C₂²	1	4	yes	complemented
57	C₂₉×#479	C₂²	1	4	yes	complemented
58	C₂₉×#477	C₂²	1	2	yes	complemented
59	C₂₉×#477	C₂²	1	2	yes	complemented
60	C₂₉×#476	C₂²	1	2	yes	—
61	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#475	C₂²	1	2	yes	complemented
63	C₂₉×#474	C₂²	1	4	yes	—
64	C₂₉×#474	C₂²	1	1	yes	characteristic
65	C₂₉×#474	C₂²	1	2	yes	—
66	C₂₉×#474	C₂²	1	2	yes	complemented
67	C₂₉×#474	C₂²	1	2	yes	complemented
68	C₂₉×#474	C₂²	1	2	yes	complemented
69	C₂₉×#474	C₂²	1	4	yes	complemented
70	C₂₉×#468	C₂²	1	4	yes	complemented
71	C₂₉×#467	C₂²	1	4	yes	complemented
72	C₂₉×#465	C₂²	1	4	yes	—
73	C₂₉×#464	C₂²	1	4	yes	complemented
74	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#461	C₂²	1	1	yes	characteristic
76	C₂₉×#461	C₂²	1	2	yes	complemented
77	C₂₉×#460	C₂²	1	2	yes	—
78	C₂₉×#452	C₂²	1	2	yes	—
79	C₂₉×#450	C₂²	1	4	yes	—
80	C₂₉×#446	C₂²	1	2	yes	complemented
81	C₂₉×#440	C₂²	1	4	yes	—
82	C₂₉×#440	C₂²	1	4	yes	complemented
83	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
85	C₂₉×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₂₉	C₂²	1	2	yes	—
87	C₂₉×#432	C₂²	1	2	yes	complemented
88	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
89	C₂₉×#428	C₂²	1	2	yes	complemented
90	C₂×C₂₉×#107	C₂²	1	4	yes	complemented
91	C₂₉×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₂₉×#417	C₂²	1	2	yes	—
94	C₂×C₂₉×#102	C₂²	1	4	yes	—
95	C₂×#41×C₂₉	—	2	1	no	—
96	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
97	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₂₉	—	2	2	no	—
99	C₂²×Q₈×C₂₉	—	2	1	no	—
100	C₂²×D₄×C₂₉	—	2	1	no	—
101	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₂₉	—	2	2	no	—
103	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
106	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
107	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
108	C₂₉×C₄⋊Q₈	—	2	2	no	—
109	C₂₉×C₄⋊Q₈	—	2	4	no	—
110	C₂₉×C₄⋊Q₈	—	2	1	no	—
111	C₂₉×C₄⋊Q₈	—	2	2	no	—
112	C₂₉×C₄⋊Q₈	—	2	1	no	—
113	C₂₉×C₄⋊Q₈	—	2	2	no	—
114	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₉×#127	C₂³	1	1	yes	characteristic
121	C₂₉×#126	—	2	2	no	—
122	C₂₉×#126	—	2	2	no	—
123	C₂₉×#125	—	2	1	no	—
124	C₂₉×#125	—	2	2	no	—
125	C₂₉×#125	—	2	4	no	—
126	C₂₉×#125	—	2	1	no	—
127	C₂₉×#125	—	2	2	no	—
128	C₂₉×#125	C₂³	1	2	yes	—
129	C₂₉×#124	—	2	1	no	—
130	C₂₉×#124	—	2	1	no	—
131	C₂₉×#124	C₂³	1	2	yes	—
132	C₂₉×#123	—	2	2	no	—
133	C₂₉×#123	—	2	2	no	—
134	C₂₉×#123	—	2	2	no	—
135	C₂₉×#123	—	2	2	no	—
136	C₂₉×C₂²⋊Q₈	—	2	1	no	—
137	C₂₉×C₂²⋊Q₈	—	2	2	no	—
138	C₂₉×C₂²⋊Q₈	—	2	1	no	—
139	C₂₉×C₂²⋊Q₈	—	2	2	no	—
140	C₂₉×C₂²⋊Q₈	—	2	2	no	—
141	C₂₉×C₂²⋊Q₈	—	2	4	no	—
142	C₂₉×C₂²⋊Q₈	—	2	4	no	—
143	C₂₉×C₂²⋊Q₈	—	2	4	no	—
144	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₂₉×#121	—	2	2	no	—
148	C₂₉×#121	—	2	1	no	—
149	C₂₉×#121	—	2	1	no	—
