Subgroups — C₆₁×#61911 #29565344

Order 15616.

1704 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3400	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3398	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3392	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3371	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3368	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3364	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3222	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3120	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#564	—	2	2	no	—
17	C₆₁×#559	C₂²	1	4	yes	—
18	C₆₁×#557	—	2	1	no	—
19	C₆₁×#557	—	2	1	no	—
20	C₆₁×#557	C₂²	1	2	yes	complemented
21	C₆₁×#557	C₂²	1	2	yes	complemented
22	C₆₁×#557	C₂²	1	2	yes	complemented
23	C₆₁×#557	C₂²	1	2	yes	complemented
24	C₆₁×#556	C₂²	1	2	yes	—
25	C₆₁×#555	—	2	1	no	—
26	C₆₁×#553	—	2	2	no	—
27	C₆₁×#550	C₂²	1	2	yes	—
28	C₆₁×#547	—	2	1	no	—
29	C₆₁×#541	—	2	2	no	—
30	C₆₁×#541	—	2	2	no	—
31	C₆₁×#541	C₂²	1	4	yes	—
32	C₆₁×#538	—	2	2	no	—
33	C₆₁×#535	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#525	—	2	2	no	—
39	C₆₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#497	C₂²	1	4	yes	—
42	C₆₁×#497	C₂²	1	2	yes	complemented
43	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#492	C₂²	1	4	yes	—
45	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#490	C₂²	1	4	yes	—
47	C₆₁×#489	C₂²	1	2	yes	complemented
48	C₆₁×#488	C₂²	1	4	yes	—
49	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#484	C₂²	1	2	yes	—
52	C₆₁×#483	C₂²	1	2	yes	—
53	C₆₁×#479	C₂²	1	4	yes	complemented
54	C₆₁×#478	C₂²	1	4	yes	complemented
55	C₆₁×#476	C₂²	1	2	yes	—
56	C₆₁×#474	C₂²	1	2	yes	—
57	C₆₁×#464	C₂²	1	4	yes	—
58	C₆₁×#464	C₂²	1	4	yes	—
59	C₆₁×#464	C₂²	1	4	yes	complemented
60	C₆₁×#462	C₂²	1	2	yes	complemented
61	C₆₁×#462	C₂²	1	4	yes	complemented
62	C₆₁×#461	C₂²	1	2	yes	—
63	C₆₁×#461	C₂²	1	2	yes	—
64	C₆₁×#461	C₂²	1	4	yes	complemented
65	C₆₁×#460	C₂²	1	4	yes	—
66	C₆₁×#460	C₂²	1	4	yes	—
67	C₆₁×#460	C₂²	1	2	yes	complemented
68	C₆₁×#452	C₂²	1	4	yes	—
69	C₆₁×#452	C₂²	1	4	yes	—
70	C₆₁×#450	C₂²	1	2	yes	—
71	C₆₁×#450	C₂²	1	2	yes	—
72	C₆₁×#446	C₂²	1	2	yes	complemented
73	C₆₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
75	C₆₁×#441	C₂²	1	4	yes	complemented
76	C₆₁×#440	C₂²	1	4	yes	—
77	C₆₁×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
82	C₆₁×#433	C₂²	1	4	yes	—
83	C₆₁×#432	C₂²	1	1	yes	characteristic
84	C₆₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₁	—	2	1	no	—
89	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
90	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₆₁	—	2	2	no	—
97	C₄⋊Q₈×C₆₁	—	2	2	no	—
98	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
106	#127×C₆₁	C₂³	1	1	yes	characteristic
107	#127×C₆₁	C₂³	1	4	yes	—
108	#126×C₆₁	—	2	4	no	—
109	#126×C₆₁	—	2	4	no	—
110	#126×C₆₁	—	2	4	no	—
111	#125×C₆₁	—	2	2	no	—
112	#125×C₆₁	—	2	2	no	—
113	#125×C₆₁	—	2	4	no	—
114	#125×C₆₁	—	2	4	no	—
115	#125×C₆₁	—	2	4	no	—
116	#125×C₆₁	—	2	4	no	—
117	#125×C₆₁	—	2	4	no	—
118	#125×C₆₁	—	2	4	no	—
119	#125×C₆₁	—	2	1	no	—
120	#125×C₆₁	—	2	1	no	—
121	#125×C₆₁	D₄	1	2	yes	—
122	#125×C₆₁	C₂³	1	4	yes	—
123	#124×C₆₁	—	2	4	no	—
124	#124×C₆₁	C₂³	1	2	yes	—
