Subgroups — #16833684

Order 3712.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271909	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271903	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271901	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271866	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271858	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271841	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271840	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271810	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271806	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271806	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271805	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271804	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271804	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271797	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271797	C₂	1	1	yes	maximal, characteristic, complemented
16	#14271765	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271763	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271761	C₂	1	1	yes	maximal, characteristic, complemented
19	#14271759	C₂	1	1	yes	maximal, characteristic, complemented
20	#14271759	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271747	C₂	1	1	yes	maximal, characteristic, complemented
22	#14271747	C₂	1	1	yes	maximal, characteristic, complemented
23	#14271745	C₂	1	1	yes	maximal, characteristic, complemented
24	#14271743	C₂	1	1	yes	maximal, characteristic, complemented
25	#14271724	C₂	1	1	yes	maximal, characteristic, complemented
26	#14271724	C₂	1	1	yes	maximal, characteristic, complemented
27	#14271721	C₂	1	1	yes	maximal, characteristic, complemented
28	#14271676	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
30	#121×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₉×#562	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#90809	C₂²	1	1	yes	characteristic, complemented
33	C₂×#90809	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#90805	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂²×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
56	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
57	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
59	#11745309	C₂²	1	1	yes	characteristic, complemented
60	#11745309	C₂²	1	1	yes	characteristic, complemented
61	#11745308	C₂²	1	1	yes	characteristic, complemented
62	#11745308	C₂²	1	1	yes	characteristic, complemented
63	#11745308	C₂²	1	1	yes	characteristic, complemented
64	#11745308	C₂²	1	1	yes	characteristic, complemented
65	#11745302	C₂²	1	1	yes	characteristic, complemented
66	#11745302	C₂²	1	1	yes	characteristic, complemented
67	#11745301	C₂²	1	1	yes	characteristic, complemented
68	#11745301	C₂²	1	1	yes	characteristic, complemented
69	#11745301	C₂²	1	1	yes	characteristic, complemented
70	#11745301	C₂²	1	1	yes	characteristic, complemented
71	#11745301	C₂²	1	1	yes	characteristic, complemented
72	#11745300	C₂²	1	1	yes	characteristic, complemented
73	#11745300	C₂²	1	1	yes	characteristic, complemented
74	#11745300	C₂²	1	1	yes	characteristic, complemented
75	#11745299	C₂²	1	1	yes	characteristic
76	#11745299	C₂²	1	1	yes	characteristic, complemented
77	#11745299	C₂²	1	1	yes	characteristic, complemented
78	#11745299	C₂²	1	1	yes	characteristic, complemented
79	#11745299	C₂²	1	1	yes	characteristic, complemented
80	#11745299	C₂²	1	1	yes	characteristic, complemented
81	#11745298	C₂²	1	1	yes	characteristic, complemented
82	#11745297	C₂²	1	1	yes	characteristic, complemented
83	#11745292	C₂²	1	1	yes	characteristic, complemented
84	#11745292	C₂²	1	1	yes	characteristic, complemented
85	#11745292	C₂²	1	1	yes	characteristic, complemented
86	#11745291	C₂²	1	1	yes	characteristic, complemented
87	#11745291	C₂²	1	1	yes	characteristic, complemented
88	#11745291	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
94	C₂×#90781	C₂²	1	1	yes	characteristic, complemented
95	#11745260	C₂²	1	1	yes	characteristic, complemented
96	#11745260	C₂²	1	1	yes	characteristic, complemented
97	#11745260	C₂²	1	1	yes	characteristic, complemented
98	#11745260	C₂²	1	1	yes	characteristic, complemented
99	#11745259	C₂²	1	1	yes	characteristic, complemented
100	#11745258	C₂²	1	1	yes	characteristic, complemented
