Subgroups — C₆₁×#60883 #29564316

Order 15616.

1742 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3508	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3241	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3235	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3234	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3096	C₂	1	4	yes	maximal, complemented
11	C₆₁×#3081	C₂	1	4	yes	maximal, complemented
12	C₆₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#559	—	2	2	no	—
14	C₆₁×#557	—	2	2	no	—
15	C₆₁×#554	—	2	4	no	—
16	C₆₁×#554	—	2	2	no	—
17	C₆₁×#550	—	2	2	no	—
18	C₆₁×#546	—	2	4	no	—
19	C₆₁×#544	C₂²	1	2	yes	—
20	C₆₁×#544	C₂²	1	4	yes	complemented
21	C₆₁×#540	C₂²	1	4	yes	—
22	C₆₁×#535	C₂²	1	2	yes	—
23	C₆₁×#533	C₂²	1	1	yes	characteristic
24	C₆₁×#533	C₂²	1	1	yes	characteristic
25	C₆₁×#533	C₂²	1	2	yes	complemented
26	C₆₁×#532	C₂²	1	4	yes	—
27	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
30	C₆₁×#520	C₂²	1	2	yes	—
31	C₆₁×#518	C₂²	1	2	yes	—
32	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#501	C₂²	1	2	yes	complemented
34	C₆₁×#501	C₂²	1	2	yes	complemented
35	C₆₁×#501	C₂²	1	4	yes	complemented
36	C₆₁×#501	C₂²	1	4	yes	complemented
37	C₆₁×#499	C₂²	1	4	yes	complemented
38	C₆₁×#490	C₂²	1	4	yes	—
39	C₆₁×#490	C₂²	1	4	yes	—
40	C₆₁×#490	C₂²	1	2	yes	—
41	C₆₁×#490	C₂²	1	2	yes	—
42	C₆₁×#486	C₂²	1	4	yes	—
43	C₆₁×#482	C₂²	1	8	yes	complemented
44	C₆₁×#482	C₂²	1	8	yes	complemented
45	C₆₁×#481	C₂²	1	8	yes	complemented
46	C₆₁×#480	C₂²	1	8	yes	complemented
47	C₆₁×#478	C₂²	1	8	yes	complemented
48	C₆₁×#478	C₂²	1	8	yes	complemented
49	C₆₁×#476	C₂²	1	8	yes	complemented
50	C₆₁×#474	C₂²	1	8	yes	complemented
51	C₆₁×#433	C₂²	1	4	yes	complemented
52	C₆₁×#432	C₂²	1	4	yes	complemented
53	C₆₁×#428	C₂²	1	4	yes	—
54	C₆₁×#427	C₂²	1	4	yes	—
55	C₆₁×#424	C₂²	1	2	yes	—
56	C₆₁×#418	C₂²	1	4	yes	—
57	C₂×#102×C₆₁	C₂²	1	4	yes	—
58	C₆₁×#408	C₂²	1	2	yes	—
59	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
60	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
61	C₂×#41×C₆₁	—	2	4	no	—
62	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₆₁	—	2	2	no	—
64	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
65	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₆₁	—	2	2	no	—
68	C₄⋊Q₈×C₆₁	—	2	4	no	—
69	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
72	#127×C₆₁	—	2	2	no	—
73	#127×C₆₁	—	2	2	no	—
74	#127×C₆₁	C₂³	1	2	yes	—
75	#127×C₆₁	C₂³	1	2	yes	—
76	#125×C₆₁	—	2	2	no	—
77	#125×C₆₁	—	2	4	no	—
78	#125×C₆₁	—	2	2	no	—
79	#125×C₆₁	—	2	4	no	—
80	#125×C₆₁	C₂³	1	1	yes	characteristic
81	#125×C₆₁	C₂³	1	2	yes	—
82	#125×C₆₁	C₂³	1	1	yes	characteristic
83	#125×C₆₁	C₂³	1	2	yes	—
84	#125×C₆₁	C₂³	1	4	yes	—
85	#125×C₆₁	C₂³	1	2	yes	—
86	#124×C₆₁	—	2	2	no	—
87	#124×C₆₁	—	2	4	no	—
88	#123×C₆₁	—	2	8	no	—
89	C₂²⋊Q₈×C₆₁	—	2	2	no	—
90	C₂²⋊Q₈×C₆₁	—	2	2	no	—
91	C₂²⋊Q₈×C₆₁	—	2	4	no	—
92	C₂²⋊Q₈×C₆₁	—	2	4	no	—
93	C₂²⋊Q₈×C₆₁	—	2	4	no	—
94	C₂²⋊Q₈×C₆₁	—	2	4	no	—
95	#121×C₆₁	—	2	4	no	—
96	#121×C₆₁	—	2	8	no	—
97	#121×C₆₁	C₂³	1	8	yes	—
98	#120×C₆₁	—	2	4	no	—
99	C₄×Q₈×C₆₁	—	2	2	no	—
100	C₄×Q₈×C₆₁	—	2	2	no	—
101	C₄×Q₈×C₆₁	—	2	2	no	—
102	C₄×Q₈×C₆₁	—	2	4	no	—
