Subgroups — C₆₁×#62054 #29565487

Order 15616.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3316	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3282	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3225	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3120	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
22	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	—
25	C₂×#135×C₆₁	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#563	—	2	2	no	—
28	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	C₂²	1	1	yes	characteristic
30	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#554	—	2	1	no	—
32	C₆₁×#554	C₂²	1	2	yes	—
33	C₆₁×#553	—	2	1	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#551	—	2	2	no	—
36	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
37	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×#548	—	2	1	no	—
40	C₆₁×#548	C₂²	1	2	yes	—
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#547	C₂²	1	1	yes	characteristic
43	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#546	C₂²	1	2	yes	—
45	C₆₁×#544	—	2	1	no	—
46	C₆₁×#542	—	2	1	no	—
47	C₆₁×#542	C₂²	1	2	yes	—
48	C₆₁×#541	C₂²	1	2	yes	complemented
49	C₆₁×#539	—	2	2	no	—
50	C₆₁×#539	—	2	2	no	—
51	C₆₁×#536	C₂²	1	2	yes	complemented
52	C₆₁×#533	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#529	C₂²	1	1	yes	characteristic
55	C₆₁×#529	C₂²	1	1	yes	characteristic
56	C₆₁×#525	—	2	1	no	—
57	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
58	C₆₁×#520	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#497	C₂²	1	2	yes	—
61	C₆₁×#495	C₂²	1	2	yes	—
62	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#487	C₂²	1	2	yes	complemented
67	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#484	C₂²	1	1	yes	characteristic
69	C₆₁×#484	C₂²	1	2	yes	complemented
70	C₆₁×#483	C₂²	1	2	yes	complemented
71	C₆₁×#481	C₂²	1	1	yes	characteristic
72	C₆₁×#479	C₂²	1	2	yes	complemented
73	C₆₁×#478	C₂²	1	1	yes	characteristic
74	C₆₁×#478	C₂²	1	1	yes	characteristic
75	C₆₁×#477	C₂²	1	2	yes	complemented
76	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#475	C₂²	1	2	yes	complemented
78	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#470	C₂²	1	2	yes	complemented
80	C₆₁×#468	C₂²	1	2	yes	—
81	C₆₁×#467	C₂²	1	2	yes	—
82	C₆₁×#467	C₂²	1	2	yes	complemented
83	C₆₁×#465	C₂²	1	2	yes	—
84	C₆₁×#465	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#464	C₂²	1	2	yes	complemented
89	C₆₁×#463	C₂²	1	1	yes	characteristic
90	C₆₁×#463	C₂²	1	2	yes	—
91	C₆₁×#463	C₂²	1	1	yes	characteristic
92	C₆₁×#462	C₂²	1	2	yes	complemented
93	C₆₁×#462	C₂²	1	2	yes	complemented
94	C₆₁×#462	C₂²	1	2	yes	complemented
95	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#461	C₂²	1	1	yes	characteristic
97	C₆₁×#461	C₂²	1	2	yes	—
98	C₆₁×#461	C₂²	1	2	yes	—
99	C₆₁×#461	C₂²	1	1	yes	characteristic
100	C₆₁×#461	C₂²	1	1	yes	characteristic
101	C₆₁×#461	C₂²	1	1	yes	characteristic
102	C₆₁×#461	C₂²	1	2	yes	—
103	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
104	C₆₁×#452	C₂²	1	2	yes	—
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#452	C₂²	1	2	yes	complemented
107	C₆₁×#451	C₂²	1	2	yes	—
