Subgroups — C₆₁×#62021 #29565454

Order 15616.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3369	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3316	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3306	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3298	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3282	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3270	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3263	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3225	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
18	C₂×C₆₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
21	C₂×#135×C₆₁	C₂²	1	2	yes	—
22	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#563	—	2	1	no	—
25	C₆₁×#562	—	2	1	no	—
26	C₆₁×#559	—	2	1	no	—
27	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
28	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	C₂²	1	2	yes	—
30	C₆₁×#554	—	2	1	no	—
31	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#551	—	2	2	no	—
33	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
35	C₆₁×#548	C₂²	1	2	yes	—
36	C₆₁×#548	C₂²	1	2	yes	—
37	C₆₁×#547	—	2	2	no	—
38	C₆₁×#547	C₂²	1	2	yes	—
39	C₆₁×#546	C₂²	1	2	yes	—
40	C₆₁×#543	—	2	1	no	—
41	C₆₁×#542	—	2	2	no	—
42	C₆₁×#542	—	2	2	no	—
43	C₆₁×#542	C₂²	1	2	yes	—
44	C₆₁×#542	C₂²	1	2	yes	complemented
45	C₆₁×#538	—	2	1	no	—
46	C₆₁×#536	C₂²	1	2	yes	—
47	C₆₁×#533	C₂²	1	1	yes	characteristic
48	C₆₁×#532	—	2	1	no	—
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#529	—	2	1	no	—
51	C₆₁×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#497	C₂²	1	2	yes	complemented
56	C₆₁×#496	C₂²	1	2	yes	—
57	C₆₁×#495	C₂²	1	2	yes	—
58	C₆₁×#489	C₂²	1	2	yes	—
59	C₆₁×#489	C₂²	1	2	yes	—
60	C₆₁×#487	C₂²	1	2	yes	complemented
61	C₆₁×#483	C₂²	1	2	yes	—
62	C₆₁×#483	C₂²	1	2	yes	complemented
63	C₆₁×#481	C₂²	1	2	yes	—
64	C₆₁×#476	C₂²	1	2	yes	—
65	C₆₁×#476	C₂²	1	2	yes	complemented
66	C₆₁×#475	C₂²	1	2	yes	complemented
67	C₆₁×#475	C₂²	1	2	yes	complemented
68	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
70	C₆₁×#470	C₂²	1	2	yes	complemented
71	C₆₁×#469	C₂²	1	2	yes	—
72	C₆₁×#465	C₂²	1	2	yes	—
73	C₆₁×#465	C₂²	1	2	yes	—
74	C₆₁×#465	C₂²	1	2	yes	—
75	C₆₁×#465	C₂²	1	2	yes	complemented
76	C₆₁×#464	C₂²	1	2	yes	—
77	C₆₁×#464	C₂²	1	2	yes	—
78	C₆₁×#464	C₂²	1	2	yes	—
79	C₆₁×#464	C₂²	1	2	yes	—
80	C₆₁×#464	C₂²	1	2	yes	—
81	C₆₁×#464	C₂²	1	2	yes	complemented
82	C₆₁×#463	C₂²	1	2	yes	—
83	C₆₁×#463	C₂²	1	2	yes	—
84	C₆₁×#463	C₂²	1	2	yes	—
85	C₆₁×#463	C₂²	1	2	yes	—
86	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#462	C₂²	1	2	yes	complemented
88	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#461	C₂²	1	2	yes	complemented
90	C₆₁×#461	C₂²	1	2	yes	complemented
91	C₆₁×#460	C₂²	1	2	yes	complemented
92	C₆₁×#452	C₂²	1	2	yes	—
93	C₆₁×#452	C₂²	1	2	yes	complemented
94	C₆₁×#451	C₂²	1	2	yes	—
95	C₆₁×#451	C₂²	1	2	yes	complemented
96	C₆₁×#449	C₂²	1	2	yes	—
97	C₆₁×#449	C₂²	1	2	yes	—
98	C₆₁×#448	C₂²	1	2	yes	—
99	C₆₁×#448	C₂²	1	2	yes	complemented
100	C₆₁×#447	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	2	yes	complemented
102	C₆₁×#442	C₂²	1	2	yes	—
103	C₆₁×#441	C₂²	1	2	yes	complemented
104	C₆₁×#441	C₂²	1	2	yes	complemented
105	C₆₁×#441	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
108	C₆₁×#435	C₂²	1	2	yes	—
109	C₆₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₆₁	C₂²	1	2	yes	—
111	C₆₁×#433	C₂²	1	2	yes	complemented
112	C₆₁×#432	C₂²	1	1	yes	characteristic
113	C₆₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
115	C₆₁×#417	C₂²	1	2	yes	—
116	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
117	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