101	#11745258	C₂²	1	1	yes	characteristic, complemented
102	#11745258	C₂²	1	1	yes	characteristic, complemented
103	#11745257	C₂²	1	1	yes	characteristic
104	#11745257	C₂²	1	1	yes	characteristic, complemented
105	#11745257	C₂²	1	1	yes	characteristic, complemented
106	#11745257	C₂²	1	1	yes	characteristic, complemented
107	#11745257	C₂²	1	1	yes	characteristic, complemented
108	#11745257	C₂²	1	1	yes	characteristic, complemented
109	#11745257	C₂²	1	1	yes	characteristic, complemented
110	#11745257	C₂²	1	1	yes	characteristic, complemented
111	#11745257	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	#11745255	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	#11745254	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	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
132	#11745251	C₂²	1	1	yes	characteristic, complemented
133	#11745251	C₂²	1	1	yes	characteristic, complemented
134	#11745251	C₂²	1	1	yes	characteristic, complemented
135	#11745248	C₂²	1	1	yes	characteristic, complemented
136	#11745248	C₂²	1	1	yes	characteristic, complemented
137	#11745247	C₂²	1	1	yes	characteristic, complemented
138	#11745246	C₂²	1	1	yes	characteristic
139	#11745246	C₂²	1	1	yes	characteristic
140	#11745246	C₂²	1	1	yes	characteristic, complemented
141	#11745246	C₂²	1	1	yes	characteristic, complemented
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	#11745246	C₂²	1	1	yes	characteristic, complemented
148	#11745246	C₂²	1	1	yes	characteristic, complemented
149	#11745246	C₂²	1	1	yes	characteristic, complemented
150	#11745245	C₂²	1	1	yes	characteristic, complemented
151	#11745245	C₂²	1	1	yes	characteristic, complemented
152	#11745245	C₂²	1	1	yes	characteristic, complemented
153	#11745245	C₂²	1	1	yes	characteristic, complemented
154	#11745245	C₂²	1	1	yes	characteristic, complemented
155	#11745245	C₂²	1	1	yes	characteristic, complemented
156	#11745245	C₂²	1	1	yes	characteristic, complemented
157	#11745245	C₂²	1	1	yes	characteristic, complemented
158	#11745244	C₂²	1	1	yes	characteristic
159	#11745244	C₂²	1	1	yes	characteristic, complemented
160	#11745244	C₂²	1	1	yes	characteristic, complemented
161	#11745244	C₂²	1	1	yes	characteristic, complemented
162	#11745244	C₂²	1	1	yes	characteristic, complemented
163	#11745244	C₂²	1	1	yes	characteristic, complemented
164	#11745244	C₂²	1	1	yes	characteristic, complemented
165	#11745244	C₂²	1	1	yes	characteristic, complemented
166	#11745244	C₂²	1	1	yes	characteristic, complemented
167	#11745244	C₂²	1	1	yes	characteristic, complemented
168	#11745243	C₂²	1	1	yes	characteristic, complemented
169	#11745243	C₂²	1	1	yes	characteristic, complemented
170	#11745243	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
172	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
173	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
174	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
175	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
176	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
177	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
179	#11745241	C₂²	1	1	yes	characteristic, complemented
180	#11745241	C₂²	1	1	yes	characteristic, complemented
181	#11745241	C₂²	1	1	yes	characteristic, complemented
182	#11745239	C₂²	1	1	yes	characteristic, complemented
183	#11745238	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×D₁₁₆	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	C₂³×D₂₉	C₂³	1	1	yes	characteristic
191	C₂³×D₂₉	C₂³	1	1	yes	characteristic
192	C₂³×D₂₉	C₂³	1	1	yes	characteristic
193	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
194	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
197	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
198	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
199	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₂₉	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	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
221	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
222	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
223	#90809	—	4	2	no	—
224	#90809	—	4	2	no	—
225	D₄×D₂₉	—	4	2	no	—
226	D₄×D₂₉	—	4	2	no	—
227	D₄×D₂₉	—	4	2	no	—
228	D₄×D₂₉	—	4	2	no	—
229	D₄×D₂₉	—	4	2	no	—
230	D₄×D₂₉	—	4	2	no	—
231	#90805	—	4	2	no	—
232	C₂×D₁₁₆	—	4	2	no	—
233	C₂×D₁₁₆	—	4	2	no	—
234	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
