Subgroups — #29699641

Order 15616.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839823	C₂	1	2	yes	maximal, complemented
2	#21446614	C₂	1	1	yes	maximal, characteristic
3	#21446614	C₂	1	1	yes	maximal, characteristic
4	#21446434	C₂	1	2	yes	maximal, complemented
5	#21446427	C₂	1	2	yes	maximal, complemented
6	#21445971	C₂	1	1	yes	maximal, characteristic, complemented
7	#21445803	C₂	1	2	yes	maximal, complemented
8	#21445688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₄×#92418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₄⋊#92418	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic
12	#16839823	—	2	8	no	—
13	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#92418	C₂²	1	2	yes	—
17	C₂×C₄⋊#92418	C₂²	1	2	yes	—
18	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊#92418	C₂²	1	2	yes	—
20	C₂×C₂²⋊#92418	C₂²	1	2	yes	—
21	C₂×C₂²⋊#92418	C₂²	1	2	yes	—
22	C₂×C₂²⋊#92418	C₂²	1	2	yes	—
23	C₂×#14519688	C₂²	1	2	yes	—
24	C₂×C₄×#92418	C₂²	1	2	yes	—
25	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
26	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
27	#16839517	C₂²	1	1	yes	characteristic
28	#16839517	C₂²	1	2	yes	—
29	#16839517	C₂²	1	1	yes	characteristic
30	#16839517	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#117×C₆₁	C₂²	1	2	yes	—
33	C₆₁×#390	C₄	1	1	yes	characteristic
34	C₆₁×#390	C₄	1	1	yes	characteristic
35	C₆₁×#389	C₄	1	1	yes	characteristic
36	C₆₁×#389	C₄	1	1	yes	characteristic
37	C₆₁×#388	C₄	1	2	yes	—
38	C₆₁×#388	C₄	1	2	yes	—
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
41	C₄³×C₆₁	C₂²	1	1	yes	characteristic
42	C₂²×#92418	C₂³	1	1	yes	characteristic
43	C₂²×#92418	C₂³	1	1	yes	characteristic
44	C₂²×#92418	C₂³	1	2	yes	—
45	C₂²×#92418	C₂³	1	2	yes	—
46	C₂²×#92418	C₂³	1	1	yes	characteristic
47	C₂²×#92418	C₂³	1	1	yes	characteristic
48	C₄⋊#92418	—	2	4	no	—
49	C₄⋊#92418	—	2	2	no	—
50	C₄⋊#92418	—	2	2	no	—
51	C₄⋊#92418	—	2	2	no	—
52	C₄⋊#92418	—	4	2	no	—
53	C₄⋊#92418	D₄	1	4	yes	complemented
54	C₂²⋊#92418	—	2	4	no	—
55	C₂²⋊#92418	—	2	4	no	—
56	C₂²⋊#92418	—	4	2	no	—
57	C₂²⋊#92418	—	4	2	no	—
58	#14519688	—	2	4	no	—
59	C₄×#92418	—	2	2	no	—
60	C₄×#92418	—	2	2	no	—
61	C₄×#92418	—	2	4	no	—
62	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
64	C₄×D₄×C₆₁	—	2	2	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	#117×C₆₁	—	2	4	no	—
67	#117×C₆₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
83	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	#95×C₆₁	C₂×C₄	1	2	yes	—
87	#95×C₆₁	C₂×C₄	1	2	yes	—
88	#95×C₆₁	C₂×C₄	1	2	yes	—
89	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₆₁	—	2	2	no	—
91	C₂×D₄×C₆₁	—	2	2	no	—
92	C₂×D₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	—	2	2	no	—
94	C₂²×C₄×C₆₁	—	2	2	no	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₄⋊C₄×C₆₁	—	2	4	no	—
111	C₄⋊C₄×C₆₁	—	2	4	no	—
112	C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₂²⋊C₄×C₆₁	—	2	4	no	—
