Subgroups — C₆₁×#19274 #29522707

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 442 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×#3079	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×#1678	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1677	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
13	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#486	—	2	1	no	—
15	C₆₁×#486	—	2	1	no	—
16	C₆₁×#486	C₂²	1	4	yes	—
17	C₆₁×#477	C₂²	1	2	yes	complemented
18	C₆₁×#476	C₂²	1	2	yes	complemented
19	C₆₁×#475	—	2	1	no	—
20	C₆₁×#474	—	2	1	no	—
21	C₆₁×#460	—	2	1	no	—
22	C₆₁×#460	C₂²	1	2	yes	—
23	C₆₁×#459	—	2	1	no	—
24	C₆₁×#459	C₂²	1	2	yes	—
25	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
26	C₈×D₄×C₆₁	—	2	2	no	—
27	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#431	—	2	1	no	—
29	C₆₁×#431	C₂²	1	1	yes	characteristic
30	C₆₁×#428	—	2	1	no	—
31	C₆₁×#423	C₂²	1	1	yes	characteristic
32	C₆₁×#423	C₂²	1	1	yes	characteristic
33	C₆₁×#418	—	2	1	no	—
34	C₆₁×#417	—	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×#334	C₂²	1	4	yes	complemented
39	C₆₁×#333	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	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
47	C₂×SD₁₆×C₆₁	—	2	2	no	—
48	C₂×D₈×C₆₁	—	2	2	no	—
49	C₂×M₁₆×C₆₁	—	2	1	no	—
50	C₂×M₁₆×C₆₁	—	2	1	no	—
51	C₂²×C₈×C₆₁	—	2	2	no	—
52	C₂²×C₈×C₆₁	D₄	1	2	yes	—
53	C₄⋊Q₈×C₆₁	—	2	1	no	—
54	C₄⋊Q₈×C₆₁	—	2	1	no	—
55	C₄⋊Q₈×C₆₁	—	2	1	no	—
56	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
57	#127×C₆₁	—	2	1	no	—
58	#127×C₆₁	—	2	1	no	—
59	#127×C₆₁	—	2	1	no	—
60	#127×C₆₁	C₂³	1	2	yes	—
61	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
62	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₆₁	—	2	1	no	—
64	C₄×D₄×C₆₁	—	2	1	no	—
65	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
66	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
67	#117×C₆₁	—	2	1	no	—
68	#117×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄²×C₆₁	—	2	1	no	—
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#107×C₆₁	—	2	2	no	—
74	#106×C₆₁	—	2	2	no	—
75	C₄⋊C₈×C₆₁	—	2	2	no	—
76	C₄⋊C₈×C₆₁	—	2	1	no	—
77	C₄⋊C₈×C₆₁	—	2	1	no	—
78	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
79	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
81	#103×C₆₁	—	2	2	no	—
82	#102×C₆₁	—	2	2	no	—
83	#102×C₆₁	—	2	4	no	—
84	#102×C₆₁	—	2	4	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	C₂²⋊C₈×C₆₁	—	2	1	no	—
88	C₂²⋊C₈×C₆₁	—	2	2	no	—
89	C₄×C₈×C₆₁	—	2	2	no	—
90	C₄×C₈×C₆₁	—	2	1	no	—
91	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
92	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	2	yes	—
94	C₂⁴×C₆₁	—	4	1	no	—
95	#41×C₆₁	—	2	2	no	—
96	#41×C₆₁	SD₁₆	1	4	yes	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	4	1	no	—
99	C₂×Q₈×C₆₁	—	8	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	—	4	4	no	—
106	C₂×D₄×C₆₁	—	4	1	no	—
107	C₂×D₄×C₆₁	—	4	1	no	—
108	C₂×D₄×C₆₁	—	4	1	no	—
109	C₂×D₄×C₆₁	—	4	2	no	—
110	C₂×D₄×C₆₁	—	4	2	no	—
111	C₂×D₄×C₆₁	—	8	2	no	—
112	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	4	1	no	—
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
120	SD₁₆×C₆₁	—	4	4	no	—
121	D₈×C₆₁	—	4	4	no	—
122	M₁₆×C₆₁	—	4	2	no	—
123	M₁₆×C₆₁	—	4	2	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	4	2	no	—
128	C₂×C₈×C₆₁	—	4	4	no	—
129	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	1	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	4	1	no	—
136	C₄⋊C₄×C₆₁	—	4	1	no	—
