Subgroups — #16833707

Order 3712.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271910	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271908	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271908	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	#14271822	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271819	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271812	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271811	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271807	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271803	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271803	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271800	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271800	C₂	1	1	yes	maximal, characteristic, complemented
16	#14271789	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271788	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271781	C₂	1	1	yes	maximal, characteristic, complemented
19	#14271777	C₂	1	1	yes	maximal, characteristic, complemented
20	#14271757	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271755	C₂	1	1	yes	maximal, characteristic, complemented
22	#14271748	C₂	1	1	yes	maximal, characteristic, complemented
23	#14271746	C₂	1	1	yes	maximal, characteristic, complemented
24	#14271742	C₂	1	1	yes	maximal, characteristic, complemented
25	#14271741	C₂	1	1	yes	maximal, characteristic, complemented
26	#14271740	C₂	1	1	yes	maximal, characteristic, complemented
27	#14271740	C₂	1	1	yes	maximal, characteristic, complemented
28	#14271669	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#11745240	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#11745301	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
36	C₂³×Dic₂₉	C₂²	1	1	yes	characteristic
37	C₂×#90807	C₂²	1	1	yes	characteristic, complemented
38	C₂×#90807	C₂²	1	1	yes	characteristic, complemented
39	C₂×#90807	C₂²	1	1	yes	characteristic, complemented
40	C₂×#90807	C₂²	1	1	yes	characteristic, complemented
41	C₂×#90805	C₂²	1	1	yes	characteristic, complemented
42	C₂×#90805	C₂²	1	1	yes	characteristic, complemented
43	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
45	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×#120	C₂²	1	1	yes	characteristic
52	C₂₉×#120	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
57	#11745315	C₂²	1	1	yes	characteristic
58	#11745315	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₂₉	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊Dic₂₉	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊Dic₂₉	C₂²	1	1	yes	characteristic
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	#11745306	C₂²	1	1	yes	characteristic, complemented
66	#11745301	C₂²	1	1	yes	characteristic
67	#11745301	C₂²	1	1	yes	characteristic
68	#11745301	C₂²	1	1	yes	characteristic
69	#11745301	C₂²	1	1	yes	characteristic
70	#11745301	C₂²	1	1	yes	characteristic
71	#11745301	C₂²	1	1	yes	characteristic
72	#11745301	C₂²	1	1	yes	characteristic
73	#11745301	C₂²	1	1	yes	characteristic
74	#11745301	C₂²	1	1	yes	characteristic
75	#11745301	C₂²	1	1	yes	characteristic, complemented
76	#11745301	C₂²	1	1	yes	characteristic, complemented
77	#11745301	C₂²	1	1	yes	characteristic, complemented
78	#11745301	C₂²	1	1	yes	characteristic, complemented
79	#11745301	C₂²	1	1	yes	characteristic, complemented
80	#11745301	C₂²	1	1	yes	characteristic, complemented
81	#11745301	C₂²	1	1	yes	characteristic, complemented
82	#11745301	C₂²	1	1	yes	characteristic, complemented
83	#11745300	C₂²	1	1	yes	characteristic, complemented
84	#11745300	C₂²	1	1	yes	characteristic, complemented
85	#11745300	C₂²	1	1	yes	characteristic, complemented