235	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
236	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
237	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
238	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
239	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
240	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
241	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
242	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
243	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
244	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
245	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
246	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
247	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
248	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₂₉	—	4	2	no	—
250	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
264	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
265	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
266	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
267	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
268	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
269	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
270	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
271	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
272	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
273	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
274	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
275	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
276	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
277	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
279	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
280	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
281	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
282	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
283	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
284	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
285	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
286	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
287	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
288	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
289	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
290	C₄²×C₂₉	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
297	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
298	C₂²⋊Dic₂₉	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	#90781	C₂³	1	1	yes	characteristic
322	#90781	C₂³	1	1	yes	characteristic
323	#90781	C₂³	1	1	yes	characteristic
324	#90781	C₂³	1	1	yes	characteristic
325	#90781	C₂³	1	1	yes	characteristic
326	#90781	C₂³	1	1	yes	characteristic
327	#90781	C₂³	1	1	yes	characteristic
328	#90781	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
331	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
332	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
333	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
334	C₄⋊Dic₂₉	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	#90779	C₂³	1	1	yes	characteristic
344	#90779	C₂³	1	1	yes	characteristic
345	#90779	C₂³	1	1	yes	characteristic
346	#90779	C₂³	1	1	yes	characteristic
347	#90779	C₂³	1	1	yes	characteristic
348	#90779	C₂³	1	1	yes	characteristic
349	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
350	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
351	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
352	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
353	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
354	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
355	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
356	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
357	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
358	C₂²×D₂₉	—	2	2	no	—
359	C₂²×D₂₉	—	2	2	no	—
360	C₂²×D₂₉	—	2	2	no	—
361	C₂²×D₂₉	—	2	2	no	—
362	C₂²×D₂₉	—	2	2	no	—
363	C₂²×D₂₉	—	4	1	no	—
364	C₂²×D₂₉	—	4	1	no	—
365	C₂²×D₂₉	—	4	1	no	—
366	C₂²×D₂₉	—	4	1	no	—
367	C₂²×D₂₉	—	4	1	no	—
368	C₂²×D₂₉	—	4	1	no	—
369	C₂²×D₂₉	—	4	1	no	—
370	C₂²×D₂₉	—	4	1	no	—
371	C₂²×D₂₉	—	4	1	no	—
372	C₂²×D₂₉	—	4	1	no	—
373	C₂²×D₂₉	—	4	1	no	—
374	C₂²×D₂₉	—	4	1	no	—
375	C₂²×D₂₉	—	4	1	no	—
376	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
