Subgroups — C₆₁×#25618 #29529051

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 652 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	C₆₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2640	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2007	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2006	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1963	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1883	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1882	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₆₁	C₂²	1	2	yes	—
13	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#556	—	2	1	no	—
17	C₆₁×#555	—	2	1	no	—
18	C₆₁×#554	—	2	1	no	—
19	C₆₁×#553	—	2	2	no	—
20	C₆₁×#548	—	2	2	no	—
21	C₆₁×#547	—	2	1	no	—
22	C₆₁×#542	—	2	2	no	—
23	C₆₁×#537	C₂²	1	2	yes	—
24	C₆₁×#533	—	2	1	no	—
25	C₆₁×#532	—	2	1	no	—
26	C₆₁×#532	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#520	C₂²	1	2	yes	—
30	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#497	—	2	1	no	—
32	C₆₁×#496	—	2	1	no	—
33	C₆₁×#495	—	2	2	no	—
34	C₆₁×#464	—	2	1	no	—
35	C₆₁×#464	—	2	1	no	—
36	C₆₁×#463	—	2	1	no	—
37	C₆₁×#463	—	2	1	no	—
38	C₆₁×#423	C₂²	1	1	yes	characteristic
39	C₂×#104×C₆₁	C₂²	1	2	yes	—
40	C₂×#104×C₆₁	C₂²	1	2	yes	—
41	C₂×#104×C₆₁	C₂²	1	2	yes	—
42	C₆₁×#419	C₂²	1	1	yes	characteristic
43	C₆₁×#418	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#397	—	2	2	no	—
46	C₆₁×#393	—	2	2	no	—
47	C₆₁×#391	C₂²	1	2	yes	—
48	C₆₁×#390	C₂²	1	2	yes	—
49	C₆₁×#376	C₂²	1	1	yes	characteristic
50	C₆₁×#343	C₂²	1	2	yes	—
51	C₆₁×#343	C₂²	1	2	yes	—
52	C₆₁×#339	C₂²	1	2	yes	—
53	C₂×#41×C₆₁	—	2	2	no	—
54	C₂×#41×C₆₁	C₂³	1	2	yes	—
55	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
57	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
59	#137×C₆₁	—	2	4	no	—
60	#137×C₆₁	—	4	2	no	—
61	#137×C₆₁	—	4	2	no	—
62	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
63	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
64	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
65	C₂×Q₁₆×C₆₁	—	2	1	no	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×SD₁₆×C₆₁	—	2	1	no	—
68	C₂×SD₁₆×C₆₁	—	2	2	no	—
69	C₂×SD₁₆×C₆₁	—	2	1	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×D₈×C₆₁	—	2	1	no	—
72	C₂×D₈×C₆₁	—	2	2	no	—
73	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
76	C₄⋊Q₈×C₆₁	—	2	1	no	—
77	C₄⋊Q₈×C₆₁	—	2	1	no	—
78	C₄⋊Q₈×C₆₁	—	2	1	no	—
79	C₄⋊Q₈×C₆₁	—	2	1	no	—
80	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
81	#127×C₆₁	D₄	1	1	yes	characteristic
82	#126×C₆₁	—	2	4	no	—
83	#125×C₆₁	—	2	2	no	—
84	#124×C₆₁	—	2	2	no	—
85	#124×C₆₁	—	2	4	no	—
86	#124×C₆₁	—	2	1	no	—
87	#124×C₆₁	—	2	1	no	—
88	#124×C₆₁	—	2	1	no	—
89	#124×C₆₁	—	2	1	no	—