125	#124×C₆₁	C₂³	1	4	yes	—
126	#123×C₆₁	—	2	4	no	—
127	#123×C₆₁	—	2	4	no	—
128	C₂²⋊Q₈×C₆₁	—	2	2	no	—
129	C₂²⋊Q₈×C₆₁	—	2	1	no	—
130	C₂²⋊Q₈×C₆₁	—	2	1	no	—
131	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
132	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
135	#121×C₆₁	—	2	1	no	—
136	#121×C₆₁	—	2	1	no	—
137	#121×C₆₁	—	2	2	no	—
138	#121×C₆₁	—	2	2	no	—
139	#121×C₆₁	—	2	4	no	—
140	#121×C₆₁	—	2	2	no	—
141	#120×C₆₁	—	2	4	no	—
142	C₄×Q₈×C₆₁	—	2	2	no	—
143	C₄×Q₈×C₆₁	—	2	2	no	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	2	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
152	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
153	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄×D₄×C₆₁	—	2	4	no	—
156	C₄×D₄×C₆₁	—	2	4	no	—
157	C₄×D₄×C₆₁	—	2	1	no	—
158	C₄×D₄×C₆₁	—	2	1	no	—
159	C₄×D₄×C₆₁	—	2	1	no	—
160	C₄×D₄×C₆₁	—	2	1	no	—
161	C₄×D₄×C₆₁	C₂³	1	2	yes	—
162	C₄×D₄×C₆₁	C₂³	1	4	yes	—
163	C₄×D₄×C₆₁	C₂³	1	2	yes	—
164	#117×C₆₁	—	2	1	no	—
165	#117×C₆₁	—	2	1	no	—
166	#117×C₆₁	—	2	2	no	—
167	#117×C₆₁	—	2	2	no	—
168	#117×C₆₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
172	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
173	#107×C₆₁	C₂³	1	4	yes	—
174	#106×C₆₁	C₂³	1	2	yes	—
175	#106×C₆₁	C₂³	1	2	yes	—
176	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
180	#103×C₆₁	C₂³	1	2	yes	—
181	#103×C₆₁	C₂³	1	2	yes	—
182	#103×C₆₁	C₂³	1	4	yes	—
183	#103×C₆₁	C₂³	1	4	yes	—
184	#103×C₆₁	C₂³	1	4	yes	—
185	#102×C₆₁	C₂³	1	2	yes	—
186	#102×C₆₁	C₂³	1	2	yes	—
187	#102×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	4	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
192	#97×C₆₁	C₂³	1	2	yes	—
193	#97×C₆₁	C₂³	1	4	yes	—
194	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	4	yes	—
197	C₂⁴×C₆₁	—	2	1	no	—
198	#41×C₆₁	—	4	4	no	—
199	#41×C₆₁	—	8	4	no	—
200	C₂×Q₈×C₆₁	—	2	1	no	—
201	C₂×Q₈×C₆₁	—	2	1	no	—
202	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
203	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
207	C₂×D₄×C₆₁	—	2	2	no	—
208	C₂×D₄×C₆₁	—	2	1	no	—
209	C₂×D₄×C₆₁	—	2	1	no	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	2	1	no	—
212	C₂×D₄×C₆₁	—	2	4	no	—
213	C₂×D₄×C₆₁	—	4	2	no	—
214	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
215	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₁	—	2	1	no	—
217	C₂²×C₄×C₆₁	—	2	2	no	—
218	C₂²×C₄×C₆₁	—	2	2	no	—
219	C₂²×C₄×C₆₁	—	2	4	no	—
220	C₂²×C₄×C₆₁	—	2	2	no	—
221	C₂²×C₄×C₆₁	—	8	2	no	—
222	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
225	Q₁₆×C₆₁	—	4	4	no	—
226	Q₁₆×C₆₁	—	4	4	no	—
227	SD₁₆×C₆₁	—	4	2	no	—
228	SD₁₆×C₆₁	—	4	4	no	—
229	SD₁₆×C₆₁	—	4	4	no	—
230	SD₁₆×C₆₁	—	4	4	no	—
231	SD₁₆×C₆₁	—	4	2	no	—
232	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
233	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
234	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
235	C₄⋊C₄×C₆₁	—	2	1	no	—
236	C₄⋊C₄×C₆₁	—	2	4	no	—
237	C₄⋊C₄×C₆₁	—	2	1	no	—
238	C₄⋊C₄×C₆₁	—	2	1	no	—
239	C₄⋊C₄×C₆₁	—	2	1	no	—
240	C₄⋊C₄×C₆₁	—	2	1	no	—
241	C₄⋊C₄×C₆₁	—	2	1	no	—
242	C₄⋊C₄×C₆₁	—	2	1	no	—
243	C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₄⋊C₄×C₆₁	—	2	1	no	—
245	C₄⋊C₄×C₆₁	—	2	2	no	—
246	C₄⋊C₄×C₆₁	—	2	2	no	—
247	C₄⋊C₄×C₆₁	—	2	4	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	4	no	—
