Subgroups — C₆₁×#62110 #29565543

Order 15616.

2030 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3384	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3345	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3318	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3253	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3235	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3109	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3077	C₂	1	2	yes	maximal, complemented
16	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₁	—	2	1	no	—
19	C₆₁×#556	—	2	1	no	—
20	C₆₁×#555	C₂²	1	2	yes	complemented
21	C₆₁×#554	C₂²	1	2	yes	complemented
22	C₆₁×#553	C₂²	1	4	yes	complemented
23	C₆₁×#550	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#548	—	2	1	no	—
26	C₆₁×#548	—	2	2	no	—
27	C₆₁×#547	—	2	1	no	—
28	C₆₁×#547	C₂²	1	2	yes	—
29	C₆₁×#547	C₂²	1	1	yes	characteristic
30	C₆₁×#546	—	2	1	no	—
31	C₆₁×#546	—	2	2	no	—
32	D₄²×C₆₁	C₂²	1	2	yes	—
33	D₄²×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#542	—	2	2	no	—
35	C₆₁×#537	—	2	1	no	—
36	C₆₁×#533	C₂²	1	2	yes	complemented
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#532	C₂²	1	2	yes	—
39	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#532	C₂²	1	2	yes	complemented
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#525	—	2	2	no	—
43	C₆₁×#525	—	2	1	no	—
44	C₆₁×#520	—	2	1	no	—
45	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
48	C₆₁×#501	C₂²	1	4	yes	complemented
49	C₆₁×#498	C₂²	1	2	yes	complemented
50	C₆₁×#490	C₂²	1	4	yes	complemented
51	C₆₁×#486	C₂²	1	2	yes	complemented
52	C₆₁×#482	C₂²	1	4	yes	complemented
53	C₆₁×#482	C₂²	1	4	yes	complemented
54	C₆₁×#481	C₂²	1	4	yes	complemented
55	C₆₁×#481	C₂²	1	4	yes	complemented
56	C₆₁×#480	C₂²	1	2	yes	complemented
57	C₆₁×#478	C₂²	1	4	yes	—
58	C₆₁×#478	C₂²	1	4	yes	complemented
59	C₆₁×#476	C₂²	1	2	yes	—
60	C₆₁×#476	C₂²	1	2	yes	—
61	C₆₁×#476	C₂²	1	2	yes	complemented
62	C₆₁×#476	C₂²	1	2	yes	complemented
63	C₆₁×#476	C₂²	1	2	yes	complemented
64	C₆₁×#476	C₂²	1	4	yes	complemented
65	C₆₁×#476	C₂²	1	2	yes	complemented
66	C₆₁×#474	C₂²	1	1	yes	characteristic
67	C₆₁×#474	C₂²	1	2	yes	complemented
68	C₆₁×#474	C₂²	1	2	yes	complemented
69	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
70	C₆₁×#469	C₂²	1	4	yes	complemented
71	C₆₁×#469	C₂²	1	4	yes	complemented
72	C₆₁×#466	C₂²	1	4	yes	complemented
73	C₆₁×#459	C₂²	1	1	yes	characteristic
74	C₆₁×#459	C₂²	1	4	yes	complemented
75	C₆₁×#459	C₂²	1	2	yes	complemented
76	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#459	C₂²	1	2	yes	complemented
78	C₆₁×#447	C₂²	1	2	yes	—
79	C₆₁×#447	C₂²	1	4	yes	—
80	C₆₁×#446	C₂²	1	2	yes	complemented
81	C₆₁×#442	C₂²	1	4	yes	—
82	C₆₁×#442	C₂²	1	4	yes	complemented
83	C₄×D₈×C₆₁	C₂²	1	2	yes	—
84	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
85	C₆₁×#436	C₂²	1	2	yes	complemented
86	C₆₁×#435	C₂²	1	4	yes	complemented
87	C₆₁×#432	C₂²	1	2	yes	complemented
88	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#428	C₂²	1	4	yes	complemented
90	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
91	C₆₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#418	C₂²	1	4	yes	—
94	C₂×#102×C₆₁	C₂²	1	2	yes	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	—	2	2	no	—
97	C₂×#41×C₆₁	—	2	1	no	—
98	C₂×#41×C₆₁	—	2	2	no	—
99	C₂×#41×C₆₁	—	2	1	no	—
100	C₂×#41×C₆₁	—	2	1	no	—
