Subgroups — #21460091

Order 7808.

1058 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840504	C₂	1	2	yes	maximal, complemented
2	#16840502	C₂	1	2	yes	maximal, complemented
3	#16840494	C₂	1	2	yes	maximal, complemented
4	#16840486	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840485	C₂	1	1	yes	maximal, characteristic, complemented
6	#16840478	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840477	C₂	1	1	yes	maximal, characteristic, complemented
8	#16840435	C₂	1	2	yes	maximal, complemented
9	#16840424	C₂	1	1	yes	maximal, characteristic, complemented
10	#16840420	C₂	1	1	yes	maximal, characteristic, complemented
11	#16840407	C₂	1	1	yes	maximal, characteristic, complemented
12	#16840405	C₂	1	1	yes	maximal, characteristic, complemented
13	#16840385	C₂	1	2	yes	maximal, complemented
14	#16840383	C₂	1	1	yes	maximal, characteristic, complemented
15	#16840378	C₂	1	2	yes	maximal, complemented
16	#16840352	C₂	1	2	yes	maximal, complemented
17	#16840351	C₂	1	2	yes	maximal, complemented
18	#16840335	C₂	1	1	yes	maximal, characteristic, complemented
19	#16840328	C₂	1	1	yes	maximal, characteristic, complemented
20	#16840275	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840274	C₂	1	1	yes	maximal, characteristic, complemented
22	#16840272	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11758226	C₂²	1	1	yes	characteristic
25	C₂×#11758222	C₂²	1	1	yes	characteristic
26	C₂×#11758224	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₆₁	C₂²	1	1	yes	characteristic, complemented
30	#14519777	C₂²	1	1	yes	characteristic, complemented
31	#14519776	C₂²	1	2	yes	complemented
32	#14519773	C₂²	1	2	yes	—
33	#14519772	C₂²	1	2	yes	complemented
34	#14519772	C₂²	1	2	yes	complemented
35	#14519772	C₂²	1	2	yes	complemented
36	#14519772	C₂²	1	2	yes	complemented
37	#14519772	C₂²	1	2	yes	complemented
38	#14519766	C₂²	1	2	yes	—
39	#14519766	C₂²	1	2	yes	complemented
40	#14519766	C₂²	1	2	yes	complemented
41	#14519765	C₂²	1	2	yes	—
42	#14519765	C₂²	1	2	yes	complemented
43	#14519765	C₂²	1	1	yes	characteristic, complemented
44	#14519763	C₂²	1	2	yes	—
45	#14519763	C₂²	1	2	yes	complemented
46	#14519763	C₂²	1	2	yes	complemented
47	#14519763	C₂²	1	2	yes	complemented
48	#14519763	C₂²	1	2	yes	complemented
49	#14519763	C₂²	1	2	yes	complemented
50	#14519762	C₂²	1	2	yes	complemented
51	#14519762	C₂²	1	2	yes	complemented
52	#14519761	C₂²	1	1	yes	characteristic
53	#14519761	C₂²	1	1	yes	characteristic, complemented
54	#14519761	C₂²	1	2	yes	complemented
55	#14519759	C₂²	1	2	yes	complemented
56	#14519759	C₂²	1	2	yes	complemented
57	#14519759	C₂²	1	2	yes	complemented