137	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₆₁	—	2	1	no	—
140	C₂²⋊C₄×C₆₁	—	2	1	no	—
141	C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₄²×C₆₁	—	2	1	no	—
143	C₄²×C₆₁	—	2	1	no	—
144	C₄²×C₆₁	—	2	1	no	—
145	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₆₁	#41	1	1	yes	characteristic
148	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	4	2	no	—
151	C₂³×C₆₁	—	8	2	no	—
152	C₂³×C₆₁	—	8	2	no	—
153	C₂³×C₆₁	—	8	2	no	—
154	C₂³×C₆₁	#121	1	1	yes	characteristic
155	Q₈×C₆₁	—	2	1	no	—
156	Q₈×C₆₁	—	8	2	no	—
157	Q₈×C₆₁	—	8	2	no	—
158	Q₈×C₆₁	C₂×SD₁₆	1	2	yes	—
159	D₄×C₆₁	—	2	4	no	—
160	D₄×C₆₁	—	2	1	no	—
161	D₄×C₆₁	—	4	2	no	—
162	D₄×C₆₁	—	4	2	no	—
163	D₄×C₆₁	—	4	4	no	—
164	D₄×C₆₁	—	8	2	no	—
165	D₄×C₆₁	—	8	2	no	—
166	D₄×C₆₁	—	8	2	no	—
167	D₄×C₆₁	—	8	2	no	—
168	D₄×C₆₁	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	1	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	8	2	no	—
179	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₆₁	#135	1	2	yes	—
184	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₆₁	—	2	2	no	—
188	C₈×C₆₁	—	2	2	no	—
189	C₈×C₆₁	—	4	2	no	—
190	C₈×C₆₁	—	4	2	no	—
191	C₈×C₆₁	—	4	2	no	—
192	#19274	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₆₁	—	2	1	no	—
194	C₂²×C₆₁	—	2	1	no	—
195	C₂²×C₆₁	—	2	2	no	—
196	C₂²×C₆₁	—	4	1	no	—
197	C₂²×C₆₁	—	4	1	no	—
198	C₂²×C₆₁	—	8	2	no	—
199	C₂²×C₆₁	—	8	2	no	—
200	C₂²×C₆₁	—	8	2	no	—
201	C₂²×C₆₁	—	16	4	no	—
202	C₂²×C₆₁	#465	1	2	yes	—
203	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
204	C₄×C₆₁	—	2	1	no	—
205	C₄×C₆₁	—	2	2	no	—
206	C₄×C₆₁	—	2	1	no	—
207	C₄×C₆₁	—	4	1	no	—
208	C₄×C₆₁	—	4	1	no	—
209	C₄×C₆₁	—	8	2	no	—
210	C₄×C₆₁	#465	1	2	yes	—
211	C₄×C₆₁	#472	1	2	yes	—
212	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
213	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
214	C₄×C₆₁	#575	1	2	yes	—
215	C₂×#486	C₂×C₆₁	1	1	yes	characteristic, complemented
216	#3079	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#3038	C₂×C₆₁	1	1	yes	characteristic
218	C₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#1678	C₂×C₆₁	1	4	yes	complemented
220	#1677	C₂×C₆₁	1	4	yes	complemented
221	#1566	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#1548	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1545	C₂×C₆₁	1	1	yes	characteristic, complemented
224	C₂×C₆₁	—	2	2	no	—
225	C₂×C₆₁	—	4	2	no	—
226	C₂×C₆₁	—	16	2	no	—
227	C₂×C₆₁	#3040	1	1	yes	characteristic
228	C₂×C₆₁	C₂×#465	1	1	yes	characteristic
229	C₂×C₆₁	C₂×#472	1	1	yes	characteristic
230	C₂×AGL(1,ℤ/8)	—	2	1	no	—
231	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
233	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
234	#486	—	2	1	no	—
235	#486	—	2	1	no	—
236	#486	C₂²×C₆₁	1	4	yes	—
237	#477	C₂²×C₆₁	1	2	yes	complemented
238	#476	C₂²×C₆₁	1	2	yes	complemented
239	#475	—	2	1	no	—
240	#474	—	2	1	no	—
241	#460	—	2	1	no	—
242	#460	C₂²×C₆₁	1	2	yes	—
243	#459	—	2	1	no	—
244	#459	C₂²×C₆₁	1	2	yes	—
245	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
246	C₈×D₄	—	2	2	no	—
247	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
248	#431	—	2	1	no	—
249	#431	C₂²×C₆₁	1	1	yes	characteristic
250	#428	—	2	1	no	—
251	#423	C₂²×C₆₁	1	1	yes	characteristic
252	#423	C₂²×C₆₁	1	1	yes	characteristic
253	#418	—	2	1	no	—
254	#417	—	2	1	no	—
255	C₂×#102	—	2	2	no	—
256	C₂×C₄×C₈	—	2	1	no	—
257	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
258	#334	C₂²×C₆₁	1	4	yes	complemented
259	#333	C₂²×C₆₁	1	4	yes	complemented