118	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₆₁	—	2	2	no	—
120	C₂×#41×C₆₁	—	2	1	no	—
121	C₂×#41×C₆₁	C₂³	1	2	yes	—
122	C₂×#41×C₆₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
125	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	#137×C₆₁	—	4	4	no	—
128	#135×C₆₁	—	4	4	no	—
129	C₂×Q₁₆×C₆₁	—	4	2	no	—
130	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₆₁	—	4	2	no	—
135	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
141	C₂×D₈×C₆₁	C₂³	1	2	yes	—
142	C₂×D₈×C₆₁	C₂³	1	2	yes	—
143	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₆₁	—	2	1	no	—
148	C₄⋊Q₈×C₆₁	—	2	2	no	—
149	C₄⋊Q₈×C₆₁	—	2	2	no	—
150	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
155	#127×C₆₁	—	2	1	no	—
156	#127×C₆₁	C₂³	1	1	yes	characteristic
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	D₄	1	2	yes	—
162	#125×C₆₁	—	2	1	no	—
163	#125×C₆₁	—	2	1	no	—
164	#125×C₆₁	D₄	1	1	yes	characteristic
165	#124×C₆₁	—	2	1	no	—
166	#124×C₆₁	—	2	2	no	—
167	#124×C₆₁	—	2	2	no	—
168	#124×C₆₁	—	2	2	no	—
169	#124×C₆₁	—	2	2	no	—
170	#124×C₆₁	—	2	1	no	—
171	#124×C₆₁	—	2	1	no	—
172	#124×C₆₁	—	2	1	no	—
173	#124×C₆₁	D₄	1	1	yes	characteristic
174	#124×C₆₁	C₂³	1	2	yes	—
175	#124×C₆₁	C₂³	1	2	yes	—
176	#124×C₆₁	C₂³	1	2	yes	—
177	#124×C₆₁	C₂³	1	2	yes	—
178	#123×C₆₁	—	2	2	no	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	D₄	1	2	yes	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
200	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	—	2	2	no	—
205	#121×C₆₁	—	2	1	no	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	D₄	1	1	yes	characteristic
209	#121×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	C₂³	1	2	yes	—
211	#121×C₆₁	C₂³	1	2	yes	—
212	#120×C₆₁	—	2	2	no	—
213	C₄×Q₈×C₆₁	—	2	1	no	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	—	2	1	no	—
216	C₄×Q₈×C₆₁	—	2	1	no	—
217	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	1	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	2	no	—
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	C₂³	1	2	yes	—
235	C₄×D₄×C₆₁	C₂³	1	2	yes	—
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	2	yes	—
238	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
239	#117×C₆₁	—	2	1	no	—
240	#117×C₆₁	—	2	2	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
245	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
250	C₂×C₄²×C₆₁	—	2	1	no	—
251	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
252	#106×C₆₁	C₂³	1	2	yes	—
253	#106×C₆₁	C₂³	1	2	yes	—
254	#106×C₆₁	C₂³	1	2	yes	—
255	#106×C₆₁	C₂³	1	2	yes	—
256	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
257	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
260	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
261	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
262	#103×C₆₁	C₂³	1	2	yes	—
263	#103×C₆₁	C₂³	1	2	yes	—
264	#103×C₆₁	C₂³	1	2	yes	—
265	#103×C₆₁	C₂³	1	2	yes	—
266	#103×C₆₁	C₂³	1	2	yes	—
267	#103×C₆₁	C₂³	1	2	yes	—
268	#103×C₆₁	C₂³	1	2	yes	—
269	#103×C₆₁	C₂³	1	2	yes	—
270	#103×C₆₁	C₂³	1	2	yes	—
271	#103×C₆₁	C₂³	1	2	yes	—
272	#102×C₆₁	C₂³	1	2	yes	—
273	#102×C₆₁	C₂³	1	2	yes	—
274	#102×C₆₁	C₂³	1	2	yes	—
275	#102×C₆₁	C₂³	1	2	yes	—
276	#102×C₆₁	C₂³	1	2	yes	—
277	#102×C₆₁	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
281	#97×C₆₁	C₂³	1	2	yes	—
282	#97×C₆₁	C₂³	1	2	yes	—
283	C₄×C₈×C₆₁	C₂³	1	2	yes	—
284	C₂⁴×C₆₁	—	2	1	no	—
285	#41×C₆₁	—	2	4	no	—
286	#41×C₆₁	—	4	2	no	—
287	#41×C₆₁	—	4	2	no	—
288	#41×C₆₁	—	4	2	no	—
289	#41×C₆₁	—	8	2	no	—
290	#41×C₆₁	—	8	4	no	—
291	C₂×Q₈×C₆₁	—	2	1	no	—
292	C₂×Q₈×C₆₁	—	2	1	no	—
293	C₂×Q₈×C₆₁	—	2	2	no	—
294	C₂×Q₈×C₆₁	—	2	1	no	—
295	C₂×Q₈×C₆₁	—	2	2	no	—
296	C₂×Q₈×C₆₁	—	2	1	no	—
297	C₂×Q₈×C₆₁	—	2	2	no	—
