Subgroups — #21460420

Order 7808.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁⋊#564	C₂	1	2	yes	maximal, complemented
2	#16840514	C₂	1	2	yes	maximal, complemented
3	#16840491	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840489	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840470	C₂	1	1	yes	maximal, characteristic, complemented
6	#16840469	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840454	C₂	1	1	yes	maximal, characteristic, complemented
8	#16840451	C₂	1	1	yes	maximal, characteristic, complemented
9	#16840449	C₂	1	2	yes	maximal, complemented
10	#16840447	C₂	1	1	yes	maximal, characteristic, complemented
11	#16840445	C₂	1	2	yes	maximal, complemented
12	#16840392	C₂	1	1	yes	maximal, characteristic, complemented
13	#16840390	C₂	1	1	yes	maximal, characteristic, complemented
14	#16840390	C₂	1	2	yes	maximal, complemented
15	#16840375	C₂	1	2	yes	maximal, complemented
16	#16840372	C₂	1	1	yes	maximal, characteristic, complemented
17	#16840370	C₂	1	1	yes	maximal, characteristic, complemented
18	#16840369	C₂	1	2	yes	maximal, complemented
19	#16840356	C₂	1	2	yes	maximal
20	#16840314	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840292	C₂	1	1	yes	maximal, characteristic
22	C₂×#14519768	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	#14519777	C₂²	1	1	yes	characteristic
25	#14519777	C₂²	1	2	yes	—
26	#14519777	C₂²	1	2	yes	—
27	#14519776	C₂²	1	1	yes	characteristic
28	#14519776	C₂²	1	2	yes	—
29	#14519776	C₂²	1	1	yes	characteristic
30	#14519776	C₂²	1	2	yes	—
31	#14519775	C₂²	1	1	yes	characteristic
32	#14519772	C₂²	1	2	yes	—
33	#14519772	C₂²	1	2	yes	—
34	#14519772	C₂²	1	1	yes	characteristic
35	#14519772	C₂²	1	2	yes	—
36	#14519771	C₂²	1	2	yes	—
37	#14519770	C₂²	1	2	yes	—
38	#14519770	C₂²	1	2	yes	—
39	#14519770	C₂²	1	1	yes	characteristic
40	#14519770	C₂²	1	2	yes	—
41	#14519769	C₂²	1	2	yes	—
42	#14519769	C₂²	1	2	yes	—
43	#14519769	C₂²	1	2	yes	—
44	#14519768	C₂²	1	2	yes	—
45	#14519768	C₂²	1	1	yes	characteristic
46	#14519768	C₂²	1	1	yes	characteristic
47	#14519768	C₂²	1	2	yes	—
48	#14519768	C₂²	1	2	yes	—
49	#14519768	C₂²	1	2	yes	—
50	#14519768	C₂²	1	1	yes	characteristic
51	#14519768	C₂²	1	2	yes	—
52	#14519768	C₂²	1	2	yes	—
53	#14519768	C₂²	1	1	yes	characteristic
54	#14519768	C₂²	1	1	yes	characteristic
55	#14519768	C₂²	1	2	yes	—
56	#14519767	C₂²	1	2	yes	—
57	#14519767	C₂²	1	2	yes	—
58	#14519767	C₂²	1	2	yes	—
59	#14519767	C₂²	1	2	yes	—
60	#14519767	C₂²	1	2	yes	—
61	#14519767	C₂²	1	2	yes	—
62	#14519767	C₂²	1	1	yes	characteristic
63	#14519767	C₂²	1	2	yes	—
64	#14519767	C₂²	1	2	yes	—
65	#14519763	C₂²	1	1	yes	characteristic
66	#14519761	C₂²	1	2	yes	—
67	#14519761	C₂²	1	1	yes	characteristic
68	#14519760	C₂²	1	2	yes	—
69	#14519759	C₂²	1	2	yes	—
70	#14519758	C₂²	1	1	yes	characteristic
71	#14519757	C₂²	1	1	yes	characteristic
72	#14519757	C₂²	1	2	yes	—
73	#14519757	C₂²	1	2	yes	—