86	#11745300	C₂²	1	1	yes	characteristic, complemented
87	#11745299	C₂²	1	1	yes	characteristic
88	#11745298	C₂²	1	1	yes	characteristic, complemented
89	#11745298	C₂²	1	1	yes	characteristic, complemented
90	#11745297	C₂²	1	1	yes	characteristic, complemented
91	#11745297	C₂²	1	1	yes	characteristic, complemented
92	#11745297	C₂²	1	1	yes	characteristic, complemented
93	#11745297	C₂²	1	1	yes	characteristic, complemented
94	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
95	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
96	D₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
98	#11745292	C₂²	1	1	yes	characteristic, complemented
99	#11745292	C₂²	1	1	yes	characteristic, complemented
100	#11745292	C₂²	1	1	yes	characteristic, complemented
101	#11745291	C₂²	1	1	yes	characteristic, complemented
102	#11745291	C₂²	1	1	yes	characteristic, complemented
103	#11745291	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
107	C₂×#90781	C₂²	1	1	yes	characteristic
108	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic, complemented
109	#11745286	C₂²	1	1	yes	characteristic
110	#11745286	C₂²	1	1	yes	characteristic, complemented
111	#11745286	C₂²	1	1	yes	characteristic, complemented
112	#11745286	C₂²	1	1	yes	characteristic, complemented
113	#11745286	C₂²	1	1	yes	characteristic, complemented
114	#11745286	C₂²	1	1	yes	characteristic, complemented
115	C₂×#90779	C₂²	1	1	yes	characteristic
116	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
117	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
118	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
119	#11745260	C₂²	1	1	yes	characteristic, complemented
120	#11745259	C₂²	1	1	yes	characteristic, complemented
121	#11745259	C₂²	1	1	yes	characteristic, complemented
122	#11745258	C₂²	1	1	yes	characteristic, complemented
123	#11745258	C₂²	1	1	yes	characteristic, complemented
124	#11745258	C₂²	1	1	yes	characteristic, complemented
125	#11745258	C₂²	1	1	yes	characteristic, complemented
126	#11745258	C₂²	1	1	yes	characteristic, complemented
127	#11745258	C₂²	1	1	yes	characteristic, complemented
128	#11745256	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
130	#11745252	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	#11745249	C₂²	1	1	yes	characteristic, complemented
135	#11745248	C₂²	1	1	yes	characteristic, complemented
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	#11745247	C₂²	1	1	yes	characteristic, complemented
141	#11745247	C₂²	1	1	yes	characteristic, complemented
142	#11745247	C₂²	1	1	yes	characteristic, complemented
143	#11745247	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	#11745245	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	#11745244	C₂²	1	1	yes	characteristic
155	#11745243	C₂²	1	1	yes	characteristic
156	#11745243	C₂²	1	1	yes	characteristic
157	#11745243	C₂²	1	1	yes	characteristic, complemented
158	#11745243	C₂²	1	1	yes	characteristic, complemented
159	#11745243	C₂²	1	1	yes	characteristic, complemented
160	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
162	#11745241	C₂²	1	1	yes	characteristic, complemented
163	#11745241	C₂²	1	1	yes	characteristic, complemented
164	#11745240	C₂²	1	1	yes	characteristic
165	#11745240	C₂²	1	1	yes	characteristic
166	#11745240	C₂²	1	1	yes	characteristic
167	#11745240	C₂²	1	1	yes	characteristic
168	#11745240	C₂²	1	1	yes	characteristic
169	#11745240	C₂²	1	1	yes	characteristic
170	#11745240	C₂²	1	1	yes	characteristic
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	#11745240	C₂²	1	1	yes	characteristic, complemented
175	#11745240	C₂²	1	1	yes	characteristic, complemented
176	#11745240	C₂²	1	1	yes	characteristic, complemented
177	#11745240	C₂²	1	1	yes	characteristic, complemented