90	#124×C₆₁	D₄	1	2	yes	—
91	#123×C₆₁	—	2	4	no	—
92	C₂²⋊Q₈×C₆₁	—	2	2	no	—
93	C₂²⋊Q₈×C₆₁	—	2	4	no	—
94	C₂²⋊Q₈×C₆₁	—	2	2	no	—
95	C₂²⋊Q₈×C₆₁	—	2	2	no	—
96	#121×C₆₁	—	2	2	no	—
97	#121×C₆₁	—	2	2	no	—
98	#121×C₆₁	—	2	2	no	—
99	#121×C₆₁	—	2	1	no	—
100	#121×C₆₁	—	2	1	no	—
101	#121×C₆₁	—	2	4	no	—
102	C₄×Q₈×C₆₁	—	2	2	no	—
103	C₄×Q₈×C₆₁	—	2	2	no	—
104	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
105	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
106	C₄×D₄×C₆₁	—	2	2	no	—
107	C₄×D₄×C₆₁	—	2	2	no	—
108	C₄×D₄×C₆₁	—	2	1	no	—
109	C₄×D₄×C₆₁	—	2	4	no	—
110	C₄×D₄×C₆₁	—	2	1	no	—
111	C₄×D₄×C₆₁	—	2	1	no	—
112	C₄×D₄×C₆₁	—	2	1	no	—
113	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
114	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
115	#117×C₆₁	—	2	2	no	—
116	#117×C₆₁	—	2	2	no	—
117	#117×C₆₁	—	2	1	no	—
118	#117×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
125	C₂×C₄²×C₆₁	—	2	1	no	—
126	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
127	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₆₁	—	2	1	no	—
129	C₄⋊C₈×C₆₁	—	2	1	no	—
130	#104×C₆₁	—	2	4	no	—
131	#104×C₆₁	—	4	2	no	—
132	#104×C₆₁	—	4	2	no	—
133	#103×C₆₁	—	2	1	no	—
134	#103×C₆₁	—	2	1	no	—
135	#102×C₆₁	—	2	1	no	—
136	#102×C₆₁	—	2	1	no	—
137	#97×C₆₁	—	2	1	no	—
138	C₄×C₈×C₆₁	—	2	1	no	—
139	#95×C₆₁	—	2	1	no	—
140	#95×C₆₁	—	2	1	no	—
141	#95×C₆₁	—	2	4	no	—
142	C₂⁴×C₆₁	—	2	1	no	—
143	#41×C₆₁	—	2	2	no	—
144	#41×C₆₁	—	2	2	no	—
145	#41×C₆₁	—	2	2	no	—
146	#41×C₆₁	—	2	2	no	—
147	#41×C₆₁	—	2	2	no	—
148	#41×C₆₁	—	2	2	no	—
149	#41×C₆₁	—	8	4	no	—
150	C₂×Q₈×C₆₁	—	2	2	no	—
151	C₂×Q₈×C₆₁	—	2	2	no	—
152	C₂×Q₈×C₆₁	—	2	1	no	—
153	C₂×Q₈×C₆₁	—	2	1	no	—
154	C₂×Q₈×C₆₁	—	2	2	no	—
155	C₂×Q₈×C₆₁	—	2	2	no	—
156	C₂×Q₈×C₆₁	—	8	2	no	—
157	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
158	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₆₁	—	2	1	no	—
160	C₂×D₄×C₆₁	—	2	2	no	—
161	C₂×D₄×C₆₁	—	2	4	no	—
162	C₂×D₄×C₆₁	—	2	1	no	—
163	C₂×D₄×C₆₁	—	2	1	no	—
164	C₂×D₄×C₆₁	—	2	1	no	—
165	C₂×D₄×C₆₁	—	2	1	no	—
166	C₂×D₄×C₆₁	—	2	2	no	—
167	C₂×D₄×C₆₁	—	2	2	no	—
168	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	—	2	4	no	—
171	C₂²×C₄×C₆₁	—	2	1	no	—
172	C₂²×C₄×C₆₁	—	2	1	no	—
173	C₂²×C₄×C₆₁	—	2	1	no	—
174	C₂²×C₄×C₆₁	—	2	2	no	—
175	C₂²×C₄×C₆₁	—	2	2	no	—
176	C₂²×C₄×C₆₁	—	2	1	no	—
177	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
181	Q₁₆×C₆₁	—	4	4	no	—
182	Q₁₆×C₆₁	—	4	2	no	—
183	SD₁₆×C₆₁	—	4	4	no	—
184	SD₁₆×C₆₁	—	4	4	no	—
185	SD₁₆×C₆₁	—	4	2	no	—
186	SD₁₆×C₆₁	—	4	2	no	—
187	D₈×C₆₁	—	4	4	no	—
188	D₈×C₆₁	—	4	2	no	—
189	M₁₆×C₆₁	—	2	2	no	—
190	M₁₆×C₆₁	—	2	2	no	—
191	M₁₆×C₆₁	—	2	2	no	—
192	M₁₆×C₆₁	#41	1	4	yes	complemented
193	C₂×C₈×C₆₁	—	2	2	no	—