58	#14519759	C₂²	1	2	yes	complemented
59	#14519757	C₂²	1	1	yes	characteristic, complemented
60	#14519757	C₂²	1	1	yes	characteristic, complemented
61	#14519757	C₂²	1	1	yes	characteristic, complemented
62	#14519757	C₂²	1	1	yes	characteristic, complemented
63	#14519757	C₂²	1	2	yes	complemented
64	#14519756	C₂²	1	1	yes	characteristic, complemented
65	#14519755	C₂²	1	2	yes	complemented
66	#14519754	C₂²	1	2	yes	complemented
67	#14519753	C₂²	1	1	yes	characteristic, complemented
68	#14519753	C₂²	1	1	yes	characteristic, complemented
69	#14519752	C₂²	1	1	yes	characteristic
70	#14519752	C₂²	1	1	yes	characteristic
71	#14519752	C₂²	1	1	yes	characteristic
72	#14519752	C₂²	1	2	yes	complemented
73	#14519752	C₂²	1	1	yes	characteristic, complemented
74	#14519752	C₂²	1	2	yes	complemented
75	#14519751	C₂²	1	2	yes	—
76	#14519751	C₂²	1	1	yes	characteristic
77	#14519751	C₂²	1	2	yes	complemented
78	#14519750	C₂²	1	2	yes	—
79	#14519750	C₂²	1	2	yes	complemented
80	#14519748	C₂²	1	1	yes	characteristic
81	#14519748	C₂²	1	1	yes	characteristic, complemented
82	#14519747	C₂²	1	1	yes	characteristic
83	#14519747	C₂²	1	2	yes	—
84	#14519747	C₂²	1	2	yes	—
85	#14519747	C₂²	1	1	yes	characteristic, complemented
86	#14519747	C₂²	1	2	yes	complemented
87	#14519747	C₂²	1	2	yes	complemented
88	#14519745	C₂²	1	2	yes	—
89	#14519745	C₂²	1	2	yes	complemented
90	Q₈×Dic₆₁	C₂²	1	2	yes	complemented
91	C₄×Dic₁₂₂	C₂²	1	2	yes	complemented
92	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
94	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
95	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₂₄₄	C₂²	1	2	yes	complemented
99	D₄×Dic₆₁	C₂²	1	2	yes	complemented
100	#14519739	C₂²	1	2	yes	complemented
101	#14519737	C₂²	1	2	yes	complemented
102	#14519737	C₂²	1	2	yes	complemented
103	#14519737	C₂²	1	2	yes	complemented
104	#14519736	C₂²	1	2	yes	complemented
105	#14519735	C₂²	1	1	yes	characteristic, complemented
106	#14519735	C₂²	1	1	yes	characteristic, complemented
107	#14519735	C₂²	1	1	yes	characteristic, complemented
108	#14519735	C₂²	1	2	yes	complemented
109	#14519735	C₂²	1	1	yes	characteristic, complemented
110	C₂×#11758198	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	#126×C₆₁	C₂²	1	2	yes	complemented
114	#124×C₆₁	C₂²	1	2	yes	complemented
115	#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	#123×C₆₁	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
119	#121×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₁	C₂³	1	1	yes	characteristic
124	C₂³×D₆₁	C₂³	1	2	yes	—
125	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
