Subgroups — C₆₁×#24523 #29527956

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3094	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#448	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2064	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2046	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1977	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1930	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1900	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1784	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#482	—	2	1	no	—
18	C₆₁×#482	—	2	1	no	—
19	C₆₁×#481	—	2	1	no	—
20	C₆₁×#480	—	2	1	no	—
21	C₆₁×#448	—	2	1	no	—
22	C₆₁×#448	—	2	1	no	—
23	C₆₁×#448	—	2	2	no	—
24	C₆₁×#433	—	2	2	no	—
25	C₆₁×#432	—	2	1	no	—
26	C₆₁×#431	—	2	1	no	—
27	C₂×#108×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#428	C₂²	1	1	yes	characteristic
29	C₆₁×#428	C₂²	1	1	yes	characteristic
30	C₆₁×#424	C₂²	1	2	yes	—
31	C₆₁×#419	—	2	1	no	—
32	C₆₁×#419	—	2	1	no	—
33	C₆₁×#419	C₂²	1	2	yes	—
34	C₆₁×#419	C₂²	1	2	yes	—
35	C₆₁×#418	C₂²	1	1	yes	characteristic
36	C₆₁×#418	C₂²	1	1	yes	characteristic
37	C₂×#103×C₆₁	—	2	1	no	—
38	C₂×#103×C₆₁	—	2	1	no	—
39	C₂×#103×C₆₁	C₂²	1	2	yes	—
40	C₂×#101×C₆₁	C₂²	1	2	yes	—
41	C₂×#101×C₆₁	C₂²	1	2	yes	—
42	C₂×#100×C₆₁	C₂²	1	2	yes	—
43	C₆₁×#407	C₂²	1	1	yes	characteristic
44	C₆₁×#407	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#405	C₂²	1	2	yes	—
47	C₆₁×#343	C₂²	1	2	yes	—
48	C₆₁×#341	C₂²	1	2	yes	—
49	C₂²×Q₈×C₆₁	—	2	1	no	—
50	C₂²×Q₈×C₆₁	—	2	4	no	—
51	C₂²×Q₈×C₆₁	—	2	1	no	—
52	C₂²×Q₈×C₆₁	—	2	1	no	—
53	C₂²×Q₈×C₆₁	—	2	1	no	—
54	C₂²×Q₈×C₆₁	—	2	1	no	—
55	C₂²×Q₈×C₆₁	—	4	2	no	—
56	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×D₄×C₆₁	—	2	1	no	—
58	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₆₁	—	2	1	no	—
60	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂×SD₁₆×C₆₁	—	2	4	no	—
62	C₂×SD₁₆×C₆₁	—	2	2	no	—
63	C₂×SD₁₆×C₆₁	—	2	2	no	—
64	C₂×SD₁₆×C₆₁	—	4	2	no	—
65	C₂×M₁₆×C₆₁	—	2	1	no	—
66	C₂×M₁₆×C₆₁	—	4	2	no	—
67	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
68	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
70	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	—	2	1	no	—
72	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
73	#121×C₆₁	—	2	1	no	—
74	#121×C₆₁	—	2	1	no	—
75	#121×C₆₁	—	2	1	no	—
76	#121×C₆₁	—	2	1	no	—
77	#117×C₆₁	—	2	1	no	—
78	#117×C₆₁	—	2	1	no	—
79	#117×C₆₁	D₄	1	1	yes	characteristic
80	#117×C₆₁	D₄	1	1	yes	characteristic
81	#117×C₆₁	C₂³	1	1	yes	characteristic
82	#117×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	#108×C₆₁	—	4	2	no	—