74	#14519756	C₂²	1	1	yes	characteristic
75	#14519756	C₂²	1	1	yes	characteristic
76	#14519755	C₂²	1	2	yes	—
77	#14519754	C₂²	1	2	yes	—
78	#14519754	C₂²	1	2	yes	—
79	#14519754	C₂²	1	2	yes	—
80	#14519754	C₂²	1	2	yes	—
81	#14519754	C₂²	1	1	yes	characteristic
82	#14519754	C₂²	1	2	yes	—
83	#14519754	C₂²	1	2	yes	—
84	#14519753	C₂²	1	1	yes	characteristic
85	#14519749	C₂²	1	1	yes	characteristic
86	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic
87	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
90	C₄×Dic₁₂₂	C₂²	1	2	yes	—
91	#14519742	C₂²	1	2	yes	—
92	#14519742	C₂²	1	1	yes	characteristic
93	#14519742	C₂²	1	1	yes	characteristic
94	#14519742	C₂²	1	2	yes	—
95	D₄×Dic₆₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
98	#14519737	C₂²	1	2	yes	—
99	#14519736	C₂²	1	2	yes	—
100	#14519736	C₂²	1	1	yes	characteristic
101	#14519735	C₂²	1	1	yes	characteristic
102	#14519734	C₂²	1	2	yes	—
103	#14519734	C₂²	1	1	yes	characteristic
104	#14519733	C₂²	1	2	yes	—
105	#14519733	C₂²	1	2	yes	—
106	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
107	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
108	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
109	C₂×#11758196	C₂²	1	2	yes	—
110	C₄⋊C₄×D₆₁	C₂²	1	1	yes	characteristic
111	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
112	#126×C₆₁	C₂²	1	2	yes	—
113	#125×C₆₁	C₂²	1	1	yes	characteristic
114	#125×C₆₁	C₂²	1	2	yes	—
115	#123×C₆₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
120	#117×C₆₁	C₂²	1	1	yes	characteristic
121	#117×C₆₁	C₂²	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
126	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
130	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
131	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
132	C₂²×Dic₆₁	C₂³	1	2	yes	—
133	C₂²×Dic₆₁	C₂³	1	2	yes	—
134	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₆₁	C₂³	1	2	yes	—
136	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
137	C₂×Dic₁₂₂	C₂³	1	2	yes	—
138	C₂×Dic₁₂₂	C₂³	1	2	yes	—
139	C₂×Dic₁₂₂	C₂³	1	2	yes	—
140	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
144	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
147	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
152	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
155	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
156	C₄²×C₆₁	C₂³	1	2	yes	—
157	C₄²×C₆₁	C₂³	1	2	yes	—
158	C₄²×C₆₁	C₂³	1	1	yes	characteristic
159	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
160	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
161	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
162	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
163	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
165	#11758198	C₂³	1	1	yes	characteristic
166	#11758198	C₂³	1	1	yes	characteristic
167	#11758198	C₂³	1	1	yes	characteristic
168	#11758198	C₂³	1	2	yes	—
169	#11758198	C₂³	1	2	yes	—