101	C₂×#41×C₆₁	—	2	2	no	—
102	C₂×#41×C₆₁	—	4	8	no	—
103	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
104	C₂²×Q₈×C₆₁	—	2	1	no	—
105	C₂²×Q₈×C₆₁	—	2	1	no	—
106	C₂²×D₄×C₆₁	—	2	2	no	—
107	C₂²×D₄×C₆₁	—	2	1	no	—
108	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
110	C₂³×C₄×C₆₁	—	2	2	no	—
111	C₂³×C₄×C₆₁	—	2	1	no	—
112	C₂×D₈×C₆₁	C₂³	1	2	yes	—
113	C₂×D₈×C₆₁	C₂³	1	2	yes	—
114	C₂×D₈×C₆₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
116	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₆₁	—	2	1	no	—
118	C₄⋊Q₈×C₆₁	—	2	1	no	—
119	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
123	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	#127×C₆₁	C₂³	1	1	yes	characteristic
125	#127×C₆₁	C₂³	1	2	yes	—
126	#127×C₆₁	C₂³	1	1	yes	characteristic
127	#126×C₆₁	—	2	4	no	—
128	#125×C₆₁	C₂³	1	4	yes	—
129	#124×C₆₁	—	2	4	no	—
130	#124×C₆₁	—	2	1	no	—
131	#124×C₆₁	—	2	2	no	—
132	#124×C₆₁	—	2	1	no	—
133	#124×C₆₁	—	2	2	no	—
134	#123×C₆₁	—	2	4	no	—
135	#123×C₆₁	—	2	2	no	—
136	#123×C₆₁	—	2	2	no	—
137	#123×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	—	2	2	no	—
141	C₂²⋊Q₈×C₆₁	—	2	4	no	—
142	C₂²⋊Q₈×C₆₁	—	2	1	no	—
143	C₂²⋊Q₈×C₆₁	—	2	2	no	—
144	C₂²⋊Q₈×C₆₁	—	2	1	no	—
145	C₂²⋊Q₈×C₆₁	—	2	2	no	—
146	#121×C₆₁	—	2	2	no	—
147	#121×C₆₁	—	2	4	no	—
148	#121×C₆₁	—	2	1	no	—
149	#121×C₆₁	—	2	2	no	—
150	#121×C₆₁	—	2	2	no	—
151	#121×C₆₁	—	2	1	no	—
152	#121×C₆₁	—	2	1	no	—
153	#121×C₆₁	—	2	2	no	—
154	#121×C₆₁	—	2	1	no	—
155	#121×C₆₁	—	2	2	no	—
156	#121×C₆₁	C₂³	1	2	yes	—
157	#121×C₆₁	C₂³	1	2	yes	—
158	#121×C₆₁	C₂³	1	2	yes	—
159	#121×C₆₁	C₂³	1	2	yes	—
160	#121×C₆₁	C₂³	1	4	yes	—
161	#120×C₆₁	—	2	2	no	—
162	#120×C₆₁	—	2	2	no	—
163	#120×C₆₁	—	2	2	no	—
164	C₄×Q₈×C₆₁	—	2	2	no	—
165	C₄×Q₈×C₆₁	—	2	2	no	—
166	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₁	—	2	4	no	—
169	C₄×D₄×C₆₁	—	2	2	no	—
170	C₄×D₄×C₆₁	—	2	1	no	—
171	C₄×D₄×C₆₁	—	2	2	no	—
172	C₄×D₄×C₆₁	—	2	1	no	—
173	C₄×D₄×C₆₁	—	2	1	no	—
174	C₄×D₄×C₆₁	—	2	2	no	—
175	C₄×D₄×C₆₁	—	2	2	no	—
176	C₄×D₄×C₆₁	—	2	1	no	—
177	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
178	C₄×D₄×C₆₁	D₄	1	2	yes	—
179	C₄×D₄×C₆₁	C₂³	1	2	yes	—
180	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₆₁	C₂³	1	4	yes	—
182	C₄×D₄×C₆₁	C₂³	1	2	yes	—
183	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₆₁	C₂³	1	2	yes	—
185	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₆₁	C₂³	1	2	yes	—
187	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₆₁	C₂³	1	2	yes	—
189	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
190	#117×C₆₁	—	2	2	no	—
191	#117×C₆₁	D₄	1	2	yes	—
192	#117×C₆₁	D₄	1	1	yes	characteristic
193	#117×C₆₁	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
201	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
203	#107×C₆₁	C₂³	1	2	yes	—
204	#107×C₆₁	C₂³	1	4	yes	—
205	#107×C₆₁	C₂³	1	2	yes	—
206	#106×C₆₁	C₂³	1	4	yes	—
207	#106×C₆₁	C₂³	1	4	yes	—
208	#106×C₆₁	C₂³	1	4	yes	—
209	#106×C₆₁	C₂³	1	4	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
214	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
215	#102×C₆₁	C₂³	1	4	yes	—
216	#102×C₆₁	C₂³	1	4	yes	—
217	#102×C₆₁	C₂³	1	2	yes	—
218	#102×C₆₁	C₂³	1	4	yes	—
219	#102×C₆₁	C₂³	1	4	yes	—
220	#102×C₆₁	C₂³	1	2	yes	—
221	#102×C₆₁	C₂³	1	2	yes	—
222	#102×C₆₁	C₂³	1	2	yes	—
223	#102×C₆₁	C₂³	1	4	yes	—
224	#102×C₆₁	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
227	#97×C₆₁	C₂³	1	4	yes	—
