Subgroups — #21459550

Order 7808.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840477	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840475	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840465	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840464	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840460	C₂	1	1	yes	maximal, characteristic, complemented
6	#16840437	C₂	1	2	yes	maximal, complemented
7	#16840435	C₂	1	2	yes	maximal, complemented
8	#16840416	C₂	1	1	yes	maximal, characteristic, complemented
9	#16840412	C₂	1	1	yes	maximal, characteristic, complemented
10	#16840407	C₂	1	2	yes	maximal, complemented
11	#16840401	C₂	1	2	yes	maximal, complemented
12	#16840392	C₂	1	1	yes	maximal, characteristic, complemented
13	#16840378	C₂	1	2	yes	maximal, complemented
14	#16840364	C₂	1	2	yes	maximal, complemented
15	#16840328	C₂	1	1	yes	maximal, characteristic, complemented
16	#16840307	C₂	1	2	yes	maximal, complemented
17	#16840292	C₂	1	2	yes	maximal, complemented
18	#16840271	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#16840242	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840234	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14519735	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11758222	C₂²	1	1	yes	characteristic
25	C₂×#11758224	C₂²	1	2	yes	complemented
26	C₂×#11758224	C₂²	1	2	yes	complemented
27	C₂×D₄×D₆₁	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₆₁	C₂²	1	2	yes	—
29	C₂²×C₄×D₆₁	C₂²	1	1	yes	characteristic
30	#14519777	C₂²	1	1	yes	characteristic, complemented
31	#14519776	C₂²	1	1	yes	characteristic, complemented
32	#14519776	C₂²	1	2	yes	complemented
33	#14519773	C₂²	1	2	yes	complemented
34	#14519772	C₂²	1	2	yes	complemented
35	#14519772	C₂²	1	2	yes	complemented
36	#14519770	C₂²	1	2	yes	complemented
37	#14519768	C₂²	1	1	yes	characteristic, complemented
38	#14519767	C₂²	1	2	yes	complemented
39	#14519765	C₂²	1	2	yes	complemented
40	#14519763	C₂²	1	2	yes	complemented
41	#14519763	C₂²	1	2	yes	complemented
42	#14519763	C₂²	1	2	yes	complemented
43	#14519763	C₂²	1	2	yes	complemented
44	#14519762	C₂²	1	1	yes	characteristic
45	#14519762	C₂²	1	2	yes	complemented
46	#14519762	C₂²	1	2	yes	complemented
47	#14519761	C₂²	1	2	yes	complemented
48	#14519761	C₂²	1	2	yes	complemented
49	#14519761	C₂²	1	2	yes	complemented
50	#14519759	C₂²	1	1	yes	characteristic
51	#14519759	C₂²	1	2	yes	complemented
52	#14519758	C₂²	1	2	yes	complemented
53	#14519757	C₂²	1	2	yes	—
54	#14519757	C₂²	1	2	yes	complemented
55	#14519755	C₂²	1	2	yes	—
56	#14519755	C₂²	1	1	yes	characteristic, complemented
57	#14519754	C₂²	1	1	yes	characteristic, complemented
