Subgroups — #29833222

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14519717	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₂²⋊D₆₁	C₂	1	1	yes	maximal, characteristic
4	#21447648	C₂	1	2	yes	maximal, complemented
5	#21447647	C₂	1	2	yes	maximal, complemented
6	#21447641	C₂	1	2	yes	maximal, complemented
7	#21447636	C₂	1	2	yes	maximal, complemented
8	#21447574	C₂	1	1	yes	maximal, characteristic, complemented
9	#21447429	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2112	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
14	C₂×#14519717	—	2	4	no	—
15	C₂×#14519717	C₂²	1	1	yes	characteristic
16	C₂×#14519717	C₂²	1	1	yes	characteristic
17	C₂×#14519717	C₂²	1	2	yes	complemented
18	C₂×#14519716	C₂²	1	2	yes	complemented
19	M₃₂×D₆₁	—	2	4	no	—
20	C₂²×#11758185	C₂²	1	2	yes	complemented
21	C₂×C₁₆×D₆₁	C₂²	1	2	yes	complemented
22	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
26	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
30	C₂×#14519706	C₄	1	1	yes	characteristic
31	C₂×C₂²⋊#92418	C₄	1	1	yes	characteristic
32	C₂×#14519689	C₄	1	1	yes	characteristic
33	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
34	#16839580	C₂²	1	2	yes	complemented
35	#16839580	C₂²	1	2	yes	complemented
36	#16839541	C₂²	1	2	yes	complemented
37	#16839541	C₂²	1	2	yes	complemented
38	#16839537	C₂²	1	2	yes	complemented
39	C₁₆×Dic₆₁	C₂²	1	2	yes	complemented
40	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
44	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
45	C₂²×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
46	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
48	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₆₁	—	2	2	no	—
50	C₂×C₈×D₆₁	—	2	2	no	—
51	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
56	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
61	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
62	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂×#11758196	C₈	1	1	yes	characteristic
64	C₂×C₂²⋊Dic₆₁	C₈	1	1	yes	characteristic
65	C₂×#11758198	C₈	1	1	yes	characteristic
66	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
67	#14519717	—	2	2	no	—
68	#14519717	—	2	4	no	—
69	#14519717	D₄	1	4	yes	complemented
70	#14519716	—	2	4	no	—
71	C₂×#11758185	—	2	4	no	—
72	C₂×#11758185	C₂³	1	2	yes	—
73	C₂×#11758185	C₂³	1	2	yes	—
74	C₁₆×D₆₁	—	2	4	no	—
75	#14519706	C₂×C₄	1	1	yes	characteristic
76	#14519706	C₂×C₄	1	1	yes	characteristic
77	#14519706	C₂×C₄	1	1	yes	characteristic
78	#14519706	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
83	#14519689	C₂×C₄	1	1	yes	characteristic
84	#14519689	C₂×C₄	1	1	yes	characteristic
85	#14519689	C₂×C₄	1	1	yes	characteristic
86	#14519689	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
90	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₆₁	—	2	2	no	—
93	C₂²×C₈×C₆₁	—	2	2	no	—
94	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	M₃₂×C₆₁	—	2	2	no	—
