Subgroups — #21460191

Order 7808.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840500	C₂	1	4	yes	maximal, complemented
2	#16840482	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840458	C₂	1	2	yes	maximal, complemented
4	#16840433	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840430	C₂	1	2	yes	maximal, complemented
6	#16840416	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840409	C₂	1	2	yes	maximal, complemented
8	#16840408	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₄₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#16840386	C₂	1	2	yes	maximal, complemented
11	#16840346	C₂	1	4	yes	maximal, complemented
12	#16840340	C₂	1	2	yes	maximal, complemented
13	#16840326	C₂	1	2	yes	maximal, complemented
14	#16840325	C₂	1	2	yes	maximal, complemented
15	#16840312	C₂	1	1	yes	maximal, characteristic, complemented
16	#16840296	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11758222	C₂²	1	2	yes	complemented
19	C₂×#11758222	C₂²	1	2	yes	complemented
20	C₂×#11758224	C₂²	1	2	yes	complemented
21	C₂²×D₂₄₄	C₂²	1	2	yes	—
22	C₂×D₄×D₆₁	C₂²	1	2	yes	—
23	#14519777	C₂²	1	1	yes	characteristic, complemented
24	#14519774	C₂²	1	1	yes	characteristic
25	#14519773	C₂²	1	4	yes	complemented
26	#14519773	C₂²	1	2	yes	complemented
27	#14519772	C₂²	1	4	yes	complemented
28	#14519771	C₂²	1	2	yes	complemented
29	#14519770	C₂²	1	4	yes	complemented
30	#14519769	C₂²	1	1	yes	characteristic, complemented
31	#14519766	C₂²	1	4	yes	complemented
32	#14519765	C₂²	1	1	yes	characteristic
33	#14519765	C₂²	1	2	yes	complemented
34	#14519764	C₂²	1	2	yes	—
35	#14519762	C₂²	1	4	yes	complemented
36	#14519761	C₂²	1	4	yes	complemented
37	#14519760	C₂²	1	2	yes	complemented
38	#14519759	C₂²	1	4	yes	complemented
39	#14519757	C₂²	1	2	yes	complemented
40	#14519756	C₂²	1	2	yes	complemented
41	#14519756	C₂²	1	1	yes	characteristic, complemented
42	#14519753	C₂²	1	4	yes	complemented
43	#14519752	C₂²	1	2	yes	—
44	#14519751	C₂²	1	2	yes	—
45	#14519751	C₂²	1	1	yes	characteristic
46	#14519751	C₂²	1	2	yes	—
47	#14519751	C₂²	1	2	yes	complemented
48	#14519751	C₂²	1	2	yes	complemented
49	#14519751	C₂²	1	2	yes	complemented
50	#14519750	C₂²	1	4	yes	complemented
51	#14519750	C₂²	1	4	yes	complemented
52	#14519749	C₂²	1	4	yes	complemented
53	#14519749	C₂²	1	4	yes	complemented
54	#14519749	C₂²	1	4	yes	complemented
55	#14519748	C₂²	1	4	yes	complemented
56	#14519747	C₂²	1	4	yes	—
57	#14519745	C₂²	1	4	yes	complemented
58	#14519745	C₂²	1	4	yes	complemented
59	#14519745	C₂²	1	4	yes	complemented
60	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
61	#14519742	C₂²	1	2	yes	complemented
