Subgroups — #30625937

Order 15616.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462732	C₂	1	2	yes	maximal, complemented
2	#21462731	C₂	1	2	yes	maximal, complemented
3	#21462729	C₂	1	2	yes	maximal, complemented
4	#21462728	C₂	1	2	yes	maximal, complemented
5	#21462727	C₂	1	2	yes	maximal, complemented
6	#21462725	C₂	1	2	yes	maximal, complemented
7	#21462724	C₂	1	2	yes	maximal, complemented
8	#21462723	C₂	1	2	yes	maximal, complemented
9	#21462617	C₂	1	1	yes	maximal, characteristic, complemented
10	#21462617	C₂	1	1	yes	maximal, characteristic, complemented
11	#21462615	C₂	1	1	yes	maximal, characteristic, complemented
12	#21462613	C₂	1	1	yes	maximal, characteristic, complemented
13	#21462612	C₂	1	1	yes	maximal, characteristic, complemented
14	#21462611	C₂	1	1	yes	maximal, characteristic, complemented
15	#21462609	C₂	1	1	yes	maximal, characteristic, complemented
16	#21462608	C₂	1	1	yes	maximal, characteristic, complemented
17	#21462512	C₂	1	1	yes	maximal, characteristic
18	#21462512	C₂	1	1	yes	maximal, characteristic
19	#21462510	C₂	1	1	yes	maximal, characteristic
20	#21462509	C₂	1	1	yes	maximal, characteristic
21	#21462500	C₂	1	1	yes	maximal, characteristic
22	D₆₁⋊#433	C₂	1	1	yes	maximal, characteristic
23	#21459223	C₂	1	1	yes	maximal, characteristic
24	#16840814	C₂²	1	2	yes	complemented
25	#16840814	C₂²	1	2	yes	complemented
26	#16840814	C₂²	1	2	yes	complemented
27	#16840814	C₂²	1	2	yes	complemented
28	#16840814	C₂²	1	2	yes	complemented
29	#16840814	C₂²	1	2	yes	complemented
30	#16840814	C₂²	1	2	yes	complemented
31	#16840814	C₂²	1	2	yes	complemented
32	#16840814	C₂²	1	2	yes	complemented
33	#16840814	C₂²	1	2	yes	complemented
34	#16840814	C₂²	1	2	yes	complemented
35	#16840814	C₂²	1	2	yes	complemented
36	#16840813	C₂²	1	2	yes	complemented
37	#16840813	C₂²	1	2	yes	complemented
38	#16840813	C₂²	1	2	yes	complemented
39	#16840813	C₂²	1	2	yes	complemented
40	#16840813	C₂²	1	2	yes	complemented
41	#16840813	C₂²	1	2	yes	complemented
42	#16840812	C₂²	1	2	yes	complemented
43	#16840812	C₂²	1	2	yes	complemented
44	#16840812	C₂²	1	2	yes	complemented
45	#16840812	C₂²	1	2	yes	complemented
46	#16840812	C₂²	1	2	yes	complemented
47	#16840812	C₂²	1	2	yes	complemented
48	#16840811	C₂²	1	2	yes	complemented
49	#16840811	C₂²	1	2	yes	complemented
50	#16840811	C₂²	1	2	yes	complemented
51	#16840811	C₂²	1	2	yes	complemented
52	#16840811	C₂²	1	2	yes	complemented
53	#16840811	C₂²	1	2	yes	complemented
54	Q₈×#92420	C₂²	1	2	yes	complemented
55	Q₈×#92420	C₂²	1	2	yes	complemented
56	#16840787	C₂²	1	1	yes	characteristic
57	#16840787	C₂²	1	2	yes	—
58	#16840787	C₂²	1	2	yes	—
59	#16840787	C₂²	1	2	yes	—
60	#16840787	C₂²	1	1	yes	characteristic
61	#16840787	C₂²	1	2	yes	—
62	#16840787	C₂²	1	2	yes	—
63	#16840787	C₂²	1	1	yes	characteristic
64	#16840787	C₂²	1	2	yes	—
65	#16840787	C₂²	1	1	yes	characteristic
66	#16840786	C₂²	1	1	yes	characteristic
67	#16840786	C₂²	1	2	yes	—
68	#16840786	C₂²	1	2	yes	—
69	#16840786	C₂²	1	2	yes	—
70	#16840786	C₂²	1	1	yes	characteristic
71	#16840786	C₂²	1	2	yes	—
72	#16840786	C₂²	1	2	yes	—
73	#16840786	C₂²	1	1	yes	characteristic
74	#16840786	C₂²	1	2	yes	—
75	#16840786	C₂²	1	1	yes	characteristic
76	#16840784	C₂²	1	2	yes	—
77	#16840784	C₂²	1	2	yes	—
78	#16840783	C₂²	1	2	yes	—