170	#11758198	C₂³	1	2	yes	—
171	#11758198	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₆₁	C₂³	1	2	yes	—
176	C₄⋊Dic₆₁	C₂³	1	2	yes	—
177	C₄⋊Dic₆₁	C₂³	1	2	yes	—
178	C₄⋊Dic₆₁	C₂³	1	2	yes	—
179	C₄⋊Dic₆₁	C₂³	1	2	yes	—
180	C₄⋊Dic₆₁	C₂³	1	2	yes	—
181	C₄⋊Dic₆₁	C₂³	1	2	yes	—
182	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₆₁	C₂³	1	2	yes	—
184	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₆₁	C₂³	1	2	yes	—
186	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₆₁	C₂³	1	2	yes	—
188	C₄⋊Dic₆₁	C₂³	1	2	yes	—
189	#11758196	C₂³	1	2	yes	—
190	#11758196	C₂³	1	2	yes	—
191	#11758196	C₂³	1	2	yes	—
192	#11758196	C₂³	1	2	yes	—
193	#11758196	C₂³	1	2	yes	—
194	#11758196	C₂³	1	2	yes	—
195	#11758196	C₂³	1	2	yes	—
196	#11758196	C₂³	1	2	yes	—
197	#11758196	C₂³	1	2	yes	—
198	#11758196	C₂³	1	1	yes	characteristic
199	#11758196	C₂³	1	1	yes	characteristic
200	#11758196	C₂³	1	2	yes	—
201	#11758196	C₂³	1	1	yes	characteristic
202	#11758196	C₂³	1	1	yes	characteristic
203	#11758196	C₂³	1	1	yes	characteristic
204	#11758196	C₂³	1	2	yes	—
205	#11758196	C₂³	1	2	yes	—
206	#11758196	C₂³	1	2	yes	—
207	#11758196	C₂³	1	2	yes	—
208	#11758196	C₂³	1	1	yes	characteristic
209	#11758196	C₂³	1	2	yes	—
210	#11758196	C₂³	1	2	yes	—
211	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
212	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
213	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
214	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
215	C₄×Dic₆₁	C₂³	1	2	yes	—
216	C₄×Dic₆₁	C₂³	1	2	yes	—
217	C₄×Dic₆₁	C₂³	1	2	yes	—
218	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₆₁	C₂³	1	2	yes	—
220	C₄×Dic₆₁	C₂³	1	2	yes	—
221	C₄×Dic₆₁	C₂³	1	2	yes	—
222	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
223	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
224	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
225	Q₈×C₆₁	—	2	2	no	—
226	D₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	4	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
231	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
234	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
235	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
236	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₂²⋊D₆₁	—	2	2	no	—
240	C₂²⋊D₆₁	—	4	1	no	—
241	C₂×Dic₆₁	—	2	2	no	—
242	C₂×Dic₆₁	—	4	2	no	—
243	C₂×Dic₆₁	—	4	1	no	—
244	C₂×Dic₆₁	—	4	2	no	—
245	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₆₁	C₂⁴	1	2	yes	—
248	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₆₁	C₂⁴	1	2	yes	—
254	C₂×Dic₆₁	C₂⁴	1	2	yes	—
255	C₂×Dic₆₁	C₂⁴	1	2	yes	—
256	C₄×D₆₁	—	2	2	no	—
257	C₄×D₆₁	—	4	2	no	—
258	Dic₁₂₂	—	2	2	no	—
259	Dic₁₂₂	—	4	2	no	—
260	Dic₁₂₂	—	4	1	no	—
261	Dic₁₂₂	—	4	2	no	—
262	Dic₁₂₂	—	4	2	no	—
263	C₂²×C₆₁	—	2	1	no	—
264	C₂²×C₆₁	—	2	1	no	—
265	C₂²×C₆₁	—	2	1	no	—
266	C₂²×C₆₁	—	2	1	no	—
267	C₂²×C₆₁	—	2	1	no	—
268	C₂²×C₆₁	2₋¹⁺⁴	1	2	yes	—
