Subgroups — #16833658

Order 3712.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271917	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271911	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271909	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271904	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271898	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271866	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271864	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271846	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271840	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271837	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271837	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271814	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271811	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271808	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271805	C₂	1	1	yes	maximal, characteristic, complemented
16	#14271785	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271779	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271769	C₂	1	1	yes	maximal, characteristic, complemented
19	#14271768	C₂	1	1	yes	maximal, characteristic, complemented
20	#14271761	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271761	C₂	1	1	yes	maximal, characteristic, complemented
22	#14271753	C₂	1	1	yes	maximal, characteristic, complemented
23	#14271753	C₂	1	1	yes	maximal, characteristic, complemented
24	#14271752	C₂	1	1	yes	maximal, characteristic, complemented
25	#14271746	C₂	1	1	yes	maximal, characteristic, complemented
26	#14271732	C₂	1	1	yes	maximal, characteristic, complemented
27	#14271724	C₂	1	1	yes	maximal, characteristic, complemented
28	#14271675	C₂	1	1	yes	maximal, characteristic, complemented
29	#14271671	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#11745256	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#90807	C₂²	1	1	yes	characteristic
33	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
34	C₂×#90805	C₂²	1	1	yes	characteristic
35	C₂×#90805	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₁₁₆	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
38	C₂₉×#126	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#126	C₂²	1	1	yes	characteristic, complemented
40	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
41	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
42	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#123	C₂²	1	1	yes	characteristic
44	C₂₉×#123	C₂²	1	1	yes	characteristic
45	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
49	C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
53	#11745309	C₂²	1	1	yes	characteristic, complemented
54	#11745309	C₂²	1	1	yes	characteristic, complemented
55	#11745309	C₂²	1	1	yes	characteristic, complemented
56	#11745308	C₂²	1	1	yes	characteristic, complemented
57	#11745301	C₂²	1	1	yes	characteristic
58	#11745299	C₂²	1	1	yes	characteristic
59	#11745292	C₂²	1	1	yes	characteristic
60	#11745292	C₂²	1	1	yes	characteristic, complemented
61	#11745292	C₂²	1	1	yes	characteristic, complemented
62	#11745291	C₂²	1	1	yes	characteristic
63	#11745291	C₂²	1	1	yes	characteristic, complemented
64	#11745291	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
66	C₂×#90781	C₂²	1	1	yes	characteristic
67	C₂×#90781	C₂²	1	1	yes	characteristic
68	C₂×#90781	C₂²	1	1	yes	characteristic, complemented
69	C₂×#90781	C₂²	1	1	yes	characteristic, complemented
70	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
71	#11745260	C₂²	1	1	yes	characteristic, complemented
72	#11745260	C₂²	1	1	yes	characteristic, complemented
73	#11745260	C₂²	1	1	yes	characteristic, complemented
74	#11745260	C₂²	1	1	yes	characteristic, complemented
75	#11745260	C₂²	1	1	yes	characteristic, complemented
76	#11745260	C₂²	1	1	yes	characteristic, complemented
77	#11745260	C₂²	1	1	yes	characteristic, complemented
78	#11745259	C₂²	1	1	yes	characteristic, complemented
79	#11745259	C₂²	1	1	yes	characteristic, complemented