250	C₄⋊C₄×C₆₁	—	2	4	no	—
251	C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	4	no	—
254	C₄⋊C₄×C₆₁	—	2	4	no	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	4	no	—
272	C₂²⋊C₄×C₆₁	—	2	2	no	—
273	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
274	C₄²×C₆₁	—	2	4	no	—
275	C₄²×C₆₁	—	2	2	no	—
276	C₄²×C₆₁	—	2	2	no	—
277	C₄²×C₆₁	—	2	4	no	—
278	C₄²×C₆₁	—	2	4	no	—
279	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
282	C₄²×C₆₁	C₂⁴	1	4	yes	—
283	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	—	2	2	no	—
286	C₂³×C₆₁	—	4	2	no	—
287	C₂³×C₆₁	—	8	1	no	—
288	C₂³×C₆₁	—	8	1	no	—
289	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₆₁	—	2	4	no	—
291	Q₈×C₆₁	—	2	2	no	—
292	Q₈×C₆₁	—	2	4	no	—
293	Q₈×C₆₁	—	2	2	no	—
294	Q₈×C₆₁	—	2	4	no	—
295	Q₈×C₆₁	—	4	2	no	—
296	Q₈×C₆₁	—	4	2	no	—
297	Q₈×C₆₁	—	4	2	no	—
298	D₄×C₆₁	—	2	2	no	—
299	D₄×C₆₁	—	2	2	no	—
300	D₄×C₆₁	—	2	4	no	—
301	D₄×C₆₁	—	4	2	no	—
302	D₄×C₆₁	—	4	4	no	—
303	D₄×C₆₁	—	4	2	no	—
304	D₄×C₆₁	—	8	1	no	—
305	D₄×C₆₁	—	8	4	no	—
306	D₄×C₆₁	—	8	4	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	4	1	no	—
316	C₂×C₄×C₆₁	—	4	4	no	—
317	C₂×C₄×C₆₁	—	4	4	no	—
318	C₂×C₄×C₆₁	—	8	2	no	—
319	C₂×C₄×C₆₁	—	8	4	no	—
320	C₂×C₄×C₆₁	—	8	1	no	—
321	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
329	C₈×C₆₁	—	2	2	no	—
330	C₈×C₆₁	—	2	4	no	—
331	C₈×C₆₁	—	2	2	no	—
332	#61911	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂²×C₆₁	—	2	1	no	—
334	C₂²×C₆₁	—	2	1	no	—
335	C₂²×C₆₁	—	2	1	no	—
336	C₂²×C₆₁	—	4	2	no	—
337	C₂²×C₆₁	—	4	2	no	—
338	C₂²×C₆₁	—	4	2	no	—
339	C₂²×C₆₁	—	4	2	no	—
340	C₂²×C₆₁	—	4	2	no	—
341	C₂²×C₆₁	—	4	2	no	—
342	C₂²×C₆₁	—	8	4	no	—
343	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
344	C₄×C₆₁	—	2	1	no	—
345	C₄×C₆₁	—	2	1	no	—
346	C₄×C₆₁	—	2	4	no	—
347	C₄×C₆₁	—	2	1	no	—
348	C₄×C₆₁	—	2	1	no	—
349	C₄×C₆₁	—	2	4	no	—
350	C₄×C₆₁	—	4	2	no	—
351	C₄×C₆₁	—	4	2	no	—
352	C₄×C₆₁	—	4	2	no	—
353	C₄×C₆₁	—	4	2	no	—
354	C₄×C₆₁	—	4	2	no	—
355	C₄×C₆₁	—	4	2	no	—
356	C₄×C₆₁	#577	1	2	yes	—
357	C₄×C₆₁	#585	1	2	yes	—
358	#3556	C₂×C₆₁	1	1	yes	characteristic, complemented
359	#3506	C₂×C₆₁	1	1	yes	characteristic
360	#3400	C₂×C₆₁	1	4	yes	complemented
361	#3398	C₂×C₆₁	1	2	yes	complemented
362	#3392	C₂×C₆₁	1	2	yes	complemented
363	#3371	C₂×C₆₁	1	4	yes	complemented
364	#3368	C₂×C₆₁	1	2	yes	complemented
365	#3364	C₂×C₆₁	1	2	yes	complemented
366	#3222	C₂×C₆₁	1	4	yes	complemented
367	#3216	C₂×C₆₁	1	1	yes	characteristic, complemented
368	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#3120	C₂×C₆₁	1	4	yes	complemented
370	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
371	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#2985	C₂×C₆₁	1	1	yes	characteristic, complemented
373	C₂×C₆₁	—	4	1	no	—
374	C₂×C₆₁	—	8	2	no	—
375	C₂×C₆₁	—	8	2	no	—
376	C₂×C₆₁	#3487	1	1	yes	characteristic
377	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
378	C₂×C₆₁	#3586	1	1	yes	characteristic
379	#564	—	2	2	no	—
380	#559	C₂²×C₆₁	1	4	yes	—
381	#557	—	2	1	no	—
382	#557	—	2	1	no	—
383	#557	C₂²×C₆₁	1	2	yes	complemented
384	#557	C₂²×C₆₁	1	2	yes	complemented
385	#557	C₂²×C₆₁	1	2	yes	complemented
386	#557	C₂²×C₆₁	1	2	yes	complemented
387	#556	C₂²×C₆₁	1	2	yes	—