377	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
378	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
379	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
380	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
381	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
382	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
383	Q₈×C₂₉	—	4	1	no	—
384	Q₈×C₂₉	—	4	1	no	—
385	D₄×C₂₉	—	4	1	no	—
386	D₄×C₂₉	—	4	1	no	—
387	D₄×C₂₉	—	4	1	no	—
388	D₄×C₂₉	—	4	1	no	—
389	D₄×C₂₉	—	4	1	no	—
390	D₄×C₂₉	—	4	1	no	—
391	C₂×C₄×C₂₉	—	4	1	no	—
392	C₂×C₄×C₂₉	—	4	1	no	—
393	C₂×C₄×C₂₉	—	4	1	no	—
394	C₂×C₄×C₂₉	—	4	1	no	—
395	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
406	C₂²⋊D₂₉	—	2	2	no	—
407	C₂²⋊D₂₉	—	2	2	no	—
408	C₂²⋊D₂₉	—	2	2	no	—
409	C₂²⋊D₂₉	—	4	1	no	—
410	C₂²⋊D₂₉	—	4	1	no	—
411	C₂²⋊D₂₉	—	4	1	no	—
412	C₂²⋊D₂₉	—	4	1	no	—
413	C₂²⋊D₂₉	—	4	1	no	—
414	C₂²⋊D₂₉	—	4	1	no	—
415	C₂²⋊D₂₉	—	4	1	no	—
416	C₂²⋊D₂₉	—	4	1	no	—
417	C₂²⋊D₂₉	—	4	1	no	—
418	C₂²⋊D₂₉	—	4	1	no	—
419	C₂²⋊D₂₉	—	4	1	no	—
420	C₂²⋊D₂₉	—	4	1	no	—
421	C₂²⋊D₂₉	—	4	1	no	—
422	C₂×Dic₂₉	—	4	1	no	—
423	C₂×Dic₂₉	—	4	1	no	—
424	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
433	D₁₁₆	—	2	2	no	—
434	D₁₁₆	—	2	2	no	—
435	D₁₁₆	—	2	2	no	—
436	D₁₁₆	—	2	2	no	—
437	D₁₁₆	—	2	2	no	—
438	D₁₁₆	—	2	2	no	—
439	D₁₁₆	—	2	2	no	—
440	D₁₁₆	—	4	1	no	—
441	D₁₁₆	—	4	1	no	—
442	D₁₁₆	—	4	1	no	—
443	D₁₁₆	—	4	1	no	—
444	D₁₁₆	—	4	1	no	—
445	D₁₁₆	—	4	1	no	—
446	D₁₁₆	—	4	1	no	—
447	D₁₁₆	—	4	1	no	—
448	C₄×D₂₉	—	2	2	no	—
449	C₄×D₂₉	—	2	2	no	—
450	C₄×D₂₉	—	2	2	no	—
451	C₄×D₂₉	—	4	1	no	—
452	C₄×D₂₉	—	4	1	no	—
453	C₄×D₂₉	—	4	1	no	—
454	C₄×D₂₉	—	4	1	no	—
455	C₄×D₂₉	—	4	1	no	—
456	C₄×D₂₉	—	4	1	no	—
457	C₄×D₂₉	—	4	1	no	—
458	C₄×D₂₉	—	4	1	no	—
459	C₄×D₂₉	—	4	1	no	—
460	C₄×D₂₉	—	4	1	no	—
461	C₄×D₂₉	—	4	1	no	—
462	C₄×D₂₉	—	4	1	no	—
463	C₄×D₂₉	—	4	1	no	—
464	C₄×D₂₉	—	4	1	no	—
465	Dic₅₈	—	4	1	no	—
466	#3534	—	29	1	no	maximal, Sylow
467	C₂²×C₂₉	—	2	1	no	—
468	C₂²×C₂₉	—	2	1	no	—
469	C₂²×C₂₉	—	2	1	no	—
470	C₂²×C₂₉	—	2	1	no	—
471	C₂²×C₂₉	—	2	1	no	—
472	C₂²×C₂₉	—	2	1	no	—
473	C₂²×C₂₉	—	2	1	no	—
474	C₂²×C₂₉	—	2	1	no	—
475	C₂²×C₂₉	—	2	1	no	—
476	C₂²×C₂₉	—	2	1	no	—
477	C₂²×C₂₉	—	2	1	no	—
478	C₂²×C₂₉	—	2	1	no	—
479	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
480	C₂×D₂₉	—	2	1	no	—
481	C₂×D₂₉	—	2	1	no	—
482	C₂×D₂₉	—	2	1	no	—
483	C₂×D₂₉	—	2	1	no	—
484	C₂×D₂₉	—	2	1	no	—
485	C₂×D₂₉	—	2	1	no	—
486	C₂×D₂₉	—	2	1	no	—
487	C₂×D₂₉	—	2	1	no	—
488	C₂×D₂₉	—	2	1	no	—
489	C₂×D₂₉	—	2	1	no	—
490	C₂×D₂₉	—	2	1	no	—
491	C₂×D₂₉	—	2	1	no	—
492	C₂×D₂₉	—	2	1	no	—
493	C₂×D₂₉	—	2	1	no	—
494	C₂×D₂₉	—	2	1	no	—
495	C₂×D₂₉	—	2	1	no	—
496	C₂×D₂₉	—	2	1	no	—
497	C₂×D₂₉	—	2	1	no	—
498	C₂×D₂₉	—	2	1	no	—
499	C₂×D₂₉	—	4	4	no	—
500	C₂×D₂₉	—	8	2	no	—
501	C₂×D₂₉	—	8	2	no	—
502	C₂×D₂₉	—	8	2	no	—
503	C₂×D₂₉	—	8	2	no	—
504	C₂×D₂₉	—	8	2	no	—
505	C₂×D₂₉	H(5,𝔽₂)	1	2	yes	—
506	C₂×D₂₉	H(5,𝔽₂)	1	2	yes	—
507	C₄×C₂₉	—	2	1	no	—
508	C₄×C₂₉	—	2	1	no	—
509	C₄×C₂₉	—	2	1	no	—
510	C₄×C₂₉	—	2	1	no	—
511	C₄×C₂₉	—	2	1	no	—
512	C₄×C₂₉	—	2	1	no	—
513	C₄×C₂₉	—	2	1	no	—
514	C₄×C₂₉	—	2	1	no	—
515	C₄×C₂₉	—	2	1	no	—
516	C₄×C₂₉	—	2	1	no	—
517	C₄×C₂₉	—	2	1	no	—
518	Dic₂₉	—	2	1	no	—
519	Dic₂₉	—	2	1	no	—
520	Dic₂₉	—	2	1	no	—
521	Dic₂₉	—	2	1	no	—
522	Dic₂₉	—	2	1	no	—
523	Dic₂₉	—	2	1	no	—
524	Dic₂₉	—	2	1	no	—
525	Dic₂₉	—	2	1	no	—
526	Dic₂₉	—	2	1	no	—
527	#562	—	29	1	no	—
528	#562	D₂₉	1	1	yes	characteristic, complemented
529	#560	—	29	1	no	—
530	#560	—	29	1	no	—
531	#553	—	29	1	no	—
532	#553	—	29	1	no	—
533	#551	—	29	1	no	—
534	#551	—	29	1	no	—
535	#546	—	29	1	no	—
536	#546	—	29	1	no	—
537	#546	—	29	1	no	—
538	#546	—	29	1	no	—
539	#546	—	29	1	no	—
540	#546	—	29	1	no	—
541	D₄²	—	29	1	no	—
542	D₄²	—	29	1	no	—
543	#540	—	29	1	no	—
544	#540	—	29	1	no	—
545	#539	—	29	1	no	—
546	#539	—	29	1	no	—
547	#539	—	29	1	no	—
548	#538	—	29	1	no	—
549	#538	—	29	1	no	—
550	#538	—	29	1	no	—
551	#537	—	29	1	no	—
552	#534	—	29	1	no	—
553	#534	—	29	1	no	—
554	#534	—	29	1	no	—
555	#525	—	29	1	no	—
556	C₂×#123	—	29	1	no	—
557	C₂×#121	—	29	1	no	—
558	C₂×C₂₉	—	4	1	no	—
559	C₂×C₂₉	—	4	1	no	—
560	C₂×C₂₉	—	4	1	no	—
561	C₂×C₂₉	—	4	1	no	—
562	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₂₉	#585	1	1	yes	characteristic
565	D₂₉	—	2	2	no	—
566	D₂₉	—	2	2	no	—
567	D₂₉	—	4	1	no	—
568	D₂₉	—	4	1	no	—
569	D₂₉	—	4	1	no	—
570	D₂₉	—	4	1	no	—
571	D₂₉	—	4	1	no	—