131	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
138	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
139	C₂²×Dic₆₁	C₂³	1	2	yes	—
140	#11758226	—	4	2	no	—
141	Q₈×D₆₁	—	4	2	no	—
142	#11758224	—	4	2	no	—
143	D₄×D₆₁	—	4	2	no	—
144	#11758222	—	4	2	no	—
145	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
146	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
147	C₂×D₂₄₄	C₂³	1	2	yes	—
148	C₂×D₂₄₄	C₂³	1	2	yes	—
149	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
150	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
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×C₄×D₆₁	—	4	2	no	—
155	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
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×Dic₁₂₂	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₂₂	C₂³	1	2	yes	—
166	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
167	C₂×Dic₁₂₂	C₂³	1	2	yes	—
168	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₄²×C₆₁	C₂³	1	1	yes	characteristic
183	C₄²×C₆₁	C₂³	1	1	yes	characteristic
184	C₄²×C₆₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
188	#11758198	C₂³	1	1	yes	characteristic
189	#11758198	C₂³	1	2	yes	—
190	#11758198	C₂³	1	1	yes	characteristic
191	#11758198	C₂³	1	2	yes	—
192	#11758198	C₂³	1	2	yes	—
193	#11758198	C₂³	1	2	yes	—
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	1	yes	characteristic
200	#11758198	C₂³	1	2	yes	—
201	#11758198	C₂³	1	2	yes	—
202	#11758198	C₂³	1	2	yes	—
203	#11758198	C₂³	1	1	yes	characteristic
204	#11758198	C₂³	1	1	yes	characteristic
205	#11758198	C₂³	1	1	yes	characteristic
206	#11758198	C₂³	1	2	yes	—
207	#11758198	C₂³	1	1	yes	characteristic
208	#11758198	C₂³	1	1	yes	characteristic
209	#11758198	C₂³	1	2	yes	—
210	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
215	C₄⋊Dic₆₁	C₂³	1	2	yes	—
216	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₆₁	C₂³	1	2	yes	—
219	#11758196	C₂³	1	2	yes	—
220	#11758196	C₂³	1	2	yes	—
221	#11758196	C₂³	1	2	yes	—
222	#11758196	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	2	yes	—
227	C₄×Dic₆₁	C₂³	1	2	yes	—
228	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₁	C₂⁴	1	2	yes	—
230	C₂²×D₆₁	—	4	1	no	—
231	C₂²×D₆₁	—	4	1	no	—
232	C₂²×D₆₁	—	4	1	no	—
233	C₂²×D₆₁	—	4	2	no	—
234	C₂²×D₆₁	—	4	2	no	—
235	C₂²×D₆₁	—	4	2	no	—
236	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
237	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
239	C₂²×D₆₁	C₂⁴	1	2	yes	—
240	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
241	Q₈×C₆₁	—	2	2	no	—
242	Q₈×C₆₁	—	4	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	—	4	2	no	—