62	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
63	C₄×D₂₄₄	C₂²	1	2	yes	complemented
64	C₄×D₂₄₄	C₂²	1	2	yes	complemented
65	#14519739	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
67	#14519737	C₂²	1	4	yes	complemented
68	#14519736	C₂²	1	2	yes	complemented
69	#14519734	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₆₁	C₂²	1	4	yes	complemented
72	C₂×#41×C₆₁	C₂²	1	2	yes	complemented
73	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
74	#127×C₆₁	C₂²	1	1	yes	characteristic
75	#124×C₆₁	C₂²	1	2	yes	complemented
76	#121×C₆₁	C₂²	1	1	yes	characteristic
77	#121×C₆₁	C₂²	1	2	yes	complemented
78	#121×C₆₁	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
81	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₆₁	C₂³	1	4	yes	—
84	#41×C₆₁	—	4	4	no	—
85	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
86	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₆₁	C₂³	1	2	yes	—
89	C₂×D₄×C₆₁	C₂³	1	2	yes	—
90	C₂×D₄×C₆₁	C₂³	1	2	yes	—
91	C₂×D₄×C₆₁	C₂³	1	2	yes	—
92	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
93	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
95	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₆₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₆₁	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₆₁	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₆₁	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₆₁	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
103	C₂²×Dic₆₁	C₂³	1	4	yes	—
104	#11758224	—	4	4	no	—
105	D₄×D₆₁	—	4	4	no	—
106	#11758222	—	4	4	no	—
107	#11758222	—	4	4	no	—
108	C₂×D₂₄₄	—	4	4	no	—
109	C₂×D₂₄₄	C₂³	1	2	yes	—
110	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
111	C₂×D₂₄₄	C₂³	1	2	yes	—
112	C₂×D₂₄₄	C₂³	1	4	yes	—
113	C₂×D₂₄₄	C₂³	1	2	yes	—
114	C₂×C₄×D₆₁	C₂³	1	2	yes	—
115	C₂×C₄×D₆₁	C₂³	1	4	yes	—
116	C₂×C₄×D₆₁	C₂³	1	4	yes	—
117	C₂×Dic₁₂₂	C₂³	1	2	yes	—
118	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
126	C₄²×C₆₁	C₂³	1	1	yes	characteristic
127	C₄²×C₆₁	C₂³	1	1	yes	characteristic
128	C₄²×C₆₁	C₂³	1	1	yes	characteristic
129	C₄²×C₆₁	C₂³	1	1	yes	characteristic
130	C₂²⋊Dic₆₁	C₂³	1	4	yes	—
131	C₂²⋊Dic₆₁	C₂³	1	4	yes	—
132	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
133	#11758198	C₂³	1	2	yes	—
134	#11758198	C₂³	1	4	yes	—
135	#11758198	C₂³	1	2	yes	—
136	#11758198	C₂³	1	2	yes	—
137	#11758198	C₂³	1	4	yes	—
138	#11758198	C₂³	1	4	yes	—
139	#11758198	C₂³	1	2	yes	—
140	#11758198	C₂³	1	4	yes	—
141	#11758198	C₂³	1	4	yes	—
142	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₆₁	C₂³	1	2	yes	—
144	C₄⋊Dic₆₁	C₂³	1	4	yes	—
145	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₆₁	C₂³	1	2	yes	—