108	C₆₁×#451	C₂²	1	2	yes	—
109	C₆₁×#451	C₂²	1	2	yes	complemented
110	C₆₁×#450	C₂²	1	1	yes	characteristic
111	C₆₁×#449	C₂²	1	2	yes	—
112	C₆₁×#448	C₂²	1	2	yes	—
113	C₆₁×#447	C₂²	1	1	yes	characteristic
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#441	C₂²	1	2	yes	complemented
117	C₆₁×#440	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
122	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
124	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₆₁	C₂²	1	2	yes	—
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
128	C₆₁×#433	C₂²	1	2	yes	complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic
130	C₆₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#417	C₂²	1	2	yes	complemented
133	C₂×#103×C₆₁	C₂²	1	2	yes	—
134	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₁	—	2	1	no	—
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₁	—	2	1	no	—
143	#137×C₆₁	—	4	4	no	—
144	#135×C₆₁	—	4	4	no	—
145	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	—	4	4	no	—
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	—	2	2	no	—
164	C₄⋊Q₈×C₆₁	—	2	1	no	—
165	C₄⋊Q₈×C₆₁	—	2	1	no	—
166	C₄⋊Q₈×C₆₁	—	2	1	no	—
167	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
174	#126×C₆₁	—	2	2	no	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	—	2	2	no	—
179	#126×C₆₁	—	2	1	no	—
180	#126×C₆₁	D₄	1	2	yes	—
181	#125×C₆₁	—	2	2	no	—
182	#125×C₆₁	—	2	2	no	—
183	#125×C₆₁	—	2	2	no	—
184	#125×C₆₁	—	2	2	no	—
185	#125×C₆₁	—	2	1	no	—
186	#125×C₆₁	—	2	1	no	—
187	#125×C₆₁	D₄	1	1	yes	characteristic
188	#125×C₆₁	C₂³	1	1	yes	characteristic
189	#124×C₆₁	—	2	2	no	—
190	#124×C₆₁	—	2	2	no	—
191	#124×C₆₁	D₄	1	1	yes	characteristic
192	#124×C₆₁	C₂³	1	1	yes	characteristic
193	#124×C₆₁	C₂³	1	2	yes	—
194	#124×C₆₁	C₂³	1	2	yes	—
195	#123×C₆₁	—	2	1	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	—	2	2	no	—
202	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	—	2	1	no	—
205	C₂²⋊Q₈×C₆₁	—	2	1	no	—
206	C₂²⋊Q₈×C₆₁	—	2	1	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	—	2	2	no	—
209	C₂²⋊Q₈×C₆₁	—	2	2	no	—
210	C₂²⋊Q₈×C₆₁	—	2	2	no	—
211	C₂²⋊Q₈×C₆₁	—	2	2	no	—
212	C₂²⋊Q₈×C₆₁	—	2	1	no	—
213	C₂²⋊Q₈×C₆₁	—	2	1	no	—
214	C₂²⋊Q₈×C₆₁	—	2	2	no	—
215	C₂²⋊Q₈×C₆₁	—	2	2	no	—
216	C₂²⋊Q₈×C₆₁	—	2	2	no	—
217	C₂²⋊Q₈×C₆₁	—	2	2	no	—
218	C₂²⋊Q₈×C₆₁	—	2	2	no	—
219	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	#121×C₆₁	—	2	2	no	—
226	#121×C₆₁	—	2	1	no	—
227	#121×C₆₁	—	2	1	no	—
228	#121×C₆₁	—	2	2	no	—
229	#121×C₆₁	D₄	1	1	yes	characteristic
230	#121×C₆₁	C₂³	1	2	yes	—
231	#121×C₆₁	C₂³	1	1	yes	characteristic
232	#120×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	1	no	—
235	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₁	—	2	2	no	—
242	C₄×D₄×C₆₁	—	2	1	no	—
243	C₄×D₄×C₆₁	—	2	2	no	—
244	C₄×D₄×C₆₁	—	2	1	no	—
245	C₄×D₄×C₆₁	—	2	2	no	—
246	C₄×D₄×C₆₁	—	2	2	no	—
247	C₄×D₄×C₆₁	—	2	2	no	—
248	C₄×D₄×C₆₁	—	2	1	no	—
249	C₄×D₄×C₆₁	—	2	1	no	—
250	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₁	C₂³	1	2	yes	—
257	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
258	#117×C₆₁	—	2	1	no	—
259	#117×C₆₁	—	2	1	no	—
260	#117×C₆₁	—	2	2	no	—
261	#117×C₆₁	—	2	1	no	—