150	C₂₉×#121	—	2	2	no	—
151	C₂₉×#121	C₂³	1	2	yes	—
152	C₂₉×#121	C₂³	1	2	yes	—
153	C₂₉×#120	—	2	2	no	—
154	C₂₉×#120	—	2	2	no	—
155	C₄×Q₈×C₂₉	—	2	2	no	—
156	C₄×Q₈×C₂₉	—	2	1	no	—
157	C₄×Q₈×C₂₉	—	2	2	no	—
158	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
162	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₂₉	—	2	1	no	—
165	C₄×D₄×C₂₉	—	2	2	no	—
166	C₄×D₄×C₂₉	—	2	4	no	—
167	C₄×D₄×C₂₉	—	2	2	no	—
168	C₄×D₄×C₂₉	—	2	1	no	—
169	C₄×D₄×C₂₉	—	2	1	no	—
170	C₄×D₄×C₂₉	—	2	1	no	—
171	C₄×D₄×C₂₉	—	2	2	no	—
172	C₄×D₄×C₂₉	—	2	1	no	—
173	C₄×D₄×C₂₉	—	2	2	no	—
174	C₄×D₄×C₂₉	—	2	2	no	—
175	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
176	C₄×D₄×C₂₉	D₄	1	2	yes	—
177	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₉	C₂³	1	2	yes	—
179	C₄×D₄×C₂₉	C₂³	1	2	yes	—
180	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₉	C₂³	1	2	yes	—
182	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₂₉	C₂³	1	2	yes	—
184	C₂₉×#117	—	2	2	no	—
185	C₂₉×#117	—	2	1	no	—
186	C₂₉×#117	—	2	1	no	—
187	C₂₉×#117	—	2	2	no	—
188	C₂₉×#117	D₄	1	2	yes	—
189	C₂₉×#117	D₄	1	1	yes	characteristic
190	C₂₉×#117	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
193	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
194	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
199	C₂×C₄²×C₂₉	—	2	1	no	—
200	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
202	C₂₉×#107	C₂³	1	2	yes	—
203	C₂₉×#107	C₂³	1	4	yes	—
204	C₂₉×#107	C₂³	1	4	yes	—
205	C₂₉×#107	C₂³	1	4	yes	—
206	C₂₉×#107	C₂³	1	4	yes	—
207	C₂₉×#106	C₂³	1	4	yes	—
208	C₂₉×#106	C₂³	1	2	yes	—
209	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
212	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
214	C₂₉×#103	C₂³	1	2	yes	—
215	C₂₉×#103	C₂³	1	2	yes	—
216	C₂₉×#103	C₂³	1	2	yes	—
217	C₂₉×#103	C₂³	1	4	yes	—
218	C₂₉×#103	C₂³	1	4	yes	—
219	C₂₉×#102	C₂³	1	2	yes	—
220	C₂₉×#102	C₂³	1	4	yes	—
221	C₂₉×#102	C₂³	1	4	yes	—
222	C₂₉×#102	C₂³	1	4	yes	—
223	C₂₉×#102	C₂³	1	4	yes	—
224	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₉×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₂₉	C₂³	1	2	yes	—
228	C₂⁴×C₂₉	—	2	2	no	—
229	#41×C₂₉	—	2	4	no	—
230	#41×C₂₉	—	2	2	no	—
231	#41×C₂₉	—	4	1	no	—
232	#41×C₂₉	—	8	2	no	—
233	C₂×Q₈×C₂₉	—	2	1	no	—
234	C₂×Q₈×C₂₉	—	2	2	no	—
235	C₂×Q₈×C₂₉	—	2	1	no	—
236	C₂×Q₈×C₂₉	—	2	4	no	—
237	C₂×Q₈×C₂₉	—	2	2	no	—
238	C₂×Q₈×C₂₉	—	8	4	no	—
239	C₂×Q₈×C₂₉	—	8	2	no	—
240	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₂₉	—	2	4	no	—
244	C₂×D₄×C₂₉	—	2	1	no	—
245	C₂×D₄×C₂₉	—	2	2	no	—
246	C₂×D₄×C₂₉	—	2	2	no	—
247	C₂×D₄×C₂₉	—	2	2	no	—
248	C₂×D₄×C₂₉	—	2	1	no	—
249	C₂×D₄×C₂₉	—	2	1	no	—
250	C₂×D₄×C₂₉	—	4	2	no	—
251	C₂×D₄×C₂₉	—	4	4	no	—
252	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
255	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₂₉	—	2	2	no	—