80	#11745259	C₂²	1	1	yes	characteristic, complemented
81	#11745258	C₂²	1	1	yes	characteristic, complemented
82	#11745258	C₂²	1	1	yes	characteristic, complemented
83	#11745258	C₂²	1	1	yes	characteristic, complemented
84	#11745258	C₂²	1	1	yes	characteristic, complemented
85	#11745258	C₂²	1	1	yes	characteristic, complemented
86	#11745258	C₂²	1	1	yes	characteristic, complemented
87	#11745258	C₂²	1	1	yes	characteristic, complemented
88	#11745258	C₂²	1	1	yes	characteristic, complemented
89	#11745257	C₂²	1	1	yes	characteristic
90	#11745257	C₂²	1	1	yes	characteristic
91	#11745257	C₂²	1	1	yes	characteristic
92	#11745257	C₂²	1	1	yes	characteristic
93	#11745257	C₂²	1	1	yes	characteristic, complemented
94	#11745257	C₂²	1	1	yes	characteristic, complemented
95	#11745257	C₂²	1	1	yes	characteristic, complemented
96	#11745257	C₂²	1	1	yes	characteristic, complemented
97	#11745257	C₂²	1	1	yes	characteristic, complemented
98	#11745257	C₂²	1	1	yes	characteristic, complemented
99	#11745257	C₂²	1	1	yes	characteristic, complemented
100	#11745257	C₂²	1	1	yes	characteristic, complemented
101	#11745257	C₂²	1	1	yes	characteristic, complemented
102	#11745256	C₂²	1	1	yes	characteristic
103	#11745256	C₂²	1	1	yes	characteristic
104	#11745256	C₂²	1	1	yes	characteristic
105	#11745256	C₂²	1	1	yes	characteristic
106	#11745256	C₂²	1	1	yes	characteristic
107	#11745256	C₂²	1	1	yes	characteristic
108	#11745256	C₂²	1	1	yes	characteristic, complemented
109	#11745256	C₂²	1	1	yes	characteristic, complemented
110	#11745256	C₂²	1	1	yes	characteristic, complemented
111	#11745256	C₂²	1	1	yes	characteristic, complemented
112	#11745256	C₂²	1	1	yes	characteristic, complemented
113	#11745256	C₂²	1	1	yes	characteristic, complemented
114	#11745256	C₂²	1	1	yes	characteristic, complemented
115	#11745256	C₂²	1	1	yes	characteristic, complemented
116	#11745256	C₂²	1	1	yes	characteristic, complemented
117	#11745256	C₂²	1	1	yes	characteristic, complemented
118	#11745256	C₂²	1	1	yes	characteristic, complemented
119	#11745256	C₂²	1	1	yes	characteristic, complemented
120	#11745256	C₂²	1	1	yes	characteristic, complemented
121	#11745256	C₂²	1	1	yes	characteristic, complemented
122	#11745256	C₂²	1	1	yes	characteristic, complemented
123	#11745255	C₂²	1	1	yes	characteristic, complemented
124	#11745255	C₂²	1	1	yes	characteristic, complemented
125	#11745255	C₂²	1	1	yes	characteristic, complemented
126	#11745255	C₂²	1	1	yes	characteristic, complemented
127	#11745255	C₂²	1	1	yes	characteristic, complemented
128	#11745254	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
130	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
131	#11745251	C₂²	1	1	yes	characteristic, complemented
132	#11745251	C₂²	1	1	yes	characteristic, complemented
133	#11745250	C₂²	1	1	yes	characteristic, complemented
134	#11745250	C₂²	1	1	yes	characteristic, complemented
135	#11745248	C₂²	1	1	yes	characteristic
136	#11745248	C₂²	1	1	yes	characteristic, complemented
137	#11745248	C₂²	1	1	yes	characteristic, complemented
138	#11745247	C₂²	1	1	yes	characteristic, complemented
139	#11745247	C₂²	1	1	yes	characteristic, complemented
140	#11745246	C₂²	1	1	yes	characteristic
141	#11745246	C₂²	1	1	yes	characteristic
142	#11745246	C₂²	1	1	yes	characteristic, complemented
143	#11745246	C₂²	1	1	yes	characteristic, complemented
144	#11745246	C₂²	1	1	yes	characteristic, complemented
145	#11745246	C₂²	1	1	yes	characteristic, complemented
146	#11745246	C₂²	1	1	yes	characteristic, complemented
147	#11745245	C₂²	1	1	yes	characteristic, complemented
148	#11745244	C₂²	1	1	yes	characteristic
149	#11745244	C₂²	1	1	yes	characteristic
150	#11745244	C₂²	1	1	yes	characteristic
151	#11745244	C₂²	1	1	yes	characteristic
152	#11745244	C₂²	1	1	yes	characteristic
153	#11745244	C₂²	1	1	yes	characteristic, complemented
154	#11745244	C₂²	1	1	yes	characteristic, complemented
155	#11745244	C₂²	1	1	yes	characteristic, complemented
156	#11745244	C₂²	1	1	yes	characteristic, complemented
157	#11745243	C₂²	1	1	yes	characteristic