90	#107×C₆₁	—	2	1	no	—
91	#107×C₆₁	—	2	1	no	—
92	#106×C₆₁	—	2	1	no	—
93	#106×C₆₁	—	2	1	no	—
94	C₄⋊C₈×C₆₁	—	2	2	no	—
95	C₄⋊C₈×C₆₁	—	2	2	no	—
96	#103×C₆₁	—	2	2	no	—
97	#103×C₆₁	—	2	2	no	—
98	#103×C₆₁	—	2	2	no	—
99	#103×C₆₁	—	2	2	no	—
100	#103×C₆₁	—	2	2	no	—
101	#103×C₆₁	—	2	2	no	—
102	#102×C₆₁	—	2	1	no	—
103	#102×C₆₁	—	2	1	no	—
104	#102×C₆₁	—	2	1	no	—
105	#102×C₆₁	—	2	1	no	—
106	#101×C₆₁	—	2	4	no	—
107	#101×C₆₁	—	4	2	no	—
108	#100×C₆₁	—	4	2	no	—
109	C₂²⋊C₈×C₆₁	—	2	1	no	—
110	C₂²⋊C₈×C₆₁	—	2	1	no	—
111	C₂²⋊C₈×C₆₁	—	2	1	no	—
112	C₂²⋊C₈×C₆₁	—	2	1	no	—
113	C₂²⋊C₈×C₆₁	D₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₆₁	D₄	1	1	yes	characteristic
115	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
116	#97×C₆₁	—	2	2	no	—
117	C₄×C₈×C₆₁	—	2	2	no	—
118	C₂⁴×C₆₁	—	2	1	no	—
119	C₂⁴×C₆₁	#41	1	1	yes	characteristic
120	C₂×Q₈×C₆₁	—	2	2	no	—
121	C₂×Q₈×C₆₁	—	2	4	no	—
122	C₂×Q₈×C₆₁	—	2	4	no	—
123	C₂×Q₈×C₆₁	—	2	2	no	—
124	C₂×Q₈×C₆₁	—	2	2	no	—
125	C₂×Q₈×C₆₁	—	2	2	no	—
126	C₂×Q₈×C₆₁	—	2	2	no	—
127	C₂×Q₈×C₆₁	—	4	4	no	—
128	C₂×Q₈×C₆₁	—	4	4	no	—
129	C₂×Q₈×C₆₁	—	4	4	no	—
130	C₂×Q₈×C₆₁	—	4	2	no	—
131	C₂×Q₈×C₆₁	—	4	2	no	—
132	C₂×Q₈×C₆₁	—	4	1	no	—
133	C₂×Q₈×C₆₁	—	4	1	no	—
134	C₂×Q₈×C₆₁	#41	1	4	yes	—
135	C₂×D₄×C₆₁	—	2	1	no	—
136	C₂×D₄×C₆₁	—	2	1	no	—
137	C₂×D₄×C₆₁	—	2	2	no	—
138	C₂×D₄×C₆₁	—	2	2	no	—
139	C₂×D₄×C₆₁	—	4	1	no	—
140	C₂×D₄×C₆₁	—	4	1	no	—
141	C₂×D₄×C₆₁	—	8	2	no	—
142	C₂²×C₄×C₆₁	—	2	2	no	—
143	C₂²×C₄×C₆₁	—	2	2	no	—
144	C₂²×C₄×C₆₁	—	2	1	no	—
145	C₂²×C₄×C₆₁	—	2	2	no	—
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	4	4	no	—
149	C₂²×C₄×C₆₁	—	4	1	no	—
150	C₂²×C₄×C₆₁	—	4	1	no	—
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
157	SD₁₆×C₆₁	—	4	4	no	—
158	SD₁₆×C₆₁	—	4	4	no	—
159	M₁₆×C₆₁	—	2	2	no	—
160	M₁₆×C₆₁	—	2	2	no	—
161	M₁₆×C₆₁	—	2	2	no	—
162	M₁₆×C₆₁	—	2	2	no	—
163	M₁₆×C₆₁	—	2	2	no	—
164	M₁₆×C₆₁	—	2	2	no	—
165	M₁₆×C₆₁	—	4	2	no	—
166	C₂×C₈×C₆₁	—	2	2	no	—
167	C₂×C₈×C₆₁	—	2	2	no	—
168	C₂×C₈×C₆₁	—	2	2	no	—
169	C₂×C₈×C₆₁	—	2	1	no	—
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	2	no	—
172	C₂×C₈×C₆₁	—	4	2	no	—
173	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₆₁	—	2	1	no	—
176	C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
182	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
183	C₂²⋊C₄×C₆₁	—	2	1	no	—
184	C₂²⋊C₄×C₆₁	—	2	1	no	—
185	C₂²⋊C₄×C₆₁	—	2	1	no	—
186	C₂²⋊C₄×C₆₁	—	2	1	no	—
187	C₂²⋊C₄×C₆₁	—	4	1	no	—
188	C₂²⋊C₄×C₆₁	—	4	1	no	—
189	C₄²×C₆₁	—	2	1	no	—
190	C₄²×C₆₁	—	2	1	no	—
191	C₄²×C₆₁	—	2	1	no	—
192	C₄²×C₆₁	—	2	1	no	—
193	C₂³×C₆₁	—	2	2	no	—
194	C₂³×C₆₁	—	2	2	no	—