147	#11758196	C₂³	1	2	yes	—
148	#11758196	C₂³	1	2	yes	—
149	#11758196	C₂³	1	2	yes	—
150	#11758196	C₂³	1	4	yes	—
151	#11758196	C₂³	1	2	yes	—
152	C₄×Dic₆₁	C₂³	1	2	yes	—
153	C₄×Dic₆₁	C₂³	1	4	yes	—
154	C₂³×C₆₁	C₂⁴	1	2	yes	—
155	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
156	C₂³×C₆₁	C₂⁴	1	2	yes	—
157	C₂²×D₆₁	—	4	4	no	—
158	C₂²×D₆₁	—	4	4	no	—
159	C₂²×D₆₁	—	4	4	no	—
160	C₂²×D₆₁	C₂⁴	1	2	yes	—
161	C₂²×D₆₁	C₂⁴	1	4	yes	—
162	Q₈×C₆₁	—	4	2	no	—
163	D₄×C₆₁	—	2	2	no	—
164	D₄×C₆₁	—	2	2	no	—
165	D₄×C₆₁	—	4	2	no	—
166	D₄×C₆₁	—	4	2	no	—
167	D₄×C₆₁	—	4	2	no	—
168	D₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	2	4	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
175	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
180	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₆₁	—	4	4	no	—
183	C₂²⋊D₆₁	—	4	4	no	—
184	C₂²⋊D₆₁	—	4	4	no	—
185	C₂²⋊D₆₁	—	4	4	no	—
186	C₂²⋊D₆₁	—	4	4	no	—
187	C₂²⋊D₆₁	—	4	2	no	—
188	C₂×Dic₆₁	—	4	4	no	—
189	C₂×Dic₆₁	C₂⁴	1	2	yes	—
190	C₂×Dic₆₁	C₂⁴	1	2	yes	—
191	C₂×Dic₆₁	C₂⁴	1	4	yes	—
192	C₂×Dic₆₁	C₂⁴	1	2	yes	—
193	D₂₄₄	—	2	2	no	—
194	D₂₄₄	—	2	4	no	—
195	D₂₄₄	—	2	4	no	—
196	D₂₄₄	—	4	4	no	—
197	D₂₄₄	—	4	2	no	—
198	C₄×D₆₁	—	2	4	no	—
199	C₄×D₆₁	—	4	4	no	—
200	C₄×D₆₁	—	4	4	no	—
201	Dic₁₂₂	—	2	2	no	—
202	Dic₁₂₂	—	2	4	no	—
203	C₂²×C₆₁	—	2	2	no	—
204	C₂²×C₆₁	—	2	1	no	—
205	C₂²×C₆₁	—	2	2	no	—
206	C₂²×C₆₁	—	2	2	no	—
207	C₂²×C₆₁	—	2	1	no	—
208	C₂²×C₆₁	—	2	2	no	—
209	C₂²×C₆₁	—	2	1	no	—
210	C₂²×C₆₁	—	2	2	no	—
211	C₂²×C₆₁	—	2	2	no	—
212	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
213	C₂×D₆₁	—	2	2	no	—
214	C₂×D₆₁	—	2	4	no	—
215	C₂×D₆₁	—	2	4	no	—
216	C₂×D₆₁	—	2	2	no	—
217	C₂×D₆₁	—	2	4	no	—
218	C₂×D₆₁	—	2	2	no	—
219	C₂×D₆₁	—	8	8	no	—
220	C₄×C₆₁	—	2	1	no	—
221	C₄×C₆₁	—	2	2	no	—
222	C₄×C₆₁	—	2	2	no	—
223	C₄×C₆₁	—	2	1	no	—
224	C₄×C₆₁	—	2	1	no	—
225	C₄×C₆₁	—	2	1	no	—
226	C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
227	C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
228	Dic₆₁	—	2	2	no	—
229	Dic₆₁	—	2	4	no	—
230	Dic₆₁	—	2	2	no	—
231	Dic₆₁	—	2	2	no	—
232	#3546	—	61	1	no	maximal, Sylow
233	C₂×C₆₁	—	4	2	no	—
234	C₂×C₆₁	—	4	2	no	—
235	C₂×C₆₁	—	4	1	no	—
236	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₆₁	#585	1	1	yes	characteristic
239	D₆₁	—	4	4	no	—
240	D₆₁	—	4	2	no	—
241	#560	—	61	4	no	—
242	#556	—	61	1	no	—
243	#553	—	61	2	no	—
244	#550	—	61	2	no	—
245	#550	—	61	1	no	—
246	#547	—	61	1	no	—
247	#546	—	61	2	no	—
248	#546	—	61	2	no	—
249	D₄²	—	61	1	no	—
250	#542	—	61	2	no	—
251	#538	—	61	4	no	—
252	#537	—	61	2	no	—
253	#535	—	61	2	no	—
254	#535	—	61	2	no	—
255	#532	—	61	1	no	—
