Subgroups — C₆₁×#25875 #29529308

Order 15616.

1430 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3498	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2037	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1965	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1792	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	—
11	C₆₁×#550	—	2	1	no	—
12	C₆₁×#550	—	2	1	no	—
13	D₄²×C₆₁	—	2	2	no	—
14	D₄²×C₆₁	—	2	2	no	—
15	D₄²×C₆₁	—	2	1	no	—
16	D₄²×C₆₁	—	2	1	no	—
17	C₆₁×#535	—	2	2	no	—
18	C₆₁×#535	C₂²	1	2	yes	—
19	C₆₁×#532	—	2	1	no	—
20	C₆₁×#532	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#127×C₆₁	—	2	1	no	—
23	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#124×C₆₁	—	2	2	no	—
25	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#489	—	2	2	no	—
27	C₆₁×#487	—	2	1	no	—
28	C₆₁×#486	—	2	1	no	—
29	C₆₁×#477	—	2	1	no	—
30	C₆₁×#476	—	2	1	no	—
31	C₆₁×#475	—	2	1	no	—
32	C₆₁×#474	—	2	1	no	—
33	C₆₁×#428	C₂²	1	2	yes	complemented
34	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
35	C₂×#104×C₆₁	C₂²	1	2	yes	—
36	C₂×#104×C₆₁	C₂²	1	4	yes	complemented
37	C₆₁×#417	C₂²	1	2	yes	—
38	C₆₁×#417	C₂²	1	4	yes	complemented
39	C₂×#100×C₆₁	C₂²	1	4	yes	complemented
40	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
41	C₆₁×#390	—	2	2	no	—
42	C₆₁×#390	C₂²	1	4	yes	complemented
43	C₄³×C₆₁	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#339	C₂²	1	2	yes	complemented
45	H(5,𝔽₂)×C₆₁	—	2	8	no	—
46	H(5,𝔽₂)×C₆₁	—	4	4	no	—
47	C₂×#41×C₆₁	—	2	2	no	—
48	C₂×#41×C₆₁	—	2	2	no	—
49	C₂×#41×C₆₁	C₂³	1	2	yes	—
50	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₆₁	—	2	1	no	—
52	C₂²×D₄×C₆₁	—	2	4	no	—
53	C₂²×D₄×C₆₁	—	2	2	no	—
54	C₂²×D₄×C₆₁	—	2	2	no	—
55	C₂²×D₄×C₆₁	—	2	2	no	—
56	C₂²×D₄×C₆₁	—	2	2	no	—
57	C₂²×D₄×C₆₁	D₄	1	2	yes	—
58	C₂²×D₄×C₆₁	D₄	1	2	yes	—
59	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	C₄⋊Q₈×C₆₁	—	2	1	no	—
65	C₄⋊Q₈×C₆₁	—	2	1	no	—
66	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
67	#127×C₆₁	—	2	2	no	—
68	#127×C₆₁	—	2	2	no	—
69	#127×C₆₁	—	2	2	no	—
70	#127×C₆₁	—	2	1	no	—
71	#127×C₆₁	—	2	1	no	—
72	#127×C₆₁	—	2	1	no	—
73	#127×C₆₁	—	2	1	no	—
74	#127×C₆₁	D₄	1	1	yes	characteristic
75	#124×C₆₁	—	2	2	no	—
76	#124×C₆₁	—	4	8	no	—
77	#124×C₆₁	D₄	1	2	yes	—
78	#121×C₆₁	—	2	2	no	—
79	#121×C₆₁	—	2	2	no	—
80	#121×C₆₁	—	2	4	no	—
81	#121×C₆₁	—	2	4	no	—
82	#121×C₆₁	—	2	1	no	—
83	#121×C₆₁	—	2	1	no	—
84	#121×C₆₁	—	2	2	no	—
85	#121×C₆₁	—	2	2	no	—
86	#120×C₆₁	—	2	4	no	—
87	#120×C₆₁	—	2	4	no	—
88	#120×C₆₁	—	2	4	no	—
89	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
91	C₄×D₄×C₆₁	—	2	2	no	—
92	C₄×D₄×C₆₁	—	2	2	no	—
93	C₄×D₄×C₆₁	—	2	1	no	—
94	C₄×D₄×C₆₁	—	2	1	no	—
95	C₄×D₄×C₆₁	—	2	1	no	—
96	C₄×D₄×C₆₁	—	2	1	no	—
97	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
98	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
99	#117×C₆₁	—	2	1	no	—
100	#117×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
104	C₂×C₄²×C₆₁	—	2	1	no	—
105	C₂×C₄²×C₆₁	—	2	1	no	—
106	C₂×C₄²×C₆₁	—	2	1	no	—
107	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
108	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
109	#107×C₆₁	—	2	2	no	—