79	#16840782	C₂²	1	2	yes	—
80	#16840780	C₂²	1	2	yes	—
81	#16840780	C₂²	1	2	yes	—
82	#16840779	C₂²	1	2	yes	—
83	#16840778	C₂²	1	2	yes	—
84	#16840769	C₂²	1	1	yes	characteristic
85	#16840769	C₂²	1	1	yes	characteristic
86	#16840769	C₂²	1	1	yes	characteristic
87	#16840769	C₂²	1	1	yes	characteristic
88	#16840769	C₂²	1	1	yes	characteristic
89	#16840769	C₂²	1	1	yes	characteristic
90	#16840769	C₂²	1	1	yes	characteristic
91	#16840769	C₂²	1	1	yes	characteristic
92	#16840767	C₂²	1	1	yes	characteristic
93	#16840766	C₂²	1	1	yes	characteristic
94	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
95	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
96	#16840733	C₂²	1	1	yes	characteristic
97	#16840733	C₂²	1	1	yes	characteristic
98	D₆₁⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
99	D₆₁⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
100	#16840727	C₂²	1	1	yes	characteristic
101	#16840727	C₂²	1	1	yes	characteristic
102	#16840727	C₂²	1	1	yes	characteristic
103	#16840727	C₂²	1	1	yes	characteristic
104	#16840727	C₂²	1	1	yes	characteristic
105	#16840727	C₂²	1	1	yes	characteristic
106	#16840727	C₂²	1	1	yes	characteristic
107	#16840727	C₂²	1	1	yes	characteristic
108	C₄×#11758213	C₂²	1	1	yes	characteristic
109	C₄×#11758213	C₂²	1	1	yes	characteristic
110	#16840721	C₂²	1	1	yes	characteristic
111	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
112	#16840393	C₄	1	1	yes	characteristic
113	#16840392	C₄	1	1	yes	characteristic
114	#16840392	C₄	1	1	yes	characteristic
115	#16840392	C₄	1	2	yes	—
116	#16840390	C₄	1	1	yes	characteristic
117	#16840390	C₄	1	1	yes	characteristic
118	#16840389	C₄	1	1	yes	characteristic
119	#16840389	C₄	1	1	yes	characteristic
120	#16840389	C₄	1	2	yes	—
121	#16840387	C₄	1	2	yes	—
122	#16840387	C₄	1	2	yes	—
123	#16840318	C₂²	1	1	yes	characteristic
124	#16840318	C₂²	1	1	yes	characteristic
125	#16840318	C₂²	1	2	yes	—
126	#16840317	C₂²	1	1	yes	characteristic
127	#16840317	C₂²	1	1	yes	characteristic
128	#16840317	C₂²	1	2	yes	—
129	#16840314	C₂²	1	2	yes	—
130	#16840314	C₂²	1	2	yes	—
131	C₂×#14519735	C₂²	1	1	yes	characteristic
132	#117×D₆₁	C₂²	1	1	yes	characteristic
133	#117×D₆₁	C₂²	1	1	yes	characteristic
134	C₆₁×#544	C₄	1	1	yes	characteristic
135	C₂×#11758213	C₂³	1	1	yes	characteristic
136	C₂×#11758213	C₂³	1	1	yes	characteristic
137	C₂×#11758213	C₂³	1	1	yes	characteristic
138	C₂×#11758213	C₂³	1	1	yes	characteristic
139	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
140	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
141	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
142	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
143	#14519844	C₂³	1	1	yes	characteristic
144	#14519844	C₂³	1	1	yes	characteristic
145	#14519844	C₂³	1	1	yes	characteristic
146	#14519844	C₂³	1	1	yes	characteristic
147	#14519844	C₂³	1	2	yes	—
148	#14519844	C₂³	1	2	yes	—
149	#14519844	C₂³	1	2	yes	—
150	#14519844	C₂³	1	2	yes	—
151	#14519844	C₂³	1	2	yes	—
152	#14519844	C₂³	1	2	yes	—
153	#14519844	C₂³	1	2	yes	—
154	#14519844	C₂³	1	2	yes	—
155	#14519844	C₂³	1	2	yes	—
156	#14519844	C₂³	1	2	yes	—
157	C₄⋊#92420	C₂³	1	1	yes	characteristic
158	C₄⋊#92420	C₂³	1	1	yes	characteristic
159	C₄⋊#92420	C₂³	1	1	yes	characteristic
160	C₄⋊#92420	C₂³	1	1	yes	characteristic