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
265	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	2	yes	—
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×C₆₁	C₂³	1	2	yes	—
298	#103×C₆₁	C₂³	1	2	yes	—
299	#103×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	1	yes	characteristic
306	#102×C₆₁	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	1	no	—
316	#41×C₆₁	—	2	4	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	2	no	—
320	#41×C₆₁	—	8	2	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	—	4	2	no	—
326	C₂×Q₈×C₆₁	—	4	2	no	—
327	C₂×Q₈×C₆₁	—	4	2	no	—
328	C₂×Q₈×C₆₁	—	4	2	no	—
329	C₂×Q₈×C₆₁	—	8	2	no	—
330	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	4	1	no	—
342	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	2	2	no	—
350	C₂²×C₄×C₆₁	—	2	2	no	—
351	C₂²×C₄×C₆₁	—	2	2	no	—
352	C₂²×C₄×C₆₁	—	2	1	no	—
353	C₂²×C₄×C₆₁	—	2	1	no	—
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	—	2	1	no	—
359	C₂²×C₄×C₆₁	—	8	2	no	—
360	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
364	Q₁₆×C₆₁	—	4	2	no	—
365	Q₁₆×C₆₁	—	4	2	no	—
366	Q₁₆×C₆₁	—	4	2	no	—
367	Q₁₆×C₆₁	—	4	2	no	—
368	Q₁₆×C₆₁	—	4	2	no	—
369	SD₁₆×C₆₁	—	2	4	no	—
370	SD₁₆×C₆₁	—	2	4	no	—
371	SD₁₆×C₆₁	—	2	2	no	—
372	SD₁₆×C₆₁	—	4	2	no	—
373	SD₁₆×C₆₁	—	4	2	no	—
374	SD₁₆×C₆₁	—	4	1	no	—
375	SD₁₆×C₆₁	—	4	2	no	—
376	D₈×C₆₁	—	2	2	no	—
377	D₈×C₆₁	—	4	1	no	—
378	M₁₆×C₆₁	—	4	2	no	—
379	C₂×C₈×C₆₁	—	4	2	no	—
380	C₂×C₈×C₆₁	—	4	2	no	—
381	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	1	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	1	no	—
403	C₄⋊C₄×C₆₁	—	2	1	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	1	no	—
408	C₄⋊C₄×C₆₁	—	2	2	no	—
409	C₄⋊C₄×C₆₁	—	2	2	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	—	2	2	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	1	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	1	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	—	2	1	no	—
439	C₂²⋊C₄×C₆₁	—	2	1	no	—
440	C₂²⋊C₄×C₆₁	—	2	1	no	—
441	C₂²⋊C₄×C₆₁	—	2	2	no	—
442	C₂²⋊C₄×C₆₁	—	2	1	no	—
443	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	—	2	1	no	—
451	C₄²×C₆₁	—	2	2	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₁	C₂⁴	1	2	yes	—
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₆₁	—	2	1	no	—
459	C₂³×C₆₁	—	2	1	no	—
460	C₂³×C₆₁	—	2	1	no	—
461	C₂³×C₆₁	—	4	2	no	—
462	C₂³×C₆₁	—	4	2	no	—
463	C₂³×C₆₁	—	8	1	no	—
464	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
465	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₆₁	—	2	2	no	—
467	Q₈×C₆₁	—	2	2	no	—
468	Q₈×C₆₁	—	2	2	no	—
469	Q₈×C₆₁	—	2	1	no	—
470	Q₈×C₆₁	—	2	2	no	—
471	Q₈×C₆₁	—	2	1	no	—
472	Q₈×C₆₁	—	2	2	no	—
473	Q₈×C₆₁	—	2	2	no	—
474	Q₈×C₆₁	—	2	2	no	—
475	Q₈×C₆₁	—	4	2	no	—
476	Q₈×C₆₁	—	8	2	no	—
477	Q₈×C₆₁	—	8	2	no	—
478	Q₈×C₆₁	—	8	2	no	—
479	D₄×C₆₁	—	2	4	no	—
480	D₄×C₆₁	—	2	2	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	2	1	no	—
483	D₄×C₆₁	—	2	1	no	—
484	D₄×C₆₁	—	2	1	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	4	2	no	—
487	D₄×C₆₁	—	4	4	no	—
488	D₄×C₆₁	—	4	2	no	—
489	D₄×C₆₁	—	8	2	no	—
490	D₄×C₆₁	—	8	2	no	—
491	D₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
