Subgroups — C₆₁×#60216 #29563649

Order 15616.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3475	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2970	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2969	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2968	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2968	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2967	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2967	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2966	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2965	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2933	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₆₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#556	C₄	1	1	yes	characteristic
31	C₆₁×#555	C₄	1	1	yes	characteristic
32	C₆₁×#554	C₄	1	1	yes	characteristic
33	C₆₁×#553	C₄	1	1	yes	characteristic
34	C₆₁×#553	C₄	1	1	yes	characteristic
35	C₆₁×#552	C₄	1	1	yes	characteristic
36	C₆₁×#552	C₄	1	1	yes	characteristic
37	C₆₁×#552	C₄	1	2	yes	—
38	C₆₁×#551	C₄	1	2	yes	—
39	C₆₁×#551	C₄	1	2	yes	—
40	C₆₁×#547	C₄	1	1	yes	characteristic
41	C₆₁×#546	C₄	1	2	yes	—
42	C₆₁×#533	C₂²	1	1	yes	characteristic
43	C₆₁×#529	C₂²	1	2	yes	—
44	C₆₁×#529	C₂²	1	2	yes	—
45	C₆₁×#529	C₂²	1	2	yes	—
46	C₆₁×#525	C₂²	1	1	yes	characteristic
47	C₆₁×#525	C₂²	1	1	yes	characteristic
48	C₄×#41×C₆₁	C₂²	1	2	yes	—
49	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#446	C₂²	1	2	yes	complemented
54	C₆₁×#446	C₂²	1	2	yes	complemented
55	C₆₁×#446	C₂²	1	2	yes	complemented
56	C₆₁×#446	C₂²	1	2	yes	complemented
57	C₆₁×#446	C₂²	1	2	yes	complemented
58	C₆₁×#446	C₂²	1	2	yes	complemented
59	C₆₁×#446	C₂²	1	2	yes	complemented
60	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
61	C₆₁×#436	C₂²	1	2	yes	—
62	C₆₁×#436	C₂²	1	2	yes	complemented
63	C₆₁×#436	C₂²	1	2	yes	complemented
64	C₆₁×#436	C₂²	1	2	yes	complemented
65	C₆₁×#436	C₂²	1	2	yes	complemented
66	C₆₁×#435	C₂²	1	1	yes	characteristic
67	C₆₁×#435	C₂²	1	1	yes	characteristic
68	C₆₁×#435	C₂²	1	1	yes	characteristic
69	C₆₁×#435	C₂²	1	1	yes	characteristic
70	C₆₁×#435	C₂²	1	1	yes	characteristic
71	C₆₁×#435	C₂²	1	1	yes	characteristic
72	C₆₁×#435	C₂²	1	1	yes	characteristic
73	C₆₁×#435	C₂²	1	1	yes	characteristic
74	C₆₁×#435	C₂²	1	2	yes	—
75	C₆₁×#435	C₂²	1	2	yes	—
76	C₆₁×#435	C₂²	1	2	yes	complemented
77	C₆₁×#435	C₂²	1	2	yes	complemented
78	C₆₁×#435	C₂²	1	2	yes	complemented
79	C₆₁×#435	C₂²	1	2	yes	complemented
80	C₆₁×#435	C₂²	1	2	yes	complemented
81	C₆₁×#435	C₂²	1	2	yes	complemented
82	C₆₁×#435	C₂²	1	2	yes	complemented
83	C₆₁×#435	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₁	C₂²	1	2	yes	—
85	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
86	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
87	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
88	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
89	C₆₁×#433	C₂²	1	2	yes	complemented
90	C₆₁×#433	C₂²	1	2	yes	complemented
91	C₆₁×#433	C₂²	1	2	yes	complemented
92	C₆₁×#433	C₂²	1	2	yes	complemented
93	C₆₁×#433	C₂²	1	2	yes	complemented
94	C₆₁×#433	C₂²	1	2	yes	complemented
95	C₆₁×#432	C₂²	1	2	yes	complemented
96	C₆₁×#432	C₂²	1	2	yes	complemented
97	C₆₁×#432	C₂²	1	2	yes	complemented
98	C₆₁×#431	C₂²	1	2	yes	complemented
99	C₆₁×#431	C₂²	1	2	yes	complemented
100	C₆₁×#431	C₂²	1	2	yes	complemented
101	C₆₁×#424	C₂²	1	1	yes	characteristic
102	C₆₁×#424	C₂²	1	1	yes	characteristic
103	C₆₁×#424	C₂²	1	1	yes	characteristic
104	C₆₁×#424	C₂²	1	1	yes	characteristic
105	C₆₁×#423	C₂²	1	1	yes	characteristic
106	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
107	C₆₁×#408	C₂²	1	1	yes	characteristic
108	C₆₁×#408	C₂²	1	1	yes	characteristic
109	C₆₁×#407	C₂²	1	1	yes	characteristic
110	C₆₁×#407	C₂²	1	1	yes	characteristic
111	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
112	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
113	C₆₁×#405	C₂²	1	1	yes	characteristic
114	C₆₁×#405	C₂²	1	1	yes	characteristic
115	C₆₁×#405	C₂²	1	1	yes	characteristic
116	C₆₁×#405	C₂²	1	1	yes	characteristic
117	C₆₁×#405	C₂²	1	1	yes	characteristic
118	C₆₁×#405	C₂²	1	1	yes	characteristic
119	C₆₁×#405	C₂²	1	1	yes	characteristic
120	C₆₁×#405	C₂²	1	1	yes	characteristic
121	C₆₁×#405	C₂²	1	2	yes	complemented
122	C₆₁×#405	C₂²	1	2	yes	complemented
123	C₆₁×#405	C₂²	1	2	yes	complemented
124	C₆₁×#405	C₂²	1	2	yes	complemented
125	C₆₁×#405	C₂²	1	2	yes	complemented
126	C₆₁×#405	C₂²	1	2	yes	complemented
127	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
128	C₄×M₁₆×C₆₁	C₂²	1	2	yes	complemented
129	C₄×M₁₆×C₆₁	C₂²	1	2	yes	complemented
130	C₄×M₁₆×C₆₁	C₂²	1	2	yes	complemented
131	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
132	C₂×#97×C₆₁	C₂²	1	2	yes	complemented
