Subgroups — C₆₁×#25595 #29529028

Order 15616.

1180 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2657	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2003	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2002	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1967	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1888	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1887	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#559	—	2	2	no	—
14	C₆₁×#556	—	2	2	no	—
15	C₆₁×#551	—	2	4	no	—
16	C₆₁×#542	—	2	2	no	—
17	C₆₁×#536	C₂²	1	1	yes	characteristic
18	C₆₁×#535	C₂²	1	1	yes	characteristic
19	C₆₁×#533	C₂²	1	1	yes	characteristic
20	C₂×#127×C₆₁	C₂²	1	2	yes	—
21	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#529	—	2	2	no	—
23	C₂×#124×C₆₁	C₂²	1	2	yes	—
24	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#519	C₂²	1	1	yes	characteristic
26	C₆₁×#518	C₂²	1	1	yes	characteristic
27	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#490	—	2	2	no	—
29	C₆₁×#486	—	2	2	no	—
30	C₆₁×#460	—	2	2	no	—
31	C₆₁×#459	—	2	2	no	—
32	C₆₁×#423	C₂²	1	1	yes	characteristic
33	C₂×#104×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#418	C₂²	1	2	yes	—
35	C₆₁×#418	C₂²	1	2	yes	—
36	C₆₁×#418	C₂²	1	2	yes	—
37	C₂×#101×C₆₁	C₂²	1	2	yes	—
38	C₂×#100×C₆₁	C₂²	1	2	yes	—
39	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#392	—	2	4	no	—
41	C₆₁×#376	C₂²	1	1	yes	characteristic
42	C₆₁×#339	C₂²	1	2	yes	—
43	C₆₁×#339	C₂²	1	2	yes	—
44	C₆₁×#339	C₂²	1	2	yes	—
45	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₆₁	—	2	4	no	—
48	C₂²×D₄×C₆₁	—	2	2	no	—
49	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
51	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
52	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×D₈×C₆₁	—	2	2	no	—
55	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
56	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₆₁	—	2	1	no	—
58	C₄⋊Q₈×C₆₁	D₄	1	2	yes	complemented
59	#127×C₆₁	—	2	1	no	—
60	#127×C₆₁	—	2	2	no	—
61	#127×C₆₁	—	2	1	no	—
62	#127×C₆₁	—	2	1	no	—
63	#127×C₆₁	—	2	4	no	—
64	#127×C₆₁	—	4	2	no	—
65	#126×C₆₁	—	2	4	no	—
66	#126×C₆₁	—	2	4	no	—
67	#125×C₆₁	D₄	1	2	yes	complemented
68	#124×C₆₁	—	2	4	no	—
69	#124×C₆₁	—	2	1	no	—
70	#124×C₆₁	—	2	1	no	—
71	#124×C₆₁	—	2	1	no	—
72	#124×C₆₁	—	2	2	no	—
73	#124×C₆₁	—	2	1	no	—
74	#124×C₆₁	—	2	4	no	—
75	#124×C₆₁	—	4	2	no	—
76	#123×C₆₁	—	2	4	no	—
77	#123×C₆₁	—	2	4	no	—
78	#123×C₆₁	—	2	2	no	—
79	C₂²⋊Q₈×C₆₁	—	2	4	no	—
80	C₂²⋊Q₈×C₆₁	—	2	2	no	—
81	C₂²⋊Q₈×C₆₁	—	2	2	no	—
82	#121×C₆₁	—	2	2	no	—
83	#120×C₆₁	—	2	2	no	—
84	C₄×Q₈×C₆₁	—	2	2	no	—
85	C₄×Q₈×C₆₁	—	2	2	no	—