256	#532	D₆₁	1	1	yes	characteristic, complemented
257	#529	—	61	1	no	—
258	C₆₁	#3546	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	61	2	no	—
260	C₂×#41	—	61	2	no	—
261	C₂×#41	—	61	2	no	—
262	C₂×#41	C₂×D₆₁	1	2	yes	complemented
263	C₂²×D₄	—	61	2	no	—
264	C₂²×D₄	—	61	2	no	—
265	C₄⋊Q₈	—	61	1	no	—
266	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
267	#127	—	61	2	no	—
268	#127	—	61	4	no	—
269	#127	—	61	1	no	—
270	#127	C₂×D₆₁	1	1	yes	characteristic
271	#126	—	61	4	no	—
272	#126	—	61	4	no	—
273	#126	—	61	2	no	—
274	#125	—	61	1	no	—
275	#124	—	61	4	no	—
276	#124	—	61	2	no	—
277	#124	—	61	1	no	—
278	#124	—	61	2	no	—
279	#124	C₂×D₆₁	1	2	yes	complemented
280	#123	—	61	2	no	—
281	#123	—	61	4	no	—
282	#123	—	61	4	no	—
283	#123	—	61	4	no	—
284	C₂²⋊Q₈	—	61	4	no	—
285	C₂²⋊Q₈	—	61	1	no	—
286	C₂²⋊Q₈	—	61	2	no	—
287	C₂²⋊Q₈	—	61	2	no	—
288	#121	—	61	4	no	—
289	#121	—	61	4	no	—
290	#121	—	61	4	no	—
291	#121	—	61	4	no	—
292	#121	—	61	1	no	—
293	#121	—	61	2	no	—
294	#121	—	61	2	no	—
295	#121	—	61	2	no	—
296	#121	—	61	2	no	—
297	#121	—	61	2	no	—
298	#121	—	61	2	no	—
299	#121	—	61	4	no	—
300	#121	—	61	4	no	—
301	#121	C₂×D₆₁	1	1	yes	characteristic
302	#121	C₂×D₆₁	1	1	yes	characteristic, complemented
303	#121	C₂×D₆₁	1	2	yes	complemented
304	#120	—	61	4	no	—
305	#120	—	61	4	no	—
306	#120	—	61	4	no	—
307	#120	—	61	4	no	—
308	C₄×Q₈	—	61	2	no	—
309	C₄×Q₈	—	61	1	no	—
310	C₄×D₄	—	61	2	no	—
311	C₄×D₄	—	61	2	no	—
312	C₄×D₄	—	61	4	no	—
313	C₄×D₄	—	61	1	no	—
314	C₄×D₄	—	61	2	no	—
315	C₄×D₄	—	61	2	no	—
316	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
317	C₄×D₄	C₂×D₆₁	1	2	yes	complemented
318	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic, complemented
319	#117	—	61	2	no	—
320	#117	—	61	2	no	—
321	C₂×C₄⋊C₄	—	61	2	no	—
322	C₂×C₂²⋊C₄	—	61	4	no	—
323	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic, complemented
324	C₂⁴	—	61	4	no	—
325	#41	—	4	4	no	—
326	#41	—	244	4	no	—
327	#41	—	244	4	no	—
328	#41	—	244	4	no	—
329	C₂×Q₈	—	61	1	no	—
330	C₂×Q₈	—	61	2	no	—
331	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
332	C₂×D₄	—	61	2	no	—
333	C₂×D₄	—	61	4	no	—
334	C₂×D₄	—	61	4	no	—
335	C₂×D₄	—	61	4	no	—
336	C₂×D₄	—	61	4	no	—
337	C₂×D₄	—	61	4	no	—
338	C₂×D₄	—	61	1	no	—
339	C₂×D₄	—	61	2	no	—
340	C₂×D₄	—	61	2	no	—
341	C₂×D₄	—	61	2	no	—
342	C₂×D₄	—	61	4	no	—
343	C₂×D₄	—	244	4	no	—
344	C₂×D₄	—	244	4	no	—
345	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
346	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
347	C₂×D₄	C₂²×D₆₁	1	2	yes	—
348	C₂×D₄	C₂²×D₆₁	1	2	yes	—
349	C₂×D₄	C₂²×D₆₁	1	2	yes	—
350	C₂×D₄	C₂²×D₆₁	1	2	yes	—
351	C₂²×C₄	—	61	4	no	—
352	C₂²×C₄	—	61	2	no	—
