Subgroups — #16833688

Order 3712.

1038 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271915	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271914	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271910	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271907	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271872	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271867	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271852	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271849	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271839	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271837	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271836	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271818	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271811	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271803	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271800	C₂	1	1	yes	maximal, characteristic, complemented
16	#14271791	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271789	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271784	C₂	1	1	yes	maximal, characteristic, complemented
19	#14271781	C₂	1	1	yes	maximal, characteristic, complemented
20	#14271757	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271756	C₂	1	1	yes	maximal, characteristic, complemented
22	#14271755	C₂	1	1	yes	maximal, characteristic, complemented
23	#14271754	C₂	1	1	yes	maximal, characteristic, complemented
24	#14271754	C₂	1	1	yes	maximal, characteristic, complemented
25	#14271748	C₂	1	1	yes	maximal, characteristic, complemented
26	#14271736	C₂	1	1	yes	maximal, characteristic, complemented
27	#14271733	C₂	1	1	yes	maximal, characteristic, complemented
28	#14271672	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#11745245	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₉×#551	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#90807	C₂²	1	1	yes	characteristic
35	C₂×#90805	C₂²	1	1	yes	characteristic
36	C₂×#90805	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
38	C₂₉×#126	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#126	C₂²	1	1	yes	characteristic, complemented
40	C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
41	C₂₉×#123	C₂²	1	1	yes	characteristic
42	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#120	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#117	C₂²	1	1	yes	characteristic
50	C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
53	#11745315	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₂₉	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₂₉	C₂²	1	1	yes	characteristic
56	#11745308	C₂²	1	1	yes	characteristic, complemented
57	#11745308	C₂²	1	1	yes	characteristic, complemented
58	#11745306	C₂²	1	1	yes	characteristic, complemented
59	#11745301	C₂²	1	1	yes	characteristic
60	#11745301	C₂²	1	1	yes	characteristic
61	#11745301	C₂²	1	1	yes	characteristic
62	#11745301	C₂²	1	1	yes	characteristic, complemented
63	#11745300	C₂²	1	1	yes	characteristic
64	#11745300	C₂²	1	1	yes	characteristic, complemented
65	#11745299	C₂²	1	1	yes	characteristic
66	#11745298	C₂²	1	1	yes	characteristic, complemented
67	#11745297	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
69	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
70	#11745292	C₂²	1	1	yes	characteristic
71	#11745291	C₂²	1	1	yes	characteristic
72	#11745291	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
76	C₂×#90781	C₂²	1	1	yes	characteristic
77	#11745288	C₂²	1	1	yes	characteristic
78	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
79	#11745286	C₂²	1	1	yes	characteristic
80	#11745286	C₂²	1	1	yes	characteristic, complemented
81	#11745286	C₂²	1	1	yes	characteristic, complemented
82	#11745286	C₂²	1	1	yes	characteristic, complemented
83	#11745286	C₂²	1	1	yes	characteristic, complemented
84	#11745286	C₂²	1	1	yes	characteristic, complemented
85	C₂×#90779	C₂²	1	1	yes	characteristic