572	C₂×#41	—	29	1	no	—
573	C₂×#41	—	29	1	no	—
574	C₂×#41	—	29	1	no	—
575	C₂²×D₄	—	29	1	no	—
576	C₂²×D₄	—	29	1	no	—
577	C₂²×D₄	—	29	1	no	—
578	C₂²×D₄	—	29	1	no	—
579	C₂²×D₄	—	29	1	no	—
580	C₂²×D₄	—	29	1	no	—
581	C₂²×D₄	—	29	1	no	—
582	C₂²×D₄	—	29	1	no	—
583	C₂³×C₄	—	29	1	no	—
584	#127	—	29	1	no	—
585	#127	—	29	1	no	—
586	#126	—	29	1	no	—
587	#126	—	29	1	no	—
588	#126	—	29	1	no	—
589	#126	—	29	1	no	—
590	#126	—	29	1	no	—
591	#126	—	29	1	no	—
592	#126	—	29	1	no	—
593	#126	—	29	1	no	—
594	#125	—	29	1	no	—
595	#125	—	29	1	no	—
596	#125	—	29	1	no	—
597	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
598	#124	—	29	1	no	—
599	#124	—	29	1	no	—
600	#124	—	29	1	no	—
601	#124	—	29	1	no	—
602	#124	C₂×D₂₉	1	1	yes	characteristic, complemented
603	#124	C₂×D₂₉	1	1	yes	characteristic, complemented
604	#123	—	29	1	no	—
605	#123	—	29	1	no	—
606	#123	—	29	1	no	—
607	#123	—	29	1	no	—
608	#123	—	29	1	no	—
609	#123	—	29	1	no	—
610	#123	—	29	1	no	—
611	#123	—	29	1	no	—
612	#123	—	29	1	no	—
613	#123	—	29	1	no	—
614	#123	—	29	1	no	—
615	#123	—	29	1	no	—
616	#123	—	29	1	no	—
617	#123	—	29	1	no	—
618	#123	—	29	1	no	—
619	#123	—	29	1	no	—
620	#123	—	29	1	no	—
621	#123	—	29	1	no	—
622	#123	—	29	1	no	—
623	#123	—	29	1	no	—
624	#123	—	29	1	no	—
625	#123	—	29	1	no	—
626	#123	—	29	1	no	—
627	#123	—	29	1	no	—
628	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
629	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
630	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
631	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
632	C₂²⋊Q₈	—	29	1	no	—
633	C₂²⋊Q₈	—	29	1	no	—
634	C₂²⋊Q₈	—	29	1	no	—
635	C₂²⋊Q₈	—	29	1	no	—
636	C₂²⋊Q₈	—	29	1	no	—
637	C₂²⋊Q₈	—	29	1	no	—
638	C₂²⋊Q₈	—	29	1	no	—
639	C₂²⋊Q₈	—	29	1	no	—
640	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
641	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
642	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
643	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
644	#121	—	29	1	no	—
645	#121	—	29	1	no	—
646	#121	—	29	1	no	—
647	#121	—	29	1	no	—
648	#121	—	29	1	no	—
649	#121	—	29	1	no	—
650	#121	—	29	1	no	—
651	#121	—	29	1	no	—
652	#121	—	29	1	no	—
653	#121	—	29	1	no	—
654	#121	—	29	1	no	—
655	#121	—	29	1	no	—
656	#121	—	29	1	no	—
657	#121	—	29	1	no	—
658	#121	—	29	1	no	—
659	#121	—	29	1	no	—
660	#121	—	29	1	no	—
661	#121	—	29	1	no	—
662	#121	—	29	1	no	—
663	#121	—	29	1	no	—
664	#121	—	29	1	no	—
665	#121	—	29	1	no	—
666	#121	—	29	1	no	—
667	#121	—	29	1	no	—
668	#121	—	29	1	no	—
669	#121	—	29	1	no	—
670	#121	—	29	1	no	—
671	#121	—	29	1	no	—
672	#121	—	29	1	no	—
673	#121	—	29	1	no	—
674	#121	—	29	1	no	—
675	#121	—	29	1	no	—
676	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
677	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
678	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
679	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
680	#120	—	29	1	no	—
681	#120	—	29	1	no	—
682	#120	—	29	1	no	—
683	#120	—	29	1	no	—
684	#120	—	29	1	no	—
685	#120	—	29	1	no	—
686	#120	—	29	1	no	—
687	#120	—	29	1	no	—
688	#120	—	29	1	no	—
689	#120	—	29	1	no	—
690	#120	—	29	1	no	—
691	#120	—	29	1	no	—
692	#120	—	29	1	no	—
693	#120	—	29	1	no	—
694	#120	—	29	1	no	—
695	#120	—	29	1	no	—
696	C₄×D₄	—	29	1	no	—
697	C₄×D₄	—	29	1	no	—
698	C₄×D₄	—	29	1	no	—
699	C₄×D₄	—	29	1	no	—
700	C₄×D₄	—	29	1	no	—
701	C₄×D₄	—	29	1	no	—
702	C₄×D₄	—	29	1	no	—
703	C₄×D₄	—	29	1	no	—
704	C₄×D₄	—	29	1	no	—
705	C₄×D₄	—	29	1	no	—
706	C₄×D₄	—	29	1	no	—
707	C₄×D₄	—	29	1	no	—
708	C₄×D₄	—	29	1	no	—
709	C₄×D₄	—	29	1	no	—
710	C₄×D₄	—	29	1	no	—
711	C₄×D₄	—	29	1	no	—
712	#117	—	29	1	no	—
713	#117	—	29	1	no	—
714	#117	—	29	1	no	—
715	C₂×C₄⋊C₄	—	29	1	no	—
716	C₂×C₄⋊C₄	—	29	1	no	—
717	C₂×C₄⋊C₄	—	29	1	no	—
718	C₂×C₂²⋊C₄	—	29	1	no	—
719	C₂×C₂²⋊C₄	—	29	1	no	—
720	C₂×C₂²⋊C₄	—	29	1	no	—
721	C₂×C₂²⋊C₄	—	29	1	no	—
722	C₂×C₂²⋊C₄	—	29	1	no	—
723	C₂×C₂²⋊C₄	—	29	1	no	—
724	C₂×C₂²⋊C₄	—	29	1	no	—
725	C₂×C₂²⋊C₄	—	29	1	no	—
726	C₂×C₂²⋊C₄	—	29	1	no	—
727	C₂₉	#3534	1	1	yes	characteristic, complemented, Sylow
728	C₂⁴	—	29	1	no	—
729	C₂⁴	—	29	1	no	—
730	C₂⁴	—	29	1	no	—
731	C₂⁴	—	29	1	no	—
732	C₂⁴	—	29	1	no	—
733	C₂⁴	—	29	1	no	—
734	#41	—	116	2	no	—
735	#41	—	116	2	no	—
736	#41	—	116	2	no	—
737	C₂×Q₈	—	29	1	no	—
738	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
739	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