257	C₂²×C₄×C₂₉	—	2	2	no	—
258	C₂²×C₄×C₂₉	—	2	4	no	—
259	C₂²×C₄×C₂₉	—	2	1	no	—
260	C₂²×C₄×C₂₉	—	2	1	no	—
261	C₂²×C₄×C₂₉	—	2	1	no	—
262	C₂²×C₄×C₂₉	—	2	2	no	—
263	C₂²×C₄×C₂₉	—	2	2	no	—
264	C₂²×C₄×C₂₉	—	2	2	no	—
265	C₂²×C₄×C₂₉	—	8	4	no	—
266	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₂₉	—	4	2	no	—
273	SD₁₆×C₂₉	—	2	4	no	—
274	SD₁₆×C₂₉	—	4	4	no	—
275	M₁₆×C₂₉	—	4	2	no	—
276	C₂×C₈×C₂₉	—	4	4	no	—
277	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
278	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
279	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₂₉	—	2	1	no	—
281	C₄⋊C₄×C₂₉	—	2	2	no	—
282	C₄⋊C₄×C₂₉	—	2	1	no	—
283	C₄⋊C₄×C₂₉	—	2	2	no	—
284	C₄⋊C₄×C₂₉	—	2	4	no	—
285	C₄⋊C₄×C₂₉	—	2	2	no	—
286	C₄⋊C₄×C₂₉	—	2	2	no	—
287	C₄⋊C₄×C₂₉	—	2	2	no	—
288	C₄⋊C₄×C₂₉	—	2	4	no	—
289	C₄⋊C₄×C₂₉	—	2	1	no	—
290	C₄⋊C₄×C₂₉	—	2	1	no	—
291	C₄⋊C₄×C₂₉	—	2	1	no	—
292	C₄⋊C₄×C₂₉	—	2	2	no	—
293	C₄⋊C₄×C₂₉	—	2	2	no	—
294	C₄⋊C₄×C₂₉	—	2	1	no	—
295	C₄⋊C₄×C₂₉	—	2	2	no	—
296	C₄⋊C₄×C₂₉	—	2	4	no	—
297	C₄⋊C₄×C₂₉	—	2	4	no	—
298	C₄⋊C₄×C₂₉	—	2	2	no	—
299	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
306	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
308	C₂²⋊C₄×C₂₉	—	2	2	no	—
309	C₂²⋊C₄×C₂₉	—	2	2	no	—
310	C₂²⋊C₄×C₂₉	—	2	4	no	—
311	C₂²⋊C₄×C₂₉	—	2	1	no	—
312	C₂²⋊C₄×C₂₉	—	2	1	no	—
313	C₂²⋊C₄×C₂₉	—	2	2	no	—
314	C₂²⋊C₄×C₂₉	—	2	2	no	—
315	C₂²⋊C₄×C₂₉	—	2	2	no	—
316	C₂²⋊C₄×C₂₉	—	2	2	no	—
317	C₂²⋊C₄×C₂₉	—	2	2	no	—
318	C₂²⋊C₄×C₂₉	—	2	1	no	—
319	C₂²⋊C₄×C₂₉	—	2	2	no	—
320	C₂²⋊C₄×C₂₉	—	2	2	no	—
321	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
324	C₄²×C₂₉	—	2	1	no	—
325	C₄²×C₂₉	—	2	1	no	—
326	C₄²×C₂₉	—	2	1	no	—
327	C₄²×C₂₉	—	2	4	no	—
328	C₄²×C₂₉	—	2	2	no	—
329	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₂₉	C₂×D₄	1	2	yes	—
332	C₄²×C₂₉	C₂×D₄	1	2	yes	—
333	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
334	C₄²×C₂₉	C₂⁴	1	2	yes	—
335	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
336	#62127	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂³×C₂₉	—	2	1	no	—
338	C₂³×C₂₉	—	2	2	no	—
339	C₂³×C₂₉	—	4	4	no	—
340	C₂³×C₂₉	—	4	4	no	—
341	C₂³×C₂₉	—	8	2	no	—
342	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
343	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
344	Q₈×C₂₉	—	2	2	no	—
345	Q₈×C₂₉	—	2	2	no	—
346	Q₈×C₂₉	—	2	1	no	—
347	Q₈×C₂₉	—	2	2	no	—
348	Q₈×C₂₉	—	2	1	no	—
349	Q₈×C₂₉	—	4	2	no	—
350	Q₈×C₂₉	—	4	4	no	—
351	Q₈×C₂₉	—	8	4	no	—
352	Q₈×C₂₉	—	8	2	no	—
353	Q₈×C₂₉	—	8	1	no	—
354	D₄×C₂₉	—	2	4	no	—
355	D₄×C₂₉	—	2	2	no	—
356	D₄×C₂₉	—	2	1	no	—
357	D₄×C₂₉	—	2	2	no	—
358	D₄×C₂₉	—	4	4	no	—
359	D₄×C₂₉	—	4	2	no	—
360	D₄×C₂₉	—	4	4	no	—
361	D₄×C₂₉	—	4	2	no	—
362	D₄×C₂₉	—	8	1	no	—
363	D₄×C₂₉	—	8	2	no	—
364	D₄×C₂₉	#137	1	4	yes	—
365	D₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