158	#11745243	C₂²	1	1	yes	characteristic, complemented
159	#11745243	C₂²	1	1	yes	characteristic, complemented
160	#11745243	C₂²	1	1	yes	characteristic, complemented
161	#11745243	C₂²	1	1	yes	characteristic, complemented
162	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
164	#11745240	C₂²	1	1	yes	characteristic, complemented
165	#11745240	C₂²	1	1	yes	characteristic, complemented
166	#11745239	C₂²	1	1	yes	characteristic, complemented
167	#11745238	C₂²	1	1	yes	characteristic, complemented
168	#11745238	C₂²	1	1	yes	characteristic, complemented
169	#11745238	C₂²	1	1	yes	characteristic, complemented
170	#11745237	C₂²	1	1	yes	characteristic
171	#11745237	C₂²	1	1	yes	characteristic, complemented
172	#11745237	C₂²	1	1	yes	characteristic, complemented
173	#11745237	C₂²	1	1	yes	characteristic, complemented
174	#11745237	C₂²	1	1	yes	characteristic, complemented
175	#11745236	C₂²	1	1	yes	characteristic
176	#11745236	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	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
183	#11745234	C₂²	1	1	yes	characteristic, complemented
184	#11745234	C₂²	1	1	yes	characteristic, complemented
185	#11745232	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₉	C₂³	1	1	yes	characteristic
188	C₂³×D₂₉	C₂³	1	1	yes	characteristic
189	C₂³×D₂₉	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
192	C₂²×C₄×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	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
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	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
205	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
206	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
207	#90807	—	4	2	no	—
208	D₄×D₂₉	—	4	2	no	—
209	#90805	—	4	2	no	—
210	#90805	—	4	2	no	—
211	C₂×D₁₁₆	—	4	2	no	—
212	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
213	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
214	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
215	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
216	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
217	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
218	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
219	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
220	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
221	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
222	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
223	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
224	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
225	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
226	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
227	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
228	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
229	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₂₉	—	4	2	no	—
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×C₄×D₂₉	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
246	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
247	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
248	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
249	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
252	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
253	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
254	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
256	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
257	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
259	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
260	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
261	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
262	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
263	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
264	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
265	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
266	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