195	C₂³×C₆₁	—	4	1	no	—
196	C₂³×C₆₁	—	4	1	no	—
197	C₂³×C₆₁	—	4	2	no	—
198	C₂³×C₆₁	—	8	1	no	—
199	C₂³×C₆₁	—	8	1	no	—
200	C₂³×C₆₁	#121	1	1	yes	characteristic
201	C₂³×C₆₁	#121	1	1	yes	characteristic
202	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
203	Q₈×C₆₁	—	2	4	no	—
204	Q₈×C₆₁	—	2	4	no	—
205	Q₈×C₆₁	—	4	4	no	—
206	Q₈×C₆₁	—	4	4	no	—
207	Q₈×C₆₁	—	4	2	no	—
208	Q₈×C₆₁	—	4	2	no	—
209	D₄×C₆₁	—	4	1	no	—
210	D₄×C₆₁	—	4	1	no	—
211	D₄×C₆₁	—	4	2	no	—
212	D₄×C₆₁	—	8	2	no	—
213	D₄×C₆₁	—	8	2	no	—
214	C₂×C₄×C₆₁	—	2	2	no	—
215	C₂×C₄×C₆₁	—	2	1	no	—
216	C₂×C₄×C₆₁	—	2	1	no	—
217	C₂×C₄×C₆₁	—	2	1	no	—
218	C₂×C₄×C₆₁	—	2	1	no	—
219	C₂×C₄×C₆₁	—	2	2	no	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	1	no	—
225	C₂×C₄×C₆₁	—	2	4	no	—
226	C₂×C₄×C₆₁	—	4	4	no	—
227	C₂×C₄×C₆₁	—	4	4	no	—
228	C₂×C₄×C₆₁	—	4	2	no	—
229	C₂×C₄×C₆₁	—	4	2	no	—
230	C₂×C₄×C₆₁	—	4	2	no	—
231	C₂×C₄×C₆₁	—	4	1	no	—
232	C₂×C₄×C₆₁	—	8	1	no	—
233	C₂×C₄×C₆₁	—	8	1	no	—
234	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
235	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
239	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
240	C₈×C₆₁	—	2	2	no	—
241	C₈×C₆₁	—	2	2	no	—
242	C₈×C₆₁	—	4	1	no	—
243	C₈×C₆₁	—	4	2	no	—
244	C₈×C₆₁	—	4	1	no	—
245	C₈×C₆₁	—	4	2	no	—
246	#24523	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₆₁	—	2	1	no	—
248	C₂²×C₆₁	—	2	1	no	—
249	C₂²×C₆₁	—	2	1	no	—
250	C₂²×C₆₁	—	2	1	no	—
251	C₂²×C₆₁	—	2	1	no	—
252	C₂²×C₆₁	—	2	1	no	—
253	C₂²×C₆₁	—	2	1	no	—
254	C₂²×C₆₁	—	4	4	no	—
255	C₂²×C₆₁	—	8	1	no	—
256	C₂²×C₆₁	—	8	1	no	—
257	C₂²×C₆₁	—	8	1	no	—
258	C₂²×C₆₁	—	16	2	no	—
259	C₂²×C₆₁	#471	1	2	yes	—
260	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
261	C₂²×C₆₁	#551	1	2	yes	—
262	C₄×C₆₁	—	2	1	no	—
263	C₄×C₆₁	—	2	1	no	—
264	C₄×C₆₁	—	4	4	no	—
265	C₄×C₆₁	—	4	1	no	—
266	C₄×C₆₁	—	4	1	no	—
267	C₄×C₆₁	—	4	1	no	—
268	C₄×C₆₁	—	4	1	no	—
269	C₄×C₆₁	—	8	1	no	—
270	C₄×C₆₁	#525	1	1	yes	characteristic
271	C₄×C₆₁	#535	1	1	yes	characteristic
272	C₄×C₆₁	#546	1	2	yes	—
273	#3094	C₂×C₆₁	1	1	yes	characteristic
274	C₂×#448	C₂×C₆₁	1	1	yes	characteristic
275	#2924	C₂×C₆₁	1	1	yes	characteristic, complemented
276	C₂×#419	C₂×C₆₁	1	1	yes	characteristic, complemented
277	#2064	C₂×C₆₁	1	2	yes	complemented
278	#2046	C₂×C₆₁	1	2	yes	complemented
279	#1977	C₂×C₆₁	1	2	yes	complemented
280	#1930	C₂×C₆₁	1	2	yes	complemented
281	#1900	C₂×C₆₁	1	1	yes	characteristic
282	#1855	C₂×C₆₁	1	1	yes	characteristic, complemented
283	#1784	C₂×C₆₁	1	1	yes	characteristic, complemented
284	C₂×C₆₁	—	2	2	no	—
285	C₂×C₆₁	—	2	2	no	—
286	C₂×C₆₁	—	4	1	no	—
287	C₂×C₆₁	—	16	1	no	—