366	C₂×C₄×C₂₉	—	2	4	no	—
367	C₂×C₄×C₂₉	—	2	2	no	—
368	C₂×C₄×C₂₉	—	2	4	no	—
369	C₂×C₄×C₂₉	—	2	2	no	—
370	C₂×C₄×C₂₉	—	2	2	no	—
371	C₂×C₄×C₂₉	—	2	1	no	—
372	C₂×C₄×C₂₉	—	2	2	no	—
373	C₂×C₄×C₂₉	—	2	1	no	—
374	C₂×C₄×C₂₉	—	2	2	no	—
375	C₂×C₄×C₂₉	—	2	1	no	—
376	C₂×C₄×C₂₉	—	2	1	no	—
377	C₂×C₄×C₂₉	—	2	1	no	—
378	C₂×C₄×C₂₉	—	2	4	no	—
379	C₂×C₄×C₂₉	—	2	2	no	—
380	C₂×C₄×C₂₉	—	2	2	no	—
381	C₂×C₄×C₂₉	—	4	2	no	—
382	C₂×C₄×C₂₉	—	4	2	no	—
383	C₂×C₄×C₂₉	—	4	2	no	—
384	C₂×C₄×C₂₉	—	4	4	no	—
385	C₂×C₄×C₂₉	—	8	2	no	—
386	C₂×C₄×C₂₉	—	8	2	no	—
387	C₂×C₄×C₂₉	—	8	2	no	—
388	C₂×C₄×C₂₉	—	8	4	no	—
389	C₂×C₄×C₂₉	—	8	2	no	—
390	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
399	C₈×C₂₉	—	2	2	no	—
400	C₈×C₂₉	—	2	2	no	—
401	C₈×C₂₉	—	2	4	no	—
402	#3503	C₂×C₂₉	1	1	yes	characteristic, complemented
403	#3481	C₂×C₂₉	1	1	yes	characteristic
404	#3385	C₂×C₂₉	1	2	yes	complemented
405	#3375	C₂×C₂₉	1	2	yes	complemented
406	#3346	C₂×C₂₉	1	4	yes	complemented
407	#3338	C₂×C₂₉	1	2	yes	complemented
408	#3314	C₂×C₂₉	1	4	yes	complemented
409	#3295	C₂×C₂₉	1	2	yes	complemented
410	#3254	C₂×C₂₉	1	1	yes	characteristic, complemented
411	#3248	C₂×C₂₉	1	2	yes	complemented
412	#3239	C₂×C₂₉	1	2	yes	complemented
413	#3226	C₂×C₂₉	1	1	yes	characteristic, complemented
414	#3110	C₂×C₂₉	1	2	yes	complemented
415	#3107	C₂×C₂₉	1	1	yes	characteristic, complemented
416	#3079	C₂×C₂₉	1	1	yes	characteristic, complemented
417	C₂×#474	C₂×C₂₉	1	2	yes	complemented
418	#2990	C₂×C₂₉	1	1	yes	characteristic, complemented
419	C₂²×C₂₉	—	2	2	no	—
420	C₂²×C₂₉	—	2	2	no	—
421	C₂²×C₂₉	—	2	1	no	—
422	C₂²×C₂₉	—	2	2	no	—
423	C₂²×C₂₉	—	2	1	no	—
424	C₂²×C₂₉	—	2	1	no	—
425	C₂²×C₂₉	—	4	1	no	—
426	C₂²×C₂₉	—	4	1	no	—
427	C₂²×C₂₉	—	4	2	no	—
428	C₂²×C₂₉	—	4	2	no	—
429	C₂²×C₂₉	—	4	2	no	—
430	C₂²×C₂₉	—	8	8	no	—
431	C₂²×C₂₉	C₂×#137	1	4	yes	—
432	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
433	C₄×C₂₉	—	2	1	no	—
434	C₄×C₂₉	—	2	2	no	—
435	C₄×C₂₉	—	2	1	no	—
436	C₄×C₂₉	—	2	2	no	—
437	C₄×C₂₉	—	2	2	no	—
438	C₄×C₂₉	—	2	1	no	—
439	C₄×C₂₉	—	4	1	no	—
440	C₄×C₂₉	—	4	2	no	—
441	C₄×C₂₉	—	4	1	no	—
442	C₄×C₂₉	—	4	1	no	—
443	C₄×C₂₉	—	4	2	no	—
444	C₄×C₂₉	—	4	2	no	—
445	C₄×C₂₉	—	4	4	no	—
446	C₄×C₂₉	C₂×#137	1	2	yes	—
447	C₄×C₂₉	#576	1	2	yes	—
448	C₄×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₄×C₂₉	#585	1	1	yes	characteristic
450	#559	C₂²×C₂₉	1	1	yes	characteristic
451	Q₈²	C₂²×C₂₉	1	2	yes	complemented
452	#557	—	2	1	no	—
453	#554	C₂²×C₂₉	1	1	yes	characteristic
454	#554	C₂²×C₂₉	1	1	yes	characteristic
455	#554	C₂²×C₂₉	1	2	yes	—
456	#554	C₂²×C₂₉	1	4	yes	complemented
457	#553	—	2	1	no	—
458	#553	C₂²×C₂₉	1	2	yes	—
459	#551	—	2	2	no	—
460	D₄×Q₈	—	2	1	no	—
461	D₄×Q₈	—	2	2	no	—
462	#546	—	2	1	no	—
463	#546	C₂²×C₂₉	1	2	yes	—
464	D₄²	C₂²×C₂₉	1	1	yes	characteristic
465	#544	—	2	2	no	—
