Subgroups — C₆₁×#32896 #29536329

Order 15616.

3610 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3028	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3022	C₂	1	3	yes	maximal, complemented
4	C₆₁×#3009	C₂	1	3	yes	maximal, complemented
5	C₆₁×#1795	C₂	1	3	yes	maximal, complemented
6	C₆₁×#1794	C₂	1	3	yes	maximal, complemented
7	C₆₁×#1791	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#585	—	2	6	no	—
9	C₆₁×#585	—	2	6	no	—
10	C₆₁×#585	C₂²	1	3	yes	—
11	C₆₁×#585	C₂²	1	1	yes	characteristic
12	C₂×H(5,𝔽₂)×C₆₁	—	2	6	no	—
13	C₂×H(5,𝔽₂)×C₆₁	—	2	4	no	—
14	C₂×H(5,𝔽₂)×C₆₁	—	2	6	no	—
15	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	3	yes	—
16	C₂×#137×C₆₁	C₂²	1	3	yes	complemented
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
18	C₆₁×#536	C₂²	1	3	yes	complemented
19	C₆₁×#458	—	2	4	no	—
20	C₆₁×#456	—	2	6	no	—
21	C₆₁×#455	—	2	6	no	—
22	C₆₁×#452	—	2	6	no	—
23	C₆₁×#450	—	2	6	no	—
24	C₆₁×#421	C₂²	1	6	yes	complemented
25	C₆₁×#418	C₂²	1	3	yes	complemented
26	C₆₁×#416	C₂²	1	3	yes	complemented
27	C₆₁×#413	C₂²	1	3	yes	complemented
28	C₆₁×#410	C₂²	1	3	yes	complemented
29	C₆₁×#408	C₂²	1	3	yes	complemented
30	2₋¹⁺⁴×C₆₁	—	2	4	no	—
31	2₋¹⁺⁴×C₆₁	—	2	12	no	—
32	2₋¹⁺⁴×C₆₁	—	2	3	no	—
33	2₋¹⁺⁴×C₆₁	—	2	6	no	—
34	2₋¹⁺⁴×C₆₁	D₄	1	6	yes	—
35	H(5,𝔽₂)×C₆₁	—	2	12	no	—
36	H(5,𝔽₂)×C₆₁	—	2	24	no	—
37	H(5,𝔽₂)×C₆₁	—	2	24	no	—
38	H(5,𝔽₂)×C₆₁	—	2	12	no	—
39	H(5,𝔽₂)×C₆₁	—	2	24	no	—
40	H(5,𝔽₂)×C₆₁	—	2	12	no	—
41	H(5,𝔽₂)×C₆₁	—	2	6	no	—
42	H(5,𝔽₂)×C₆₁	—	2	3	no	—
43	H(5,𝔽₂)×C₆₁	—	2	6	no	—
44	H(5,𝔽₂)×C₆₁	—	2	12	no	—
45	H(5,𝔽₂)×C₆₁	D₄	1	6	yes	—
46	H(5,𝔽₂)×C₆₁	D₄	1	4	yes	—
47	C₂×#41×C₆₁	—	2	24	no	—
48	C₂×#41×C₆₁	—	2	12	no	—
49	C₂×#41×C₆₁	—	2	12	no	—
50	C₂×#41×C₆₁	—	2	24	no	—
51	C₂×#41×C₆₁	—	2	12	no	—
52	C₂×#41×C₆₁	—	2	3	no	—
53	C₂×#41×C₆₁	—	2	6	no	—
54	C₂×#41×C₆₁	—	2	6	no	—
55	C₂×#41×C₆₁	D₄	1	6	yes	—
56	C₂×#41×C₆₁	C₂³	1	3	yes	—
57	C₂×#41×C₆₁	C₂³	1	3	yes	—
58	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₆₁	—	2	24	no	—
60	C₂²×D₄×C₆₁	—	2	12	no	—
61	C₂²×D₄×C₆₁	—	2	4	no	—
62	C₂²×D₄×C₆₁	—	2	6	no	—
63	C₂²×D₄×C₆₁	—	2	3	no	—
64	C₂²×D₄×C₆₁	D₄	1	6	yes	—
65	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
66	#137×C₆₁	—	2	12	no	—
67	C₂×Q₁₆×C₆₁	—	2	3	no	—
68	C₂×SD₁₆×C₆₁	—	2	6	no	—
69	C₂×SD₁₆×C₆₁	—	2	3	no	—
70	C₂×M₁₆×C₆₁	C₂³	1	3	yes	complemented