133	C₂×#97×C₆₁	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
138	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
140	#131×C₆₁	—	2	4	no	—
141	#131×C₆₁	—	2	4	no	—
142	C₂×M₁₆×C₆₁	—	2	4	no	—
143	C₂×M₁₆×C₆₁	—	2	4	no	—
144	C₂×M₁₆×C₆₁	—	2	4	no	—
145	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₆₁	—	2	4	no	—
158	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
166	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
168	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
169	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
172	#126×C₆₁	C₂×C₄	1	2	yes	—
173	#126×C₆₁	C₂×C₄	1	2	yes	—
174	#126×C₆₁	C₂×C₄	1	2	yes	—
175	#126×C₆₁	C₂×C₄	1	2	yes	—
176	#126×C₆₁	C₂×C₄	1	2	yes	—
177	#126×C₆₁	C₂×C₄	1	2	yes	—
178	#125×C₆₁	C₂×C₄	1	1	yes	characteristic
179	#125×C₆₁	C₂×C₄	1	1	yes	characteristic
180	#125×C₆₁	C₂×C₄	1	2	yes	—
181	#125×C₆₁	C₂×C₄	1	2	yes	—
182	#125×C₆₁	C₂×C₄	1	2	yes	—
183	#124×C₆₁	C₂×C₄	1	2	yes	—
184	#124×C₆₁	C₂×C₄	1	2	yes	—
185	#124×C₆₁	C₂×C₄	1	2	yes	—
186	#123×C₆₁	C₂×C₄	1	2	yes	—
187	#123×C₆₁	C₂×C₄	1	2	yes	—
188	#123×C₆₁	C₂×C₄	1	2	yes	—
189	#123×C₆₁	C₂×C₄	1	2	yes	—
190	#123×C₆₁	C₂×C₄	1	2	yes	—
191	#123×C₆₁	C₂×C₄	1	2	yes	—
192	#123×C₆₁	C₂×C₄	1	2	yes	—
193	#123×C₆₁	C₂×C₄	1	2	yes	—
194	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
197	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
198	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
200	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
202	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
203	#121×C₆₁	C₂×C₄	1	2	yes	—
204	#121×C₆₁	C₂×C₄	1	2	yes	—
205	#121×C₆₁	C₂×C₄	1	2	yes	—
206	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
207	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
208	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
209	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
210	#120×C₆₁	C₂×C₄	1	2	yes	—
211	#120×C₆₁	C₂×C₄	1	2	yes	—
212	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
213	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
214	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
217	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
218	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
219	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
223	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
224	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
225	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
228	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₆₁	C₂³	1	2	yes	—
230	C₄×D₄×C₆₁	C₂³	1	2	yes	—
231	C₄×D₄×C₆₁	C₂³	1	2	yes	—
232	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	2	yes	—
236	#117×C₆₁	C₂×C₄	1	2	yes	—
237	#117×C₆₁	C₂×C₄	1	2	yes	—
238	#117×C₆₁	C₂×C₄	1	2	yes	—
239	#117×C₆₁	C₂×C₄	1	2	yes	—
240	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
241	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
242	#117×C₆₁	C₂×C₄	1	2	yes	—
243	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
244	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
245	#117×C₆₁	C₂³	1	1	yes	characteristic
246	#117×C₆₁	C₂³	1	1	yes	characteristic
247	#117×C₆₁	C₂³	1	1	yes	characteristic
248	#117×C₆₁	C₂³	1	2	yes	—
249	#117×C₆₁	C₂³	1	2	yes	—
250	#117×C₆₁	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
257	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
258	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
260	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
262	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
263	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
265	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
266	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
267	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
268	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
269	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
270	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
271	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
272	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
273	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
275	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
276	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
288	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
289	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
290	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
291	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
292	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
293	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
294	#97×C₆₁	C₂³	1	1	yes	characteristic
295	#97×C₆₁	C₂³	1	1	yes	characteristic
296	#97×C₆₁	C₂³	1	1	yes	characteristic