466	#544	—	2	1	no	—
467	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
468	#533	C₂²×C₂₉	1	2	yes	complemented
469	#532	C₂²×C₂₉	1	1	yes	characteristic
470	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
471	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	complemented
472	#529	—	2	1	no	—
473	#529	C₂²×C₂₉	1	2	yes	—
474	#525	—	2	2	no	—
475	#520	—	2	1	no	—
476	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
477	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
478	C₂×C₄×D₄	—	2	1	no	—
479	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
480	#501	C₂²×C₂₉	1	4	yes	complemented
481	#500	C₂²×C₂₉	1	2	yes	complemented
482	#489	C₂²×C₂₉	1	4	yes	complemented
483	#486	C₂²×C₂₉	1	2	yes	—
484	#485	C₂²×C₂₉	1	2	yes	complemented
485	#484	C₂²×C₂₉	1	4	yes	complemented
486	#484	C₂²×C₂₉	1	4	yes	complemented
487	#481	C₂²×C₂₉	1	4	yes	—
488	#480	C₂²×C₂₉	1	4	yes	complemented
489	#479	C₂²×C₂₉	1	4	yes	complemented
490	#477	C₂²×C₂₉	1	2	yes	complemented
491	#477	C₂²×C₂₉	1	2	yes	complemented
492	#476	C₂²×C₂₉	1	2	yes	—
493	#475	C₂²×C₂₉	1	2	yes	complemented
494	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
495	#474	C₂²×C₂₉	1	2	yes	—
496	#474	C₂²×C₂₉	1	1	yes	characteristic
497	#474	C₂²×C₂₉	1	4	yes	—
498	#474	C₂²×C₂₉	1	4	yes	complemented
499	#474	C₂²×C₂₉	1	2	yes	complemented
500	#474	C₂²×C₂₉	1	2	yes	complemented
501	#474	C₂²×C₂₉	1	2	yes	complemented
502	#468	C₂²×C₂₉	1	4	yes	complemented
503	#467	C₂²×C₂₉	1	4	yes	complemented
504	#465	C₂²×C₂₉	1	4	yes	—
505	#464	C₂²×C₂₉	1	4	yes	complemented
506	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
507	#461	C₂²×C₂₉	1	1	yes	characteristic
508	#461	C₂²×C₂₉	1	2	yes	complemented
509	#460	C₂²×C₂₉	1	2	yes	—
510	#452	C₂²×C₂₉	1	2	yes	—
511	#450	C₂²×C₂₉	1	4	yes	—
512	#446	C₂²×C₂₉	1	2	yes	complemented
513	#440	C₂²×C₂₉	1	4	yes	—
514	#440	C₂²×C₂₉	1	4	yes	complemented
515	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
516	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
517	#435	C₂²×C₂₉	1	4	yes	complemented
518	C₈×D₄	C₂²×C₂₉	1	2	yes	—
519	#432	C₂²×C₂₉	1	2	yes	complemented
520	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
521	#428	C₂²×C₂₉	1	2	yes	complemented
522	C₂×#107	C₂²×C₂₉	1	4	yes	complemented
523	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
524	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
525	#417	C₂²×C₂₉	1	2	yes	—
526	C₂×#102	C₂²×C₂₉	1	4	yes	—
527	C₂×C₂₉	—	2	4	no	—
528	C₂×C₂₉	—	4	1	no	—
529	C₂×C₂₉	—	4	2	no	—
530	C₂×C₂₉	—	8	2	no	—
531	C₂×C₂₉	#3489	1	1	yes	characteristic
532	C₂×C₂₉	C₂²×#137	1	1	yes	characteristic
533	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
534	C₂×#41	—	2	1	no	—
535	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
536	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