353	C₂²×C₄	—	61	4	no	—
354	C₂²×C₄	—	61	4	no	—
355	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
356	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
357	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
358	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
359	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
360	C₄⋊C₄	—	61	1	no	—
361	C₄⋊C₄	—	61	2	no	—
362	C₄⋊C₄	—	61	4	no	—
363	C₄⋊C₄	—	61	2	no	—
364	C₄⋊C₄	—	61	2	no	—
365	C₄⋊C₄	—	61	2	no	—
366	C₄⋊C₄	—	61	4	no	—
367	C₄⋊C₄	—	61	2	no	—
368	C₄⋊C₄	—	61	1	no	—
369	C₄⋊C₄	—	61	2	no	—
370	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
373	C₂²⋊C₄	—	61	4	no	—
374	C₂²⋊C₄	—	61	4	no	—
375	C₂²⋊C₄	—	61	2	no	—
376	C₂²⋊C₄	—	61	2	no	—
377	C₂²⋊C₄	—	61	4	no	—
378	C₂²⋊C₄	—	61	2	no	—
379	C₂²⋊C₄	—	61	2	no	—
380	C₂²⋊C₄	—	61	2	no	—
381	C₂²⋊C₄	—	61	4	no	—
382	C₂²⋊C₄	—	61	4	no	—
383	C₂²⋊C₄	—	61	4	no	—
384	C₂²⋊C₄	—	61	4	no	—
385	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
387	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
388	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
389	C₄²	—	61	2	no	—
390	C₄²	—	61	4	no	—
391	C₄²	C₂²×D₆₁	1	1	yes	characteristic
392	C₄²	C₂²×D₆₁	1	1	yes	characteristic
393	C₄²	C₂²×D₆₁	1	1	yes	characteristic
394	C₄²	C₂²×D₆₁	1	1	yes	characteristic
395	C₂³	—	61	2	no	—
396	C₂³	—	61	4	no	—
397	C₂³	—	244	4	no	—
398	C₂³	—	244	4	no	—
399	C₂³	—	244	4	no	—
400	C₂³	C₂³×D₆₁	1	2	yes	—
401	C₂³	C₂³×D₆₁	1	1	yes	characteristic
402	C₂³	C₂³×D₆₁	1	2	yes	—
403	Q₈	—	4	2	no	—
404	Q₈	—	122	2	no	—
405	Q₈	—	122	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	122	2	no	—
413	D₄	—	122	4	no	—
414	D₄	—	122	4	no	—
415	D₄	—	244	2	no	—
416	D₄	—	244	4	no	—
417	D₄	—	244	2	no	—
418	D₄	—	244	4	no	—
419	D₄	—	244	4	no	—
420	D₄	—	244	4	no	—
421	D₄	—	244	4	no	—
422	D₄	—	244	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	61	2	no	—
429	C₂×C₄	—	61	2	no	—
430	C₂×C₄	—	61	4	no	—
431	C₂×C₄	—	61	2	no	—
432	C₂×C₄	—	122	4	no	—
433	C₂×C₄	—	244	4	no	—
434	C₂×C₄	—	244	4	no	—
435	C₂×C₄	—	244	4	no	—
436	C₂×C₄	C₂³×D₆₁	1	2	yes	—
437	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
441	C₂×C₄	C₂³×D₆₁	1	2	yes	—
442	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
443	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
444	C₂²	—	2	1	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	122	4	no	—
454	C₂²	—	122	2	no	—
455	C₂²	—	122	2	no	—
456	C₂²	—	122	4	no	—
457	C₂²	—	122	4	no	—
458	C₂²	—	122	2	no	—
459	C₂²	—	488	8	no	—
460	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	122	2	no	—
468	C₄	—	122	2	no	—
469	C₄	—	122	4	no	—
470	C₄	—	122	2	no	—
471	C₄	#14519822	1	2	yes	—