298	C₂×Q₈×C₆₁	—	4	1	no	—
299	C₂×Q₈×C₆₁	—	4	1	no	—
300	C₂×Q₈×C₆₁	—	4	2	no	—
301	C₂×Q₈×C₆₁	—	4	1	no	—
302	C₂×Q₈×C₆₁	—	4	2	no	—
303	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
307	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
308	C₂×D₄×C₆₁	—	2	2	no	—
309	C₂×D₄×C₆₁	—	2	2	no	—
310	C₂×D₄×C₆₁	—	2	2	no	—
311	C₂×D₄×C₆₁	—	2	2	no	—
312	C₂×D₄×C₆₁	—	2	2	no	—
313	C₂×D₄×C₆₁	—	2	1	no	—
314	C₂×D₄×C₆₁	—	2	1	no	—
315	C₂×D₄×C₆₁	—	2	1	no	—
316	C₂×D₄×C₆₁	—	4	1	no	—
317	C₂×D₄×C₆₁	—	4	1	no	—
318	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
319	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
321	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₁	—	2	1	no	—
323	C₂²×C₄×C₆₁	—	2	1	no	—
324	C₂²×C₄×C₆₁	—	2	1	no	—
325	C₂²×C₄×C₆₁	—	2	2	no	—
326	C₂²×C₄×C₆₁	—	2	2	no	—
327	C₂²×C₄×C₆₁	—	2	2	no	—
328	C₂²×C₄×C₆₁	—	2	2	no	—
329	C₂²×C₄×C₆₁	—	2	2	no	—
330	C₂²×C₄×C₆₁	—	2	2	no	—
331	C₂²×C₄×C₆₁	—	2	2	no	—
332	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
336	Q₁₆×C₆₁	—	2	4	no	—
337	Q₁₆×C₆₁	—	2	4	no	—
338	Q₁₆×C₆₁	—	4	2	no	—
339	Q₁₆×C₆₁	—	4	2	no	—
340	SD₁₆×C₆₁	—	2	4	no	—
341	SD₁₆×C₆₁	—	4	2	no	—
342	SD₁₆×C₆₁	—	4	2	no	—
343	SD₁₆×C₆₁	—	4	2	no	—
344	SD₁₆×C₆₁	—	4	2	no	—
345	SD₁₆×C₆₁	—	4	2	no	—
346	D₈×C₆₁	—	4	2	no	—
347	D₈×C₆₁	—	4	2	no	—
348	M₁₆×C₆₁	—	4	2	no	—
349	C₂×C₈×C₆₁	—	4	1	no	—
350	C₂×C₈×C₆₁	—	4	1	no	—
351	C₂×C₈×C₆₁	—	4	2	no	—
352	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
353	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
354	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
355	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₆₁	—	2	1	no	—
357	C₄⋊C₄×C₆₁	—	2	2	no	—
358	C₄⋊C₄×C₆₁	—	2	2	no	—
359	C₄⋊C₄×C₆₁	—	2	1	no	—
360	C₄⋊C₄×C₆₁	—	2	1	no	—
361	C₄⋊C₄×C₆₁	—	2	1	no	—
362	C₄⋊C₄×C₆₁	—	2	1	no	—
363	C₄⋊C₄×C₆₁	—	2	2	no	—
364	C₄⋊C₄×C₆₁	—	2	1	no	—
365	C₄⋊C₄×C₆₁	—	2	1	no	—
366	C₄⋊C₄×C₆₁	—	2	1	no	—
367	C₄⋊C₄×C₆₁	—	2	2	no	—
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	2	no	—
370	C₄⋊C₄×C₆₁	—	2	2	no	—
371	C₄⋊C₄×C₆₁	—	2	1	no	—
372	C₄⋊C₄×C₆₁	—	2	2	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
385	C₂²⋊C₄×C₆₁	—	2	2	no	—
386	C₂²⋊C₄×C₆₁	—	2	2	no	—
387	C₂²⋊C₄×C₆₁	—	2	2	no	—
388	C₂²⋊C₄×C₆₁	—	2	2	no	—
389	C₂²⋊C₄×C₆₁	—	2	2	no	—
390	C₂²⋊C₄×C₆₁	—	2	2	no	—
391	C₂²⋊C₄×C₆₁	—	2	2	no	—
392	C₂²⋊C₄×C₆₁	—	2	2	no	—
393	C₂²⋊C₄×C₆₁	—	2	2	no	—
394	C₂²⋊C₄×C₆₁	—	2	2	no	—
395	C₂²⋊C₄×C₆₁	—	2	2	no	—
396	C₂²⋊C₄×C₆₁	—	2	2	no	—
397	C₂²⋊C₄×C₆₁	—	2	2	no	—
398	C₂²⋊C₄×C₆₁	—	2	2	no	—
399	C₂²⋊C₄×C₆₁	—	2	2	no	—
400	C₂²⋊C₄×C₆₁	—	2	2	no	—
401	C₂²⋊C₄×C₆₁	—	2	2	no	—
402	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
407	C₄²×C₆₁	—	2	1	no	—
408	C₄²×C₆₁	—	2	1	no	—
409	C₄²×C₆₁	—	2	1	no	—
410	C₄²×C₆₁	—	2	1	no	—
411	C₄²×C₆₁	—	2	2	no	—
412	C₄²×C₆₁	—	2	2	no	—
413	C₄²×C₆₁	—	2	2	no	—
414	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₆₁	C₂⁴	1	2	yes	—
417	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₂³×C₆₁	—	2	2	no	—
420	C₂³×C₆₁	—	2	2	no	—
421	C₂³×C₆₁	—	4	2	no	—
422	C₂³×C₆₁	—	8	1	no	—
423	C₂³×C₆₁	—	8	1	no	—
424	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
425	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
426	Q₈×C₆₁	—	2	1	no	—
427	Q₈×C₆₁	—	2	2	no	—
428	Q₈×C₆₁	—	2	1	no	—
429	Q₈×C₆₁	—	2	2	no	—
430	Q₈×C₆₁	—	2	2	no	—
431	Q₈×C₆₁	—	2	1	no	—
432	Q₈×C₆₁	—	2	2	no	—
433	Q₈×C₆₁	—	4	1	no	—
434	Q₈×C₆₁	—	4	2	no	—
435	Q₈×C₆₁	—	8	1	no	—
436	Q₈×C₆₁	—	8	2	no	—
437	Q₈×C₆₁	—	8	1	no	—
438	Q₈×C₆₁	—	8	1	no	—
439	Q₈×C₆₁	—	8	2	no	—
440	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
441	D₄×C₆₁	—	2	4	no	—
442	D₄×C₆₁	—	2	2	no	—
443	D₄×C₆₁	—	2	2	no	—
444	D₄×C₆₁	—	2	2	no	—
445	D₄×C₆₁	—	2	2	no	—
446	D₄×C₆₁	—	4	1	no	—
447	D₄×C₆₁	—	4	4	no	—