178	#11745240	C₂²	1	1	yes	characteristic, complemented
179	#11745240	C₂²	1	1	yes	characteristic, complemented
180	#11745240	C₂²	1	1	yes	characteristic, complemented
181	#11745240	C₂²	1	1	yes	characteristic, complemented
182	#11745239	C₂²	1	1	yes	characteristic, complemented
183	#11745238	C₂²	1	1	yes	characteristic, complemented
184	#11745237	C₂²	1	1	yes	characteristic, complemented
185	#11745232	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
188	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
189	C₂³×D₂₉	C₂³	1	1	yes	characteristic
190	#41×C₂₉	—	4	2	no	—
191	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₂₉	—	4	2	no	—
193	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
194	C₂×D₄×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	C₂×D₄×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	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₂₉	—	4	2	no	—
209	C₂×C₂²⋊D₂₉	—	4	2	no	—
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	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
226	C₂²×Dic₂₉	—	4	2	no	—
227	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
228	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
229	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
230	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
231	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
232	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
233	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
234	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
235	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
236	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
237	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
238	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
239	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
240	#90807	—	4	2	no	—
241	#90807	—	4	2	no	—
242	#90807	—	4	2	no	—
243	#90807	—	4	2	no	—
244	#90805	—	4	2	no	—
245	#90805	—	4	2	no	—
246	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
247	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
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×Dic₅₈	—	4	2	no	—
256	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
257	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
258	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
259	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
260	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
261	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
262	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
263	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
265	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
266	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
267	C₄⋊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	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
275	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
277	C₂²⋊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	C₄²×C₂₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₂₉	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	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₂₉	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	#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	#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	—	2	2	no	—
355	C₂³×C₂₉	—	2	2	no	—
356	C₂³×C₂₉	—	2	2	no	—
357	C₂³×C₂₉	—	4	1	no	—
358	C₂³×C₂₉	—	4	1	no	—
359	C₂³×C₂₉	—	4	1	no	—
360	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
361	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
362	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
363	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