228	C₄×C₈×C₆₁	C₂³	1	2	yes	—
229	C₂⁴×C₆₁	—	2	2	no	—
230	C₂⁴×C₆₁	—	2	1	no	—
231	#41×C₆₁	—	2	4	no	—
232	#41×C₆₁	—	4	8	no	—
233	#41×C₆₁	—	4	8	no	—
234	#41×C₆₁	—	4	4	no	—
235	#41×C₆₁	—	4	4	no	—
236	#41×C₆₁	—	4	4	no	—
237	#41×C₆₁	—	4	4	no	—
238	#41×C₆₁	—	8	4	no	—
239	C₂×Q₈×C₆₁	—	2	1	no	—
240	C₂×Q₈×C₆₁	—	2	2	no	—
241	C₂×Q₈×C₆₁	—	2	2	no	—
242	C₂×Q₈×C₆₁	—	2	1	no	—
243	C₂×Q₈×C₆₁	—	2	2	no	—
244	C₂×Q₈×C₆₁	—	4	4	no	—
245	C₂×Q₈×C₆₁	—	8	2	no	—
246	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₆₁	—	2	2	no	—
248	C₂×D₄×C₆₁	—	2	4	no	—
249	C₂×D₄×C₆₁	—	2	2	no	—
250	C₂×D₄×C₆₁	—	2	2	no	—
251	C₂×D₄×C₆₁	—	2	2	no	—
252	C₂×D₄×C₆₁	—	2	2	no	—
253	C₂×D₄×C₆₁	—	2	4	no	—
254	C₂×D₄×C₆₁	—	2	2	no	—
255	C₂×D₄×C₆₁	—	2	1	no	—
256	C₂×D₄×C₆₁	—	2	1	no	—
257	C₂×D₄×C₆₁	—	2	1	no	—
258	C₂×D₄×C₆₁	—	2	2	no	—
259	C₂×D₄×C₆₁	—	2	1	no	—
260	C₂×D₄×C₆₁	—	2	1	no	—
261	C₂×D₄×C₆₁	—	2	2	no	—
262	C₂×D₄×C₆₁	—	4	1	no	—
263	C₂×D₄×C₆₁	—	4	2	no	—
264	C₂×D₄×C₆₁	—	4	8	no	—
265	C₂×D₄×C₆₁	—	4	4	no	—
266	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
270	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
271	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₁	—	2	2	no	—
273	C₂²×C₄×C₆₁	—	2	1	no	—
274	C₂²×C₄×C₆₁	—	2	2	no	—
275	C₂²×C₄×C₆₁	—	2	2	no	—
276	C₂²×C₄×C₆₁	—	2	1	no	—
277	C₂²×C₄×C₆₁	—	2	2	no	—
278	C₂²×C₄×C₆₁	—	2	1	no	—
279	C₂²×C₄×C₆₁	—	2	2	no	—
280	C₂²×C₄×C₆₁	—	2	1	no	—
281	C₂²×C₄×C₆₁	—	2	2	no	—
282	C₂²×C₄×C₆₁	—	2	1	no	—
283	C₂²×C₄×C₆₁	—	2	4	no	—
284	C₂²×C₄×C₆₁	—	4	8	no	—
285	C₂²×C₄×C₆₁	—	4	4	no	—
286	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
292	D₈×C₆₁	—	2	4	no	—
293	D₈×C₆₁	—	4	4	no	—
294	D₈×C₆₁	—	4	2	no	—
295	M₁₆×C₆₁	—	4	4	no	—
296	C₂×C₈×C₆₁	—	4	2	no	—
297	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
298	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
299	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₆₁	—	2	2	no	—
301	C₄⋊C₄×C₆₁	—	2	2	no	—
302	C₄⋊C₄×C₆₁	—	2	4	no	—
303	C₄⋊C₄×C₆₁	—	2	2	no	—
304	C₄⋊C₄×C₆₁	—	2	1	no	—
305	C₄⋊C₄×C₆₁	—	2	2	no	—
306	C₄⋊C₄×C₆₁	—	2	1	no	—
307	C₄⋊C₄×C₆₁	—	2	1	no	—
308	C₄⋊C₄×C₆₁	—	2	2	no	—
309	C₄⋊C₄×C₆₁	—	2	4	no	—
310	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
319	C₂²⋊C₄×C₆₁	—	2	4	no	—
320	C₂²⋊C₄×C₆₁	—	2	1	no	—
321	C₂²⋊C₄×C₆₁	—	2	1	no	—
322	C₂²⋊C₄×C₆₁	—	2	2	no	—
323	C₂²⋊C₄×C₆₁	—	2	1	no	—
324	C₂²⋊C₄×C₆₁	—	2	2	no	—
325	C₂²⋊C₄×C₆₁	—	2	1	no	—
326	C₂²⋊C₄×C₆₁	—	2	2	no	—
327	C₂²⋊C₄×C₆₁	—	2	4	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	—	2	4	no	—
333	C₂²⋊C₄×C₆₁	—	2	2	no	—
334	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
337	C₄²×C₆₁	—	2	4	no	—
338	C₄²×C₆₁	C₂×D₄	1	2	yes	—
339	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₆₁	C₂×D₄	1	2	yes	—
342	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₆₁	C₂⁴	1	2	yes	—
344	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
345	C₂³×C₆₁	—	2	1	no	—
346	C₂³×C₆₁	—	2	2	no	—
347	C₂³×C₆₁	—	2	2	no	—
348	C₂³×C₆₁	—	2	1	no	—
349	C₂³×C₆₁	—	4	2	no	—
350	C₂³×C₆₁	—	4	4	no	—
351	C₂³×C₆₁	—	4	4	no	—
352	C₂³×C₆₁	—	4	2	no	—
353	C₂³×C₆₁	—	8	1	no	—
354	C₂³×C₆₁	—	8	2	no	—
355	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
356	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₆₁	—	2	2	no	—
358	Q₈×C₆₁	—	4	4	no	—
359	Q₈×C₆₁	—	4	4	no	—
360	Q₈×C₆₁	—	4	2	no	—
361	Q₈×C₆₁	—	4	2	no	—
362	Q₈×C₆₁	—	8	2	no	—
363	D₄×C₆₁	—	2	4	no	—
364	D₄×C₆₁	—	2	2	no	—
365	D₄×C₆₁	—	2	2	no	—