297	#97×C₆₁	C₂³	1	1	yes	characteristic
298	#97×C₆₁	C₂³	1	2	yes	—
299	#97×C₆₁	C₂³	1	2	yes	—
300	#97×C₆₁	C₂³	1	2	yes	—
301	#97×C₆₁	C₂³	1	2	yes	—
302	#97×C₆₁	C₂³	1	2	yes	—
303	#97×C₆₁	C₂³	1	2	yes	—
304	#97×C₆₁	C₂³	1	2	yes	—
305	#97×C₆₁	C₂³	1	2	yes	—
306	#97×C₆₁	C₂³	1	2	yes	—
307	C₄×C₈×C₆₁	C₂³	1	2	yes	—
308	C₄×C₈×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	2	yes	—
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₄×C₈×C₆₁	C₂³	1	2	yes	—
316	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
317	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
318	#41×C₆₁	—	2	2	no	—
319	#41×C₆₁	—	2	2	no	—
320	#41×C₆₁	—	4	4	no	—
321	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
323	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₆₁	—	4	2	no	—
325	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
327	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
329	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
331	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
335	C₂²×C₄×C₆₁	—	2	2	no	—
336	C₂²×C₄×C₆₁	—	2	2	no	—
337	C₂²×C₄×C₆₁	—	2	2	no	—
338	C₂²×C₄×C₆₁	—	2	2	no	—
339	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
348	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
349	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
350	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
352	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
353	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	M₁₆×C₆₁	—	2	2	no	—
360	M₁₆×C₆₁	—	2	2	no	—
361	M₁₆×C₆₁	—	2	2	no	—
362	M₁₆×C₆₁	—	2	2	no	—
363	M₁₆×C₆₁	—	2	2	no	—
364	M₁₆×C₆₁	—	2	4	no	—
365	M₁₆×C₆₁	—	2	4	no	—
366	M₁₆×C₆₁	—	2	2	no	—
367	M₁₆×C₆₁	—	2	2	no	—
368	M₁₆×C₆₁	—	2	4	no	—
369	M₁₆×C₆₁	—	2	4	no	—
370	M₁₆×C₆₁	#41	1	4	yes	complemented
371	C₂×C₈×C₆₁	—	2	2	no	—
372	C₂×C₈×C₆₁	—	2	2	no	—
373	C₂×C₈×C₆₁	—	2	2	no	—
374	C₂×C₈×C₆₁	—	2	2	no	—
375	C₂×C₈×C₆₁	—	2	2	no	—
376	C₂×C₈×C₆₁	—	2	2	no	—
377	C₂×C₈×C₆₁	—	2	2	no	—
378	C₂×C₈×C₆₁	—	2	4	no	—
379	C₂×C₈×C₆₁	—	2	4	no	—
380	C₂×C₈×C₆₁	—	2	4	no	—
381	C₂×C₈×C₆₁	—	2	4	no	—
382	C₂×C₈×C₆₁	#41	1	4	yes	complemented
383	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
393	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
431	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
433	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
446	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
447	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
448	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
449	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
450	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
451	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
453	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
454	C₄²×C₆₁	C₂⁴	1	2	yes	—
455	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₁	C₂⁴	1	2	yes	—
457	C₄²×C₆₁	C₂⁴	1	2	yes	—
458	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
459	C₂³×C₆₁	—	2	2	no	—
460	C₂³×C₆₁	—	2	2	no	—
461	C₂³×C₆₁	—	2	2	no	—
462	C₂³×C₆₁	—	4	1	no	—
463	C₂³×C₆₁	—	4	1	no	—
464	C₂³×C₆₁	—	4	1	no	—
465	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
466	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
468	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
469	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
470	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
471	Q₈×C₆₁	—	2	2	no	—
472	Q₈×C₆₁	—	4	2	no	—
473	Q₈×C₆₁	—	4	2	no	—
474	D₄×C₆₁	—	2	4	no	—
475	D₄×C₆₁	—	2	2	no	—
476	D₄×C₆₁	—	2	2	no	—
477	D₄×C₆₁	—	2	4	no	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	4	1	no	—
480	D₄×C₆₁	—	4	1	no	—
481	D₄×C₆₁	—	4	2	no	—
482	D₄×C₆₁	—	4	2	no	—
483	D₄×C₆₁	—	4	2	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
485	C₂×C₄×C₆₁	—	2	2	no	—
486	C₂×C₄×C₆₁	—	2	4	no	—
487	C₂×C₄×C₆₁	—	2	2	no	—
488	C₂×C₄×C₆₁	—	2	2	no	—
489	C₂×C₄×C₆₁	—	2	2	no	—
490	C₂×C₄×C₆₁	—	2	2	no	—
491	C₂×C₄×C₆₁	—	2	1	no	—
492	C₂×C₄×C₆₁	—	2	1	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	2	no	—
496	C₂×C₄×C₆₁	—	2	2	no	—
497	C₂×C₄×C₆₁	—	2	1	no	—
498	C₂×C₄×C₆₁	—	2	1	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	4	2	no	—
502	C₂×C₄×C₆₁	—	4	2	no	—
503	C₂×C₄×C₆₁	—	4	2	no	—
504	C₂×C₄×C₆₁	—	4	1	no	—
505	C₂×C₄×C₆₁	—	4	1	no	—
506	C₂×C₄×C₆₁	—	4	2	no	—
507	C₂×C₄×C₆₁	—	4	2	no	—
508	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
509	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
513	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
515	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
517	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
518	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
519	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