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic, complemented
72	C₄⋊Q₈×C₆₁	—	2	3	no	—
73	#124×C₆₁	—	2	3	no	—
74	#123×C₆₁	—	2	6	no	—
75	C₂²⋊Q₈×C₆₁	—	2	6	no	—
76	#117×C₆₁	C₂³	1	3	yes	complemented
77	#104×C₆₁	—	2	12	no	—
78	#103×C₆₁	—	2	3	no	—
79	#102×C₆₁	—	2	3	no	—
80	#102×C₆₁	—	2	6	no	—
81	#101×C₆₁	—	2	3	no	—
82	#100×C₆₁	—	2	3	no	—
83	#99×C₆₁	—	2	6	no	—
84	C₂²⋊C₈×C₆₁	—	2	6	no	—
85	C₂⁴×C₆₁	—	2	8	no	—
86	C₂⁴×C₆₁	—	2	6	no	—
87	C₂⁴×C₆₁	—	2	1	no	—
88	#41×C₆₁	—	2	24	no	—
89	#41×C₆₁	—	2	24	no	—
90	#41×C₆₁	—	2	48	no	—
91	#41×C₆₁	—	2	24	no	—
92	#41×C₆₁	—	2	24	no	—
93	#41×C₆₁	—	2	12	no	—
94	#41×C₆₁	—	2	12	no	—
95	#41×C₆₁	—	2	12	no	—
96	#41×C₆₁	—	2	4	no	—
97	#41×C₆₁	—	2	12	no	—
98	#41×C₆₁	—	2	12	no	—
99	#41×C₆₁	—	2	12	no	—
100	#41×C₆₁	—	2	12	no	—
101	#41×C₆₁	—	2	12	no	—
102	#41×C₆₁	—	2	12	no	—
103	#41×C₆₁	—	2	6	no	—
104	#41×C₆₁	—	2	6	no	—
105	#41×C₆₁	—	2	6	no	—
106	#41×C₆₁	C₂×D₄	1	12	yes	—
107	C₂×Q₈×C₆₁	—	2	8	no	—
108	C₂×Q₈×C₆₁	—	2	6	no	—
109	C₂×Q₈×C₆₁	—	2	6	no	—
110	C₂×Q₈×C₆₁	—	2	12	no	—
111	C₂×Q₈×C₆₁	—	2	3	no	—
112	C₂×Q₈×C₆₁	—	2	3	no	—
113	C₂×Q₈×C₆₁	C₂×D₄	1	3	yes	—
114	C₂×Q₈×C₆₁	C₂×D₄	1	3	yes	—
115	C₂×D₄×C₆₁	—	2	24	no	—
116	C₂×D₄×C₆₁	—	2	48	no	—
117	C₂×D₄×C₆₁	—	2	24	no	—
118	C₂×D₄×C₆₁	—	2	24	no	—
119	C₂×D₄×C₆₁	—	2	24	no	—
120	C₂×D₄×C₆₁	—	2	48	no	—
121	C₂×D₄×C₆₁	—	2	24	no	—
122	C₂×D₄×C₆₁	—	2	6	no	—
123	C₂×D₄×C₆₁	—	2	6	no	—
124	C₂×D₄×C₆₁	—	2	12	no	—
125	C₂×D₄×C₆₁	—	2	12	no	—
126	C₂×D₄×C₆₁	—	2	6	no	—
127	C₂×D₄×C₆₁	—	2	3	no	—
128	C₂×D₄×C₆₁	—	2	12	no	—
129	C₂×D₄×C₆₁	—	2	12	no	—
130	C₂×D₄×C₆₁	—	2	12	no	—
131	C₂×D₄×C₆₁	—	2	6	no	—
132	C₂×D₄×C₆₁	—	2	3	no	—
133	C₂×D₄×C₆₁	C₂×D₄	1	6	yes	—
134	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
135	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
136	C₂×D₄×C₆₁	C₂×D₄	1	6	yes	—
137	C₂²×C₄×C₆₁	—	2	24	no	—
138	C₂²×C₄×C₆₁	—	2	12	no	—
139	C₂²×C₄×C₆₁	—	2	4	no	—
140	C₂²×C₄×C₆₁	—	2	6	no	—
141	C₂²×C₄×C₆₁	—	2	3	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	6	yes	—
144	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₆₁	—	4	6	no	—
146	SD₁₆×C₆₁	—	4	4	no	—
147	SD₁₆×C₆₁	—	4	6	no	—
148	M₁₆×C₆₁	—	2	6	no	—
149	C₂×C₈×C₆₁	—	2	3	no	—
150	C₂×C₈×C₆₁	—	2	3	no	—
151	C₄⋊C₄×C₆₁	—	2	3	no	—
152	C₄⋊C₄×C₆₁	—	4	6	no	—
153	C₂²⋊C₄×C₆₁	—	2	3	no	—
154	C₂²⋊C₄×C₆₁	—	4	6	no	—
155	C₄²×C₆₁	—	2	3	no	—
156	C₂³×C₆₁	—	2	4	no	—