86	C₄×Q₈×C₆₁	—	2	2	no	—
87	C₄×Q₈×C₆₁	D₄	1	2	yes	complemented
88	C₄×D₄×C₆₁	—	2	4	no	—
89	C₄×D₄×C₆₁	—	2	2	no	—
90	C₄×D₄×C₆₁	—	2	2	no	—
91	C₄×D₄×C₆₁	—	2	2	no	—
92	C₄×D₄×C₆₁	D₄	1	2	yes	complemented
93	#117×C₆₁	—	2	4	no	—
94	#117×C₆₁	—	2	2	no	—
95	#117×C₆₁	—	2	1	no	—
96	#117×C₆₁	C₂³	1	1	yes	characteristic
97	#117×C₆₁	C₂³	1	1	yes	characteristic
98	#117×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₆₁	D₄	1	4	yes	—
102	C₂×C₄²×C₆₁	—	2	1	no	—
103	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₆₁	—	2	2	no	—
106	#104×C₆₁	—	2	4	no	—
107	#102×C₆₁	—	2	4	no	—
108	#102×C₆₁	—	2	4	no	—
109	#102×C₆₁	—	2	4	no	—
110	#101×C₆₁	—	4	2	no	—
111	#100×C₆₁	—	4	2	no	—
112	#97×C₆₁	—	2	1	no	—
113	C₄×C₈×C₆₁	—	2	1	no	—
114	#95×C₆₁	—	2	2	no	—
115	C₂⁴×C₆₁	—	2	2	no	—
116	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
117	#41×C₆₁	—	2	2	no	—
118	#41×C₆₁	—	2	2	no	—
119	C₂×Q₈×C₆₁	—	2	2	no	—
120	C₂×Q₈×C₆₁	—	2	1	no	—
121	C₂×Q₈×C₆₁	—	2	1	no	—
122	C₂×Q₈×C₆₁	—	2	2	no	—
123	C₂×Q₈×C₆₁	—	2	2	no	—
124	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₆₁	—	2	1	no	—
126	C₂×D₄×C₆₁	—	2	4	no	—
127	C₂×D₄×C₆₁	—	2	1	no	—
128	C₂×D₄×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	2	no	—
130	C₂×D₄×C₆₁	—	2	2	no	—
131	C₂×D₄×C₆₁	—	2	2	no	—
132	C₂×D₄×C₆₁	—	2	2	no	—
133	C₂×D₄×C₆₁	—	2	2	no	—
134	C₂×D₄×C₆₁	—	2	2	no	—
135	C₂×D₄×C₆₁	—	2	2	no	—
136	C₂×D₄×C₆₁	—	2	2	no	—
137	C₂×D₄×C₆₁	—	4	8	no	—
138	C₂×D₄×C₆₁	—	4	2	no	—
139	C₂×D₄×C₆₁	—	4	2	no	—
140	C₂×D₄×C₆₁	—	8	4	no	—
141	C₂×D₄×C₆₁	—	8	8	no	—
142	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	—	2	2	no	—
144	C₂²×C₄×C₆₁	—	2	4	no	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	2	no	—
147	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
150	SD₁₆×C₆₁	—	4	4	no	—
151	D₈×C₆₁	—	4	4	no	—
152	M₁₆×C₆₁	—	2	2	no	—
153	M₁₆×C₆₁	—	2	2	no	—
154	M₁₆×C₆₁	—	2	2	no	—
155	M₁₆×C₆₁	—	2	2	no	—
156	C₂×C₈×C₆₁	—	2	2	no	—
157	C₂×C₈×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	4	no	—
159	C₄⋊C₄×C₆₁	—	2	4	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
167	C₂²⋊C₄×C₆₁	—	2	4	no	—
168	C₂²⋊C₄×C₆₁	—	2	4	no	—
169	C₂²⋊C₄×C₆₁	—	2	4	no	—
170	C₂²⋊C₄×C₆₁	—	2	1	no	—
171	C₂²⋊C₄×C₆₁	—	2	1	no	—
172	C₂²⋊C₄×C₆₁	—	2	1	no	—
173	C₂²⋊C₄×C₆₁	—	2	4	no	—
174	C₂²⋊C₄×C₆₁	—	2	4	no	—
175	C₂²⋊C₄×C₆₁	—	2	2	no	—
176	C₂²⋊C₄×C₆₁	—	4	8	no	—
177	C₄²×C₆₁	—	2	4	no	—
178	C₄²×C₆₁	—	2	2	no	—
179	C₄²×C₆₁	—	2	1	no	—
180	C₄²×C₆₁	—	2	1	no	—
181	C₄²×C₆₁	—	2	1	no	—
182	C₄²×C₆₁	—	2	2	no	—
183	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₆₁	C₂×D₄	1	2	yes	—
186	C₄²×C₆₁	#41	1	4	yes	—
187	C₂³×C₆₁	—	2	2	no	—
188	C₂³×C₆₁	—	2	1	no	—
189	C₂³×C₆₁	—	2	4	no	—