58	#14519754	C₂²	1	2	yes	complemented
59	#14519752	C₂²	1	1	yes	characteristic
60	#14519752	C₂²	1	1	yes	characteristic, complemented
61	#14519752	C₂²	1	2	yes	complemented
62	#14519751	C₂²	1	1	yes	characteristic
63	#14519751	C₂²	1	2	yes	complemented
64	#14519751	C₂²	1	1	yes	characteristic, complemented
65	#14519751	C₂²	1	2	yes	complemented
66	#14519750	C₂²	1	2	yes	—
67	#14519750	C₂²	1	2	yes	complemented
68	#14519750	C₂²	1	1	yes	characteristic, complemented
69	#14519749	C₂²	1	2	yes	—
70	#14519749	C₂²	1	2	yes	complemented
71	#14519749	C₂²	1	1	yes	characteristic, complemented
72	#14519748	C₂²	1	1	yes	characteristic
73	#14519748	C₂²	1	1	yes	characteristic, complemented
74	#14519747	C₂²	1	1	yes	characteristic
75	#14519747	C₂²	1	2	yes	—
76	#14519745	C₂²	1	1	yes	characteristic
77	#14519745	C₂²	1	2	yes	—
78	C₄×Dic₁₂₂	C₂²	1	2	yes	complemented
79	C₄×D₂₄₄	C₂²	1	2	yes	—
80	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₆₁	C₂²	1	2	yes	complemented
84	#14519739	C₂²	1	1	yes	characteristic, complemented
85	#14519739	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
90	#14519737	C₂²	1	2	yes	—
91	#14519737	C₂²	1	2	yes	complemented
92	#14519737	C₂²	1	2	yes	complemented
93	#14519736	C₂²	1	2	yes	complemented
94	#14519735	C₂²	1	1	yes	characteristic
95	#14519735	C₂²	1	1	yes	characteristic
96	#14519735	C₂²	1	2	yes	—
97	#14519735	C₂²	1	1	yes	characteristic, complemented
98	#14519735	C₂²	1	1	yes	characteristic, complemented
99	#14519735	C₂²	1	1	yes	characteristic, complemented
100	#14519735	C₂²	1	2	yes	complemented
101	#14519734	C₂²	1	1	yes	characteristic
102	#14519734	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₆₁	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₆₁	C₂²	1	1	yes	characteristic, complemented
107	C₂×#11758198	C₂²	1	2	yes	—
108	C₂×#11758198	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
111	C₂×C₄×Dic₆₁	C₂²	1	2	yes	complemented
112	#126×C₆₁	C₂²	1	2	yes	complemented
113	#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	#123×C₆₁	C₂²	1	2	yes	complemented
115	#121×C₆₁	C₂²	1	1	yes	characteristic
116	#121×C₆₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₆₁	C₂²	1	2	yes	complemented
118	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
121	#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₁	C₂³	1	1	yes	characteristic
124	C₂³×D₆₁	C₂³	1	2	yes	—
125	C₂×D₄×C₆₁	C₂³	1	2	yes	—
126	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₆₁	C₂³	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
142	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
143	C₂²×Dic₆₁	C₂³	1	2	yes	—
144	C₂²×Dic₆₁	C₂³	1	2	yes	—
145	C₂²×Dic₆₁	C₂³	1	2	yes	—
146	#11758224	—	4	4	no	—