388	#555	—	2	1	no	—
389	#553	—	2	2	no	—
390	#550	C₂²×C₆₁	1	2	yes	—
391	#547	—	2	1	no	—
392	#541	—	2	2	no	—
393	#541	—	2	2	no	—
394	#541	C₂²×C₆₁	1	4	yes	—
395	#538	—	2	2	no	—
396	#535	C₂²×C₆₁	1	2	yes	—
397	#533	C₂²×C₆₁	1	1	yes	characteristic
398	#533	C₂²×C₆₁	1	1	yes	characteristic
399	#533	C₂²×C₆₁	1	1	yes	characteristic
400	#532	C₂²×C₆₁	1	1	yes	characteristic
401	#525	—	2	2	no	—
402	#520	C₂²×C₆₁	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
404	#497	C₂²×C₆₁	1	4	yes	—
405	#497	C₂²×C₆₁	1	2	yes	complemented
406	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
407	#492	C₂²×C₆₁	1	4	yes	—
408	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
409	#490	C₂²×C₆₁	1	4	yes	—
410	#489	C₂²×C₆₁	1	2	yes	complemented
411	#488	C₂²×C₆₁	1	4	yes	—
412	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
413	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
414	#484	C₂²×C₆₁	1	2	yes	—
415	#483	C₂²×C₆₁	1	2	yes	—
416	#479	C₂²×C₆₁	1	4	yes	complemented
417	#478	C₂²×C₆₁	1	4	yes	complemented
418	#476	C₂²×C₆₁	1	2	yes	—
419	#474	C₂²×C₆₁	1	2	yes	—
420	#464	C₂²×C₆₁	1	4	yes	—
421	#464	C₂²×C₆₁	1	4	yes	—
422	#464	C₂²×C₆₁	1	4	yes	complemented
423	#462	C₂²×C₆₁	1	2	yes	complemented
424	#462	C₂²×C₆₁	1	4	yes	complemented
425	#461	C₂²×C₆₁	1	2	yes	—
426	#461	C₂²×C₆₁	1	2	yes	—
427	#461	C₂²×C₆₁	1	4	yes	complemented
428	#460	C₂²×C₆₁	1	4	yes	—
429	#460	C₂²×C₆₁	1	4	yes	—
430	#460	C₂²×C₆₁	1	2	yes	complemented
431	#452	C₂²×C₆₁	1	4	yes	—
432	#452	C₂²×C₆₁	1	4	yes	—
433	#450	C₂²×C₆₁	1	2	yes	—
434	#450	C₂²×C₆₁	1	2	yes	—
435	#446	C₂²×C₆₁	1	2	yes	complemented
436	#446	C₂²×C₆₁	1	4	yes	complemented
437	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
438	#441	C₂²×C₆₁	1	4	yes	complemented
439	#440	C₂²×C₆₁	1	4	yes	—
440	#440	C₂²×C₆₁	1	4	yes	complemented
441	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
442	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
443	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
444	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
445	#433	C₂²×C₆₁	1	4	yes	—
446	#432	C₂²×C₆₁	1	1	yes	characteristic
447	#431	C₂²×C₆₁	1	1	yes	characteristic
448	C₆₁	#61911	1	1	yes	characteristic, direct product factor, Sylow
449	C₂×#41	—	2	2	no	—
450	C₂×#41	C₂³×C₆₁	1	2	yes	—
451	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
452	C₂³×C₄	—	2	1	no	—
453	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
454	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
455	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
456	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
457	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
459	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
463	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
468	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
470	#127	C₂³×C₆₁	1	1	yes	characteristic
471	#127	C₂³×C₆₁	1	4	yes	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	—	2	2	no	—
477	#125	—	2	4	no	—
478	#125	—	2	4	no	—
479	#125	—	2	4	no	—
480	#125	—	2	4	no	—
481	#125	—	2	4	no	—
482	#125	—	2	4	no	—
483	#125	—	2	1	no	—
484	#125	—	2	1	no	—
485	#125	D₄×C₆₁	1	2	yes	—
486	#125	C₂³×C₆₁	1	4	yes	—
487	#124	—	2	4	no	—
488	#124	C₂³×C₆₁	1	2	yes	—