157	C₂³×C₆₁	—	2	24	no	—
158	C₂³×C₆₁	—	2	12	no	—
159	C₂³×C₆₁	—	2	6	no	—
160	C₂³×C₆₁	—	2	3	no	—
161	C₂³×C₆₁	—	16	1	no	—
162	C₂³×C₆₁	—	16	6	no	—
163	C₂³×C₆₁	—	16	8	no	—
164	C₂³×C₆₁	#120	1	6	yes	—
165	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₆₁	—	2	12	no	—
167	Q₈×C₆₁	—	2	4	no	—
168	Q₈×C₆₁	—	2	3	no	—
169	Q₈×C₆₁	—	2	6	no	—
170	Q₈×C₆₁	—	4	1	no	—
171	Q₈×C₆₁	—	4	3	no	—
172	Q₈×C₆₁	#120	1	6	yes	—
173	D₄×C₆₁	—	2	24	no	—
174	D₄×C₆₁	—	2	24	no	—
175	D₄×C₆₁	—	2	12	no	—
176	D₄×C₆₁	—	2	12	no	—
177	D₄×C₆₁	—	2	24	no	—
178	D₄×C₆₁	—	2	12	no	—
179	D₄×C₆₁	—	2	12	no	—
180	D₄×C₆₁	—	2	6	no	—
181	D₄×C₆₁	—	2	6	no	—
182	D₄×C₆₁	—	2	3	no	—
183	D₄×C₆₁	#120	1	6	yes	—
184	D₄×C₆₁	#120	1	4	yes	—
185	C₂×C₄×C₆₁	—	2	12	no	—
186	C₂×C₄×C₆₁	—	2	24	no	—
187	C₂×C₄×C₆₁	—	2	24	no	—
188	C₂×C₄×C₆₁	—	2	12	no	—
189	C₂×C₄×C₆₁	—	2	3	no	—
190	C₂×C₄×C₆₁	—	2	12	no	—
191	C₂×C₄×C₆₁	—	2	6	no	—
192	C₂×C₄×C₆₁	—	2	6	no	—
193	C₂×C₄×C₆₁	—	4	3	no	—
194	C₂×C₄×C₆₁	—	4	3	no	—
195	C₂×C₄×C₆₁	#120	1	6	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
198	C₈×C₆₁	—	4	1	no	—
199	C₈×C₆₁	—	4	3	no	—
200	#32896	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₆₁	—	2	6	no	—
202	C₂²×C₆₁	—	2	4	no	—
203	C₂²×C₆₁	—	2	6	no	—
204	C₂²×C₆₁	—	4	1	no	—
205	C₂²×C₆₁	—	4	6	no	—
206	C₂²×C₆₁	—	8	6	no	—
207	C₂²×C₆₁	—	8	3	no	—
208	C₂²×C₆₁	—	8	4	no	—
209	C₂²×C₆₁	—	8	24	no	—
210	C₂²×C₆₁	—	8	12	no	—
211	C₂²×C₆₁	C₂×#120	1	3	yes	—
212	C₄×C₆₁	—	2	6	no	—
213	C₄×C₆₁	—	2	6	no	—
214	C₄×C₆₁	—	8	3	no	—
215	C₄×C₆₁	—	8	1	no	—
216	C₄×C₆₁	C₂×#120	1	3	yes	—
217	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
218	H(7,𝔽₂)	C₂×C₆₁	1	1	yes	characteristic
219	#3028	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#3022	C₂×C₆₁	1	3	yes	complemented
221	#3009	C₂×C₆₁	1	3	yes	complemented
222	#1795	C₂×C₆₁	1	3	yes	complemented
223	#1794	C₂×C₆₁	1	3	yes	complemented
224	#1791	C₂×C₆₁	1	1	yes	characteristic, complemented
225	C₂×C₆₁	—	2	3	no	—
226	C₂×C₆₁	—	4	6	no	—
227	C₂×C₆₁	—	4	4	no	—
228	C₂×C₆₁	—	4	6	no	—
229	C₂×C₆₁	#2846	1	1	yes	characteristic
230	#585	—	2	6	no	—
231	#585	—	2	6	no	—
232	#585	C₂²×C₆₁	1	3	yes	—
233	#585	C₂²×C₆₁	1	1	yes	characteristic
234	C₂×H(5,𝔽₂)	—	2	6	no	—
235	C₂×H(5,𝔽₂)	—	2	4	no	—
236	C₂×H(5,𝔽₂)	—	2	6	no	—
237	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	3	yes	—
