Subgroups — #30606175

Order 15616.

586 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₁⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₆₁⋊M₃₂	C₂	1	1	yes	maximal, characteristic
3	#21460870	C₂	1	2	yes	maximal, complemented
4	#21460869	C₂	1	2	yes	maximal, complemented
5	#405×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#14519852	—	2	1	no	—
7	C₂×#14519852	C₄	1	2	yes	complemented
8	D₆₁⋊M₃₂	—	2	1	no	—
9	D₆₁⋊M₃₂	—	2	1	no	—
10	D₆₁⋊M₃₂	—	2	1	no	—
11	D₆₁⋊M₃₂	—	2	1	no	—
12	D₆₁⋊M₃₂	—	2	1	no	—
13	D₆₁⋊M₃₂	—	2	1	no	—
14	D₆₁⋊M₃₂	C₄	1	2	yes	complemented
15	D₆₁⋊M₃₂	C₄	1	2	yes	complemented
16	C₂×#14519851	C₂²	1	2	yes	—
17	C₂×#14519851	C₂²	1	2	yes	—
18	C₂×D₆₁⋊C₁₆	—	2	1	no	—
19	C₂×D₆₁⋊C₁₆	C₄	1	2	yes	complemented
20	C₂×M₁₆×D₆₁	C₄	1	1	yes	characteristic
21	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
22	#117×D₆₁	C₄	1	1	yes	characteristic
23	#16839720	C₂²	1	1	yes	characteristic
24	#16839719	—	2	1	no	—
25	#16839718	C₂²	1	1	yes	characteristic
26	#16839717	C₄	1	1	yes	characteristic
27	#16839716	—	2	1	no	—
28	#97×D₆₁	—	2	1	no	—
29	C₄×C₈×D₆₁	—	2	1	no	—
30	C₆₁×#405	C₄	1	1	yes	characteristic
31	#14519852	—	2	2	no	—
32	#14519852	—	2	2	no	—
33	#14519852	—	2	2	no	—
34	#14519852	—	2	2	no	—
35	#14519851	—	2	2	no	—
36	#14519851	—	2	2	no	—
37	#14519851	—	2	2	no	—
38	#14519851	C₂×C₄	1	4	yes	complemented
39	D₆₁⋊C₁₆	—	2	2	no	—
40	D₆₁⋊C₁₆	—	2	2	no	—
41	D₆₁⋊C₁₆	—	2	2	no	—
42	D₆₁⋊C₁₆	—	2	2	no	—
43	C₂×#11758187	—	2	2	no	—
44	C₂×#11758187	C₂×C₄	1	4	yes	complemented
45	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
47	C₂×#11758189	—	2	1	no	—
48	M₁₆×D₆₁	—	2	1	no	—
49	M₁₆×D₆₁	—	2	1	no	—
50	M₁₆×D₆₁	C₈	1	2	yes	—
51	M₁₆×D₆₁	C₈	1	2	yes	—
52	C₂²×#92418	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₆₁	—	2	1	no	—
54	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
59	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
60	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
61	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
62	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
63	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
64	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
65	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
66	#14519736	C₂×C₄	1	1	yes	characteristic
67	#14519735	—	2	1	no	—
68	#14519734	—	2	1	no	—
69	#14519733	C₈	1	2	yes	—
70	C₄⋊C₄×D₆₁	—	2	1	no	—
71	C₂²⋊C₄×D₆₁	C₈	1	2	yes	—
72	C₄²×D₆₁	—	2	1	no	—
73	#14519688	—	2	1	no	—
74	#14519687	—	2	1	no	—
75	#14519687	—	2	1	no	—
76	C₄×#92418	—	2	1	no	—
77	C₈×Dic₆₁	—	2	1	no	—
78	C₈×Dic₆₁	—	2	1	no	—
79	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
81	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
82	#97×C₆₁	—	2	1	no	—
83	C₄×C₈×C₆₁	—	2	1	no	—
84	C₂³×D₆₁	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
87	C₂×C₄×D₆₁	—	2	2	no	—
88	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₆₁	M₁₆	1	1	yes	characteristic
97	C₂×C₄×D₆₁	M₁₆	1	1	yes	characteristic