147	#11758224	—	4	4	no	—
148	D₄×D₆₁	—	2	4	no	—
149	D₄×D₆₁	—	4	4	no	—
150	#11758222	—	2	4	no	—
151	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
152	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
153	C₂×D₂₄₄	C₂³	1	2	yes	—
154	C₂×D₂₄₄	C₂³	1	2	yes	—
155	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₆₁	—	2	4	no	—
157	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₆₁	C₂³	1	2	yes	—
162	C₂×C₄×D₆₁	C₂³	1	2	yes	—
163	C₂×C₄×D₆₁	C₂³	1	2	yes	—
164	C₂×C₄×D₆₁	C₂³	1	2	yes	—
165	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
167	C₂×Dic₁₂₂	C₂³	1	2	yes	—
168	C₂×Dic₁₂₂	C₂³	1	2	yes	—
169	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
178	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₄²×C₆₁	C₂³	1	2	yes	—
183	C₄²×C₆₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
189	#11758198	C₂³	1	1	yes	characteristic
190	#11758198	C₂³	1	2	yes	—
191	#11758198	C₂³	1	2	yes	—
192	#11758198	C₂³	1	2	yes	—
193	#11758198	C₂³	1	1	yes	characteristic
194	#11758198	C₂³	1	2	yes	—
195	#11758198	C₂³	1	2	yes	—
196	#11758198	C₂³	1	2	yes	—
197	#11758198	C₂³	1	2	yes	—
198	#11758198	C₂³	1	2	yes	—
199	#11758198	C₂³	1	2	yes	—
200	#11758198	C₂³	1	2	yes	—
201	#11758198	C₂³	1	2	yes	—
202	#11758198	C₂³	1	1	yes	characteristic
203	#11758198	C₂³	1	1	yes	characteristic
204	#11758198	C₂³	1	1	yes	characteristic
205	#11758198	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₆₁	C₂³	1	2	yes	—
210	C₄⋊Dic₆₁	C₂³	1	2	yes	—
211	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₆₁	C₂³	1	2	yes	—
213	C₄⋊Dic₆₁	C₂³	1	2	yes	—
214	#11758196	C₂³	1	2	yes	—
215	#11758196	C₂³	1	2	yes	—
216	#11758196	C₂³	1	1	yes	characteristic
217	#11758196	C₂³	1	1	yes	characteristic
218	#11758196	C₂³	1	1	yes	characteristic
219	#11758196	C₂³	1	2	yes	—
220	#11758196	C₂³	1	2	yes	—
221	#11758196	C₂³	1	1	yes	characteristic
222	C₄×Dic₆₁	C₂³	1	2	yes	—
223	C₄×Dic₆₁	C₂³	1	2	yes	—
224	C₄×Dic₆₁	C₂³	1	2	yes	—
225	C₄×Dic₆₁	C₂³	1	2	yes	—
226	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₆₁	C₂³	1	2	yes	—
228	C₂³×C₆₁	C₂⁴	1	2	yes	—
229	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₁	—	2	2	no	—
232	C₂²×D₆₁	—	2	2	no	—
233	C₂²×D₆₁	—	2	4	no	—
234	C₂²×D₆₁	—	4	1	no	—
235	C₂²×D₆₁	—	4	2	no	—
236	C₂²×D₆₁	—	4	2	no	—
237	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₆₁	C₂⁴	1	2	yes	—
239	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
240	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
241	D₄×C₆₁	—	2	4	no	—
242	D₄×C₆₁	—	2	2	no	—
243	D₄×C₆₁	—	2	2	no	—
244	D₄×C₆₁	—	4	2	no	—
245	C₂×C₄×C₆₁	—	2	2	no	—
246	C₂×C₄×C₆₁	—	2	2	no	—
247	C₂×C₄×C₆₁	—	4	2	no	—
248	C₂×C₄×C₆₁	—	4	2	no	—
249	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₆₁	—	2	4	no	—