110	#106×C₆₁	—	2	2	no	—
111	C₄⋊C₈×C₆₁	—	2	1	no	—
112	C₄⋊C₈×C₆₁	—	2	1	no	—
113	#104×C₆₁	—	2	4	no	—
114	#104×C₆₁	—	4	4	no	—
115	#103×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	2	4	no	—
117	#102×C₆₁	—	2	2	no	—
118	#102×C₆₁	—	2	4	no	—
119	#100×C₆₁	—	4	4	no	—
120	#97×C₆₁	—	2	1	no	—
121	C₄×C₈×C₆₁	—	2	1	no	—
122	C₂⁴×C₆₁	—	2	4	no	—
123	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
124	#41×C₆₁	—	2	2	no	—
125	#41×C₆₁	—	2	4	no	—
126	#41×C₆₁	—	2	4	no	—
127	#41×C₆₁	—	4	8	no	—
128	#41×C₆₁	—	4	4	no	—
129	#41×C₆₁	—	4	4	no	—
130	#41×C₆₁	#41	1	4	yes	—
131	C₂×Q₈×C₆₁	—	4	4	no	—
132	C₂×Q₈×C₆₁	—	4	1	no	—
133	C₂×Q₈×C₆₁	—	4	1	no	—
134	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₆₁	—	2	1	no	—
137	C₂×D₄×C₆₁	—	2	4	no	—
138	C₂×D₄×C₆₁	—	2	4	no	—
139	C₂×D₄×C₆₁	—	2	2	no	—
140	C₂×D₄×C₆₁	—	2	4	no	—
141	C₂×D₄×C₆₁	—	2	4	no	—
142	C₂×D₄×C₆₁	—	2	2	no	—
143	C₂×D₄×C₆₁	—	2	2	no	—
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	—	2	1	no	—
146	C₂×D₄×C₆₁	—	2	2	no	—
147	C₂×D₄×C₆₁	—	2	2	no	—
148	C₂×D₄×C₆₁	—	2	2	no	—
149	C₂×D₄×C₆₁	—	2	2	no	—
150	C₂×D₄×C₆₁	—	2	4	no	—
151	C₂×D₄×C₆₁	—	2	4	no	—
152	C₂×D₄×C₆₁	—	4	8	no	—
153	C₂×D₄×C₆₁	—	4	4	no	—
154	C₂×D₄×C₆₁	—	4	4	no	—
155	C₂×D₄×C₆₁	—	4	16	no	—
156	C₂×D₄×C₆₁	—	4	4	no	—
157	C₂×D₄×C₆₁	—	4	4	no	—
158	C₂×D₄×C₆₁	—	8	4	no	—
159	C₂×D₄×C₆₁	—	8	4	no	—
160	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	4	no	—
164	C₂²×C₄×C₆₁	—	2	2	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	2	1	no	—
167	C₂²×C₄×C₆₁	—	2	2	no	—
168	C₂²×C₄×C₆₁	—	2	2	no	—
169	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₆₁	—	2	2	no	—
173	M₁₆×C₆₁	—	2	2	no	—
174	M₁₆×C₆₁	—	2	4	no	—
175	C₂×C₈×C₆₁	—	2	2	no	—
176	C₂×C₈×C₆₁	—	2	2	no	—
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₄⋊C₄×C₆₁	—	2	2	no	—
182	C₄⋊C₄×C₆₁	—	2	2	no	—
183	C₄⋊C₄×C₆₁	—	4	1	no	—
184	C₄⋊C₄×C₆₁	—	4	1	no	—
185	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
186	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
187	C₂²⋊C₄×C₆₁	—	2	4	no	—
188	C₂²⋊C₄×C₆₁	—	2	4	no	—
189	C₂²⋊C₄×C₆₁	—	2	1	no	—
190	C₂²⋊C₄×C₆₁	—	2	1	no	—
191	C₂²⋊C₄×C₆₁	—	2	1	no	—
192	C₂²⋊C₄×C₆₁	—	2	2	no	—
193	C₂²⋊C₄×C₆₁	—	2	2	no	—
194	C₂²⋊C₄×C₆₁	—	4	16	no	—
195	C₄²×C₆₁	—	2	4	no	—
196	C₄²×C₆₁	—	2	1	no	—
197	C₄²×C₆₁	—	2	1	no	—
198	C₄²×C₆₁	—	2	1	no	—
199	C₄²×C₆₁	—	2	2	no	—
200	C₄²×C₆₁	—	2	2	no	—
201	C₄²×C₆₁	—	4	2	no	—
202	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
206	C₂³×C₆₁	—	2	1	no	—
207	C₂³×C₆₁	—	2	4	no	—
208	C₂³×C₆₁	—	2	2	no	—
209	C₂³×C₆₁	—	2	8	no	—
210	C₂³×C₆₁	—	4	8	no	—
211	C₂³×C₆₁	—	4	4	no	—
212	C₂³×C₆₁	—	4	4	no	—
213	C₂³×C₆₁	—	8	4	no	—
214	C₂³×C₆₁	—	8	4	no	—
215	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₆₁	—	2	1	no	—
217	Q₈×C₆₁	—	2	4	no	—
218	Q₈×C₆₁	—	8	2	no	—
219	Q₈×C₆₁	—	8	2	no	—
220	Q₈×C₆₁	#124	1	2	yes	complemented
221	D₄×C₆₁	—	2	4	no	—
222	D₄×C₆₁	—	2	1	no	—
223	D₄×C₆₁	—	2	4	no	—
224	D₄×C₆₁	—	4	8	no	—
225	D₄×C₆₁	—	4	8	no	—
226	D₄×C₆₁	—	4	4	no	—
227	D₄×C₆₁	—	4	2	no	—
228	D₄×C₆₁	—	4	2	no	—
229	D₄×C₆₁	—	4	4	no	—
230	D₄×C₆₁	—	4	4	no	—
231	D₄×C₆₁	—	4	2	no	—
232	D₄×C₆₁	—	4	4	no	—
233	D₄×C₆₁	—	4	2	no	—
234	D₄×C₆₁	—	8	2	no	—
235	D₄×C₆₁	—	8	2	no	—
236	D₄×C₆₁	—	8	4	no	—
