Subgroups — C₆₁×#61009 #29564442

Order 15616.

1696 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3512	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3261	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3260	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3259	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3232	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3212	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3204	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3203	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3183	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3168	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3120	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3119	C₂	1	4	yes	maximal, complemented
13	C₆₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#553	—	2	4	no	—
15	C₆₁×#553	—	2	4	no	—
16	C₆₁×#553	—	2	4	no	—
17	C₆₁×#552	—	2	4	no	—
18	C₆₁×#541	C₂²	1	2	yes	—
19	C₆₁×#541	C₂²	1	2	yes	—
20	C₆₁×#540	C₂²	1	2	yes	—
21	C₆₁×#540	C₂²	1	2	yes	—
22	C₆₁×#537	C₂²	1	4	yes	—
23	C₆₁×#532	C₂²	1	2	yes	—
24	C₆₁×#529	C₂²	1	4	yes	—
25	C₆₁×#529	C₂²	1	4	yes	—
26	C₂×#125×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#520	C₂²	1	4	yes	—
28	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#499	C₂²	1	2	yes	—
30	C₆₁×#499	C₂²	1	2	yes	—
31	C₆₁×#495	C₂²	1	2	yes	—
32	C₆₁×#495	C₂²	1	2	yes	—
33	C₆₁×#488	C₂²	1	4	yes	—
34	C₆₁×#488	C₂²	1	4	yes	—
35	C₆₁×#484	C₂²	1	4	yes	—
36	C₆₁×#483	C₂²	1	4	yes	—
37	C₆₁×#481	C₂²	1	4	yes	—
38	C₆₁×#480	C₂²	1	4	yes	—
39	C₆₁×#479	C₂²	1	4	yes	—
40	C₆₁×#479	C₂²	1	4	yes	—
41	C₆₁×#478	C₂²	1	4	yes	—
42	C₆₁×#478	C₂²	1	4	yes	—
43	C₆₁×#470	C₂²	1	2	yes	—
44	C₆₁×#469	C₂²	1	2	yes	—
45	C₆₁×#468	C₂²	1	4	yes	—
46	C₆₁×#467	C₂²	1	2	yes	—
47	C₆₁×#466	C₂²	1	2	yes	—
48	C₆₁×#465	C₂²	1	4	yes	—
49	C₆₁×#462	C₂²	1	4	yes	—
50	C₆₁×#461	C₂²	1	4	yes	—
51	C₆₁×#460	C₂²	1	4	yes	—
52	C₆₁×#459	C₂²	1	4	yes	—
53	C₆₁×#452	C₂²	1	4	yes	—
54	C₆₁×#452	C₂²	1	4	yes	—
55	C₆₁×#449	C₂²	1	4	yes	—
56	C₆₁×#449	C₂²	1	4	yes	—
57	C₆₁×#442	C₂²	1	2	yes	—
58	C₆₁×#441	C₂²	1	2	yes	—
59	C₆₁×#440	C₂²	1	4	yes	—
60	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
61	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
62	C₄×D₈×C₆₁	C₂²	1	2	yes	—
63	C₆₁×#433	C₂²	1	4	yes	—
64	C₆₁×#431	C₂²	1	4	yes	—
65	C₆₁×#424	C₂²	1	1	yes	characteristic
66	C₆₁×#424	C₂²	1	1	yes	characteristic
67	C₆₁×#408	C₂²	1	1	yes	characteristic
68	C₆₁×#408	C₂²	1	1	yes	characteristic
69	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
70	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
71	C₂×#41×C₆₁	C₂³	1	4	yes	—
72	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
74	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
75	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
76	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