366	D₄×C₆₁	—	2	1	no	—
367	D₄×C₆₁	—	2	2	no	—
368	D₄×C₆₁	—	2	1	no	—
369	D₄×C₆₁	—	2	2	no	—
370	D₄×C₆₁	—	2	2	no	—
371	D₄×C₆₁	—	2	1	no	—
372	D₄×C₆₁	—	4	2	no	—
373	D₄×C₆₁	—	4	4	no	—
374	D₄×C₆₁	—	4	4	no	—
375	D₄×C₆₁	—	4	2	no	—
376	D₄×C₆₁	—	4	4	no	—
377	D₄×C₆₁	—	4	4	no	—
378	D₄×C₆₁	—	4	4	no	—
379	D₄×C₆₁	—	4	4	no	—
380	D₄×C₆₁	—	4	2	no	—
381	D₄×C₆₁	—	4	2	no	—
382	D₄×C₆₁	—	8	2	no	—
383	D₄×C₆₁	—	8	1	no	—
384	D₄×C₆₁	—	8	4	no	—
385	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
386	C₂×C₄×C₆₁	—	2	4	no	—
387	C₂×C₄×C₆₁	—	2	1	no	—
388	C₂×C₄×C₆₁	—	2	2	no	—
389	C₂×C₄×C₆₁	—	2	1	no	—
390	C₂×C₄×C₆₁	—	2	2	no	—
391	C₂×C₄×C₆₁	—	2	2	no	—
392	C₂×C₄×C₆₁	—	2	4	no	—
393	C₂×C₄×C₆₁	—	2	1	no	—
394	C₂×C₄×C₆₁	—	2	2	no	—
395	C₂×C₄×C₆₁	—	2	1	no	—
396	C₂×C₄×C₆₁	—	4	1	no	—
397	C₂×C₄×C₆₁	—	4	2	no	—
398	C₂×C₄×C₆₁	—	4	4	no	—
399	C₂×C₄×C₆₁	—	4	4	no	—
400	C₂×C₄×C₆₁	—	4	4	no	—
401	C₂×C₄×C₆₁	—	4	2	no	—
402	C₂×C₄×C₆₁	—	4	2	no	—
403	C₂×C₄×C₆₁	—	4	2	no	—
404	C₂×C₄×C₆₁	—	4	2	no	—
405	C₂×C₄×C₆₁	—	4	4	no	—
406	C₂×C₄×C₆₁	—	4	2	no	—
407	C₂×C₄×C₆₁	—	4	4	no	—
408	C₂×C₄×C₆₁	—	8	4	no	—
409	C₂×C₄×C₆₁	—	8	2	no	—
410	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
411	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
420	C₈×C₆₁	—	2	2	no	—
421	C₈×C₆₁	—	2	4	no	—
422	C₈×C₆₁	—	2	2	no	—
423	#62110	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂²×C₆₁	—	2	1	no	—
425	C₂²×C₆₁	—	2	1	no	—
426	C₂²×C₆₁	—	2	2	no	—
427	C₂²×C₆₁	—	2	2	no	—
428	C₂²×C₆₁	—	2	2	no	—
429	C₂²×C₆₁	—	2	2	no	—
430	C₂²×C₆₁	—	4	1	no	—
431	C₂²×C₆₁	—	4	1	no	—
432	C₂²×C₆₁	—	4	2	no	—
433	C₂²×C₆₁	—	4	1	no	—
434	C₂²×C₆₁	—	4	2	no	—
435	C₂²×C₆₁	—	4	1	no	—
436	C₂²×C₆₁	—	4	2	no	—
437	C₂²×C₆₁	—	4	2	no	—
438	C₂²×C₆₁	—	4	2	no	—
439	C₂²×C₆₁	—	4	1	no	—
440	C₂²×C₆₁	—	4	2	no	—
441	C₂²×C₆₁	—	8	4	no	—
442	C₂²×C₆₁	—	8	8	no	—
443	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
444	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₆₁	—	2	1	no	—
446	C₄×C₆₁	—	2	2	no	—
447	C₄×C₆₁	—	2	1	no	—
448	C₄×C₆₁	—	2	1	no	—
449	C₄×C₆₁	—	2	2	no	—
450	C₄×C₆₁	—	2	2	no	—
451	C₄×C₆₁	—	4	4	no	—
452	C₄×C₆₁	—	4	1	no	—
453	C₄×C₆₁	—	4	2	no	—
454	C₄×C₆₁	—	4	1	no	—
455	C₄×C₆₁	—	4	2	no	—
456	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
457	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
458	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
459	C₄×C₆₁	#585	1	1	yes	characteristic
460	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
461	D₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
462	#3384	C₂×C₆₁	1	2	yes	complemented
463	#3366	C₂×C₆₁	1	2	yes	complemented
464	#3354	C₂×C₆₁	1	2	yes	complemented
465	#3345	C₂×C₆₁	1	4	yes	complemented
466	#3325	C₂×C₆₁	1	2	yes	complemented
467	#3318	C₂×C₆₁	1	4	yes	complemented
468	#3253	C₂×C₆₁	1	2	yes	complemented
469	#3245	C₂×C₆₁	1	1	yes	characteristic, complemented
470	#3235	C₂×C₆₁	1	2	yes	complemented
471	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
472	#3109	C₂×C₆₁	1	2	yes	complemented
473	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
474	#3077	C₂×C₆₁	1	2	yes	complemented
475	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
476	#2989	C₂×C₆₁	1	1	yes	characteristic, complemented
477	C₂×C₆₁	—	2	2	no	—
478	C₂×C₆₁	—	4	2	no	—
479	C₂×C₆₁	—	4	2	no	—
480	C₂×C₆₁	—	8	2	no	—
481	C₂×C₆₁	—	8	1	no	—
482	C₂×C₆₁	—	8	2	no	—
483	C₂×C₆₁	#3489	1	1	yes	characteristic
484	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