238	C₂×#137	C₂²×C₆₁	1	3	yes	complemented
239	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
240	#536	C₂²×C₆₁	1	3	yes	complemented
241	#458	—	2	4	no	—
242	#456	—	2	6	no	—
243	#455	—	2	6	no	—
244	#452	—	2	6	no	—
245	#450	—	2	6	no	—
246	#421	C₂²×C₆₁	1	6	yes	complemented
247	#418	C₂²×C₆₁	1	3	yes	complemented
248	#416	C₂²×C₆₁	1	3	yes	complemented
249	#413	C₂²×C₆₁	1	3	yes	complemented
250	#410	C₂²×C₆₁	1	3	yes	complemented
251	#408	C₂²×C₆₁	1	3	yes	complemented
252	C₆₁	#32896	1	1	yes	characteristic, direct product factor, Sylow
253	2₋¹⁺⁴	—	2	4	no	—
254	2₋¹⁺⁴	—	2	12	no	—
255	2₋¹⁺⁴	—	2	3	no	—
256	2₋¹⁺⁴	—	2	6	no	—
257	2₋¹⁺⁴	D₄×C₆₁	1	6	yes	—
258	H(5,𝔽₂)	—	2	12	no	—
259	H(5,𝔽₂)	—	2	24	no	—
260	H(5,𝔽₂)	—	2	24	no	—
261	H(5,𝔽₂)	—	2	12	no	—
262	H(5,𝔽₂)	—	2	24	no	—
263	H(5,𝔽₂)	—	2	12	no	—
264	H(5,𝔽₂)	—	2	6	no	—
265	H(5,𝔽₂)	—	2	3	no	—
266	H(5,𝔽₂)	—	2	6	no	—
267	H(5,𝔽₂)	—	2	12	no	—
268	H(5,𝔽₂)	D₄×C₆₁	1	6	yes	—
269	H(5,𝔽₂)	D₄×C₆₁	1	4	yes	—
270	C₂×#41	—	2	24	no	—
271	C₂×#41	—	2	12	no	—
272	C₂×#41	—	2	12	no	—
273	C₂×#41	—	2	24	no	—
274	C₂×#41	—	2	12	no	—
275	C₂×#41	—	2	3	no	—
276	C₂×#41	—	2	6	no	—
277	C₂×#41	—	2	6	no	—
278	C₂×#41	D₄×C₆₁	1	6	yes	—
279	C₂×#41	C₂³×C₆₁	1	3	yes	—
280	C₂×#41	C₂³×C₆₁	1	3	yes	—
281	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic, complemented
282	C₂²×D₄	—	2	24	no	—
283	C₂²×D₄	—	2	12	no	—
284	C₂²×D₄	—	2	4	no	—
285	C₂²×D₄	—	2	6	no	—
286	C₂²×D₄	—	2	3	no	—
287	C₂²×D₄	D₄×C₆₁	1	6	yes	—
288	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
289	#137	—	2	12	no	—
290	C₂×Q₁₆	—	2	3	no	—
291	C₂×SD₁₆	—	2	6	no	—
292	C₂×SD₁₆	—	2	3	no	—
293	C₂×M₁₆	C₂³×C₆₁	1	3	yes	complemented
294	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic, complemented
295	C₄⋊Q₈	—	2	3	no	—
296	#124	—	2	3	no	—
297	#123	—	2	6	no	—
298	C₂²⋊Q₈	—	2	6	no	—
299	#117	C₂³×C₆₁	1	3	yes	complemented
300	#104	—	2	12	no	—
301	#103	—	2	3	no	—
302	#102	—	2	3	no	—
303	#102	—	2	6	no	—
304	#101	—	2	3	no	—
305	#100	—	2	3	no	—
306	#99	—	2	6	no	—
307	C₂²⋊C₈	—	2	6	no	—
308	C₂⁴	—	2	8	no	—
309	C₂⁴	—	2	6	no	—
310	C₂⁴	—	2	1	no	—
311	#41	—	2	24	no	—
312	#41	—	2	24	no	—
313	#41	—	2	48	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	—	2	12	no	—
317	#41	—	2	12	no	—
318	#41	—	2	12	no	—
319	#41	—	2	4	no	—
320	#41	—	2	12	no	—
321	#41	—	2	12	no	—
322	#41	—	2	12	no	—
323	#41	—	2	12	no	—