77	C₂×D₈×C₆₁	C₂³	1	2	yes	—
78	C₂×D₈×C₆₁	C₂³	1	2	yes	—
79	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
84	#127×C₆₁	C₂³	1	2	yes	—
85	#126×C₆₁	—	2	4	no	—
86	#126×C₆₁	—	2	4	no	—
87	#126×C₆₁	—	2	4	no	—
88	#126×C₆₁	—	2	4	no	—
89	#125×C₆₁	—	2	4	no	—
90	#125×C₆₁	—	2	4	no	—
91	#125×C₆₁	—	2	4	no	—
92	#125×C₆₁	C₂³	1	2	yes	—
93	#125×C₆₁	C₂³	1	2	yes	—
94	#125×C₆₁	C₂³	1	4	yes	—
95	#124×C₆₁	C₂³	1	4	yes	—
96	#123×C₆₁	—	2	4	no	—
97	#123×C₆₁	—	2	4	no	—
98	#123×C₆₁	—	2	4	no	—
99	#123×C₆₁	—	2	4	no	—
100	C₂²⋊Q₈×C₆₁	—	2	4	no	—
101	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
102	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
103	#121×C₆₁	—	2	4	no	—
104	#121×C₆₁	—	2	4	no	—
105	#121×C₆₁	—	2	4	no	—
106	#121×C₆₁	—	2	4	no	—
107	#121×C₆₁	—	2	4	no	—
108	#121×C₆₁	—	2	4	no	—
109	#121×C₆₁	C₂³	1	4	yes	—
110	#121×C₆₁	C₂³	1	4	yes	—
111	C₄×Q₈×C₆₁	D₄	1	2	yes	—
112	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
113	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
114	C₄×D₄×C₆₁	—	2	4	no	—
115	C₄×D₄×C₆₁	—	2	4	no	—
116	C₄×D₄×C₆₁	—	2	4	no	—
117	C₄×D₄×C₆₁	—	2	4	no	—
118	C₄×D₄×C₆₁	—	2	4	no	—
119	C₄×D₄×C₆₁	D₄	1	2	yes	—
120	C₄×D₄×C₆₁	D₄	1	4	yes	—
121	C₄×D₄×C₆₁	C₂³	1	4	yes	—
122	C₄×D₄×C₆₁	C₂³	1	4	yes	—
123	#117×C₆₁	—	2	4	no	—
124	#117×C₆₁	—	2	4	no	—
125	#117×C₆₁	—	2	4	no	—
126	#117×C₆₁	C₂³	1	1	yes	characteristic
127	#117×C₆₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
129	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
131	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
133	#107×C₆₁	C₂³	1	2	yes	—
134	#107×C₆₁	C₂³	1	2	yes	—
135	#107×C₆₁	C₂³	1	4	yes	—
136	#106×C₆₁	C₂³	1	4	yes	—
137	#106×C₆₁	C₂³	1	2	yes	—
138	#106×C₆₁	C₂³	1	2	yes	—
139	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
140	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
141	#103×C₆₁	C₂³	1	4	yes	—
142	#103×C₆₁	C₂³	1	4	yes	—
143	#103×C₆₁	C₂³	1	4	yes	—
144	#103×C₆₁	C₂³	1	4	yes	—
145	#102×C₆₁	C₂³	1	4	yes	—
146	#102×C₆₁	C₂³	1	4	yes	—
147	#102×C₆₁	C₂³	1	4	yes	—
148	#102×C₆₁	C₂³	1	4	yes	—
149	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
150	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
151	#97×C₆₁	C₂³	1	2	yes	—
152	C₄×C₈×C₆₁	C₂³	1	2	yes	—
153	C₄×C₈×C₆₁	C₂³	1	2	yes	—
154	C₄×C₈×C₆₁	C₂³	1	2	yes	—
155	#41×C₆₁	—	4	1	no	—
156	#41×C₆₁	—	4	1	no	—
157	#41×C₆₁	—	4	4	no	—
158	#41×C₆₁	—	4	4	no	—
159	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
161	C₂×D₄×C₆₁	—	2	4	no	—
162	C₂×D₄×C₆₁	—	2	4	no	—
163	C₂×D₄×C₆₁	—	2	4	no	—
164	C₂×D₄×C₆₁	—	2	4	no	—
165	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₆₁	—	2	4	no	—
169	C₂²×C₄×C₆₁	—	2	4	no	—
170	C₂²×C₄×C₆₁	—	2	4	no	—
171	C₂²×C₄×C₆₁	—	2	4	no	—
172	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
176	Q₁₆×C₆₁	—	4	2	no	—
177	Q₁₆×C₆₁	—	4	2	no	—
178	SD₁₆×C₆₁	—	4	4	no	—
