Subgroups — C₆₁×#19700 #29523133

Order 15616.

778 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3147	C₂	1	1	yes	maximal, characteristic
6	C₂×C₆₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1723	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1719	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1717	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1714	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	—	2	2	no	—
13	C₆₁×#532	C₂²	1	1	yes	characteristic
14	C₆₁×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#500	C₂²	1	2	yes	—
18	C₆₁×#500	C₂²	1	2	yes	—
19	C₆₁×#498	C₂²	1	2	yes	—
20	C₆₁×#495	—	2	2	no	—
21	C₆₁×#494	C₂²	1	1	yes	characteristic
22	C₆₁×#493	C₂²	1	1	yes	characteristic
23	C₆₁×#492	C₂²	1	1	yes	characteristic
24	C₆₁×#492	C₂²	1	1	yes	characteristic
25	C₆₁×#492	C₂²	1	2	yes	—
26	C₆₁×#487	—	2	2	no	—
27	C₆₁×#487	C₂²	1	2	yes	—
28	C₆₁×#487	C₂²	1	2	yes	—
29	C₆₁×#487	C₂²	1	2	yes	—
30	C₆₁×#486	C₂²	1	2	yes	—
31	C₆₁×#486	C₂²	1	2	yes	—
32	C₆₁×#486	C₂²	1	2	yes	—
33	C₆₁×#481	—	2	2	no	—
34	C₆₁×#480	—	2	2	no	—
35	C₆₁×#480	—	2	2	no	—
36	C₆₁×#476	—	2	2	no	—
37	C₆₁×#474	—	2	2	no	—
38	C₆₁×#474	—	2	2	no	—
39	C₆₁×#461	—	2	2	no	—
40	C₆₁×#448	—	2	2	no	—
41	C₆₁×#431	C₂²	1	1	yes	characteristic
42	C₆₁×#431	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₁	—	2	2	no	—
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#322	C₂²	1	2	yes	—
46	C₆₁×#322	C₂²	1	2	yes	—
47	C₂×#41×C₆₁	—	2	1	no	—
48	C₂×#41×C₆₁	—	2	1	no	—
49	C₂²×Q₈×C₆₁	—	2	1	no	—
50	C₂²×Q₈×C₆₁	—	2	1	no	—
51	#135×C₆₁	—	4	8	no	—
52	C₂×Q₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	2	no	—
55	C₂×SD₁₆×C₆₁	—	2	4	no	—
56	C₂×D₈×C₆₁	—	2	2	no	—
57	C₂²×C₈×C₆₁	D₄	1	2	yes	—
58	C₄⋊Q₈×C₆₁	—	2	1	no	—
59	C₄⋊Q₈×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	#127×C₆₁	C₂³	1	1	yes	characteristic
69	#127×C₆₁	C₂³	1	1	yes	characteristic
70	#124×C₆₁	—	2	1	no	—
71	#124×C₆₁	—	2	1	no	—
72	#121×C₆₁	—	2	1	no	—
73	#121×C₆₁	—	2	1	no	—
74	#121×C₆₁	—	2	1	no	—
75	#121×C₆₁	—	2	1	no	—
76	C₄×D₄×C₆₁	—	2	1	no	—
77	C₄×D₄×C₆₁	—	2	1	no	—
78	C₄×D₄×C₆₁	—	2	1	no	—
79	C₄×D₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	#107×C₆₁	—	2	4	no	—
86	#107×C₆₁	—	2	4	no	—
87	#106×C₆₁	—	2	4	no	—
88	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
89	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
90	#103×C₆₁	—	2	4	no	—
91	#103×C₆₁	—	2	4	no	—
92	#103×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	2	4	no	—
94	#102×C₆₁	—	2	4	no	—
95	#102×C₆₁	—	2	4	no	—
96	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
97	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
98	C₄×C₈×C₆₁	D₄	1	2	yes	—
99	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₁	C₂³	1	2	yes	—
102	C₄×C₈×C₆₁	C₂³	1	2	yes	—
103	#41×C₆₁	—	4	4	no	—
104	#41×C₆₁	—	4	4	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	4	1	no	—
110	C₂×Q₈×C₆₁	—	4	1	no	—
111	C₂×Q₈×C₆₁	—	4	4	no	—
112	C₂×Q₈×C₆₁	—	8	2	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	—	2	1	no	—
116	C₂×D₄×C₆₁	—	2	1	no	—
117	C₂×D₄×C₆₁	—	2	1	no	—
118	C₂×D₄×C₆₁	—	2	1	no	—
119	C₂×D₄×C₆₁	—	4	1	no	—
120	C₂×D₄×C₆₁	—	4	1	no	—
121	C₂²×C₄×C₆₁	—	4	1	no	—
122	C₂²×C₄×C₆₁	—	4	1	no	—
123	C₂²×C₄×C₆₁	—	4	1	no	—
124	C₂²×C₄×C₆₁	—	4	1	no	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₆₁	—	4	4	no	—
129	SD₁₆×C₆₁	—	4	4	no	—
130	SD₁₆×C₆₁	—	4	4	no	—
131	SD₁₆×C₆₁	—	8	4	no	—
132	D₈×C₆₁	—	4	4	no	—
133	C₂×C₈×C₆₁	—	2	4	no	—
134	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	2	2	no	—
140	C₄⋊C₄×C₆₁	—	2	2	no	—
141	C₄⋊C₄×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	1	no	—