190	C₂³×C₆₁	—	4	4	no	—
191	C₂³×C₆₁	—	4	8	no	—
192	C₂³×C₆₁	—	4	2	no	—
193	C₂³×C₆₁	—	4	2	no	—
194	C₂³×C₆₁	—	4	2	no	—
195	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₆₁	—	2	1	no	—
197	Q₈×C₆₁	—	2	1	no	—
198	Q₈×C₆₁	—	4	1	no	—
199	Q₈×C₆₁	—	4	1	no	—
200	Q₈×C₆₁	—	4	2	no	—
201	Q₈×C₆₁	—	8	2	no	—
202	D₄×C₆₁	—	2	1	no	—
203	D₄×C₆₁	—	2	1	no	—
204	D₄×C₆₁	—	4	2	no	—
205	D₄×C₆₁	—	4	1	no	—
206	D₄×C₆₁	—	4	2	no	—
207	D₄×C₆₁	—	4	1	no	—
208	D₄×C₆₁	—	4	2	no	—
209	D₄×C₆₁	—	4	2	no	—
210	D₄×C₆₁	—	4	2	no	—
211	D₄×C₆₁	—	4	2	no	—
212	D₄×C₆₁	—	8	4	no	—
213	D₄×C₆₁	—	8	4	no	—
214	D₄×C₆₁	—	8	4	no	—
215	D₄×C₆₁	—	8	16	no	—
216	C₂×C₄×C₆₁	—	2	2	no	—
217	C₂×C₄×C₆₁	—	2	2	no	—
218	C₂×C₄×C₆₁	—	2	2	no	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	2	4	no	—
222	C₂×C₄×C₆₁	—	2	4	no	—
223	C₂×C₄×C₆₁	—	4	2	no	—
224	C₂×C₄×C₆₁	—	4	4	no	—
225	C₂×C₄×C₆₁	—	4	2	no	—
226	C₂×C₄×C₆₁	—	8	2	no	—
227	C₂×C₄×C₆₁	—	8	4	no	—
228	C₂×C₄×C₆₁	#120	1	2	yes	—
229	C₂×C₄×C₆₁	#120	1	2	yes	—
230	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
233	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
234	C₈×C₆₁	—	4	2	no	—
235	C₈×C₆₁	—	4	2	no	—
236	#25595	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₆₁	—	2	2	no	—
238	C₂²×C₆₁	—	4	1	no	—
239	C₂²×C₆₁	—	4	2	no	—
240	C₂²×C₆₁	—	4	2	no	—
241	C₂²×C₆₁	—	4	4	no	—
242	C₂²×C₆₁	—	8	4	no	—
243	C₂²×C₆₁	—	8	4	no	—
244	C₂²×C₆₁	—	8	4	no	—
245	C₂²×C₆₁	—	8	2	no	—
246	C₂²×C₆₁	—	8	4	no	—
247	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
248	C₂²×C₆₁	#546	1	2	yes	—
249	C₄×C₆₁	—	2	2	no	—
250	C₄×C₆₁	—	2	2	no	—
251	C₄×C₆₁	—	4	4	no	—
252	C₄×C₆₁	—	4	2	no	—
253	C₄×C₆₁	—	4	1	no	—
254	C₄×C₆₁	—	4	2	no	—
255	C₄×C₆₁	—	4	2	no	—
256	C₄×C₆₁	—	4	2	no	—
257	C₄×C₆₁	#532	1	1	yes	characteristic
258	C₄×C₆₁	#535	1	1	yes	characteristic
259	C₄×C₆₁	#550	1	2	yes	—
260	#3510	C₂×C₆₁	1	1	yes	characteristic, complemented
261	#3138	C₂×C₆₁	1	1	yes	characteristic, complemented
262	#3038	C₂×C₆₁	1	1	yes	characteristic, complemented
263	#2657	C₂×C₆₁	1	1	yes	characteristic, complemented
264	#2003	C₂×C₆₁	1	2	yes	complemented
265	#2002	C₂×C₆₁	1	2	yes	complemented
266	#1995	C₂×C₆₁	1	1	yes	characteristic, complemented
267	#1967	C₂×C₆₁	1	1	yes	characteristic, complemented
268	#1888	C₂×C₆₁	1	2	yes	complemented
269	#1887	C₂×C₆₁	1	2	yes	complemented
270	#1759	C₂×C₆₁	1	1	yes	characteristic, complemented
271	C₂×C₆₁	—	2	2	no	—
272	C₂×C₆₁	—	8	1	no	—
273	C₂×C₆₁	—	8	2	no	—
274	C₂×C₆₁	—	16	2	no	—
275	C₂×C₆₁	#2431	1	1	yes	characteristic
276	C₂×C₆₁	#3021	1	2	yes	—
277	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
278	#559	—	2	2	no	—
279	#556	—	2	2	no	—
280	#551	—	2	4	no	—