260	#331	C₂²×C₆₁	1	4	yes	—
261	C₆₁	#19274	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	AGL(1,ℤ/8)	—	4	4	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	D₄×C₆₁	1	2	yes	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	—	2	1	no	—
281	#127	C₂³×C₆₁	1	2	yes	—
282	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
283	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
287	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
288	#117	—	2	1	no	—
289	#117	D₄×C₆₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
294	#107	—	2	2	no	—
295	#106	—	2	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
300	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
301	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
302	#103	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
313	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
314	C₄×C₈	C₂³×C₆₁	1	2	yes	—
315	C₂⁴	—	4	1	no	—
316	#41	—	2	2	no	—
317	#41	SD₁₆×C₆₁	1	4	yes	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	8	2	no	—
333	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
341	SD₁₆	—	4	4	no	—
342	D₈	—	4	4	no	—
343	M₁₆	—	4	2	no	—
344	M₁₆	—	4	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	4	no	—
350	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₄²	#41×C₆₁	1	1	yes	characteristic
369	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	#121×C₆₁	1	1	yes	characteristic
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	8	2	no	—
379	Q₈	C₂×SD₁₆×C₆₁	1	2	yes	—
380	D₄	—	2	4	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	C₂×SD₁₆×C₆₁	1	2	yes	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
401	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
402	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
403	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
404	C₂×C₄	#135×C₆₁	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₆₁×#465	1	2	yes	—
423	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	C₆₁×#465	1	2	yes	—
431	C₄	C₆₁×#472	1	2	yes	—
432	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
433	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
434	C₄	C₆₁×#575	1	2	yes	—
435	C₂	—	2	2	no	—
436	C₂	—	4	2	no	—
437	C₂	—	16	2	no	—
438	C₂	C₆₁×#3040	1	1	yes	characteristic
439	C₂	C₂×C₆₁×#465	1	1	yes	characteristic
440	C₂	C₂×C₆₁×#472	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×#3079	C₂	semidirect
4. C₈×#41×C₆₁	C₂	semidirect
5. C₆₁×#1678	C₂	semidirect
6. C₆₁×#1677	C₂	semidirect
7. C₆₁×#1566	C₂	semidirect
8. C₆₁×#1548	C₂	semidirect
9. C₆₁×#1545	C₂	semidirect
17. C₆₁×#477	C₂²	semidirect
18. C₆₁×#476	C₂²	semidirect
25. C₈×Q₈×C₆₁	C₂²	semidirect
27. C₈×D₄×C₆₁	C₂²	semidirect
38. C₆₁×#334	C₂²	semidirect
39. C₆₁×#333	C₂²	semidirect
192. #19274	C₆₁	direct (N × H)
215. C₂×#486	C₂×C₆₁	semidirect
216. #3079	C₂×C₆₁	semidirect
218. C₈×#41	C₂×C₆₁	semidirect
219. #1678	C₂×C₆₁	semidirect
220. #1677	C₂×C₆₁	semidirect
221. #1566	C₂×C₆₁	semidirect
222. #1548	C₂×C₆₁	semidirect
223. #1545	C₂×C₆₁	semidirect
237. #477	C₂²×C₆₁	semidirect
238. #476	C₂²×C₆₁	semidirect
245. C₈×Q₈	C₂²×C₆₁	semidirect
247. C₈×D₄	C₂²×C₆₁	semidirect
258. #334	C₂²×C₆₁	semidirect
259. #333	C₂²×C₆₁	semidirect
261. C₆₁	#19274	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×#3079	2
C₆₁×#3038	2
C₈×#41×C₆₁	2
C₆₁×#1678	2
C₆₁×#1677	2
C₆₁×#1566	2
C₆₁×#1548	2
C₆₁×#1545	2
#19274	61

Subgroups — C61×#19274 #29522707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19274 #29522707