179	SD₁₆×C₆₁	—	4	4	no	—
180	D₈×C₆₁	—	4	2	no	—
181	D₈×C₆₁	—	4	2	no	—
182	M₁₆×C₆₁	—	4	1	no	—
183	M₁₆×C₆₁	—	4	1	no	—
184	C₂×C₈×C₆₁	—	4	1	no	—
185	C₂×C₈×C₆₁	—	4	1	no	—
186	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
187	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
188	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
189	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
190	C₄⋊C₄×C₆₁	—	2	4	no	—
191	C₄⋊C₄×C₆₁	—	2	4	no	—
192	C₄⋊C₄×C₆₁	—	2	4	no	—
193	C₄⋊C₄×C₆₁	—	2	4	no	—
194	C₄⋊C₄×C₆₁	—	2	4	no	—
195	C₄⋊C₄×C₆₁	—	2	4	no	—
196	C₄⋊C₄×C₆₁	—	2	4	no	—
197	C₄⋊C₄×C₆₁	—	2	4	no	—
198	C₄⋊C₄×C₆₁	—	2	4	no	—
199	C₄⋊C₄×C₆₁	—	2	4	no	—
200	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
201	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
202	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
203	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
204	C₂²⋊C₄×C₆₁	—	2	4	no	—
205	C₂²⋊C₄×C₆₁	—	2	4	no	—
206	C₂²⋊C₄×C₆₁	—	2	4	no	—
207	C₂²⋊C₄×C₆₁	—	2	4	no	—
208	C₂²⋊C₄×C₆₁	—	2	4	no	—
209	C₂²⋊C₄×C₆₁	—	2	4	no	—
210	C₂²⋊C₄×C₆₁	—	2	4	no	—
211	C₂²⋊C₄×C₆₁	—	2	4	no	—
212	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
213	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
214	C₄²×C₆₁	—	2	4	no	—
215	C₄²×C₆₁	—	2	4	no	—
216	C₄²×C₆₁	C₂×D₄	1	2	yes	—
217	C₄²×C₆₁	C₂×D₄	1	4	yes	—
218	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
219	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
220	C₄²×C₆₁	C₂⁴	1	2	yes	—
221	C₂³×C₆₁	—	2	4	no	—
222	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
223	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
224	Q₈×C₆₁	—	2	4	no	—
225	Q₈×C₆₁	—	2	4	no	—
226	Q₈×C₆₁	—	4	1	no	—
227	D₄×C₆₁	—	2	4	no	—
228	D₄×C₆₁	—	2	4	no	—
229	D₄×C₆₁	—	4	2	no	—
230	D₄×C₆₁	—	4	1	no	—
231	D₄×C₆₁	—	4	8	no	—
232	D₄×C₆₁	—	8	4	no	—
233	D₄×C₆₁	—	8	4	no	—
234	D₄×C₆₁	—	8	4	no	—
235	C₂×C₄×C₆₁	—	2	1	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	—	2	2	no	—
239	C₂×C₄×C₆₁	—	2	4	no	—
240	C₂×C₄×C₆₁	—	2	4	no	—
241	C₂×C₄×C₆₁	—	2	4	no	—
242	C₂×C₄×C₆₁	—	4	2	no	—
243	C₂×C₄×C₆₁	—	4	4	no	—
244	C₂×C₄×C₆₁	—	4	8	no	—
245	C₂×C₄×C₆₁	—	8	4	no	—
246	C₂×C₄×C₆₁	—	8	4	no	—
247	C₂×C₄×C₆₁	—	8	4	no	—
248	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
254	C₈×C₆₁	—	2	2	no	—
255	C₈×C₆₁	—	2	2	no	—
256	C₈×C₆₁	—	2	2	no	—
257	C₈×C₆₁	—	2	2	no	—
258	#61009	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₆₁	—	2	4	no	—
260	C₂²×C₆₁	—	2	2	no	—
261	C₂²×C₆₁	—	2	2	no	—
262	C₂²×C₆₁	—	2	1	no	—
263	C₂²×C₆₁	—	4	4	no	—
264	C₂²×C₆₁	—	4	4	no	—
265	C₂²×C₆₁	—	4	4	no	—
266	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
267	C₄×C₆₁	—	2	2	no	—
268	C₄×C₆₁	—	2	2	no	—
269	C₄×C₆₁	—	2	4	no	—
270	C₄×C₆₁	—	2	2	no	—
271	C₄×C₆₁	—	2	1	no	—
272	C₄×C₆₁	—	4	4	no	—
273	C₄×C₆₁	—	4	4	no	—
274	C₄×C₆₁	—	4	4	no	—
275	C₄×C₆₁	#585	1	1	yes	characteristic