237	D₄×C₆₁	—	8	4	no	—
238	D₄×C₆₁	#124	1	2	yes	complemented
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	4	no	—
241	C₂×C₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	2	2	no	—
243	C₂×C₄×C₆₁	—	2	4	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	2	2	no	—
247	C₂×C₄×C₆₁	—	4	8	no	—
248	C₂×C₄×C₆₁	—	4	2	no	—
249	C₂×C₄×C₆₁	—	4	2	no	—
250	C₂×C₄×C₆₁	—	4	2	no	—
251	C₂×C₄×C₆₁	—	4	2	no	—
252	C₂×C₄×C₆₁	—	4	2	no	—
253	C₂×C₄×C₆₁	—	4	2	no	—
254	C₂×C₄×C₆₁	—	4	4	no	—
255	C₂×C₄×C₆₁	—	4	2	no	—
256	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
257	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
258	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
259	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
260	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
263	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
264	C₈×C₆₁	—	4	2	no	—
265	C₈×C₆₁	—	4	2	no	—
266	#25875	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₆₁	—	2	1	no	—
268	C₂²×C₆₁	—	2	1	no	—
269	C₂²×C₆₁	—	2	2	no	—
270	C₂²×C₆₁	—	4	1	no	—
271	C₂²×C₆₁	—	4	1	no	—
272	C₂²×C₆₁	—	4	2	no	—
273	C₂²×C₆₁	—	4	4	no	—
274	C₂²×C₆₁	—	4	4	no	—
275	C₂²×C₆₁	—	4	2	no	—
276	C₂²×C₆₁	—	4	4	no	—
277	C₂²×C₆₁	—	4	2	no	—
278	C₂²×C₆₁	—	8	8	no	—
279	C₂²×C₆₁	—	16	8	no	—
280	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
281	C₂²×C₆₁	#546	1	2	yes	—
282	C₄×C₆₁	—	2	2	no	—
283	C₄×C₆₁	—	2	1	no	—
284	C₄×C₆₁	—	2	1	no	—
285	C₄×C₆₁	—	4	4	no	—
286	C₄×C₆₁	—	4	2	no	—
287	C₄×C₆₁	—	4	1	no	—
288	C₄×C₆₁	—	4	1	no	—
289	C₄×C₆₁	—	8	2	no	—
290	C₄×C₆₁	#453	1	2	yes	—
291	C₄×C₆₁	#455	1	2	yes	—
292	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
293	C₄×C₆₁	#535	1	1	yes	characteristic
294	C₄×C₆₁	#546	1	2	yes	—
295	#3498	C₂×C₆₁	1	1	yes	characteristic
296	#3141	C₂×C₆₁	1	1	yes	characteristic, complemented
297	#3079	C₂×C₆₁	1	1	yes	characteristic, complemented
298	#2858	C₂×C₆₁	1	1	yes	characteristic, complemented
299	#2037	C₂×C₆₁	1	4	yes	complemented
300	#1965	C₂×C₆₁	1	1	yes	characteristic, complemented
301	#1962	C₂×C₆₁	1	1	yes	characteristic, complemented
302	#1792	C₂×C₆₁	1	4	yes	complemented
303	C₄×#104	C₂×C₆₁	1	1	yes	characteristic, complemented
304	C₂×C₆₁	—	2	2	no	—
305	C₂×C₆₁	—	4	2	no	—
306	C₂×C₆₁	—	8	4	no	—
307	C₂×C₆₁	—	8	2	no	—
308	C₂×C₆₁	#2435	1	1	yes	characteristic
309	C₂×C₆₁	C₂×#453	1	1	yes	characteristic
310	C₂×C₆₁	C₂×#455	1	1	yes	characteristic
311	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	—
312	#550	—	2	1	no	—
313	#550	—	2	1	no	—
314	D₄²	—	2	2	no	—
315	D₄²	—	2	2	no	—
316	D₄²	—	2	1	no	—
317	D₄²	—	2	1	no	—
318	#535	—	2	2	no	—
319	#535	C₂²×C₆₁	1	2	yes	—
320	#532	—	2	1	no	—
321	#532	C₂²×C₆₁	1	1	yes	characteristic
322	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
323	C₂×#127	—	2	1	no	—
324	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
325	C₂×#124	—	2	2	no	—
326	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
327	#489	—	2	2	no	—
328	#487	—	2	1	no	—
329	#486	—	2	1	no	—
330	#477	—	2	1	no	—
331	#476	—	2	1	no	—
332	#475	—	2	1	no	—
333	#474	—	2	1	no	—
334	#428	C₂²×C₆₁	1	2	yes	complemented
335	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