520	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
525	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
526	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
527	C₈×C₆₁	—	2	1	no	—
528	C₈×C₆₁	—	2	1	no	—
529	C₈×C₆₁	—	2	1	no	—
530	C₈×C₆₁	—	2	1	no	—
531	C₈×C₆₁	—	2	1	no	—
532	C₈×C₆₁	—	2	1	no	—
533	C₈×C₆₁	—	2	2	no	—
534	C₈×C₆₁	—	2	2	no	—
535	C₈×C₆₁	—	2	2	no	—
536	C₈×C₆₁	C₂×#41	1	2	yes	—
537	C₈×C₆₁	C₂×#41	1	4	yes	—
538	C₈×C₆₁	C₂×#41	1	2	yes	—
539	#60216	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
540	C₂²×C₆₁	—	2	1	no	—
541	C₂²×C₆₁	—	2	1	no	—
542	C₂²×C₆₁	—	2	1	no	—
543	C₂²×C₆₁	—	2	1	no	—
544	C₂²×C₆₁	—	2	1	no	—
545	C₂²×C₆₁	—	2	1	no	—
546	C₂²×C₆₁	—	2	1	no	—
547	C₂²×C₆₁	—	2	2	no	—
548	C₂²×C₆₁	—	2	1	no	—
549	C₂²×C₆₁	—	2	2	no	—
550	C₂²×C₆₁	—	2	1	no	—
551	C₂²×C₆₁	—	2	1	no	—
552	C₂²×C₆₁	—	2	1	no	—
553	C₂²×C₆₁	—	2	2	no	—
554	C₂²×C₆₁	—	2	1	no	—
555	C₂²×C₆₁	—	2	1	no	—
556	C₂²×C₆₁	—	4	4	no	—
557	C₂²×C₆₁	—	8	2	no	—
558	C₂²×C₆₁	C₄×#41	1	2	yes	—
559	C₂²×C₆₁	#568	1	2	yes	—
560	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
561	C₄×C₆₁	—	2	1	no	—
562	C₄×C₆₁	—	2	1	no	—
563	C₄×C₆₁	—	2	1	no	—
564	C₄×C₆₁	—	2	1	no	—
565	C₄×C₆₁	—	2	2	no	—
566	C₄×C₆₁	—	2	2	no	—
567	C₄×C₆₁	—	2	2	no	—
568	C₄×C₆₁	—	2	1	no	—
569	C₄×C₆₁	—	2	1	no	—
570	C₄×C₆₁	—	2	2	no	—
571	C₄×C₆₁	—	2	1	no	—
572	C₄×C₆₁	—	2	2	no	—
573	C₄×C₆₁	—	2	2	no	—
574	C₄×C₆₁	—	2	2	no	—
575	C₄×C₆₁	—	2	1	no	—
576	C₄×C₆₁	C₄×#41	1	2	yes	—
577	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
578	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
579	#3475	C₂×C₆₁	1	1	yes	characteristic
580	#2970	C₂×C₆₁	1	2	yes	complemented
581	#2969	C₂×C₆₁	1	2	yes	complemented
582	#2968	C₂×C₆₁	1	2	yes	complemented
583	#2968	C₂×C₆₁	1	2	yes	complemented
584	#2967	C₂×C₆₁	1	2	yes	complemented
585	#2967	C₂×C₆₁	1	2	yes	complemented
586	#2966	C₂×C₆₁	1	2	yes	complemented
587	#2965	C₂×C₆₁	1	2	yes	complemented
588	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#2961	C₂×C₆₁	1	1	yes	characteristic, complemented
590	D₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#2933	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#2933	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#2930	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#2929	C₂×C₆₁	1	1	yes	characteristic, complemented
595	C₂×#435	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#2925	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#2924	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#2924	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#2875	C₂×C₆₁	1	1	yes	characteristic, complemented
600	#2873	C₂×C₆₁	1	1	yes	characteristic, complemented
601	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
602	C₂×C₆₁	—	2	2	no	—
603	C₂×C₆₁	—	2	2	no	—
604	C₂×C₆₁	—	4	2	no	—
605	C₂×C₆₁	—	4	1	no	—
606	C₂×C₆₁	—	4	1	no	—
607	C₂×C₆₁	—	4	1	no	—
608	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
609	C₂×C₆₁	C₂×#568	1	1	yes	characteristic
610	C₂×C₆₁	#3573	1	1	yes	characteristic
611	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
612	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
613	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
614	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
615	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
616	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
617	#556	C₄×C₆₁	1	1	yes	characteristic
618	#555	C₄×C₆₁	1	1	yes	characteristic
619	#554	C₄×C₆₁	1	1	yes	characteristic
620	#553	C₄×C₆₁	1	1	yes	characteristic
621	#553	C₄×C₆₁	1	1	yes	characteristic
622	#552	C₄×C₆₁	1	1	yes	characteristic
623	#552	C₄×C₆₁	1	1	yes	characteristic
624	#552	C₄×C₆₁	1	2	yes	—
625	#551	C₄×C₆₁	1	2	yes	—
626	#551	C₄×C₆₁	1	2	yes	—
627	#547	C₄×C₆₁	1	1	yes	characteristic
628	#546	C₄×C₆₁	1	2	yes	—
629	#533	C₂²×C₆₁	1	1	yes	characteristic
630	#529	C₂²×C₆₁	1	2	yes	—
631	#529	C₂²×C₆₁	1	2	yes	—
632	#529	C₂²×C₆₁	1	2	yes	—
633	#525	C₂²×C₆₁	1	1	yes	characteristic
634	#525	C₂²×C₆₁	1	1	yes	characteristic
635	C₄×#41	C₂²×C₆₁	1	2	yes	—
636	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
638	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
639	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
640	#446	C₂²×C₆₁	1	2	yes	complemented
641	#446	C₂²×C₆₁	1	2	yes	complemented
642	#446	C₂²×C₆₁	1	2	yes	complemented
643	#446	C₂²×C₆₁	1	2	yes	complemented
644	#446	C₂²×C₆₁	1	2	yes	complemented
645	#446	C₂²×C₆₁	1	2	yes	complemented
646	#446	C₂²×C₆₁	1	2	yes	complemented
647	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
648	#436	C₂²×C₆₁	1	2	yes	—
649	#436	C₂²×C₆₁	1	2	yes	complemented
650	#436	C₂²×C₆₁	1	2	yes	complemented
651	#436	C₂²×C₆₁	1	2	yes	complemented
652	#436	C₂²×C₆₁	1	2	yes	complemented
653	#435	C₂²×C₆₁	1	1	yes	characteristic