276	C₄×C₆₁	#585	1	1	yes	characteristic
277	#3512	C₂×C₆₁	1	2	yes	complemented
278	#3261	C₂×C₆₁	1	1	yes	characteristic, complemented
279	#3260	C₂×C₆₁	1	2	yes	complemented
280	#3259	C₂×C₆₁	1	1	yes	characteristic, complemented
281	#3232	C₂×C₆₁	1	4	yes	complemented
282	#3212	C₂×C₆₁	1	4	yes	complemented
283	#3204	C₂×C₆₁	1	2	yes	complemented
284	#3203	C₂×C₆₁	1	2	yes	complemented
285	#3183	C₂×C₆₁	1	2	yes	complemented
286	#3168	C₂×C₆₁	1	2	yes	complemented
287	#3120	C₂×C₆₁	1	4	yes	complemented
288	#3119	C₂×C₆₁	1	4	yes	complemented
289	#2922	C₂×C₆₁	1	1	yes	characteristic, complemented
290	C₂×C₆₁	—	4	2	no	—
291	C₂×C₆₁	—	4	1	no	—
292	C₂×C₆₁	—	8	4	no	—
293	C₂×C₆₁	#3449	1	1	yes	characteristic
294	C₂×C₆₁	#3584	1	2	yes	—
295	#553	—	2	4	no	—
296	#553	—	2	4	no	—
297	#553	—	2	4	no	—
298	#552	—	2	4	no	—
299	#541	C₂²×C₆₁	1	2	yes	—
300	#541	C₂²×C₆₁	1	2	yes	—
301	#540	C₂²×C₆₁	1	2	yes	—
302	#540	C₂²×C₆₁	1	2	yes	—
303	#537	C₂²×C₆₁	1	4	yes	—
304	#532	C₂²×C₆₁	1	2	yes	—
305	#529	C₂²×C₆₁	1	4	yes	—
306	#529	C₂²×C₆₁	1	4	yes	—
307	C₂×#125	C₂²×C₆₁	1	2	yes	—
308	#520	C₂²×C₆₁	1	4	yes	—
309	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
310	#499	C₂²×C₆₁	1	2	yes	—
311	#499	C₂²×C₆₁	1	2	yes	—
312	#495	C₂²×C₆₁	1	2	yes	—
313	#495	C₂²×C₆₁	1	2	yes	—
314	#488	C₂²×C₆₁	1	4	yes	—
315	#488	C₂²×C₆₁	1	4	yes	—
316	#484	C₂²×C₆₁	1	4	yes	—
317	#483	C₂²×C₆₁	1	4	yes	—
318	#481	C₂²×C₆₁	1	4	yes	—
319	#480	C₂²×C₆₁	1	4	yes	—
320	#479	C₂²×C₆₁	1	4	yes	—
321	#479	C₂²×C₆₁	1	4	yes	—
322	#478	C₂²×C₆₁	1	4	yes	—
323	#478	C₂²×C₆₁	1	4	yes	—
324	#470	C₂²×C₆₁	1	2	yes	—
325	#469	C₂²×C₆₁	1	2	yes	—
326	#468	C₂²×C₆₁	1	4	yes	—
327	#467	C₂²×C₆₁	1	2	yes	—
328	#466	C₂²×C₆₁	1	2	yes	—
329	#465	C₂²×C₆₁	1	4	yes	—
330	#462	C₂²×C₆₁	1	4	yes	—
331	#461	C₂²×C₆₁	1	4	yes	—
332	#460	C₂²×C₆₁	1	4	yes	—
333	#459	C₂²×C₆₁	1	4	yes	—
334	#452	C₂²×C₆₁	1	4	yes	—
335	#452	C₂²×C₆₁	1	4	yes	—
336	#449	C₂²×C₆₁	1	4	yes	—
337	#449	C₂²×C₆₁	1	4	yes	—
338	#442	C₂²×C₆₁	1	2	yes	—
339	#441	C₂²×C₆₁	1	2	yes	—
340	#440	C₂²×C₆₁	1	4	yes	—
341	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
342	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
343	C₄×D₈	C₂²×C₆₁	1	2	yes	—
344	#433	C₂²×C₆₁	1	4	yes	—
345	#431	C₂²×C₆₁	1	4	yes	—
346	#424	C₂²×C₆₁	1	1	yes	characteristic
347	#424	C₂²×C₆₁	1	1	yes	characteristic
348	#408	C₂²×C₆₁	1	1	yes	characteristic
349	#408	C₂²×C₆₁	1	1	yes	characteristic
350	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
352	C₆₁	#61009	1	1	yes	characteristic, direct product factor, Sylow
353	C₂×#41	C₂³×C₆₁	1	4	yes	—
354	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
355	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
356	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
357	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
358	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