258	C₂²⋊D₆₁	—	2	2	no	—
259	C₂²⋊D₆₁	—	2	2	no	—
260	C₂²⋊D₆₁	—	2	2	no	—
261	C₂²⋊D₆₁	—	2	4	no	—
262	C₂²⋊D₆₁	—	4	2	no	—
263	C₂²⋊D₆₁	—	4	2	no	—
264	C₂²⋊D₆₁	—	4	2	no	—
265	C₂²⋊D₆₁	—	4	1	no	—
266	C₂×Dic₆₁	—	2	4	no	—
267	C₂×Dic₆₁	—	2	2	no	—
268	C₂×Dic₆₁	—	4	2	no	—
269	C₂×Dic₆₁	—	4	2	no	—
270	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₆₁	C₂⁴	1	2	yes	—
273	C₂×Dic₆₁	C₂⁴	1	2	yes	—
274	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₆₁	C₂⁴	1	2	yes	—
276	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
278	D₂₄₄	—	2	2	no	—
279	D₂₄₄	—	2	2	no	—
280	D₂₄₄	—	4	1	no	—
281	D₂₄₄	—	4	2	no	—
282	D₂₄₄	—	4	2	no	—
283	C₄×D₆₁	—	2	2	no	—
284	C₄×D₆₁	—	2	2	no	—
285	C₄×D₆₁	—	2	2	no	—
286	C₄×D₆₁	—	2	2	no	—
287	C₄×D₆₁	—	4	2	no	—
288	C₄×D₆₁	—	4	2	no	—
289	C₄×D₆₁	—	4	2	no	—
290	C₄×D₆₁	—	4	2	no	—
291	C₄×D₆₁	#41	1	4	yes	complemented
292	Dic₁₂₂	—	2	2	no	—
293	Dic₁₂₂	—	4	2	no	—
294	Dic₁₂₂	—	4	2	no	—
295	C₂²×C₆₁	—	2	1	no	—
296	C₂²×C₆₁	—	2	1	no	—
297	C₂²×C₆₁	—	2	1	no	—
298	C₂²×C₆₁	—	2	2	no	—
299	C₂²×C₆₁	—	2	1	no	—
300	C₂²×C₆₁	—	2	2	no	—
301	C₂²×C₆₁	—	2	1	no	—
302	C₂²×C₆₁	—	2	2	no	—
303	C₂²×C₆₁	H(5,𝔽₂)	1	2	yes	—
304	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
305	C₂×D₆₁	—	2	1	no	—
306	C₂×D₆₁	—	2	1	no	—
307	C₂×D₆₁	—	2	1	no	—
308	C₂×D₆₁	—	2	1	no	—
309	C₂×D₆₁	—	2	2	no	—
310	C₂×D₆₁	—	2	1	no	—
311	C₂×D₆₁	—	2	2	no	—
312	C₂×D₆₁	—	2	1	no	—
313	C₂×D₆₁	—	2	2	no	—
314	C₂×D₆₁	—	2	1	no	—
315	C₂×D₆₁	—	2	1	no	—
316	C₂×D₆₁	—	4	4	no	—
317	C₂×D₆₁	—	8	4	no	—
318	C₂×D₆₁	C₂×#41	1	2	yes	—
319	C₄×C₆₁	—	2	1	no	—
320	C₄×C₆₁	—	2	1	no	—
321	C₄×C₆₁	—	2	1	no	—
322	C₄×C₆₁	—	2	2	no	—
323	C₄×C₆₁	—	2	2	no	—
324	C₄×C₆₁	—	2	1	no	—
325	C₄×C₆₁	—	2	2	no	—
326	C₄×C₆₁	C₂×#41	1	2	yes	—
327	Dic₆₁	—	2	1	no	—
328	Dic₆₁	—	2	1	no	—
329	Dic₆₁	—	2	2	no	—
330	Dic₆₁	—	2	1	no	—
331	Dic₆₁	—	2	2	no	—
332	Dic₆₁	—	2	2	no	—
333	Dic₆₁	—	2	1	no	—
334	Dic₆₁	C₂×#41	1	2	yes	—
335	#3494	—	61	1	no	maximal, Sylow
336	C₂×C₆₁	—	2	2	no	—
337	C₂×C₆₁	—	4	2	no	—
338	C₂×C₆₁	—	4	1	no	—
339	C₂×C₆₁	C₂²×#41	1	1	yes	characteristic
340	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₆₁	#585	1	1	yes	characteristic
342	D₆₁	—	2	2	no	—
343	D₆₁	—	4	1	no	—
344	D₆₁	—	4	1	no	—
345	D₆₁	—	4	2	no	—
346	#555	—	61	1	no	—
347	#555	—	61	1	no	—
348	#553	—	61	1	no	—
349	#553	—	61	1	no	—
350	#553	—	61	1	no	—
351	#553	D₆₁	1	1	yes	characteristic, complemented
352	#551	—	61	2	no	—
353	#551	—	61	2	no	—
354	#547	—	61	1	no	—
355	#547	—	61	1	no	—
356	#546	—	61	2	no	—
357	#546	—	61	2	no	—
358	#544	—	61	1	no	—
359	#542	—	61	2	no	—
360	#540	—	61	2	no	—
361	#535	—	61	1	no	—
362	#532	—	61	2	no	—
363	#529	—	61	2	no	—
364	#525	—	61	1	no	—
365	C₂×#121	—	61	1	no	—