288	C₂×C₆₁	#2411	1	1	yes	characteristic
289	C₂×C₆₁	C₂×#471	1	1	yes	characteristic
290	C₂×C₆₁	#3069	1	1	yes	characteristic
291	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
292	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
293	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
294	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
295	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
296	#482	—	2	1	no	—
297	#482	—	2	1	no	—
298	#481	—	2	1	no	—
299	#480	—	2	1	no	—
300	#448	—	2	1	no	—
301	#448	—	2	1	no	—
302	#448	—	2	2	no	—
303	#433	—	2	2	no	—
304	#432	—	2	1	no	—
305	#431	—	2	1	no	—
306	C₂×#108	C₂²×C₆₁	1	2	yes	—
307	#428	C₂²×C₆₁	1	1	yes	characteristic
308	#428	C₂²×C₆₁	1	1	yes	characteristic
309	#424	C₂²×C₆₁	1	2	yes	—
310	#419	—	2	1	no	—
311	#419	—	2	1	no	—
312	#419	C₂²×C₆₁	1	2	yes	—
313	#419	C₂²×C₆₁	1	2	yes	—
314	#418	C₂²×C₆₁	1	1	yes	characteristic
315	#418	C₂²×C₆₁	1	1	yes	characteristic
316	C₂×#103	—	2	1	no	—
317	C₂×#103	—	2	1	no	—
318	C₂×#103	C₂²×C₆₁	1	2	yes	—
319	C₂×#101	C₂²×C₆₁	1	2	yes	—
320	C₂×#101	C₂²×C₆₁	1	2	yes	—
321	C₂×#100	C₂²×C₆₁	1	2	yes	—
322	#407	C₂²×C₆₁	1	1	yes	characteristic
323	#407	C₂²×C₆₁	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
325	#405	C₂²×C₆₁	1	2	yes	—
326	#343	C₂²×C₆₁	1	2	yes	—
327	#341	C₂²×C₆₁	1	2	yes	—
328	C₆₁	#24523	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×Q₈	—	2	4	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	—	4	2	no	—
336	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	4	2	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	4	2	no	—
347	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
348	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
349	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
350	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	—	2	1	no	—
356	#121	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	#117	D₄×C₆₁	1	1	yes	characteristic
360	#117	D₄×C₆₁	1	1	yes	characteristic
361	#117	C₂³×C₆₁	1	1	yes	characteristic
362	#117	C₂³×C₆₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	#108	—	4	2	no	—
370	#107	—	2	1	no	—
371	#107	—	2	1	no	—
372	#106	—	2	1	no	—
373	#106	—	2	1	no	—
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#102	—	2	1	no	—
383	#102	—	2	1	no	—
384	#102	—	2	1	no	—
385	#102	—	2	1	no	—
386	#101	—	2	4	no	—
387	#101	—	4	2	no	—
388	#100	—	4	2	no	—
389	C₂²⋊C₈	—	2	1	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	D₄×C₆₁	1	1	yes	characteristic
394	C₂²⋊C₈	D₄×C₆₁	1	1	yes	characteristic
395	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