161	C₄⋊#92420	C₂³	1	2	yes	—
162	C₄⋊#92420	C₂³	1	2	yes	—
163	C₄⋊#92420	C₂³	1	2	yes	—
164	C₄⋊#92420	C₂³	1	2	yes	—
165	C₄⋊#92420	C₂³	1	2	yes	—
166	C₄⋊#92420	C₂³	1	2	yes	—
167	C₄⋊#92420	C₂³	1	2	yes	—
168	C₄⋊#92420	C₂³	1	2	yes	—
169	C₄⋊#92420	C₂³	1	2	yes	—
170	C₄⋊#92420	C₂³	1	2	yes	—
171	#14519834	C₂³	1	1	yes	characteristic
172	#14519834	C₂³	1	1	yes	characteristic
173	#14519834	C₂³	1	1	yes	characteristic
174	#14519834	C₂³	1	1	yes	characteristic
175	#14519834	C₂³	1	2	yes	—
176	#14519834	C₂³	1	2	yes	—
177	C₂²⋊#92420	C₂³	1	1	yes	characteristic
178	C₂²⋊#92420	C₂³	1	1	yes	characteristic
179	C₂²⋊#92420	C₂³	1	1	yes	characteristic
180	C₂²⋊#92420	C₂³	1	1	yes	characteristic
181	C₂²⋊#92420	C₂³	1	2	yes	—
182	C₂²⋊#92420	C₂³	1	2	yes	—
183	#14519832	C₂³	1	1	yes	characteristic
184	#14519832	C₂³	1	1	yes	characteristic
185	#14519832	C₂³	1	1	yes	characteristic
186	#14519832	C₂³	1	1	yes	characteristic
187	#14519832	C₂³	1	2	yes	—
188	#14519832	C₂³	1	2	yes	—
189	#14519832	C₂³	1	2	yes	—
190	#14519832	C₂³	1	2	yes	—
191	#14519832	C₂³	1	2	yes	—
192	#14519832	C₂³	1	2	yes	—
193	#14519832	C₂³	1	2	yes	—
194	#14519832	C₂³	1	2	yes	—
195	#14519832	C₂³	1	2	yes	—
196	#14519832	C₂³	1	2	yes	—
197	C₄×#92420	C₂³	1	1	yes	characteristic
198	C₄×#92420	C₂³	1	1	yes	characteristic
199	C₄×#92420	C₂³	1	1	yes	characteristic
200	C₄×#92420	C₂³	1	1	yes	characteristic
201	C₄×#92420	C₂³	1	2	yes	—
202	C₄×#92420	C₂³	1	2	yes	—
203	C₄×#92420	C₂³	1	2	yes	—
204	C₄×#92420	C₂³	1	2	yes	—
205	C₄×#92420	C₂³	1	2	yes	—
206	C₄×#92420	C₂³	1	2	yes	—
207	C₄×#92420	C₂³	1	2	yes	—
208	C₄×#92420	C₂³	1	2	yes	—
209	C₄×#92420	C₂³	1	2	yes	—
210	C₄×#92420	C₂³	1	2	yes	—
211	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
212	#14519777	C₂×C₄	1	1	yes	characteristic
213	#14519777	C₂×C₄	1	1	yes	characteristic
214	#14519777	C₂×C₄	1	2	yes	—
215	#14519776	C₂×C₄	1	2	yes	—
216	#14519776	C₂×C₄	1	2	yes	—
217	#14519776	C₂×C₄	1	1	yes	characteristic
218	#14519776	C₂×C₄	1	1	yes	characteristic
219	#14519776	C₂×C₄	1	2	yes	—
220	#14519776	C₂×C₄	1	1	yes	characteristic
221	#14519776	C₂×C₄	1	1	yes	characteristic
222	#14519776	C₂×C₄	1	2	yes	—
223	#14519775	C₂×C₄	1	2	yes	—
224	#14519775	C₂×C₄	1	2	yes	—
225	#14519769	C₂×C₄	1	1	yes	characteristic
226	#14519769	C₂×C₄	1	1	yes	characteristic
227	#14519769	C₂×C₄	1	2	yes	—
228	#14519768	C₂×C₄	1	1	yes	characteristic
229	#14519768	C₂×C₄	1	1	yes	characteristic
230	#14519768	C₂×C₄	1	2	yes	—
231	#14519768	C₂×C₄	1	1	yes	characteristic
232	#14519768	C₂×C₄	1	1	yes	characteristic
233	#14519768	C₂×C₄	1	2	yes	—
234	#14519767	C₂×C₄	1	2	yes	—
235	#14519767	C₂×C₄	1	2	yes	—
236	#14519767	C₂×C₄	1	2	yes	—
237	#14519767	C₂×C₄	1	2	yes	—
238	#14519757	C₂×C₄	1	2	yes	—
239	#14519757	C₂×C₄	1	2	yes	—
240	#14519757	C₂×C₄	1	2	yes	—
241	#14519757	C₂×C₄	1	2	yes	—
242	#14519756	C₂×C₄	1	2	yes	—
243	#14519756	C₂×C₄	1	2	yes	—
244	#14519755	C₂×C₄	1	2	yes	—
245	#14519755	C₂×C₄	1	2	yes	—
246	#14519755	C₂×C₄	1	2	yes	—
247	#14519755	C₂×C₄	1	2	yes	—
248	#14519755	C₂×C₄	1	2	yes	—
249	#14519755	C₂×C₄	1	2	yes	—
250	#14519755	C₂×C₄	1	2	yes	—
251	#14519755	C₂×C₄	1	2	yes	—
252	#14519754	C₂×C₄	1	2	yes	—
253	#14519754	C₂×C₄	1	2	yes	—
254	#14519754	C₂×C₄	1	2	yes	—
255	#14519754	C₂×C₄	1	2	yes	—
256	#14519753	C₂×C₄	1	2	yes	—
257	#14519753	C₂×C₄	1	2	yes	—