366	#520	—	61	1	no	—
367	#518	—	61	1	no	—
368	C₂×#117	—	61	1	no	—
369	C₆₁	#3494	1	1	yes	characteristic, complemented, Sylow
370	C₂×#41	—	61	2	no	—
371	C₂×#41	—	61	2	no	—
372	C₂×#41	—	61	1	no	—
373	C₂²×D₄	—	61	1	no	—
374	C₂²×D₄	—	61	2	no	—
375	C₂³×C₄	—	61	1	no	—
376	C₄⋊Q₈	—	61	2	no	—
377	C₄⋊Q₈	—	61	1	no	—
378	C₄⋊Q₈	—	61	1	no	—
379	#127	—	61	2	no	—
380	#126	—	61	2	no	—
381	#126	—	61	2	no	—
382	#126	—	61	2	no	—
383	#126	C₂×D₆₁	1	2	yes	complemented
384	#125	—	61	2	no	—
385	#125	—	61	1	no	—
386	#125	C₂×D₆₁	1	1	yes	characteristic, complemented
387	#124	—	61	2	no	—
388	#124	—	61	2	no	—
389	#124	—	61	2	no	—
390	#124	—	61	2	no	—
391	#124	—	61	2	no	—
392	#123	—	61	2	no	—
393	#123	—	61	1	no	—
394	#123	—	61	2	no	—
395	#123	—	61	2	no	—
396	#123	—	61	1	no	—
397	#123	—	61	2	no	—
398	#123	—	61	2	no	—
399	#123	—	61	2	no	—
400	#123	—	61	2	no	—
401	#123	C₂×D₆₁	1	2	yes	complemented
402	C₂²⋊Q₈	—	61	1	no	—
403	C₂²⋊Q₈	—	61	2	no	—
404	C₂²⋊Q₈	—	61	2	no	—
405	C₂²⋊Q₈	—	61	2	no	—
406	C₂²⋊Q₈	—	61	1	no	—
407	C₂²⋊Q₈	—	61	2	no	—
408	#121	—	61	2	no	—
409	#121	—	61	1	no	—
410	#121	—	61	1	no	—
411	#121	—	61	1	no	—
412	#121	—	61	2	no	—
413	#121	—	61	1	no	—
414	#121	—	61	2	no	—
415	#121	—	61	1	no	—
416	#121	—	61	2	no	—
417	#121	—	61	1	no	—
418	#121	—	61	1	no	—
419	#121	—	61	2	no	—
420	#121	—	61	2	no	—
421	#121	—	61	1	no	—
422	#121	—	61	2	no	—
423	#121	C₂×D₆₁	1	1	yes	characteristic
424	#121	C₂×D₆₁	1	2	yes	complemented
425	#121	C₂×D₆₁	1	1	yes	characteristic, complemented
426	#120	—	61	1	no	—
427	#120	—	61	2	no	—
428	#120	—	61	1	no	—
429	#120	—	61	2	no	—
430	C₄×Q₈	—	61	2	no	—
431	C₄×D₄	—	61	1	no	—
432	C₄×D₄	—	61	2	no	—
433	C₄×D₄	—	61	2	no	—
434	C₄×D₄	—	61	1	no	—
435	C₄×D₄	—	61	1	no	—
436	C₄×D₄	—	61	2	no	—
437	C₄×D₄	—	61	1	no	—
438	C₄×D₄	—	61	2	no	—
439	C₄×D₄	—	61	2	no	—
440	C₄×D₄	—	61	2	no	—
441	C₄×D₄	—	61	2	no	—
442	C₄×D₄	—	61	1	no	—
443	C₄×D₄	—	61	2	no	—
444	C₄×D₄	—	61	1	no	—
445	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic, complemented
446	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic, complemented
447	C₄×D₄	C₂×D₆₁	1	2	yes	complemented
448	#117	—	61	2	no	—
449	#117	—	61	1	no	—
450	#117	—	61	1	no	—
451	#117	—	61	2	no	—
452	#117	—	61	2	no	—
453	#117	—	61	1	no	—
454	#117	—	61	1	no	—
455	#117	—	61	1	no	—
456	#117	—	61	1	no	—
457	#117	—	61	2	no	—
458	#117	C₂×D₆₁	1	1	yes	characteristic, complemented
459	C₂×C₄⋊C₄	—	61	1	no	—
460	C₂×C₄⋊C₄	—	61	1	no	—
461	C₂×C₄⋊C₄	—	61	1	no	—
462	C₂×C₄⋊C₄	—	61	1	no	—
463	C₂×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊C₄	—	61	2	no	—
465	C₂×C₂²⋊C₄	—	61	2	no	—
466	C₂×C₂²⋊C₄	—	61	2	no	—
467	C₂×C₂²⋊C₄	—	61	2	no	—
468	C₂×C₄²	—	61	2	no	—
469	C₂⁴	—	61	1	no	—