359	C₂×D₈	C₂³×C₆₁	1	2	yes	—
360	C₂×D₈	C₂³×C₆₁	1	2	yes	—
361	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
366	#127	C₂³×C₆₁	1	2	yes	—
367	#126	—	2	4	no	—
368	#126	—	2	4	no	—
369	#126	—	2	4	no	—
370	#126	—	2	4	no	—
371	#125	—	2	4	no	—
372	#125	—	2	4	no	—
373	#125	—	2	4	no	—
374	#125	C₂³×C₆₁	1	4	yes	—
375	#125	C₂³×C₆₁	1	2	yes	—
376	#125	C₂³×C₆₁	1	2	yes	—
377	#124	C₂³×C₆₁	1	4	yes	—
378	#123	—	2	4	no	—
379	#123	—	2	4	no	—
380	#123	—	2	4	no	—
381	#123	—	2	4	no	—
382	C₂²⋊Q₈	—	2	4	no	—
383	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
384	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
385	#121	—	2	4	no	—
386	#121	—	2	4	no	—
387	#121	—	2	4	no	—
388	#121	—	2	4	no	—
389	#121	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	C₂³×C₆₁	1	4	yes	—
392	#121	C₂³×C₆₁	1	4	yes	—
393	C₄×Q₈	D₄×C₆₁	1	2	yes	—
394	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
395	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
396	C₄×D₄	—	2	4	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	D₄×C₆₁	1	2	yes	—
402	C₄×D₄	D₄×C₆₁	1	4	yes	—
403	C₄×D₄	C₂³×C₆₁	1	4	yes	—
404	C₄×D₄	C₂³×C₆₁	1	4	yes	—
405	#117	—	2	4	no	—
406	#117	—	2	4	no	—
407	#117	—	2	4	no	—
408	#117	C₂³×C₆₁	1	2	yes	—
409	#117	C₂³×C₆₁	1	1	yes	characteristic
410	C₂×C₄⋊C₄	—	2	4	no	—
411	C₂×C₄⋊C₄	—	2	4	no	—
412	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
413	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
414	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
415	#107	C₂³×C₆₁	1	2	yes	—
416	#107	C₂³×C₆₁	1	2	yes	—
417	#107	C₂³×C₆₁	1	4	yes	—
418	#106	C₂³×C₆₁	1	4	yes	—
419	#106	C₂³×C₆₁	1	2	yes	—
420	#106	C₂³×C₆₁	1	2	yes	—
421	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
422	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
423	#103	C₂³×C₆₁	1	4	yes	—
424	#103	C₂³×C₆₁	1	4	yes	—
425	#103	C₂³×C₆₁	1	4	yes	—
426	#103	C₂³×C₆₁	1	4	yes	—
427	#102	C₂³×C₆₁	1	4	yes	—
428	#102	C₂³×C₆₁	1	4	yes	—
429	#102	C₂³×C₆₁	1	4	yes	—
430	#102	C₂³×C₆₁	1	4	yes	—
431	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
432	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
433	#97	C₂³×C₆₁	1	2	yes	—
434	C₄×C₈	C₂³×C₆₁	1	2	yes	—
435	C₄×C₈	C₂³×C₆₁	1	2	yes	—
436	C₄×C₈	C₂³×C₆₁	1	2	yes	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	4	no	—
440	#41	—	4	4	no	—
441	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
442	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
448	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
449	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
455	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
458	Q₁₆	—	4	2	no	—
459	Q₁₆	—	4	2	no	—
460	SD₁₆	—	4	4	no	—
461	SD₁₆	—	4	4	no	—
462	D₈	—	4	2	no	—
463	D₈	—	4	2	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	—	4	1	no	—
468	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