485	C₂×C₆₁	#3585	1	1	yes	characteristic
486	C₂²×#41	—	2	1	no	—
487	#556	—	2	1	no	—
488	#555	C₂²×C₆₁	1	2	yes	complemented
489	#554	C₂²×C₆₁	1	2	yes	complemented
490	#553	C₂²×C₆₁	1	4	yes	complemented
491	#550	C₂²×C₆₁	1	1	yes	characteristic
492	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
493	#548	—	2	1	no	—
494	#548	—	2	2	no	—
495	#547	—	2	1	no	—
496	#547	C₂²×C₆₁	1	2	yes	—
497	#547	C₂²×C₆₁	1	1	yes	characteristic
498	#546	—	2	1	no	—
499	#546	—	2	2	no	—
500	D₄²	C₂²×C₆₁	1	2	yes	—
501	D₄²	C₂²×C₆₁	1	1	yes	characteristic
502	#542	—	2	2	no	—
503	#537	—	2	1	no	—
504	#533	C₂²×C₆₁	1	2	yes	complemented
505	#532	C₂²×C₆₁	1	1	yes	characteristic
506	#532	C₂²×C₆₁	1	2	yes	—
507	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
508	#532	C₂²×C₆₁	1	2	yes	complemented
509	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
510	#525	—	2	1	no	—
511	#525	—	2	2	no	—
512	#520	—	2	1	no	—
513	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
516	#501	C₂²×C₆₁	1	4	yes	complemented
517	#498	C₂²×C₆₁	1	2	yes	complemented
518	#490	C₂²×C₆₁	1	4	yes	complemented
519	#486	C₂²×C₆₁	1	2	yes	complemented
520	#482	C₂²×C₆₁	1	4	yes	complemented
521	#482	C₂²×C₆₁	1	4	yes	complemented
522	#481	C₂²×C₆₁	1	4	yes	complemented
523	#481	C₂²×C₆₁	1	4	yes	complemented
524	#480	C₂²×C₆₁	1	2	yes	complemented
525	#478	C₂²×C₆₁	1	4	yes	—
526	#478	C₂²×C₆₁	1	4	yes	complemented
527	#476	C₂²×C₆₁	1	2	yes	—
528	#476	C₂²×C₆₁	1	2	yes	—
529	#476	C₂²×C₆₁	1	2	yes	complemented
530	#476	C₂²×C₆₁	1	4	yes	complemented
531	#476	C₂²×C₆₁	1	2	yes	complemented
532	#476	C₂²×C₆₁	1	2	yes	complemented
533	#476	C₂²×C₆₁	1	2	yes	complemented
534	#474	C₂²×C₆₁	1	1	yes	characteristic
535	#474	C₂²×C₆₁	1	2	yes	complemented
536	#474	C₂²×C₆₁	1	2	yes	complemented
537	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
538	#469	C₂²×C₆₁	1	4	yes	complemented
539	#469	C₂²×C₆₁	1	4	yes	complemented
540	#466	C₂²×C₆₁	1	4	yes	complemented
541	#459	C₂²×C₆₁	1	1	yes	characteristic
542	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
543	#459	C₂²×C₆₁	1	2	yes	complemented
544	#459	C₂²×C₆₁	1	2	yes	complemented
545	#459	C₂²×C₆₁	1	4	yes	complemented
546	#447	C₂²×C₆₁	1	2	yes	—
547	#447	C₂²×C₆₁	1	4	yes	—
548	#446	C₂²×C₆₁	1	2	yes	complemented
549	#442	C₂²×C₆₁	1	4	yes	—
550	#442	C₂²×C₆₁	1	4	yes	complemented
551	C₄×D₈	C₂²×C₆₁	1	2	yes	—
552	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
553	#436	C₂²×C₆₁	1	2	yes	complemented
554	#435	C₂²×C₆₁	1	4	yes	complemented
555	#432	C₂²×C₆₁	1	2	yes	complemented
556	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
557	#428	C₂²×C₆₁	1	4	yes	complemented
558	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
559	#423	C₂²×C₆₁	1	2	yes	complemented
560	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
561	#418	C₂²×C₆₁	1	4	yes	—
562	C₂×#102	C₂²×C₆₁	1	2	yes	—
563	C₆₁	#62110	1	1	yes	characteristic, direct product factor, Sylow
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	1	no	—
568	C₂×#41	—	2	2	no	—
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	—	4	8	no	—
572	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
573	C₂²×Q₈	—	2	1	no	—
574	C₂²×Q₈	—	2	1	no	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
579	C₂³×C₄	—	2	2	no	—
580	C₂³×C₄	—	2	1	no	—
581	C₂×D₈	C₂³×C₆₁	1	2	yes	—
582	C₂×D₈	C₂³×C₆₁	1	2	yes	—
583	C₂×D₈	C₂³×C₆₁	1	4	yes	—