281	#542	—	2	2	no	—
282	#536	C₂²×C₆₁	1	1	yes	characteristic
283	#535	C₂²×C₆₁	1	1	yes	characteristic
284	#533	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#127	C₂²×C₆₁	1	2	yes	—
287	#529	—	2	2	no	—
288	C₂×#124	C₂²×C₆₁	1	2	yes	—
289	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
290	#519	C₂²×C₆₁	1	1	yes	characteristic
291	#518	C₂²×C₆₁	1	1	yes	characteristic
292	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
293	#490	—	2	2	no	—
294	#486	—	2	2	no	—
295	#460	—	2	2	no	—
296	#459	—	2	2	no	—
297	#423	C₂²×C₆₁	1	1	yes	characteristic
298	C₂×#104	C₂²×C₆₁	1	2	yes	—
299	#418	C₂²×C₆₁	1	2	yes	—
300	#418	C₂²×C₆₁	1	2	yes	—
301	#418	C₂²×C₆₁	1	2	yes	—
302	C₂×#101	C₂²×C₆₁	1	2	yes	—
303	C₂×#100	C₂²×C₆₁	1	2	yes	—
304	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
305	#392	—	2	4	no	—
306	#376	C₂²×C₆₁	1	1	yes	characteristic
307	#339	C₂²×C₆₁	1	2	yes	—
308	#339	C₂²×C₆₁	1	2	yes	—
309	#339	C₂²×C₆₁	1	2	yes	—
310	C₆₁	#25595	1	1	yes	characteristic, direct product factor, Sylow
311	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
312	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
316	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
317	AGL(1,ℤ/8)	—	4	2	no	—
318	AGL(1,ℤ/8)	—	4	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
322	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	D₄×C₆₁	1	2	yes	complemented
325	#127	—	2	1	no	—
326	#127	—	2	2	no	—
327	#127	—	2	1	no	—
328	#127	—	2	1	no	—
329	#127	—	2	4	no	—
330	#127	—	4	2	no	—
331	#126	—	2	4	no	—
332	#126	—	2	4	no	—
333	#125	D₄×C₆₁	1	2	yes	complemented
334	#124	—	2	4	no	—
335	#124	—	2	1	no	—
336	#124	—	2	1	no	—
337	#124	—	2	1	no	—
338	#124	—	2	1	no	—
339	#124	—	2	2	no	—
340	#124	—	2	4	no	—
341	#124	—	4	2	no	—
342	#123	—	2	4	no	—
343	#123	—	2	4	no	—
344	#123	—	2	2	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	#121	—	2	2	no	—
349	#120	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	D₄×C₆₁	1	2	yes	complemented
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	D₄×C₆₁	1	2	yes	complemented
359	#117	—	2	4	no	—
360	#117	—	2	2	no	—
361	#117	—	2	1	no	—
362	#117	C₂³×C₆₁	1	1	yes	characteristic
363	#117	C₂³×C₆₁	1	1	yes	characteristic
364	#117	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₂²⋊C₄	D₄×C₆₁	1	4	yes	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
370	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
371	C₄⋊C₈	—	2	2	no	—
372	#104	—	2	4	no	—
373	#102	—	2	4	no	—
374	#102	—	2	4	no	—
375	#102	—	2	4	no	—
376	#101	—	4	2	no	—
377	#100	—	4	2	no	—