258	#14519753	C₂×C₄	1	2	yes	—
259	#14519753	C₂×C₄	1	2	yes	—
260	Q₈×Dic₆₁	C₂³	1	2	yes	—
261	Q₈×Dic₆₁	C₂³	1	2	yes	—
262	#14519742	C₂³	1	2	yes	—
263	#14519742	C₂³	1	2	yes	—
264	#14519742	C₂³	1	2	yes	—
265	#14519742	C₂³	1	2	yes	—
266	#14519742	C₂³	1	2	yes	—
267	#14519742	C₂³	1	2	yes	—
268	#14519736	C₂×C₄	1	1	yes	characteristic
269	#14519736	C₂×C₄	1	1	yes	characteristic
270	#14519735	C₂×C₄	1	2	yes	—
271	#14519735	C₂×C₄	1	1	yes	characteristic
272	#14519735	C₂×C₄	1	1	yes	characteristic
273	#14519735	C₂³	1	1	yes	characteristic
274	#14519735	C₂³	1	1	yes	characteristic
275	#14519735	C₂³	1	1	yes	characteristic
276	#14519735	C₂³	1	1	yes	characteristic
277	#14519735	C₂³	1	1	yes	characteristic
278	#14519735	C₂³	1	1	yes	characteristic
279	#14519735	C₂³	1	2	yes	—
280	#14519734	C₂×C₄	1	1	yes	characteristic
281	#14519734	C₂×C₄	1	1	yes	characteristic
282	#14519734	C₂×C₄	1	2	yes	—
283	#14519733	C₂³	1	1	yes	characteristic
284	#14519733	C₂³	1	1	yes	characteristic
285	#14519733	C₂³	1	2	yes	—
286	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
287	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
288	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
289	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
290	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
291	C₂×#11758198	C₂×C₄	1	2	yes	—
292	C₂²⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
293	C₂²⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
294	C₂²⋊C₄×D₆₁	C₂×C₄	1	2	yes	—
295	C₂×C₄×Dic₆₁	C₂³	1	2	yes	—
296	C₄²×D₆₁	C₂³	1	1	yes	characteristic
297	C₄²×D₆₁	C₂³	1	1	yes	characteristic
298	C₄²×D₆₁	C₂³	1	2	yes	—
299	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
300	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
301	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
302	#125×C₆₁	C₂×C₄	1	1	yes	characteristic
303	#125×C₆₁	C₂×C₄	1	1	yes	characteristic
304	#125×C₆₁	C₂×C₄	1	2	yes	—
305	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
306	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
307	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
308	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
309	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
310	C₂³×D₆₁	C₂²×C₄	1	1	yes	characteristic
311	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
312	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
314	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
315	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
316	C₂²×Dic₆₁	C₂⁴	1	1	yes	characteristic
317	C₂×C₄×D₆₁	—	2	2	no	—
318	C₂×C₄×D₆₁	—	2	2	no	—
319	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
320	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
321	C₂×C₄×D₆₁	C₂²×C₄	1	2	yes	—
322	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
323	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₄×D₆₁	C₂²×C₄	1	2	yes	—
325	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
329	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
330	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
331	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
332	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
333	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
334	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