324	#41	—	2	12	no	—
325	#41	—	2	12	no	—
326	#41	—	2	6	no	—
327	#41	—	2	6	no	—
328	#41	—	2	6	no	—
329	#41	C₂×D₄×C₆₁	1	12	yes	—
330	C₂×Q₈	—	2	8	no	—
331	C₂×Q₈	—	2	6	no	—
332	C₂×Q₈	—	2	6	no	—
333	C₂×Q₈	—	2	12	no	—
334	C₂×Q₈	—	2	3	no	—
335	C₂×Q₈	—	2	3	no	—
336	C₂×Q₈	C₂×D₄×C₆₁	1	3	yes	—
337	C₂×Q₈	C₂×D₄×C₆₁	1	3	yes	—
338	C₂×D₄	—	2	24	no	—
339	C₂×D₄	—	2	48	no	—
340	C₂×D₄	—	2	24	no	—
341	C₂×D₄	—	2	24	no	—
342	C₂×D₄	—	2	24	no	—
343	C₂×D₄	—	2	48	no	—
344	C₂×D₄	—	2	24	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	2	6	no	—
347	C₂×D₄	—	2	12	no	—
348	C₂×D₄	—	2	12	no	—
349	C₂×D₄	—	2	6	no	—
350	C₂×D₄	—	2	3	no	—
351	C₂×D₄	—	2	12	no	—
352	C₂×D₄	—	2	12	no	—
353	C₂×D₄	—	2	12	no	—
354	C₂×D₄	—	2	6	no	—
355	C₂×D₄	—	2	3	no	—
356	C₂×D₄	C₂×D₄×C₆₁	1	6	yes	—
357	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
358	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
359	C₂×D₄	C₂×D₄×C₆₁	1	6	yes	—
360	C₂²×C₄	—	2	24	no	—
361	C₂²×C₄	—	2	12	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	6	no	—
364	C₂²×C₄	—	2	3	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	6	yes	—
367	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
368	Q₁₆	—	4	6	no	—
369	SD₁₆	—	4	4	no	—
370	SD₁₆	—	4	6	no	—
371	M₁₆	—	2	6	no	—
372	C₂×C₈	—	2	3	no	—
373	C₂×C₈	—	2	3	no	—
374	C₄⋊C₄	—	2	3	no	—
375	C₄⋊C₄	—	4	6	no	—
376	C₂²⋊C₄	—	2	3	no	—
377	C₂²⋊C₄	—	4	6	no	—
378	C₄²	—	2	3	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	24	no	—
381	C₂³	—	2	12	no	—
382	C₂³	—	2	6	no	—
383	C₂³	—	2	3	no	—
384	C₂³	—	16	1	no	—
385	C₂³	—	16	6	no	—
386	C₂³	—	16	8	no	—
387	C₂³	#120×C₆₁	1	6	yes	—
388	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
389	Q₈	—	2	12	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	2	3	no	—
392	Q₈	—	2	6	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	4	3	no	—
395	Q₈	#120×C₆₁	1	6	yes	—
396	D₄	—	2	24	no	—
397	D₄	—	2	24	no	—
398	D₄	—	2	12	no	—
399	D₄	—	2	12	no	—
400	D₄	—	2	24	no	—
401	D₄	—	2	12	no	—
402	D₄	—	2	12	no	—
403	D₄	—	2	6	no	—
404	D₄	—	2	6	no	—
405	D₄	—	2	3	no	—
406	D₄	#120×C₆₁	1	6	yes	—
407	D₄	#120×C₆₁	1	4	yes	—
408	C₂×C₄	—	2	12	no	—
409	C₂×C₄	—	2	24	no	—
410	C₂×C₄	—	2	24	no	—
411	C₂×C₄	—	2	12	no	—
412	C₂×C₄	—	2	3	no	—
413	C₂×C₄	—	2	12	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	4	3	no	—
417	C₂×C₄	—	4	3	no	—