740	C₂×D₄	—	29	1	no	—
741	C₂×D₄	—	29	1	no	—
742	C₂×D₄	—	29	1	no	—
743	C₂×D₄	—	29	1	no	—
744	C₂×D₄	—	29	1	no	—
745	C₂×D₄	—	29	1	no	—
746	C₂×D₄	—	29	1	no	—
747	C₂×D₄	—	29	1	no	—
748	C₂×D₄	—	29	1	no	—
749	C₂×D₄	—	29	1	no	—
750	C₂×D₄	—	29	1	no	—
751	C₂×D₄	—	29	1	no	—
752	C₂×D₄	—	29	1	no	—
753	C₂×D₄	—	29	1	no	—
754	C₂×D₄	—	29	1	no	—
755	C₂×D₄	—	29	1	no	—
756	C₂×D₄	—	29	1	no	—
757	C₂×D₄	—	29	1	no	—
758	C₂×D₄	—	29	1	no	—
759	C₂×D₄	—	29	1	no	—
760	C₂×D₄	—	29	1	no	—
761	C₂×D₄	—	29	1	no	—
762	C₂×D₄	—	29	1	no	—
763	C₂×D₄	—	29	1	no	—
764	C₂×D₄	—	29	1	no	—
765	C₂×D₄	—	29	1	no	—
766	C₂×D₄	—	29	1	no	—
767	C₂×D₄	—	29	1	no	—
768	C₂×D₄	—	29	1	no	—
769	C₂×D₄	—	29	1	no	—
770	C₂×D₄	—	29	1	no	—
771	C₂×D₄	—	116	2	no	—
772	C₂×D₄	—	116	2	no	—
773	C₂×D₄	—	116	2	no	—
774	C₂×D₄	—	116	2	no	—
775	C₂×D₄	—	116	2	no	—
776	C₂×D₄	—	116	2	no	—
777	C₂×D₄	—	116	2	no	—
778	C₂×D₄	—	116	2	no	—
779	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
780	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
781	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
782	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
784	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
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	—	116	2	no	—
805	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
806	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
807	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
808	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
809	C₄⋊C₄	—	29	1	no	—
810	C₄⋊C₄	—	29	1	no	—
811	C₄⋊C₄	—	29	1	no	—
812	C₄⋊C₄	—	29	1	no	—
813	C₄⋊C₄	—	29	1	no	—
814	C₄⋊C₄	—	29	1	no	—
815	C₄⋊C₄	—	29	1	no	—
816	C₄⋊C₄	—	29	1	no	—
817	C₄⋊C₄	—	29	1	no	—
818	C₄⋊C₄	—	29	1	no	—
819	C₄⋊C₄	—	29	1	no	—
820	C₄⋊C₄	—	29	1	no	—
821	C₄⋊C₄	—	29	1	no	—
822	C₄⋊C₄	—	29	1	no	—
823	C₄⋊C₄	—	29	1	no	—
824	C₄⋊C₄	—	29	1	no	—
825	C₄⋊C₄	—	29	1	no	—
826	C₄⋊C₄	—	29	1	no	—
827	C₄⋊C₄	—	29	1	no	—
828	C₄⋊C₄	—	29	1	no	—
829	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
830	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
831	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
832	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
833	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
834	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
835	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
838	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
839	C₂²⋊C₄	—	29	1	no	—
840	C₂²⋊C₄	—	29	1	no	—
841	C₂²⋊C₄	—	29	1	no	—
842	C₂²⋊C₄	—	29	1	no	—
843	C₂²⋊C₄	—	29	1	no	—
844	C₂²⋊C₄	—	29	1	no	—
845	C₂²⋊C₄	—	29	1	no	—
846	C₂²⋊C₄	—	29	1	no	—
847	C₂²⋊C₄	—	29	1	no	—
848	C₂²⋊C₄	—	29	1	no	—
849	C₂²⋊C₄	—	29	1	no	—
850	C₂²⋊C₄	—	29	1	no	—
851	C₂²⋊C₄	—	29	1	no	—
852	C₂²⋊C₄	—	29	1	no	—
853	C₂²⋊C₄	—	29	1	no	—
854	C₂²⋊C₄	—	29	1	no	—
855	C₂²⋊C₄	—	29	1	no	—
856	C₂²⋊C₄	—	29	1	no	—
857	C₂²⋊C₄	—	29	1	no	—
858	C₂²⋊C₄	—	29	1	no	—
859	C₂²⋊C₄	—	29	1	no	—
860	C₂²⋊C₄	—	29	1	no	—
861	C₂²⋊C₄	—	29	1	no	—
862	C₂²⋊C₄	—	29	1	no	—
863	C₂²⋊C₄	—	29	1	no	—
864	C₂²⋊C₄	—	29	1	no	—
865	C₂²⋊C₄	—	29	1	no	—
866	C₂²⋊C₄	—	29	1	no	—
867	C₂²⋊C₄	—	29	1	no	—
868	C₂²⋊C₄	—	29	1	no	—
869	C₂²⋊C₄	—	29	1	no	—
870	C₂²⋊C₄	—	29	1	no	—
871	C₂²⋊C₄	—	29	1	no	—
872	C₂²⋊C₄	—	29	1	no	—
873	C₂²⋊C₄	—	29	1	no	—
874	C₂²⋊C₄	—	29	1	no	—
875	C₂²⋊C₄	—	29	1	no	—
876	C₂²⋊C₄	—	29	1	no	—
877	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
886	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
889	C₄²	—	29	1	no	—
890	C₄²	—	29	1	no	—
891	C₄²	—	29	1	no	—
892	C₄²	—	29	1	no	—
893	C₄²	—	29	1	no	—
894	C₄²	C₂²×D₂₉	1	1	yes	characteristic
895	C₂³	—	29	1	no	—
896	C₂³	—	29	1	no	—
897	C₂³	—	29	1	no	—
898	C₂³	—	29	1	no	—
899	C₂³	—	29	1	no	—
900	C₂³	—	29	1	no	—
901	C₂³	—	29	1	no	—
902	C₂³	—	58	2	no	—
903	C₂³	—	58	2	no	—
904	C₂³	—	58	2	no	—
905	C₂³	—	58	2	no	—
906	C₂³	—	58	2	no	—
907	C₂³	—	116	1	no	—
908	C₂³	—	116	1	no	—
909	C₂³	—	116	1	no	—
910	C₂³	—	116	1	no	—
911	C₂³	—	116	1	no	—
912	C₂³	—	116	1	no	—
913	C₂³	—	116	1	no	—
914	C₂³	—	116	1	no	—
915	C₂³	—	116	1	no	—
916	C₂³	—	116	1	no	—
917	C₂³	—	116	1	no	—
918	C₂³	—	116	1	no	—
919	C₂³	—	116	1	no	—
920	C₂³	C₂³×D₂₉	1	1	yes	characteristic
921	C₂³	C₂³×D₂₉	1	1	yes	characteristic
922	C₂³	C₂³×D₂₉	1	1	yes	characteristic
923	C₂³	C₂³×D₂₉	1	1	yes	characteristic
924	Q₈	—	4	1	no	—
925	Q₈	—	4	1	no	—
926	Q₈	—	116	1	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	58	2	no	—