470	C₂⁴	—	61	2	no	—
471	#41	—	122	4	no	—
472	#41	—	244	4	no	—
473	#41	—	244	4	no	—
474	C₂×Q₈	—	61	1	no	—
475	C₂×Q₈	—	61	2	no	—
476	C₂×Q₈	—	61	2	no	—
477	C₂×D₄	—	61	1	no	—
478	C₂×D₄	—	61	2	no	—
479	C₂×D₄	—	61	1	no	—
480	C₂×D₄	—	61	1	no	—
481	C₂×D₄	—	61	2	no	—
482	C₂×D₄	—	61	1	no	—
483	C₂×D₄	—	61	2	no	—
484	C₂×D₄	—	61	2	no	—
485	C₂×D₄	—	61	2	no	—
486	C₂×D₄	—	61	1	no	—
487	C₂×D₄	—	61	1	no	—
488	C₂×D₄	—	61	1	no	—
489	C₂×D₄	—	61	2	no	—
490	C₂×D₄	—	61	2	no	—
491	C₂×D₄	—	122	4	no	—
492	C₂×D₄	—	244	4	no	—
493	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₆₁	1	2	yes	—
496	C₂×D₄	C₂²×D₆₁	1	2	yes	—
497	C₂²×C₄	—	61	1	no	—
498	C₂²×C₄	—	61	1	no	—
499	C₂²×C₄	—	61	2	no	—
500	C₂²×C₄	—	61	2	no	—
501	C₂²×C₄	—	61	2	no	—
502	C₂²×C₄	—	61	1	no	—
503	C₂²×C₄	—	61	1	no	—
504	C₂²×C₄	—	61	1	no	—
505	C₂²×C₄	—	61	1	no	—
506	C₂²×C₄	—	61	2	no	—
507	C₂²×C₄	—	61	2	no	—
508	C₂²×C₄	—	61	2	no	—
509	C₂²×C₄	—	61	2	no	—
510	C₂²×C₄	—	122	4	no	—
511	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
514	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
515	C₄⋊C₄	—	61	1	no	—
516	C₄⋊C₄	—	61	1	no	—
517	C₄⋊C₄	—	61	2	no	—
518	C₄⋊C₄	—	61	2	no	—
519	C₄⋊C₄	—	61	1	no	—
520	C₄⋊C₄	—	61	2	no	—
521	C₄⋊C₄	—	61	2	no	—
522	C₄⋊C₄	—	61	1	no	—
523	C₄⋊C₄	—	61	1	no	—
524	C₄⋊C₄	—	61	1	no	—
525	C₄⋊C₄	—	61	2	no	—
526	C₄⋊C₄	—	61	2	no	—
527	C₄⋊C₄	—	61	1	no	—
528	C₄⋊C₄	—	61	1	no	—
529	C₄⋊C₄	—	61	2	no	—
530	C₄⋊C₄	—	61	2	no	—
531	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
535	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
536	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
537	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
538	C₂²⋊C₄	—	61	2	no	—
539	C₂²⋊C₄	—	61	2	no	—
540	C₂²⋊C₄	—	61	2	no	—
541	C₂²⋊C₄	—	61	1	no	—
542	C₂²⋊C₄	—	61	1	no	—
543	C₂²⋊C₄	—	61	2	no	—
544	C₂²⋊C₄	—	61	1	no	—
545	C₂²⋊C₄	—	61	1	no	—
546	C₂²⋊C₄	—	61	2	no	—
547	C₂²⋊C₄	—	61	2	no	—
548	C₂²⋊C₄	—	61	2	no	—
549	C₂²⋊C₄	—	61	2	no	—
550	C₂²⋊C₄	—	61	2	no	—
551	C₂²⋊C₄	—	61	2	no	—
552	C₂²⋊C₄	—	61	2	no	—
553	C₂²⋊C₄	—	61	2	no	—
554	C₂²⋊C₄	—	61	2	no	—
555	C₂²⋊C₄	—	61	1	no	—
556	C₂²⋊C₄	—	61	2	no	—
557	C₂²⋊C₄	—	61	1	no	—
558	C₂²⋊C₄	—	61	1	no	—
559	C₂²⋊C₄	—	61	1	no	—
560	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
564	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
565	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
566	C₄²	—	61	2	no	—
567	C₄²	—	61	2	no	—
568	C₄²	—	61	2	no	—
569	C₄²	—	61	2	no	—
570	C₄²	—	61	2	no	—
571	C₄²	—	61	1	no	—
572	C₄²	C₂²×D₆₁	1	2	yes	—
573	C₄²	C₂²×D₆₁	1	1	yes	characteristic
574	C₂³	—	61	1	no	—
575	C₂³	—	61	1	no	—
576	C₂³	—	61	2	no	—
577	C₂³	—	61	1	no	—
578	C₂³	—	122	4	no	—
579	C₂³	—	122	2	no	—
580	C₂³	—	122	2	no	—