448	D₄×C₆₁	—	4	2	no	—
449	D₄×C₆₁	—	4	4	no	—
450	D₄×C₆₁	—	8	1	no	—
451	D₄×C₆₁	—	8	1	no	—
452	D₄×C₆₁	—	8	2	no	—
453	D₄×C₆₁	—	8	2	no	—
454	D₄×C₆₁	—	8	2	no	—
455	C₂×C₄×C₆₁	—	2	2	no	—
456	C₂×C₄×C₆₁	—	2	1	no	—
457	C₂×C₄×C₆₁	—	2	1	no	—
458	C₂×C₄×C₆₁	—	2	2	no	—
459	C₂×C₄×C₆₁	—	2	1	no	—
460	C₂×C₄×C₆₁	—	2	2	no	—
461	C₂×C₄×C₆₁	—	2	1	no	—
462	C₂×C₄×C₆₁	—	2	2	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	1	no	—
465	C₂×C₄×C₆₁	—	2	2	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	2	2	no	—
468	C₂×C₄×C₆₁	—	4	1	no	—
469	C₂×C₄×C₆₁	—	4	4	no	—
470	C₂×C₄×C₆₁	—	4	2	no	—
471	C₂×C₄×C₆₁	—	4	2	no	—
472	C₂×C₄×C₆₁	—	8	2	no	—
473	C₂×C₄×C₆₁	—	8	2	no	—
474	C₂×C₄×C₆₁	—	8	2	no	—
475	C₂×C₄×C₆₁	—	8	2	no	—
476	C₂×C₄×C₆₁	—	8	2	no	—
477	C₂×C₄×C₆₁	—	8	1	no	—
478	C₂×C₄×C₆₁	—	8	2	no	—
479	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
488	C₈×C₆₁	—	2	2	no	—
489	C₈×C₆₁	—	2	2	no	—
490	C₈×C₆₁	—	2	2	no	—
491	C₈×C₆₁	—	2	2	no	—
492	#62021	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
493	C₂²×C₆₁	—	2	1	no	—
494	C₂²×C₆₁	—	2	1	no	—
495	C₂²×C₆₁	—	2	2	no	—
496	C₂²×C₆₁	—	2	2	no	—
497	C₂²×C₆₁	—	2	2	no	—
498	C₂²×C₆₁	—	4	2	no	—
499	C₂²×C₆₁	—	4	2	no	—
500	C₂²×C₆₁	—	4	2	no	—
501	C₂²×C₆₁	—	4	2	no	—
502	C₂²×C₆₁	—	4	2	no	—
503	C₂²×C₆₁	—	4	2	no	—
504	C₂²×C₆₁	—	16	2	no	—
505	C₂²×C₆₁	#577	1	2	yes	—
506	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
507	C₄×C₆₁	—	2	1	no	—
508	C₄×C₆₁	—	2	1	no	—
509	C₄×C₆₁	—	2	2	no	—
510	C₄×C₆₁	—	2	2	no	—
511	C₄×C₆₁	—	2	1	no	—
512	C₄×C₆₁	—	2	2	no	—
513	C₄×C₆₁	—	2	1	no	—
514	C₄×C₆₁	—	2	1	no	—
515	C₄×C₆₁	—	2	2	no	—
516	C₄×C₆₁	—	4	2	no	—
517	C₄×C₆₁	—	4	1	no	—
518	C₄×C₆₁	—	4	2	no	—
519	C₄×C₆₁	—	4	2	no	—
520	C₄×C₆₁	—	4	1	no	—
521	C₄×C₆₁	—	4	1	no	—
522	C₄×C₆₁	—	4	2	no	—
523	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₄×C₆₁	#585	1	1	yes	characteristic
525	#3561	C₂×C₆₁	1	1	yes	characteristic, complemented
526	#3522	C₂×C₆₁	1	1	yes	characteristic, complemented
527	#3401	C₂×C₆₁	1	2	yes	complemented
528	#3369	C₂×C₆₁	1	2	yes	complemented
529	#3316	C₂×C₆₁	1	2	yes	complemented
530	#3306	C₂×C₆₁	1	2	yes	complemented
531	#3298	C₂×C₆₁	1	2	yes	complemented
532	#3282	C₂×C₆₁	1	2	yes	complemented
533	#3271	C₂×C₆₁	1	2	yes	complemented
534	#3270	C₂×C₆₁	1	2	yes	complemented
535	#3263	C₂×C₆₁	1	2	yes	complemented
536	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
537	#3225	C₂×C₆₁	1	2	yes	complemented
538	#3213	C₂×C₆₁	1	1	yes	characteristic, complemented
539	#3125	C₂×C₆₁	1	2	yes	complemented
540	#3113	C₂×C₆₁	1	1	yes	characteristic, complemented
541	#3046	C₂×C₆₁	1	2	yes	complemented
542	C₂×#464	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#2992	C₂×C₆₁	1	1	yes	characteristic, complemented
544	C₂×C₆₁	—	2	2	no	—
545	C₂×C₆₁	—	4	2	no	—
546	C₂×C₆₁	—	8	2	no	—
547	C₂×C₆₁	—	8	2	no	—
548	C₂×C₆₁	#3488	1	1	yes	characteristic
549	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
550	C₂×C₆₁	#3586	1	1	yes	characteristic
551	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
552	C₂×#135	C₂²×C₆₁	1	2	yes	—
553	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
554	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
555	#563	—	2	1	no	—
556	#562	—	2	1	no	—
557	#559	—	2	1	no	—
558	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
559	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
560	#556	C₂²×C₆₁	1	2	yes	—
561	#554	—	2	1	no	—
562	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
563	#551	—	2	2	no	—
564	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
565	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
566	#548	C₂²×C₆₁	1	2	yes	—
567	#548	C₂²×C₆₁	1	2	yes	—
568	#547	—	2	2	no	—
569	#547	C₂²×C₆₁	1	2	yes	—