492	C₂×C₄×C₆₁	—	2	2	no	—
493	C₂×C₄×C₆₁	—	2	2	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	2	no	—
496	C₂×C₄×C₆₁	—	2	1	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	2	1	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	2	no	—
501	C₂×C₄×C₆₁	—	2	1	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	2	2	no	—
504	C₂×C₄×C₆₁	—	2	2	no	—
505	C₂×C₄×C₆₁	—	2	2	no	—
506	C₂×C₄×C₆₁	—	2	1	no	—
507	C₂×C₄×C₆₁	—	4	4	no	—
508	C₂×C₄×C₆₁	—	4	2	no	—
509	C₂×C₄×C₆₁	—	4	2	no	—
510	C₂×C₄×C₆₁	—	4	2	no	—
511	C₂×C₄×C₆₁	—	8	1	no	—
512	C₂×C₄×C₆₁	—	8	1	no	—
513	C₂×C₄×C₆₁	—	8	2	no	—
514	C₂×C₄×C₆₁	—	8	2	no	—
515	C₂×C₄×C₆₁	—	8	1	no	—
516	C₂×C₄×C₆₁	—	8	2	no	—
517	C₂×C₄×C₆₁	—	8	2	no	—
518	C₂×C₄×C₆₁	—	8	2	no	—
519	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
528	C₈×C₆₁	—	2	1	no	—
529	C₈×C₆₁	—	2	2	no	—
530	C₈×C₆₁	—	2	2	no	—
531	C₈×C₆₁	—	2	1	no	—
532	C₈×C₆₁	—	2	1	no	—
533	C₈×C₆₁	—	2	1	no	—
534	#62054	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
535	C₂²×C₆₁	—	2	1	no	—
536	C₂²×C₆₁	—	2	1	no	—
537	C₂²×C₆₁	—	2	2	no	—
538	C₂²×C₆₁	—	2	2	no	—
539	C₂²×C₆₁	—	2	2	no	—
540	C₂²×C₆₁	—	2	2	no	—
541	C₂²×C₆₁	—	4	1	no	—
542	C₂²×C₆₁	—	4	1	no	—
543	C₂²×C₆₁	—	4	1	no	—
544	C₂²×C₆₁	—	4	1	no	—
545	C₂²×C₆₁	—	4	1	no	—
546	C₂²×C₆₁	—	4	1	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	8	4	no	—
550	C₂²×C₆₁	#578	1	2	yes	—
551	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₆₁	—	2	2	no	—
553	C₄×C₆₁	—	2	1	no	—
554	C₄×C₆₁	—	2	1	no	—
555	C₄×C₆₁	—	2	2	no	—
556	C₄×C₆₁	—	2	1	no	—
557	C₄×C₆₁	—	2	1	no	—
558	C₄×C₆₁	—	2	2	no	—
559	C₄×C₆₁	—	4	2	no	—
560	C₄×C₆₁	—	4	2	no	—
561	C₄×C₆₁	—	4	2	no	—
562	C₄×C₆₁	—	4	1	no	—
563	C₄×C₆₁	—	4	1	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	1	no	—
566	C₄×C₆₁	—	4	2	no	—
567	C₄×C₆₁	—	4	1	no	—
568	C₄×C₆₁	#577	1	2	yes	—
569	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄×C₆₁	#585	1	1	yes	characteristic
571	#3552	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3520	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3393	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3359	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3330	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3316	C₂×C₆₁	1	2	yes	complemented
579	#3299	C₂×C₆₁	1	2	yes	complemented
580	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3283	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3282	C₂×C₆₁	1	2	yes	complemented
583	#3276	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3266	C₂×C₆₁	1	2	yes	complemented
585	#3258	C₂×C₆₁	1	2	yes	complemented
586	#3248	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3225	C₂×C₆₁	1	2	yes	complemented
588	#3209	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3120	C₂×C₆₁	1	2	yes	complemented
590	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3046	C₂×C₆₁	1	2	yes	complemented
592	C₂×#461	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
594	C₂×C₆₁	—	2	2	no	—
595	C₂×C₆₁	—	4	2	no	—
596	C₂×C₆₁	—	4	2	no	—
597	C₂×C₆₁	—	8	1	no	—
598	C₂×C₆₁	—	8	1	no	—
599	C₂×C₆₁	#3488	1	1	yes	characteristic
600	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