103	C₄×Q₈×C₆₁	D₄	1	2	yes	—
104	C₄×D₄×C₆₁	—	2	4	no	—
105	C₄×D₄×C₆₁	—	2	2	no	—
106	C₄×D₄×C₆₁	—	2	4	no	—
107	C₄×D₄×C₆₁	—	2	4	no	—
108	C₄×D₄×C₆₁	D₄	1	4	yes	—
109	C₄×D₄×C₆₁	D₄	1	2	yes	—
110	C₄×D₄×C₆₁	C₂³	1	8	yes	—
111	#117×C₆₁	C₂³	1	2	yes	—
112	#117×C₆₁	C₂³	1	2	yes	—
113	#117×C₆₁	C₂³	1	4	yes	—
114	#117×C₆₁	C₂³	1	2	yes	—
115	#117×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
121	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
123	#107×C₆₁	C₂³	1	4	yes	—
124	#107×C₆₁	C₂³	1	4	yes	—
125	#107×C₆₁	C₂³	1	8	yes	—
126	#106×C₆₁	C₂³	1	4	yes	—
127	#106×C₆₁	C₂³	1	4	yes	—
128	#106×C₆₁	C₂³	1	8	yes	—
129	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
130	#102×C₆₁	C₂³	1	8	yes	—
131	#102×C₆₁	C₂³	1	8	yes	—
132	#102×C₆₁	C₂³	1	8	yes	—
133	#102×C₆₁	C₂³	1	8	yes	—
134	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
135	#97×C₆₁	C₂³	1	2	yes	—
136	#97×C₆₁	C₂³	1	2	yes	—
137	#97×C₆₁	C₂³	1	2	yes	—
138	C₄×C₈×C₆₁	C₂³	1	2	yes	—
139	C₂⁴×C₆₁	—	2	2	no	—
140	#41×C₆₁	—	2	4	no	—
141	#41×C₆₁	—	8	8	no	—
142	C₂×Q₈×C₆₁	—	2	2	no	—
143	C₂×Q₈×C₆₁	—	2	4	no	—
144	C₂×Q₈×C₆₁	—	2	2	no	—
145	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₆₁	—	2	8	no	—
147	C₂×D₄×C₆₁	—	2	2	no	—
148	C₂×D₄×C₆₁	—	2	4	no	—
149	C₂×D₄×C₆₁	—	2	4	no	—
150	C₂×D₄×C₆₁	—	2	8	no	—
151	C₂×D₄×C₆₁	—	8	4	no	—
152	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₆₁	—	2	4	no	—
156	C₂²×C₄×C₆₁	—	2	2	no	—
157	C₂²×C₄×C₆₁	—	2	8	no	—
158	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₆₁	—	2	4	no	—
163	C₂×C₈×C₆₁	—	2	4	no	—
164	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
165	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
166	C₄⋊C₄×C₆₁	—	2	4	no	—
167	C₄⋊C₄×C₆₁	—	2	2	no	—
168	C₄⋊C₄×C₆₁	—	2	4	no	—
169	C₄⋊C₄×C₆₁	—	2	4	no	—
170	C₄⋊C₄×C₆₁	—	2	4	no	—
171	C₄⋊C₄×C₆₁	—	2	4	no	—
172	C₄⋊C₄×C₆₁	—	2	2	no	—
173	C₄⋊C₄×C₆₁	—	2	2	no	—
174	C₄⋊C₄×C₆₁	—	2	2	no	—
175	C₄⋊C₄×C₆₁	—	2	4	no	—
176	C₄⋊C₄×C₆₁	—	2	4	no	—
177	C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
180	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
181	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
182	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
183	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
184	C₂²⋊C₄×C₆₁	—	2	2	no	—
185	C₂²⋊C₄×C₆₁	—	2	4	no	—
186	C₂²⋊C₄×C₆₁	—	2	2	no	—
187	C₂²⋊C₄×C₆₁	—	2	8	no	—
188	C₂²⋊C₄×C₆₁	—	2	8	no	—
189	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
190	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
191	C₄²×C₆₁	—	2	2	no	—
192	C₄²×C₆₁	—	2	4	no	—
193	C₄²×C₆₁	—	2	2	no	—
194	C₄²×C₆₁	C₂×D₄	1	4	yes	—
195	C₄²×C₆₁	C₂×D₄	1	2	yes	—
196	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
197	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
198	C₄²×C₆₁	C₂⁴	1	2	yes	—
199	C₂³×C₆₁	—	2	4	no	—
200	C₂³×C₆₁	—	4	4	no	—
201	C₂³×C₆₁	—	8	4	no	—
202	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
203	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₆₁	—	2	2	no	—
205	Q₈×C₆₁	—	4	4	no	—
206	Q₈×C₆₁	—	8	4	no	—
207	Q₈×C₆₁	—	8	2	no	—
208	D₄×C₆₁	—	2	4	no	—
209	D₄×C₆₁	—	2	2	no	—
210	D₄×C₆₁	—	2	8	no	—
211	D₄×C₆₁	—	4	8	no	—
212	D₄×C₆₁	—	4	4	no	—