581	C₂³	—	244	2	no	—
582	C₂³	—	244	2	no	—
583	C₂³	—	244	1	no	—
584	C₂³	C₂³×D₆₁	1	2	yes	—
585	C₂³	C₂³×D₆₁	1	1	yes	characteristic
586	C₂³	C₂³×D₆₁	1	1	yes	characteristic
587	Q₈	—	122	2	no	—
588	Q₈	—	244	2	no	—
589	Q₈	—	244	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	122	2	no	—
595	D₄	—	122	4	no	—
596	D₄	—	122	2	no	—
597	D₄	—	122	2	no	—
598	D₄	—	122	4	no	—
599	D₄	—	122	2	no	—
600	D₄	—	122	2	no	—
601	D₄	—	244	1	no	—
602	D₄	—	244	2	no	—
603	D₄	—	244	2	no	—
604	D₄	—	244	1	no	—
605	D₄	—	244	2	no	—
606	D₄	—	244	2	no	—
607	D₄	—	244	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	61	1	no	—
613	C₂×C₄	—	61	4	no	—
614	C₂×C₄	—	61	1	no	—
615	C₂×C₄	—	61	1	no	—
616	C₂×C₄	—	61	2	no	—
617	C₂×C₄	—	61	2	no	—
618	C₂×C₄	—	61	1	no	—
619	C₂×C₄	—	61	1	no	—
620	C₂×C₄	—	61	2	no	—
621	C₂×C₄	—	122	2	no	—
622	C₂×C₄	—	122	2	no	—
623	C₂×C₄	—	122	2	no	—
624	C₂×C₄	—	122	4	no	—
625	C₂×C₄	—	122	2	no	—
626	C₂×C₄	—	122	2	no	—
627	C₂×C₄	—	244	2	no	—
628	C₂×C₄	—	244	2	no	—
629	C₂×C₄	—	244	2	no	—
630	C₂×C₄	—	244	2	no	—
631	C₂×C₄	—	244	2	no	—
632	C₂×C₄	—	244	2	no	—
633	C₂×C₄	C₂³×D₆₁	1	2	yes	—
634	C₂×C₄	C₂³×D₆₁	1	2	yes	—
635	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₆₁	1	2	yes	—
639	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	61	2	no	—
650	C₂²	—	122	1	no	—
651	C₂²	—	122	1	no	—
652	C₂²	—	122	1	no	—
653	C₂²	—	122	1	no	—
654	C₂²	—	122	2	no	—
655	C₂²	—	122	1	no	—
656	C₂²	—	122	2	no	—
657	C₂²	—	122	1	no	—
658	C₂²	—	122	2	no	—
659	C₂²	—	122	1	no	—
660	C₂²	—	122	1	no	—
661	C₂²	—	488	4	no	—
662	C₂²	—	244	4	no	—
663	C₂²	#14519823	1	2	yes	—
664	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	61	2	no	—
673	C₄	—	122	1	no	—
674	C₄	—	122	1	no	—
675	C₄	—	122	2	no	—
676	C₄	—	122	2	no	—
677	C₄	—	122	2	no	—
678	C₄	—	122	1	no	—
679	C₄	—	122	1	no	—
680	C₄	#41×D₆₁	1	2	yes	—
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	122	2	no	—
685	C₂	—	244	2	no	—
686	C₂	—	244	1	no	—
687	C₂	—	244	1	no	—
688	C₂	C₂×#41×D₆₁	1	1	yes	characteristic
689	C₂	C₂×#14519823	1	1	yes	characteristic
690	C₂	#16840597	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#553	C₂
hypercenter	#553	D₆₁
hypocenter	C₆₁	#3494
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #16840477	C₂	semidirect
2. #16840475	C₂	semidirect
3. #16840465	C₂	semidirect
4. #16840464	C₂	semidirect
5. #16840460	C₂	semidirect
6. #16840437	C₂	semidirect
7. #16840435	C₂	semidirect
8. #16840416	C₂	semidirect
9. #16840412	C₂	semidirect
10. #16840407	C₂	semidirect
11. #16840401	C₂	semidirect
12. #16840392	C₂	semidirect
13. #16840378	C₂	semidirect
14. #16840364	C₂	semidirect
15. #16840328	C₂	semidirect
16. #16840307	C₂	semidirect
17. #16840292	C₂	semidirect