269	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
270	C₂×D₆₁	—	2	1	no	—
271	C₂×D₆₁	—	2	1	no	—
272	C₂×D₆₁	—	2	1	no	—
273	C₄×C₆₁	—	2	2	no	—
274	C₄×C₆₁	—	2	2	no	—
275	C₄×C₆₁	—	2	1	no	—
276	C₄×C₆₁	—	2	1	no	—
277	C₄×C₆₁	—	2	1	no	—
278	C₄×C₆₁	—	2	2	no	—
279	C₄×C₆₁	—	2	1	no	—
280	C₄×C₆₁	—	2	2	no	—
281	C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
282	Dic₆₁	—	2	2	no	—
283	Dic₆₁	—	2	1	no	—
284	Dic₆₁	—	2	1	no	—
285	Dic₆₁	—	2	1	no	—
286	Dic₆₁	—	2	1	no	—
287	Dic₆₁	—	2	1	no	—
288	Dic₆₁	—	2	1	no	—
289	Dic₆₁	—	2	2	no	—
290	Dic₆₁	—	2	2	no	—
291	Dic₆₁	—	2	2	no	—
292	Dic₆₁	—	2	1	no	—
293	#3563	—	61	1	no	maximal, Sylow
294	C₂×C₆₁	—	2	2	no	—
295	C₂×C₆₁	—	4	1	no	—
296	C₂×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
297	C₂×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
298	C₂×C₆₁	#585	1	1	yes	characteristic
299	D₆₁	—	4	1	no	—
300	#564	—	61	2	no	—
301	#563	—	61	2	no	—
302	#557	—	61	1	no	—
303	#557	—	61	1	no	—
304	#554	—	61	1	no	—
305	#554	—	61	1	no	—
306	#552	—	61	2	no	—
307	#552	—	61	1	no	—
308	#552	—	61	1	no	—
309	#552	—	61	2	no	—
310	#552	—	61	1	no	—
311	#552	D₆₁	1	1	yes	characteristic, complemented
312	#544	—	61	1	no	—
313	#544	—	61	2	no	—
314	#544	—	61	1	no	—
315	#541	—	61	2	no	—
316	#541	—	61	2	no	—
317	#541	—	61	1	no	—
318	#541	—	61	1	no	—
319	#539	—	61	2	no	—
320	#533	—	61	1	no	—
321	#529	—	61	1	no	—
322	C₂×#125	—	61	1	no	—
323	C₆₁	#3563	1	1	yes	characteristic, complemented, Sylow
324	C₄⋊Q₈	—	61	1	no	—
325	C₄⋊Q₈	—	61	1	no	—
326	C₄⋊Q₈	—	61	2	no	—
327	C₄⋊Q₈	—	61	1	no	—
328	C₄⋊Q₈	—	61	2	no	—
329	C₄⋊Q₈	—	61	2	no	—
330	C₄⋊Q₈	—	61	1	no	—
331	C₄⋊Q₈	—	61	2	no	—
332	#126	—	61	1	no	—
333	#126	—	61	2	no	—
334	#126	—	61	2	no	—
335	#126	—	61	2	no	—
336	#126	—	61	1	no	—
337	#126	—	61	2	no	—
338	#126	—	61	2	no	—
339	#126	—	61	2	no	—
340	#126	—	61	2	no	—
341	#126	C₂×D₆₁	1	2	yes	—
342	#125	—	61	2	no	—
343	#125	—	61	1	no	—
344	#125	—	61	1	no	—
345	#125	—	61	1	no	—
346	#125	—	61	1	no	—
347	#125	—	61	2	no	—
348	#125	—	61	1	no	—
349	#125	—	61	2	no	—
350	#125	—	61	2	no	—
351	#125	—	61	2	no	—
352	#125	—	61	2	no	—
353	#125	—	61	2	no	—
354	#125	—	61	2	no	—
355	#125	—	61	2	no	—
356	#125	—	61	2	no	—
357	#125	—	61	2	no	—
358	#125	—	61	2	no	—
359	#125	—	61	2	no	—
360	#125	—	61	1	no	—
361	#125	—	61	2	no	—
362	#125	—	61	2	no	—
363	#125	—	61	2	no	—
364	#125	—	61	2	no	—
365	#125	—	61	2	no	—
366	#125	C₂×D₆₁	1	2	yes	—
367	#125	C₂×D₆₁	1	1	yes	characteristic
368	#124	—	61	1	no	—
369	#123	—	61	1	no	—
370	#123	—	61	2	no	—
371	#123	—	61	1	no	—
372	#123	—	61	2	no	—
373	#123	—	61	2	no	—
374	#123	C₂×D₆₁	1	2	yes	—
375	C₂²⋊Q₈	—	61	1	no	—
376	C₂²⋊Q₈	—	61	1	no	—
377	C₂²⋊Q₈	—	61	1	no	—
378	C₂²⋊Q₈	—	61	2	no	—
379	C₂²⋊Q₈	—	61	1	no	—
380	C₂²⋊Q₈	—	61	2	no	—
381	C₂²⋊Q₈	—	61	2	no	—
382	C₂²⋊Q₈	—	61	1	no	—
383	C₂²⋊Q₈	—	61	2	no	—
384	C₂²⋊Q₈	—	61	2	no	—
385	C₂²⋊Q₈	—	61	2	no	—
386	C₂²⋊Q₈	—	61	2	no	—
387	C₂²⋊Q₈	—	61	2	no	—
388	C₂²⋊Q₈	—	61	2	no	—