213	D₄×C₆₁	—	8	4	no	—
214	D₄×C₆₁	—	8	8	no	—
215	C₂×C₄×C₆₁	—	2	4	no	—
216	C₂×C₄×C₆₁	—	2	2	no	—
217	C₂×C₄×C₆₁	—	2	4	no	—
218	C₂×C₄×C₆₁	—	2	4	no	—
219	C₂×C₄×C₆₁	—	2	2	no	—
220	C₂×C₄×C₆₁	—	4	2	no	—
221	C₂×C₄×C₆₁	—	4	4	no	—
222	C₂×C₄×C₆₁	—	8	8	no	—
223	C₂×C₄×C₆₁	—	8	2	no	—
224	C₂×C₄×C₆₁	—	8	4	no	—
225	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
231	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
232	C₈×C₆₁	—	2	4	no	—
233	C₈×C₆₁	—	2	4	no	—
234	#60883	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₆₁	—	2	2	no	—
236	C₂²×C₆₁	—	2	4	no	—
237	C₂²×C₆₁	—	2	2	no	—
238	C₂²×C₆₁	—	4	8	no	—
239	C₂²×C₆₁	—	4	4	no	—
240	C₂²×C₆₁	—	16	4	no	—
241	C₂²×C₆₁	#536	1	2	yes	—
242	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
243	C₄×C₆₁	—	2	2	no	—
244	C₄×C₆₁	—	2	4	no	—
245	C₄×C₆₁	—	2	2	no	—
246	C₄×C₆₁	—	2	2	no	—
247	C₄×C₆₁	—	4	4	no	—
248	C₄×C₆₁	—	4	4	no	—
249	C₄×C₆₁	—	4	2	no	—
250	C₄×C₆₁	—	4	2	no	—
251	C₄×C₆₁	#536	1	2	yes	—
252	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
253	#3508	C₂×C₆₁	1	1	yes	characteristic
254	#3504	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#3241	C₂×C₆₁	1	8	yes	complemented
256	#3235	C₂×C₆₁	1	4	yes	complemented
257	#3234	C₂×C₆₁	1	4	yes	complemented
258	#3166	C₂×C₆₁	1	1	yes	characteristic, complemented
259	#3162	C₂×C₆₁	1	1	yes	characteristic, complemented
260	#3138	C₂×C₆₁	1	1	yes	characteristic, complemented
261	C₂×#490	C₂×C₆₁	1	1	yes	characteristic, complemented
262	#3096	C₂×C₆₁	1	4	yes	complemented
263	#3081	C₂×C₆₁	1	4	yes	complemented
264	#2923	C₂×C₆₁	1	1	yes	characteristic, complemented
265	C₂×C₆₁	—	2	2	no	—
266	C₂×C₆₁	—	4	2	no	—
267	C₂×C₆₁	—	8	4	no	—
268	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
269	C₂×C₆₁	#3585	1	2	yes	—
270	#559	—	2	2	no	—
271	#557	—	2	2	no	—
272	#554	—	2	4	no	—
273	#554	—	2	2	no	—
274	#550	—	2	2	no	—
275	#546	—	2	4	no	—
276	#544	C₂²×C₆₁	1	2	yes	—
277	#544	C₂²×C₆₁	1	4	yes	complemented
278	#540	C₂²×C₆₁	1	4	yes	—
279	#535	C₂²×C₆₁	1	2	yes	—
280	#533	C₂²×C₆₁	1	1	yes	characteristic
281	#533	C₂²×C₆₁	1	1	yes	characteristic
282	#533	C₂²×C₆₁	1	2	yes	complemented
283	#532	C₂²×C₆₁	1	4	yes	—
284	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
287	#520	C₂²×C₆₁	1	2	yes	—
288	#518	C₂²×C₆₁	1	2	yes	—
289	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
290	#501	C₂²×C₆₁	1	2	yes	complemented
291	#501	C₂²×C₆₁	1	2	yes	complemented
292	#501	C₂²×C₆₁	1	4	yes	complemented
293	#501	C₂²×C₆₁	1	4	yes	complemented
294	#499	C₂²×C₆₁	1	4	yes	complemented
295	#490	C₂²×C₆₁	1	4	yes	—
296	#490	C₂²×C₆₁	1	4	yes	—
297	#490	C₂²×C₆₁	1	2	yes	—
298	#490	C₂²×C₆₁	1	2	yes	—
299	#486	C₂²×C₆₁	1	4	yes	—
300	#482	C₂²×C₆₁	1	8	yes	complemented
301	#482	C₂²×C₆₁	1	8	yes	complemented
302	#481	C₂²×C₆₁	1	8	yes	complemented
303	#480	C₂²×C₆₁	1	8	yes	complemented
304	#478	C₂²×C₆₁	1	8	yes	complemented
305	#478	C₂²×C₆₁	1	8	yes	complemented
306	#476	C₂²×C₆₁	1	8	yes	complemented
307	#474	C₂²×C₆₁	1	8	yes	complemented
308	#433	C₂²×C₆₁	1	4	yes	complemented
309	#432	C₂²×C₆₁	1	4	yes	complemented
310	#428	C₂²×C₆₁	1	4	yes	—
311	#427	C₂²×C₆₁	1	4	yes	—
312	#424	C₂²×C₆₁	1	2	yes	—