18. #16840271	C₂	semidirect
19. #121×D₆₁	C₂	semidirect
20. #16840242	C₂	semidirect
21. #16840234	C₂	semidirect
22. C₂×#14519735	C₂	semidirect
23. C₆₁×#553	C₂	semidirect
25. C₂×#11758224	C₂²	semidirect
26. C₂×#11758224	C₂²	semidirect
30. #14519777	C₂²	semidirect
31. #14519776	C₂²	semidirect
32. #14519776	C₂²	semidirect
33. #14519773	C₂²	semidirect
34. #14519772	C₂²	semidirect
35. #14519772	C₂²	semidirect
36. #14519770	C₂²	semidirect
37. #14519768	C₂²	semidirect
38. #14519767	C₂²	semidirect
39. #14519765	C₂²	semidirect
40. #14519763	C₂²	semidirect
41. #14519763	C₂²	semidirect
42. #14519763	C₂²	semidirect
43. #14519763	C₂²	semidirect
45. #14519762	C₂²	semidirect
46. #14519762	C₂²	semidirect
47. #14519761	C₂²	semidirect
48. #14519761	C₂²	semidirect
49. #14519761	C₂²	semidirect
51. #14519759	C₂²	semidirect
52. #14519758	C₂²	semidirect
54. #14519757	C₂²	semidirect
56. #14519755	C₂²	semidirect
57. #14519754	C₂²	semidirect
58. #14519754	C₂²	semidirect
60. #14519752	C₂²	semidirect
61. #14519752	C₂²	semidirect
63. #14519751	C₂²	semidirect
64. #14519751	C₂²	semidirect
65. #14519751	C₂²	semidirect
67. #14519750	C₂²	semidirect
68. #14519750	C₂²	semidirect
70. #14519749	C₂²	semidirect
71. #14519749	C₂²	semidirect
73. #14519748	C₂²	semidirect
78. C₄×Dic₁₂₂	C₂²	semidirect
80. C₄×D₂₄₄	C₂²	semidirect
81. C₄×D₂₄₄	C₂²	semidirect
82. D₄×Dic₆₁	C₂²	semidirect
83. D₄×Dic₆₁	C₂²	semidirect
84. #14519739	C₂²	semidirect
85. #14519739	C₂²	semidirect
86. C₄×C₂²⋊D₆₁	C₂²	semidirect
87. C₄×C₂²⋊D₆₁	C₂²	semidirect
88. C₄×C₂²⋊D₆₁	C₂²	semidirect
89. C₄×C₂²⋊D₆₁	C₂²	semidirect
91. #14519737	C₂²	semidirect
92. #14519737	C₂²	semidirect
93. #14519736	C₂²	semidirect
97. #14519735	C₂²	semidirect
98. #14519735	C₂²	semidirect
99. #14519735	C₂²	semidirect
100. #14519735	C₂²	semidirect
102. #14519734	C₂²	semidirect
103. C₂×C₄⋊Dic₆₁	C₂²	semidirect
104. C₂×C₄⋊Dic₆₁	C₂²	semidirect
106. C₄⋊C₄×D₆₁	C₂²	semidirect
111. C₂×C₄×Dic₆₁	C₂²	semidirect
112. #126×C₆₁	C₂²	semidirect
113. #125×C₆₁	C₂²	semidirect
114. #123×C₆₁	C₂²	semidirect
116. #121×C₆₁	C₂²	semidirect
117. #121×C₆₁	C₂²	semidirect
118. C₄×D₄×C₆₁	C₂²	semidirect
119. C₄×D₄×C₆₁	C₂²	semidirect
120. C₄×D₄×C₆₁	C₂²	semidirect
121. #117×C₆₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₁	C₂²	semidirect
291. C₄×D₆₁	#41	semidirect
351. #553	D₆₁	semidirect
369. C₆₁	#3494	semidirect
383. #126	C₂×D₆₁	semidirect
386. #125	C₂×D₆₁	semidirect
401. #123	C₂×D₆₁	semidirect
424. #121	C₂×D₆₁	semidirect
425. #121	C₂×D₆₁	semidirect
445. C₄×D₄	C₂×D₆₁	semidirect
446. C₄×D₄	C₂×D₆₁	semidirect
447. C₄×D₄	C₂×D₆₁	semidirect
458. #117	C₂×D₆₁	semidirect
463. C₂×C₄⋊C₄	C₂×D₆₁	semidirect