537	C₂²×Q₈	—	2	2	no	—
538	C₂²×Q₈	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
541	C₂³×C₄	—	2	2	no	—
542	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
545	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
546	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
547	C₄⋊Q₈	—	2	2	no	—
548	C₄⋊Q₈	—	2	4	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
556	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
558	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
559	#127	C₂³×C₂₉	1	1	yes	characteristic
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	1	no	—
563	#125	—	2	2	no	—
564	#125	—	2	4	no	—
565	#125	—	2	1	no	—
566	#125	—	2	2	no	—
567	#125	C₂³×C₂₉	1	2	yes	—
568	#124	—	2	1	no	—
569	#124	—	2	1	no	—
570	#124	C₂³×C₂₉	1	2	yes	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
585	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	C₂³×C₂₉	1	2	yes	—
591	#121	C₂³×C₂₉	1	2	yes	—
592	#120	—	2	2	no	—
593	#120	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
601	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
602	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
615	C₄×D₄	D₄×C₂₉	1	2	yes	—
616	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₂₉	1	2	yes	—
618	C₄×D₄	C₂³×C₂₉	1	2	yes	—
619	C₄×D₄	C₂³×C₂₉	1	2	yes	—
620	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₂₉	1	2	yes	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	D₄×C₂₉	1	2	yes	—
628	#117	D₄×C₂₉	1	1	yes	characteristic
629	#117	C₂³×C₂₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
641	#107	C₂³×C₂₉	1	2	yes	—
642	#107	C₂³×C₂₉	1	4	yes	—
643	#107	C₂³×C₂₉	1	4	yes	—
644	#107	C₂³×C₂₉	1	4	yes	—
645	#107	C₂³×C₂₉	1	4	yes	—
646	#106	C₂³×C₂₉	1	4	yes	—
647	#106	C₂³×C₂₉	1	2	yes	—
648	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
649	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
650	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
651	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
652	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
653	#103	C₂³×C₂₉	1	4	yes	—
654	#103	C₂³×C₂₉	1	2	yes	—
655	#103	C₂³×C₂₉	1	2	yes	—
656	#103	C₂³×C₂₉	1	2	yes	—
657	#103	C₂³×C₂₉	1	4	yes	—
658	#102	C₂³×C₂₉	1	2	yes	—
659	#102	C₂³×C₂₉	1	4	yes	—
660	#102	C₂³×C₂₉	1	4	yes	—
661	#102	C₂³×C₂₉	1	4	yes	—
662	#102	C₂³×C₂₉	1	4	yes	—
663	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
665	#97	C₂³×C₂₉	1	4	yes	—
666	C₄×C₈	C₂³×C₂₉	1	2	yes	—
667	C₂₉	#62127	1	1	yes	characteristic, direct product factor, Sylow
668	C₂⁴	—	2	2	no	—
669	#41	—	2	4	no	—
670	#41	—	2	2	no	—
671	#41	—	4	1	no	—
672	#41	—	8	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	8	4	no	—
679	C₂×Q₈	—	8	2	no	—
680	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
682	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
