Subgroups — C₆₁×#29821 #29533254

Order 15616.

800 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3040	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2047	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2046	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2045	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2019	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2018	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1967	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1837	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₆₁	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
16	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₆₁	C₂²	1	2	yes	—
18	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#495	—	2	2	no	—
20	C₆₁×#495	—	2	2	no	—
21	C₆₁×#464	—	2	4	no	—
22	C₆₁×#463	—	2	4	no	—
23	C₆₁×#433	—	2	2	no	—
24	C₆₁×#431	—	2	2	no	—
25	C₆₁×#424	C₂²	1	1	yes	characteristic
26	C₆₁×#424	C₂²	1	1	yes	characteristic
27	C₆₁×#423	C₂²	1	2	yes	—
28	C₆₁×#419	C₂²	1	2	yes	—
29	C₆₁×#418	C₂²	1	2	yes	—
30	C₂×#101×C₆₁	C₂²	1	2	yes	—
31	C₂×#101×C₆₁	C₂²	1	2	yes	—
32	C₂×#100×C₆₁	C₂²	1	2	yes	—
33	C₂×#100×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#408	C₂²	1	1	yes	characteristic
35	C₆₁×#408	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#341	C₂²	1	1	yes	characteristic
39	C₆₁×#341	C₂²	1	2	yes	—
40	C₆₁×#341	C₂²	1	1	yes	characteristic
41	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
44	#137×C₆₁	—	4	2	no	—
45	#137×C₆₁	—	4	2	no	—
46	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
47	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	—	2	2	no	—
50	C₂×Q₁₆×C₆₁	—	4	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×SD₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	4	no	—
54	C₂×SD₁₆×C₆₁	—	4	2	no	—
55	C₂×SD₁₆×C₆₁	—	4	2	no	—
56	C₂×D₈×C₆₁	—	2	2	no	—
57	C₂×D₈×C₆₁	—	2	2	no	—
58	C₂×D₈×C₆₁	—	4	2	no	—
59	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
65	#124×C₆₁	—	2	4	no	—
66	#124×C₆₁	—	2	2	no	—
67	#124×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	D₄	1	2	yes	—
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₄×D₄×C₆₁	D₄	1	2	yes	—
71	#117×C₆₁	—	2	1	no	—
72	#117×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₆₁	—	2	2	no	—
77	C₄⋊C₈×C₆₁	—	2	2	no	—
78	C₄⋊C₈×C₆₁	—	2	4	no	—
79	#103×C₆₁	—	2	4	no	—
80	#102×C₆₁	—	2	4	no	—
81	#101×C₆₁	—	4	2	no	—
82	#101×C₆₁	—	4	2	no	—
83	#100×C₆₁	—	4	2	no	—
84	#100×C₆₁	—	4	2	no	—
85	C₂²⋊C₈×C₆₁	—	2	2	no	—
86	C₂²⋊C₈×C₆₁	—	2	2	no	—
87	#97×C₆₁	—	2	1	no	—
88	C₄×C₈×C₆₁	—	2	1	no	—
89	C₄×C₈×C₆₁	D₄	1	2	yes	—
90	C₄×C₈×C₆₁	D₄	1	2	yes	—
91	C₂⁴×C₆₁	—	2	2	no	—
92	#41×C₆₁	—	2	2	no	—
93	#41×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	2	no	—
100	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₆₁	—	2	1	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	—	2	2	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	2	no	—
108	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	#41	1	2	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₆₁	—	4	4	no	—
115	Q₁₆×C₆₁	—	4	4	no	—
116	SD₁₆×C₆₁	—	4	8	no	—
117	SD₁₆×C₆₁	—	4	4	no	—
118	SD₁₆×C₆₁	—	4	4	no	—
119	D₈×C₆₁	—	4	4	no	—
120	D₈×C₆₁	—	4	4	no	—
121	M₁₆×C₆₁	—	2	2	no	—
122	M₁₆×C₆₁	—	2	2	no	—
123	M₁₆×C₆₁	—	2	2	no	—
124	M₁₆×C₆₁	—	2	2	no	—
125	M₁₆×C₆₁	—	2	2	no	—
126	M₁₆×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	1	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	—	2	2	no	—