364	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
365	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
366	C₂²×D₂₉	—	2	2	no	—
367	C₂²×D₂₉	—	4	1	no	—
368	C₂²×D₂₉	—	4	1	no	—
369	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
370	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
371	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
372	Q₈×C₂₉	—	4	1	no	—
373	D₄×C₂₉	—	2	2	no	—
374	D₄×C₂₉	—	2	2	no	—
375	D₄×C₂₉	—	2	2	no	—
376	D₄×C₂₉	—	2	2	no	—
377	D₄×C₂₉	—	4	1	no	—
378	D₄×C₂₉	—	4	1	no	—
379	D₄×C₂₉	—	4	1	no	—
380	D₄×C₂₉	—	4	1	no	—
381	D₄×C₂₉	—	4	1	no	—
382	C₂×C₄×C₂₉	—	2	2	no	—
383	C₂×C₄×C₂₉	—	4	1	no	—
384	C₂×C₄×C₂₉	—	4	1	no	—
385	C₂×C₄×C₂₉	—	4	1	no	—
386	C₂×C₄×C₂₉	—	4	1	no	—
387	C₂×C₄×C₂₉	—	4	1	no	—
388	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
397	C₂²⋊D₂₉	—	2	2	no	—
398	C₂²⋊D₂₉	—	2	2	no	—
399	C₂²⋊D₂₉	—	2	2	no	—
400	C₂²⋊D₂₉	—	2	2	no	—
401	C₂²⋊D₂₉	—	2	2	no	—
402	C₂²⋊D₂₉	—	2	2	no	—
403	C₂²⋊D₂₉	—	4	1	no	—
404	C₂²⋊D₂₉	—	4	1	no	—
405	C₂²⋊D₂₉	—	4	1	no	—
406	C₂²⋊D₂₉	—	4	1	no	—
407	C₂²⋊D₂₉	—	4	1	no	—
408	C₂²⋊D₂₉	—	4	1	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	C₂×Dic₂₉	—	2	2	no	—
414	C₂×Dic₂₉	—	2	2	no	—
415	C₂×Dic₂₉	—	2	2	no	—
416	C₂×Dic₂₉	—	2	2	no	—
417	C₂×Dic₂₉	—	2	2	no	—
418	C₂×Dic₂₉	—	4	1	no	—
419	C₂×Dic₂₉	—	4	1	no	—
420	C₂×Dic₂₉	—	4	1	no	—
421	C₂×Dic₂₉	—	4	1	no	—
422	C₂×Dic₂₉	—	4	1	no	—
423	C₂×Dic₂₉	—	4	1	no	—
424	C₂×Dic₂₉	—	4	1	no	—
425	C₂×Dic₂₉	—	4	1	no	—
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	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
439	D₁₁₆	—	4	1	no	—
440	D₁₁₆	—	4	1	no	—
441	C₄×D₂₉	—	2	2	no	—
442	C₄×D₂₉	—	4	1	no	—
443	C₄×D₂₉	—	4	1	no	—
444	C₄×D₂₉	—	4	1	no	—
445	C₄×D₂₉	—	4	1	no	—
446	C₄×D₂₉	—	4	1	no	—
447	C₄×D₂₉	—	4	1	no	—
448	Dic₅₈	—	2	2	no	—
449	Dic₅₈	—	2	2	no	—
450	Dic₅₈	—	4	1	no	—
451	Dic₅₈	—	4	1	no	—
452	Dic₅₈	—	4	1	no	—
453	Dic₅₈	—	4	1	no	—
454	Dic₅₈	—	4	1	no	—
455	Dic₅₈	—	4	1	no	—
456	#3536	—	29	1	no	maximal, Sylow
457	C₂²×C₂₉	—	2	1	no	—
458	C₂²×C₂₉	—	2	1	no	—
459	C₂²×C₂₉	—	2	1	no	—
460	C₂²×C₂₉	—	2	1	no	—
461	C₂²×C₂₉	—	2	1	no	—
462	C₂²×C₂₉	—	2	1	no	—
463	C₂²×C₂₉	—	2	1	no	—
464	C₂²×C₂₉	—	2	1	no	—
465	C₂²×C₂₉	—	2	1	no	—
466	C₂²×C₂₉	—	2	1	no	—
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	—	4	4	no	—
474	C₂²×C₂₉	—	8	2	no	—
475	C₂²×C₂₉	H(5,𝔽₂)	1	2	yes	—
476	C₂²×C₂₉	2₋¹⁺⁴	1	2	yes	—
477	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
478	C₂×D₂₉	—	2	1	no	—
479	C₂×D₂₉	—	2	1	no	—
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	—	8	2	no	—
488	C₄×C₂₉	—	2	1	no	—
489	C₄×C₂₉	—	2	1	no	—
490	C₄×C₂₉	—	2	1	no	—
491	C₄×C₂₉	—	2	1	no	—
492	C₄×C₂₉	—	2	1	no	—
493	C₄×C₂₉	—	2	1	no	—
494	C₄×C₂₉	—	2	1	no	—
495	C₄×C₂₉	—	2	1	no	—
496	C₄×C₂₉	—	2	1	no	—
497	Dic₂₉	—	2	1	no	—
498	Dic₂₉	—	2	1	no	—
499	Dic₂₉	—	2	1	no	—
500	Dic₂₉	—	2	1	no	—
501	Dic₂₉	—	2	1	no	—
502	Dic₂₉	—	2	1	no	—
503	Dic₂₉	—	2	1	no	—
504	Dic₂₉	—	2	1	no	—
505	Dic₂₉	—	2	1	no	—
506	Dic₂₉	—	2	1	no	—
507	Dic₂₉	—	2	1	no	—
508	Dic₂₉	—	2	1	no	—
509	Dic₂₉	H(5,𝔽₂)	1	2	yes	—
510	#562	—	29	1	no	—
511	#562	—	29	1	no	—
512	#562	—	29	1	no	—
513	#562	—	29	1	no	—
514	#554	—	29	1	no	—
515	#554	—	29	1	no	—
516	#548	—	29	1	no	—
517	#548	—	29	1	no	—
518	#547	—	29	1	no	—
519	#547	—	29	1	no	—
520	#546	—	29	1	no	—
521	#546	—	29	1	no	—
522	#546	—	29	1	no	—
523	#546	—	29	1	no	—
524	#546	—	29	1	no	—
525	#546	D₂₉	1	1	yes	characteristic, complemented
526	#543	—	29	1	no	—
527	#543	—	29	1	no	—
528	#542	—	29	1	no	—
529	#542	—	29	1	no	—
530	#539	—	29	1	no	—
531	#539	—	29	1	no	—
532	#538	—	29	1	no	—
533	#538	—	29	1	no	—
534	#537	—	29	1	no	—
535	#537	—	29	1	no	—
536	#537	—	29	1	no	—
537	#537	—	29	1	no	—
538	#525	—	29	1	no	—
539	C₂×C₂²⋊Q₈	—	29	1	no	—