693	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
694	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
695	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	8	4	no	—
706	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
709	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
712	Q₁₆	—	4	2	no	—
713	SD₁₆	—	2	4	no	—
714	SD₁₆	—	4	4	no	—
715	M₁₆	—	4	2	no	—
716	C₂×C₈	—	4	4	no	—
717	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
718	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
719	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
742	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
763	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₂₉	1	2	yes	—
772	C₄²	C₂×D₄×C₂₉	1	2	yes	—
773	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
774	C₄²	C₂⁴×C₂₉	1	2	yes	—
775	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	8	2	no	—
781	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
782	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	8	4	no	—
791	Q₈	—	8	2	no	—
792	Q₈	—	8	1	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	2	no	—
803	D₄	C₂₉×#137	1	4	yes	—
804	D₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
837	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
838	C₈	—	2	2	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	4	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	8	8	no	—
853	C₂²	C₂×C₂₉×#137	1	4	yes	—
854	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	4	no	—
868	C₄	C₂×C₂₉×#137	1	2	yes	—
869	C₄	C₂₉×#576	1	2	yes	—
870	C₄	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
871	C₄	C₂₉×#585	1	1	yes	characteristic
872	C₂	—	2	4	no	—
873	C₂	—	4	1	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	2	no	—
876	C₂	C₂₉×#3489	1	1	yes	characteristic
877	C₂	C₂²×C₂₉×#137	1	1	yes	characteristic
878	C₂	C₂×C₂₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3481	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3503	C₂	semidirect
3. C₂₉×#3385	C₂	semidirect
4. C₂₉×#3375	C₂	semidirect
5. C₂₉×#3346	C₂	semidirect
6. C₂₉×#3338	C₂	semidirect
7. C₂₉×#3314	C₂	semidirect
8. C₂₉×#3295	C₂	semidirect
9. C₂₉×#3254	C₂	semidirect
10. C₂₉×#3248	C₂	semidirect
11. C₂₉×#3239	C₂	semidirect
12. C₂₉×#3226	C₂	semidirect
13. C₂₉×#3110	C₂	semidirect
14. C₂₉×#3107	C₂	semidirect
15. C₂₉×#3079	C₂	semidirect
16. C₂×C₂₉×#474	C₂	semidirect
17. C₂₉×#2990	C₂	semidirect
19. Q₈²×C₂₉	C₂²	semidirect
24. C₂₉×#554	C₂²	semidirect
35. C₂₉×#533	C₂²	semidirect
36. C₂₉×#533	C₂²	semidirect
38. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
48. C₂₉×#501	C₂²	semidirect
49. C₂₉×#500	C₂²	semidirect
50. C₂₉×#489	C₂²	semidirect
52. C₂₉×#485	C₂²	semidirect
53. C₂₉×#484	C₂²	semidirect
54. C₂₉×#484	C₂²	semidirect
56. C₂₉×#480	C₂²	semidirect
57. C₂₉×#479	C₂²	semidirect