489	#124	C₂³×C₆₁	1	4	yes	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
496	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
497	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#120	—	2	4	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	1	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
513	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
514	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
515	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
516	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
517	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
518	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	C₂³×C₆₁	1	2	yes	—
526	C₄×D₄	C₂³×C₆₁	1	2	yes	—
527	C₄×D₄	C₂³×C₆₁	1	4	yes	—
528	#117	—	2	1	no	—
529	#117	—	2	1	no	—
530	#117	—	2	2	no	—
531	#117	—	2	2	no	—
532	#117	C₂³×C₆₁	1	2	yes	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
537	#107	C₂³×C₆₁	1	4	yes	—
538	#106	C₂³×C₆₁	1	2	yes	—
539	#106	C₂³×C₆₁	1	2	yes	—
540	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
541	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
542	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
543	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
544	#103	C₂³×C₆₁	1	2	yes	—
545	#103	C₂³×C₆₁	1	2	yes	—
546	#103	C₂³×C₆₁	1	4	yes	—
547	#103	C₂³×C₆₁	1	4	yes	—
548	#103	C₂³×C₆₁	1	4	yes	—
549	#102	C₂³×C₆₁	1	2	yes	—
550	#102	C₂³×C₆₁	1	2	yes	—
551	#102	C₂³×C₆₁	1	4	yes	—
552	#102	C₂³×C₆₁	1	4	yes	—
553	#102	C₂³×C₆₁	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
556	#97	C₂³×C₆₁	1	2	yes	—
557	#97	C₂³×C₆₁	1	4	yes	—
558	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₆₁	1	4	yes	—
561	C₂⁴	—	2	1	no	—
562	#41	—	4	4	no	—
563	#41	—	8	4	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
567	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
568	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
569	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
570	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
579	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	8	2	no	—
586	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
589	Q₁₆	—	4	4	no	—
590	Q₁₆	—	4	4	no	—
591	SD₁₆	—	4	2	no	—
592	SD₁₆	—	4	4	no	—
593	SD₁₆	—	4	4	no	—
594	SD₁₆	—	4	4	no	—
595	SD₁₆	—	4	2	no	—
596	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
597	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
598	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
622	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
623	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
625	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
645	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
646	C₄²	C₂⁴×C₆₁	1	4	yes	—
647	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	8	1	no	—
652	C₂³	—	8	1	no	—
653	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
654	Q₈	—	2	4	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	2	4	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	2	2	no	—
664	D₄	—	2	4	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	2	no	—
668	D₄	—	8	1	no	—
669	D₄	—	8	4	no	—
670	D₄	—	8	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	8	2	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	1	no	—