336	C₂×#104	C₂²×C₆₁	1	2	yes	—
337	C₂×#104	C₂²×C₆₁	1	4	yes	complemented
338	#417	C₂²×C₆₁	1	2	yes	—
339	#417	C₂²×C₆₁	1	4	yes	complemented
340	C₂×#100	C₂²×C₆₁	1	4	yes	complemented
341	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
342	#390	—	2	2	no	—
343	#390	C₂²×C₆₁	1	4	yes	complemented
344	C₄³	C₂²×C₆₁	1	1	yes	characteristic, complemented
345	#339	C₂²×C₆₁	1	2	yes	complemented
346	C₆₁	#25875	1	1	yes	characteristic, direct product factor, Sylow
347	H(5,𝔽₂)	—	2	8	no	—
348	H(5,𝔽₂)	—	4	4	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	C₂³×C₆₁	1	2	yes	—
352	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
353	C₂²×Q₈	—	2	1	no	—
354	C₂²×D₄	—	2	4	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	D₄×C₆₁	1	2	yes	—
360	C₂²×D₄	D₄×C₆₁	1	2	yes	—
361	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
362	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
363	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
369	#127	—	2	2	no	—
370	#127	—	2	2	no	—
371	#127	—	2	2	no	—
372	#127	—	2	1	no	—
373	#127	—	2	1	no	—
374	#127	—	2	1	no	—
375	#127	—	2	1	no	—
376	#127	D₄×C₆₁	1	1	yes	characteristic
377	#124	—	2	2	no	—
378	#124	—	4	8	no	—
379	#124	D₄×C₆₁	1	2	yes	—
380	#121	—	2	2	no	—
381	#121	—	2	2	no	—
382	#121	—	2	4	no	—
383	#121	—	2	4	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#120	—	2	4	no	—
389	#120	—	2	4	no	—
390	#120	—	2	4	no	—
391	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
392	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
400	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
401	#117	—	2	1	no	—
402	#117	C₂³×C₆₁	1	1	yes	characteristic
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
405	C₂×C₂²⋊C₄	—	2	8	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
410	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
411	#107	—	2	2	no	—
412	#106	—	2	2	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	—	2	1	no	—
415	#104	—	2	4	no	—
416	#104	—	4	4	no	—
417	#103	—	2	2	no	—
418	#103	—	2	4	no	—
419	#102	—	2	2	no	—
420	#102	—	2	4	no	—
421	#100	—	4	4	no	—
422	#97	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₂⁴	—	2	4	no	—
425	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
426	#41	—	2	2	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	4	8	no	—
430	#41	—	4	4	no	—
431	#41	—	4	4	no	—
432	#41	#41×C₆₁	1	4	yes	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×Q₈	—	4	1	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
437	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	4	8	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	16	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	8	4	no	—
461	C₂×D₄	—	8	4	no	—
462	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
463	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	4	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
488	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	4	16	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	4	2	no	—
504	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
505	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