540	C₂×#121	—	29	1	no	—
541	C₂×C₂₉	—	2	2	no	—
542	C₂×C₂₉	—	2	2	no	—
543	C₂×C₂₉	—	4	1	no	—
544	C₂×C₂₉	—	4	1	no	—
545	C₂×C₂₉	—	4	1	no	—
546	C₂×C₂₉	—	4	1	no	—
547	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	D₂₉	—	4	1	no	—
551	D₂₉	—	4	1	no	—
552	D₂₉	—	4	1	no	—
553	C₂×#41	—	29	1	no	—
554	C₂×#41	—	29	1	no	—
555	C₂×#41	—	29	1	no	—
556	C₂×#41	—	29	1	no	—
557	C₂×#41	—	29	1	no	—
558	C₂×#41	—	29	1	no	—
559	C₂×#41	C₂×D₂₉	1	1	yes	characteristic, complemented
560	C₂²×Q₈	—	29	1	no	—
561	C₂²×D₄	—	29	1	no	—
562	C₂²×D₄	—	29	1	no	—
563	C₂²×D₄	C₂×D₂₉	1	1	yes	characteristic
564	C₂³×C₄	—	29	1	no	—
565	C₄⋊Q₈	—	29	1	no	—
566	C₄⋊Q₈	—	29	1	no	—
567	#126	—	29	1	no	—
568	#126	—	29	1	no	—
569	#126	—	29	1	no	—
570	#126	—	29	1	no	—
571	#125	—	29	1	no	—
572	#125	—	29	1	no	—
573	#125	—	29	1	no	—
574	#125	—	29	1	no	—
575	#124	—	29	1	no	—
576	#124	—	29	1	no	—
577	#124	—	29	1	no	—
578	#124	—	29	1	no	—
579	#124	—	29	1	no	—
580	#124	—	29	1	no	—
581	#124	—	29	1	no	—
582	#124	—	29	1	no	—
583	#124	—	29	1	no	—
584	#124	C₂×D₂₉	1	1	yes	characteristic, complemented
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	C₂×D₂₉	1	1	yes	characteristic, complemented
602	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
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	—	29	1	no	—
625	C₂²⋊Q₈	—	29	1	no	—
626	C₂²⋊Q₈	—	29	1	no	—
627	C₂²⋊Q₈	—	29	1	no	—
628	C₂²⋊Q₈	—	29	1	no	—
629	C₂²⋊Q₈	—	29	1	no	—
630	C₂²⋊Q₈	—	29	1	no	—
631	C₂²⋊Q₈	—	29	1	no	—
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	C₂×D₂₉	1	1	yes	characteristic
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	#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	C₂×D₂₉	1	1	yes	characteristic, complemented
669	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
670	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
671	#120	—	29	1	no	—
672	#120	—	29	1	no	—
673	#120	—	29	1	no	—
674	#120	—	29	1	no	—
675	#120	C₂×D₂₉	1	1	yes	characteristic
676	#120	C₂×D₂₉	1	1	yes	characteristic
677	C₄×Q₈	—	29	1	no	—
678	C₄×Q₈	—	29	1	no	—
679	C₄×D₄	—	29	1	no	—
680	C₄×D₄	—	29	1	no	—
681	C₄×D₄	—	29	1	no	—
682	C₄×D₄	—	29	1	no	—
683	C₄×D₄	—	29	1	no	—
684	C₄×D₄	—	29	1	no	—
685	C₄×D₄	—	29	1	no	—
686	C₄×D₄	—	29	1	no	—
687	C₄×D₄	—	29	1	no	—
688	C₄×D₄	—	29	1	no	—
689	C₄×D₄	—	29	1	no	—
690	C₄×D₄	—	29	1	no	—
691	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
692	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic, complemented
693	#117	—	29	1	no	—
694	C₂×C₄⋊C₄	—	29	1	no	—
695	C₂×C₄⋊C₄	—	29	1	no	—
696	C₂×C₄⋊C₄	—	29	1	no	—
697	C₂×C₄⋊C₄	—	29	1	no	—
698	C₂×C₄⋊C₄	—	29	1	no	—
699	C₂×C₄⋊C₄	—	29	1	no	—
700	C₂×C₂²⋊C₄	—	29	1	no	—
701	C₂×C₂²⋊C₄	—	29	1	no	—
702	C₂×C₂²⋊C₄	—	29	1	no	—
703	C₂×C₂²⋊C₄	—	29	1	no	—
704	C₂×C₂²⋊C₄	—	29	1	no	—
705	C₂×C₂²⋊C₄	—	29	1	no	—
706	C₂×C₂²⋊C₄	C₂×D₂₉	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂×D₂₉	1	1	yes	characteristic
708	C₂₉	#3536	1	1	yes	characteristic, complemented, Sylow
709	C₂⁴	—	29	1	no	—
710	C₂⁴	C₂²×D₂₉	1	1	yes	characteristic
711	C₂⁴	C₂²×D₂₉	1	1	yes	characteristic
712	#41	—	4	2	no	—
713	#41	—	116	2	no	—
714	#41	—	116	2	no	—
715	#41	—	116	2	no	—
716	#41	—	116	2	no	—
717	#41	—	116	2	no	—
718	#41	—	116	2	no	—
719	C₂×Q₈	—	29	1	no	—
720	C₂×Q₈	—	29	1	no	—
721	C₂×Q₈	—	29	1	no	—
722	C₂×Q₈	—	29	1	no	—
723	C₂×Q₈	—	29	1	no	—
724	C₂×Q₈	—	29	1	no	—
725	C₂×Q₈	—	29	1	no	—
726	C₂×Q₈	—	29	1	no	—
727	C₂×Q₈	—	116	2	no	—
728	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	29	1	no	—
731	C₂×D₄	—	29	1	no	—
732	C₂×D₄	—	29	1	no	—
733	C₂×D₄	—	29	1	no	—
734	C₂×D₄	—	29	1	no	—
735	C₂×D₄	—	29	1	no	—
736	C₂×D₄	—	29	1	no	—
737	C₂×D₄	—	29	1	no	—
738	C₂×D₄	—	29	1	no	—
739	C₂×D₄	—	29	1	no	—
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	—	116	2	no	—