86	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
87	#11745260	C₂²	1	1	yes	characteristic, complemented
88	#11745260	C₂²	1	1	yes	characteristic, complemented
89	#11745260	C₂²	1	1	yes	characteristic, complemented
90	#11745260	C₂²	1	1	yes	characteristic, complemented
91	#11745259	C₂²	1	1	yes	characteristic, complemented
92	#11745259	C₂²	1	1	yes	characteristic, complemented
93	#11745259	C₂²	1	1	yes	characteristic, complemented
94	#11745258	C₂²	1	1	yes	characteristic, complemented
95	#11745258	C₂²	1	1	yes	characteristic, complemented
96	#11745258	C₂²	1	1	yes	characteristic, complemented
97	#11745258	C₂²	1	1	yes	characteristic, complemented
98	#11745258	C₂²	1	1	yes	characteristic, complemented
99	#11745258	C₂²	1	1	yes	characteristic, complemented
100	#11745256	C₂²	1	1	yes	characteristic, complemented
101	#11745256	C₂²	1	1	yes	characteristic, complemented
102	#11745256	C₂²	1	1	yes	characteristic, complemented
103	#11745254	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
108	#11745252	C₂²	1	1	yes	characteristic, complemented
109	#11745252	C₂²	1	1	yes	characteristic, complemented
110	#11745252	C₂²	1	1	yes	characteristic, complemented
111	#11745252	C₂²	1	1	yes	characteristic, complemented
112	#11745251	C₂²	1	1	yes	characteristic, complemented
113	#11745251	C₂²	1	1	yes	characteristic, complemented
114	#11745251	C₂²	1	1	yes	characteristic, complemented
115	#11745250	C₂²	1	1	yes	characteristic, complemented
116	#11745250	C₂²	1	1	yes	characteristic, complemented
117	#11745250	C₂²	1	1	yes	characteristic, complemented
118	#11745249	C₂²	1	1	yes	characteristic, complemented
119	#11745248	C₂²	1	1	yes	characteristic
120	#11745248	C₂²	1	1	yes	characteristic, complemented
121	#11745248	C₂²	1	1	yes	characteristic, complemented
122	#11745248	C₂²	1	1	yes	characteristic, complemented
123	#11745247	C₂²	1	1	yes	characteristic
124	#11745247	C₂²	1	1	yes	characteristic
125	#11745247	C₂²	1	1	yes	characteristic, complemented
126	#11745247	C₂²	1	1	yes	characteristic, complemented
127	#11745247	C₂²	1	1	yes	characteristic, complemented
128	#11745246	C₂²	1	1	yes	characteristic
129	#11745246	C₂²	1	1	yes	characteristic
130	#11745246	C₂²	1	1	yes	characteristic, complemented
131	#11745245	C₂²	1	1	yes	characteristic
132	#11745245	C₂²	1	1	yes	characteristic
133	#11745245	C₂²	1	1	yes	characteristic
134	#11745245	C₂²	1	1	yes	characteristic
135	#11745245	C₂²	1	1	yes	characteristic
136	#11745245	C₂²	1	1	yes	characteristic
137	#11745245	C₂²	1	1	yes	characteristic
138	#11745245	C₂²	1	1	yes	characteristic
139	#11745245	C₂²	1	1	yes	characteristic
140	#11745245	C₂²	1	1	yes	characteristic
141	#11745245	C₂²	1	1	yes	characteristic, complemented
142	#11745245	C₂²	1	1	yes	characteristic, complemented
143	#11745245	C₂²	1	1	yes	characteristic, complemented
144	#11745245	C₂²	1	1	yes	characteristic, complemented
145	#11745245	C₂²	1	1	yes	characteristic, complemented
146	#11745244	C₂²	1	1	yes	characteristic
147	#11745243	C₂²	1	1	yes	characteristic
148	#11745243	C₂²	1	1	yes	characteristic
149	#11745243	C₂²	1	1	yes	characteristic
150	#11745243	C₂²	1	1	yes	characteristic, complemented
151	#11745243	C₂²	1	1	yes	characteristic, complemented
152	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
153	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
154	#11745241	C₂²	1	1	yes	characteristic, complemented
155	#11745241	C₂²	1	1	yes	characteristic, complemented
156	#11745241	C₂²	1	1	yes	characteristic, complemented
157	#11745241	C₂²	1	1	yes	characteristic, complemented
158	#11745241	C₂²	1	1	yes	characteristic, complemented
159	#11745240	C₂²	1	1	yes	characteristic
160	#11745240	C₂²	1	1	yes	characteristic
161	#11745240	C₂²	1	1	yes	characteristic
162	#11745240	C₂²	1	1	yes	characteristic
163	#11745240	C₂²	1	1	yes	characteristic
164	#11745240	C₂²	1	1	yes	characteristic
165	#11745240	C₂²	1	1	yes	characteristic
166	#11745240	C₂²	1	1	yes	characteristic, complemented