268	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
270	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
271	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
272	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
273	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
274	C₄²×C₂₉	C₂³	1	1	yes	characteristic
275	C₄²×C₂₉	C₂³	1	1	yes	characteristic
276	C₄²×C₂₉	C₂³	1	1	yes	characteristic
277	C₄²×C₂₉	C₂³	1	1	yes	characteristic
278	C₄²×C₂₉	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	#90781	C₂³	1	1	yes	characteristic
300	#90781	C₂³	1	1	yes	characteristic
301	#90781	C₂³	1	1	yes	characteristic
302	#90781	C₂³	1	1	yes	characteristic
303	#90781	C₂³	1	1	yes	characteristic
304	#90781	C₂³	1	1	yes	characteristic
305	#90781	C₂³	1	1	yes	characteristic
306	#90781	C₂³	1	1	yes	characteristic
307	#90781	C₂³	1	1	yes	characteristic
308	#90781	C₂³	1	1	yes	characteristic
309	#90781	C₂³	1	1	yes	characteristic
310	#90781	C₂³	1	1	yes	characteristic
311	#90781	C₂³	1	1	yes	characteristic
312	#90781	C₂³	1	1	yes	characteristic
313	#90781	C₂³	1	1	yes	characteristic
314	#90781	C₂³	1	1	yes	characteristic
315	#90781	C₂³	1	1	yes	characteristic
316	#90781	C₂³	1	1	yes	characteristic
317	#90781	C₂³	1	1	yes	characteristic
318	#90781	C₂³	1	1	yes	characteristic
319	#90781	C₂³	1	1	yes	characteristic
320	#90781	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₂₉	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	#90779	C₂³	1	1	yes	characteristic
342	#90779	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	C₂⁴	1	1	yes	characteristic
349	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
350	C₂²×D₂₉	—	2	2	no	—
351	C₂²×D₂₉	—	2	2	no	—
352	C₂²×D₂₉	—	4	1	no	—
353	C₂²×D₂₉	—	4	1	no	—
354	C₂²×D₂₉	—	4	1	no	—
355	C₂²×D₂₉	—	4	1	no	—
356	C₂²×D₂₉	—	4	1	no	—
357	C₂²×D₂₉	—	4	1	no	—
358	C₂²×D₂₉	—	4	1	no	—
359	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
360	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
361	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
362	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
363	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
364	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
365	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
366	Q₈×C₂₉	—	4	1	no	—
367	D₄×C₂₉	—	2	2	no	—
368	C₂×C₄×C₂₉	—	2	2	no	—
369	C₂×C₄×C₂₉	—	2	2	no	—
370	C₂×C₄×C₂₉	—	4	1	no	—
371	C₂×C₄×C₂₉	—	4	1	no	—
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	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
385	C₂²⋊D₂₉	—	2	2	no	—
386	C₂²⋊D₂₉	—	2	2	no	—
387	C₂²⋊D₂₉	—	2	2	no	—
388	C₂²⋊D₂₉	—	4	1	no	—
389	C₂²⋊D₂₉	—	4	1	no	—
390	C₂²⋊D₂₉	—	4	1	no	—
391	C₂²⋊D₂₉	—	4	1	no	—
392	C₂²⋊D₂₉	—	4	1	no	—
393	C₂×Dic₂₉	—	2	2	no	—
394	C₂×Dic₂₉	—	4	1	no	—
395	C₂×Dic₂₉	—	4	1	no	—
396	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
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	D₁₁₆	—	4	1	no	—
406	D₁₁₆	—	4	1	no	—
407	D₁₁₆	—	4	1	no	—
408	D₁₁₆	—	4	1	no	—
409	D₁₁₆	—	4	1	no	—
410	D₁₁₆	—	4	1	no	—
411	D₁₁₆	—	4	1	no	—
412	D₁₁₆	—	4	1	no	—
413	D₁₁₆	—	4	1	no	—
414	D₁₁₆	—	4	1	no	—
415	D₁₁₆	—	4	1	no	—
416	D₁₁₆	—	4	1	no	—
417	D₁₁₆	—	4	1	no	—
418	D₁₁₆	—	4	1	no	—
419	D₁₁₆	—	4	1	no	—
420	D₁₁₆	—	4	1	no	—
421	D₁₁₆	—	4	1	no	—
422	D₁₁₆	—	4	1	no	—
423	C₄×D₂₉	—	4	1	no	—
424	C₄×D₂₉	—	4	1	no	—
425	C₄×D₂₉	—	4	1	no	—
426	C₄×D₂₉	—	4	1	no	—
427	C₄×D₂₉	—	4	1	no	—
428	C₄×D₂₉	—	4	1	no	—
429	C₄×D₂₉	—	4	1	no	—
430	C₄×D₂₉	—	4	1	no	—
431	C₄×D₂₉	—	4	1	no	—
432	C₄×D₂₉	—	4	1	no	—
433	C₄×D₂₉	—	4	1	no	—
434	C₄×D₂₉	—	4	1	no	—
435	C₄×D₂₉	—	4	1	no	—
436	C₄×D₂₉	—	4	1	no	—
437	C₄×D₂₉	—	4	1	no	—
438	Dic₅₈	—	4	1	no	—
439	Dic₅₈	—	4	1	no	—
440	Dic₅₈	—	4	1	no	—
441	Dic₅₈	—	4	1	no	—
442	#3533	—	29	1	no	maximal, Sylow
443	C₂²×C₂₉	—	2	1	no	—
444	C₂²×C₂₉	—	2	1	no	—
445	C₂²×C₂₉	—	2	1	no	—
446	C₂²×C₂₉	—	2	1	no	—
447	C₂²×C₂₉	—	2	1	no	—
448	C₂²×C₂₉	H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
456	C₂×D₂₉	—	2	1	no	—
457	C₂×D₂₉	—	2	1	no	—
458	C₂×D₂₉	—	2	1	no	—
459	C₂×D₂₉	—	2	1	no	—
460	C₂×D₂₉	—	2	1	no	—
461	C₂×D₂₉	—	2	1	no	—
462	C₂×D₂₉	—	2	1	no	—