115	C₂²⋊C₄×C₆₁	—	2	4	no	—
116	C₂²⋊C₄×C₆₁	—	2	4	no	—
117	C₂²⋊C₄×C₆₁	—	2	4	no	—
118	C₂²⋊C₄×C₆₁	—	4	2	no	—
119	C₄²×C₆₁	—	2	2	no	—
120	C₄²×C₆₁	—	2	2	no	—
121	C₄²×C₆₁	—	2	2	no	—
122	C₄²×C₆₁	—	2	2	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	2	1	no	—
125	C₄²×C₆₁	—	2	1	no	—
126	C₄²×C₆₁	—	4	1	no	—
127	C₄²×C₆₁	C₂×D₄	1	2	yes	—
128	C₄²×C₆₁	#41	1	2	yes	—
129	C₄²×C₆₁	#41	1	2	yes	—
130	C₄²×C₆₁	#41	1	2	yes	—
131	C₂×#92418	—	2	1	no	—
132	C₂×#92418	—	2	1	no	—
133	C₂×#92418	—	2	1	no	—
134	C₂×#92418	—	2	1	no	—
135	C₂×#92418	—	2	2	no	—
136	C₂×#92418	—	2	2	no	—
137	C₂×#92418	—	2	1	no	—
138	C₂×#92418	—	2	1	no	—
139	C₂×#92418	—	2	2	no	—
140	C₂×#92418	—	2	2	no	—
141	C₂×#92418	—	2	1	no	—
142	C₂×#92418	—	2	1	no	—
143	C₂×#92418	—	2	1	no	—
144	C₂×#92418	—	2	1	no	—
145	C₂×#92418	—	2	2	no	—
146	C₂×#92418	—	2	2	no	—
147	C₂×#92418	C₂×D₄	1	2	yes	—
148	C₂×#92418	C₂×D₄	1	2	yes	—
149	C₂³×C₆₁	—	2	2	no	—
150	C₂³×C₆₁	—	2	2	no	—
151	C₂³×C₆₁	—	2	2	no	—
152	C₂³×C₆₁	—	2	2	no	—
153	C₂³×C₆₁	—	2	2	no	—
154	C₂³×C₆₁	—	2	2	no	—
155	C₂³×C₆₁	—	2	2	no	—
156	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
157	D₄×C₆₁	—	4	4	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	2	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	#117	1	2	yes	—
183	C₂×C₄×C₆₁	#117	1	2	yes	—
184	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₆₁	#131	1	2	yes	—
187	C₂×C₄×C₆₁	#131	1	2	yes	—
188	C₂×C₄×C₆₁	#131	1	2	yes	—
189	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
195	#92418	—	2	2	no	—
196	#92418	—	2	2	no	—
197	#92418	—	4	2	no	—
198	#92418	—	4	2	no	—
199	#92418	—	4	1	no	—
200	#92418	—	4	1	no	—
201	#22796	—	61	1	no	maximal, Sylow
202	C₂²×C₆₁	—	4	2	no	—
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	—	4	2	no	—
208	C₂²×C₆₁	—	4	2	no	—
209	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
210	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₆₁	#520	1	1	yes	characteristic
212	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
213	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
214	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
215	C₂²×C₆₁	#568	1	1	yes	characteristic
216	C₄×C₆₁	—	2	2	no	—
217	C₄×C₆₁	—	2	2	no	—
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	2	2	no	—
220	C₄×C₆₁	—	4	2	no	—
221	C₄×C₆₁	—	4	2	no	—
222	C₄×C₆₁	—	4	2	no	—
223	C₄×C₆₁	—	4	1	no	—
224	C₄×C₆₁	#433	1	4	yes	complemented
225	C₄×C₆₁	#547	1	1	yes	characteristic
226	C₄×C₆₁	#550	1	1	yes	characteristic
227	C₄×C₆₁	#555	1	1	yes	characteristic
228	C₄×C₆₁	#556	1	1	yes	characteristic
229	C₂×#433	—	61	2	no	—
230	#2293	D₆₁	1	1	yes	characteristic
231	#1954	—	61	1	no	—
232	#1954	—	61	1	no	—
233	#1924	—	61	2	no	—
234	#1923	—	61	2	no	—
235	#1842	—	61	1	no	—
236	#1798	—	61	2	no	—
237	#1770	—	61	1	no	—
238	C₈×C₄⋊C₄	—	61	1	no	—
239	C₄×C₄⋊C₈	—	61	1	no	—
240	C₂×C₆₁	—	8	2	no	—
241	C₂×C₆₁	#2354	1	1	yes	characteristic