167	#11745240	C₂²	1	1	yes	characteristic, complemented
168	#11745240	C₂²	1	1	yes	characteristic, complemented
169	#11745240	C₂²	1	1	yes	characteristic, complemented
170	#11745240	C₂²	1	1	yes	characteristic, complemented
171	#11745240	C₂²	1	1	yes	characteristic, complemented
172	#11745240	C₂²	1	1	yes	characteristic, complemented
173	#11745240	C₂²	1	1	yes	characteristic, complemented
174	#11745239	C₂²	1	1	yes	characteristic, complemented
175	#11745238	C₂²	1	1	yes	characteristic, complemented
176	#11745237	C₂²	1	1	yes	characteristic, complemented
177	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
179	#11745234	C₂²	1	1	yes	characteristic, complemented
180	#11745234	C₂²	1	1	yes	characteristic, complemented
181	#11745232	C₂²	1	1	yes	characteristic, complemented
182	#11745232	C₂²	1	1	yes	characteristic, complemented
183	#11745232	C₂²	1	1	yes	characteristic, complemented
184	#11745231	C₂²	1	1	yes	characteristic, complemented
185	#11745231	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
188	C₂³×D₂₉	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₂₉	—	4	2	no	—
199	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
209	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
210	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
211	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
212	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
213	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
214	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
215	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
216	Q₈×D₂₉	—	4	2	no	—
217	#90807	—	4	2	no	—
218	#90805	—	4	2	no	—
219	#90805	—	4	2	no	—
220	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
221	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₂₉	—	4	2	no	—
223	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
234	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
235	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
236	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
237	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
238	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
239	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
240	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
241	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
250	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
251	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
252	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
253	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
254	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
255	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
256	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
257	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
258	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
259	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
260	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
262	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
263	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
264	C₄²×C₂₉	C₂³	1	1	yes	characteristic
265	C₄²×C₂₉	C₂³	1	1	yes	characteristic
266	C₄²×C₂₉	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
281	#90781	C₂³	1	1	yes	characteristic
282	#90781	C₂³	1	1	yes	characteristic
283	#90781	C₂³	1	1	yes	characteristic
284	#90781	C₂³	1	1	yes	characteristic
285	#90781	C₂³	1	1	yes	characteristic
286	#90781	C₂³	1	1	yes	characteristic
287	#90781	C₂³	1	1	yes	characteristic
288	#90781	C₂³	1	1	yes	characteristic
289	#90781	C₂³	1	1	yes	characteristic
290	#90781	C₂³	1	1	yes	characteristic
291	#90781	C₂³	1	1	yes	characteristic
292	#90781	C₂³	1	1	yes	characteristic
293	#90781	C₂³	1	1	yes	characteristic
294	#90781	C₂³	1	1	yes	characteristic
295	#90781	C₂³	1	1	yes	characteristic
296	#90781	C₂³	1	1	yes	characteristic
297	#90781	C₂³	1	1	yes	characteristic
298	#90781	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