463	C₂×D₂₉	—	2	1	no	—
464	C₂×D₂₉	—	2	1	no	—
465	C₂×D₂₉	—	2	1	no	—
466	C₂×D₂₉	—	2	1	no	—
467	C₂×D₂₉	—	2	1	no	—
468	C₂×D₂₉	—	2	1	no	—
469	C₂×D₂₉	—	2	1	no	—
470	C₂×D₂₉	—	2	1	no	—
471	C₂×D₂₉	—	4	4	no	—
472	C₂×D₂₉	—	8	2	no	—
473	C₂×D₂₉	—	8	2	no	—
474	C₄×C₂₉	—	2	1	no	—
475	C₄×C₂₉	—	2	1	no	—
476	C₄×C₂₉	—	2	1	no	—
477	C₄×C₂₉	—	2	1	no	—
478	C₄×C₂₉	—	2	1	no	—
479	C₄×C₂₉	—	2	1	no	—
480	C₄×C₂₉	—	2	1	no	—
481	C₄×C₂₉	—	2	1	no	—
482	C₄×C₂₉	—	2	1	no	—
483	C₄×C₂₉	—	2	1	no	—
484	C₄×C₂₉	—	2	1	no	—
485	C₄×C₂₉	—	2	1	no	—
486	C₄×C₂₉	—	2	1	no	—
487	Dic₂₉	—	2	1	no	—
488	Dic₂₉	—	2	1	no	—
489	Dic₂₉	—	2	1	no	—
490	Dic₂₉	—	2	1	no	—
491	Dic₂₉	—	2	1	no	—
492	Dic₂₉	—	2	1	no	—
493	Dic₂₉	—	2	1	no	—
494	Dic₂₉	—	2	1	no	—
495	Dic₂₉	—	2	1	no	—
496	#563	—	29	1	no	—
497	#562	—	29	1	no	—
498	#562	—	29	1	no	—
499	#560	—	29	1	no	—
500	#559	—	29	1	no	—
501	#553	—	29	1	no	—
502	#553	—	29	1	no	—
503	#552	—	29	1	no	—
504	#552	D₂₉	1	1	yes	characteristic, complemented
505	#551	—	29	1	no	—
506	#551	—	29	1	no	—
507	#551	—	29	1	no	—
508	#547	—	29	1	no	—
509	#547	—	29	1	no	—
510	#546	—	29	1	no	—
511	#546	—	29	1	no	—
512	#542	—	29	1	no	—
513	#542	—	29	1	no	—
514	#540	—	29	1	no	—
515	#540	—	29	1	no	—
516	#539	—	29	1	no	—
517	#539	—	29	1	no	—
518	#538	—	29	1	no	—
519	#538	—	29	1	no	—
520	#538	—	29	1	no	—
521	#538	—	29	1	no	—
522	#535	—	29	1	no	—
523	#534	—	29	1	no	—
524	#525	—	29	1	no	—
525	#525	—	29	1	no	—
526	C₂×#123	—	29	1	no	—
527	C₂×C₂₉	—	2	2	no	—
528	C₂×C₂₉	—	4	1	no	—
529	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂×C₂₉	#585	1	1	yes	characteristic
531	C₂×C₂₉	#585	1	1	yes	characteristic
532	D₂₉	—	4	1	no	—
533	D₂₉	—	4	1	no	—
534	D₂₉	—	4	1	no	—
535	D₂₉	—	4	1	no	—
536	D₂₉	—	4	1	no	—
537	D₂₉	—	4	1	no	—
538	D₂₉	—	4	1	no	—
539	C₂×#41	—	29	1	no	—
540	C₂×#41	—	29	1	no	—
541	C₂×#41	—	29	1	no	—
542	C₂²×D₄	—	29	1	no	—
543	C₂²×D₄	—	29	1	no	—
544	C₂³×C₄	—	29	1	no	—
545	C₄⋊Q₈	—	29	1	no	—
546	C₄⋊Q₈	—	29	1	no	—
547	#127	—	29	1	no	—
548	#127	—	29	1	no	—
549	#126	—	29	1	no	—
550	#126	—	29	1	no	—
551	#126	—	29	1	no	—
552	#126	—	29	1	no	—
553	#126	—	29	1	no	—
554	#126	—	29	1	no	—
555	#126	—	29	1	no	—
556	#126	—	29	1	no	—
557	#126	—	29	1	no	—
558	#126	—	29	1	no	—
559	#126	C₂×D₂₉	1	1	yes	characteristic, complemented
560	#126	C₂×D₂₉	1	1	yes	characteristic, complemented
561	#125	—	29	1	no	—
562	#125	—	29	1	no	—
563	#125	—	29	1	no	—
564	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
565	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
566	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
567	#124	—	29	1	no	—
568	#124	—	29	1	no	—
569	#124	—	29	1	no	—
570	#124	—	29	1	no	—
571	#124	—	29	1	no	—
572	#124	—	29	1	no	—
573	#124	—	29	1	no	—
574	#124	—	29	1	no	—
575	#124	—	29	1	no	—
576	#124	—	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	—	29	1	no	—
590	#123	—	29	1	no	—
591	#123	—	29	1	no	—
592	#123	—	29	1	no	—
593	#123	—	29	1	no	—
594	#123	—	29	1	no	—
595	#123	—	29	1	no	—
596	#123	—	29	1	no	—
597	#123	—	29	1	no	—
598	#123	—	29	1	no	—
599	#123	—	29	1	no	—
600	#123	—	29	1	no	—
601	#123	—	29	1	no	—
602	#123	—	29	1	no	—
603	#123	—	29	1	no	—
604	#123	—	29	1	no	—
605	#123	C₂×D₂₉	1	1	yes	characteristic
606	#123	C₂×D₂₉	1	1	yes	characteristic
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	C₂×D₂₉	1	1	yes	characteristic, complemented
622	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
623	#121	—	29	1	no	—
624	#121	—	29	1	no	—
625	#121	—	29	1	no	—
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	#121	—	29	1	no	—
637	#121	—	29	1	no	—
638	#121	—	29	1	no	—
639	#121	—	29	1	no	—
640	#121	—	29	1	no	—
641	#121	—	29	1	no	—
642	#121	—	29	1	no	—
643	#121	—	29	1	no	—
644	#121	—	29	1	no	—
645	#121	—	29	1	no	—
646	#121	—	29	1	no	—
647	#120	—	29	1	no	—
648	#120	—	29	1	no	—
649	#120	—	29	1	no	—
650	#120	—	29	1	no	—
651	#120	—	29	1	no	—
652	#120	—	29	1	no	—
653	#120	—	29	1	no	—
654	#120	—	29	1	no	—
655	#120	—	29	1	no	—
656	#120	—	29	1	no	—
657	C₄×Q₈	—	29	1	no	—
658	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
659	C₄×D₄	—	29	1	no	—