584	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
585	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
586	C₄⋊Q₈	—	2	1	no	—
587	C₄⋊Q₈	—	2	1	no	—
588	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
591	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
593	#127	C₂³×C₆₁	1	1	yes	characteristic
594	#127	C₂³×C₆₁	1	2	yes	—
595	#127	C₂³×C₆₁	1	1	yes	characteristic
596	#126	—	2	4	no	—
597	#125	C₂³×C₆₁	1	4	yes	—
598	#124	—	2	4	no	—
599	#124	—	2	1	no	—
600	#124	—	2	2	no	—
601	#124	—	2	1	no	—
602	#124	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	4	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	—	2	1	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	4	no	—
615	#121	—	2	2	no	—
616	#121	—	2	4	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	1	no	—
621	#121	—	2	1	no	—
622	#121	—	2	2	no	—
623	#121	—	2	1	no	—
624	#121	—	2	2	no	—
625	#121	C₂³×C₆₁	1	2	yes	—
626	#121	C₂³×C₆₁	1	2	yes	—
627	#121	C₂³×C₆₁	1	2	yes	—
628	#121	C₂³×C₆₁	1	2	yes	—
629	#121	C₂³×C₆₁	1	4	yes	—
630	#120	—	2	2	no	—
631	#120	—	2	2	no	—
632	#120	—	2	2	no	—
633	C₄×Q₈	—	2	2	no	—
634	C₄×Q₈	—	2	2	no	—
635	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
636	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
637	C₄×D₄	—	2	4	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
647	C₄×D₄	D₄×C₆₁	1	2	yes	—
648	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
649	C₄×D₄	C₂³×C₆₁	1	2	yes	—
650	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₆₁	1	2	yes	—
653	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₆₁	1	2	yes	—
655	C₄×D₄	C₂³×C₆₁	1	4	yes	—
656	C₄×D₄	C₂³×C₆₁	1	2	yes	—
657	C₄×D₄	C₂³×C₆₁	1	2	yes	—
658	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
659	#117	—	2	2	no	—
660	#117	D₄×C₆₁	1	1	yes	characteristic
661	#117	D₄×C₆₁	1	2	yes	—
662	#117	C₂³×C₆₁	1	4	yes	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
672	#107	C₂³×C₆₁	1	2	yes	—
673	#107	C₂³×C₆₁	1	4	yes	—
674	#107	C₂³×C₆₁	1	2	yes	—
675	#106	C₂³×C₆₁	1	4	yes	—
676	#106	C₂³×C₆₁	1	4	yes	—
677	#106	C₂³×C₆₁	1	4	yes	—
678	#106	C₂³×C₆₁	1	4	yes	—
679	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
680	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
681	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
682	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
683	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
684	#102	C₂³×C₆₁	1	4	yes	—
685	#102	C₂³×C₆₁	1	4	yes	—
686	#102	C₂³×C₆₁	1	2	yes	—
687	#102	C₂³×C₆₁	1	4	yes	—
688	#102	C₂³×C₆₁	1	4	yes	—
689	#102	C₂³×C₆₁	1	2	yes	—
690	#102	C₂³×C₆₁	1	2	yes	—
691	#102	C₂³×C₆₁	1	2	yes	—
692	#102	C₂³×C₆₁	1	4	yes	—
693	#102	C₂³×C₆₁	1	4	yes	—
694	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
695	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
696	#97	C₂³×C₆₁	1	4	yes	—
697	C₄×C₈	C₂³×C₆₁	1	2	yes	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	1	no	—
700	#41	—	2	4	no	—
701	#41	—	4	8	no	—
702	#41	—	4	8	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	#41	—	4	4	no	—
706	#41	—	4	4	no	—
707	#41	—	8	4	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	4	4	no	—
714	C₂×Q₈	—	8	2	no	—
715	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	1	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	8	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
736	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