247	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₆₁	—	4	1	no	—
257	C₂²⋊D₆₁	—	4	1	no	—
258	C₂²⋊D₆₁	—	4	2	no	—
259	C₂²⋊D₆₁	—	4	2	no	—
260	C₂²⋊D₆₁	—	4	2	no	—
261	C₂²⋊D₆₁	—	4	2	no	—
262	C₂²⋊D₆₁	—	4	2	no	—
263	C₂×Dic₆₁	—	4	1	no	—
264	C₂×Dic₆₁	—	4	2	no	—
265	C₂×Dic₆₁	C₂⁴	1	2	yes	—
266	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₆₁	C₂⁴	1	2	yes	—
268	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₆₁	C₂⁴	1	2	yes	—
272	D₂₄₄	—	2	2	no	—
273	D₂₄₄	—	4	1	no	—
274	D₂₄₄	—	4	1	no	—
275	D₂₄₄	—	4	1	no	—
276	D₂₄₄	—	4	2	no	—
277	D₂₄₄	—	4	2	no	—
278	D₂₄₄	—	4	1	no	—
279	D₂₄₄	—	4	1	no	—
280	D₂₄₄	—	4	2	no	—
281	C₄×D₆₁	—	2	2	no	—
282	C₄×D₆₁	—	2	2	no	—
283	C₄×D₆₁	—	2	2	no	—
284	C₄×D₆₁	—	2	2	no	—
285	C₄×D₆₁	—	4	1	no	—
286	C₄×D₆₁	—	4	1	no	—
287	C₄×D₆₁	—	4	2	no	—
288	C₄×D₆₁	—	4	2	no	—
289	C₄×D₆₁	—	4	2	no	—
290	Dic₁₂₂	—	2	2	no	—
291	Dic₁₂₂	—	4	2	no	—
292	Dic₁₂₂	—	4	1	no	—
293	Dic₁₂₂	—	4	2	no	—
294	C₂²×C₆₁	—	2	1	no	—
295	C₂²×C₆₁	—	2	2	no	—
296	C₂²×C₆₁	—	2	1	no	—
297	C₂²×C₆₁	—	2	2	no	—
298	C₂²×C₆₁	—	2	2	no	—
299	C₂²×C₆₁	—	2	1	no	—
300	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
301	C₂×D₆₁	—	2	1	no	—
302	C₂×D₆₁	—	2	1	no	—
303	C₂×D₆₁	—	2	1	no	—
304	C₂×D₆₁	—	2	1	no	—
305	C₂×D₆₁	—	2	2	no	—
306	C₂×D₆₁	—	2	2	no	—
307	C₂×D₆₁	—	2	1	no	—
308	C₂×D₆₁	—	2	1	no	—
309	C₂×D₆₁	—	2	1	no	—
310	C₂×D₆₁	—	2	2	no	—
311	C₂×D₆₁	—	2	1	no	—
312	C₂×D₆₁	—	2	1	no	—
313	C₂×D₆₁	—	2	1	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	C₄×C₆₁	—	2	1	no	—
319	C₄×C₆₁	—	2	2	no	—
320	C₄×C₆₁	—	2	1	no	—
321	C₄×C₆₁	—	2	1	no	—
322	C₄×C₆₁	—	2	1	no	—
323	C₄×C₆₁	—	2	2	no	—
324	C₄×C₆₁	—	2	2	no	—
325	C₄×C₆₁	—	2	1	no	—
326	C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
327	Dic₆₁	—	2	2	no	—
328	Dic₆₁	—	2	1	no	—
329	Dic₆₁	—	2	1	no	—
330	Dic₆₁	—	2	1	no	—
331	Dic₆₁	—	2	1	no	—
332	Dic₆₁	—	2	2	no	—
333	Dic₆₁	—	2	2	no	—
334	#3540	—	61	1	no	maximal, Sylow
335	C₂×C₆₁	—	4	1	no	—
336	C₂×C₆₁	—	4	2	no	—
337	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₆₁	#585	1	1	yes	characteristic
339	C₂×C₆₁	#585	1	1	yes	characteristic
340	D₆₁	—	4	1	no	—
341	D₆₁	—	4	1	no	—
342	D₆₁	—	4	1	no	—
343	D₆₁	—	4	2	no	—
344	D₆₁	—	4	1	no	—
345	H(3,𝔽₄)	—	61	2	no	—
346	#560	—	61	2	no	—
347	#559	—	61	2	no	—
348	#556	—	61	1	no	—
349	#556	—	61	1	no	—
350	#555	—	61	1	no	—
351	#555	—	61	1	no	—
352	#551	—	61	2	no	—
353	#548	—	61	1	no	—
354	#548	—	61	1	no	—
355	#546	—	61	1	no	—
356	#546	—	61	1	no	—
357	#542	—	61	2	no	—
358	#542	—	61	2	no	—
359	#542	—	61	1	no	—
360	#542	D₆₁	1	1	yes	characteristic, complemented
361	#538	—	61	2	no	—
362	#538	—	61	2	no	—
363	#536	—	61	1	no	—
364	#535	—	61	1	no	—
365	#525	—	61	1	no	—
366	#525	—	61	1	no	—