685	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
692	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
693	C₈	—	2	2	no	—
694	C₈	—	2	4	no	—
695	C₈	—	2	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	8	4	no	—
706	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	4	no	—
712	C₄	—	2	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	C₆₁×#577	1	2	yes	—
720	C₄	C₆₁×#585	1	2	yes	—
721	C₂	—	4	1	no	—
722	C₂	—	8	2	no	—
723	C₂	—	8	2	no	—
724	C₂	C₆₁×#3487	1	1	yes	characteristic
725	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
726	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3556	C₂	semidirect
3. C₆₁×#3400	C₂	semidirect
4. C₆₁×#3398	C₂	semidirect
5. C₆₁×#3392	C₂	semidirect
6. C₆₁×#3371	C₂	semidirect
7. C₆₁×#3368	C₂	semidirect
8. C₆₁×#3364	C₂	semidirect
9. C₆₁×#3222	C₂	semidirect
10. C₆₁×#3216	C₂	semidirect
11. C₆₁×#3210	C₂	semidirect
12. C₆₁×#3120	C₂	semidirect
13. C₆₁×#3110	C₂	semidirect
14. C₆₁×#3101	C₂	semidirect
15. C₆₁×#2985	C₂	semidirect
20. C₆₁×#557	C₂²	semidirect
21. C₆₁×#557	C₂²	semidirect
22. C₆₁×#557	C₂²	semidirect
23. C₆₁×#557	C₂²	semidirect
42. C₆₁×#497	C₂²	semidirect
43. C₆₁×#494	C₂²	semidirect
45. C₆₁×#492	C₂²	semidirect
47. C₆₁×#489	C₂²	semidirect
49. C₆₁×#487	C₂²	semidirect
50. C₆₁×#486	C₂²	semidirect
53. C₆₁×#479	C₂²	semidirect
54. C₆₁×#478	C₂²	semidirect
59. C₆₁×#464	C₂²	semidirect
60. C₆₁×#462	C₂²	semidirect
61. C₆₁×#462	C₂²	semidirect
64. C₆₁×#461	C₂²	semidirect
67. C₆₁×#460	C₂²	semidirect
72. C₆₁×#446	C₂²	semidirect
73. C₆₁×#446	C₂²	semidirect
74. C₈×Q₈×C₆₁	C₂²	semidirect
75. C₆₁×#441	C₂²	semidirect
77. C₆₁×#440	C₂²	semidirect
78. C₄×Q₁₆×C₆₁	C₂²	semidirect
81. C₄×SD₁₆×C₆₁	C₂²	semidirect
332. #61911	C₆₁	direct (N × H)
358. #3556	C₂×C₆₁	semidirect
360. #3400	C₂×C₆₁	semidirect
361. #3398	C₂×C₆₁	semidirect
362. #3392	C₂×C₆₁	semidirect
363. #3371	C₂×C₆₁	semidirect
364. #3368	C₂×C₆₁	semidirect
365. #3364	C₂×C₆₁	semidirect
366. #3222	C₂×C₆₁	semidirect
367. #3216	C₂×C₆₁	semidirect
368. #3210	C₂×C₆₁	semidirect
369. #3120	C₂×C₆₁	semidirect
370. #3110	C₂×C₆₁	semidirect
371. #3101	C₂×C₆₁	semidirect
372. #2985	C₂×C₆₁	semidirect
383. #557	C₂²×C₆₁	semidirect
384. #557	C₂²×C₆₁	semidirect
385. #557	C₂²×C₆₁	semidirect
386. #557	C₂²×C₆₁	semidirect
405. #497	C₂²×C₆₁	semidirect
406. #494	C₂²×C₆₁	semidirect
408. #492	C₂²×C₆₁	semidirect
410. #489	C₂²×C₆₁	semidirect
412. #487	C₂²×C₆₁	semidirect
413. #486	C₂²×C₆₁	semidirect
416. #479	C₂²×C₆₁	semidirect
417. #478	C₂²×C₆₁	semidirect
422. #464	C₂²×C₆₁	semidirect
423. #462	C₂²×C₆₁	semidirect
424. #462	C₂²×C₆₁	semidirect
427. #461	C₂²×C₆₁	semidirect
430. #460	C₂²×C₆₁	semidirect
435. #446	C₂²×C₆₁	semidirect
436. #446	C₂²×C₆₁	semidirect
437. C₈×Q₈	C₂²×C₆₁	semidirect
438. #441	C₂²×C₆₁	semidirect
440. #440	C₂²×C₆₁	semidirect
441. C₄×Q₁₆	C₂²×C₆₁	semidirect
444. C₄×SD₁₆	C₂²×C₆₁	semidirect
448. C₆₁	#61911	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×#3556	2
C₆₁×#3506	2
C₆₁×#3400	2
C₆₁×#3398	2
C₆₁×#3392	2
C₆₁×#3371	2
C₆₁×#3368	2
C₆₁×#3364	2
C₆₁×#3222	2
C₆₁×#3216	2
C₆₁×#3210	2
C₆₁×#3120	2
C₆₁×#3110	2
C₆₁×#3101	2
C₆₁×#2985	2
#61911	61

Subgroups — C61×#61911 #29565344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61911 #29565344