58. C₂₉×#477	C₂²	semidirect
59. C₂₉×#477	C₂²	semidirect
61. C₂₉×#475	C₂²	semidirect
62. C₂₉×#475	C₂²	semidirect
66. C₂₉×#474	C₂²	semidirect
67. C₂₉×#474	C₂²	semidirect
68. C₂₉×#474	C₂²	semidirect
69. C₂₉×#474	C₂²	semidirect
70. C₂₉×#468	C₂²	semidirect
71. C₂₉×#467	C₂²	semidirect
73. C₂₉×#464	C₂²	semidirect
74. C₂₉×#462	C₂²	semidirect
76. C₂₉×#461	C₂²	semidirect
80. C₂₉×#446	C₂²	semidirect
82. C₂₉×#440	C₂²	semidirect
83. C₄×Q₁₆×C₂₉	C₂²	semidirect
85. C₂₉×#435	C₂²	semidirect
87. C₂₉×#432	C₂²	semidirect
88. C₂₉×#431	C₂²	semidirect
89. C₂₉×#428	C₂²	semidirect
90. C₂×C₂₉×#107	C₂²	semidirect
91. C₂₉×#423	C₂²	semidirect
92. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
336. #62127	C₂₉	direct (N × H)
402. #3503	C₂×C₂₉	semidirect
404. #3385	C₂×C₂₉	semidirect
405. #3375	C₂×C₂₉	semidirect
406. #3346	C₂×C₂₉	semidirect
407. #3338	C₂×C₂₉	semidirect
408. #3314	C₂×C₂₉	semidirect
409. #3295	C₂×C₂₉	semidirect
410. #3254	C₂×C₂₉	semidirect
411. #3248	C₂×C₂₉	semidirect
412. #3239	C₂×C₂₉	semidirect
413. #3226	C₂×C₂₉	semidirect
414. #3110	C₂×C₂₉	semidirect
415. #3107	C₂×C₂₉	semidirect
416. #3079	C₂×C₂₉	semidirect
417. C₂×#474	C₂×C₂₉	semidirect
418. #2990	C₂×C₂₉	semidirect
451. Q₈²	C₂²×C₂₉	semidirect
456. #554	C₂²×C₂₉	semidirect
467. #533	C₂²×C₂₉	semidirect
468. #533	C₂²×C₂₉	semidirect
470. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
471. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
480. #501	C₂²×C₂₉	semidirect
481. #500	C₂²×C₂₉	semidirect
482. #489	C₂²×C₂₉	semidirect
484. #485	C₂²×C₂₉	semidirect
485. #484	C₂²×C₂₉	semidirect
486. #484	C₂²×C₂₉	semidirect
488. #480	C₂²×C₂₉	semidirect
489. #479	C₂²×C₂₉	semidirect
490. #477	C₂²×C₂₉	semidirect
491. #477	C₂²×C₂₉	semidirect
493. #475	C₂²×C₂₉	semidirect
494. #475	C₂²×C₂₉	semidirect
498. #474	C₂²×C₂₉	semidirect
499. #474	C₂²×C₂₉	semidirect
500. #474	C₂²×C₂₉	semidirect
501. #474	C₂²×C₂₉	semidirect
502. #468	C₂²×C₂₉	semidirect
503. #467	C₂²×C₂₉	semidirect
505. #464	C₂²×C₂₉	semidirect
506. #462	C₂²×C₂₉	semidirect
508. #461	C₂²×C₂₉	semidirect
512. #446	C₂²×C₂₉	semidirect
514. #440	C₂²×C₂₉	semidirect
515. C₄×Q₁₆	C₂²×C₂₉	semidirect
517. #435	C₂²×C₂₉	semidirect
519. #432	C₂²×C₂₉	semidirect
520. #431	C₂²×C₂₉	semidirect
521. #428	C₂²×C₂₉	semidirect
522. C₂×#107	C₂²×C₂₉	semidirect
523. #423	C₂²×C₂₉	semidirect
524. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
667. C₂₉	#62127	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×#3503	2
C₂₉×#3481	2
C₂₉×#3385	2
C₂₉×#3375	2
C₂₉×#3346	2
C₂₉×#3338	2
C₂₉×#3314	2
C₂₉×#3295	2
C₂₉×#3254	2
C₂₉×#3248	2
C₂₉×#3239	2
C₂₉×#3226	2
C₂₉×#3110	2
C₂₉×#3107	2
C₂₉×#3079	2
C₂×C₂₉×#474	2
C₂₉×#2990	2
#62127	29

Subgroups — C29×#62127 #20357027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62127 #20357027