367	#525	—	61	1	no	—
368	C₆₁	#3540	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	61	1	no	—
370	C₂×#41	—	61	1	no	—
371	C₂×#41	—	61	1	no	—
372	C₂²×Q₈	—	61	1	no	—
373	C₂²×D₄	—	61	1	no	—
374	C₂³×C₄	—	61	1	no	—
375	C₄⋊Q₈	—	61	2	no	—
376	C₄⋊Q₈	—	61	1	no	—
377	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
378	#127	—	61	2	no	—
379	#126	—	61	2	no	—
380	#126	—	61	2	no	—
381	#126	—	61	2	no	—
382	#126	—	61	2	no	—
383	#126	—	61	2	no	—
384	#126	C₂×D₆₁	1	2	yes	complemented
385	#124	—	61	2	no	—
386	#124	—	61	2	no	—
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	#124	—	61	2	no	—
393	#124	—	61	2	no	—
394	#124	—	61	2	no	—
395	#124	—	61	1	no	—
396	#124	—	61	2	no	—
397	#124	C₂×D₆₁	1	1	yes	characteristic, complemented
398	#124	C₂×D₆₁	1	2	yes	complemented
399	#123	—	61	2	no	—
400	#123	—	61	2	no	—
401	#123	—	61	2	no	—
402	#123	—	61	1	no	—
403	#123	—	61	1	no	—
404	#123	—	61	2	no	—
405	#123	—	61	2	no	—
406	#123	—	61	2	no	—
407	#123	—	61	2	no	—
408	#123	C₂×D₆₁	1	2	yes	complemented
409	C₂²⋊Q₈	—	61	1	no	—
410	C₂²⋊Q₈	—	61	1	no	—
411	C₂²⋊Q₈	—	61	1	no	—
412	C₂²⋊Q₈	—	61	1	no	—
413	C₂²⋊Q₈	—	61	1	no	—
414	C₂²⋊Q₈	—	61	1	no	—
415	C₂²⋊Q₈	—	61	1	no	—
416	C₂²⋊Q₈	—	61	2	no	—
417	C₂²⋊Q₈	—	61	2	no	—
418	C₂²⋊Q₈	—	61	2	no	—
419	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	C₂×D₆₁	1	2	yes	complemented
421	#121	—	61	1	no	—
422	#121	—	61	1	no	—
423	#121	—	61	1	no	—
424	#121	—	61	2	no	—
425	#121	—	61	2	no	—
426	#121	—	61	1	no	—
427	#121	—	61	1	no	—
428	#121	—	61	1	no	—
429	#121	—	61	1	no	—
430	#121	—	61	2	no	—
431	#121	—	61	2	no	—
432	#121	—	61	2	no	—
433	#121	—	61	2	no	—
434	#121	C₂×D₆₁	1	1	yes	characteristic
435	#120	—	61	2	no	—
436	#120	—	61	2	no	—
437	#120	—	61	1	no	—
438	#120	—	61	2	no	—
439	#120	—	61	1	no	—
440	#120	—	61	2	no	—
441	#120	—	61	2	no	—
442	#120	—	61	2	no	—
443	C₄×Q₈	—	61	2	no	—
444	C₄×Q₈	—	61	1	no	—
445	C₄×Q₈	—	61	2	no	—
446	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
447	C₄×D₄	—	61	2	no	—
448	C₄×D₄	—	61	2	no	—
449	C₄×D₄	—	61	2	no	—
450	C₄×D₄	—	61	2	no	—
451	C₄×D₄	—	61	2	no	—
452	C₄×D₄	—	61	1	no	—
453	C₄×D₄	—	61	1	no	—
454	C₄×D₄	—	61	1	no	—
455	C₄×D₄	—	61	1	no	—
456	C₄×D₄	—	61	2	no	—
457	C₄×D₄	—	61	1	no	—
458	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic, complemented
459	#117	—	61	2	no	—
460	#117	—	61	1	no	—
461	#117	—	61	1	no	—
462	#117	—	61	1	no	—
463	#117	—	61	1	no	—
464	#117	—	61	2	no	—
465	#117	C₂×D₆₁	1	1	yes	characteristic, complemented
466	C₂×C₂²⋊C₄	—	61	2	no	—
467	C₂×C₂²⋊C₄	—	61	2	no	—
468	C₂⁴	—	61	2	no	—
469	C₂⁴	—	61	1	no	—
470	#41	—	244	2	no	—
471	#41	—	244	2	no	—
472	#41	—	244	2	no	—
473	C₂×Q₈	—	61	1	no	—