315	#90779	C₂³	1	1	yes	characteristic
316	#90779	C₂³	1	1	yes	characteristic
317	#90779	C₂³	1	1	yes	characteristic
318	#90779	C₂³	1	1	yes	characteristic
319	#90779	C₂³	1	1	yes	characteristic
320	#90779	C₂³	1	1	yes	characteristic
321	#90779	C₂³	1	1	yes	characteristic
322	#90779	C₂³	1	1	yes	characteristic
323	#90779	C₂³	1	1	yes	characteristic
324	#90779	C₂³	1	1	yes	characteristic
325	#90779	C₂³	1	1	yes	characteristic
326	#90779	C₂³	1	1	yes	characteristic
327	#90779	C₂³	1	1	yes	characteristic
328	#90779	C₂³	1	1	yes	characteristic
329	#90779	C₂³	1	1	yes	characteristic
330	#90779	C₂³	1	1	yes	characteristic
331	#90779	C₂³	1	1	yes	characteristic
332	#90779	C₂³	1	1	yes	characteristic
333	#90779	C₂³	1	1	yes	characteristic
334	#90779	C₂³	1	1	yes	characteristic
335	#90779	C₂³	1	1	yes	characteristic
336	#90779	C₂³	1	1	yes	characteristic
337	#90779	C₂³	1	1	yes	characteristic
338	#90779	C₂³	1	1	yes	characteristic
339	#90779	C₂³	1	1	yes	characteristic
340	#90779	C₂³	1	1	yes	characteristic
341	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
342	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
343	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
344	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
345	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
346	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
347	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
348	C₂³×C₂₉	—	2	2	no	—
349	C₂³×C₂₉	—	4	1	no	—
350	C₂³×C₂₉	—	4	1	no	—
351	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
352	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
353	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
354	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
355	C₂²×D₂₉	—	2	2	no	—
356	C₂²×D₂₉	—	2	2	no	—
357	C₂²×D₂₉	—	4	1	no	—
358	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
359	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
360	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
361	Q₈×C₂₉	—	4	1	no	—
362	D₄×C₂₉	—	2	2	no	—
363	D₄×C₂₉	—	4	1	no	—
364	D₄×C₂₉	—	4	1	no	—
365	C₂×C₄×C₂₉	—	2	2	no	—
366	C₂×C₄×C₂₉	—	4	1	no	—
367	C₂×C₄×C₂₉	—	4	1	no	—
368	C₂×C₄×C₂₉	—	4	1	no	—
369	C₂×C₄×C₂₉	—	4	1	no	—
370	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
381	C₂²⋊D₂₉	—	2	2	no	—
382	C₂²⋊D₂₉	—	2	2	no	—
383	C₂²⋊D₂₉	—	2	2	no	—
384	C₂²⋊D₂₉	—	2	2	no	—
385	C₂²⋊D₂₉	—	4	1	no	—
386	C₂²⋊D₂₉	—	4	1	no	—
387	C₂²⋊D₂₉	—	4	1	no	—
388	C₂²⋊D₂₉	—	4	1	no	—
389	C₂²⋊D₂₉	—	4	1	no	—
390	C₂²⋊D₂₉	—	4	1	no	—
391	C₂×Dic₂₉	—	4	1	no	—
392	C₂×Dic₂₉	—	4	1	no	—
393	C₂×Dic₂₉	—	4	1	no	—
394	C₂×Dic₂₉	—	4	1	no	—
395	C₂×Dic₂₉	—	4	1	no	—
396	C₂×Dic₂₉	—	4	1	no	—
397	C₂×Dic₂₉	—	4	1	no	—
398	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
411	D₁₁₆	—	2	2	no	—
412	D₁₁₆	—	4	1	no	—
413	C₄×D₂₉	—	2	2	no	—
414	C₄×D₂₉	—	2	2	no	—
415	C₄×D₂₉	—	2	2	no	—
416	C₄×D₂₉	—	2	2	no	—
417	C₄×D₂₉	—	4	1	no	—
418	C₄×D₂₉	—	4	1	no	—
419	C₄×D₂₉	—	4	1	no	—
420	C₄×D₂₉	—	4	1	no	—
421	C₄×D₂₉	—	4	1	no	—
422	C₄×D₂₉	—	4	1	no	—
423	C₄×D₂₉	—	4	1	no	—
424	Dic₅₈	—	4	1	no	—
425	Dic₅₈	—	4	1	no	—
426	Dic₅₈	—	4	1	no	—
427	Dic₅₈	—	4	1	no	—
428	Dic₅₈	—	4	1	no	—
429	Dic₅₈	—	4	1	no	—
430	Dic₅₈	—	4	1	no	—
431	Dic₅₈	—	4	1	no	—
432	#3535	—	29	1	no	maximal, Sylow
433	C₂²×C₂₉	—	2	1	no	—
434	C₂²×C₂₉	—	2	1	no	—
435	C₂²×C₂₉	—	2	1	no	—
436	C₂²×C₂₉	—	2	1	no	—
437	C₂²×C₂₉	—	2	1	no	—
438	C₂²×C₂₉	—	2	1	no	—
439	C₂²×C₂₉	—	2	1	no	—
440	C₂²×C₂₉	—	2	1	no	—
441	C₂²×C₂₉	—	2	1	no	—
442	C₂²×C₂₉	—	2	1	no	—
443	C₂²×C₂₉	—	2	1	no	—
444	C₂²×C₂₉	—	8	2	no	—
445	C₂²×C₂₉	2₋¹⁺⁴	1	2	yes	—
446	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
447	C₂×D₂₉	—	2	1	no	—
448	C₂×D₂₉	—	2	1	no	—
449	C₂×D₂₉	—	2	1	no	—
450	C₂×D₂₉	—	2	1	no	—
451	C₂×D₂₉	—	2	1	no	—
452	C₂×D₂₉	—	2	1	no	—
453	C₂×D₂₉	—	2	1	no	—
454	C₂×D₂₉	—	2	1	no	—
455	C₂×D₂₉	—	4	4	no	—
456	C₂×D₂₉	H(5,𝔽₂)	1	2	yes	—
457	C₄×C₂₉	—	2	1	no	—
458	C₄×C₂₉	—	2	1	no	—
459	C₄×C₂₉	—	2	1	no	—
460	C₄×C₂₉	—	2	1	no	—
461	C₄×C₂₉	—	2	1	no	—
462	C₄×C₂₉	—	2	1	no	—
463	C₄×C₂₉	—	2	1	no	—