335	C₂×#92420	C₂⁴	1	1	yes	characteristic
336	C₂×#92420	C₂⁴	1	1	yes	characteristic
337	C₂×#92420	C₂⁴	1	2	yes	—
338	C₂×#92420	C₂⁴	1	2	yes	—
339	C₂×#92420	C₂⁴	1	2	yes	—
340	C₂×#92420	C₂⁴	1	2	yes	—
341	C₂×#92420	C₂⁴	1	1	yes	characteristic
342	C₂×#92420	C₂⁴	1	1	yes	characteristic
343	C₂×#92420	C₂⁴	1	1	yes	characteristic
344	C₂×#92420	C₂⁴	1	1	yes	characteristic
345	C₂×#92420	C₂⁴	1	1	yes	characteristic
346	C₂×#92420	C₂⁴	1	1	yes	characteristic
347	#11758213	—	2	2	no	—
348	#11758213	—	2	2	no	—
349	#11758213	—	2	2	no	—
350	#11758213	—	2	2	no	—
351	D₆₁⋊C₈	—	2	2	no	—
352	D₆₁⋊C₈	—	2	2	no	—
353	D₆₁⋊C₈	—	2	2	no	—
354	D₆₁⋊C₈	—	2	2	no	—
355	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
357	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
358	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
359	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
360	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
361	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
362	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
369	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
370	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
371	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
372	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
374	C₂²⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
375	C₂²⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
376	C₂²⋊Dic₆₁	C₂²×C₄	1	2	yes	—
377	#11758198	C₂²×C₄	1	1	yes	characteristic
378	#11758198	C₂²×C₄	1	1	yes	characteristic
379	#11758198	C₂²×C₄	1	2	yes	—
380	#11758198	C₂²×C₄	1	1	yes	characteristic
381	#11758198	C₂²×C₄	1	1	yes	characteristic
382	#11758198	C₂²×C₄	1	2	yes	—
383	#11758198	C₂²×C₄	1	2	yes	—
384	#11758198	C₂²×C₄	1	2	yes	—
385	#11758198	C₂²×C₄	1	2	yes	—
386	#11758198	C₂²×C₄	1	2	yes	—
387	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
390	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
392	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
393	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
395	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
396	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
397	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
398	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
399	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
400	#11758196	C₂²×C₄	1	1	yes	characteristic
401	#11758196	C₂²×C₄	1	1	yes	characteristic
402	#11758196	C₂²×C₄	1	2	yes	—
403	#11758196	C₂²×C₄	1	1	yes	characteristic
404	#11758196	C₂²×C₄	1	1	yes	characteristic
405	#11758196	C₂²×C₄	1	2	yes	—
406	#11758196	C₂²×C₄	1	2	yes	—
407	#11758196	C₂²×C₄	1	2	yes	—
408	#11758196	C₂²×C₄	1	2	yes	—
409	#11758196	C₂²×C₄	1	2	yes	—
410	#11758196	C₂²×C₄	1	2	yes	—
411	#11758196	C₂²×C₄	1	2	yes	—
412	#11758196	C₂²×C₄	1	2	yes	—
413	#11758196	C₂²×C₄	1	2	yes	—
414	#11758196	C₂²×C₄	1	2	yes	—
415	#11758196	C₂²×C₄	1	2	yes	—
416	#11758196	C₂²×C₄	1	2	yes	—
417	#11758196	C₂²×C₄	1	2	yes	—
418	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
419	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
422	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
423	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
424	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