101	M₃₂×C₆₁	—	2	2	no	—
102	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂⁴×C₆₁	C₂×C₈	1	1	yes	characteristic
105	C₂³×D₆₁	C₂×C₈	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₆₁	—	2	4	no	—
115	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
116	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
119	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₆₁	—	2	2	no	—
123	C₂×C₄×D₆₁	—	2	2	no	—
124	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	1	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₆₁	#41	1	2	yes	—
140	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
141	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
142	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
145	#11758198	C₂×C₈	1	1	yes	characteristic
146	#11758198	C₂×C₈	1	1	yes	characteristic
147	#11758198	C₂×C₈	1	1	yes	characteristic
148	#11758198	C₂×C₈	1	1	yes	characteristic
149	#11758196	C₂×C₈	1	1	yes	characteristic
150	#11758196	C₂×C₈	1	1	yes	characteristic
151	#11758196	C₂×C₈	1	1	yes	characteristic
152	#11758196	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×#92418	—	2	2	no	—
158	C₂×#92418	—	2	2	no	—
159	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
160	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
161	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
162	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
163	C₈×D₆₁	—	2	2	no	—
164	C₈×D₆₁	—	2	2	no	—
165	C₈×D₆₁	—	2	1	no	—
166	C₈×D₆₁	—	2	1	no	—
167	C₈×D₆₁	—	2	1	no	—
168	C₈×D₆₁	—	2	1	no	—
169	C₁₆×C₆₁	—	2	2	no	—
170	C₁₆×C₆₁	—	2	2	no	—
171	#11758185	—	2	2	no	—
172	#11758185	C₂×D₄	1	4	yes	complemented
173	C₂³×C₆₁	—	2	2	no	—
174	C₂³×C₆₁	—	2	2	no	—
175	C₂³×C₆₁	—	4	1	no	—
176	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
178	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
179	C₂²×D₆₁	—	2	2	no	—
180	C₂²×D₆₁	—	2	2	no	—
181	C₂²×D₆₁	—	4	1	no	—
182	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
183	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	1	no	—
188	C₂×C₄×C₆₁	—	2	1	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₆₁	#131	1	2	yes	—
196	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
197	C₂²⋊D₆₁	—	2	2	no	—
198	C₂²⋊D₆₁	—	2	2	no	—
199	C₂²⋊D₆₁	—	2	2	no	—
200	C₂²⋊D₆₁	M₃₂	1	4	yes	complemented
201	C₂×Dic₆₁	—	2	2	no	—
202	C₂×Dic₆₁	—	2	2	no	—
203	C₂×Dic₆₁	—	4	1	no	—
204	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
205	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
210	C₄×D₆₁	—	2	1	no	—
211	C₄×D₆₁	—	2	1	no	—
212	C₄×D₆₁	—	2	1	no	—
213	C₄×D₆₁	—	2	1	no	—
214	C₄×D₆₁	—	2	2	no	—
215	C₄×D₆₁	—	2	2	no	—
216	C₈×C₆₁	—	2	1	no	—
217	C₈×C₆₁	—	2	1	no	—
218	C₈×C₆₁	C₄×D₄	1	2	yes	—
219	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
220	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
221	#92418	—	2	1	no	—
222	#92418	—	2	1	no	—
223	#92418	—	2	1	no	—
224	#92418	—	2	1	no	—
225	D₄×M₃₂	—	61	1	no	maximal, Sylow