749	C₂×D₄	—	116	2	no	—
750	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
751	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
752	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
753	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
754	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
755	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
756	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
757	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
758	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
759	C₂²×C₄	—	29	1	no	—
760	C₂²×C₄	—	29	1	no	—
761	C₂²×C₄	—	29	1	no	—
762	C₂²×C₄	—	29	1	no	—
763	C₂²×C₄	—	29	1	no	—
764	C₂²×C₄	—	29	1	no	—
765	C₂²×C₄	—	29	1	no	—
766	C₂²×C₄	—	29	1	no	—
767	C₂²×C₄	—	29	1	no	—
768	C₂²×C₄	—	29	1	no	—
769	C₂²×C₄	—	29	1	no	—
770	C₂²×C₄	—	29	1	no	—
771	C₂²×C₄	—	29	1	no	—
772	C₂²×C₄	—	29	1	no	—
773	C₂²×C₄	—	29	1	no	—
774	C₂²×C₄	—	29	1	no	—
775	C₂²×C₄	—	29	1	no	—
776	C₂²×C₄	—	29	1	no	—
777	C₂²×C₄	—	29	1	no	—
778	C₂²×C₄	—	29	1	no	—
779	C₂²×C₄	—	116	2	no	—
780	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
781	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
782	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
783	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
784	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
785	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
786	C₄⋊C₄	—	29	1	no	—
787	C₄⋊C₄	—	29	1	no	—
788	C₄⋊C₄	—	29	1	no	—
789	C₄⋊C₄	—	29	1	no	—
790	C₄⋊C₄	—	29	1	no	—
791	C₄⋊C₄	—	29	1	no	—
792	C₄⋊C₄	—	29	1	no	—
793	C₄⋊C₄	—	29	1	no	—
794	C₄⋊C₄	—	29	1	no	—
795	C₄⋊C₄	—	29	1	no	—
796	C₄⋊C₄	—	29	1	no	—
797	C₄⋊C₄	—	29	1	no	—
798	C₄⋊C₄	—	29	1	no	—
799	C₄⋊C₄	—	29	1	no	—
800	C₄⋊C₄	—	29	1	no	—
801	C₄⋊C₄	—	29	1	no	—
802	C₄⋊C₄	—	29	1	no	—
803	C₄⋊C₄	—	29	1	no	—
804	C₄⋊C₄	—	29	1	no	—
805	C₄⋊C₄	—	29	1	no	—
806	C₄⋊C₄	—	29	1	no	—
807	C₄⋊C₄	—	29	1	no	—
808	C₄⋊C₄	—	29	1	no	—
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	C₂²×D₂₉	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
822	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
823	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
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	—	29	1	no	—
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	C₂²×D₂₉	1	1	yes	characteristic
859	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
860	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
869	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
870	C₄²	—	29	1	no	—
871	C₄²	—	29	1	no	—
872	C₄²	—	29	1	no	—
873	C₄²	—	29	1	no	—
874	C₄²	—	29	1	no	—
875	C₄²	C₂²×D₂₉	1	1	yes	characteristic
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	4	1	no	—
880	C₂³	—	4	1	no	—
881	C₂³	—	4	1	no	—
882	C₂³	—	29	1	no	—
883	C₂³	—	29	1	no	—
884	C₂³	—	29	1	no	—
885	C₂³	—	58	2	no	—
886	C₂³	—	116	1	no	—
887	C₂³	—	116	1	no	—
888	C₂³	C₂³×D₂₉	1	1	yes	characteristic
889	C₂³	C₂³×D₂₉	1	1	yes	characteristic
890	C₂³	C₂³×D₂₉	1	1	yes	characteristic
891	C₂³	C₂³×D₂₉	1	1	yes	characteristic
892	C₂³	C₂³×D₂₉	1	1	yes	characteristic
893	C₂³	C₂³×D₂₉	1	1	yes	characteristic
894	Q₈	—	4	1	no	—
895	Q₈	—	58	2	no	—
896	Q₈	—	58	2	no	—
897	Q₈	—	116	1	no	—
898	Q₈	—	116	1	no	—
899	Q₈	—	116	1	no	—
900	Q₈	—	116	1	no	—
901	Q₈	—	116	1	no	—
902	Q₈	—	116	1	no	—
903	D₄	—	2	2	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	1	no	—
910	D₄	—	4	1	no	—
911	D₄	—	4	1	no	—
912	D₄	—	58	2	no	—
913	D₄	—	58	2	no	—
914	D₄	—	58	2	no	—
915	D₄	—	58	2	no	—
916	D₄	—	58	2	no	—
917	D₄	—	58	2	no	—
918	D₄	—	116	1	no	—
919	D₄	—	116	1	no	—
920	D₄	—	116	1	no	—
921	D₄	—	116	1	no	—
922	D₄	—	116	1	no	—
923	D₄	—	116	1	no	—
924	D₄	—	116	1	no	—
925	D₄	—	116	1	no	—
926	D₄	—	116	1	no	—