378	#97	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	#95	—	2	2	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	8	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	8	4	no	—
407	C₂×D₄	—	8	8	no	—
408	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
416	SD₁₆	—	4	4	no	—
417	D₈	—	4	4	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	4	8	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₆₁	1	2	yes	—
452	C₄²	#41×C₆₁	1	4	yes	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	8	2	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	4	no	—
479	D₄	—	8	4	no	—
480	D₄	—	8	4	no	—
481	D₄	—	8	16	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	4	no	—
494	C₂×C₄	#120×C₆₁	1	2	yes	—
495	C₂×C₄	#120×C₆₁	1	2	yes	—
496	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
499	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
500	C₈	—	4	2	no	—
501	C₈	—	4	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	8	4	no	—
508	C₂²	—	8	4	no	—
509	C₂²	—	8	4	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	4	no	—
512	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
513	C₂²	C₆₁×#546	1	2	yes	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	C₆₁×#532	1	1	yes	characteristic
523	C₄	C₆₁×#535	1	1	yes	characteristic
524	C₄	C₆₁×#550	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	8	2	no	—
527	C₂	—	8	1	no	—
528	C₂	—	16	2	no	—
529	C₂	C₆₁×#2431	1	1	yes	characteristic
530	C₂	C₆₁×#3021	1	2	yes	—

	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×#3510	C₂	semidirect
2. C₆₁×#3138	C₂	semidirect
3. C₆₁×#3038	C₂	semidirect
4. C₆₁×#2657	C₂	semidirect
5. C₆₁×#2003	C₂	semidirect
6. C₆₁×#2002	C₂	semidirect
7. C₆₁×#1995	C₂	semidirect
8. C₆₁×#1967	C₂	semidirect
9. C₆₁×#1888	C₂	semidirect
10. C₆₁×#1887	C₂	semidirect
11. C₆₁×#1759	C₂	semidirect
58. C₄⋊Q₈×C₆₁	D₄	semidirect
67. #125×C₆₁	D₄	semidirect
87. C₄×Q₈×C₆₁	D₄	semidirect
92. C₄×D₄×C₆₁	D₄	semidirect
236. #25595	C₆₁	direct (N × H)
260. #3510	C₂×C₆₁	semidirect
261. #3138	C₂×C₆₁	semidirect
262. #3038	C₂×C₆₁	semidirect
263. #2657	C₂×C₆₁	semidirect
264. #2003	C₂×C₆₁	semidirect
265. #2002	C₂×C₆₁	semidirect
266. #1995	C₂×C₆₁	semidirect
267. #1967	C₂×C₆₁	semidirect
268. #1888	C₂×C₆₁	semidirect
269. #1887	C₂×C₆₁	semidirect
270. #1759	C₂×C₆₁	semidirect
310. C₆₁	#25595	direct (N × H)
324. C₄⋊Q₈	D₄×C₆₁	semidirect
333. #125	D₄×C₆₁	semidirect
353. C₄×Q₈	D₄×C₆₁	semidirect
358. C₄×D₄	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3510	2
C₆₁×#3138	2
C₆₁×#3038	2
C₆₁×#2657	2
C₆₁×#2003	2
C₆₁×#2002	2
C₆₁×#1995	2
C₆₁×#1967	2
C₆₁×#1888	2
C₆₁×#1887	2
C₆₁×#1759	2
#25595	61

Subgroups — C61×#25595 #29529028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25595 #29529028