242	C₂×C₆₁	C₂×#433	1	1	yes	characteristic
243	C₂×C₆₁	#2925	1	1	yes	characteristic
244	C₂×C₆₁	#2931	1	1	yes	characteristic
245	C₂×C₆₁	#2935	1	1	yes	characteristic
246	C₂×C₆₁	#2993	1	1	yes	characteristic
247	C₂×C₆₁	#2994	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
249	C₂×#117	C₂×D₆₁	1	2	yes	—
250	#433	—	122	8	no	—
251	C₂×C₄⋊C₈	—	61	1	no	—
252	C₂×C₄⋊C₈	—	61	1	no	—
253	C₂×C₄⋊C₈	—	61	2	no	—
254	C₂×C₄⋊C₈	—	61	1	no	—
255	C₂×C₄⋊C₈	—	61	1	no	—
256	C₂×C₄⋊C₈	—	61	2	no	—
257	C₂×C₂²⋊C₈	—	61	2	no	—
258	C₂×C₂²⋊C₈	—	61	2	no	—
259	C₂×C₂²⋊C₈	—	61	2	no	—
260	C₂×C₂²⋊C₈	—	61	2	no	—
261	C₂×#97	—	61	2	no	—
262	C₂×C₄×C₈	—	61	2	no	—
263	C₂×C₄×C₈	—	61	1	no	—
264	C₂×C₄×C₈	—	61	1	no	—
265	#390	Dic₆₁	1	1	yes	characteristic
266	#390	Dic₆₁	1	1	yes	characteristic
267	#389	Dic₆₁	1	1	yes	characteristic
268	#389	Dic₆₁	1	1	yes	characteristic
269	#388	Dic₆₁	1	2	yes	—
270	#388	Dic₆₁	1	2	yes	—
271	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
272	C₄×C₂²⋊C₄	C₂×D₆₁	1	2	yes	—
273	C₄³	C₂×D₆₁	1	1	yes	characteristic
274	#336	—	61	2	no	—
275	#336	—	61	2	no	—
276	#336	—	61	1	no	—
277	#336	—	61	1	no	—
278	C₆₁	#22796	1	1	yes	characteristic, complemented, Sylow
279	C₂²×D₄	C₂×Dic₆₁	1	1	yes	characteristic
280	C₂³×C₄	C₂²×D₆₁	1	2	yes	—
281	C₂²×C₈	—	61	1	no	—
282	C₂²×C₈	—	61	1	no	—
283	C₂²×C₈	—	61	1	no	—
284	C₂²×C₈	—	61	1	no	—
285	C₂²×C₈	—	61	2	no	—
286	C₂²×C₈	—	61	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	#117	—	2	4	no	—
290	#117	—	2	4	no	—
291	C₂×C₄⋊C₄	C₂×Dic₆₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂×Dic₆₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
301	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
302	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
303	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
304	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
305	C₂×C₄²	C₂²×D₆₁	1	2	yes	—
306	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
309	C₄⋊C₈	—	61	4	no	—
310	C₄⋊C₈	—	122	2	no	—
311	C₄⋊C₈	—	122	2	no	—
312	C₄⋊C₈	—	122	4	no	—
313	C₄⋊C₈	—	122	2	no	—
314	C₄⋊C₈	—	244	2	no	—
315	C₂²⋊C₈	—	122	4	no	—
316	C₂²⋊C₈	—	122	4	no	—
317	C₂²⋊C₈	—	244	2	no	—
318	C₂²⋊C₈	—	244	2	no	—
319	#97	—	122	4	no	—
320	C₄×C₈	—	122	4	no	—
321	C₄×C₈	—	122	2	no	—
322	C₄×C₈	—	122	2	no	—
323	#95	C₂×Dic₆₁	1	2	yes	—
324	#95	C₂×Dic₆₁	1	2	yes	—
325	#95	C₂×Dic₆₁	1	2	yes	—
326	C₂⁴	C₂²×Dic₆₁	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
338	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
339	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
340	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
345	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
346	C₂×C₈	—	61	2	no	—
347	C₂×C₈	—	61	2	no	—
348	C₂×C₈	—	122	1	no	—
349	C₂×C₈	—	122	1	no	—
350	C₂×C₈	—	122	1	no	—
351	C₂×C₈	—	122	1	no	—
352	C₂×C₈	—	122	2	no	—
353	C₂×C₈	—	122	2	no	—
354	C₂×C₈	—	122	1	no	—
355	C₂×C₈	—	122	1	no	—
356	C₂×C₈	—	122	1	no	—