927	D₄	—	116	1	no	—
928	D₄	—	116	1	no	—
929	D₄	—	116	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	29	1	no	—
937	C₂×C₄	—	29	1	no	—
938	C₂×C₄	—	29	1	no	—
939	C₂×C₄	—	29	1	no	—
940	C₂×C₄	—	29	1	no	—
941	C₂×C₄	—	29	1	no	—
942	C₂×C₄	—	29	1	no	—
943	C₂×C₄	—	29	1	no	—
944	C₂×C₄	—	29	1	no	—
945	C₂×C₄	—	29	1	no	—
946	C₂×C₄	—	29	1	no	—
947	C₂×C₄	—	29	1	no	—
948	C₂×C₄	—	29	1	no	—
949	C₂×C₄	—	58	2	no	—
950	C₂×C₄	—	58	2	no	—
951	C₂×C₄	—	58	2	no	—
952	C₂×C₄	—	58	2	no	—
953	C₂×C₄	—	58	2	no	—
954	C₂×C₄	—	58	2	no	—
955	C₂×C₄	—	116	1	no	—
956	C₂×C₄	—	116	1	no	—
957	C₂×C₄	—	116	1	no	—
958	C₂×C₄	—	116	1	no	—
959	C₂×C₄	—	116	1	no	—
960	C₂×C₄	—	116	1	no	—
961	C₂×C₄	—	116	1	no	—
962	C₂×C₄	—	116	1	no	—
963	C₂×C₄	—	116	1	no	—
964	C₂×C₄	—	116	1	no	—
965	C₂×C₄	—	116	1	no	—
966	C₂×C₄	—	116	1	no	—
967	C₂×C₄	—	116	1	no	—
968	C₂×C₄	—	116	1	no	—
969	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
970	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
971	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
972	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
973	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
974	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
975	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
976	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
977	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	4	4	no	—
995	C₂²	—	8	2	no	—
996	C₂²	—	58	1	no	—
997	C₂²	—	58	1	no	—
998	C₂²	—	58	1	no	—
999	C₂²	—	58	1	no	—
1000	C₂²	—	58	1	no	—
1001	C₂²	—	58	1	no	—
1002	C₂²	—	58	1	no	—
1003	C₂²	—	58	1	no	—
1004	C₂²	—	58	1	no	—
1005	C₂²	—	232	2	no	—
1006	C₂²	#11745359	1	2	yes	—
1007	C₂²	#11745365	1	2	yes	—
1008	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	29	2	no	—
1019	C₄	—	58	1	no	—
1020	C₄	—	58	1	no	—
1021	C₄	—	58	1	no	—
1022	C₄	—	58	1	no	—
1023	C₄	—	58	1	no	—
1024	C₄	—	58	1	no	—
1025	C₄	—	58	1	no	—
1026	C₄	—	58	1	no	—
1027	C₄	—	58	1	no	—
1028	C₄	—	58	1	no	—
1029	C₄	—	58	1	no	—
1030	C₄	—	58	1	no	—
1031	C₂	—	2	2	no	—
1032	C₂	—	2	2	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	4	1	no	—
1036	C₂	—	4	1	no	—
1037	C₂	—	116	1	no	—
1038	C₂	—	116	1	no	—
1039	C₂	—	116	1	no	—
1040	C₂	H(5,𝔽₂)×D₂₉	1	1	yes	characteristic
1041	C₂	C₂×#11745359	1	1	yes	characteristic
1042	C₂	C₂×#11745365	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#546	C₂
hypercenter	#546	D₂₉
hypocenter	C₂₉	#3536
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #14271910	C₂	semidirect
2. #14271908	C₂	semidirect
3. #14271908	C₂	semidirect
4. #14271907	C₂	semidirect
5. #14271872	C₂	semidirect
6. #14271867	C₂	semidirect
7. #14271822	C₂	semidirect
8. #14271819	C₂	semidirect
9. #14271812	C₂	semidirect
10. #14271811	C₂	semidirect
11. #14271807	C₂	semidirect
12. #14271803	C₂	semidirect
13. #14271803	C₂	semidirect
14. #14271800	C₂	semidirect
15. #14271800	C₂	semidirect
16. #14271789	C₂	semidirect
17. #14271788	C₂	semidirect
18. #14271781	C₂	semidirect
19. #14271777	C₂	semidirect
20. #14271757	C₂	semidirect
21. #14271755	C₂	semidirect
22. #14271748	C₂	semidirect
23. #14271746	C₂	semidirect
24. #14271742	C₂	semidirect
25. #14271741	C₂	semidirect
26. #14271740	C₂	semidirect
27. #14271740	C₂	semidirect
28. #14271669	C₂	semidirect
29. C₂×#11745240	C₂	semidirect
30. C₂×#11745301	C₂	semidirect
31. C₂₉×#546	C₂	semidirect
32. C₂×#41×C₂₉	C₂²	semidirect
37. C₂×#90807	C₂²	semidirect
38. C₂×#90807	C₂²	semidirect
39. C₂×#90807	C₂²	semidirect
40. C₂×#90807	C₂²	semidirect
41. C₂×#90805	C₂²	semidirect
42. C₂×#90805	C₂²	semidirect
43. C₂²×Dic₅₈	C₂²	semidirect
44. C₂₉×#124	C₂²	semidirect
45. C₂₉×#123	C₂²	semidirect
46. C₂₉×#123	C₂²	semidirect
48. C₂₉×#121	C₂²	semidirect
49. C₂₉×#121	C₂²	semidirect