425	C₄×Dic₆₁	C₂⁴	1	2	yes	—
426	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
427	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
428	C₄×Dic₆₁	C₂⁴	1	2	yes	—
429	C₄×Dic₆₁	C₂⁴	1	2	yes	—
430	C₄×Dic₆₁	C₂⁴	1	2	yes	—
431	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
432	C₂²×D₆₁	—	2	2	no	—
433	C₂²×D₆₁	—	4	1	no	—
434	C₂²×D₆₁	—	4	1	no	—
435	C₂²×D₆₁	C₂³×C₄	1	1	yes	characteristic
436	C₂²×D₆₁	C₂³×C₄	1	1	yes	characteristic
437	Q₈×C₆₁	—	4	2	no	—
438	Q₈×C₆₁	—	4	2	no	—
439	C₂×C₄×C₆₁	—	2	2	no	—
440	C₂×C₄×C₆₁	—	4	2	no	—
441	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
442	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
443	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
445	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
446	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
448	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
449	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
450	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
451	C₂×Dic₆₁	—	2	1	no	—
452	C₂×Dic₆₁	—	2	1	no	—
453	C₂×Dic₆₁	—	4	2	no	—
454	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
455	C₂×Dic₆₁	C₂³×C₄	1	2	yes	—
456	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
457	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
458	C₂×Dic₆₁	C₂³×C₄	1	2	yes	—
459	C₂×Dic₆₁	C₂³×C₄	1	2	yes	—
460	C₂×Dic₆₁	C₂³×C₄	1	2	yes	—
461	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
462	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
463	C₂×Dic₆₁	C₂⁵	1	1	yes	characteristic
464	C₄×D₆₁	—	2	2	no	—
465	C₄×D₆₁	—	2	2	no	—
466	C₄×D₆₁	—	2	1	no	—
467	C₄×D₆₁	—	2	1	no	—
468	C₄×D₆₁	—	4	1	no	—
469	C₄×D₆₁	—	4	1	no	—
470	C₄×D₆₁	—	4	2	no	—
471	C₄×D₆₁	—	4	1	no	—
472	C₄×D₆₁	—	4	1	no	—
473	C₄×D₆₁	—	4	2	no	—
474	C₄×D₆₁	2₋¹⁺⁴	1	2	yes	—
475	C₄×D₆₁	2₋¹⁺⁴	1	2	yes	—
476	Dic₁₂₂	—	4	2	no	—
477	Dic₁₂₂	—	4	2	no	—
478	Dic₁₂₂	—	4	2	no	—
479	Dic₁₂₂	—	4	2	no	—
480	Dic₁₂₂	—	4	2	no	—
481	Dic₁₂₂	—	4	2	no	—
482	#92420	—	2	1	no	—
483	#92420	—	2	1	no	—
484	#92420	—	2	1	no	—
485	#92420	—	2	1	no	—
486	#92420	—	2	1	no	—
487	#92420	—	2	1	no	—
488	#92420	—	2	1	no	—
489	#92420	—	2	1	no	—
490	#92420	—	2	2	no	—
491	#92420	—	2	2	no	—
492	#92420	—	2	2	no	—
493	#92420	—	2	2	no	—
494	#60252	—	61	1	no	maximal, Sylow
495	C₂²×C₆₁	—	2	1	no	—
496	C₂²×C₆₁	—	2	1	no	—
497	C₂²×C₆₁	—	2	1	no	—
498	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
499	C₂×D₆₁	—	2	1	no	—
500	C₂×D₆₁	—	2	1	no	—
501	C₂×D₆₁	—	2	1	no	—
502	C₂×D₆₁	—	2	1	no	—
503	C₂×D₆₁	—	2	1	no	—
504	C₂×D₆₁	—	8	2	no	—
505	C₂×D₆₁	#519	1	2	yes	—
506	C₄×C₆₁	—	2	1	no	—
507	C₄×C₆₁	—	2	1	no	—
508	C₄×C₆₁	—	2	1	no	—
509	C₄×C₆₁	—	2	2	no	—
510	C₄×C₆₁	—	2	2	no	—
511	C₄×C₆₁	—	2	2	no	—
512	C₄×C₆₁	—	2	1	no	—
513	C₄×C₆₁	—	2	1	no	—
514	C₄×C₆₁	—	2	2	no	—
515	C₄×C₆₁	#519	1	2	yes	—
516	Dic₆₁	—	2	1	no	—
517	Dic₆₁	—	2	1	no	—
518	Dic₆₁	—	2	1	no	—
519	Dic₆₁	—	2	2	no	—
520	Dic₆₁	—	2	1	no	—
521	Dic₆₁	—	2	1	no	—
522	Dic₆₁	—	2	2	no	—
523	Dic₆₁	—	2	2	no	—
524	Dic₆₁	—	2	2	no	—
525	Dic₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	Dic₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	#3458	—	61	1	no	—
528	#2987	—	61	2	no	—
529	#2987	—	61	2	no	—
530	#2986	—	61	2	no	—
531	#2986	—	61	2	no	—
532	#2985	—	61	2	no	—
533	#2985	—	61	2	no	—
534	#2985	—	61	2	no	—