418	C₂×C₄	#120×C₆₁	1	6	yes	—
419	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
420	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
421	C₈	—	4	1	no	—
422	C₈	—	4	3	no	—
423	C₂²	—	2	6	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	6	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	6	no	—
428	C₂²	—	8	6	no	—
429	C₂²	—	8	3	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	24	no	—
432	C₂²	—	8	12	no	—
433	C₂²	C₂×#120×C₆₁	1	3	yes	—
434	C₄	—	2	6	no	—
435	C₄	—	2	6	no	—
436	C₄	—	8	3	no	—
437	C₄	—	8	1	no	—
438	C₄	C₂×#120×C₆₁	1	3	yes	—
439	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
440	C₂	—	2	3	no	—
441	C₂	—	4	6	no	—
442	C₂	—	4	4	no	—
443	C₂	—	4	6	no	—
444	C₂	C₆₁×#2846	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	#2846
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×H(7,𝔽₂)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3028	C₂	semidirect
3. C₆₁×#3022	C₂	semidirect
4. C₆₁×#3009	C₂	semidirect
5. C₆₁×#1795	C₂	semidirect
6. C₆₁×#1794	C₂	semidirect
7. C₆₁×#1791	C₂	semidirect
16. C₂×#137×C₆₁	C₂²	semidirect
17. C₂²×SD₁₆×C₆₁	C₂²	semidirect
18. C₆₁×#536	C₂²	semidirect
24. C₆₁×#421	C₂²	semidirect
25. C₆₁×#418	C₂²	semidirect
26. C₆₁×#416	C₂²	semidirect
27. C₆₁×#413	C₂²	semidirect
28. C₆₁×#410	C₂²	semidirect
29. C₆₁×#408	C₂²	semidirect
58. C₂²×Q₈×C₆₁	C₂³	semidirect
70. C₂×M₁₆×C₆₁	C₂³	semidirect
71. C₂²×C₈×C₆₁	C₂³	semidirect
76. #117×C₆₁	C₂³	semidirect
200. #32896	C₆₁	direct (N × H)
219. #3028	C₂×C₆₁	semidirect
220. #3022	C₂×C₆₁	semidirect
221. #3009	C₂×C₆₁	semidirect
222. #1795	C₂×C₆₁	semidirect
223. #1794	C₂×C₆₁	semidirect
224. #1791	C₂×C₆₁	semidirect
238. C₂×#137	C₂²×C₆₁	semidirect
239. C₂²×SD₁₆	C₂²×C₆₁	semidirect
240. #536	C₂²×C₆₁	semidirect
246. #421	C₂²×C₆₁	semidirect
247. #418	C₂²×C₆₁	semidirect
248. #416	C₂²×C₆₁	semidirect
249. #413	C₂²×C₆₁	semidirect
250. #410	C₂²×C₆₁	semidirect
251. #408	C₂²×C₆₁	semidirect
252. C₆₁	#32896	direct (N × H)
281. C₂²×Q₈	C₂³×C₆₁	semidirect
293. C₂×M₁₆	C₂³×C₆₁	semidirect
294. C₂²×C₈	C₂³×C₆₁	semidirect
299. #117	C₂³×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×H(7,𝔽₂)	2
C₆₁×#3028	2
C₆₁×#3022	2
C₆₁×#3009	2
C₆₁×#1795	2
C₆₁×#1794	2
C₆₁×#1791	2
#32896	61

Subgroups — C61×#32896 #29536329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#32896 #29536329