98	C₂×C₄×D₆₁	M₁₆	1	1	yes	characteristic
99	C₂×C₄×D₆₁	M₁₆	1	1	yes	characteristic
100	M₁₆×C₆₁	—	2	1	no	—
101	M₁₆×C₆₁	C₂×C₈	1	2	yes	—
102	C₂×C₈×C₆₁	—	2	1	no	—
103	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
104	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
105	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄⋊C₄×C₆₁	—	2	1	no	—
110	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
111	C₄²×C₆₁	—	2	1	no	—
112	C₂²⋊Dic₆₁	C₂×C₈	1	2	yes	—
113	#11758198	—	2	2	no	—
114	C₄⋊Dic₆₁	—	2	1	no	—
115	#11758196	—	2	2	no	—
116	C₄×Dic₆₁	—	2	1	no	—
117	C₄×Dic₆₁	—	2	2	no	—
118	#11758194	—	2	1	no	—
119	#11758194	C₂×C₈	1	2	yes	—
120	C₂×#92418	—	2	1	no	—
121	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
122	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
123	C₂×#92418	C₂×D₄	1	1	yes	characteristic
124	C₂×#92418	C₂×D₄	1	1	yes	characteristic
125	C₂×#92418	C₂×D₄	1	1	yes	characteristic
126	C₂×#92418	C₂×Q₈	1	1	yes	characteristic
127	#11758189	—	2	2	no	—
128	#11758189	—	2	2	no	—
129	C₈×D₆₁	—	2	2	no	—
130	C₈×D₆₁	—	2	2	no	—
131	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
132	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
133	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
134	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
135	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
136	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
137	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
138	C₈×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
139	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
140	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
141	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
142	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
143	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
144	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
145	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
146	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
147	#11758187	—	2	4	no	—
148	#11758187	—	2	4	no	—
149	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
150	C₂²×D₆₁	—	4	2	no	—
151	C₂²×D₆₁	C₄×C₈	1	1	yes	characteristic
152	C₂²×D₆₁	C₄×C₈	1	1	yes	characteristic
153	C₂²×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
154	C₂²×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
155	C₂²×D₆₁	C₄⋊C₈	1	1	yes	characteristic
156	C₂²×D₆₁	C₄⋊C₈	1	1	yes	characteristic
157	C₂×C₄×C₆₁	—	2	2	no	—
158	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
164	C₂×Dic₆₁	—	2	2	no	—
165	C₂×Dic₆₁	C₄×C₈	1	1	yes	characteristic
166	C₂×Dic₆₁	C₄×C₈	1	1	yes	characteristic
167	C₂×Dic₆₁	C₂²⋊C₈	1	1	yes	characteristic
168	C₂×Dic₆₁	C₂²⋊C₈	1	1	yes	characteristic
169	C₂×Dic₆₁	C₄⋊C₈	1	1	yes	characteristic
170	C₂×Dic₆₁	C₄⋊C₈	1	1	yes	characteristic
171	C₄×D₆₁	—	4	4	no	—
172	C₄×D₆₁	#95	1	1	yes	characteristic
173	C₄×D₆₁	#95	1	1	yes	characteristic
174	C₄×D₆₁	#95	1	1	yes	characteristic