601	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
602	C₂×#137	C₂²×C₆₁	1	2	yes	—
603	C₂×#135	C₂²×C₆₁	1	2	yes	—
604	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
605	#563	—	2	2	no	—
606	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
607	#556	C₂²×C₆₁	1	1	yes	characteristic
608	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
609	#554	—	2	1	no	—
610	#554	C₂²×C₆₁	1	2	yes	—
611	#553	—	2	1	no	—
612	#552	—	2	1	no	—
613	#551	—	2	2	no	—
614	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
615	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
616	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
617	#548	—	2	1	no	—
618	#548	C₂²×C₆₁	1	2	yes	—
619	#547	C₂²×C₆₁	1	1	yes	characteristic
620	#547	C₂²×C₆₁	1	1	yes	characteristic
621	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
622	#546	C₂²×C₆₁	1	2	yes	—
623	#544	—	2	1	no	—
624	#542	—	2	1	no	—
625	#542	C₂²×C₆₁	1	2	yes	—
626	#541	C₂²×C₆₁	1	2	yes	complemented
627	#539	—	2	2	no	—
628	#539	—	2	2	no	—
629	#536	C₂²×C₆₁	1	2	yes	complemented
630	#533	C₂²×C₆₁	1	1	yes	characteristic
631	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
632	#529	C₂²×C₆₁	1	1	yes	characteristic
633	#529	C₂²×C₆₁	1	1	yes	characteristic
634	#525	—	2	1	no	—
635	C₂×C₂²⋊Q₈	—	2	1	no	—
636	#520	C₂²×C₆₁	1	2	yes	—
637	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
638	#497	C₂²×C₆₁	1	2	yes	—
639	#495	C₂²×C₆₁	1	2	yes	—
640	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
642	#489	C₂²×C₆₁	1	2	yes	complemented
643	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
644	#487	C₂²×C₆₁	1	2	yes	complemented
645	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#484	C₂²×C₆₁	1	1	yes	characteristic
647	#484	C₂²×C₆₁	1	2	yes	complemented
648	#483	C₂²×C₆₁	1	2	yes	complemented
649	#481	C₂²×C₆₁	1	1	yes	characteristic
650	#479	C₂²×C₆₁	1	2	yes	complemented
651	#478	C₂²×C₆₁	1	1	yes	characteristic
652	#478	C₂²×C₆₁	1	1	yes	characteristic
653	#477	C₂²×C₆₁	1	2	yes	complemented
654	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#475	C₂²×C₆₁	1	2	yes	complemented
656	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#470	C₂²×C₆₁	1	2	yes	complemented
658	#468	C₂²×C₆₁	1	2	yes	—
659	#467	C₂²×C₆₁	1	2	yes	—
660	#467	C₂²×C₆₁	1	2	yes	complemented
661	#465	C₂²×C₆₁	1	2	yes	—
662	#465	C₂²×C₆₁	1	2	yes	—
663	#464	C₂²×C₆₁	1	2	yes	—
664	#464	C₂²×C₆₁	1	2	yes	—
665	#464	C₂²×C₆₁	1	2	yes	complemented
666	#464	C₂²×C₆₁	1	2	yes	complemented
667	#463	C₂²×C₆₁	1	1	yes	characteristic
668	#463	C₂²×C₆₁	1	1	yes	characteristic
669	#463	C₂²×C₆₁	1	2	yes	—
670	#462	C₂²×C₆₁	1	2	yes	complemented
671	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
672	#462	C₂²×C₆₁	1	2	yes	complemented
673	#462	C₂²×C₆₁	1	2	yes	complemented
674	#461	C₂²×C₆₁	1	1	yes	characteristic
675	#461	C₂²×C₆₁	1	2	yes	—
676	#461	C₂²×C₆₁	1	1	yes	characteristic
677	#461	C₂²×C₆₁	1	1	yes	characteristic
678	#461	C₂²×C₆₁	1	2	yes	—
679	#461	C₂²×C₆₁	1	1	yes	characteristic
680	#461	C₂²×C₆₁	1	2	yes	—
681	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	#452	C₂²×C₆₁	1	2	yes	—
683	#452	C₂²×C₆₁	1	2	yes	—
684	#452	C₂²×C₆₁	1	2	yes	complemented
685	#451	C₂²×C₆₁	1	2	yes	—