396	#97	—	2	2	no	—
397	C₄×C₈	—	2	2	no	—
398	C₂⁴	—	2	1	no	—
399	C₂⁴	#41×C₆₁	1	1	yes	characteristic
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	—	4	1	no	—
414	C₂×Q₈	#41×C₆₁	1	4	yes	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
435	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
437	SD₁₆	—	4	4	no	—
438	SD₁₆	—	4	4	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	4	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	4	2	no	—
453	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
454	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
460	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	8	1	no	—
479	C₂³	—	8	1	no	—
480	C₂³	#121×C₆₁	1	1	yes	characteristic
481	C₂³	#121×C₆₁	1	1	yes	characteristic
482	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
483	Q₈	—	2	4	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	4	4	no	—
486	Q₈	—	4	4	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	1	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
515	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
519	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	2	no	—
525	C₈	—	4	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	16	2	no	—
538	C₂²	C₆₁×#471	1	2	yes	—
539	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
540	C₂²	C₆₁×#551	1	2	yes	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	4	no	—
548	C₄	—	8	1	no	—
549	C₄	C₆₁×#525	1	1	yes	characteristic
550	C₄	C₆₁×#535	1	1	yes	characteristic
551	C₄	C₆₁×#546	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	1	no	—
555	C₂	—	16	1	no	—
556	C₂	C₆₁×#2411	1	1	yes	characteristic
557	C₂	C₂×C₆₁×#471	1	1	yes	characteristic
558	C₂	C₆₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂³×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2924	C₂	semidirect
4. C₂×C₆₁×#419	C₂	semidirect
5. C₆₁×#2064	C₂	semidirect
6. C₆₁×#2046	C₂	semidirect
7. C₆₁×#1977	C₂	semidirect
8. C₆₁×#1930	C₂	semidirect
10. C₆₁×#1855	C₂	semidirect
11. C₆₁×#1784	C₂	semidirect
246. #24523	C₆₁	direct (N × H)
275. #2924	C₂×C₆₁	semidirect
276. C₂×#419	C₂×C₆₁	semidirect
277. #2064	C₂×C₆₁	semidirect
278. #2046	C₂×C₆₁	semidirect
279. #1977	C₂×C₆₁	semidirect
280. #1930	C₂×C₆₁	semidirect
282. #1855	C₂×C₆₁	semidirect
283. #1784	C₂×C₆₁	semidirect
328. C₆₁	#24523	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×#3094	2
C₂×C₆₁×#448	2
C₆₁×#2924	2
C₂×C₆₁×#419	2
C₆₁×#2064	2
C₆₁×#2046	2
C₆₁×#1977	2
C₆₁×#1930	2
C₆₁×#1900	2
C₆₁×#1855	2
C₆₁×#1784	2
#24523	61

Subgroups — C61×#24523 #29527956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24523 #29527956