464	C₄×C₂₉	—	2	1	no	—
465	C₄×C₂₉	—	2	1	no	—
466	C₄×C₂₉	—	2	1	no	—
467	C₄×C₂₉	—	2	1	no	—
468	Dic₂₉	—	2	1	no	—
469	Dic₂₉	—	2	1	no	—
470	Dic₂₉	—	2	1	no	—
471	Dic₂₉	—	2	1	no	—
472	Dic₂₉	—	2	1	no	—
473	Dic₂₉	—	2	1	no	—
474	Dic₂₉	—	2	1	no	—
475	Dic₂₉	—	2	1	no	—
476	Dic₂₉	—	2	1	no	—
477	Dic₂₉	—	2	1	no	—
478	Dic₂₉	—	2	1	no	—
479	Dic₂₉	—	2	1	no	—
480	Dic₂₉	—	2	1	no	—
481	#563	—	29	1	no	—
482	#563	—	29	1	no	—
483	#562	—	29	1	no	—
484	#562	—	29	1	no	—
485	#554	—	29	1	no	—
486	#554	—	29	1	no	—
487	#552	—	29	1	no	—
488	#552	—	29	1	no	—
489	#551	—	29	1	no	—
490	#551	—	29	1	no	—
491	#551	—	29	1	no	—
492	#551	D₂₉	1	1	yes	characteristic, complemented
493	#547	—	29	1	no	—
494	#547	—	29	1	no	—
495	#546	—	29	1	no	—
496	#546	—	29	1	no	—
497	#544	—	29	1	no	—
498	#543	—	29	1	no	—
499	#542	—	29	1	no	—
500	#542	—	29	1	no	—
501	#539	—	29	1	no	—
502	#539	—	29	1	no	—
503	#539	—	29	1	no	—
504	#539	—	29	1	no	—
505	#539	—	29	1	no	—
506	#538	—	29	1	no	—
507	#536	—	29	1	no	—
508	#536	—	29	1	no	—
509	#525	—	29	1	no	—
510	C₂×#123	—	29	1	no	—
511	C₂×C₂²⋊Q₈	—	29	1	no	—
512	C₂×C₂₉	—	2	2	no	—
513	C₂×C₂₉	—	4	1	no	—
514	C₂×C₂₉	—	4	1	no	—
515	C₂×C₂₉	—	4	1	no	—
516	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂×C₂₉	#585	1	1	yes	characteristic
519	D₂₉	—	2	2	no	—
520	D₂₉	—	4	1	no	—
521	D₂₉	—	4	1	no	—
522	C₂×#41	—	29	1	no	—
523	C₂×#41	—	29	1	no	—
524	C₂×#41	—	29	1	no	—
525	C₂²×Q₈	—	29	1	no	—
526	C₂²×D₄	—	29	1	no	—
527	C₂³×C₄	—	29	1	no	—
528	C₄⋊Q₈	—	29	1	no	—
529	C₄⋊Q₈	—	29	1	no	—
530	C₄⋊Q₈	—	29	1	no	—
531	C₄⋊Q₈	—	29	1	no	—
532	C₄⋊Q₈	—	29	1	no	—
533	C₄⋊Q₈	—	29	1	no	—
534	#126	—	29	1	no	—
535	#126	—	29	1	no	—
536	#126	—	29	1	no	—
537	#126	—	29	1	no	—
538	#126	—	29	1	no	—
539	#126	—	29	1	no	—
540	#126	—	29	1	no	—
541	#126	—	29	1	no	—
542	#126	—	29	1	no	—
543	#126	—	29	1	no	—
544	#126	C₂×D₂₉	1	1	yes	characteristic, complemented
545	#126	C₂×D₂₉	1	1	yes	characteristic, complemented
546	#125	—	29	1	no	—
547	#125	—	29	1	no	—
548	#125	—	29	1	no	—
549	#125	—	29	1	no	—
550	#125	—	29	1	no	—
551	#125	—	29	1	no	—
552	#125	—	29	1	no	—
553	#125	—	29	1	no	—
554	#125	—	29	1	no	—
555	#125	—	29	1	no	—
556	#124	—	29	1	no	—
557	#124	—	29	1	no	—
558	#124	—	29	1	no	—
559	#124	—	29	1	no	—
560	#124	—	29	1	no	—
561	#124	—	29	1	no	—
562	#124	—	29	1	no	—
563	#124	C₂×D₂₉	1	1	yes	characteristic, complemented
564	#123	—	29	1	no	—
565	#123	—	29	1	no	—
566	#123	—	29	1	no	—
567	#123	—	29	1	no	—
568	#123	—	29	1	no	—
569	#123	—	29	1	no	—
570	#123	—	29	1	no	—
571	#123	—	29	1	no	—
572	#123	—	29	1	no	—
573	#123	—	29	1	no	—
574	#123	—	29	1	no	—
575	#123	—	29	1	no	—
576	#123	—	29	1	no	—
577	#123	—	29	1	no	—
578	#123	—	29	1	no	—
579	#123	—	29	1	no	—
580	#123	—	29	1	no	—
581	#123	—	29	1	no	—
582	#123	—	29	1	no	—
583	#123	—	29	1	no	—
584	#123	—	29	1	no	—
585	#123	—	29	1	no	—
586	#123	—	29	1	no	—
587	#123	—	29	1	no	—
588	#123	—	29	1	no	—
589	#123	C₂×D₂₉	1	1	yes	characteristic
590	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
591	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
592	C₂²⋊Q₈	—	29	1	no	—
593	C₂²⋊Q₈	—	29	1	no	—
594	C₂²⋊Q₈	—	29	1	no	—
595	C₂²⋊Q₈	—	29	1	no	—
596	C₂²⋊Q₈	—	29	1	no	—
597	C₂²⋊Q₈	—	29	1	no	—
598	C₂²⋊Q₈	—	29	1	no	—
599	C₂²⋊Q₈	—	29	1	no	—
600	C₂²⋊Q₈	—	29	1	no	—
601	C₂²⋊Q₈	—	29	1	no	—
602	C₂²⋊Q₈	—	29	1	no	—
603	C₂²⋊Q₈	—	29	1	no	—
604	C₂²⋊Q₈	—	29	1	no	—
605	C₂²⋊Q₈	—	29	1	no	—
606	C₂²⋊Q₈	—	29	1	no	—
607	C₂²⋊Q₈	—	29	1	no	—
608	C₂²⋊Q₈	—	29	1	no	—
609	C₂²⋊Q₈	—	29	1	no	—
610	C₂²⋊Q₈	—	29	1	no	—
611	C₂²⋊Q₈	—	29	1	no	—
612	C₂²⋊Q₈	—	29	1	no	—
613	C₂²⋊Q₈	—	29	1	no	—
614	C₂²⋊Q₈	—	29	1	no	—
615	C₂²⋊Q₈	—	29	1	no	—
616	C₂²⋊Q₈	—	29	1	no	—
617	C₂²⋊Q₈	—	29	1	no	—
618	C₂²⋊Q₈	—	29	1	no	—
619	C₂²⋊Q₈	—	29	1	no	—
620	C₂²⋊Q₈	—	29	1	no	—
621	C₂²⋊Q₈	—	29	1	no	—
622	C₂²⋊Q₈	—	29	1	no	—
623	C₂²⋊Q₈	—	29	1	no	—
624	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
625	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
626	#121	—	29	1	no	—
627	#121	—	29	1	no	—
628	#121	—	29	1	no	—