686	#451	C₂²×C₆₁	1	2	yes	—
687	#451	C₂²×C₆₁	1	2	yes	complemented
688	#450	C₂²×C₆₁	1	1	yes	characteristic
689	#449	C₂²×C₆₁	1	2	yes	—
690	#448	C₂²×C₆₁	1	2	yes	—
691	#447	C₂²×C₆₁	1	1	yes	characteristic
692	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
693	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	#441	C₂²×C₆₁	1	2	yes	complemented
695	#440	C₂²×C₆₁	1	2	yes	—
696	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
698	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
699	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
700	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
701	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
702	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#435	C₂²×C₆₁	1	2	yes	—
704	C₈×D₄	C₂²×C₆₁	1	2	yes	—
705	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#433	C₂²×C₆₁	1	2	yes	complemented
707	#431	C₂²×C₆₁	1	1	yes	characteristic
708	#424	C₂²×C₆₁	1	2	yes	complemented
709	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
710	#417	C₂²×C₆₁	1	2	yes	complemented
711	C₂×#103	C₂²×C₆₁	1	2	yes	—
712	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
713	C₆₁	#62054	1	1	yes	characteristic, direct product factor, Sylow
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₆₁	1	2	yes	—
716	C₂×#41	C₂³×C₆₁	1	2	yes	—
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
719	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
720	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
721	C₂³×C₄	—	2	1	no	—
722	#137	—	4	4	no	—
723	#135	—	4	4	no	—
724	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
729	C₂×SD₁₆	—	4	4	no	—
730	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
740	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
742	C₄⋊Q₈	—	2	2	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
747	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#126	D₄×C₆₁	1	2	yes	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	—	2	1	no	—
766	#125	D₄×C₆₁	1	1	yes	characteristic
767	#125	C₂³×C₆₁	1	1	yes	characteristic
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	D₄×C₆₁	1	1	yes	characteristic
771	#124	C₂³×C₆₁	1	1	yes	characteristic
772	#124	C₂³×C₆₁	1	2	yes	—
773	#124	C₂³×C₆₁	1	2	yes	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	D₄×C₆₁	1	2	yes	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	D₄×C₆₁	1	1	yes	characteristic
809	#121	C₂³×C₆₁	1	1	yes	characteristic
810	#121	C₂³×C₆₁	1	2	yes	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
816	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
818	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
819	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₆₁	1	2	yes	—
834	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₆₁	1	2	yes	—
836	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₆₁	1	2	yes	—
843	C₂×C₄⋊C₄	—	2	1	no	—
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
853	#107	C₂³×C₆₁	1	1	yes	characteristic
854	#107	C₂³×C₆₁	1	1	yes	characteristic
855	#107	C₂³×C₆₁	1	2	yes	—
856	#106	C₂³×C₆₁	1	1	yes	characteristic
857	#106	C₂³×C₆₁	1	2	yes	—
858	#106	C₂³×C₆₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