313	#418	C₂²×C₆₁	1	4	yes	—
314	C₂×#102	C₂²×C₆₁	1	4	yes	—
315	#408	C₂²×C₆₁	1	2	yes	—
316	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
317	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
318	C₆₁	#60883	1	1	yes	characteristic, direct product factor, Sylow
319	C₂×#41	—	2	4	no	—
320	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
323	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
324	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	4	no	—
327	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
329	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
330	#127	—	2	2	no	—
331	#127	—	2	2	no	—
332	#127	C₂³×C₆₁	1	2	yes	—
333	#127	C₂³×C₆₁	1	2	yes	—
334	#125	—	2	2	no	—
335	#125	—	2	4	no	—
336	#125	—	2	2	no	—
337	#125	—	2	4	no	—
338	#125	C₂³×C₆₁	1	2	yes	—
339	#125	C₂³×C₆₁	1	2	yes	—
340	#125	C₂³×C₆₁	1	1	yes	characteristic
341	#125	C₂³×C₆₁	1	4	yes	—
342	#125	C₂³×C₆₁	1	1	yes	characteristic
343	#125	C₂³×C₆₁	1	2	yes	—
344	#124	—	2	2	no	—
345	#124	—	2	4	no	—
346	#123	—	2	8	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	8	no	—
355	#121	C₂³×C₆₁	1	8	yes	—
356	#120	—	2	4	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×Q₈	D₄×C₆₁	1	2	yes	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	D₄×C₆₁	1	4	yes	—
367	C₄×D₄	D₄×C₆₁	1	2	yes	—
368	C₄×D₄	C₂³×C₆₁	1	8	yes	—
369	#117	C₂³×C₆₁	1	2	yes	—
370	#117	C₂³×C₆₁	1	2	yes	—
371	#117	C₂³×C₆₁	1	4	yes	—
372	#117	C₂³×C₆₁	1	1	yes	characteristic
373	#117	C₂³×C₆₁	1	2	yes	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	4	no	—
376	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
381	#107	C₂³×C₆₁	1	4	yes	—
382	#107	C₂³×C₆₁	1	4	yes	—
383	#107	C₂³×C₆₁	1	8	yes	—
384	#106	C₂³×C₆₁	1	4	yes	—
385	#106	C₂³×C₆₁	1	4	yes	—
386	#106	C₂³×C₆₁	1	8	yes	—
387	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
388	#102	C₂³×C₆₁	1	8	yes	—
389	#102	C₂³×C₆₁	1	8	yes	—
390	#102	C₂³×C₆₁	1	8	yes	—
391	#102	C₂³×C₆₁	1	8	yes	—
392	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
393	#97	C₂³×C₆₁	1	2	yes	—
394	#97	C₂³×C₆₁	1	2	yes	—
395	#97	C₂³×C₆₁	1	2	yes	—
396	C₄×C₈	C₂³×C₆₁	1	2	yes	—
397	C₂⁴	—	2	2	no	—
398	#41	—	2	4	no	—
399	#41	—	8	8	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	8	4	no	—
410	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
411	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
412	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
417	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
420	M₁₆	—	2	4	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
423	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
438	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
439	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
440	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
441	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
448	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄×C₆₁	1	4	yes	—
453	C₄²	C₂×D₄×C₆₁	1	2	yes	—
454	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
455	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
456	C₄²	C₂⁴×C₆₁	1	2	yes	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	8	4	no	—