474	C₂×Q₈	—	61	2	no	—
475	C₂×Q₈	—	61	2	no	—
476	C₂×Q₈	—	61	1	no	—
477	C₂×Q₈	—	244	2	no	—
478	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
480	C₂×D₄	—	61	2	no	—
481	C₂×D₄	—	61	2	no	—
482	C₂×D₄	—	61	2	no	—
483	C₂×D₄	—	61	1	no	—
484	C₂×D₄	—	61	2	no	—
485	C₂×D₄	—	61	1	no	—
486	C₂×D₄	—	61	2	no	—
487	C₂×D₄	—	61	1	no	—
488	C₂×D₄	—	61	1	no	—
489	C₂×D₄	—	61	1	no	—
490	C₂×D₄	—	61	2	no	—
491	C₂×D₄	—	61	1	no	—
492	C₂×D₄	—	61	1	no	—
493	C₂×D₄	—	61	2	no	—
494	C₂×D₄	—	61	1	no	—
495	C₂×D₄	—	61	2	no	—
496	C₂×D₄	—	244	2	no	—
497	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₆₁	1	2	yes	—
499	C₂²×C₄	—	61	2	no	—
500	C₂²×C₄	—	61	1	no	—
501	C₂²×C₄	—	61	1	no	—
502	C₂²×C₄	—	61	1	no	—
503	C₂²×C₄	—	61	1	no	—
504	C₂²×C₄	—	61	1	no	—
505	C₂²×C₄	—	61	2	no	—
506	C₂²×C₄	—	61	2	no	—
507	C₂²×C₄	—	61	2	no	—
508	C₂²×C₄	—	61	1	no	—
509	C₂²×C₄	—	61	1	no	—
510	C₂²×C₄	—	244	2	no	—
511	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
513	C₄⋊C₄	—	61	2	no	—
514	C₄⋊C₄	—	61	2	no	—
515	C₄⋊C₄	—	61	2	no	—
516	C₄⋊C₄	—	61	2	no	—
517	C₄⋊C₄	—	61	1	no	—
518	C₄⋊C₄	—	61	1	no	—
519	C₄⋊C₄	—	61	1	no	—
520	C₄⋊C₄	—	61	1	no	—
521	C₄⋊C₄	—	61	2	no	—
522	C₄⋊C₄	—	61	2	no	—
523	C₄⋊C₄	—	61	1	no	—
524	C₄⋊C₄	—	61	1	no	—
525	C₄⋊C₄	—	61	2	no	—
526	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
529	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
532	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
533	C₂²⋊C₄	—	61	2	no	—
534	C₂²⋊C₄	—	61	2	no	—
535	C₂²⋊C₄	—	61	2	no	—
536	C₂²⋊C₄	—	61	1	no	—
537	C₂²⋊C₄	—	61	1	no	—
538	C₂²⋊C₄	—	61	2	no	—
539	C₂²⋊C₄	—	61	2	no	—
540	C₂²⋊C₄	—	61	2	no	—
541	C₂²⋊C₄	—	61	2	no	—
542	C₂²⋊C₄	—	61	2	no	—
543	C₂²⋊C₄	—	61	2	no	—
544	C₂²⋊C₄	—	61	2	no	—
545	C₂²⋊C₄	—	61	2	no	—
546	C₂²⋊C₄	—	61	2	no	—
547	C₂²⋊C₄	—	61	1	no	—
548	C₂²⋊C₄	—	61	1	no	—
549	C₂²⋊C₄	—	61	1	no	—
550	C₂²⋊C₄	—	61	1	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	1	no	—
557	C₂²⋊C₄	—	61	2	no	—
558	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
565	C₄²	—	61	2	no	—
566	C₄²	—	61	2	no	—
567	C₄²	—	61	2	no	—
568	C₄²	—	61	2	no	—
569	C₄²	—	61	2	no	—
570	C₄²	C₂²×D₆₁	1	1	yes	characteristic
571	C₄²	C₂²×D₆₁	1	1	yes	characteristic
572	C₄²	C₂²×D₆₁	1	2	yes	—
573	C₂³	—	61	1	no	—
574	C₂³	—	61	1	no	—
575	C₂³	—	61	1	no	—
576	C₂³	—	61	2	no	—
577	C₂³	—	61	1	no	—
578	C₂³	—	244	2	no	—
579	C₂³	—	244	2	no	—
580	C₂³	—	244	2	no	—
581	C₂³	—	244	1	no	—
582	C₂³	—	244	1	no	—
583	C₂³	—	244	1	no	—
584	C₂³	C₂³×D₆₁	1	1	yes	characteristic
585	C₂³	C₂³×D₆₁	1	2	yes	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	122	2	no	—
589	Q₈	—	244	2	no	—
590	Q₈	—	244	2	no	—