570	#546	C₂²×C₆₁	1	2	yes	—
571	#543	—	2	1	no	—
572	#542	—	2	2	no	—
573	#542	—	2	2	no	—
574	#542	C₂²×C₆₁	1	2	yes	—
575	#542	C₂²×C₆₁	1	2	yes	complemented
576	#538	—	2	1	no	—
577	#536	C₂²×C₆₁	1	2	yes	—
578	#533	C₂²×C₆₁	1	1	yes	characteristic
579	#532	—	2	1	no	—
580	#532	C₂²×C₆₁	1	1	yes	characteristic
581	#529	—	2	1	no	—
582	#529	C₂²×C₆₁	1	1	yes	characteristic
583	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
584	#520	C₂²×C₆₁	1	2	yes	complemented
585	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
586	#497	C₂²×C₆₁	1	2	yes	complemented
587	#496	C₂²×C₆₁	1	2	yes	—
588	#495	C₂²×C₆₁	1	2	yes	—
589	#489	C₂²×C₆₁	1	2	yes	—
590	#489	C₂²×C₆₁	1	2	yes	—
591	#487	C₂²×C₆₁	1	2	yes	complemented
592	#483	C₂²×C₆₁	1	2	yes	—
593	#483	C₂²×C₆₁	1	2	yes	complemented
594	#481	C₂²×C₆₁	1	2	yes	—
595	#476	C₂²×C₆₁	1	2	yes	—
596	#476	C₂²×C₆₁	1	2	yes	complemented
597	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
598	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
599	#475	C₂²×C₆₁	1	2	yes	complemented
600	#475	C₂²×C₆₁	1	2	yes	complemented
601	#470	C₂²×C₆₁	1	2	yes	complemented
602	#469	C₂²×C₆₁	1	2	yes	—
603	#465	C₂²×C₆₁	1	2	yes	—
604	#465	C₂²×C₆₁	1	2	yes	—
605	#465	C₂²×C₆₁	1	2	yes	—
606	#465	C₂²×C₆₁	1	2	yes	complemented
607	#464	C₂²×C₆₁	1	2	yes	—
608	#464	C₂²×C₆₁	1	2	yes	—
609	#464	C₂²×C₆₁	1	2	yes	—
610	#464	C₂²×C₆₁	1	2	yes	—
611	#464	C₂²×C₆₁	1	2	yes	—
612	#464	C₂²×C₆₁	1	2	yes	complemented
613	#463	C₂²×C₆₁	1	2	yes	—
614	#463	C₂²×C₆₁	1	2	yes	—
615	#463	C₂²×C₆₁	1	2	yes	—
616	#463	C₂²×C₆₁	1	2	yes	—
617	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
619	#462	C₂²×C₆₁	1	2	yes	complemented
620	#461	C₂²×C₆₁	1	2	yes	complemented
621	#461	C₂²×C₆₁	1	2	yes	complemented
622	#460	C₂²×C₆₁	1	2	yes	complemented
623	#452	C₂²×C₆₁	1	2	yes	—
624	#452	C₂²×C₆₁	1	2	yes	complemented
625	#451	C₂²×C₆₁	1	2	yes	—
626	#451	C₂²×C₆₁	1	2	yes	complemented
627	#449	C₂²×C₆₁	1	2	yes	—
628	#449	C₂²×C₆₁	1	2	yes	—
629	#448	C₂²×C₆₁	1	2	yes	—
630	#448	C₂²×C₆₁	1	2	yes	complemented
631	#447	C₂²×C₆₁	1	2	yes	—
632	#446	C₂²×C₆₁	1	2	yes	complemented
633	#442	C₂²×C₆₁	1	2	yes	—
634	#441	C₂²×C₆₁	1	2	yes	complemented
635	#441	C₂²×C₆₁	1	2	yes	complemented
636	#441	C₂²×C₆₁	1	2	yes	complemented
637	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
638	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
639	#435	C₂²×C₆₁	1	2	yes	—
640	#435	C₂²×C₆₁	1	2	yes	complemented
641	C₈×D₄	C₂²×C₆₁	1	2	yes	—
642	#433	C₂²×C₆₁	1	2	yes	complemented
643	#432	C₂²×C₆₁	1	1	yes	characteristic
644	#424	C₂²×C₆₁	1	2	yes	complemented
645	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
646	#417	C₂²×C₆₁	1	2	yes	—
647	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
648	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
649	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
650	C₆₁	#62021	1	1	yes	characteristic, direct product factor, Sylow
651	C₂×#41	—	2	2	no	—
652	C₂×#41	—	2	1	no	—
653	C₂×#41	C₂³×C₆₁	1	2	yes	—
654	C₂×#41	C₂³×C₆₁	1	2	yes	—
655	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
656	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
657	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
658	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
659	#137	—	4	4	no	—
660	#135	—	4	4	no	—
661	C₂×Q₁₆	—	4	2	no	—
662	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
666	C₂×SD₁₆	—	4	2	no	—
667	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
671	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
673	C₂×D₈	C₂³×C₆₁	1	2	yes	—
674	C₂×D₈	C₂³×C₆₁	1	2	yes	—
675	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
676	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