194	C₂×C₈×C₆₁	—	2	1	no	—
195	C₂×C₈×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	4	no	—
197	C₄⋊C₄×C₆₁	—	2	4	no	—
198	C₄⋊C₄×C₆₁	—	2	2	no	—
199	C₄⋊C₄×C₆₁	—	2	2	no	—
200	C₄⋊C₄×C₆₁	—	2	1	no	—
201	C₄⋊C₄×C₆₁	—	2	1	no	—
202	C₄⋊C₄×C₆₁	—	2	1	no	—
203	C₄⋊C₄×C₆₁	—	2	1	no	—
204	C₄⋊C₄×C₆₁	—	2	2	no	—
205	C₄⋊C₄×C₆₁	—	2	2	no	—
206	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	1	no	—
212	C₂²⋊C₄×C₆₁	—	2	1	no	—
213	C₂²⋊C₄×C₆₁	—	2	1	no	—
214	C₂²⋊C₄×C₆₁	—	2	2	no	—
215	C₂²⋊C₄×C₆₁	—	2	2	no	—
216	C₂²⋊C₄×C₆₁	—	4	1	no	—
217	C₂²⋊C₄×C₆₁	—	4	1	no	—
218	C₂²⋊C₄×C₆₁	—	4	1	no	—
219	C₂²⋊C₄×C₆₁	—	4	1	no	—
220	C₂²⋊C₄×C₆₁	—	8	4	no	—
221	C₄²×C₆₁	—	2	4	no	—
222	C₄²×C₆₁	—	2	1	no	—
223	C₄²×C₆₁	—	2	1	no	—
224	C₄²×C₆₁	—	2	1	no	—
225	C₄²×C₆₁	—	2	2	no	—
226	C₄²×C₆₁	—	2	2	no	—
227	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₆₁	—	2	1	no	—
232	C₂³×C₆₁	—	2	2	no	—
233	C₂³×C₆₁	—	4	2	no	—
234	C₂³×C₆₁	—	4	2	no	—
235	C₂³×C₆₁	—	4	1	no	—
236	C₂³×C₆₁	—	4	2	no	—
237	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₆₁	—	2	1	no	—
239	Q₈×C₆₁	—	2	1	no	—
240	Q₈×C₆₁	—	2	2	no	—
241	Q₈×C₆₁	—	2	2	no	—
242	Q₈×C₆₁	—	4	4	no	—
243	Q₈×C₆₁	—	4	1	no	—
244	Q₈×C₆₁	—	4	1	no	—
245	Q₈×C₆₁	—	4	2	no	—
246	Q₈×C₆₁	—	8	2	no	—
247	D₄×C₆₁	—	2	1	no	—
248	D₄×C₆₁	—	2	1	no	—
249	D₄×C₆₁	—	2	2	no	—
250	D₄×C₆₁	—	2	2	no	—
251	D₄×C₆₁	—	4	2	no	—
252	D₄×C₆₁	—	4	2	no	—
253	D₄×C₆₁	—	4	2	no	—
254	D₄×C₆₁	—	4	2	no	—
255	D₄×C₆₁	—	4	2	no	—
256	D₄×C₆₁	—	4	1	no	—
257	D₄×C₆₁	—	4	1	no	—
258	D₄×C₆₁	—	4	2	no	—
259	D₄×C₆₁	—	8	4	no	—
260	C₂×C₄×C₆₁	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	2	no	—
262	C₂×C₄×C₆₁	—	2	1	no	—
263	C₂×C₄×C₆₁	—	2	1	no	—
264	C₂×C₄×C₆₁	—	2	4	no	—
265	C₂×C₄×C₆₁	—	4	1	no	—
266	C₂×C₄×C₆₁	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	2	no	—
268	C₂×C₄×C₆₁	—	4	2	no	—
269	C₂×C₄×C₆₁	—	4	2	no	—
270	C₂×C₄×C₆₁	—	4	2	no	—
271	C₂×C₄×C₆₁	—	4	2	no	—
272	C₂×C₄×C₆₁	—	4	4	no	—
273	C₂×C₄×C₆₁	—	4	2	no	—
274	C₂×C₄×C₆₁	—	4	2	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	4	2	no	—
277	C₂×C₄×C₆₁	—	4	2	no	—
278	C₂×C₄×C₆₁	—	8	4	no	—
279	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
280	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
281	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
282	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
283	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
286	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
287	C₈×C₆₁	—	2	4	no	—
288	C₈×C₆₁	—	4	1	no	—
289	C₈×C₆₁	—	4	1	no	—
290	#25618	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂²×C₆₁	—	2	1	no	—
292	C₂²×C₆₁	—	2	1	no	—
293	C₂²×C₆₁	—	4	2	no	—
294	C₂²×C₆₁	—	4	1	no	—
295	C₂²×C₆₁	—	4	1	no	—
296	C₂²×C₆₁	—	4	2	no	—
297	C₂²×C₆₁	—	4	1	no	—
298	C₂²×C₆₁	—	4	2	no	—