133	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₆₁	—	2	1	no	—
138	C₂²⋊C₄×C₆₁	—	2	2	no	—
139	C₂²⋊C₄×C₆₁	—	4	4	no	—
140	C₂²⋊C₄×C₆₁	—	4	4	no	—
141	C₄²×C₆₁	—	2	2	no	—
142	C₄²×C₆₁	—	2	1	no	—
143	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₆₁	C₂×D₄	1	2	yes	—
146	C₂³×C₆₁	—	2	1	no	—
147	C₂³×C₆₁	—	4	2	no	—
148	C₂³×C₆₁	—	4	2	no	—
149	C₂³×C₆₁	—	4	2	no	—
150	C₂³×C₆₁	—	8	4	no	—
151	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
152	Q₈×C₆₁	—	2	2	no	—
153	Q₈×C₆₁	—	4	2	no	—
154	Q₈×C₆₁	—	4	2	no	—
155	Q₈×C₆₁	—	4	2	no	—
156	Q₈×C₆₁	—	4	2	no	—
157	D₄×C₆₁	—	2	2	no	—
158	D₄×C₆₁	—	4	2	no	—
159	D₄×C₆₁	—	4	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	4	2	no	—
162	D₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	4	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	1	no	—
169	C₂×C₄×C₆₁	—	4	2	no	—
170	C₂×C₄×C₆₁	—	4	2	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	#121	1	2	yes	—
173	C₂×C₄×C₆₁	#121	1	2	yes	—
174	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
177	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
178	C₈×C₆₁	—	2	2	no	—
179	C₈×C₆₁	—	2	2	no	—
180	C₈×C₆₁	—	4	1	no	—
181	C₈×C₆₁	—	4	1	no	—
182	C₈×C₆₁	—	4	2	no	—
183	C₈×C₆₁	—	4	2	no	—
184	#29821	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₆₁	—	2	2	no	—
186	C₂²×C₆₁	—	4	1	no	—
187	C₂²×C₆₁	—	4	2	no	—
188	C₂²×C₆₁	—	8	2	no	—
189	C₂²×C₆₁	—	8	4	no	—
190	C₂²×C₆₁	—	16	2	no	—
191	C₂²×C₆₁	—	16	2	no	—
192	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
193	C₂²×C₆₁	#540	1	2	yes	—
194	C₄×C₆₁	—	2	2	no	—
195	C₄×C₆₁	—	2	2	no	—
196	C₄×C₆₁	—	4	1	no	—
197	C₄×C₆₁	—	4	2	no	—
198	C₄×C₆₁	—	8	2	no	—
199	C₄×C₆₁	#535	1	1	yes	characteristic
200	C₄×C₆₁	#535	1	1	yes	characteristic
201	C₄×C₆₁	#535	1	2	yes	—
202	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#3040	C₂×C₆₁	1	2	yes	complemented
204	#2922	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#2047	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#2046	C₂×C₆₁	1	2	yes	complemented
207	#2045	C₂×C₆₁	1	1	yes	characteristic, complemented
208	#2020	C₂×C₆₁	1	1	yes	characteristic, complemented
209	#2019	C₂×C₆₁	1	2	yes	complemented
210	#2018	C₂×C₆₁	1	1	yes	characteristic
211	#1967	C₂×C₆₁	1	2	yes	complemented
212	#1837	C₂×C₆₁	1	1	yes	characteristic, complemented
213	C₂×C₆₁	—	2	2	no	—
214	C₂×C₆₁	—	8	1	no	—
215	C₂×C₆₁	—	16	2	no	—
216	C₂×C₆₁	#2619	1	1	yes	characteristic
217	C₂×C₆₁	#3067	1	2	yes	—
218	C₂×#137	C₂²×C₆₁	1	2	yes	—
219	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
220	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
221	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
222	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×#124	C₂²×C₆₁	1	2	yes	—
224	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
225	#495	—	2	2	no	—
226	#495	—	2	2	no	—
227	#464	—	2	4	no	—
228	#463	—	2	4	no	—
229	#433	—	2	2	no	—
230	#431	—	2	2	no	—
231	#424	C₂²×C₆₁	1	1	yes	characteristic
232	#424	C₂²×C₆₁	1	1	yes	characteristic
233	#423	C₂²×C₆₁	1	2	yes	—
234	#419	C₂²×C₆₁	1	2	yes	—
235	#418	C₂²×C₆₁	1	2	yes	—
236	C₂×#101	C₂²×C₆₁	1	2	yes	—
237	C₂×#101	C₂²×C₆₁	1	2	yes	—
238	C₂×#100	C₂²×C₆₁	1	2	yes	—
239	C₂×#100	C₂²×C₆₁	1	2	yes	—
240	#408	C₂²×C₆₁	1	1	yes	characteristic
241	#408	C₂²×C₆₁	1	1	yes	characteristic
242	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
244	#341	C₂²×C₆₁	1	1	yes	characteristic
245	#341	C₂²×C₆₁	1	2	yes	—