389	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
390	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
391	#121	—	61	1	no	—
392	C₄×Q₈	—	61	1	no	—
393	C₄×Q₈	—	61	1	no	—
394	C₄×Q₈	—	61	2	no	—
395	C₄×Q₈	—	61	1	no	—
396	C₄×Q₈	—	61	2	no	—
397	C₄×Q₈	—	61	1	no	—
398	C₄×Q₈	—	61	1	no	—
399	C₄×Q₈	—	61	2	no	—
400	C₄×Q₈	—	61	1	no	—
401	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
402	C₄×D₄	—	61	2	no	—
403	C₄×D₄	—	61	1	no	—
404	C₄×D₄	—	61	1	no	—
405	C₄×D₄	—	61	2	no	—
406	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
407	#117	—	61	1	no	—
408	#117	—	61	2	no	—
409	#117	—	61	1	no	—
410	#117	—	61	2	no	—
411	#117	—	61	2	no	—
412	#117	—	61	1	no	—
413	#117	—	61	2	no	—
414	#117	C₂×D₆₁	1	1	yes	characteristic
415	#117	C₂×D₆₁	1	2	yes	—
416	C₂×C₄⋊C₄	—	61	2	no	—
417	C₂×C₄⋊C₄	—	61	2	no	—
418	C₂×C₄⋊C₄	—	61	1	no	—
419	C₂×C₄⋊C₄	—	61	1	no	—
420	C₂×C₄⋊C₄	—	61	1	no	—
421	C₂×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
422	C₂×C₄²	—	61	1	no	—
423	C₂×Q₈	—	61	1	no	—
424	C₂×Q₈	—	61	2	no	—
425	C₂×Q₈	—	61	2	no	—
426	C₂×Q₈	—	61	2	no	—
427	C₂×Q₈	—	61	1	no	—
428	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
429	C₂×D₄	—	61	1	no	—
430	C₂×D₄	—	61	1	no	—
431	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
432	C₂²×C₄	—	61	1	no	—
433	C₂²×C₄	—	61	1	no	—
434	C₂²×C₄	—	61	2	no	—
435	C₂²×C₄	—	61	2	no	—
436	C₂²×C₄	—	61	1	no	—
437	C₂²×C₄	—	61	2	no	—
438	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
440	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
441	C₄⋊C₄	—	61	1	no	—
442	C₄⋊C₄	—	61	1	no	—
443	C₄⋊C₄	—	61	2	no	—
444	C₄⋊C₄	—	61	2	no	—
445	C₄⋊C₄	—	61	2	no	—
446	C₄⋊C₄	—	61	2	no	—
447	C₄⋊C₄	—	61	2	no	—
448	C₄⋊C₄	—	61	1	no	—
449	C₄⋊C₄	—	61	2	no	—
450	C₄⋊C₄	—	61	2	no	—
451	C₄⋊C₄	—	61	2	no	—
452	C₄⋊C₄	—	61	2	no	—
453	C₄⋊C₄	—	61	2	no	—
454	C₄⋊C₄	—	61	2	no	—
455	C₄⋊C₄	—	61	2	no	—
456	C₄⋊C₄	—	61	2	no	—
457	C₄⋊C₄	—	61	2	no	—
458	C₄⋊C₄	—	61	1	no	—
459	C₄⋊C₄	—	61	1	no	—
460	C₄⋊C₄	—	61	2	no	—
461	C₄⋊C₄	—	61	1	no	—
462	C₄⋊C₄	—	61	2	no	—
463	C₄⋊C₄	—	61	1	no	—
464	C₄⋊C₄	—	61	1	no	—
465	C₄⋊C₄	—	61	1	no	—
466	C₄⋊C₄	—	61	2	no	—
467	C₄⋊C₄	—	61	2	no	—
468	C₄⋊C₄	—	61	2	no	—
469	C₄⋊C₄	—	61	2	no	—
470	C₄⋊C₄	—	61	2	no	—
471	C₄⋊C₄	—	61	2	no	—
472	C₄⋊C₄	—	61	2	no	—
473	C₄⋊C₄	—	61	1	no	—
474	C₄⋊C₄	—	61	2	no	—
475	C₄⋊C₄	—	61	1	no	—
476	C₄⋊C₄	—	61	2	no	—
477	C₄⋊C₄	—	61	1	no	—
478	C₄⋊C₄	—	61	2	no	—
479	C₄⋊C₄	—	61	2	no	—
480	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
484	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
485	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
486	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
488	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
489	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
490	C₂²⋊C₄	—	61	2	no	—
491	C₂²⋊C₄	—	61	1	no	—
492	C₂²⋊C₄	—	61	1	no	—
493	C₂²⋊C₄	—	61	1	no	—
494	C₂²⋊C₄	—	61	1	no	—
495	C₂²⋊C₄	—	61	2	no	—
496	C₂²⋊C₄	—	61	1	no	—