469	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
470	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
471	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
483	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
484	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
485	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
495	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	4	no	—
498	C₄²	C₂×D₄×C₆₁	1	2	yes	—
499	C₄²	C₂×D₄×C₆₁	1	4	yes	—
500	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
501	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
502	C₄²	C₂⁴×C₆₁	1	2	yes	—
503	C₂³	—	2	4	no	—
504	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
505	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
506	Q₈	—	2	4	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	4	1	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	4	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	8	no	—
514	D₄	—	8	4	no	—
515	D₄	—	8	4	no	—
516	D₄	—	8	4	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	—	8	4	no	—
530	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
532	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
533	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
535	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
536	C₈	—	2	2	no	—
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	4	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	C₆₁×#585	1	1	yes	characteristic
557	C₄	C₆₁×#585	1	1	yes	characteristic
558	C₂	—	4	2	no	—
559	C₂	—	4	1	no	—
560	C₂	—	8	4	no	—
561	C₂	C₆₁×#3449	1	1	yes	characteristic
562	C₂	C₆₁×#3584	1	2	yes	—

	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×#3512	C₂	semidirect
2. C₆₁×#3261	C₂	semidirect
3. C₆₁×#3260	C₂	semidirect
4. C₆₁×#3259	C₂	semidirect
5. C₆₁×#3232	C₂	semidirect
6. C₆₁×#3212	C₂	semidirect
7. C₆₁×#3204	C₂	semidirect
8. C₆₁×#3203	C₂	semidirect
9. C₆₁×#3183	C₂	semidirect
10. C₆₁×#3168	C₂	semidirect
11. C₆₁×#3120	C₂	semidirect
12. C₆₁×#3119	C₂	semidirect
13. C₆₁×#2922	C₂	semidirect
258. #61009	C₆₁	direct (N × H)
277. #3512	C₂×C₆₁	semidirect
278. #3261	C₂×C₆₁	semidirect
279. #3260	C₂×C₆₁	semidirect
280. #3259	C₂×C₆₁	semidirect
281. #3232	C₂×C₆₁	semidirect
282. #3212	C₂×C₆₁	semidirect
283. #3204	C₂×C₆₁	semidirect
284. #3203	C₂×C₆₁	semidirect
285. #3183	C₂×C₆₁	semidirect
286. #3168	C₂×C₆₁	semidirect
287. #3120	C₂×C₆₁	semidirect
288. #3119	C₂×C₆₁	semidirect
289. #2922	C₂×C₆₁	semidirect
352. C₆₁	#61009	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×#3512	2
C₆₁×#3261	2
C₆₁×#3260	2
C₆₁×#3259	2
C₆₁×#3232	2
C₆₁×#3212	2
C₆₁×#3204	2
C₆₁×#3203	2
C₆₁×#3183	2
C₆₁×#3168	2
C₆₁×#3120	2
C₆₁×#3119	2
C₆₁×#2922	2
#61009	61

Subgroups — C61×#61009 #29564442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61009 #29564442