226	C₂²×C₆₁	—	2	1	no	—
227	C₂²×C₆₁	—	2	1	no	—
228	C₂²×C₆₁	—	2	1	no	—
229	C₂²×C₆₁	—	2	1	no	—
230	C₂²×C₆₁	—	2	1	no	—
231	C₂²×C₆₁	—	2	1	no	—
232	C₂²×C₆₁	—	2	1	no	—
233	C₂²×C₆₁	—	4	4	no	—
234	C₂²×C₆₁	C₈×D₄	1	2	yes	—
235	C₂²×C₆₁	C₂×M₃₂	1	2	yes	complemented
236	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
237	C₂×D₆₁	—	2	1	no	—
238	C₂×D₆₁	—	2	1	no	—
239	C₂×D₆₁	—	2	1	no	—
240	C₂×D₆₁	—	2	1	no	—
241	C₂×D₆₁	—	2	1	no	—
242	C₂×D₆₁	—	4	4	no	—
243	C₂×D₆₁	C₂×M₃₂	1	2	yes	complemented
244	C₄×C₆₁	—	2	1	no	—
245	C₄×C₆₁	—	2	1	no	—
246	C₄×C₆₁	C₈×D₄	1	2	yes	—
247	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
249	Dic₆₁	—	2	1	no	—
250	Dic₆₁	—	2	1	no	—
251	Dic₆₁	—	2	1	no	—
252	Dic₆₁	—	2	1	no	—
253	Dic₆₁	—	2	1	no	—
254	Dic₆₁	C₂×M₃₂	1	2	yes	complemented
255	C₂²×M₃₂	—	61	1	no	—
256	C₂²×M₃₂	—	61	1	no	—
257	C₂×C₈×D₄	—	61	1	no	—
258	#2169	—	61	2	no	—
259	#2168	—	61	2	no	—
260	#2168	—	61	2	no	—
261	D₄×C₁₆	—	61	2	no	—
262	#2150	—	61	1	no	—
263	#2112	—	61	1	no	—
264	#2112	D₆₁	1	1	yes	characteristic, complemented
265	C₄×M₃₂	—	61	1	no	—
266	C₂×C₆₁	—	2	2	no	—
267	C₂×C₆₁	—	2	2	no	—
268	C₂×C₆₁	—	4	1	no	—
269	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
270	C₂×C₆₁	C₂²×M₃₂	1	1	yes	characteristic
271	C₂×C₆₁	#3407	1	1	yes	characteristic
272	D₆₁	—	2	2	no	—
273	D₆₁	—	4	1	no	—
274	C₂³×C₈	—	61	1	no	—
275	C₂³×C₈	C₂×D₆₁	1	1	yes	characteristic
276	C₂×C₄×D₄	—	61	1	no	—
277	C₂×M₃₂	—	61	1	no	—
278	C₂×M₃₂	—	61	1	no	—
279	C₂×M₃₂	—	61	2	no	—
280	C₂×M₃₂	—	61	2	no	—
281	C₂×M₃₂	—	122	4	no	—
282	C₂×M₃₂	—	122	4	no	—
283	C₂×M₃₂	C₂×D₆₁	1	1	yes	characteristic
284	C₂×M₃₂	C₂×D₆₁	1	1	yes	characteristic
285	C₂²×C₁₆	—	61	2	no	—
286	C₂²×C₁₆	—	61	2	no	—
287	C₈×D₄	—	61	1	no	—
288	C₈×D₄	—	61	1	no	—
289	C₈×D₄	—	61	1	no	—
290	C₈×D₄	—	61	1	no	—
291	C₈×D₄	—	61	1	no	—
292	C₈×D₄	—	61	1	no	—
293	C₈×D₄	—	61	1	no	—
294	C₈×D₄	—	61	1	no	—
295	C₂×C₄⋊C₈	—	61	1	no	—
296	C₂×C₂²⋊C₈	—	61	1	no	—
297	C₂×C₂²⋊C₈	—	61	1	no	—
298	C₂×C₄×C₈	—	61	1	no	—
299	C₄⋊C₁₆	—	61	2	no	—
300	C₄⋊C₁₆	—	61	2	no	—
301	C₂²⋊C₁₆	—	61	2	no	—
302	C₂²⋊C₁₆	—	61	2	no	—
303	C₂²⋊C₁₆	C₂×D₆₁	1	2	yes	complemented
304	C₂²⋊C₁₆	C₂×D₆₁	1	2	yes	complemented
305	#346	—	61	2	no	—
306	C₄×C₁₆	—	61	2	no	—
307	C₆₁	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
308	C₂²×D₄	—	61	1	no	—
309	C₂³×C₄	—	61	1	no	—
310	C₂³×C₄	C₄×D₆₁	1	1	yes	characteristic
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	61	1	no	—
314	C₂²×C₈	—	61	1	no	—
315	C₂²×C₈	—	61	1	no	—
316	C₂²×C₈	—	61	1	no	—
317	C₂²×C₈	—	61	1	no	—
318	C₂²×C₈	—	61	1	no	—
319	C₂²×C₈	—	122	2	no	—
320	C₂²×C₈	—	122	2	no	—
321	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
322	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
323	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
324	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
327	C₄×D₄	—	61	1	no	—
328	C₄×D₄	—	61	1	no	—
329	C₄×D₄	—	61	1	no	—
330	C₄×D₄	—	61	1	no	—
331	C₄×D₄	—	61	1	no	—
332	C₄×D₄	—	61	1	no	—