678	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
683	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
684	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
687	#127	—	2	1	no	—
688	#127	C₂³×C₆₁	1	1	yes	characteristic
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	D₄×C₆₁	1	2	yes	—
694	#125	—	2	1	no	—
695	#125	—	2	1	no	—
696	#125	D₄×C₆₁	1	1	yes	characteristic
697	#124	—	2	1	no	—
698	#124	—	2	2	no	—
699	#124	—	2	2	no	—
700	#124	—	2	2	no	—
701	#124	—	2	2	no	—
702	#124	—	2	1	no	—
703	#124	—	2	1	no	—
704	#124	—	2	1	no	—
705	#124	D₄×C₆₁	1	1	yes	characteristic
706	#124	C₂³×C₆₁	1	2	yes	—
707	#124	C₂³×C₆₁	1	2	yes	—
708	#124	C₂³×C₆₁	1	2	yes	—
709	#124	C₂³×C₆₁	1	2	yes	—
710	#123	—	2	2	no	—
711	#123	—	2	2	no	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	D₄×C₆₁	1	2	yes	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
732	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	1	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	D₄×C₆₁	1	1	yes	characteristic
741	#121	C₂³×C₆₁	1	2	yes	—
742	#121	C₂³×C₆₁	1	2	yes	—
743	#121	C₂³×C₆₁	1	2	yes	—
744	#120	—	2	2	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
753	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
754	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
755	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
756	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	C₂³×C₆₁	1	2	yes	—
767	C₄×D₄	C₂³×C₆₁	1	2	yes	—
768	C₄×D₄	C₂³×C₆₁	1	2	yes	—
769	C₄×D₄	C₂³×C₆₁	1	2	yes	—
770	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
771	#117	—	2	1	no	—
772	#117	—	2	2	no	—
773	#117	—	2	2	no	—
774	#117	C₂³×C₆₁	1	2	yes	—
775	C₂×C₄⋊C₄	—	2	1	no	—
776	C₂×C₄⋊C₄	—	2	2	no	—
777	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
779	C₂×C₂²⋊C₄	—	2	1	no	—
780	C₂×C₂²⋊C₄	—	2	1	no	—
781	C₂×C₂²⋊C₄	—	2	2	no	—
782	C₂×C₄²	—	2	1	no	—
783	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
784	#106	C₂³×C₆₁	1	2	yes	—
785	#106	C₂³×C₆₁	1	2	yes	—
786	#106	C₂³×C₆₁	1	2	yes	—
787	#106	C₂³×C₆₁	1	2	yes	—
788	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
789	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
790	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
791	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
792	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
793	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
794	#103	C₂³×C₆₁	1	2	yes	—
795	#103	C₂³×C₆₁	1	2	yes	—
796	#103	C₂³×C₆₁	1	2	yes	—
797	#103	C₂³×C₆₁	1	2	yes	—
798	#103	C₂³×C₆₁	1	2	yes	—
799	#103	C₂³×C₆₁	1	2	yes	—
800	#103	C₂³×C₆₁	1	2	yes	—
801	#103	C₂³×C₆₁	1	2	yes	—
802	#103	C₂³×C₆₁	1	2	yes	—
803	#103	C₂³×C₆₁	1	2	yes	—
804	#102	C₂³×C₆₁	1	2	yes	—
805	#102	C₂³×C₆₁	1	2	yes	—
806	#102	C₂³×C₆₁	1	2	yes	—
807	#102	C₂³×C₆₁	1	2	yes	—
808	#102	C₂³×C₆₁	1	2	yes	—
809	#102	C₂³×C₆₁	1	2	yes	—
810	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
811	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
813	#97	C₂³×C₆₁	1	2	yes	—
814	#97	C₂³×C₆₁	1	2	yes	—
815	C₄×C₈	C₂³×C₆₁	1	2	yes	—
816	C₂⁴	—	2	1	no	—
817	#41	—	2	4	no	—
818	#41	—	4	2	no	—
819	#41	—	4	2	no	—
820	#41	—	4	2	no	—
821	#41	—	8	2	no	—
822	#41	—	8	4	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	2	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	4	1	no	—
831	C₂×Q₈	—	4	1	no	—
832	C₂×Q₈	—	4	2	no	—
833	C₂×Q₈	—	4	1	no	—
834	C₂×Q₈	—	4	2	no	—
835	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
836	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
837	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
838	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
839	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	4	1	no	—