866	#103	C₂³×C₆₁	1	2	yes	—
867	#103	C₂³×C₆₁	1	2	yes	—
868	#103	C₂³×C₆₁	1	2	yes	—
869	#103	C₂³×C₆₁	1	2	yes	—
870	#103	C₂³×C₆₁	1	1	yes	characteristic
871	#103	C₂³×C₆₁	1	2	yes	—
872	#103	C₂³×C₆₁	1	2	yes	—
873	#103	C₂³×C₆₁	1	2	yes	—
874	#103	C₂³×C₆₁	1	2	yes	—
875	#103	C₂³×C₆₁	1	1	yes	characteristic
876	#103	C₂³×C₆₁	1	2	yes	—
877	#103	C₂³×C₆₁	1	2	yes	—
878	#103	C₂³×C₆₁	1	2	yes	—
879	#102	C₂³×C₆₁	1	1	yes	characteristic
880	#102	C₂³×C₆₁	1	2	yes	—
881	#102	C₂³×C₆₁	1	1	yes	characteristic
882	#102	C₂³×C₆₁	1	1	yes	characteristic
883	#102	C₂³×C₆₁	1	1	yes	characteristic
884	#102	C₂³×C₆₁	1	1	yes	characteristic
885	#102	C₂³×C₆₁	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
890	#97	C₂³×C₆₁	1	2	yes	—
891	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₆₁	1	2	yes	—
894	C₂⁴	—	2	1	no	—
895	#41	—	2	4	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
911	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
922	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	8	2	no	—
939	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
943	Q₁₆	—	4	2	no	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	2	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	1	no	—
954	SD₁₆	—	4	2	no	—
955	D₈	—	2	2	no	—
956	D₈	—	4	1	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
965	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₆₁	1	2	yes	—
1036	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	8	1	no	—
1043	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	8	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1106	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	8	4	no	—
1128	C₂²	C₆₁×#578	1	2	yes	—
1129	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	C₆₁×#577	1	2	yes	—
1147	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1148	C₄	C₆₁×#585	1	1	yes	characteristic
1149	C₂	—	2	2	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	4	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	C₆₁×#3488	1	1	yes	characteristic
1155	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1156	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3552	C₂	semidirect
2. C₆₁×#3520	C₂	semidirect
3. C₆₁×#3398	C₂	semidirect
4. C₆₁×#3393	C₂	semidirect
5. C₆₁×#3367	C₂	semidirect
6. C₆₁×#3359	C₂	semidirect
7. C₆₁×#3330	C₂	semidirect
8. C₆₁×#3316	C₂	semidirect
9. C₆₁×#3299	C₂	semidirect
10. C₆₁×#3298	C₂	semidirect
11. C₆₁×#3283	C₂	semidirect
12. C₆₁×#3282	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3266	C₂	semidirect
15. C₆₁×#3258	C₂	semidirect
16. C₆₁×#3248	C₂	semidirect
17. C₆₁×#3225	C₂	semidirect
18. C₆₁×#3209	C₂	semidirect
19. C₆₁×#3120	C₂	semidirect
20. C₆₁×#3105	C₂	semidirect
21. C₆₁×#3046	C₂	semidirect
22. C₂×C₆₁×#461	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
28. C₆₁×#557	C₂²	semidirect
30. C₆₁×#556	C₂²	semidirect
38. D₄×Q₈×C₆₁	C₂²	semidirect
43. C₆₁×#547	C₂²	semidirect
48. C₆₁×#541	C₂²	semidirect
51. C₆₁×#536	C₂²	semidirect
62. C₆₁×#494	C₂²	semidirect
63. C₆₁×#494	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#487	C₂²	semidirect
67. C₆₁×#487	C₂²	semidirect
69. C₆₁×#484	C₂²	semidirect
