Subgroups — C₆₁×#19276 #29522709

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3038	C₂	1	1	yes	maximal, characteristic
4	C₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1682	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1681	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₆₁	—	2	1	no	—
11	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#486	—	2	1	no	—
16	C₆₁×#486	—	2	1	no	—
17	C₆₁×#486	C₂²	1	4	yes	—
18	C₆₁×#462	—	2	1	no	—
19	C₆₁×#462	C₂²	1	2	yes	complemented
20	C₆₁×#461	—	2	1	no	—
21	C₆₁×#461	C₂²	1	2	yes	complemented
22	C₆₁×#460	—	2	1	no	—
23	C₆₁×#460	C₂²	1	2	yes	—
24	C₆₁×#459	—	2	1	no	—
25	C₆₁×#459	C₂²	1	2	yes	—
26	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
27	C₈×D₄×C₆₁	—	2	2	no	—
28	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
29	C₆₁×#431	—	2	1	no	—
30	C₆₁×#431	C₂²	1	1	yes	characteristic
31	C₆₁×#423	C₂²	1	1	yes	characteristic
32	C₆₁×#423	C₂²	1	1	yes	characteristic
33	C₆₁×#419	—	2	1	no	—
34	C₆₁×#418	—	2	1	no	—
35	C₂×#102×C₆₁	—	2	2	no	—
36	C₂×C₄×C₈×C₆₁	—	2	1	no	—
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#335	C₂²	1	4	yes	complemented
39	C₆₁×#332	C₂²	1	4	yes	complemented
40	C₆₁×#331	C₂²	1	4	yes	—
41	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₆₁	—	2	1	no	—
43	C₂²×D₄×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	—	2	1	no	—
45	C₂²×D₄×C₆₁	—	2	1	no	—
46	#137×C₆₁	—	4	4	no	—
47	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×D₈×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	1	no	—
53	C₂×M₁₆×C₆₁	—	2	1	no	—
54	C₂²×C₈×C₆₁	—	2	2	no	—
55	C₂²×C₈×C₆₁	D₄	1	2	yes	—
56	C₄⋊Q₈×C₆₁	—	2	1	no	—
57	C₄⋊Q₈×C₆₁	—	2	1	no	—
58	C₄⋊Q₈×C₆₁	—	2	1	no	—
59	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
60	#127×C₆₁	—	2	1	no	—
61	#127×C₆₁	—	2	1	no	—
62	#127×C₆₁	—	2	1	no	—
63	#127×C₆₁	C₂³	1	2	yes	—
64	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₆₁	—	2	1	no	—
67	C₄×D₄×C₆₁	—	2	1	no	—
68	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
69	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
70	#117×C₆₁	—	2	1	no	—
71	#117×C₆₁	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	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	1	no	—
78	C₄⋊C₈×C₆₁	—	2	1	no	—
79	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
81	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
82	#103×C₆₁	—	2	2	no	—
83	#103×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	4	no	—
85	#102×C₆₁	—	2	4	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	2	2	no	—
88	C₂²⋊C₈×C₆₁	—	2	1	no	—
89	C₂²⋊C₈×C₆₁	—	2	2	no	—
90	C₄×C₈×C₆₁	—	2	2	no	—
91	C₄×C₈×C₆₁	—	2	1	no	—
92	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
93	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂³	1	2	yes	—
95	C₂⁴×C₆₁	—	4	1	no	—
96	#41×C₆₁	—	2	2	no	—
97	#41×C₆₁	D₈	1	4	yes	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	4	1	no	—
100	C₂×Q₈×C₆₁	—	4	2	no	—
101	C₂×Q₈×C₆₁	—	4	2	no	—
102	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₆₁	—	2	1	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	—	4	4	no	—
108	C₂×D₄×C₆₁	—	4	1	no	—
109	C₂×D₄×C₆₁	—	4	1	no	—
110	C₂×D₄×C₆₁	—	4	1	no	—
111	C₂×D₄×C₆₁	—	4	2	no	—
112	C₂×D₄×C₆₁	—	4	2	no	—
113	C₂×D₄×C₆₁	—	8	2	no	—
114	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	4	1	no	—
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
122	Q₁₆×C₆₁	—	4	4	no	—
123	SD₁₆×C₆₁	—	4	4	no	—
124	SD₁₆×C₆₁	—	4	4	no	—
125	D₈×C₆₁	—	4	4	no	—
126	M₁₆×C₆₁	—	4	2	no	—
127	M₁₆×C₆₁	—	4	2	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	—	4	2	no	—
132	C₂×C₈×C₆₁	—	4	4	no	—
133	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	4	1	no	—