738	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
739	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
740	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	4	8	no	—
754	C₂²×C₄	—	4	4	no	—
755	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
756	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
758	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
761	D₈	—	2	4	no	—
762	D₈	—	4	4	no	—
763	D₈	—	4	2	no	—
764	M₁₆	—	4	4	no	—
765	C₂×C₈	—	4	2	no	—
766	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
767	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
768	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
782	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
783	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
784	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
785	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
786	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
787	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
805	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
806	C₄²	—	2	4	no	—
807	C₄²	C₂×D₄×C₆₁	1	2	yes	—
808	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
810	C₄²	C₂×D₄×C₆₁	1	2	yes	—
811	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
812	C₄²	C₂⁴×C₆₁	1	2	yes	—
813	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	8	1	no	—
823	C₂³	—	8	2	no	—
824	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
825	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
826	Q₈	—	2	2	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	4	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	4	2	no	—
831	Q₈	—	8	2	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	1	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	4	2	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	1	no	—
853	D₄	—	8	4	no	—
854	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	8	4	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
880	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
888	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
889	C₈	—	2	2	no	—
890	C₈	—	2	4	no	—
891	C₈	—	2	2	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
912	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
925	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
926	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
927	C₄	C₆₁×#585	1	1	yes	characteristic
928	C₂	—	2	2	no	—
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	8	1	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₆₁×#3489	1	1	yes	characteristic
935	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
936	C₂	C₆₁×#3585	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 ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3511	C₂	semidirect
2. D₄×#41×C₆₁	C₂	semidirect
3. C₆₁×#3384	C₂	semidirect
4. C₆₁×#3366	C₂	semidirect
5. C₆₁×#3354	C₂	semidirect
6. C₆₁×#3345	C₂	semidirect
7. C₆₁×#3325	C₂	semidirect
8. C₆₁×#3318	C₂	semidirect
9. C₆₁×#3253	C₂	semidirect
10. C₆₁×#3245	C₂	semidirect
11. C₆₁×#3235	C₂	semidirect
12. C₆₁×#3227	C₂	semidirect
13. C₆₁×#3109	C₂	semidirect
14. C₆₁×#3100	C₂	semidirect
15. C₆₁×#3077	C₂	semidirect
16. C₂×C₆₁×#476	C₂	semidirect
17. C₆₁×#2989	C₂	semidirect
20. C₆₁×#555	C₂²	semidirect
21. C₆₁×#554	C₂²	semidirect
22. C₆₁×#553	C₂²	semidirect
36. C₆₁×#533	C₂²	semidirect
39. C₆₁×#532	C₂²	semidirect