660	C₄×D₄	—	29	1	no	—
661	C₄×D₄	—	29	1	no	—
662	C₄×D₄	—	29	1	no	—
663	C₄×D₄	—	29	1	no	—
664	C₄×D₄	—	29	1	no	—
665	C₄×D₄	—	29	1	no	—
666	C₄×D₄	—	29	1	no	—
667	C₄×D₄	—	29	1	no	—
668	C₄×D₄	—	29	1	no	—
669	C₄×D₄	—	29	1	no	—
670	C₄×D₄	—	29	1	no	—
671	C₄×D₄	—	29	1	no	—
672	C₄×D₄	—	29	1	no	—
673	C₄×D₄	—	29	1	no	—
674	C₄×D₄	—	29	1	no	—
675	C₄×D₄	—	29	1	no	—
676	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
677	#117	—	29	1	no	—
678	#117	—	29	1	no	—
679	#117	—	29	1	no	—
680	#117	—	29	1	no	—
681	#117	C₂×D₂₉	1	1	yes	characteristic, complemented
682	#117	C₂×D₂₉	1	1	yes	characteristic, complemented
683	#117	C₂×D₂₉	1	1	yes	characteristic, complemented
684	C₂×C₄⋊C₄	—	29	1	no	—
685	C₂×C₄⋊C₄	—	29	1	no	—
686	C₂×C₄⋊C₄	—	29	1	no	—
687	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic, complemented
688	C₂×C₂²⋊C₄	—	29	1	no	—
689	C₂×C₂²⋊C₄	—	29	1	no	—
690	C₂×C₂²⋊C₄	—	29	1	no	—
691	C₂×C₂²⋊C₄	—	29	1	no	—
692	C₂×C₂²⋊C₄	—	29	1	no	—
693	C₂×C₂²⋊C₄	—	29	1	no	—
694	C₂₉	#3533	1	1	yes	characteristic, complemented, Sylow
695	C₂⁴	—	29	1	no	—
696	C₂⁴	—	29	1	no	—
697	C₂⁴	—	29	1	no	—
698	#41	—	116	2	no	—
699	#41	—	116	2	no	—
700	#41	—	116	2	no	—
701	C₂×Q₈	—	29	1	no	—
702	C₂×Q₈	—	29	1	no	—
703	C₂×Q₈	—	29	1	no	—
704	C₂×Q₈	—	29	1	no	—
705	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
706	C₂×D₄	—	29	1	no	—
707	C₂×D₄	—	29	1	no	—
708	C₂×D₄	—	29	1	no	—
709	C₂×D₄	—	29	1	no	—
710	C₂×D₄	—	29	1	no	—
711	C₂×D₄	—	29	1	no	—
712	C₂×D₄	—	29	1	no	—
713	C₂×D₄	—	29	1	no	—
714	C₂×D₄	—	29	1	no	—
715	C₂×D₄	—	29	1	no	—
716	C₂×D₄	—	29	1	no	—
717	C₂×D₄	—	29	1	no	—
718	C₂×D₄	—	29	1	no	—
719	C₂×D₄	—	29	1	no	—
720	C₂×D₄	—	29	1	no	—
721	C₂×D₄	—	29	1	no	—
722	C₂×D₄	—	29	1	no	—
723	C₂×D₄	—	29	1	no	—
724	C₂×D₄	—	29	1	no	—
725	C₂×D₄	—	29	1	no	—
726	C₂×D₄	—	29	1	no	—
727	C₂×D₄	—	29	1	no	—
728	C₂×D₄	—	29	1	no	—
729	C₂×D₄	—	29	1	no	—
730	C₂×D₄	—	29	1	no	—
731	C₂×D₄	—	29	1	no	—
732	C₂×D₄	—	116	2	no	—
733	C₂×D₄	—	116	2	no	—
734	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
735	C₂²×C₄	—	29	1	no	—
736	C₂²×C₄	—	29	1	no	—
737	C₂²×C₄	—	29	1	no	—
738	C₂²×C₄	—	29	1	no	—
739	C₂²×C₄	—	29	1	no	—
740	C₂²×C₄	—	29	1	no	—
741	C₂²×C₄	—	29	1	no	—
742	C₂²×C₄	—	29	1	no	—
743	C₂²×C₄	—	29	1	no	—
744	C₂²×C₄	—	29	1	no	—
745	C₂²×C₄	—	29	1	no	—
746	C₂²×C₄	—	29	1	no	—
747	C₂²×C₄	—	29	1	no	—
748	C₂²×C₄	—	29	1	no	—
749	C₂²×C₄	—	29	1	no	—
750	C₂²×C₄	—	29	1	no	—
751	C₂²×C₄	—	29	1	no	—
752	C₂²×C₄	—	29	1	no	—
753	C₂²×C₄	—	116	2	no	—
754	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
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	—	29	1	no	—
776	C₄⋊C₄	—	29	1	no	—
777	C₄⋊C₄	—	29	1	no	—
778	C₄⋊C₄	—	29	1	no	—
779	C₄⋊C₄	—	29	1	no	—
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	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
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	—	29	1	no	—
816	C₂²⋊C₄	—	29	1	no	—
817	C₂²⋊C₄	—	29	1	no	—
818	C₂²⋊C₄	—	29	1	no	—
819	C₂²⋊C₄	—	29	1	no	—
820	C₂²⋊C₄	—	29	1	no	—
821	C₂²⋊C₄	—	29	1	no	—
822	C₂²⋊C₄	—	29	1	no	—
823	C₂²⋊C₄	—	29	1	no	—
824	C₂²⋊C₄	—	29	1	no	—
825	C₂²⋊C₄	—	29	1	no	—
826	C₂²⋊C₄	—	29	1	no	—
827	C₂²⋊C₄	—	29	1	no	—
828	C₂²⋊C₄	—	29	1	no	—
829	C₂²⋊C₄	—	29	1	no	—
830	C₂²⋊C₄	—	29	1	no	—
831	C₂²⋊C₄	—	29	1	no	—
832	C₂²⋊C₄	—	29	1	no	—
833	C₂²⋊C₄	—	29	1	no	—
834	C₂²⋊C₄	—	29	1	no	—
835	C₂²⋊C₄	—	29	1	no	—
836	C₂²⋊C₄	—	29	1	no	—
837	C₂²⋊C₄	—	29	1	no	—
838	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
846	C₄²	—	29	1	no	—
847	C₄²	—	29	1	no	—
848	C₄²	—	29	1	no	—
849	C₄²	—	29	1	no	—
850	C₄²	—	29	1	no	—
851	C₄²	C₂²×D₂₉	1	1	yes	characteristic
852	C₄²	C₂²×D₂₉	1	1	yes	characteristic
853	C₄²	C₂²×D₂₉	1	1	yes	characteristic
854	C₄²	C₂²×D₂₉	1	1	yes	characteristic
855	C₄²	C₂²×D₂₉	1	1	yes	characteristic
856	C₂³	—	29	1	no	—
857	C₂³	—	29	1	no	—
858	C₂³	—	29	1	no	—
859	C₂³	—	29	1	no	—
860	C₂³	—	29	1	no	—
861	C₂³	—	29	1	no	—
862	C₂³	—	29	1	no	—
863	C₂³	—	58	2	no	—
864	C₂³	—	58	2	no	—
865	C₂³	—	116	1	no	—
866	C₂³	—	116	1	no	—
867	C₂³	—	116	1	no	—
868	C₂³	—	116	1	no	—
869	C₂³	—	116	1	no	—
870	C₂³	—	116	1	no	—
871	C₂³	—	116	1	no	—