140	C₄⋊C₄×C₆₁	—	4	1	no	—
141	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₆₁	—	2	1	no	—
144	C₂²⋊C₄×C₆₁	—	2	1	no	—
145	C₂²⋊C₄×C₆₁	—	2	1	no	—
146	C₄²×C₆₁	—	2	1	no	—
147	C₄²×C₆₁	—	2	1	no	—
148	C₄²×C₆₁	—	2	1	no	—
149	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₁	#41	1	1	yes	characteristic
152	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
153	C₂³×C₆₁	—	2	1	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	—	8	2	no	—
156	C₂³×C₆₁	—	8	2	no	—
157	C₂³×C₆₁	—	8	2	no	—
158	C₂³×C₆₁	#121	1	1	yes	characteristic
159	Q₈×C₆₁	—	2	1	no	—
160	Q₈×C₆₁	—	4	2	no	—
161	Q₈×C₆₁	—	4	2	no	—
162	Q₈×C₆₁	—	8	2	no	—
163	Q₈×C₆₁	C₂×D₈	1	2	yes	—
164	D₄×C₆₁	—	2	4	no	—
165	D₄×C₆₁	—	2	1	no	—
166	D₄×C₆₁	—	4	2	no	—
167	D₄×C₆₁	—	4	2	no	—
168	D₄×C₆₁	—	4	4	no	—
169	D₄×C₆₁	—	8	2	no	—
170	D₄×C₆₁	—	8	2	no	—
171	D₄×C₆₁	—	8	2	no	—
172	D₄×C₆₁	—	8	2	no	—
173	D₄×C₆₁	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	4	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	8	2	no	—
184	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
188	C₂×C₄×C₆₁	#135	1	2	yes	—
189	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
192	C₈×C₆₁	—	2	2	no	—
193	C₈×C₆₁	—	2	2	no	—
194	C₈×C₆₁	—	4	2	no	—
195	C₈×C₆₁	—	4	2	no	—
196	C₈×C₆₁	—	4	2	no	—
197	#19276	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₆₁	—	2	1	no	—
199	C₂²×C₆₁	—	2	1	no	—
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	4	1	no	—
202	C₂²×C₆₁	—	4	1	no	—
203	C₂²×C₆₁	—	8	2	no	—
204	C₂²×C₆₁	—	8	2	no	—
205	C₂²×C₆₁	—	8	2	no	—
206	C₂²×C₆₁	—	16	4	no	—
207	C₂²×C₆₁	#466	1	2	yes	—
208	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
209	C₄×C₆₁	—	2	1	no	—
210	C₄×C₆₁	—	2	2	no	—
211	C₄×C₆₁	—	2	1	no	—
212	C₄×C₆₁	—	4	1	no	—
213	C₄×C₆₁	—	4	1	no	—
214	C₄×C₆₁	—	8	2	no	—
215	C₄×C₆₁	#466	1	2	yes	—
216	C₄×C₆₁	#471	1	2	yes	—
217	C₄×C₆₁	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
219	C₄×C₆₁	#575	1	2	yes	—
220	C₂×#486	C₂×C₆₁	1	1	yes	characteristic, complemented
221	#3039	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#3038	C₂×C₆₁	1	1	yes	characteristic
223	C₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
224	#1682	C₂×C₆₁	1	4	yes	complemented
225	#1681	C₂×C₆₁	1	4	yes	complemented
226	#1567	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#1546	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#1545	C₂×C₆₁	1	1	yes	characteristic, complemented
229	C₂×C₆₁	—	2	2	no	—
230	C₂×C₆₁	—	4	2	no	—
231	C₂×C₆₁	—	16	2	no	—
232	C₂×C₆₁	#3040	1	1	yes	characteristic
233	C₂×C₆₁	C₂×#466	1	1	yes	characteristic
234	C₂×C₆₁	C₂×#471	1	1	yes	characteristic
235	C₂×#137	—	2	1	no	—
236	C₂×AGL(1,ℤ/8)	—	2	1	no	—
237	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
239	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
240	#486	—	2	1	no	—
241	#486	—	2	1	no	—
242	#486	C₂²×C₆₁	1	4	yes	—
243	#462	—	2	1	no	—
244	#462	C₂²×C₆₁	1	2	yes	complemented
245	#461	—	2	1	no	—
246	#461	C₂²×C₆₁	1	2	yes	complemented
247	#460	—	2	1	no	—
248	#460	C₂²×C₆₁	1	2	yes	—
249	#459	—	2	1	no	—
250	#459	C₂²×C₆₁	1	2	yes	—
251	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
252	C₈×D₄	—	2	2	no	—
253	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
254	#431	—	2	1	no	—
255	#431	C₂²×C₆₁	1	1	yes	characteristic
256	#423	C₂²×C₆₁	1	1	yes	characteristic
257	#423	C₂²×C₆₁	1	1	yes	characteristic
258	#419	—	2	1	no	—
259	#418	—	2	1	no	—
260	C₂×#102	—	2	2	no	—
261	C₂×C₄×C₈	—	2	1	no	—
262	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
263	#335	C₂²×C₆₁	1	4	yes	complemented
264	#332	C₂²×C₆₁	1	4	yes	complemented
265	#331	C₂²×C₆₁	1	4	yes	—
266	C₆₁	#19276	1	1	yes	characteristic, direct product factor, Sylow