654	#435	C₂²×C₆₁	1	1	yes	characteristic
655	#435	C₂²×C₆₁	1	1	yes	characteristic
656	#435	C₂²×C₆₁	1	1	yes	characteristic
657	#435	C₂²×C₆₁	1	1	yes	characteristic
658	#435	C₂²×C₆₁	1	1	yes	characteristic
659	#435	C₂²×C₆₁	1	1	yes	characteristic
660	#435	C₂²×C₆₁	1	1	yes	characteristic
661	#435	C₂²×C₆₁	1	2	yes	—
662	#435	C₂²×C₆₁	1	2	yes	—
663	#435	C₂²×C₆₁	1	2	yes	complemented
664	#435	C₂²×C₆₁	1	2	yes	complemented
665	#435	C₂²×C₆₁	1	2	yes	complemented
666	#435	C₂²×C₆₁	1	2	yes	complemented
667	#435	C₂²×C₆₁	1	2	yes	complemented
668	#435	C₂²×C₆₁	1	2	yes	complemented
669	#435	C₂²×C₆₁	1	2	yes	complemented
670	#435	C₂²×C₆₁	1	2	yes	complemented
671	C₈×D₄	C₂²×C₆₁	1	2	yes	—
672	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
673	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
674	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
675	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
676	#433	C₂²×C₆₁	1	2	yes	complemented
677	#433	C₂²×C₆₁	1	2	yes	complemented
678	#433	C₂²×C₆₁	1	2	yes	complemented
679	#433	C₂²×C₆₁	1	2	yes	complemented
680	#433	C₂²×C₆₁	1	2	yes	complemented
681	#433	C₂²×C₆₁	1	2	yes	complemented
682	#432	C₂²×C₆₁	1	2	yes	complemented
683	#432	C₂²×C₆₁	1	2	yes	complemented
684	#432	C₂²×C₆₁	1	2	yes	complemented
685	#431	C₂²×C₆₁	1	2	yes	complemented
686	#431	C₂²×C₆₁	1	2	yes	complemented
687	#431	C₂²×C₆₁	1	2	yes	complemented
688	#424	C₂²×C₆₁	1	1	yes	characteristic
689	#424	C₂²×C₆₁	1	1	yes	characteristic
690	#424	C₂²×C₆₁	1	1	yes	characteristic
691	#424	C₂²×C₆₁	1	1	yes	characteristic
692	#423	C₂²×C₆₁	1	1	yes	characteristic
693	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
694	#408	C₂²×C₆₁	1	1	yes	characteristic
695	#408	C₂²×C₆₁	1	1	yes	characteristic
696	#407	C₂²×C₆₁	1	1	yes	characteristic
697	#407	C₂²×C₆₁	1	1	yes	characteristic
698	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
699	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
700	#405	C₂²×C₆₁	1	1	yes	characteristic
701	#405	C₂²×C₆₁	1	1	yes	characteristic
702	#405	C₂²×C₆₁	1	1	yes	characteristic
703	#405	C₂²×C₆₁	1	1	yes	characteristic
704	#405	C₂²×C₆₁	1	1	yes	characteristic
705	#405	C₂²×C₆₁	1	1	yes	characteristic
706	#405	C₂²×C₆₁	1	1	yes	characteristic
707	#405	C₂²×C₆₁	1	1	yes	characteristic
708	#405	C₂²×C₆₁	1	2	yes	complemented
709	#405	C₂²×C₆₁	1	2	yes	complemented
710	#405	C₂²×C₆₁	1	2	yes	complemented
711	#405	C₂²×C₆₁	1	2	yes	complemented
712	#405	C₂²×C₆₁	1	2	yes	complemented
713	#405	C₂²×C₆₁	1	2	yes	complemented
714	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
715	C₄×M₁₆	C₂²×C₆₁	1	2	yes	complemented
716	C₄×M₁₆	C₂²×C₆₁	1	2	yes	complemented
717	C₄×M₁₆	C₂²×C₆₁	1	2	yes	complemented
718	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
719	C₂×#97	C₂²×C₆₁	1	2	yes	complemented
720	C₂×#97	C₂²×C₆₁	1	2	yes	complemented
721	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	complemented
722	C₆₁	#60216	1	1	yes	characteristic, direct product factor, Sylow
723	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
724	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
725	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
727	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
728	#131	—	2	4	no	—
729	#131	—	2	4	no	—
730	C₂×M₁₆	—	2	4	no	—
731	C₂×M₁₆	—	2	4	no	—
732	C₂×M₁₆	—	2	4	no	—
733	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
734	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
735	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
741	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
744	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
745	C₂²×C₈	—	2	4	no	—
746	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
752	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
754	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
756	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
757	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
758	C₄⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
759	C₄⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
760	#126	C₂×C₄×C₆₁	1	2	yes	—
761	#126	C₂×C₄×C₆₁	1	2	yes	—
762	#126	C₂×C₄×C₆₁	1	2	yes	—
763	#126	C₂×C₄×C₆₁	1	2	yes	—
764	#126	C₂×C₄×C₆₁	1	2	yes	—
765	#126	C₂×C₄×C₆₁	1	2	yes	—
766	#125	C₂×C₄×C₆₁	1	2	yes	—
767	#125	C₂×C₄×C₆₁	1	2	yes	—
768	#125	C₂×C₄×C₆₁	1	2	yes	—
769	#125	C₂×C₄×C₆₁	1	1	yes	characteristic
770	#125	C₂×C₄×C₆₁	1	1	yes	characteristic
771	#124	C₂×C₄×C₆₁	1	2	yes	—
772	#124	C₂×C₄×C₆₁	1	2	yes	—
773	#124	C₂×C₄×C₆₁	1	2	yes	—
774	#123	C₂×C₄×C₆₁	1	2	yes	—
775	#123	C₂×C₄×C₆₁	1	2	yes	—
776	#123	C₂×C₄×C₆₁	1	2	yes	—
777	#123	C₂×C₄×C₆₁	1	2	yes	—
778	#123	C₂×C₄×C₆₁	1	2	yes	—
779	#123	C₂×C₄×C₆₁	1	2	yes	—
780	#123	C₂×C₄×C₆₁	1	2	yes	—
781	#123	C₂×C₄×C₆₁	1	2	yes	—