497	C₂²⋊C₄	—	61	1	no	—
498	C₂²⋊C₄	—	61	2	no	—
499	C₂²⋊C₄	—	61	1	no	—
500	C₂²⋊C₄	—	61	2	no	—
501	C₂²⋊C₄	—	61	2	no	—
502	C₂²⋊C₄	—	61	1	no	—
503	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
508	C₄²	—	61	1	no	—
509	C₄²	—	61	1	no	—
510	C₄²	—	61	1	no	—
511	C₄²	—	61	1	no	—
512	C₄²	—	61	2	no	—
513	C₄²	—	61	2	no	—
514	C₄²	—	61	2	no	—
515	C₄²	—	61	1	no	—
516	C₄²	—	61	2	no	—
517	C₄²	—	61	2	no	—
518	C₄²	—	61	2	no	—
519	C₄²	C₂²×D₆₁	1	2	yes	—
520	C₄²	C₂²×D₆₁	1	1	yes	characteristic
521	C₄²	C₂²×D₆₁	1	2	yes	—
522	C₂³	—	61	1	no	—
523	C₂³	C₂³×D₆₁	1	1	yes	characteristic
524	C₂³	C₂³×D₆₁	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	122	2	no	—
527	Q₈	—	244	2	no	—
528	Q₈	—	244	2	no	—
529	Q₈	—	244	2	no	—
530	Q₈	—	244	1	no	—
531	D₄	—	2	2	no	—
532	D₄	—	122	2	no	—
533	D₄	—	244	1	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	61	1	no	—
538	C₂×C₄	—	61	2	no	—
539	C₂×C₄	—	61	1	no	—
540	C₂×C₄	—	61	1	no	—
541	C₂×C₄	—	61	1	no	—
542	C₂×C₄	—	61	1	no	—
543	C₂×C₄	—	61	1	no	—
544	C₂×C₄	—	61	2	no	—
545	C₂×C₄	—	61	1	no	—
546	C₂×C₄	—	61	2	no	—
547	C₂×C₄	—	61	2	no	—
548	C₂×C₄	—	122	2	no	—
549	C₂×C₄	—	122	2	no	—
550	C₂×C₄	—	244	2	no	—
551	C₂×C₄	—	244	2	no	—
552	C₂×C₄	—	244	2	no	—
553	C₂×C₄	—	244	1	no	—
554	C₂×C₄	C₂³×D₆₁	1	2	yes	—
555	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₆₁	1	2	yes	—
558	C₂×C₄	C₂³×D₆₁	1	2	yes	—
559	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
560	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
561	C₂×C₄	C₂³×D₆₁	1	2	yes	—
562	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	122	1	no	—
569	C₂²	—	122	1	no	—
570	C₂²	—	122	1	no	—
571	C₂²	#14519824	1	2	yes	—
572	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₄	—	122	1	no	—
582	C₄	—	122	1	no	—
583	C₄	—	122	1	no	—
584	C₄	—	122	1	no	—
585	C₄	—	122	2	no	—
586	C₄	—	122	2	no	—
587	C₄	—	122	2	no	—
588	C₄	—	122	1	no	—
589	C₄	—	122	1	no	—
590	C₄	—	122	2	no	—
591	C₄	—	122	1	no	—
592	C₄	#14519824	1	2	yes	—
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	244	1	no	—
596	C₂	C₂×#14519824	1	1	yes	characteristic
597	C₂	C₂×#14519824	1	1	yes	characteristic
598	C₂	#16840599	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#552	C₂
hypercenter	#552	D₆₁
hypocenter	C₆₁	#3563
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₆₁⋊#564	C₂	semidirect
2. #16840514	C₂	semidirect
3. #16840491	C₂	semidirect
4. #16840489	C₂	semidirect
5. #16840470	C₂	semidirect
6. #16840469	C₂	semidirect
7. #16840454	C₂	semidirect
8. #16840451	C₂	semidirect
9. #16840449	C₂	semidirect
10. #16840447	C₂	semidirect
11. #16840445	C₂	semidirect
12. #16840392	C₂	semidirect
13. #16840390	C₂	semidirect
14. #16840390	C₂	semidirect
15. #16840375	C₂	semidirect
16. #16840372	C₂	semidirect
17. #16840370	C₂	semidirect
18. #16840369	C₂	semidirect
20. #16840314	C₂	semidirect
22. C₂×#14519768	C₂	semidirect
23. C₆₁×#552	C₂	semidirect
311. #552	D₆₁	semidirect
323. C₆₁	#3563	semidirect