333	C₄×D₄	—	61	1	no	—
334	C₄×D₄	—	61	1	no	—
335	C₂×C₄⋊C₄	—	61	1	no	—
336	C₂×C₂²⋊C₄	—	61	1	no	—
337	C₂×C₂²⋊C₄	—	61	1	no	—
338	C₂×C₄²	—	61	1	no	—
339	M₃₂	—	2	2	no	—
340	M₃₂	—	2	2	no	—
341	M₃₂	—	61	4	no	—
342	M₃₂	—	122	4	no	—
343	M₃₂	—	122	4	no	—
344	M₃₂	—	122	2	no	—
345	C₂×C₁₆	—	61	2	no	—
346	C₂×C₁₆	—	61	2	no	—
347	C₂×C₁₆	—	122	4	no	—
348	C₂×C₁₆	—	122	4	no	—
349	C₂×C₁₆	C₂²×D₆₁	1	2	yes	—
350	C₂×C₁₆	C₂²×D₆₁	1	2	yes	—
351	C₄⋊C₈	—	61	1	no	—
352	C₄⋊C₈	—	61	1	no	—
353	C₄⋊C₈	—	61	1	no	—
354	C₄⋊C₈	—	61	1	no	—
355	C₂²⋊C₈	—	61	1	no	—
356	C₂²⋊C₈	—	61	1	no	—
357	C₂²⋊C₈	—	61	1	no	—
358	C₂²⋊C₈	—	61	1	no	—
359	C₂²⋊C₈	—	61	1	no	—
360	C₂²⋊C₈	—	61	1	no	—
361	C₂²⋊C₈	—	61	1	no	—
362	C₂²⋊C₈	—	61	1	no	—
363	C₄×C₈	—	61	1	no	—
364	C₄×C₈	—	61	1	no	—
365	C₄×C₈	—	61	1	no	—
366	C₄×C₈	—	61	1	no	—
367	C₂⁴	—	61	1	no	—
368	C₂⁴	C₈×D₆₁	1	1	yes	characteristic
369	C₂×D₄	—	61	1	no	—
370	C₂×D₄	—	61	1	no	—
371	C₂×D₄	—	61	1	no	—
372	C₂×D₄	—	61	1	no	—
373	C₂×D₄	—	122	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	61	1	no	—
377	C₂²×C₄	—	61	1	no	—
378	C₂²×C₄	—	61	1	no	—
379	C₂²×C₄	—	61	1	no	—
380	C₂²×C₄	—	61	1	no	—
381	C₂²×C₄	—	61	1	no	—
382	C₂²×C₄	—	61	1	no	—
383	C₂²×C₄	—	122	2	no	—
384	C₂²×C₄	—	122	2	no	—
385	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
387	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	61	1	no	—
399	C₂×C₈	—	61	1	no	—
400	C₂×C₈	—	61	1	no	—
401	C₂×C₈	—	61	1	no	—
402	C₂×C₈	—	122	2	no	—
403	C₂×C₈	—	122	2	no	—
404	C₂×C₈	—	122	1	no	—
405	C₂×C₈	—	122	1	no	—
406	C₂×C₈	—	122	1	no	—
407	C₂×C₈	—	122	1	no	—
408	C₂×C₈	—	122	2	no	—
409	C₂×C₈	—	122	2	no	—
410	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
411	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
412	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
413	C₂×C₈	D₄×D₆₁	1	2	yes	—
414	C₂×C₈	#11758224	1	2	yes	—
415	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
416	C₄⋊C₄	—	61	1	no	—
417	C₄⋊C₄	—	61	1	no	—
418	C₄⋊C₄	—	61	1	no	—
419	C₄⋊C₄	—	61	1	no	—
420	C₂²⋊C₄	—	61	1	no	—
421	C₂²⋊C₄	—	61	1	no	—
422	C₂²⋊C₄	—	61	1	no	—
423	C₂²⋊C₄	—	61	1	no	—
424	C₂²⋊C₄	—	61	1	no	—
425	C₂²⋊C₄	—	61	1	no	—
426	C₂²⋊C₄	—	61	1	no	—
427	C₂²⋊C₄	—	61	1	no	—
428	C₄²	—	61	1	no	—
429	C₄²	—	61	1	no	—
430	C₄²	—	61	1	no	—
431	C₄²	—	61	1	no	—
432	C₁₆	—	2	2	no	—
433	C₁₆	—	2	2	no	—
434	C₁₆	—	61	4	no	—
435	C₁₆	—	122	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	61	1	no	—
440	C₂³	—	61	1	no	—
441	C₂³	—	122	2	no	—
442	C₂³	—	122	2	no	—
443	C₂³	—	244	1	no	—
444	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
445	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
446	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
447	D₄	—	61	4	no	—
448	D₄	—	122	2	no	—
449	D₄	—	122	2	no	—
450	D₄	—	122	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	61	1	no	—
459	C₂×C₄	—	61	1	no	—
460	C₂×C₄	—	61	1	no	—
461	C₂×C₄	—	61	1	no	—
462	C₂×C₄	—	61	1	no	—
463	C₂×C₄	—	61	1	no	—
464	C₂×C₄	—	122	2	no	—