50. C₂₉×#121	C₂²	semidirect
54. C₄×D₄×C₂₉	C₂²	semidirect
62. #11745308	C₂²	semidirect
63. #11745308	C₂²	semidirect
64. #11745308	C₂²	semidirect
65. #11745306	C₂²	semidirect
75. #11745301	C₂²	semidirect
76. #11745301	C₂²	semidirect
77. #11745301	C₂²	semidirect
78. #11745301	C₂²	semidirect
79. #11745301	C₂²	semidirect
80. #11745301	C₂²	semidirect
81. #11745301	C₂²	semidirect
82. #11745301	C₂²	semidirect
83. #11745300	C₂²	semidirect
84. #11745300	C₂²	semidirect
85. #11745300	C₂²	semidirect
86. #11745300	C₂²	semidirect
88. #11745298	C₂²	semidirect
89. #11745298	C₂²	semidirect
90. #11745297	C₂²	semidirect
91. #11745297	C₂²	semidirect
92. #11745297	C₂²	semidirect
93. #11745297	C₂²	semidirect
96. D₄×Dic₂₉	C₂²	semidirect
97. D₄×Dic₂₉	C₂²	semidirect
98. #11745292	C₂²	semidirect
99. #11745292	C₂²	semidirect
100. #11745292	C₂²	semidirect
101. #11745291	C₂²	semidirect
102. #11745291	C₂²	semidirect
103. #11745291	C₂²	semidirect
105. C₄×C₂²⋊D₂₉	C₂²	semidirect
106. C₄×C₂²⋊D₂₉	C₂²	semidirect
108. C₂×C₄⋊Dic₂₉	C₂²	semidirect
110. #11745286	C₂²	semidirect
111. #11745286	C₂²	semidirect
112. #11745286	C₂²	semidirect
113. #11745286	C₂²	semidirect
114. #11745286	C₂²	semidirect
116. C₂×#90779	C₂²	semidirect
117. C₂×#90779	C₂²	semidirect
118. C₂×#90779	C₂²	semidirect
119. #11745260	C₂²	semidirect
120. #11745259	C₂²	semidirect
121. #11745259	C₂²	semidirect
122. #11745258	C₂²	semidirect
123. #11745258	C₂²	semidirect
124. #11745258	C₂²	semidirect
125. #11745258	C₂²	semidirect
126. #11745258	C₂²	semidirect
127. #11745258	C₂²	semidirect
128. #11745256	C₂²	semidirect
129. C₄⋊C₄×D₂₉	C₂²	semidirect
130. #11745252	C₂²	semidirect
131. #11745251	C₂²	semidirect
132. #11745251	C₂²	semidirect
133. #11745250	C₂²	semidirect
134. #11745249	C₂²	semidirect
135. #11745248	C₂²	semidirect
136. #11745248	C₂²	semidirect
137. #11745248	C₂²	semidirect
138. #11745247	C₂²	semidirect
139. #11745247	C₂²	semidirect
140. #11745247	C₂²	semidirect
141. #11745247	C₂²	semidirect
142. #11745247	C₂²	semidirect
143. #11745247	C₂²	semidirect
144. #11745246	C₂²	semidirect
145. #11745246	C₂²	semidirect
146. #11745246	C₂²	semidirect
147. #11745246	C₂²	semidirect
148. #11745246	C₂²	semidirect
149. #11745245	C₂²	semidirect
150. #11745245	C₂²	semidirect
151. #11745245	C₂²	semidirect
152. #11745245	C₂²	semidirect
153. #11745245	C₂²	semidirect
157. #11745243	C₂²	semidirect
158. #11745243	C₂²	semidirect
159. #11745243	C₂²	semidirect
162. #11745241	C₂²	semidirect
163. #11745241	C₂²	semidirect
171. #11745240	C₂²	semidirect
172. #11745240	C₂²	semidirect
173. #11745240	C₂²	semidirect
174. #11745240	C₂²	semidirect
175. #11745240	C₂²	semidirect
176. #11745240	C₂²	semidirect
177. #11745240	C₂²	semidirect
178. #11745240	C₂²	semidirect
179. #11745240	C₂²	semidirect
180. #11745240	C₂²	semidirect
181. #11745240	C₂²	semidirect
182. #11745239	C₂²	semidirect
183. #11745238	C₂²	semidirect
184. #11745237	C₂²	semidirect
185. #11745232	C₂²	semidirect
186. C₄×Dic₅₈	C₂²	semidirect
525. #546	D₂₉	semidirect
559. C₂×#41	C₂×D₂₉	semidirect
584. #124	C₂×D₂₉	semidirect
601. #123	C₂×D₂₉	semidirect
602. #123	C₂×D₂₉	semidirect
668. #121	C₂×D₂₉	semidirect
669. #121	C₂×D₂₉	semidirect
670. #121	C₂×D₂₉	semidirect
692. C₄×D₄	C₂×D₂₉	semidirect
708. C₂₉	#3536	semidirect

Maximal subgroups

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

subgroup	index
#14271910	2
#14271908	2
#14271907	2
#14271872	2
#14271867	2
#14271822	2
#14271819	2
#14271812	2
#14271811	2
#14271807	2
#14271803	2
#14271800	2
#14271789	2
#14271788	2
#14271781	2
#14271777	2
#14271757	2
#14271755	2
#14271748	2
#14271746	2
#14271742	2
#14271741	2
#14271740	2
#14271669	2
C₂×#11745240	2
C₂×#11745301	2
C₂₉×#546	2
#3536	29