460	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
461	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	4	4	no	—
464	Q₈	—	8	4	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	8	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	4	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	4	no	—
483	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
486	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
488	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
489	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
490	C₈	—	2	4	no	—
491	C₈	—	2	4	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	8	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	16	4	no	—
498	C₂²	C₆₁×#536	1	2	yes	—
499	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	C₆₁×#536	1	2	yes	—
509	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	4	no	—
513	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
514	C₂	C₆₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3508	C₂
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
2. C₆₁×#3504	C₂	semidirect
3. C₆₁×#3241	C₂	semidirect
4. C₆₁×#3235	C₂	semidirect
5. C₆₁×#3234	C₂	semidirect
6. C₆₁×#3166	C₂	semidirect
7. C₆₁×#3162	C₂	semidirect
8. C₆₁×#3138	C₂	semidirect
9. C₂×C₆₁×#490	C₂	semidirect
10. C₆₁×#3096	C₂	semidirect
11. C₆₁×#3081	C₂	semidirect
12. C₆₁×#2923	C₂	semidirect
20. C₆₁×#544	C₂²	semidirect
25. C₆₁×#533	C₂²	semidirect
29. C₂×#125×C₆₁	C₂²	semidirect
33. C₆₁×#501	C₂²	semidirect
34. C₆₁×#501	C₂²	semidirect
35. C₆₁×#501	C₂²	semidirect
36. C₆₁×#501	C₂²	semidirect
37. C₆₁×#499	C₂²	semidirect
43. C₆₁×#482	C₂²	semidirect
44. C₆₁×#482	C₂²	semidirect
45. C₆₁×#481	C₂²	semidirect
46. C₆₁×#480	C₂²	semidirect
47. C₆₁×#478	C₂²	semidirect
48. C₆₁×#478	C₂²	semidirect
49. C₆₁×#476	C₂²	semidirect
50. C₆₁×#474	C₂²	semidirect
51. C₆₁×#433	C₂²	semidirect
52. C₆₁×#432	C₂²	semidirect
234. #60883	C₆₁	direct (N × H)
254. #3504	C₂×C₆₁	semidirect
255. #3241	C₂×C₆₁	semidirect
256. #3235	C₂×C₆₁	semidirect
257. #3234	C₂×C₆₁	semidirect
258. #3166	C₂×C₆₁	semidirect
259. #3162	C₂×C₆₁	semidirect
260. #3138	C₂×C₆₁	semidirect
261. C₂×#490	C₂×C₆₁	semidirect
262. #3096	C₂×C₆₁	semidirect
263. #3081	C₂×C₆₁	semidirect
264. #2923	C₂×C₆₁	semidirect
277. #544	C₂²×C₆₁	semidirect
282. #533	C₂²×C₆₁	semidirect
286. C₂×#125	C₂²×C₆₁	semidirect
290. #501	C₂²×C₆₁	semidirect
291. #501	C₂²×C₆₁	semidirect
292. #501	C₂²×C₆₁	semidirect
293. #501	C₂²×C₆₁	semidirect
294. #499	C₂²×C₆₁	semidirect
300. #482	C₂²×C₆₁	semidirect
301. #482	C₂²×C₆₁	semidirect
302. #481	C₂²×C₆₁	semidirect
303. #480	C₂²×C₆₁	semidirect
304. #478	C₂²×C₆₁	semidirect
305. #478	C₂²×C₆₁	semidirect
306. #476	C₂²×C₆₁	semidirect
307. #474	C₂²×C₆₁	semidirect
308. #433	C₂²×C₆₁	semidirect
309. #432	C₂²×C₆₁	semidirect
318. C₆₁	#60883	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×#3508	2
C₆₁×#3504	2
C₆₁×#3241	2
C₆₁×#3235	2
C₆₁×#3234	2
C₆₁×#3166	2
C₆₁×#3162	2
C₆₁×#3138	2
C₂×C₆₁×#490	2
C₆₁×#3096	2
C₆₁×#3081	2
C₆₁×#2923	2
#60883	61

Subgroups — C61×#60883 #29564316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60883 #29564316