144	C₄⋊C₄×C₆₁	—	2	1	no	—
145	C₄⋊C₄×C₆₁	—	2	1	no	—
146	C₄⋊C₄×C₆₁	—	4	1	no	—
147	C₄⋊C₄×C₆₁	—	4	1	no	—
148	C₄⋊C₄×C₆₁	—	4	1	no	—
149	C₄⋊C₄×C₆₁	—	4	1	no	—
150	C₂²⋊C₄×C₆₁	—	4	1	no	—
151	C₂²⋊C₄×C₆₁	—	4	1	no	—
152	C₂²⋊C₄×C₆₁	—	4	1	no	—
153	C₂²⋊C₄×C₆₁	—	4	1	no	—
154	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
158	C₂³×C₆₁	—	4	1	no	—
159	C₂³×C₆₁	—	4	1	no	—
160	C₂³×C₆₁	#127	1	1	yes	characteristic
161	Q₈×C₆₁	—	4	2	no	—
162	Q₈×C₆₁	—	4	2	no	—
163	Q₈×C₆₁	—	4	4	no	—
164	Q₈×C₆₁	—	4	4	no	—
165	Q₈×C₆₁	—	8	2	no	—
166	Q₈×C₆₁	—	8	2	no	—
167	D₄×C₆₁	—	4	2	no	—
168	D₄×C₆₁	—	4	2	no	—
169	D₄×C₆₁	—	4	2	no	—
170	D₄×C₆₁	—	4	2	no	—
171	D₄×C₆₁	—	4	2	no	—
172	D₄×C₆₁	—	4	2	no	—
173	D₄×C₆₁	—	8	2	no	—
174	D₄×C₆₁	—	8	2	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	1	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	8	2	no	—
182	C₂×C₄×C₆₁	—	8	2	no	—
183	C₂×C₄×C₆₁	—	8	2	no	—
184	C₂×C₄×C₆₁	—	8	2	no	—
185	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
186	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
187	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
188	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
189	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₆₁	—	2	2	no	—
193	C₈×C₆₁	—	2	2	no	—
194	C₈×C₆₁	—	2	4	no	—
195	C₈×C₆₁	—	2	4	no	—
196	#19700	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₆₁	—	2	1	no	—
198	C₂²×C₆₁	—	2	1	no	—
199	C₂²×C₆₁	—	8	1	no	—
200	C₂²×C₆₁	—	8	1	no	—
201	C₂²×C₆₁	—	8	1	no	—
202	C₂²×C₆₁	—	8	1	no	—
203	C₂²×C₆₁	—	8	1	no	—
204	C₂²×C₆₁	—	8	1	no	—
205	C₂²×C₆₁	#496	1	2	yes	—
206	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
207	C₄×C₆₁	—	2	1	no	—
208	C₄×C₆₁	—	2	1	no	—
209	C₄×C₆₁	—	8	1	no	—
210	C₄×C₆₁	—	8	1	no	—
211	C₄×C₆₁	—	8	2	no	—
212	C₄×C₆₁	—	8	2	no	—
213	C₄×C₆₁	#496	1	2	yes	—
214	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₄×C₆₁	#577	1	2	yes	—
216	C₄×C₆₁	#578	1	2	yes	—
217	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#3226	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#3226	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#3206	C₂×C₆₁	1	1	yes	characteristic, complemented
221	#3147	C₂×C₆₁	1	1	yes	characteristic
222	C₂×#487	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1723	C₂×C₆₁	1	2	yes	complemented
224	#1719	C₂×C₆₁	1	2	yes	complemented
225	#1717	C₂×C₆₁	1	2	yes	complemented
226	#1714	C₂×C₆₁	1	2	yes	complemented
227	#1452	C₂×C₆₁	1	1	yes	characteristic, complemented
228	C₂×C₆₁	—	2	2	no	—
229	C₂×C₆₁	—	16	1	no	—
230	C₂×C₆₁	—	16	1	no	—
231	C₂×C₆₁	C₂×#496	1	1	yes	characteristic
232	C₂×C₆₁	#3154	1	1	yes	characteristic
233	C₂×C₆₁	#3156	1	1	yes	characteristic
234	C₂×#135	—	2	2	no	—
235	#532	C₂²×C₆₁	1	1	yes	characteristic
236	#532	C₂²×C₆₁	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
239	#500	C₂²×C₆₁	1	2	yes	—
240	#500	C₂²×C₆₁	1	2	yes	—
241	#498	C₂²×C₆₁	1	2	yes	—
242	#495	—	2	2	no	—
243	#494	C₂²×C₆₁	1	1	yes	characteristic
244	#493	C₂²×C₆₁	1	1	yes	characteristic
245	#492	C₂²×C₆₁	1	1	yes	characteristic
246	#492	C₂²×C₆₁	1	1	yes	characteristic
247	#492	C₂²×C₆₁	1	2	yes	—
248	#487	—	2	2	no	—
249	#487	C₂²×C₆₁	1	2	yes	—
250	#487	C₂²×C₆₁	1	2	yes	—
251	#487	C₂²×C₆₁	1	2	yes	—
252	#486	C₂²×C₆₁	1	2	yes	—
253	#486	C₂²×C₆₁	1	2	yes	—
254	#486	C₂²×C₆₁	1	2	yes	—
255	#481	—	2	2	no	—
256	#480	—	2	2	no	—
257	#480	—	2	2	no	—
258	#476	—	2	2	no	—
259	#474	—	2	2	no	—
260	#474	—	2	2	no	—
261	#461	—	2	2	no	—
262	#448	—	2	2	no	—
263	#431	C₂²×C₆₁	1	1	yes	characteristic
264	#431	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×#103	—	2	2	no	—