934	D₄	—	58	2	no	—
935	D₄	—	58	2	no	—
936	D₄	—	58	2	no	—
937	D₄	—	58	2	no	—
938	D₄	—	58	2	no	—
939	D₄	—	58	2	no	—
940	D₄	—	58	2	no	—
941	D₄	—	58	2	no	—
942	D₄	—	58	2	no	—
943	D₄	—	116	1	no	—
944	D₄	—	116	1	no	—
945	D₄	—	116	1	no	—
946	D₄	—	116	1	no	—
947	D₄	—	116	1	no	—
948	D₄	—	116	1	no	—
949	D₄	—	116	1	no	—
950	D₄	—	116	1	no	—
951	D₄	—	116	1	no	—
952	D₄	—	116	1	no	—
953	D₄	—	116	1	no	—
954	D₄	—	116	1	no	—
955	D₄	—	116	1	no	—
956	D₄	—	116	1	no	—
957	D₄	—	116	1	no	—
958	D₄	—	116	1	no	—
959	D₄	—	116	1	no	—
960	D₄	—	116	1	no	—
961	D₄	—	116	1	no	—
962	D₄	—	116	1	no	—
963	D₄	—	116	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	29	1	no	—
969	C₂×C₄	—	29	1	no	—
970	C₂×C₄	—	29	1	no	—
971	C₂×C₄	—	29	1	no	—
972	C₂×C₄	—	29	1	no	—
973	C₂×C₄	—	29	1	no	—
974	C₂×C₄	—	29	1	no	—
975	C₂×C₄	—	29	1	no	—
976	C₂×C₄	—	29	1	no	—
977	C₂×C₄	—	58	2	no	—
978	C₂×C₄	—	58	2	no	—
979	C₂×C₄	—	58	2	no	—
980	C₂×C₄	—	116	1	no	—
981	C₂×C₄	—	116	1	no	—
982	C₂×C₄	—	116	1	no	—
983	C₂×C₄	—	116	1	no	—
984	C₂×C₄	—	116	1	no	—
985	C₂×C₄	—	116	1	no	—
986	C₂×C₄	—	116	1	no	—
987	C₂×C₄	—	116	1	no	—
988	C₂×C₄	—	116	1	no	—
989	C₂×C₄	—	116	1	no	—
990	C₂×C₄	—	116	1	no	—
991	C₂×C₄	—	116	1	no	—
992	C₂×C₄	—	116	1	no	—
993	C₂×C₄	—	116	1	no	—
994	C₂×C₄	—	116	1	no	—
995	C₂×C₄	—	116	1	no	—
996	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
997	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1006	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	29	2	no	—
1020	C₂²	—	29	2	no	—
1021	C₂²	—	58	1	no	—
1022	C₂²	—	58	1	no	—
1023	C₂²	—	58	1	no	—
1024	C₂²	—	58	1	no	—
1025	C₂²	—	58	1	no	—
1026	C₂²	—	58	1	no	—
1027	C₂²	—	58	1	no	—
1028	C₂²	—	58	1	no	—
1029	C₂²	—	58	1	no	—
1030	C₂²	—	58	1	no	—
1031	C₂²	—	58	1	no	—
1032	C₂²	—	58	1	no	—
1033	C₂²	—	58	1	no	—
1034	C₂²	—	58	1	no	—
1035	C₂²	—	58	1	no	—
1036	C₂²	—	58	1	no	—
1037	C₂²	—	58	1	no	—
1038	C₂²	—	58	1	no	—
1039	C₂²	—	58	1	no	—
1040	C₂²	—	116	4	no	—
1041	C₂²	—	232	2	no	—
1042	C₂²	—	232	2	no	—
1043	C₂²	—	232	2	no	—
1044	C₂²	—	232	2	no	—
1045	C₂²	—	232	2	no	—
1046	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	58	1	no	—
1059	C₄	—	58	1	no	—
1060	C₄	—	58	1	no	—
1061	C₄	—	58	1	no	—
1062	C₄	—	58	1	no	—
1063	C₄	—	58	1	no	—
1064	C₄	—	58	1	no	—
1065	C₄	—	58	1	no	—
1066	C₄	—	58	1	no	—
1067	C₂	—	4	1	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	58	2	no	—
1072	C₂	—	58	2	no	—
1073	C₂	—	116	1	no	—
1074	C₂	—	116	1	no	—
1075	C₂	—	116	1	no	—
1076	C₂	—	116	1	no	—
1077	C₂	—	116	1	no	—
1078	C₂	H(5,𝔽₂)×D₂₉	1	1	yes	characteristic
1079	C₂	H(5,𝔽₂)×D₂₉	1	1	yes	characteristic
1080	C₂	#14272000	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#562	C₂
hypercenter	#562	D₂₉
hypocenter	C₂₉	#3534
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #14271909	C₂	semidirect
2. #14271903	C₂	semidirect
3. #14271901	C₂	semidirect
4. #14271866	C₂	semidirect
5. #14271858	C₂	semidirect
6. #14271841	C₂	semidirect
7. #14271840	C₂	semidirect
8. #14271810	C₂	semidirect
9. #14271806	C₂	semidirect
10. #14271806	C₂	semidirect
11. #14271805	C₂	semidirect
12. #14271804	C₂	semidirect
13. #14271804	C₂	semidirect
14. #14271797	C₂	semidirect
15. #14271797	C₂	semidirect
16. #14271765	C₂	semidirect
17. #14271763	C₂	semidirect
18. #14271761	C₂	semidirect
19. #14271759	C₂	semidirect
20. #14271759	C₂	semidirect
21. #14271747	C₂	semidirect
22. #14271747	C₂	semidirect
23. #14271745	C₂	semidirect
24. #14271743	C₂	semidirect
25. #14271724	C₂	semidirect
26. #14271724	C₂	semidirect
27. #14271721	C₂	semidirect
28. #14271676	C₂	semidirect
29. #123×D₂₉	C₂	semidirect
30. #121×D₂₉	C₂	semidirect
31. C₂₉×#562	C₂	semidirect
32. C₂×#90809	C₂²	semidirect
33. C₂×#90809	C₂²	semidirect
35. C₂×D₄×D₂₉	C₂²	semidirect
36. C₂×D₄×D₂₉	C₂²	semidirect
37. C₂×D₄×D₂₉	C₂²	semidirect
38. C₂×D₄×D₂₉	C₂²	semidirect
39. C₂×D₄×D₂₉	C₂²	semidirect
40. C₂×#90805	C₂²	semidirect
41. C₂²×D₁₁₆	C₂²	semidirect
42. C₂²×D₁₁₆	C₂²	semidirect
43. C₂²×C₄×D₂₉	C₂²	semidirect
44. C₂₉×#125	C₂²	semidirect
45. C₂₉×#124	C₂²	semidirect
46. C₂₉×#124	C₂²	semidirect
47. C₂₉×#123	C₂²	semidirect
48. C₂₉×#123	C₂²	semidirect
49. C₂₉×#123	C₂²	semidirect
50. C₂₉×#123	C₂²	semidirect
51. C₂₉×C₂²⋊Q₈	C₂²	semidirect
52. C₂₉×C₂²⋊Q₈	C₂²	semidirect
53. C₂₉×C₂²⋊Q₈	C₂²	semidirect
54. C₂₉×C₂²⋊Q₈	C₂²	semidirect
55. C₂₉×#121	C₂²	semidirect
56. C₂₉×#121	C₂²	semidirect
57. C₂₉×#121	C₂²	semidirect
58. C₂₉×#121	C₂²	semidirect