782	C₂²⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
787	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
788	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
789	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
790	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
791	#121	C₂×C₄×C₆₁	1	1	yes	characteristic
792	#121	C₂×C₄×C₆₁	1	1	yes	characteristic
793	#121	C₂×C₄×C₆₁	1	1	yes	characteristic
794	#121	C₂×C₄×C₆₁	1	1	yes	characteristic
795	#121	C₂×C₄×C₆₁	1	2	yes	—
796	#121	C₂×C₄×C₆₁	1	2	yes	—
797	#121	C₂×C₄×C₆₁	1	2	yes	—
798	#120	C₂×C₄×C₆₁	1	2	yes	—
799	#120	C₂×C₄×C₆₁	1	2	yes	—
800	C₄×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
801	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
802	C₄×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
805	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
806	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
807	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
808	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
809	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
810	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
811	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
812	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
813	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
814	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
815	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₆₁	1	2	yes	—
821	C₄×D₄	C₂³×C₆₁	1	2	yes	—
822	C₄×D₄	C₂³×C₆₁	1	2	yes	—
823	C₄×D₄	C₂³×C₆₁	1	2	yes	—
824	#117	C₂×C₄×C₆₁	1	2	yes	—
825	#117	C₂×C₄×C₆₁	1	2	yes	—
826	#117	C₂×C₄×C₆₁	1	1	yes	characteristic
827	#117	C₂×C₄×C₆₁	1	1	yes	characteristic
828	#117	C₂×C₄×C₆₁	1	1	yes	characteristic
829	#117	C₂×C₄×C₆₁	1	1	yes	characteristic
830	#117	C₂×C₄×C₆₁	1	2	yes	—
831	#117	C₂×C₄×C₆₁	1	2	yes	—
832	#117	C₂×C₄×C₆₁	1	2	yes	—
833	#117	C₂³×C₆₁	1	1	yes	characteristic
834	#117	C₂³×C₆₁	1	1	yes	characteristic
835	#117	C₂³×C₆₁	1	1	yes	characteristic
836	#117	C₂³×C₆₁	1	2	yes	—
837	#117	C₂³×C₆₁	1	2	yes	—
838	#117	C₂³×C₆₁	1	2	yes	—
839	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
849	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
850	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
882	#97	C₂³×C₆₁	1	1	yes	characteristic
883	#97	C₂³×C₆₁	1	1	yes	characteristic
884	#97	C₂³×C₆₁	1	1	yes	characteristic
885	#97	C₂³×C₆₁	1	1	yes	characteristic
886	#97	C₂³×C₆₁	1	2	yes	—
887	#97	C₂³×C₆₁	1	2	yes	—
888	#97	C₂³×C₆₁	1	2	yes	—
889	#97	C₂³×C₆₁	1	2	yes	—
890	#97	C₂³×C₆₁	1	2	yes	—
891	#97	C₂³×C₆₁	1	2	yes	—
892	#97	C₂³×C₆₁	1	2	yes	—
893	#97	C₂³×C₆₁	1	2	yes	—
894	#97	C₂³×C₆₁	1	2	yes	—
895	C₄×C₈	C₂³×C₆₁	1	2	yes	—
896	C₄×C₈	C₂³×C₆₁	1	2	yes	—
897	C₄×C₈	C₂³×C₆₁	1	2	yes	—
898	C₄×C₈	C₂³×C₆₁	1	2	yes	—
899	C₄×C₈	C₂³×C₆₁	1	2	yes	—
900	C₄×C₈	C₂³×C₆₁	1	2	yes	—
901	C₄×C₈	C₂³×C₆₁	1	2	yes	—
902	C₄×C₈	C₂³×C₆₁	1	2	yes	—
903	C₄×C₈	C₂³×C₆₁	1	2	yes	—
904	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
905	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	4	4	no	—
909	C₂×Q₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
910	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
911	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
914	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
915	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
916	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
917	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
918	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
920	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
921	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
922	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
928	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
929	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
930	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
931	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
932	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
933	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
934	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
935	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
936	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
937	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
938	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	2	2	no	—
952	M₁₆	—	2	4	no	—
953	M₁₆	—	2	4	no	—
954	M₁₆	—	2	2	no	—
955	M₁₆	—	2	2	no	—
956	M₁₆	—	2	4	no	—
957	M₁₆	—	2	4	no	—
958	M₁₆	#41×C₆₁	1	4	yes	complemented
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	—	2	2	no	—
964	C₂×C₈	—	2	2	no	—
965	C₂×C₈	—	2	2	no	—
966	C₂×C₈	—	2	4	no	—
967	C₂×C₈	—	2	4	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	—	2	4	no	—