591	Q₈	—	244	1	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	122	2	no	—
595	D₄	—	244	1	no	—
596	D₄	—	244	2	no	—
597	D₄	—	244	2	no	—
598	D₄	—	244	1	no	—
599	D₄	—	244	1	no	—
600	D₄	—	244	1	no	—
601	D₄	—	244	1	no	—
602	D₄	—	244	2	no	—
603	D₄	—	244	2	no	—
604	D₄	—	244	2	no	—
605	D₄	—	244	2	no	—
606	D₄	—	244	2	no	—
607	D₄	—	244	1	no	—
608	D₄	—	244	1	no	—
609	D₄	—	244	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	61	2	no	—
613	C₂×C₄	—	61	2	no	—
614	C₂×C₄	—	61	1	no	—
615	C₂×C₄	—	61	1	no	—
616	C₂×C₄	—	61	1	no	—
617	C₂×C₄	—	61	1	no	—
618	C₂×C₄	—	61	2	no	—
619	C₂×C₄	—	122	2	no	—
620	C₂×C₄	—	122	2	no	—
621	C₂×C₄	—	122	2	no	—
622	C₂×C₄	—	122	2	no	—
623	C₂×C₄	—	244	2	no	—
624	C₂×C₄	—	244	1	no	—
625	C₂×C₄	—	244	1	no	—
626	C₂×C₄	—	244	2	no	—
627	C₂×C₄	—	244	2	no	—
628	C₂×C₄	—	244	1	no	—
629	C₂×C₄	—	244	2	no	—
630	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₆₁	1	2	yes	—
632	C₂×C₄	C₂³×D₆₁	1	2	yes	—
633	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₆₁	1	2	yes	—
637	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	122	1	no	—
646	C₂²	—	122	1	no	—
647	C₂²	—	122	1	no	—
648	C₂²	—	122	1	no	—
649	C₂²	—	122	2	no	—
650	C₂²	—	122	1	no	—
651	C₂²	—	122	2	no	—
652	C₂²	—	122	1	no	—
653	C₂²	—	122	1	no	—
654	C₂²	—	122	1	no	—
655	C₂²	—	122	2	no	—
656	C₂²	—	122	1	no	—
657	C₂²	—	122	1	no	—
658	C₂²	—	122	1	no	—
659	C₂²	—	122	1	no	—
660	C₂²	—	488	4	no	—
661	C₂²	—	244	4	no	—
662	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	122	1	no	—
672	C₄	—	122	1	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	#14519823	1	2	yes	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	244	1	no	—
682	C₂	—	244	2	no	—
683	C₂	—	244	1	no	—
684	C₂	—	244	1	no	—
685	C₂	—	244	1	no	—
686	C₂	C₂×#14519823	1	1	yes	characteristic
687	C₂	#16840597	1	1	yes	characteristic
688	C₂	#16840599	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#542	C₂
hypercenter	#542	D₆₁
hypocenter	C₆₁	#3540
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #16840504	C₂	semidirect
2. #16840502	C₂	semidirect
3. #16840494	C₂	semidirect
4. #16840486	C₂	semidirect
5. #16840485	C₂	semidirect
6. #16840478	C₂	semidirect
7. #16840477	C₂	semidirect
8. #16840435	C₂	semidirect
9. #16840424	C₂	semidirect
10. #16840420	C₂	semidirect
11. #16840407	C₂	semidirect
12. #16840405	C₂	semidirect
13. #16840385	C₂	semidirect
14. #16840383	C₂	semidirect
15. #16840378	C₂	semidirect
16. #16840352	C₂	semidirect
17. #16840351	C₂	semidirect
18. #16840335	C₂	semidirect
19. #16840328	C₂	semidirect
20. #16840275	C₂	semidirect
21. #16840274	C₂	semidirect
22. #16840272	C₂	semidirect
23. C₆₁×#542	C₂	semidirect