40. C₆₁×#532	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
48. C₆₁×#501	C₂²	semidirect
49. C₆₁×#498	C₂²	semidirect
50. C₆₁×#490	C₂²	semidirect
51. C₆₁×#486	C₂²	semidirect
52. C₆₁×#482	C₂²	semidirect
53. C₆₁×#482	C₂²	semidirect
54. C₆₁×#481	C₂²	semidirect
55. C₆₁×#481	C₂²	semidirect
56. C₆₁×#480	C₂²	semidirect
58. C₆₁×#478	C₂²	semidirect
61. C₆₁×#476	C₂²	semidirect
62. C₆₁×#476	C₂²	semidirect
63. C₆₁×#476	C₂²	semidirect
64. C₆₁×#476	C₂²	semidirect
65. C₆₁×#476	C₂²	semidirect
67. C₆₁×#474	C₂²	semidirect
68. C₆₁×#474	C₂²	semidirect
69. C₆₁×#474	C₂²	semidirect
70. C₆₁×#469	C₂²	semidirect
71. C₆₁×#469	C₂²	semidirect
72. C₆₁×#466	C₂²	semidirect
74. C₆₁×#459	C₂²	semidirect
75. C₆₁×#459	C₂²	semidirect
76. C₆₁×#459	C₂²	semidirect
77. C₆₁×#459	C₂²	semidirect
80. C₆₁×#446	C₂²	semidirect
82. C₆₁×#442	C₂²	semidirect
84. C₄×D₈×C₆₁	C₂²	semidirect
85. C₆₁×#436	C₂²	semidirect
86. C₆₁×#435	C₂²	semidirect
87. C₆₁×#432	C₂²	semidirect
88. C₆₁×#431	C₂²	semidirect
89. C₆₁×#428	C₂²	semidirect
90. C₂×#106×C₆₁	C₂²	semidirect
91. C₆₁×#423	C₂²	semidirect
92. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
423. #62110	C₆₁	direct (N × H)
460. #3511	C₂×C₆₁	semidirect
461. D₄×#41	C₂×C₆₁	semidirect
462. #3384	C₂×C₆₁	semidirect
463. #3366	C₂×C₆₁	semidirect
464. #3354	C₂×C₆₁	semidirect
465. #3345	C₂×C₆₁	semidirect
466. #3325	C₂×C₆₁	semidirect
467. #3318	C₂×C₆₁	semidirect
468. #3253	C₂×C₆₁	semidirect
469. #3245	C₂×C₆₁	semidirect
470. #3235	C₂×C₆₁	semidirect
471. #3227	C₂×C₆₁	semidirect
472. #3109	C₂×C₆₁	semidirect
473. #3100	C₂×C₆₁	semidirect
474. #3077	C₂×C₆₁	semidirect
475. C₂×#476	C₂×C₆₁	semidirect
476. #2989	C₂×C₆₁	semidirect
488. #555	C₂²×C₆₁	semidirect
489. #554	C₂²×C₆₁	semidirect
490. #553	C₂²×C₆₁	semidirect
504. #533	C₂²×C₆₁	semidirect
507. #532	C₂²×C₆₁	semidirect
508. #532	C₂²×C₆₁	semidirect
509. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
516. #501	C₂²×C₆₁	semidirect
517. #498	C₂²×C₆₁	semidirect
518. #490	C₂²×C₆₁	semidirect
519. #486	C₂²×C₆₁	semidirect
520. #482	C₂²×C₆₁	semidirect
521. #482	C₂²×C₆₁	semidirect
522. #481	C₂²×C₆₁	semidirect
523. #481	C₂²×C₆₁	semidirect
524. #480	C₂²×C₆₁	semidirect
526. #478	C₂²×C₆₁	semidirect
529. #476	C₂²×C₆₁	semidirect
530. #476	C₂²×C₆₁	semidirect
531. #476	C₂²×C₆₁	semidirect
532. #476	C₂²×C₆₁	semidirect
533. #476	C₂²×C₆₁	semidirect
535. #474	C₂²×C₆₁	semidirect
536. #474	C₂²×C₆₁	semidirect
537. #474	C₂²×C₆₁	semidirect
538. #469	C₂²×C₆₁	semidirect
539. #469	C₂²×C₆₁	semidirect
540. #466	C₂²×C₆₁	semidirect
542. #459	C₂²×C₆₁	semidirect
543. #459	C₂²×C₆₁	semidirect
544. #459	C₂²×C₆₁	semidirect
545. #459	C₂²×C₆₁	semidirect
548. #446	C₂²×C₆₁	semidirect
550. #442	C₂²×C₆₁	semidirect
552. C₄×D₈	C₂²×C₆₁	semidirect
553. #436	C₂²×C₆₁	semidirect
554. #435	C₂²×C₆₁	semidirect
555. #432	C₂²×C₆₁	semidirect
556. #431	C₂²×C₆₁	semidirect
557. #428	C₂²×C₆₁	semidirect
558. C₂×#106	C₂²×C₆₁	semidirect
559. #423	C₂²×C₆₁	semidirect
560. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
563. C₆₁	#62110	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×#3511	2
D₄×#41×C₆₁	2
C₆₁×#3384	2
C₆₁×#3366	2
C₆₁×#3354	2
C₆₁×#3345	2
C₆₁×#3325	2
C₆₁×#3318	2
C₆₁×#3253	2
C₆₁×#3245	2
C₆₁×#3235	2
C₆₁×#3227	2
C₆₁×#3109	2
C₆₁×#3100	2
C₆₁×#3077	2
C₂×C₆₁×#476	2
C₆₁×#2989	2
#62110	61

Subgroups — C61×#62110 #29565543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62110 #29565543