246	#341	C₂²×C₆₁	1	1	yes	characteristic
247	C₆₁	#29821	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
250	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
251	#137	—	4	2	no	—
252	#137	—	4	2	no	—
253	AGL(1,ℤ/8)	—	4	2	no	—
254	AGL(1,ℤ/8)	—	4	2	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	4	2	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	4	2	no	—
262	C₂×SD₁₆	—	4	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	2	2	no	—
265	C₂×D₈	—	4	2	no	—
266	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
267	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
268	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
269	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
272	#124	—	2	4	no	—
273	#124	—	2	2	no	—
274	#124	—	2	2	no	—
275	C₄×Q₈	D₄×C₆₁	1	2	yes	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	D₄×C₆₁	1	2	yes	—
278	#117	—	2	1	no	—
279	#117	C₂³×C₆₁	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	4	no	—
286	#103	—	2	4	no	—
287	#102	—	2	4	no	—
288	#101	—	4	2	no	—
289	#101	—	4	2	no	—
290	#100	—	4	2	no	—
291	#100	—	4	2	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	#97	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	D₄×C₆₁	1	2	yes	—
297	C₄×C₈	D₄×C₆₁	1	2	yes	—
298	C₂⁴	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	#41×C₆₁	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
321	Q₁₆	—	4	4	no	—
322	Q₁₆	—	4	4	no	—
323	SD₁₆	—	4	8	no	—
324	SD₁₆	—	4	4	no	—
325	SD₁₆	—	4	4	no	—
326	D₈	—	4	4	no	—
327	D₈	—	4	4	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₆₁	1	2	yes	—
353	C₂³	—	2	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	4	no	—
358	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	#121×C₆₁	1	2	yes	—
380	C₂×C₄	#121×C₆₁	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
383	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
384	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	8	4	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	16	2	no	—
397	C₂²	—	16	2	no	—
398	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
399	C₂²	C₆₁×#540	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	8	2	no	—
405	C₄	C₆₁×#535	1	1	yes	characteristic
406	C₄	C₆₁×#535	1	1	yes	characteristic
407	C₄	C₆₁×#535	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	8	1	no	—
410	C₂	—	16	2	no	—
411	C₂	C₆₁×#2619	1	1	yes	characteristic
412	C₂	C₆₁×#3067	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2018	C₂
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. C₂×C₆₁×#495	C₂	semidirect
2. C₆₁×#3040	C₂	semidirect
3. C₆₁×#2922	C₂	semidirect
4. C₆₁×#2047	C₂	semidirect
5. C₆₁×#2046	C₂	semidirect
6. C₆₁×#2045	C₂	semidirect
7. C₆₁×#2020	C₂	semidirect
8. C₆₁×#2019	C₂	semidirect
10. C₆₁×#1967	C₂	semidirect
11. C₆₁×#1837	C₂	semidirect
184. #29821	C₆₁	direct (N × H)
202. C₂×#495	C₂×C₆₁	semidirect
203. #3040	C₂×C₆₁	semidirect
204. #2922	C₂×C₆₁	semidirect
205. #2047	C₂×C₆₁	semidirect
206. #2046	C₂×C₆₁	semidirect
207. #2045	C₂×C₆₁	semidirect
208. #2020	C₂×C₆₁	semidirect
209. #2019	C₂×C₆₁	semidirect
211. #1967	C₂×C₆₁	semidirect
212. #1837	C₂×C₆₁	semidirect
247. C₆₁	#29821	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#495	2
C₆₁×#3040	2
C₆₁×#2922	2
C₆₁×#2047	2
C₆₁×#2046	2
C₆₁×#2045	2
C₆₁×#2020	2
C₆₁×#2019	2
C₆₁×#2018	2
C₆₁×#1967	2
C₆₁×#1837	2
#29821	61

Subgroups — C61×#29821 #29533254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29821 #29533254