59. #11745309	C₂²	semidirect
60. #11745309	C₂²	semidirect
61. #11745308	C₂²	semidirect
62. #11745308	C₂²	semidirect
63. #11745308	C₂²	semidirect
64. #11745308	C₂²	semidirect
65. #11745302	C₂²	semidirect
66. #11745302	C₂²	semidirect
67. #11745301	C₂²	semidirect
68. #11745301	C₂²	semidirect
69. #11745301	C₂²	semidirect
70. #11745301	C₂²	semidirect
71. #11745301	C₂²	semidirect
72. #11745300	C₂²	semidirect
73. #11745300	C₂²	semidirect
74. #11745300	C₂²	semidirect
76. #11745299	C₂²	semidirect
77. #11745299	C₂²	semidirect
78. #11745299	C₂²	semidirect
79. #11745299	C₂²	semidirect
80. #11745299	C₂²	semidirect
81. #11745298	C₂²	semidirect
82. #11745297	C₂²	semidirect
83. #11745292	C₂²	semidirect
84. #11745292	C₂²	semidirect
85. #11745292	C₂²	semidirect
86. #11745291	C₂²	semidirect
87. #11745291	C₂²	semidirect
88. #11745291	C₂²	semidirect
89. C₄×C₂²⋊D₂₉	C₂²	semidirect
90. C₄×C₂²⋊D₂₉	C₂²	semidirect
91. C₄×C₂²⋊D₂₉	C₂²	semidirect
92. C₄×C₂²⋊D₂₉	C₂²	semidirect
93. C₄×C₂²⋊D₂₉	C₂²	semidirect
94. C₂×#90781	C₂²	semidirect
95. #11745260	C₂²	semidirect
96. #11745260	C₂²	semidirect
97. #11745260	C₂²	semidirect
98. #11745260	C₂²	semidirect
99. #11745259	C₂²	semidirect
100. #11745258	C₂²	semidirect
101. #11745258	C₂²	semidirect
102. #11745258	C₂²	semidirect
104. #11745257	C₂²	semidirect
105. #11745257	C₂²	semidirect
106. #11745257	C₂²	semidirect
107. #11745257	C₂²	semidirect
108. #11745257	C₂²	semidirect
109. #11745257	C₂²	semidirect
110. #11745257	C₂²	semidirect
111. #11745257	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. #11745255	C₂²	semidirect
123. #11745255	C₂²	semidirect
124. #11745255	C₂²	semidirect
125. #11745255	C₂²	semidirect
126. #11745255	C₂²	semidirect
127. #11745254	C₂²	semidirect
128. #11745254	C₂²	semidirect
129. C₄⋊C₄×D₂₉	C₂²	semidirect
130. C₄⋊C₄×D₂₉	C₂²	semidirect
131. C₄⋊C₄×D₂₉	C₂²	semidirect
132. #11745251	C₂²	semidirect
133. #11745251	C₂²	semidirect
134. #11745251	C₂²	semidirect
135. #11745248	C₂²	semidirect
136. #11745248	C₂²	semidirect
137. #11745247	C₂²	semidirect
140. #11745246	C₂²	semidirect
141. #11745246	C₂²	semidirect
142. #11745246	C₂²	semidirect
143. #11745246	C₂²	semidirect
144. #11745246	C₂²	semidirect
145. #11745246	C₂²	semidirect
146. #11745246	C₂²	semidirect
147. #11745246	C₂²	semidirect
148. #11745246	C₂²	semidirect
149. #11745246	C₂²	semidirect
150. #11745245	C₂²	semidirect
151. #11745245	C₂²	semidirect
152. #11745245	C₂²	semidirect
153. #11745245	C₂²	semidirect
154. #11745245	C₂²	semidirect
155. #11745245	C₂²	semidirect
156. #11745245	C₂²	semidirect
157. #11745245	C₂²	semidirect
159. #11745244	C₂²	semidirect
160. #11745244	C₂²	semidirect
161. #11745244	C₂²	semidirect
162. #11745244	C₂²	semidirect
163. #11745244	C₂²	semidirect
164. #11745244	C₂²	semidirect
165. #11745244	C₂²	semidirect
166. #11745244	C₂²	semidirect
167. #11745244	C₂²	semidirect
168. #11745243	C₂²	semidirect
169. #11745243	C₂²	semidirect
170. #11745243	C₂²	semidirect
171. C₂²⋊C₄×D₂₉	C₂²	semidirect
172. C₂²⋊C₄×D₂₉	C₂²	semidirect
173. C₂²⋊C₄×D₂₉	C₂²	semidirect
174. C₂²⋊C₄×D₂₉	C₂²	semidirect
175. C₂²⋊C₄×D₂₉	C₂²	semidirect
176. C₂²⋊C₄×D₂₉	C₂²	semidirect
177. C₂²⋊C₄×D₂₉	C₂²	semidirect
178. C₂²⋊C₄×D₂₉	C₂²	semidirect
179. #11745241	C₂²	semidirect
180. #11745241	C₂²	semidirect
181. #11745241	C₂²	semidirect
182. #11745239	C₂²	semidirect
183. #11745238	C₂²	semidirect
184. C₄×D₁₁₆	C₂²	semidirect
185. C₄×D₁₁₆	C₂²	semidirect
186. C₄×D₁₁₆	C₂²	semidirect
528. #562	D₂₉	semidirect
597. #125	C₂×D₂₉	semidirect
602. #124	C₂×D₂₉	semidirect
603. #124	C₂×D₂₉	semidirect
628. #123	C₂×D₂₉	semidirect
629. #123	C₂×D₂₉	semidirect
630. #123	C₂×D₂₉	semidirect
631. #123	C₂×D₂₉	semidirect
640. C₂²⋊Q₈	C₂×D₂₉	semidirect
641. C₂²⋊Q₈	C₂×D₂₉	semidirect
642. C₂²⋊Q₈	C₂×D₂₉	semidirect
643. C₂²⋊Q₈	C₂×D₂₉	semidirect
676. #121	C₂×D₂₉	semidirect
677. #121	C₂×D₂₉	semidirect
678. #121	C₂×D₂₉	semidirect
679. #121	C₂×D₂₉	semidirect
727. C₂₉	#3534	semidirect

Maximal subgroups

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

subgroup	index
#14271909	2
#14271903	2
#14271901	2
#14271866	2
#14271858	2
#14271841	2
#14271840	2
#14271810	2
#14271806	2
#14271805	2
#14271804	2
#14271797	2
#14271765	2
#14271763	2
#14271761	2
#14271759	2
#14271747	2
#14271745	2
#14271743	2
#14271724	2
#14271721	2
#14271676	2
#123×D₂₉	2
#121×D₂₉	2
C₂₉×#562	2
#3534	29