299	C₂²×C₆₁	—	8	4	no	—
300	C₂²×C₆₁	—	8	1	no	—
301	C₂²×C₆₁	—	8	1	no	—
302	C₂²×C₆₁	—	8	1	no	—
303	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
304	C₂²×C₆₁	#550	1	2	yes	—
305	C₄×C₆₁	—	2	1	no	—
306	C₄×C₆₁	—	2	1	no	—
307	C₄×C₆₁	—	2	1	no	—
308	C₄×C₆₁	—	2	1	no	—
309	C₄×C₆₁	—	4	2	no	—
310	C₄×C₆₁	—	4	1	no	—
311	C₄×C₆₁	—	4	1	no	—
312	C₄×C₆₁	—	4	4	no	—
313	C₄×C₆₁	—	4	1	no	—
314	C₄×C₆₁	—	8	2	no	—
315	C₄×C₆₁	—	8	1	no	—
316	C₄×C₆₁	#532	1	1	yes	characteristic
317	C₄×C₆₁	#535	1	1	yes	characteristic
318	C₄×C₆₁	#546	1	2	yes	—
319	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
320	#3153	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#3040	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#2640	C₂×C₆₁	1	1	yes	characteristic, complemented
323	#2007	C₂×C₆₁	1	2	yes	complemented
324	#2006	C₂×C₆₁	1	2	yes	complemented
325	#1997	C₂×C₆₁	1	1	yes	characteristic, complemented
326	#1963	C₂×C₆₁	1	1	yes	characteristic, complemented
327	#1883	C₂×C₆₁	1	2	yes	complemented
328	#1882	C₂×C₆₁	1	2	yes	complemented
329	#1759	C₂×C₆₁	1	1	yes	characteristic, complemented
330	C₂×C₆₁	—	2	2	no	—
331	C₂×C₆₁	—	8	1	no	—
332	C₂×C₆₁	—	8	2	no	—
333	C₂×C₆₁	—	16	1	no	—
334	C₂×C₆₁	#2431	1	1	yes	characteristic
335	C₂×C₆₁	#3019	1	1	yes	characteristic
336	C₂×C₆₁	#3020	1	1	yes	characteristic
337	C₂×#137	C₂²×C₆₁	1	2	yes	—
338	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
339	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
340	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
341	#556	—	2	1	no	—
342	#555	—	2	1	no	—
343	#554	—	2	1	no	—
344	#553	—	2	2	no	—
345	#548	—	2	2	no	—
346	#547	—	2	1	no	—
347	#542	—	2	2	no	—
348	#537	C₂²×C₆₁	1	2	yes	—
349	#533	—	2	1	no	—
350	#532	—	2	1	no	—
351	#532	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
354	#520	C₂²×C₆₁	1	2	yes	—
355	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
356	#497	—	2	1	no	—
357	#496	—	2	1	no	—
358	#495	—	2	2	no	—
359	#464	—	2	1	no	—
360	#464	—	2	1	no	—
361	#463	—	2	1	no	—
362	#463	—	2	1	no	—
363	#423	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#104	C₂²×C₆₁	1	2	yes	—
365	C₂×#104	C₂²×C₆₁	1	2	yes	—
366	C₂×#104	C₂²×C₆₁	1	2	yes	—
367	#419	C₂²×C₆₁	1	1	yes	characteristic
368	#418	C₂²×C₆₁	1	1	yes	characteristic
369	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
370	#397	—	2	2	no	—
371	#393	—	2	2	no	—
372	#391	C₂²×C₆₁	1	2	yes	—
373	#390	C₂²×C₆₁	1	2	yes	—
374	#376	C₂²×C₆₁	1	1	yes	characteristic
375	#343	C₂²×C₆₁	1	2	yes	—
376	#343	C₂²×C₆₁	1	2	yes	—
377	#339	C₂²×C₆₁	1	2	yes	—
378	C₆₁	#25618	1	1	yes	characteristic, direct product factor, Sylow
379	C₂×#41	—	2	2	no	—
380	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
381	C₂×#41	C₂³×C₆₁	1	2	yes	—