465	C₂×C₄	—	122	2	no	—
466	C₂×C₄	—	122	1	no	—
467	C₂×C₄	—	122	1	no	—
468	C₂×C₄	—	122	1	no	—
469	C₂×C₄	—	122	1	no	—
470	C₂×C₄	—	122	2	no	—
471	C₂×C₄	—	122	2	no	—
472	C₂×C₄	—	244	1	no	—
473	C₂×C₄	#14519737	1	2	yes	—
474	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
475	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
476	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
477	C₂×C₄	#14519785	1	2	yes	—
478	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	122	1	no	—
482	C₈	—	122	1	no	—
483	C₈	—	122	1	no	—
484	C₈	—	122	1	no	—
485	C₈	#14519737	1	2	yes	—
486	C₈	C₂×D₄×D₆₁	1	1	yes	characteristic
487	C₈	C₂×#11758224	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	61	2	no	—
497	C₂²	—	122	1	no	—
498	C₂²	—	122	1	no	—
499	C₂²	—	122	1	no	—
500	C₂²	—	122	1	no	—
501	C₂²	—	122	1	no	—
502	C₂²	—	244	4	no	—
503	C₂²	#16839825	1	2	yes	—
504	C₂²	M₃₂×D₆₁	1	2	yes	complemented
505	C₂²	C₂²×C₈×D₆₁	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	61	2	no	—
509	C₄	—	122	1	no	—
510	C₄	—	122	1	no	—
511	C₄	—	122	1	no	—
512	C₄	—	122	1	no	—
513	C₄	—	122	1	no	—
514	C₄	#16839825	1	2	yes	—
515	C₄	C₂×#14519737	1	1	yes	characteristic
516	C₄	C₂×#14519785	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	122	2	no	—
521	C₂	—	244	1	no	—
522	C₂	C₂×#16839825	1	1	yes	characteristic
523	C₂	C₂×M₃₂×D₆₁	1	1	yes	characteristic
524	C₂	#21458921	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₈
Fitting	C₆₁×#2112	C₂
prime radical	C₂²×C₂²⋊D₆₁	C₈
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	#2112	D₆₁
hypocenter	C₆₁	D₄×M₃₂
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ #2112

Complements

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

N	H ≅ G/N	type
1. C₂²×#14519717	C₂	semidirect
2. C₂×M₃₂×D₆₁	C₂	semidirect
4. #21447648	C₂	semidirect
5. #21447647	C₂	semidirect
6. #21447641	C₂	semidirect
7. #21447636	C₂	semidirect
8. #21447574	C₂	semidirect
9. #21447429	C₂	semidirect
10. M₃₂×Dic₆₁	C₂	semidirect
11. C₆₁×#2112	C₂	semidirect
17. C₂×#14519717	C₂²	semidirect
18. C₂×#14519716	C₂²	semidirect
20. C₂²×#11758185	C₂²	semidirect
21. C₂×C₁₆×D₆₁	C₂²	semidirect
34. #16839580	C₂²	semidirect
35. #16839580	C₂²	semidirect
36. #16839541	C₂²	semidirect
37. #16839541	C₂²	semidirect
38. #16839537	C₂²	semidirect
39. C₁₆×Dic₆₁	C₂²	semidirect
43. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
44. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
69. #14519717	D₄	semidirect
172. #11758185	C₂×D₄	semidirect
200. C₂²⋊D₆₁	M₃₂	semidirect
235. C₂²×C₆₁	C₂×M₃₂	semidirect
243. C₂×D₆₁	C₂×M₃₂	semidirect
254. Dic₆₁	C₂×M₃₂	semidirect
264. #2112	D₆₁	semidirect
303. C₂²⋊C₁₆	C₂×D₆₁	semidirect
304. C₂²⋊C₁₆	C₂×D₆₁	semidirect
307. C₆₁	D₄×M₃₂	semidirect
504. C₂²	M₃₂×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14519717	2
C₂×M₃₂×D₆₁	2
C₂×C₈×C₂²⋊D₆₁	2
#21447648	2
#21447647	2
#21447641	2
#21447636	2
#21447574	2
#21447429	2
M₃₂×Dic₆₁	2
C₆₁×#2112	2
D₄×M₃₂	61