175	C₄×D₆₁	#95	1	1	yes	characteristic
176	C₄×D₆₁	#97	1	1	yes	characteristic
177	C₄×D₆₁	#97	1	1	yes	characteristic
178	C₄×D₆₁	#97	1	1	yes	characteristic
179	C₄×D₆₁	#97	1	1	yes	characteristic
180	C₄×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
181	C₄×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
182	C₄×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
183	C₄×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
184	C₄×D₆₁	C₄⋊C₈	1	1	yes	characteristic
185	C₄×D₆₁	C₄⋊C₈	1	1	yes	characteristic
186	C₄×D₆₁	C₄⋊C₈	1	1	yes	characteristic
187	C₄×D₆₁	C₄⋊C₈	1	1	yes	characteristic
188	C₈×C₆₁	—	2	2	no	—
189	C₈×C₆₁	#95	1	1	yes	characteristic
190	C₈×C₆₁	#95	1	1	yes	characteristic
191	C₈×C₆₁	#95	1	1	yes	characteristic
192	C₈×C₆₁	#95	1	1	yes	characteristic
193	#92418	—	2	2	no	—
194	#92418	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	#92418	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	#92418	C₂×C₄⋊C₄	1	1	yes	characteristic
197	#92418	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×#1378	—	61	1	no	maximal, Sylow
199	C₂²×C₆₁	—	4	1	no	—
200	C₂²×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
201	C₂²×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
202	C₂²×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
203	C₂×D₆₁	—	2	2	no	—
204	C₂×D₆₁	—	2	2	no	—
205	C₂×D₆₁	—	2	2	no	—
206	C₂×D₆₁	—	4	1	no	—
207	C₂×D₆₁	—	4	1	no	—
208	C₂×D₆₁	—	4	1	no	—
209	C₂×D₆₁	#336	1	1	yes	characteristic
210	C₂×D₆₁	#336	1	1	yes	characteristic
211	C₂×D₆₁	#336	1	1	yes	characteristic
212	C₂×D₆₁	#336	1	1	yes	characteristic
213	C₄×C₆₁	—	4	2	no	—
214	C₄×C₆₁	C₂×#95	1	1	yes	characteristic
215	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
216	C₄×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
217	C₄×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
218	Dic₆₁	—	4	2	no	—
219	Dic₆₁	#336	1	1	yes	characteristic
220	Dic₆₁	#336	1	1	yes	characteristic
221	Dic₆₁	#336	1	1	yes	characteristic
222	Dic₆₁	#336	1	1	yes	characteristic
223	C₂²×M₃₂	—	61	1	no	—
224	C₂²×M₃₂	—	61	1	no	—
225	C₂×#405	—	61	1	no	—
226	#1378	—	61	2	no	—
227	#1378	—	61	2	no	—
228	C₂×C₆₁	—	2	1	no	—
229	C₂×C₆₁	—	2	1	no	—
230	C₂×C₆₁	—	2	1	no	—
231	C₂×C₆₁	C₂×#336	1	1	yes	characteristic
232	D₆₁	—	2	1	no	—
233	D₆₁	—	2	1	no	—
234	D₆₁	—	2	1	no	—
235	D₆₁	#1378	1	2	yes	complemented
236	C₂²×M₁₆	—	61	1	no	—
237	C₂³×C₈	—	61	1	no	—
238	C₂×#117	—	61	1	no	—
239	C₂×M₃₂	—	61	2	no	—
240	C₂×M₃₂	—	61	2	no	—
241	C₂×M₃₂	—	61	2	no	—
242	C₂×M₃₂	—	61	2	no	—
243	C₂×M₃₂	—	61	2	no	—
244	C₂×M₃₂	—	122	1	no	—
245	C₂×M₃₂	—	122	1	no	—
246	C₂×M₃₂	—	122	1	no	—
247	C₂×M₃₂	—	122	1	no	—
248	C₂×M₃₂	—	122	1	no	—
249	C₂×M₃₂	—	122	1	no	—
250	C₂×M₃₂	—	122	1	no	—
251	C₂²×C₁₆	—	61	2	no	—
252	C₂²×C₁₆	—	122	1	no	—
253	#405	—	61	1	no	—
254	#405	—	61	1	no	—
255	#405	—	61	1	no	—
256	#405	—	122	1	no	—
257	#405	—	122	1	no	—
258	#405	#6923	1	1	yes	characteristic
259	C₂×#97	—	122	1	no	—
260	C₂×C₄×C₈	—	122	1	no	—