849	C₂×D₄	—	4	1	no	—
850	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
851	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
852	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
853	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
865	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
868	Q₁₆	—	2	4	no	—
869	Q₁₆	—	2	4	no	—
870	Q₁₆	—	4	2	no	—
871	Q₁₆	—	4	2	no	—
872	SD₁₆	—	2	4	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	SD₁₆	—	4	2	no	—
876	SD₁₆	—	4	2	no	—
877	SD₁₆	—	4	2	no	—
878	D₈	—	4	2	no	—
879	D₈	—	4	2	no	—
880	M₁₆	—	4	2	no	—
881	C₂×C₈	—	4	1	no	—
882	C₂×C₈	—	4	1	no	—
883	C₂×C₈	—	4	2	no	—
884	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
885	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
886	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
887	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
908	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
909	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
910	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
914	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
915	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
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	—	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	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
935	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
936	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
937	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
938	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
947	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
948	C₄²	C₂⁴×C₆₁	1	2	yes	—
949	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	4	2	no	—
954	C₂³	—	8	1	no	—
955	C₂³	—	8	1	no	—
956	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
957	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
958	Q₈	—	2	1	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	2	1	no	—
961	Q₈	—	2	2	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	1	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	4	1	no	—
966	Q₈	—	4	2	no	—
967	Q₈	—	8	1	no	—
968	Q₈	—	8	2	no	—
969	Q₈	—	8	1	no	—
970	Q₈	—	8	1	no	—
971	Q₈	—	8	2	no	—
972	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
973	D₄	—	2	4	no	—
974	D₄	—	2	2	no	—
975	D₄	—	2	2	no	—
976	D₄	—	2	2	no	—
977	D₄	—	2	2	no	—
978	D₄	—	4	1	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	2	no	—
981	D₄	—	4	4	no	—
982	D₄	—	8	1	no	—
983	D₄	—	8	1	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	D₄	—	8	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	4	1	no	—
1001	C₂×C₄	—	4	4	no	—
1002	C₂×C₄	—	4	2	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	8	2	no	—
1005	C₂×C₄	—	8	2	no	—
1006	C₂×C₄	—	8	2	no	—
1007	C₂×C₄	—	8	2	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	1	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1012	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1014	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1015	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1019	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1020	C₈	—	2	2	no	—
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	2	2	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	16	2	no	—
1036	C₂²	C₆₁×#577	1	2	yes	—
1037	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1055	C₄	C₆₁×#585	1	1	yes	characteristic
1056	C₂	—	2	2	no	—
1057	C₂	—	4	2	no	—
1058	C₂	—	8	2	no	—
1059	C₂	—	8	2	no	—
1060	C₂	C₆₁×#3488	1	1	yes	characteristic
1061	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1062	C₂	C₆₁×#3586	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×#3561	C₂	semidirect