872	C₂³	C₂³×D₂₉	1	1	yes	characteristic
873	C₂³	C₂³×D₂₉	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	116	1	no	—
876	Q₈	—	116	1	no	—
877	Q₈	—	116	1	no	—
878	Q₈	—	116	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	58	2	no	—
881	D₄	—	58	2	no	—
882	D₄	—	58	2	no	—
883	D₄	—	116	1	no	—
884	D₄	—	116	1	no	—
885	D₄	—	116	1	no	—
886	D₄	—	116	1	no	—
887	D₄	—	116	1	no	—
888	D₄	—	116	1	no	—
889	D₄	—	116	1	no	—
890	D₄	—	116	1	no	—
891	D₄	—	116	1	no	—
892	D₄	—	116	1	no	—
893	D₄	—	116	1	no	—
894	D₄	—	116	1	no	—
895	D₄	—	116	1	no	—
896	D₄	—	116	1	no	—
897	D₄	—	116	1	no	—
898	D₄	—	116	1	no	—
899	D₄	—	116	1	no	—
900	D₄	—	116	1	no	—
901	D₄	—	116	1	no	—
902	D₄	—	116	1	no	—
903	D₄	—	116	1	no	—
904	D₄	—	116	1	no	—
905	D₄	—	116	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	29	1	no	—
911	C₂×C₄	—	29	1	no	—
912	C₂×C₄	—	29	1	no	—
913	C₂×C₄	—	29	1	no	—
914	C₂×C₄	—	29	1	no	—
915	C₂×C₄	—	29	1	no	—
916	C₂×C₄	—	29	1	no	—
917	C₂×C₄	—	29	1	no	—
918	C₂×C₄	—	29	1	no	—
919	C₂×C₄	—	58	2	no	—
920	C₂×C₄	—	116	1	no	—
921	C₂×C₄	—	116	1	no	—
922	C₂×C₄	—	116	1	no	—
923	C₂×C₄	—	116	1	no	—
924	C₂×C₄	—	116	1	no	—
925	C₂×C₄	—	116	1	no	—
926	C₂×C₄	—	116	1	no	—
927	C₂×C₄	—	116	1	no	—
928	C₂×C₄	—	116	1	no	—
929	C₂×C₄	—	116	1	no	—
930	C₂×C₄	—	116	1	no	—
931	C₂×C₄	—	116	1	no	—
932	C₂×C₄	—	116	1	no	—
933	C₂×C₄	—	116	1	no	—
934	C₂×C₄	—	116	1	no	—
935	C₂×C₄	—	116	1	no	—
936	C₂×C₄	—	116	1	no	—
937	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
938	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	58	1	no	—
956	C₂²	—	58	1	no	—
957	C₂²	—	58	1	no	—
958	C₂²	—	58	1	no	—
959	C₂²	—	58	1	no	—
960	C₂²	—	58	1	no	—
961	C₂²	—	58	1	no	—
962	C₂²	—	58	1	no	—
963	C₂²	—	58	1	no	—
964	C₂²	—	58	1	no	—
965	C₂²	—	58	1	no	—
966	C₂²	—	58	1	no	—
967	C₂²	—	58	1	no	—
968	C₂²	—	58	1	no	—
969	C₂²	—	58	1	no	—
970	C₂²	—	58	1	no	—
971	C₂²	—	58	1	no	—
972	C₂²	—	58	1	no	—
973	C₂²	—	58	1	no	—
974	C₂²	—	58	1	no	—
975	C₂²	—	58	1	no	—
976	C₂²	—	116	4	no	—
977	C₂²	—	232	2	no	—
978	C₂²	—	232	2	no	—
979	C₂²	#11745364	1	2	yes	—
980	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	58	1	no	—
995	C₄	—	58	1	no	—
996	C₄	—	58	1	no	—
997	C₄	—	58	1	no	—
998	C₄	—	58	1	no	—
999	C₄	—	58	1	no	—
1000	C₄	—	58	1	no	—
1001	C₄	—	58	1	no	—
1002	C₄	—	58	1	no	—
1003	C₂	—	2	2	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	116	1	no	—
1006	C₂	—	116	1	no	—
1007	C₂	—	116	1	no	—
1008	C₂	—	116	1	no	—
1009	C₂	—	116	1	no	—
1010	C₂	—	116	1	no	—
1011	C₂	—	116	1	no	—
1012	C₂	C₂×#11745364	1	1	yes	characteristic
1013	C₂	#14271999	1	1	yes	characteristic
1014	C₂	#14272000	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#552	C₂
hypercenter	#552	D₂₉
hypocenter	C₂₉	#3533
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #14271917	C₂	semidirect
2. #14271911	C₂	semidirect
3. #14271909	C₂	semidirect
4. #14271904	C₂	semidirect
5. #14271898	C₂	semidirect
6. #14271866	C₂	semidirect
7. #14271864	C₂	semidirect
8. #14271846	C₂	semidirect
9. #14271840	C₂	semidirect
10. #14271837	C₂	semidirect
11. #14271837	C₂	semidirect
12. #14271814	C₂	semidirect
13. #14271811	C₂	semidirect
14. #14271808	C₂	semidirect
15. #14271805	C₂	semidirect
16. #14271785	C₂	semidirect
17. #14271779	C₂	semidirect
18. #14271769	C₂	semidirect
19. #14271768	C₂	semidirect
20. #14271761	C₂	semidirect
21. #14271761	C₂	semidirect
22. #14271753	C₂	semidirect
23. #14271753	C₂	semidirect
24. #14271752	C₂	semidirect
25. #14271746	C₂	semidirect
26. #14271732	C₂	semidirect
27. #14271724	C₂	semidirect
28. #14271675	C₂	semidirect
29. #14271671	C₂	semidirect
30. C₂×#11745256	C₂	semidirect
31. C₂₉×#552	C₂	semidirect
35. C₂×#90805	C₂²	semidirect
37. C₂²×C₄×D₂₉	C₂²	semidirect
38. C₂₉×#126	C₂²	semidirect
39. C₂₉×#126	C₂²	semidirect
40. C₂₉×#125	C₂²	semidirect
41. C₂₉×#125	C₂²	semidirect
42. C₂₉×#125	C₂²	semidirect
45. C₂₉×C₂²⋊Q₈	C₂²	semidirect
46. C₂₉×C₂²⋊Q₈	C₂²	semidirect
47. C₄×Q₈×C₂₉	C₂²	semidirect
49. C₂₉×#117	C₂²	semidirect
50. C₂₉×#117	C₂²	semidirect
51. C₂₉×#117	C₂²	semidirect
52. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