629	#121	—	29	1	no	—
630	#121	—	29	1	no	—
631	#121	—	29	1	no	—
632	#121	—	29	1	no	—
633	#121	—	29	1	no	—
634	#121	—	29	1	no	—
635	#121	—	29	1	no	—
636	#120	—	29	1	no	—
637	#120	—	29	1	no	—
638	#120	—	29	1	no	—
639	#120	C₂×D₂₉	1	1	yes	characteristic
640	C₄×Q₈	—	29	1	no	—
641	C₄×Q₈	—	29	1	no	—
642	C₄×D₄	—	29	1	no	—
643	C₄×D₄	—	29	1	no	—
644	C₄×D₄	—	29	1	no	—
645	C₄×D₄	—	29	1	no	—
646	C₄×D₄	—	29	1	no	—
647	C₄×D₄	—	29	1	no	—
648	C₄×D₄	—	29	1	no	—
649	C₄×D₄	—	29	1	no	—
650	C₄×D₄	—	29	1	no	—
651	C₄×D₄	—	29	1	no	—
652	C₄×D₄	—	29	1	no	—
653	C₄×D₄	—	29	1	no	—
654	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
655	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic, complemented
656	#117	—	29	1	no	—
657	#117	—	29	1	no	—
658	#117	—	29	1	no	—
659	#117	—	29	1	no	—
660	#117	—	29	1	no	—
661	#117	C₂×D₂₉	1	1	yes	characteristic
662	#117	C₂×D₂₉	1	1	yes	characteristic, complemented
663	C₂×C₄⋊C₄	—	29	1	no	—
664	C₂×C₄⋊C₄	—	29	1	no	—
665	C₂×C₄⋊C₄	—	29	1	no	—
666	C₂×C₄⋊C₄	—	29	1	no	—
667	C₂×C₄⋊C₄	—	29	1	no	—
668	C₂×C₄⋊C₄	—	29	1	no	—
669	C₂×C₄⋊C₄	—	29	1	no	—
670	C₂×C₂²⋊C₄	—	29	1	no	—
671	C₂×C₂²⋊C₄	—	29	1	no	—
672	C₂×C₂²⋊C₄	—	29	1	no	—
673	C₂×C₂²⋊C₄	—	29	1	no	—
674	C₂×C₂²⋊C₄	—	29	1	no	—
675	C₂×C₂²⋊C₄	C₂×D₂₉	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂×D₂₉	1	1	yes	characteristic
677	C₂₉	#3535	1	1	yes	characteristic, complemented, Sylow
678	C₂⁴	—	29	1	no	—
679	C₂⁴	C₂²×D₂₉	1	1	yes	characteristic
680	#41	—	116	2	no	—
681	#41	—	116	2	no	—
682	#41	—	116	2	no	—
683	C₂×Q₈	—	29	1	no	—
684	C₂×Q₈	—	29	1	no	—
685	C₂×Q₈	—	29	1	no	—
686	C₂×Q₈	—	29	1	no	—
687	C₂×Q₈	—	29	1	no	—
688	C₂×Q₈	—	29	1	no	—
689	C₂×Q₈	—	29	1	no	—
690	C₂×Q₈	—	29	1	no	—
691	C₂×Q₈	—	116	2	no	—
692	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
693	C₂×D₄	—	29	1	no	—
694	C₂×D₄	—	29	1	no	—
695	C₂×D₄	—	29	1	no	—
696	C₂×D₄	—	29	1	no	—
697	C₂×D₄	—	29	1	no	—
698	C₂×D₄	—	29	1	no	—
699	C₂×D₄	—	29	1	no	—
700	C₂×D₄	—	29	1	no	—
701	C₂×D₄	—	29	1	no	—
702	C₂×D₄	—	29	1	no	—
703	C₂×D₄	—	29	1	no	—
704	C₂×D₄	—	29	1	no	—
705	C₂×D₄	—	116	2	no	—
706	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
707	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
708	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
709	C₂²×C₄	—	29	1	no	—
710	C₂²×C₄	—	29	1	no	—
711	C₂²×C₄	—	29	1	no	—
712	C₂²×C₄	—	29	1	no	—
713	C₂²×C₄	—	29	1	no	—
714	C₂²×C₄	—	29	1	no	—
715	C₂²×C₄	—	29	1	no	—
716	C₂²×C₄	—	29	1	no	—
717	C₂²×C₄	—	29	1	no	—
718	C₂²×C₄	—	29	1	no	—
719	C₂²×C₄	—	29	1	no	—
720	C₂²×C₄	—	29	1	no	—
721	C₂²×C₄	—	29	1	no	—
722	C₂²×C₄	—	29	1	no	—
723	C₂²×C₄	—	29	1	no	—
724	C₂²×C₄	—	29	1	no	—
725	C₂²×C₄	—	29	1	no	—
726	C₂²×C₄	—	29	1	no	—
727	C₂²×C₄	—	116	2	no	—
728	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
733	C₄⋊C₄	—	29	1	no	—
734	C₄⋊C₄	—	29	1	no	—
735	C₄⋊C₄	—	29	1	no	—
736	C₄⋊C₄	—	29	1	no	—
737	C₄⋊C₄	—	29	1	no	—
738	C₄⋊C₄	—	29	1	no	—
739	C₄⋊C₄	—	29	1	no	—
740	C₄⋊C₄	—	29	1	no	—
741	C₄⋊C₄	—	29	1	no	—
742	C₄⋊C₄	—	29	1	no	—
743	C₄⋊C₄	—	29	1	no	—
744	C₄⋊C₄	—	29	1	no	—
745	C₄⋊C₄	—	29	1	no	—
746	C₄⋊C₄	—	29	1	no	—
747	C₄⋊C₄	—	29	1	no	—
748	C₄⋊C₄	—	29	1	no	—
749	C₄⋊C₄	—	29	1	no	—
750	C₄⋊C₄	—	29	1	no	—
751	C₄⋊C₄	—	29	1	no	—
752	C₄⋊C₄	—	29	1	no	—
753	C₄⋊C₄	—	29	1	no	—
754	C₄⋊C₄	—	29	1	no	—
755	C₄⋊C₄	—	29	1	no	—
756	C₄⋊C₄	—	29	1	no	—
757	C₄⋊C₄	—	29	1	no	—
758	C₄⋊C₄	—	29	1	no	—
759	C₄⋊C₄	—	29	1	no	—
760	C₄⋊C₄	—	29	1	no	—
761	C₄⋊C₄	—	29	1	no	—
762	C₄⋊C₄	—	29	1	no	—
763	C₄⋊C₄	—	29	1	no	—
764	C₄⋊C₄	—	29	1	no	—
765	C₄⋊C₄	—	29	1	no	—
766	C₄⋊C₄	—	29	1	no	—
767	C₄⋊C₄	—	29	1	no	—
768	C₄⋊C₄	—	29	1	no	—
769	C₄⋊C₄	—	29	1	no	—
770	C₄⋊C₄	—	29	1	no	—
771	C₄⋊C₄	—	29	1	no	—
772	C₄⋊C₄	—	29	1	no	—
773	C₄⋊C₄	—	29	1	no	—
774	C₄⋊C₄	—	29	1	no	—
775	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
783	C₂²⋊C₄	—	29	1	no	—
784	C₂²⋊C₄	—	29	1	no	—
785	C₂²⋊C₄	—	29	1	no	—
786	C₂²⋊C₄	—	29	1	no	—
787	C₂²⋊C₄	—	29	1	no	—
788	C₂²⋊C₄	—	29	1	no	—
789	C₂²⋊C₄	—	29	1	no	—
790	C₂²⋊C₄	—	29	1	no	—
791	C₂²⋊C₄	—	29	1	no	—
792	C₂²⋊C₄	—	29	1	no	—