357	C₂×C₈	—	122	1	no	—
358	C₂×C₈	—	122	2	no	—
359	C₂×C₈	—	122	2	no	—
360	C₂×C₈	—	122	1	no	—
361	C₂×C₈	—	122	1	no	—
362	C₂×C₈	—	122	2	no	—
363	C₂×C₈	—	122	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	1	no	—
382	C₄²	#11758222	1	2	yes	—
383	C₄²	#11758222	1	2	yes	—
384	C₄²	D₄×D₆₁	1	2	yes	—
385	C₄²	#11758224	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
394	D₄	—	4	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	#14519736	1	2	yes	—
420	C₂×C₄	#14519736	1	2	yes	—
421	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
422	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
423	C₂×C₄	#14519784	1	2	yes	—
424	C₂×C₄	#14519784	1	2	yes	—
425	C₂×C₄	#14519784	1	2	yes	—
426	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
427	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
428	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
429	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
430	C₂×C₄	#14519823	1	1	yes	characteristic
431	C₂×C₄	#14519824	1	1	yes	characteristic
432	C₈	—	122	2	no	—
433	C₈	—	122	2	no	—
434	C₈	—	244	1	no	—
435	C₈	—	244	1	no	—
436	C₈	—	244	2	no	—
437	C₈	—	244	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×#14519736	1	1	yes	characteristic
446	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
447	C₂²	#16840245	1	1	yes	characteristic
448	C₂²	C₂×#14519784	1	1	yes	characteristic
449	C₂²	C₂×#14519784	1	1	yes	characteristic
450	C₂²	C₂×#14519784	1	1	yes	characteristic
451	C₂²	#16840529	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	#16839823	1	4	yes	complemented
461	C₄	#16840417	1	1	yes	characteristic
462	C₄	#16840433	1	1	yes	characteristic
463	C₄	#16840477	1	1	yes	characteristic
464	C₄	#16840482	1	1	yes	characteristic
465	C₂	—	8	2	no	—
466	C₂	#21448768	1	1	yes	characteristic
467	C₂	C₂×#16839823	1	1	yes	characteristic
468	C₂	#21454485	1	1	yes	characteristic
469	C₂	#21454531	1	1	yes	characteristic
470	C₂	#21454563	1	1	yes	characteristic
471	C₂	#21454968	1	1	yes	characteristic
472	C₂	#21454979	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂³×C₄
Fitting	C₆₁×#2293	C₂
prime radical	C₂²×D₄×C₆₁	C₂×C₄
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#2293	D₆₁
hypocenter	C₆₁	#22796
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ #2293

Complements

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

N	H ≅ G/N	type
1. C₂×#16839823	C₂	semidirect
4. #21446434	C₂	semidirect
5. #21446427	C₂	semidirect
6. #21445971	C₂	semidirect
7. #21445803	C₂	semidirect
8. #21445688	C₂	semidirect
9. C₄⋊C₄×#92418	C₂	semidirect
10. C₄×C₄⋊#92418	C₂	semidirect
53. C₄⋊#92418	D₄	semidirect
224. C₄×C₆₁	#433	semidirect
278. C₆₁	#22796	semidirect
460. C₄	#16839823	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839823	2
#21446614	2
#21446434	2
#21446427	2
#21445971	2
#21445803	2
#21445688	2
C₄⋊C₄×#92418	2
C₄×C₄⋊#92418	2
C₆₁×#2293	2
#22796	61