53. #11745309	C₂²	semidirect
54. #11745309	C₂²	semidirect
55. #11745309	C₂²	semidirect
56. #11745308	C₂²	semidirect
60. #11745292	C₂²	semidirect
61. #11745292	C₂²	semidirect
63. #11745291	C₂²	semidirect
64. #11745291	C₂²	semidirect
65. C₄×C₂²⋊D₂₉	C₂²	semidirect
68. C₂×#90781	C₂²	semidirect
69. C₂×#90781	C₂²	semidirect
70. C₂×#90779	C₂²	semidirect
71. #11745260	C₂²	semidirect
72. #11745260	C₂²	semidirect
73. #11745260	C₂²	semidirect
74. #11745260	C₂²	semidirect
75. #11745260	C₂²	semidirect
76. #11745260	C₂²	semidirect
77. #11745260	C₂²	semidirect
78. #11745259	C₂²	semidirect
79. #11745259	C₂²	semidirect
80. #11745259	C₂²	semidirect
81. #11745258	C₂²	semidirect
82. #11745258	C₂²	semidirect
83. #11745258	C₂²	semidirect
84. #11745258	C₂²	semidirect
85. #11745258	C₂²	semidirect
86. #11745258	C₂²	semidirect
87. #11745258	C₂²	semidirect
88. #11745258	C₂²	semidirect
93. #11745257	C₂²	semidirect
94. #11745257	C₂²	semidirect
95. #11745257	C₂²	semidirect
96. #11745257	C₂²	semidirect
97. #11745257	C₂²	semidirect
98. #11745257	C₂²	semidirect
99. #11745257	C₂²	semidirect
100. #11745257	C₂²	semidirect
101. #11745257	C₂²	semidirect
108. #11745256	C₂²	semidirect
109. #11745256	C₂²	semidirect
110. #11745256	C₂²	semidirect
111. #11745256	C₂²	semidirect
112. #11745256	C₂²	semidirect
113. #11745256	C₂²	semidirect
114. #11745256	C₂²	semidirect
115. #11745256	C₂²	semidirect
116. #11745256	C₂²	semidirect
117. #11745256	C₂²	semidirect
118. #11745256	C₂²	semidirect
119. #11745256	C₂²	semidirect
120. #11745256	C₂²	semidirect
121. #11745256	C₂²	semidirect
122. #11745256	C₂²	semidirect
123. #11745255	C₂²	semidirect
124. #11745255	C₂²	semidirect
125. #11745255	C₂²	semidirect
126. #11745255	C₂²	semidirect
127. #11745255	C₂²	semidirect
128. #11745254	C₂²	semidirect
129. C₄⋊C₄×D₂₉	C₂²	semidirect
130. C₄⋊C₄×D₂₉	C₂²	semidirect
131. #11745251	C₂²	semidirect
132. #11745251	C₂²	semidirect
133. #11745250	C₂²	semidirect
134. #11745250	C₂²	semidirect
136. #11745248	C₂²	semidirect
137. #11745248	C₂²	semidirect
138. #11745247	C₂²	semidirect
139. #11745247	C₂²	semidirect
142. #11745246	C₂²	semidirect
143. #11745246	C₂²	semidirect
144. #11745246	C₂²	semidirect
145. #11745246	C₂²	semidirect
146. #11745246	C₂²	semidirect
147. #11745245	C₂²	semidirect
153. #11745244	C₂²	semidirect
154. #11745244	C₂²	semidirect
155. #11745244	C₂²	semidirect
156. #11745244	C₂²	semidirect
158. #11745243	C₂²	semidirect
159. #11745243	C₂²	semidirect
160. #11745243	C₂²	semidirect
161. #11745243	C₂²	semidirect
163. C₂²⋊C₄×D₂₉	C₂²	semidirect
164. #11745240	C₂²	semidirect
165. #11745240	C₂²	semidirect
166. #11745239	C₂²	semidirect
167. #11745238	C₂²	semidirect
168. #11745238	C₂²	semidirect
169. #11745238	C₂²	semidirect
171. #11745237	C₂²	semidirect
172. #11745237	C₂²	semidirect
173. #11745237	C₂²	semidirect
174. #11745237	C₂²	semidirect
176. #11745236	C₂²	semidirect
177. C₄×D₁₁₆	C₂²	semidirect
178. C₄×D₁₁₆	C₂²	semidirect
179. C₄×D₁₁₆	C₂²	semidirect
180. C₄×D₁₁₆	C₂²	semidirect
181. C₄×D₁₁₆	C₂²	semidirect
182. C₄×D₁₁₆	C₂²	semidirect
183. #11745234	C₂²	semidirect
184. #11745234	C₂²	semidirect
185. #11745232	C₂²	semidirect
186. C₄×Dic₅₈	C₂²	semidirect
504. #552	D₂₉	semidirect
559. #126	C₂×D₂₉	semidirect
560. #126	C₂×D₂₉	semidirect
564. #125	C₂×D₂₉	semidirect
565. #125	C₂×D₂₉	semidirect
566. #125	C₂×D₂₉	semidirect
621. C₂²⋊Q₈	C₂×D₂₉	semidirect
622. C₂²⋊Q₈	C₂×D₂₉	semidirect
658. C₄×Q₈	C₂×D₂₉	semidirect
681. #117	C₂×D₂₉	semidirect
682. #117	C₂×D₂₉	semidirect
683. #117	C₂×D₂₉	semidirect
687. C₂×C₄⋊C₄	C₂×D₂₉	semidirect
694. C₂₉	#3533	semidirect

Maximal subgroups

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

subgroup	index
#14271917	2
#14271911	2
#14271909	2
#14271904	2
#14271898	2
#14271866	2
#14271864	2
#14271846	2
#14271840	2
#14271837	2
#14271814	2
#14271811	2
#14271808	2
#14271805	2
#14271785	2
#14271779	2
#14271769	2
#14271768	2
#14271761	2
#14271753	2
#14271752	2
#14271746	2
#14271732	2
#14271724	2
#14271675	2
#14271671	2
C₂×#11745256	2
C₂₉×#552	2
#3533	29