793	C₂²⋊C₄	—	29	1	no	—
794	C₂²⋊C₄	—	29	1	no	—
795	C₂²⋊C₄	—	29	1	no	—
796	C₂²⋊C₄	—	29	1	no	—
797	C₂²⋊C₄	—	29	1	no	—
798	C₂²⋊C₄	—	29	1	no	—
799	C₂²⋊C₄	—	29	1	no	—
800	C₂²⋊C₄	—	29	1	no	—
801	C₂²⋊C₄	—	29	1	no	—
802	C₂²⋊C₄	—	29	1	no	—
803	C₂²⋊C₄	—	29	1	no	—
804	C₂²⋊C₄	—	29	1	no	—
805	C₂²⋊C₄	—	29	1	no	—
806	C₂²⋊C₄	—	29	1	no	—
807	C₂²⋊C₄	—	29	1	no	—
808	C₂²⋊C₄	—	29	1	no	—
809	C₂²⋊C₄	—	29	1	no	—
810	C₂²⋊C₄	—	29	1	no	—
811	C₂²⋊C₄	—	29	1	no	—
812	C₂²⋊C₄	—	29	1	no	—
813	C₂²⋊C₄	—	29	1	no	—
814	C₂²⋊C₄	—	29	1	no	—
815	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
829	C₄²	—	29	1	no	—
830	C₄²	—	29	1	no	—
831	C₄²	—	29	1	no	—
832	C₄²	—	29	1	no	—
833	C₄²	—	29	1	no	—
834	C₄²	—	29	1	no	—
835	C₄²	—	29	1	no	—
836	C₄²	C₂²×D₂₉	1	1	yes	characteristic
837	C₄²	C₂²×D₂₉	1	1	yes	characteristic
838	C₄²	C₂²×D₂₉	1	1	yes	characteristic
839	C₂³	—	2	2	no	—
840	C₂³	—	4	1	no	—
841	C₂³	—	4	1	no	—
842	C₂³	—	29	1	no	—
843	C₂³	—	29	1	no	—
844	C₂³	—	29	1	no	—
845	C₂³	—	58	2	no	—
846	C₂³	—	58	2	no	—
847	C₂³	—	116	1	no	—
848	C₂³	C₂³×D₂₉	1	1	yes	characteristic
849	C₂³	C₂³×D₂₉	1	1	yes	characteristic
850	C₂³	C₂³×D₂₉	1	1	yes	characteristic
851	C₂³	C₂³×D₂₉	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	116	1	no	—
854	Q₈	—	116	1	no	—
855	Q₈	—	116	1	no	—
856	Q₈	—	116	1	no	—
857	Q₈	—	116	1	no	—
858	Q₈	—	116	1	no	—
859	Q₈	—	116	1	no	—
860	Q₈	—	116	1	no	—
861	D₄	—	2	2	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	58	2	no	—
865	D₄	—	58	2	no	—
866	D₄	—	58	2	no	—
867	D₄	—	58	2	no	—
868	D₄	—	58	2	no	—
869	D₄	—	116	1	no	—
870	D₄	—	116	1	no	—
871	D₄	—	116	1	no	—
872	D₄	—	116	1	no	—
873	D₄	—	116	1	no	—
874	D₄	—	116	1	no	—
875	D₄	—	116	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	29	1	no	—
882	C₂×C₄	—	29	1	no	—
883	C₂×C₄	—	29	1	no	—
884	C₂×C₄	—	29	1	no	—
885	C₂×C₄	—	29	1	no	—
886	C₂×C₄	—	29	1	no	—
887	C₂×C₄	—	29	1	no	—
888	C₂×C₄	—	29	1	no	—
889	C₂×C₄	—	29	1	no	—
890	C₂×C₄	—	29	1	no	—
891	C₂×C₄	—	29	1	no	—
892	C₂×C₄	—	29	1	no	—
893	C₂×C₄	—	29	1	no	—
894	C₂×C₄	—	58	2	no	—
895	C₂×C₄	—	58	2	no	—
896	C₂×C₄	—	58	2	no	—
897	C₂×C₄	—	58	2	no	—
898	C₂×C₄	—	116	1	no	—
899	C₂×C₄	—	116	1	no	—
900	C₂×C₄	—	116	1	no	—
901	C₂×C₄	—	116	1	no	—
902	C₂×C₄	—	116	1	no	—
903	C₂×C₄	—	116	1	no	—
904	C₂×C₄	—	116	1	no	—
905	C₂×C₄	—	116	1	no	—
906	C₂×C₄	—	116	1	no	—
907	C₂×C₄	—	116	1	no	—
908	C₂×C₄	—	116	1	no	—
909	C₂×C₄	—	116	1	no	—
910	C₂×C₄	—	116	1	no	—
911	C₂×C₄	—	116	1	no	—
912	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	1	no	—
934	C₂²	—	8	2	no	—
935	C₂²	—	29	2	no	—
936	C₂²	—	58	1	no	—
937	C₂²	—	58	1	no	—
938	C₂²	—	58	1	no	—
939	C₂²	—	58	1	no	—
940	C₂²	—	58	1	no	—
941	C₂²	—	58	1	no	—
942	C₂²	—	58	1	no	—
943	C₂²	—	58	1	no	—
944	C₂²	—	116	4	no	—
945	C₂²	#11745365	1	2	yes	—
946	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	58	1	no	—
959	C₄	—	58	1	no	—
960	C₄	—	58	1	no	—
961	C₄	—	58	1	no	—
962	C₄	—	58	1	no	—
963	C₄	—	58	1	no	—
964	C₄	—	58	1	no	—
965	C₄	—	58	1	no	—
966	C₄	—	58	1	no	—
967	C₄	—	58	1	no	—
968	C₄	—	58	1	no	—
969	C₄	—	58	1	no	—
970	C₄	—	58	1	no	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	4	1	no	—
975	C₂	—	58	2	no	—
976	C₂	—	116	1	no	—
977	C₂	—	116	1	no	—
978	C₂	H(5,𝔽₂)×D₂₉	1	1	yes	characteristic
979	C₂	C₂×#11745365	1	1	yes	characteristic
980	C₂	#14271999	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#551	C₂
hypercenter	#551	D₂₉
hypocenter	C₂₉	#3535
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #14271915	C₂	semidirect
2. #14271914	C₂	semidirect
3. #14271910	C₂	semidirect
4. #14271907	C₂	semidirect
5. #14271872	C₂	semidirect
6. #14271867	C₂	semidirect
7. #14271852	C₂	semidirect
8. #14271849	C₂	semidirect
9. #14271839	C₂	semidirect
10. #14271837	C₂	semidirect
11. #14271836	C₂	semidirect
12. #14271818	C₂	semidirect
13. #14271811	C₂	semidirect
14. #14271803	C₂	semidirect
15. #14271800	C₂	semidirect
16. #14271791	C₂	semidirect
17. #14271789	C₂	semidirect
18. #14271784	C₂	semidirect
19. #14271781	C₂	semidirect
20. #14271757	C₂	semidirect