27. C₂×Q₈×D₆₁	C₂²	semidirect
28. C₂×D₄×D₆₁	C₂²	semidirect
29. C₂²×C₄×D₆₁	C₂²	semidirect
30. #14519777	C₂²	semidirect
31. #14519776	C₂²	semidirect
33. #14519772	C₂²	semidirect
34. #14519772	C₂²	semidirect
35. #14519772	C₂²	semidirect
36. #14519772	C₂²	semidirect
37. #14519772	C₂²	semidirect
39. #14519766	C₂²	semidirect
40. #14519766	C₂²	semidirect
42. #14519765	C₂²	semidirect
43. #14519765	C₂²	semidirect
45. #14519763	C₂²	semidirect
46. #14519763	C₂²	semidirect
47. #14519763	C₂²	semidirect
48. #14519763	C₂²	semidirect
49. #14519763	C₂²	semidirect
50. #14519762	C₂²	semidirect
51. #14519762	C₂²	semidirect
53. #14519761	C₂²	semidirect
54. #14519761	C₂²	semidirect
55. #14519759	C₂²	semidirect
56. #14519759	C₂²	semidirect
57. #14519759	C₂²	semidirect
58. #14519759	C₂²	semidirect
59. #14519757	C₂²	semidirect
60. #14519757	C₂²	semidirect
61. #14519757	C₂²	semidirect
62. #14519757	C₂²	semidirect
63. #14519757	C₂²	semidirect
64. #14519756	C₂²	semidirect
65. #14519755	C₂²	semidirect
66. #14519754	C₂²	semidirect
67. #14519753	C₂²	semidirect
68. #14519753	C₂²	semidirect
72. #14519752	C₂²	semidirect
73. #14519752	C₂²	semidirect
74. #14519752	C₂²	semidirect
77. #14519751	C₂²	semidirect
79. #14519750	C₂²	semidirect
81. #14519748	C₂²	semidirect
85. #14519747	C₂²	semidirect
86. #14519747	C₂²	semidirect
87. #14519747	C₂²	semidirect
89. #14519745	C₂²	semidirect
90. Q₈×Dic₆₁	C₂²	semidirect
91. C₄×Dic₁₂₂	C₂²	semidirect
92. C₄×Dic₁₂₂	C₂²	semidirect
95. C₄×D₂₄₄	C₂²	semidirect
96. C₄×D₂₄₄	C₂²	semidirect
97. C₄×D₂₄₄	C₂²	semidirect
98. C₄×D₂₄₄	C₂²	semidirect
99. D₄×Dic₆₁	C₂²	semidirect
100. #14519739	C₂²	semidirect
101. #14519737	C₂²	semidirect
102. #14519737	C₂²	semidirect
103. #14519737	C₂²	semidirect
104. #14519736	C₂²	semidirect
105. #14519735	C₂²	semidirect
106. #14519735	C₂²	semidirect
107. #14519735	C₂²	semidirect
108. #14519735	C₂²	semidirect
109. #14519735	C₂²	semidirect
110. C₂×#11758198	C₂²	semidirect
111. C₂²⋊C₄×D₆₁	C₂²	semidirect
112. C₄⋊Q₈×C₆₁	C₂²	semidirect
113. #126×C₆₁	C₂²	semidirect
114. #124×C₆₁	C₂²	semidirect
115. #124×C₆₁	C₂²	semidirect
116. #123×C₆₁	C₂²	semidirect
117. C₂²⋊Q₈×C₆₁	C₂²	semidirect
118. C₂²⋊Q₈×C₆₁	C₂²	semidirect
120. C₄×Q₈×C₆₁	C₂²	semidirect
121. C₄×D₄×C₆₁	C₂²	semidirect
122. #117×C₆₁	C₂²	semidirect
360. #542	D₆₁	semidirect
368. C₆₁	#3540	semidirect
377. C₄⋊Q₈	C₂×D₆₁	semidirect
384. #126	C₂×D₆₁	semidirect
397. #124	C₂×D₆₁	semidirect
398. #124	C₂×D₆₁	semidirect
408. #123	C₂×D₆₁	semidirect
419. C₂²⋊Q₈	C₂×D₆₁	semidirect
420. C₂²⋊Q₈	C₂×D₆₁	semidirect
446. C₄×Q₈	C₂×D₆₁	semidirect
458. C₄×D₄	C₂×D₆₁	semidirect
465. #117	C₂×D₆₁	semidirect