2. C₆₁×#3522	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3369	C₂	semidirect
5. C₆₁×#3316	C₂	semidirect
6. C₆₁×#3306	C₂	semidirect
7. C₆₁×#3298	C₂	semidirect
8. C₆₁×#3282	C₂	semidirect
9. C₆₁×#3271	C₂	semidirect
10. C₆₁×#3270	C₂	semidirect
11. C₆₁×#3263	C₂	semidirect
12. C₆₁×#3246	C₂	semidirect
13. C₆₁×#3225	C₂	semidirect
14. C₆₁×#3213	C₂	semidirect
15. C₆₁×#3125	C₂	semidirect
16. C₆₁×#3113	C₂	semidirect
17. C₆₁×#3046	C₂	semidirect
18. C₂×C₆₁×#464	C₂	semidirect
19. C₆₁×#2992	C₂	semidirect
20. C₂×#137×C₆₁	C₂²	semidirect
27. C₆₁×#559	C₂²	semidirect
28. Q₈²×C₆₁	C₂²	semidirect
31. C₆₁×#554	C₂²	semidirect
33. C₆₁×#550	C₂²	semidirect
44. C₆₁×#542	C₂²	semidirect
53. C₆₁×#520	C₂²	semidirect
55. C₆₁×#497	C₂²	semidirect
60. C₆₁×#487	C₂²	semidirect
62. C₆₁×#483	C₂²	semidirect
65. C₆₁×#476	C₂²	semidirect
66. C₆₁×#475	C₂²	semidirect
67. C₆₁×#475	C₂²	semidirect
68. C₆₁×#475	C₂²	semidirect
69. C₆₁×#475	C₂²	semidirect
70. C₆₁×#470	C₂²	semidirect
75. C₆₁×#465	C₂²	semidirect
81. C₆₁×#464	C₂²	semidirect
86. C₆₁×#462	C₂²	semidirect
87. C₆₁×#462	C₂²	semidirect
88. C₆₁×#462	C₂²	semidirect
89. C₆₁×#461	C₂²	semidirect
90. C₆₁×#461	C₂²	semidirect
91. C₆₁×#460	C₂²	semidirect
93. C₆₁×#452	C₂²	semidirect
95. C₆₁×#451	C₂²	semidirect
99. C₆₁×#448	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
103. C₆₁×#441	C₂²	semidirect
104. C₆₁×#441	C₂²	semidirect
105. C₆₁×#441	C₂²	semidirect
107. C₄×SD₁₆×C₆₁	C₂²	semidirect
109. C₆₁×#435	C₂²	semidirect
111. C₆₁×#433	C₂²	semidirect
113. C₆₁×#424	C₂²	semidirect
117. C₂×#103×C₆₁	C₂²	semidirect
492. #62021	C₆₁	direct (N × H)
525. #3561	C₂×C₆₁	semidirect
526. #3522	C₂×C₆₁	semidirect
527. #3401	C₂×C₆₁	semidirect
528. #3369	C₂×C₆₁	semidirect
529. #3316	C₂×C₆₁	semidirect
530. #3306	C₂×C₆₁	semidirect
531. #3298	C₂×C₆₁	semidirect
532. #3282	C₂×C₆₁	semidirect
533. #3271	C₂×C₆₁	semidirect
534. #3270	C₂×C₆₁	semidirect
535. #3263	C₂×C₆₁	semidirect
536. #3246	C₂×C₆₁	semidirect
537. #3225	C₂×C₆₁	semidirect
538. #3213	C₂×C₆₁	semidirect
539. #3125	C₂×C₆₁	semidirect
540. #3113	C₂×C₆₁	semidirect
541. #3046	C₂×C₆₁	semidirect
542. C₂×#464	C₂×C₆₁	semidirect
543. #2992	C₂×C₆₁	semidirect
551. C₂×#137	C₂²×C₆₁	semidirect
558. #559	C₂²×C₆₁	semidirect
559. Q₈²	C₂²×C₆₁	semidirect
562. #554	C₂²×C₆₁	semidirect
564. #550	C₂²×C₆₁	semidirect
575. #542	C₂²×C₆₁	semidirect
584. #520	C₂²×C₆₁	semidirect
586. #497	C₂²×C₆₁	semidirect
591. #487	C₂²×C₆₁	semidirect
593. #483	C₂²×C₆₁	semidirect
596. #476	C₂²×C₆₁	semidirect
597. #475	C₂²×C₆₁	semidirect
598. #475	C₂²×C₆₁	semidirect
599. #475	C₂²×C₆₁	semidirect
600. #475	C₂²×C₆₁	semidirect
601. #470	C₂²×C₆₁	semidirect
606. #465	C₂²×C₆₁	semidirect
612. #464	C₂²×C₆₁	semidirect
617. #462	C₂²×C₆₁	semidirect
618. #462	C₂²×C₆₁	semidirect
619. #462	C₂²×C₆₁	semidirect
620. #461	C₂²×C₆₁	semidirect
621. #461	C₂²×C₆₁	semidirect
622. #460	C₂²×C₆₁	semidirect
624. #452	C₂²×C₆₁	semidirect
626. #451	C₂²×C₆₁	semidirect
630. #448	C₂²×C₆₁	semidirect
632. #446	C₂²×C₆₁	semidirect
634. #441	C₂²×C₆₁	semidirect
635. #441	C₂²×C₆₁	semidirect
636. #441	C₂²×C₆₁	semidirect
638. C₄×SD₁₆	C₂²×C₆₁	semidirect
640. #435	C₂²×C₆₁	semidirect
642. #433	C₂²×C₆₁	semidirect
644. #424	C₂²×C₆₁	semidirect
648. C₂×#103	C₂²×C₆₁	semidirect
650. C₆₁	#62021	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×#3561	2
C₆₁×#3522	2
C₆₁×#3401	2
C₆₁×#3369	2
C₆₁×#3316	2
C₆₁×#3306	2
C₆₁×#3298	2
C₆₁×#3282	2
C₆₁×#3271	2
C₆₁×#3270	2
C₆₁×#3263	2
C₆₁×#3246	2
C₆₁×#3225	2
C₆₁×#3213	2
C₆₁×#3125	2
C₆₁×#3113	2
C₆₁×#3046	2
C₂×C₆₁×#464	2
C₆₁×#2992	2
#62021	61

Subgroups — C61×#62021 #29565454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62021 #29565454