535	#2985	—	61	2	no	—
536	#2962	—	61	1	no	—
537	#2962	—	61	1	no	—
538	#2962	—	61	1	no	—
539	#2962	—	61	1	no	—
540	#2961	—	61	1	no	—
541	#2961	—	61	1	no	—
542	#2960	—	61	1	no	—
543	#2960	—	61	1	no	—
544	#2924	—	61	1	no	—
545	#2924	—	61	1	no	—
546	#2924	—	61	1	no	—
547	#2924	—	61	1	no	—
548	#2921	—	61	1	no	—
549	C₂×#433	—	61	1	no	—
550	C₂×C₆₁	—	4	1	no	—
551	C₂×C₆₁	C₂×#519	1	1	yes	characteristic
552	C₂×C₆₁	#3573	1	1	yes	characteristic
553	C₂×C₆₁	#3573	1	1	yes	characteristic
554	D₆₁	—	2	2	no	—
555	D₆₁	—	4	1	no	—
556	#544	—	61	2	no	—
557	#544	—	61	1	no	—
558	#544	—	61	1	no	—
559	#544	—	61	2	no	—
560	#544	—	61	1	no	—
561	#544	—	61	1	no	—
562	#544	—	61	1	no	—
563	#544	—	61	1	no	—
564	#544	—	61	1	no	—
565	#544	#6923	1	1	yes	characteristic
566	#543	—	61	2	no	—
567	#543	—	61	2	no	—
568	#533	—	61	1	no	—
569	#533	—	61	1	no	—
570	#533	—	61	2	no	—
571	#533	—	61	1	no	—
572	#533	—	61	1	no	—
573	#533	—	61	2	no	—
574	#533	—	61	2	no	—
575	#533	—	61	2	no	—
576	C₂×#117	—	61	1	no	—
577	C₂×#117	—	61	1	no	—
578	C₂×#117	—	61	1	no	—
579	#446	—	61	2	no	—
580	#446	—	61	2	no	—
581	#446	—	61	2	no	—
582	#446	—	61	2	no	—
583	#446	—	61	2	no	—
584	#446	—	61	2	no	—
585	#446	—	61	2	no	—
586	#446	—	61	2	no	—
587	#446	—	61	2	no	—
588	#446	—	61	2	no	—
589	#446	—	61	2	no	—
590	#446	—	61	2	no	—
591	#446	—	61	2	no	—
592	#446	—	61	2	no	—
593	#446	—	61	2	no	—
594	#446	—	61	2	no	—
595	#446	—	61	2	no	—
596	#446	—	61	2	no	—
597	#446	—	61	2	no	—
598	#446	—	61	2	no	—
599	#446	—	61	2	no	—
600	#446	—	61	2	no	—
601	#446	—	61	2	no	—
602	#446	—	61	2	no	—
603	C₈×Q₈	—	61	2	no	—
604	C₈×Q₈	—	61	2	no	—
605	C₈×Q₈	—	61	2	no	—
606	C₈×Q₈	—	61	2	no	—
607	C₈×Q₈	—	61	2	no	—
608	C₈×Q₈	—	61	2	no	—
609	C₈×Q₈	—	61	2	no	—
610	C₈×Q₈	—	61	2	no	—
611	#433	—	61	1	no	—
612	#433	—	61	1	no	—
613	#433	—	61	1	no	—
614	#433	—	61	1	no	—
615	#433	—	61	2	no	—
616	#433	—	61	2	no	—
617	#433	—	61	2	no	—
618	#433	—	61	2	no	—
619	#433	—	61	2	no	—
620	#433	—	61	2	no	—
621	#433	—	61	1	no	—
622	#433	—	61	1	no	—
623	#433	—	61	1	no	—
624	#433	—	61	1	no	—
625	#433	—	61	2	no	—
626	#433	—	61	2	no	—
627	#433	—	61	2	no	—
628	#433	—	61	2	no	—
629	#433	—	61	2	no	—
630	#433	—	61	2	no	—
631	#432	—	61	2	no	—
632	#432	—	61	2	no	—
633	#432	—	61	2	no	—
634	#432	—	61	2	no	—
635	#431	—	61	2	no	—
636	#431	—	61	2	no	—
637	#431	—	61	2	no	—
638	#431	—	61	2	no	—
639	#424	—	61	1	no	—
640	#424	—	61	1	no	—
641	#424	—	61	1	no	—
642	#424	—	61	1	no	—
643	#424	—	61	1	no	—
644	#424	—	61	1	no	—
645	#424	—	61	1	no	—
646	#424	—	61	1	no	—
647	#423	—	61	1	no	—
648	#423	—	61	1	no	—
649	C₂×C₄⋊C₈	—	61	1	no	—
650	C₂×C₄⋊C₈	—	61	1	no	—
651	#407	—	61	1	no	—
652	#407	—	61	1	no	—
653	C₂×C₂²⋊C₈	—	61	1	no	—
654	C₂×C₂²⋊C₈	—	61	1	no	—
655	#405	—	61	1	no	—
656	#405	—	61	1	no	—
657	#405	—	61	1	no	—
658	#405	—	61	1	no	—
659	#405	—	61	1	no	—
660	#405	—	61	1	no	—
661	#405	—	61	1	no	—
662	#405	—	61	1	no	—
663	C₄×M₁₆	—	61	1	no	—
664	C₄×M₁₆	—	61	1	no	—
665	C₂×#97	—	61	1	no	—
666	C₂×C₄×C₈	—	61	1	no	—
667	C₆₁	#60252	1	1	yes	characteristic, complemented, Sylow
668	C₂³×C₄	—	61	1	no	—
669	C₂×M₁₆	—	61	1	no	—
670	C₂×M₁₆	—	61	1	no	—
671	C₂×M₁₆	—	61	1	no	—
672	C₂×M₁₆	—	61	1	no	—
673	C₂²×C₈	—	61	1	no	—
674	C₂²×C₈	—	61	1	no	—
675	C₂²×C₈	—	61	1	no	—
676	C₂²×C₈	—	61	1	no	—
677	C₄⋊Q₈	—	61	2	no	—
678	C₄⋊Q₈	—	61	2	no	—