970	C₂×C₈	#41×C₆₁	1	4	yes	complemented
971	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
977	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
981	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
991	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
992	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
998	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
999	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1000	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1001	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1002	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1003	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1004	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1005	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1006	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1007	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1008	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1009	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1012	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1014	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1019	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1020	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1021	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1022	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1026	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1027	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1028	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1029	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1030	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1031	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1032	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1033	C₂²⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
1034	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
1035	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
1036	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
1037	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
1038	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
1039	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
1040	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
1041	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
1042	C₄²	C₂⁴×C₆₁	1	2	yes	—
1043	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₆₁	1	2	yes	—
1045	C₄²	C₂⁴×C₆₁	1	2	yes	—
1046	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
1054	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
1055	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
1056	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
1057	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
1058	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	4	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	4	no	—
1065	D₄	—	2	4	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	C₂×C₄	—	2	4	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1097	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1098	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1100	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1101	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1102	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1103	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1104	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1105	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1106	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1107	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1108	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1109	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1110	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1111	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
1112	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1113	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1114	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	2	no	—
1124	C₈	C₂×#41×C₆₁	1	2	yes	—
1125	C₈	C₂×#41×C₆₁	1	4	yes	—
1126	C₈	C₂×#41×C₆₁	1	2	yes	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	4	no	—
1144	C₂²	—	8	2	no	—
1145	C₂²	C₄×#41×C₆₁	1	2	yes	—
1146	C₂²	C₆₁×#568	1	2	yes	—
1147	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	C₄×#41×C₆₁	1	2	yes	—
1164	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1165	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	4	2	no	—
1172	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
1173	C₂	C₂×C₆₁×#568	1	1	yes	characteristic
1174	C₂	C₆₁×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂⁴×C₄