70. C₆₁×#483	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
75. C₆₁×#477	C₂²	semidirect
76. C₆₁×#475	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
79. C₆₁×#470	C₂²	semidirect
82. C₆₁×#467	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#464	C₂²	semidirect
92. C₆₁×#462	C₂²	semidirect
93. C₆₁×#462	C₂²	semidirect
94. C₆₁×#462	C₂²	semidirect
95. C₆₁×#462	C₂²	semidirect
103. C₆₁×#461	C₂²	semidirect
106. C₆₁×#452	C₂²	semidirect
109. C₆₁×#451	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#441	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
124. C₆₁×#436	C₂²	semidirect
127. C₈×D₄×C₆₁	C₂²	semidirect
128. C₆₁×#433	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
132. C₆₁×#417	C₂²	semidirect
134. C₂×#103×C₆₁	C₂²	semidirect
534. #62054	C₆₁	direct (N × H)
571. #3552	C₂×C₆₁	semidirect
572. #3520	C₂×C₆₁	semidirect
573. #3398	C₂×C₆₁	semidirect
574. #3393	C₂×C₆₁	semidirect
575. #3367	C₂×C₆₁	semidirect
576. #3359	C₂×C₆₁	semidirect
577. #3330	C₂×C₆₁	semidirect
578. #3316	C₂×C₆₁	semidirect
579. #3299	C₂×C₆₁	semidirect
580. #3298	C₂×C₆₁	semidirect
581. #3283	C₂×C₆₁	semidirect
582. #3282	C₂×C₆₁	semidirect
583. #3276	C₂×C₆₁	semidirect
584. #3266	C₂×C₆₁	semidirect
585. #3258	C₂×C₆₁	semidirect
586. #3248	C₂×C₆₁	semidirect
587. #3225	C₂×C₆₁	semidirect
588. #3209	C₂×C₆₁	semidirect
589. #3120	C₂×C₆₁	semidirect
590. #3105	C₂×C₆₁	semidirect
591. #3046	C₂×C₆₁	semidirect
592. C₂×#461	C₂×C₆₁	semidirect
593. #2994	C₂×C₆₁	semidirect
606. #557	C₂²×C₆₁	semidirect
608. #556	C₂²×C₆₁	semidirect
616. D₄×Q₈	C₂²×C₆₁	semidirect
621. #547	C₂²×C₆₁	semidirect
626. #541	C₂²×C₆₁	semidirect
629. #536	C₂²×C₆₁	semidirect
640. #494	C₂²×C₆₁	semidirect
641. #494	C₂²×C₆₁	semidirect
642. #489	C₂²×C₆₁	semidirect
643. #487	C₂²×C₆₁	semidirect
644. #487	C₂²×C₆₁	semidirect
645. #487	C₂²×C₆₁	semidirect
647. #484	C₂²×C₆₁	semidirect
648. #483	C₂²×C₆₁	semidirect
650. #479	C₂²×C₆₁	semidirect
653. #477	C₂²×C₆₁	semidirect
654. #475	C₂²×C₆₁	semidirect
655. #475	C₂²×C₆₁	semidirect
656. #474	C₂²×C₆₁	semidirect
657. #470	C₂²×C₆₁	semidirect
660. #467	C₂²×C₆₁	semidirect
665. #464	C₂²×C₆₁	semidirect
666. #464	C₂²×C₆₁	semidirect
670. #462	C₂²×C₆₁	semidirect
671. #462	C₂²×C₆₁	semidirect
672. #462	C₂²×C₆₁	semidirect
673. #462	C₂²×C₆₁	semidirect
681. #461	C₂²×C₆₁	semidirect
684. #452	C₂²×C₆₁	semidirect
687. #451	C₂²×C₆₁	semidirect
692. #446	C₂²×C₆₁	semidirect
693. C₈×Q₈	C₂²×C₆₁	semidirect
694. #441	C₂²×C₆₁	semidirect
696. C₄×Q₁₆	C₂²×C₆₁	semidirect
702. #436	C₂²×C₆₁	semidirect
705. C₈×D₄	C₂²×C₆₁	semidirect
706. #433	C₂²×C₆₁	semidirect
708. #424	C₂²×C₆₁	semidirect
710. #417	C₂²×C₆₁	semidirect
712. C₂×#103	C₂²×C₆₁	semidirect
713. C₆₁	#62054	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3552	2
C₆₁×#3520	2
C₆₁×#3398	2
C₆₁×#3393	2
C₆₁×#3367	2
C₆₁×#3359	2
C₆₁×#3330	2
C₆₁×#3316	2
C₆₁×#3299	2
C₆₁×#3298	2
C₆₁×#3283	2
C₆₁×#3282	2
C₆₁×#3276	2
C₆₁×#3266	2
C₆₁×#3258	2
C₆₁×#3248	2
C₆₁×#3225	2
C₆₁×#3209	2
C₆₁×#3120	2
C₆₁×#3105	2
C₆₁×#3046	2
C₂×C₆₁×#461	2
C₆₁×#2994	2
#62054	61

Subgroups — C61×#62054 #29565487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62054 #29565487