382	C₂²×Q₈	D₄×C₆₁	1	2	yes	—
383	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
385	#137	—	2	4	no	—
386	#137	—	4	2	no	—
387	#137	—	4	2	no	—
388	AGL(1,ℤ/8)	—	2	4	no	—
389	AGL(1,ℤ/8)	—	4	2	no	—
390	AGL(1,ℤ/8)	—	4	2	no	—
391	C₂×Q₁₆	—	2	1	no	—
392	C₂×Q₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	—	2	1	no	—
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×D₈	—	2	1	no	—
398	C₂×D₈	—	2	2	no	—
399	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
401	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
402	C₄⋊Q₈	—	2	1	no	—
403	C₄⋊Q₈	—	2	1	no	—
404	C₄⋊Q₈	—	2	1	no	—
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
407	#127	D₄×C₆₁	1	1	yes	characteristic
408	#126	—	2	4	no	—
409	#125	—	2	2	no	—
410	#124	—	2	2	no	—
411	#124	—	2	4	no	—
412	#124	—	2	1	no	—
413	#124	—	2	1	no	—
414	#124	—	2	1	no	—
415	#124	—	2	1	no	—
416	#124	D₄×C₆₁	1	2	yes	—
417	#123	—	2	4	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	4	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	#121	—	2	2	no	—
423	#121	—	2	2	no	—
424	#121	—	2	2	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	—	2	4	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
431	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	—	2	4	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
440	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
441	#117	—	2	2	no	—
442	#117	—	2	2	no	—
443	#117	—	2	1	no	—
444	#117	C₂³×C₆₁	1	1	yes	characteristic
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	4	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
453	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
454	C₄⋊C₈	—	2	1	no	—
455	C₄⋊C₈	—	2	1	no	—
456	#104	—	2	4	no	—
457	#104	—	4	2	no	—
458	#104	—	4	2	no	—
459	#103	—	2	1	no	—
460	#103	—	2	1	no	—
461	#102	—	2	1	no	—
462	#102	—	2	1	no	—
463	#97	—	2	1	no	—
464	C₄×C₈	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	4	no	—
468	C₂⁴	—	2	1	no	—
469	#41	—	2	2	no	—
470	#41	—	2	2	no	—
471	#41	—	2	2	no	—
472	#41	—	2	2	no	—
473	#41	—	2	2	no	—
474	#41	—	2	2	no	—
475	#41	—	8	4	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	8	2	no	—
483	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
484	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
495	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
504	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
507	Q₁₆	—	4	4	no	—
508	Q₁₆	—	4	2	no	—
509	SD₁₆	—	4	4	no	—
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	4	2	no	—
512	SD₁₆	—	4	2	no	—
513	D₈	—	4	4	no	—
514	D₈	—	4	2	no	—
515	M₁₆	—	2	2	no	—
516	M₁₆	—	2	2	no	—
517	M₁₆	—	2	2	no	—
518	M₁₆	#41×C₆₁	1	4	yes	complemented
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