266	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
267	#322	C₂²×C₆₁	1	2	yes	—
268	#322	C₂²×C₆₁	1	2	yes	—
269	C₆₁	#19700	1	1	yes	characteristic, direct product factor, Sylow
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	#135	—	4	8	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂²×C₈	D₄×C₆₁	1	2	yes	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
291	#127	C₂³×C₆₁	1	1	yes	characteristic
292	#127	C₂³×C₆₁	1	1	yes	characteristic
293	#124	—	2	1	no	—
294	#124	—	2	1	no	—
295	#121	—	2	1	no	—
296	#121	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
308	#107	—	2	4	no	—
309	#107	—	2	4	no	—
310	#106	—	2	4	no	—
311	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
312	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
313	#103	—	2	4	no	—
314	#103	—	2	4	no	—
315	#103	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	#102	—	2	4	no	—
319	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
320	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
321	C₄×C₈	D₄×C₆₁	1	2	yes	—
322	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₆₁	1	2	yes	—
325	C₄×C₈	C₂³×C₆₁	1	2	yes	—
326	#41	—	4	4	no	—
327	#41	—	4	4	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	—	4	4	no	—
335	C₂×Q₈	—	8	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
351	Q₁₆	—	4	4	no	—
352	SD₁₆	—	4	4	no	—
353	SD₁₆	—	4	4	no	—
354	SD₁₆	—	8	4	no	—
355	D₈	—	4	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
360	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
379	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
380	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	#127×C₆₁	1	1	yes	characteristic
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	4	4	no	—
388	Q₈	—	8	2	no	—
389	Q₈	—	8	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
409	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
410	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
411	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
412	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	4	no	—
418	C₈	—	2	4	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₆₁×#496	1	2	yes	—
428	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₆₁×#496	1	2	yes	—
436	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
437	C₄	C₆₁×#577	1	2	yes	—
438	C₄	C₆₁×#578	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	—	16	1	no	—
441	C₂	—	16	1	no	—
442	C₂	C₂×C₆₁×#496	1	1	yes	characteristic
443	C₂	C₆₁×#3154	1	1	yes	characteristic
444	C₂	C₆₁×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3147	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3227	C₂	semidirect
2. C₆₁×#3226	C₂	semidirect
3. C₆₁×#3226	C₂	semidirect
4. C₆₁×#3206	C₂	semidirect
6. C₂×C₆₁×#487	C₂	semidirect
7. C₆₁×#1723	C₂	semidirect
8. C₆₁×#1719	C₂	semidirect
9. C₆₁×#1717	C₂	semidirect
10. C₆₁×#1714	C₂	semidirect
11. C₆₁×#1452	C₂	semidirect
196. #19700	C₆₁	direct (N × H)
217. #3227	C₂×C₆₁	semidirect
218. #3226	C₂×C₆₁	semidirect
219. #3226	C₂×C₆₁	semidirect
220. #3206	C₂×C₆₁	semidirect
222. C₂×#487	C₂×C₆₁	semidirect
223. #1723	C₂×C₆₁	semidirect
224. #1719	C₂×C₆₁	semidirect
225. #1717	C₂×C₆₁	semidirect
226. #1714	C₂×C₆₁	semidirect
227. #1452	C₂×C₆₁	semidirect
269. C₆₁	#19700	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×#3227	2
C₆₁×#3226	2
C₆₁×#3206	2
C₆₁×#3147	2
C₂×C₆₁×#487	2
C₆₁×#1723	2
C₆₁×#1719	2
C₆₁×#1717	2
C₆₁×#1714	2
C₆₁×#1452	2
#19700	61

Subgroups — C61×#19700 #29523133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19700 #29523133