267	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	#137	—	4	4	no	—
273	AGL(1,ℤ/8)	—	4	4	no	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	D₄×C₆₁	1	2	yes	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
286	#127	—	2	1	no	—
287	#127	—	2	1	no	—
288	#127	—	2	1	no	—
289	#127	C₂³×C₆₁	1	2	yes	—
290	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
291	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
295	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	D₄×C₆₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
306	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
307	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#102	—	2	4	no	—
311	#102	—	2	4	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
319	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₆₁	1	2	yes	—
321	C₂⁴	—	4	1	no	—
322	#41	—	2	2	no	—
323	#41	D₈×C₆₁	1	4	yes	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
347	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
348	Q₁₆	—	4	4	no	—
349	SD₁₆	—	4	4	no	—
350	SD₁₆	—	4	4	no	—
351	D₈	—	4	4	no	—
352	M₁₆	—	4	2	no	—
353	M₁₆	—	4	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
377	C₄²	#41×C₆₁	1	1	yes	characteristic
378	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
379	C₂³	—	2	1	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	8	2	no	—
382	C₂³	—	8	2	no	—
383	C₂³	—	8	2	no	—
384	C₂³	#121×C₆₁	1	1	yes	characteristic
385	Q₈	—	2	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	8	2	no	—
389	Q₈	C₂×D₈×C₆₁	1	2	yes	—
390	D₄	—	2	4	no	—
391	D₄	—	2	1	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	4	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	D₄	C₂×D₈×C₆₁	1	2	yes	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
411	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
412	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
413	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
414	C₂×C₄	#135×C₆₁	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	16	4	no	—
432	C₂²	C₆₁×#466	1	2	yes	—
433	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	8	2	no	—
440	C₄	C₆₁×#466	1	2	yes	—
441	C₄	C₆₁×#471	1	2	yes	—
442	C₄	C₂²×D₈×C₆₁	1	1	yes	characteristic
443	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
444	C₄	C₆₁×#575	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	4	2	no	—
447	C₂	—	16	2	no	—
448	C₂	C₆₁×#3040	1	1	yes	characteristic
449	C₂	C₂×C₆₁×#466	1	1	yes	characteristic
450	C₂	C₂×C₆₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#486	C₂	semidirect
2. C₆₁×#3039	C₂	semidirect
4. C₈×#41×C₆₁	C₂	semidirect
5. C₆₁×#1682	C₂	semidirect
6. C₆₁×#1681	C₂	semidirect
7. C₆₁×#1567	C₂	semidirect
8. C₆₁×#1546	C₂	semidirect
9. C₆₁×#1545	C₂	semidirect
19. C₆₁×#462	C₂²	semidirect
21. C₆₁×#461	C₂²	semidirect
26. C₈×Q₈×C₆₁	C₂²	semidirect
28. C₈×D₄×C₆₁	C₂²	semidirect
38. C₆₁×#335	C₂²	semidirect
39. C₆₁×#332	C₂²	semidirect
197. #19276	C₆₁	direct (N × H)
220. C₂×#486	C₂×C₆₁	semidirect
221. #3039	C₂×C₆₁	semidirect
223. C₈×#41	C₂×C₆₁	semidirect
224. #1682	C₂×C₆₁	semidirect
225. #1681	C₂×C₆₁	semidirect
226. #1567	C₂×C₆₁	semidirect
227. #1546	C₂×C₆₁	semidirect
228. #1545	C₂×C₆₁	semidirect
244. #462	C₂²×C₆₁	semidirect
246. #461	C₂²×C₆₁	semidirect
251. C₈×Q₈	C₂²×C₆₁	semidirect
253. C₈×D₄	C₂²×C₆₁	semidirect
263. #335	C₂²×C₆₁	semidirect
264. #332	C₂²×C₆₁	semidirect
266. C₆₁	#19276	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×#486	2
C₆₁×#3039	2
C₆₁×#3038	2
C₈×#41×C₆₁	2
C₆₁×#1682	2
C₆₁×#1681	2
C₆₁×#1567	2
C₆₁×#1546	2
C₆₁×#1545	2
#19276	61

Subgroups — C61×#19276 #29522709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19276 #29522709