533	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	8	4	no	—
547	C₄²	—	2	4	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	2	no	—
553	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
554	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
555	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
556	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
557	C₂³	—	2	1	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	1	no	—
563	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
564	Q₈	—	2	1	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	4	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	2	no	—
572	Q₈	—	8	2	no	—
573	D₄	—	2	1	no	—
574	D₄	—	2	1	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	2	no	—
585	D₄	—	8	4	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
606	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
607	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
608	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
612	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
613	C₈	—	2	4	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	4	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
629	C₂²	C₆₁×#550	1	2	yes	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	4	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	2	no	—
640	C₄	—	8	1	no	—
641	C₄	C₆₁×#532	1	1	yes	characteristic
642	C₄	C₆₁×#535	1	1	yes	characteristic
643	C₄	C₆₁×#546	1	2	yes	—
644	C₂	—	2	2	no	—
645	C₂	—	8	1	no	—
646	C₂	—	8	2	no	—
647	C₂	—	16	1	no	—
648	C₂	C₆₁×#2431	1	1	yes	characteristic
649	C₂	C₆₁×#3019	1	1	yes	characteristic
650	C₂	C₆₁×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3511	C₂	semidirect
2. C₆₁×#3153	C₂	semidirect
3. C₆₁×#3040	C₂	semidirect
4. C₆₁×#2640	C₂	semidirect
5. C₆₁×#2007	C₂	semidirect
6. C₆₁×#2006	C₂	semidirect
7. C₆₁×#1997	C₂	semidirect
8. C₆₁×#1963	C₂	semidirect
9. C₆₁×#1883	C₂	semidirect
10. C₆₁×#1882	C₂	semidirect
11. C₆₁×#1759	C₂	semidirect
192. M₁₆×C₆₁	#41	semidirect
290. #25618	C₆₁	direct (N × H)
319. #3511	C₂×C₆₁	semidirect
320. #3153	C₂×C₆₁	semidirect
321. #3040	C₂×C₆₁	semidirect
322. #2640	C₂×C₆₁	semidirect
323. #2007	C₂×C₆₁	semidirect
324. #2006	C₂×C₆₁	semidirect
325. #1997	C₂×C₆₁	semidirect
326. #1963	C₂×C₆₁	semidirect
327. #1883	C₂×C₆₁	semidirect
328. #1882	C₂×C₆₁	semidirect
329. #1759	C₂×C₆₁	semidirect
378. C₆₁	#25618	direct (N × H)
518. M₁₆	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3511	2
C₆₁×#3153	2
C₆₁×#3040	2
C₆₁×#2640	2
C₆₁×#2007	2
C₆₁×#2006	2
C₆₁×#1997	2
C₆₁×#1963	2
C₆₁×#1883	2
C₆₁×#1882	2
C₆₁×#1759	2
#25618	61

Subgroups — C61×#25618 #29529051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25618 #29529051