508	C₂³	—	2	1	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	—	4	4	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	8	4	no	—
516	C₂³	—	8	4	no	—
517	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	2	4	no	—
520	Q₈	—	8	2	no	—
521	Q₈	—	8	2	no	—
522	Q₈	#124×C₆₁	1	2	yes	complemented
523	D₄	—	2	4	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	4	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	2	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	4	no	—
539	D₄	—	8	4	no	—
540	D₄	#124×C₆₁	1	2	yes	complemented
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
559	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
560	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
561	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
564	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
565	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
566	C₈	—	4	2	no	—
567	C₈	—	4	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	8	no	—
580	C₂²	—	16	8	no	—
581	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
582	C₂²	C₆₁×#546	1	2	yes	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	8	2	no	—
591	C₄	C₆₁×#453	1	2	yes	—
592	C₄	C₆₁×#455	1	2	yes	—
593	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
594	C₄	C₆₁×#535	1	1	yes	characteristic
595	C₄	C₆₁×#546	1	2	yes	—
596	C₂	—	2	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	8	4	no	—
599	C₂	—	8	2	no	—
600	C₂	C₆₁×#2435	1	1	yes	characteristic
601	C₂	C₂×C₆₁×#453	1	1	yes	characteristic
602	C₂	C₂×C₆₁×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3498	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
2. C₆₁×#3141	C₂	semidirect
3. C₆₁×#3079	C₂	semidirect
4. C₆₁×#2858	C₂	semidirect
5. C₆₁×#2037	C₂	semidirect
6. C₆₁×#1965	C₂	semidirect
7. C₆₁×#1962	C₂	semidirect
8. C₆₁×#1792	C₂	semidirect
9. C₄×#104×C₆₁	C₂	semidirect
21. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
33. C₆₁×#428	C₂²	semidirect
34. C₆₁×#423	C₂²	semidirect
36. C₂×#104×C₆₁	C₂²	semidirect
38. C₆₁×#417	C₂²	semidirect
39. C₂×#100×C₆₁	C₂²	semidirect
40. C₄×M₁₆×C₆₁	C₂²	semidirect
42. C₆₁×#390	C₂²	semidirect
43. C₄³×C₆₁	C₂²	semidirect
44. C₆₁×#339	C₂²	semidirect
220. Q₈×C₆₁	#124	semidirect
238. D₄×C₆₁	#124	semidirect
266. #25875	C₆₁	direct (N × H)
296. #3141	C₂×C₆₁	semidirect
297. #3079	C₂×C₆₁	semidirect
298. #2858	C₂×C₆₁	semidirect
299. #2037	C₂×C₆₁	semidirect
300. #1965	C₂×C₆₁	semidirect
301. #1962	C₂×C₆₁	semidirect
302. #1792	C₂×C₆₁	semidirect
303. C₄×#104	C₂×C₆₁	semidirect
322. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
334. #428	C₂²×C₆₁	semidirect
335. #423	C₂²×C₆₁	semidirect
337. C₂×#104	C₂²×C₆₁	semidirect
339. #417	C₂²×C₆₁	semidirect
340. C₂×#100	C₂²×C₆₁	semidirect
341. C₄×M₁₆	C₂²×C₆₁	semidirect
343. #390	C₂²×C₆₁	semidirect
344. C₄³	C₂²×C₆₁	semidirect
345. #339	C₂²×C₆₁	semidirect
346. C₆₁	#25875	direct (N × H)
522. Q₈	#124×C₆₁	semidirect
540. D₄	#124×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3498	2
C₆₁×#3141	2
C₆₁×#3079	2
C₆₁×#2858	2
C₆₁×#2037	2
C₆₁×#1965	2
C₆₁×#1962	2
C₆₁×#1792	2
C₄×#104×C₆₁	2
#25875	61

Subgroups — C61×#25875 #29529308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25875 #29529308