prime radical	C₆₁×#3475	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2970	C₂	semidirect
3. C₆₁×#2969	C₂	semidirect
4. C₆₁×#2968	C₂	semidirect
5. C₆₁×#2968	C₂	semidirect
6. C₆₁×#2967	C₂	semidirect
7. C₆₁×#2967	C₂	semidirect
8. C₆₁×#2966	C₂	semidirect
9. C₆₁×#2965	C₂	semidirect
10. C₆₁×#2962	C₂	semidirect
11. C₆₁×#2961	C₂	semidirect
12. D₄×M₁₆×C₆₁	C₂	semidirect
13. C₆₁×#2933	C₂	semidirect
14. C₆₁×#2933	C₂	semidirect
15. C₆₁×#2930	C₂	semidirect
16. C₆₁×#2929	C₂	semidirect
17. C₂×C₆₁×#435	C₂	semidirect
18. C₆₁×#2925	C₂	semidirect
19. C₆₁×#2924	C₂	semidirect
20. C₆₁×#2924	C₂	semidirect
21. C₆₁×#2875	C₂	semidirect
22. C₆₁×#2873	C₂	semidirect
23. C₂×C₆₁×#405	C₂	semidirect
53. C₆₁×#446	C₂²	semidirect
54. C₆₁×#446	C₂²	semidirect
55. C₆₁×#446	C₂²	semidirect
56. C₆₁×#446	C₂²	semidirect
57. C₆₁×#446	C₂²	semidirect
58. C₆₁×#446	C₂²	semidirect
59. C₆₁×#446	C₂²	semidirect
60. C₈×Q₈×C₆₁	C₂²	semidirect
62. C₆₁×#436	C₂²	semidirect
63. C₆₁×#436	C₂²	semidirect
64. C₆₁×#436	C₂²	semidirect
65. C₆₁×#436	C₂²	semidirect
76. C₆₁×#435	C₂²	semidirect
77. C₆₁×#435	C₂²	semidirect
78. C₆₁×#435	C₂²	semidirect
79. C₆₁×#435	C₂²	semidirect
80. C₆₁×#435	C₂²	semidirect
81. C₆₁×#435	C₂²	semidirect
82. C₆₁×#435	C₂²	semidirect
83. C₆₁×#435	C₂²	semidirect
85. C₈×D₄×C₆₁	C₂²	semidirect
86. C₈×D₄×C₆₁	C₂²	semidirect
87. C₈×D₄×C₆₁	C₂²	semidirect
88. C₈×D₄×C₆₁	C₂²	semidirect
89. C₆₁×#433	C₂²	semidirect
90. C₆₁×#433	C₂²	semidirect
91. C₆₁×#433	C₂²	semidirect
92. C₆₁×#433	C₂²	semidirect
93. C₆₁×#433	C₂²	semidirect
94. C₆₁×#433	C₂²	semidirect
95. C₆₁×#432	C₂²	semidirect
96. C₆₁×#432	C₂²	semidirect
97. C₆₁×#432	C₂²	semidirect
98. C₆₁×#431	C₂²	semidirect
99. C₆₁×#431	C₂²	semidirect
100. C₆₁×#431	C₂²	semidirect
121. C₆₁×#405	C₂²	semidirect
122. C₆₁×#405	C₂²	semidirect
123. C₆₁×#405	C₂²	semidirect
124. C₆₁×#405	C₂²	semidirect
125. C₆₁×#405	C₂²	semidirect
126. C₆₁×#405	C₂²	semidirect
128. C₄×M₁₆×C₆₁	C₂²	semidirect
129. C₄×M₁₆×C₆₁	C₂²	semidirect
130. C₄×M₁₆×C₆₁	C₂²	semidirect
132. C₂×#97×C₆₁	C₂²	semidirect
133. C₂×#97×C₆₁	C₂²	semidirect
134. C₂×C₄×C₈×C₆₁	C₂²	semidirect
370. M₁₆×C₆₁	#41	semidirect
382. C₂×C₈×C₆₁	#41	semidirect
539. #60216	C₆₁	direct (N × H)
580. #2970	C₂×C₆₁	semidirect
581. #2969	C₂×C₆₁	semidirect
582. #2968	C₂×C₆₁	semidirect
583. #2968	C₂×C₆₁	semidirect
584. #2967	C₂×C₆₁	semidirect
585. #2967	C₂×C₆₁	semidirect
586. #2966	C₂×C₆₁	semidirect
587. #2965	C₂×C₆₁	semidirect
588. #2962	C₂×C₆₁	semidirect
589. #2961	C₂×C₆₁	semidirect
590. D₄×M₁₆	C₂×C₆₁	semidirect
591. #2933	C₂×C₆₁	semidirect
592. #2933	C₂×C₆₁	semidirect
593. #2930	C₂×C₆₁	semidirect
594. #2929	C₂×C₆₁	semidirect
595. C₂×#435	C₂×C₆₁	semidirect
596. #2925	C₂×C₆₁	semidirect
597. #2924	C₂×C₆₁	semidirect
598. #2924	C₂×C₆₁	semidirect
599. #2875	C₂×C₆₁	semidirect
600. #2873	C₂×C₆₁	semidirect
601. C₂×#405	C₂×C₆₁	semidirect
640. #446	C₂²×C₆₁	semidirect
641. #446	C₂²×C₆₁	semidirect
642. #446	C₂²×C₆₁	semidirect
643. #446	C₂²×C₆₁	semidirect
644. #446	C₂²×C₆₁	semidirect
645. #446	C₂²×C₆₁	semidirect
646. #446	C₂²×C₆₁	semidirect
647. C₈×Q₈	C₂²×C₆₁	semidirect
649. #436	C₂²×C₆₁	semidirect
650. #436	C₂²×C₆₁	semidirect
651. #436	C₂²×C₆₁	semidirect
652. #436	C₂²×C₆₁	semidirect
663. #435	C₂²×C₆₁	semidirect
664. #435	C₂²×C₆₁	semidirect
665. #435	C₂²×C₆₁	semidirect
666. #435	C₂²×C₆₁	semidirect
667. #435	C₂²×C₆₁	semidirect
668. #435	C₂²×C₆₁	semidirect
669. #435	C₂²×C₆₁	semidirect
670. #435	C₂²×C₆₁	semidirect
672. C₈×D₄	C₂²×C₆₁	semidirect
673. C₈×D₄	C₂²×C₆₁	semidirect
674. C₈×D₄	C₂²×C₆₁	semidirect
675. C₈×D₄	C₂²×C₆₁	semidirect
676. #433	C₂²×C₆₁	semidirect
677. #433	C₂²×C₆₁	semidirect
678. #433	C₂²×C₆₁	semidirect
679. #433	C₂²×C₆₁	semidirect
680. #433	C₂²×C₆₁	semidirect
681. #433	C₂²×C₆₁	semidirect
682. #432	C₂²×C₆₁	semidirect
683. #432	C₂²×C₆₁	semidirect
684. #432	C₂²×C₆₁	semidirect
685. #431	C₂²×C₆₁	semidirect
686. #431	C₂²×C₆₁	semidirect
687. #431	C₂²×C₆₁	semidirect
708. #405	C₂²×C₆₁	semidirect
709. #405	C₂²×C₆₁	semidirect
710. #405	C₂²×C₆₁	semidirect
711. #405	C₂²×C₆₁	semidirect
712. #405	C₂²×C₆₁	semidirect
713. #405	C₂²×C₆₁	semidirect
715. C₄×M₁₆	C₂²×C₆₁	semidirect
716. C₄×M₁₆	C₂²×C₆₁	semidirect
717. C₄×M₁₆	C₂²×C₆₁	semidirect
719. C₂×#97	C₂²×C₆₁	semidirect
720. C₂×#97	C₂²×C₆₁	semidirect
721. C₂×C₄×C₈	C₂²×C₆₁	semidirect
722. C₆₁	#60216	direct (N × H)
958. M₁₆	#41×C₆₁	semidirect
970. C₂×C₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3475	2
C₆₁×#2970	2
C₆₁×#2969	2
C₆₁×#2968	2
C₆₁×#2967	2
C₆₁×#2966	2
C₆₁×#2965	2
C₆₁×#2962	2
C₆₁×#2961	2
D₄×M₁₆×C₆₁	2
C₆₁×#2933	2
C₆₁×#2930	2
C₆₁×#2929	2
C₂×C₆₁×#435	2
C₆₁×#2925	2
C₆₁×#2924	2
C₆₁×#2875	2
C₆₁×#2873	2
C₂×C₆₁×#405	2
#60216	61

Subgroups — C61×#60216 #29563649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60216 #29563649