261	C₆₁	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₄	—	61	1	no	—
263	C₂×M₁₆	—	61	1	no	—
264	C₂×M₁₆	—	61	2	no	—
265	C₂×M₁₆	—	61	2	no	—
266	C₂×M₁₆	—	122	1	no	—
267	C₂×M₁₆	—	122	1	no	—
268	C₂×M₁₆	—	122	1	no	—
269	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
270	C₂²×C₈	—	61	1	no	—
271	C₂²×C₈	—	61	1	no	—
272	C₂²×C₈	—	61	1	no	—
273	C₂²×C₈	—	61	1	no	—
274	C₂²×C₈	—	61	1	no	—
275	C₂²×C₈	—	61	1	no	—
276	C₂²×C₈	—	61	1	no	—
277	C₂²×C₈	—	61	1	no	—
278	C₂²×C₈	—	61	1	no	—
279	C₂²×C₈	—	61	1	no	—
280	C₂²×C₈	—	61	1	no	—
281	C₂²×C₈	—	61	1	no	—
282	C₂²×C₈	—	61	1	no	—
283	C₂²×C₈	—	122	1	no	—
284	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
285	#117	—	61	1	no	—
286	#117	—	61	2	no	—
287	#117	—	122	1	no	—
288	#117	—	122	1	no	—
289	#117	C₂×#6923	1	1	yes	characteristic
290	C₂×C₄⋊C₄	—	122	1	no	—
291	C₂×C₂²⋊C₄	—	61	2	no	—
292	C₂×C₄²	—	122	1	no	—
293	M₃₂	—	61	4	no	—
294	M₃₂	—	122	2	no	—
295	M₃₂	—	122	2	no	—
296	M₃₂	—	122	2	no	—
297	M₃₂	—	122	2	no	—
298	M₃₂	—	122	2	no	—
299	M₃₂	—	122	2	no	—
300	M₃₂	—	122	2	no	—
301	C₂×C₁₆	—	61	4	no	—
302	C₂×C₁₆	—	122	2	no	—
303	C₂×C₁₆	—	122	2	no	—
304	C₂×C₁₆	—	122	2	no	—
305	C₂×C₁₆	—	122	2	no	—
306	C₂×C₁₆	—	122	2	no	—
307	#97	—	2	1	no	—
308	#97	—	122	1	no	—
309	#97	—	122	1	no	—
310	#97	—	122	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	122	1	no	—
313	C₄×C₈	—	122	1	no	—
314	C₄×C₈	—	122	1	no	—
315	C₂⁴	—	61	1	no	—
316	C₂²×C₄	—	61	1	no	—
317	C₂²×C₄	—	61	1	no	—
318	C₂²×C₄	—	61	1	no	—
319	C₂²×C₄	—	61	1	no	—
320	C₂²×C₄	—	61	1	no	—
321	C₂²×C₄	—	61	1	no	—
322	C₂²×C₄	—	61	1	no	—
323	C₂²×C₄	—	61	1	no	—
324	C₂²×C₄	—	61	1	no	—
325	C₂²×C₄	—	61	1	no	—
326	C₂²×C₄	—	61	1	no	—
327	C₂²×C₄	—	61	1	no	—
328	C₂²×C₄	—	61	1	no	—
329	C₂²×C₄	—	122	2	no	—
330	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
331	M₁₆	—	2	1	no	—
332	M₁₆	—	61	2	no	—
333	M₁₆	—	122	2	no	—
334	M₁₆	—	122	2	no	—
335	M₁₆	—	122	1	no	—
336	M₁₆	D₆₁⋊C₈	1	2	yes	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	61	1	no	—
339	C₂×C₈	—	61	1	no	—
340	C₂×C₈	—	61	1	no	—
341	C₂×C₈	—	61	1	no	—
342	C₂×C₈	—	61	1	no	—
343	C₂×C₈	—	61	1	no	—
344	C₂×C₈	—	61	1	no	—
345	C₂×C₈	—	61	1	no	—
346	C₂×C₈	—	61	1	no	—
347	C₂×C₈	—	61	1	no	—
348	C₂×C₈	—	61	1	no	—
349	C₂×C₈	—	61	1	no	—
350	C₂×C₈	—	61	1	no	—
351	C₂×C₈	—	61	1	no	—
352	C₂×C₈	—	61	1	no	—
353	C₂×C₈	—	61	1	no	—
354	C₂×C₈	—	61	1	no	—
355	C₂×C₈	—	61	1	no	—
356	C₂×C₈	—	61	1	no	—
357	C₂×C₈	—	61	1	no	—
358	C₂×C₈	—	61	1	no	—
359	C₂×C₈	—	61	1	no	—
360	C₂×C₈	—	122	2	no	—
361	C₂×C₈	—	122	2	no	—
362	C₂×C₈	—	122	1	no	—
363	C₂×C₈	C₄×#6923	1	1	yes	characteristic
364	C₂×C₈	C₄×#6923	1	1	yes	characteristic
365	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
366	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
367	C₂×C₈	C₂²⋊#6923	1	1	yes	characteristic
368	C₂×C₈	C₂²⋊#6923	1	1	yes	characteristic
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	122	2	no	—
371	C₄⋊C₄	—	122	1	no	—
372	C₂²⋊C₄	—	61	2	no	—
373	C₂²⋊C₄	—	122	2	no	—
374	C₂²⋊C₄	D₆₁⋊C₈	1	2	yes	—