21. #14271756	C₂	semidirect
22. #14271755	C₂	semidirect
23. #14271754	C₂	semidirect
24. #14271754	C₂	semidirect
25. #14271748	C₂	semidirect
26. #14271736	C₂	semidirect
27. #14271733	C₂	semidirect
28. #14271672	C₂	semidirect
29. C₂×#11745245	C₂	semidirect
30. C₂²⋊Q₈×D₂₉	C₂	semidirect
31. C₂₉×#551	C₂	semidirect
33. C₂×Q₈×D₂₉	C₂²	semidirect
36. C₂×#90805	C₂²	semidirect
38. C₂₉×#126	C₂²	semidirect
39. C₂₉×#126	C₂²	semidirect
40. C₂₉×#124	C₂²	semidirect
42. C₂₉×#123	C₂²	semidirect
43. C₂₉×#123	C₂²	semidirect
45. C₂₉×C₂²⋊Q₈	C₂²	semidirect
48. C₄×D₄×C₂₉	C₂²	semidirect
50. C₂₉×#117	C₂²	semidirect
56. #11745308	C₂²	semidirect
57. #11745308	C₂²	semidirect
58. #11745306	C₂²	semidirect
62. #11745301	C₂²	semidirect
64. #11745300	C₂²	semidirect
66. #11745298	C₂²	semidirect
67. #11745297	C₂²	semidirect
75. C₄×C₂²⋊D₂₉	C₂²	semidirect
80. #11745286	C₂²	semidirect
81. #11745286	C₂²	semidirect
82. #11745286	C₂²	semidirect
83. #11745286	C₂²	semidirect
84. #11745286	C₂²	semidirect
86. C₂×#90779	C₂²	semidirect
87. #11745260	C₂²	semidirect
88. #11745260	C₂²	semidirect
89. #11745260	C₂²	semidirect
90. #11745260	C₂²	semidirect
91. #11745259	C₂²	semidirect
92. #11745259	C₂²	semidirect
93. #11745259	C₂²	semidirect
94. #11745258	C₂²	semidirect
95. #11745258	C₂²	semidirect
96. #11745258	C₂²	semidirect
97. #11745258	C₂²	semidirect
98. #11745258	C₂²	semidirect
99. #11745258	C₂²	semidirect
100. #11745256	C₂²	semidirect
101. #11745256	C₂²	semidirect
102. #11745256	C₂²	semidirect
103. #11745254	C₂²	semidirect
104. C₄⋊C₄×D₂₉	C₂²	semidirect
105. C₄⋊C₄×D₂₉	C₂²	semidirect
106. C₄⋊C₄×D₂₉	C₂²	semidirect
107. C₄⋊C₄×D₂₉	C₂²	semidirect
108. #11745252	C₂²	semidirect
109. #11745252	C₂²	semidirect
110. #11745252	C₂²	semidirect
111. #11745252	C₂²	semidirect
112. #11745251	C₂²	semidirect
113. #11745251	C₂²	semidirect
114. #11745251	C₂²	semidirect
115. #11745250	C₂²	semidirect
116. #11745250	C₂²	semidirect
117. #11745250	C₂²	semidirect
118. #11745249	C₂²	semidirect
120. #11745248	C₂²	semidirect
121. #11745248	C₂²	semidirect
122. #11745248	C₂²	semidirect
125. #11745247	C₂²	semidirect
126. #11745247	C₂²	semidirect
127. #11745247	C₂²	semidirect
130. #11745246	C₂²	semidirect
141. #11745245	C₂²	semidirect
142. #11745245	C₂²	semidirect
143. #11745245	C₂²	semidirect
144. #11745245	C₂²	semidirect
145. #11745245	C₂²	semidirect
150. #11745243	C₂²	semidirect
151. #11745243	C₂²	semidirect
154. #11745241	C₂²	semidirect
155. #11745241	C₂²	semidirect
156. #11745241	C₂²	semidirect
157. #11745241	C₂²	semidirect
158. #11745241	C₂²	semidirect
166. #11745240	C₂²	semidirect
167. #11745240	C₂²	semidirect
168. #11745240	C₂²	semidirect
169. #11745240	C₂²	semidirect
170. #11745240	C₂²	semidirect
171. #11745240	C₂²	semidirect
172. #11745240	C₂²	semidirect
173. #11745240	C₂²	semidirect
174. #11745239	C₂²	semidirect
175. #11745238	C₂²	semidirect
176. #11745237	C₂²	semidirect
177. C₄×D₁₁₆	C₂²	semidirect
178. C₄×D₁₁₆	C₂²	semidirect
179. #11745234	C₂²	semidirect
180. #11745234	C₂²	semidirect
181. #11745232	C₂²	semidirect
182. #11745232	C₂²	semidirect
183. #11745232	C₂²	semidirect
184. #11745231	C₂²	semidirect
185. #11745231	C₂²	semidirect
186. C₄×Dic₅₈	C₂²	semidirect
492. #551	D₂₉	semidirect
544. #126	C₂×D₂₉	semidirect
545. #126	C₂×D₂₉	semidirect
563. #124	C₂×D₂₉	semidirect
590. #123	C₂×D₂₉	semidirect
591. #123	C₂×D₂₉	semidirect
625. C₂²⋊Q₈	C₂×D₂₉	semidirect
655. C₄×D₄	C₂×D₂₉	semidirect
662. #117	C₂×D₂₉	semidirect
677. C₂₉	#3535	semidirect

Maximal subgroups

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

subgroup	index
#14271915	2
#14271914	2
#14271910	2
#14271907	2
#14271872	2
#14271867	2
#14271852	2
#14271849	2
#14271839	2
#14271837	2
#14271836	2
#14271818	2
#14271811	2
#14271803	2
#14271800	2
#14271791	2
#14271789	2
#14271784	2
#14271781	2
#14271757	2
#14271756	2
#14271755	2
#14271754	2
#14271748	2
#14271736	2
#14271733	2
#14271672	2
C₂×#11745245	2
C₂²⋊Q₈×D₂₉	2
C₂₉×#551	2
#3535	29