472	C₄	#14519823	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	4	2	no	—
476	C₂	—	244	2	no	—
477	C₂	—	244	4	no	—
478	C₂	C₂×#14519822	1	1	yes	characteristic
479	C₂	C₂×#14519823	1	1	yes	characteristic
480	C₂	#16840598	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#532	C₂
hypercenter	#532	D₆₁
hypocenter	C₆₁	#3546
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #16840500	C₂	semidirect
2. #16840482	C₂	semidirect
3. #16840458	C₂	semidirect
4. #16840433	C₂	semidirect
5. #16840430	C₂	semidirect
6. #16840416	C₂	semidirect
7. #16840409	C₂	semidirect
8. #16840408	C₂	semidirect
9. D₄×D₂₄₄	C₂	semidirect
10. #16840386	C₂	semidirect
11. #16840346	C₂	semidirect
12. #16840340	C₂	semidirect
13. #16840326	C₂	semidirect
14. #16840325	C₂	semidirect
15. #16840312	C₂	semidirect
16. #16840296	C₂	semidirect
17. C₆₁×#532	C₂	semidirect
18. C₂×#11758222	C₂²	semidirect
19. C₂×#11758222	C₂²	semidirect
20. C₂×#11758224	C₂²	semidirect
23. #14519777	C₂²	semidirect
25. #14519773	C₂²	semidirect
26. #14519773	C₂²	semidirect
27. #14519772	C₂²	semidirect
28. #14519771	C₂²	semidirect
29. #14519770	C₂²	semidirect
30. #14519769	C₂²	semidirect
31. #14519766	C₂²	semidirect
33. #14519765	C₂²	semidirect
35. #14519762	C₂²	semidirect
36. #14519761	C₂²	semidirect
37. #14519760	C₂²	semidirect
38. #14519759	C₂²	semidirect
39. #14519757	C₂²	semidirect
40. #14519756	C₂²	semidirect
41. #14519756	C₂²	semidirect
42. #14519753	C₂²	semidirect
47. #14519751	C₂²	semidirect
48. #14519751	C₂²	semidirect
49. #14519751	C₂²	semidirect
50. #14519750	C₂²	semidirect
51. #14519750	C₂²	semidirect
52. #14519749	C₂²	semidirect
53. #14519749	C₂²	semidirect
54. #14519749	C₂²	semidirect
55. #14519748	C₂²	semidirect
57. #14519745	C₂²	semidirect
58. #14519745	C₂²	semidirect
59. #14519745	C₂²	semidirect
60. C₄×Dic₁₂₂	C₂²	semidirect
61. #14519742	C₂²	semidirect
63. C₄×D₂₄₄	C₂²	semidirect
64. C₄×D₂₄₄	C₂²	semidirect
65. #14519739	C₂²	semidirect
66. C₄×C₂²⋊D₆₁	C₂²	semidirect
67. #14519737	C₂²	semidirect
68. #14519736	C₂²	semidirect
69. #14519734	C₂²	semidirect
70. C₂×C₄⋊Dic₆₁	C₂²	semidirect
71. C₂²⋊C₄×D₆₁	C₂²	semidirect
72. C₂×#41×C₆₁	C₂²	semidirect
73. C₄⋊Q₈×C₆₁	C₂²	semidirect
75. #124×C₆₁	C₂²	semidirect
77. #121×C₆₁	C₂²	semidirect
78. #121×C₆₁	C₂²	semidirect
80. C₄×D₄×C₆₁	C₂²	semidirect
81. C₄×D₄×C₆₁	C₂²	semidirect
82. C₂×C₄²×C₆₁	C₂²	semidirect
256. #532	D₆₁	semidirect
258. C₆₁	#3546	semidirect
262. C₂×#41	C₂×D₆₁	semidirect
266. C₄⋊Q₈	C₂×D₆₁	semidirect
279. #124	C₂×D₆₁	semidirect
302. #121	C₂×D₆₁	semidirect
303. #121	C₂×D₆₁	semidirect
317. C₄×D₄	C₂×D₆₁	semidirect
318. C₄×D₄	C₂×D₆₁	semidirect
323. C₂×C₄²	C₂×D₆₁	semidirect