375	C₄²	—	2	1	no	—
376	C₄²	—	122	2	no	—
377	C₄²	—	122	1	no	—
378	C₁₆	—	122	4	no	—
379	C₁₆	—	122	4	no	—
380	C₂³	—	61	1	no	—
381	C₂³	—	61	1	no	—
382	C₂³	—	61	1	no	—
383	C₂³	—	61	1	no	—
384	C₂³	—	61	1	no	—
385	C₂³	—	61	1	no	—
386	C₂³	—	244	2	no	—
387	C₂³	C₂×D₆₁⋊C₈	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	61	1	no	—
390	C₂×C₄	—	61	1	no	—
391	C₂×C₄	—	61	1	no	—
392	C₂×C₄	—	61	1	no	—
393	C₂×C₄	—	61	1	no	—
394	C₂×C₄	—	61	1	no	—
395	C₂×C₄	—	61	1	no	—
396	C₂×C₄	—	61	1	no	—
397	C₂×C₄	—	61	1	no	—
398	C₂×C₄	—	61	1	no	—
399	C₂×C₄	—	61	1	no	—
400	C₂×C₄	—	61	1	no	—
401	C₂×C₄	—	61	1	no	—
402	C₂×C₄	—	61	1	no	—
403	C₂×C₄	—	61	1	no	—
404	C₂×C₄	—	61	1	no	—
405	C₂×C₄	—	61	1	no	—
406	C₂×C₄	—	61	1	no	—
407	C₂×C₄	—	61	1	no	—
408	C₂×C₄	—	61	1	no	—
409	C₂×C₄	—	61	1	no	—
410	C₂×C₄	—	61	1	no	—
411	C₂×C₄	—	122	2	no	—
412	C₂×C₄	—	244	4	no	—
413	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
414	C₂×C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
416	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
417	C₂×C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
418	C₂×C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
419	C₈	—	2	2	no	—
420	C₈	—	61	1	no	—
421	C₈	—	61	1	no	—
422	C₈	—	61	1	no	—
423	C₈	—	61	1	no	—
424	C₈	—	122	2	no	—
425	C₈	(C₂×#6923)⋊C₄	1	1	yes	characteristic
426	C₈	(C₂×#6923)⋊C₄	1	1	yes	characteristic
427	C₈	(C₂×#6923)⋊C₄	1	1	yes	characteristic
428	C₈	(C₂×#6923)⋊C₄	1	1	yes	characteristic
429	C₂²	—	4	1	no	—
430	C₂²	—	61	1	no	—
431	C₂²	—	61	1	no	—
432	C₂²	—	61	1	no	—
433	C₂²	—	61	1	no	—
434	C₂²	—	122	2	no	—
435	C₂²	—	122	2	no	—
436	C₂²	—	122	2	no	—
437	C₂²	—	244	1	no	—
438	C₂²	—	244	1	no	—
439	C₂²	—	244	1	no	—
440	C₂²	C₄×D₆₁⋊C₈	1	1	yes	characteristic
441	C₂²	D₆₁⋊(C₂²⋊C₈)	1	1	yes	characteristic
442	C₂²	D₆₁⋊(C₄⋊C₈)	1	1	yes	characteristic
443	C₄	—	4	2	no	—
444	C₄	—	61	1	no	—
445	C₄	—	61	1	no	—
446	C₄	—	61	1	no	—
447	C₄	—	61	1	no	—
448	C₄	—	244	2	no	—
449	C₄	C₂×(C₂×#6923)⋊C₄	1	1	yes	characteristic
450	C₄	#16840721	1	1	yes	characteristic
451	C₄	D₆₁⋊(C₂²⋊C₈)	1	1	yes	characteristic
452	C₄	D₆₁⋊(C₄⋊C₈)	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	61	2	no	—
457	C₂	—	122	1	no	—
458	C₂	—	122	1	no	—
459	C₂	—	122	1	no	—
460	C₂	#21461480	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×#6923)⋊C₄
commutator	C₂²×C₆₁	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#6923
Fitting	C₆₁×#405	C₄
socle	C₂×C₆₁	C₂×#336
prime radical	C₂³×D₆₁	C₂×C₈
cosocle	C₂²×#92418	C₂³
hypercenter	#405	#6923
hypocenter	C₆₁	C₂×#1378
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #21460870	C₂	semidirect
4. #21460869	C₂	semidirect
7. C₂×#14519852	C₄	semidirect
14. D₆₁⋊M₃₂	C₄	semidirect
15. D₆₁⋊M₃₂	C₄	semidirect
19. C₂×D₆₁⋊C₁₆	C₄	semidirect
38. #14519851	C₂×C₄	semidirect
44. C₂×#11758187	C₂×C₄	semidirect
235. D₆₁	#1378	semidirect
261. C₆₁	C₂×#1378	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₆₁⋊M₃₂	2
#21460870	2
#21460869	2
#405×D₆₁	2
C₂×#1378	61