679	C₄⋊Q₈	—	61	2	no	—
680	C₄⋊Q₈	—	61	2	no	—
681	C₄⋊Q₈	—	61	1	no	—
682	C₄⋊Q₈	—	61	1	no	—
683	C₄⋊Q₈	—	61	2	no	—
684	C₄⋊Q₈	—	61	1	no	—
685	C₄⋊Q₈	—	61	1	no	—
686	C₄⋊Q₈	—	61	2	no	—
687	C₄⋊Q₈	—	61	1	no	—
688	C₄⋊Q₈	—	61	1	no	—
689	C₄⋊Q₈	—	61	2	no	—
690	C₄⋊Q₈	C₂×#6923	1	1	yes	characteristic
691	C₄⋊Q₈	C₂×#6923	1	1	yes	characteristic
692	C₄⋊Q₈	C₂×#6923	1	2	yes	—
693	#125	—	61	2	no	—
694	#125	—	61	2	no	—
695	#125	—	61	2	no	—
696	#125	—	61	2	no	—
697	#125	—	61	1	no	—
698	#125	—	61	1	no	—
699	#125	—	61	2	no	—
700	#125	—	61	1	no	—
701	#125	—	61	1	no	—
702	#125	—	61	2	no	—
703	#125	—	61	1	no	—
704	#125	—	61	1	no	—
705	#125	—	61	2	no	—
706	#125	C₂×#6923	1	1	yes	characteristic
707	#125	C₂×#6923	1	1	yes	characteristic
708	#125	C₂×#6923	1	2	yes	—
709	C₂²⋊Q₈	—	61	2	no	—
710	C₂²⋊Q₈	—	61	2	no	—
711	C₂²⋊Q₈	—	61	2	no	—
712	C₂²⋊Q₈	—	61	2	no	—
713	C₂²⋊Q₈	—	61	2	no	—
714	C₂²⋊Q₈	—	61	2	no	—
715	C₂²⋊Q₈	—	61	2	no	—
716	C₂²⋊Q₈	—	61	2	no	—
717	C₂²⋊Q₈	—	61	2	no	—
718	C₂²⋊Q₈	—	61	2	no	—
719	C₂²⋊Q₈	—	61	2	no	—
720	C₂²⋊Q₈	—	61	2	no	—
721	C₂²⋊Q₈	—	61	2	no	—
722	C₂²⋊Q₈	—	61	2	no	—
723	C₂²⋊Q₈	—	61	2	no	—
724	C₂²⋊Q₈	—	61	2	no	—
725	C₂²⋊Q₈	—	61	2	no	—
726	C₂²⋊Q₈	—	61	2	no	—
727	C₂²⋊Q₈	—	61	2	no	—
728	C₂²⋊Q₈	—	61	2	no	—
729	C₂²⋊Q₈	—	61	2	no	—
730	C₂²⋊Q₈	—	61	2	no	—
731	C₂²⋊Q₈	C₂×#6923	1	2	yes	—
732	C₂²⋊Q₈	C₂×#6923	1	2	yes	—
733	C₄×Q₈	—	61	2	no	—
734	C₄×Q₈	—	61	2	no	—
735	C₄×Q₈	—	61	2	no	—
736	C₄×Q₈	—	61	2	no	—
737	C₄×Q₈	—	61	2	no	—
738	C₄×Q₈	—	61	2	no	—
739	C₄×Q₈	—	61	2	no	—
740	C₄×Q₈	—	61	2	no	—
741	#117	—	61	1	no	—
742	#117	—	61	1	no	—
743	#117	—	61	1	no	—
744	#117	—	61	1	no	—
745	#117	—	61	1	no	—
746	#117	—	61	1	no	—
747	#117	—	61	1	no	—
748	#117	—	61	1	no	—
749	#117	—	61	2	no	—
750	#117	—	61	2	no	—
751	#117	—	61	1	no	—
752	#117	—	61	1	no	—
753	#117	—	61	1	no	—
754	#117	—	61	1	no	—
755	#117	—	61	2	no	—
756	#117	—	61	1	no	—
757	#117	—	61	1	no	—
758	#117	—	61	2	no	—
759	#117	C₂×#6923	1	1	yes	characteristic
760	#117	C₂×#6923	1	1	yes	characteristic
761	C₂×C₄⋊C₄	—	61	1	no	—
762	C₂×C₄⋊C₄	—	61	1	no	—
763	C₂×C₄⋊C₄	—	61	1	no	—
764	C₂×C₄⋊C₄	—	61	1	no	—
765	C₂×C₄⋊C₄	—	61	1	no	—
766	C₂×C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	—	61	2	no	—
768	C₂×C₂²⋊C₄	—	61	1	no	—
769	C₂×C₂²⋊C₄	—	61	1	no	—
770	C₂×C₂²⋊C₄	—	61	2	no	—
771	C₂×C₄²	—	61	2	no	—
772	C₂×C₄²	—	61	1	no	—
773	C₂×C₄²	—	61	1	no	—
774	C₂×C₄²	—	61	2	no	—
775	C₄⋊C₈	—	61	1	no	—
776	C₄⋊C₈	—	61	1	no	—
777	C₄⋊C₈	—	61	1	no	—
778	C₄⋊C₈	—	61	1	no	—
779	C₄⋊C₈	—	61	2	no	—
780	C₄⋊C₈	—	61	2	no	—
781	C₄⋊C₈	—	61	2	no	—
782	C₄⋊C₈	—	61	2	no	—
783	C₄⋊C₈	—	61	2	no	—
784	C₄⋊C₈	—	61	2	no	—
785	C₄⋊C₈	—	61	2	no	—
786	C₄⋊C₈	—	61	2	no	—
787	C₄⋊C₈	—	61	2	no	—
788	C₄⋊C₈	—	61	2	no	—
789	C₄⋊C₈	—	61	1	no	—
790	C₄⋊C₈	—	61	1	no	—
791	C₄⋊C₈	—	61	1	no	—
792	C₄⋊C₈	—	61	1	no	—
793	C₄⋊C₈	—	61	2	no	—
794	C₄⋊C₈	—	61	2	no	—
795	C₄⋊C₈	—	61	2	no	—
796	C₄⋊C₈	—	61	2	no	—
797	C₄⋊C₈	—	61	2	no	—
798	C₄⋊C₈	—	61	2	no	—
799	C₄⋊C₈	—	61	2	no	—
800	C₄⋊C₈	—	61	2	no	—
801	C₄⋊C₈	—	61	2	no	—
802	C₄⋊C₈	—	61	2	no	—
803	C₂²⋊C₈	—	61	1	no	—
804	C₂²⋊C₈	—	61	1	no	—
805	C₂²⋊C₈	—	61	1	no	—
806	C₂²⋊C₈	—	61	1	no	—
807	C₂²⋊C₈	—	61	2	no	—
808	C₂²⋊C₈	—	61	2	no	—
809	C₂²⋊C₈	—	61	1	no	—
810	C₂²⋊C₈	—	61	1	no	—
811	C₂²⋊C₈	—	61	1	no	—
812	C₂²⋊C₈	—	61	1	no	—
813	C₂²⋊C₈	—	61	2	no	—
814	C₂²⋊C₈	—	61	2	no	—
815	#97	—	61	1	no	—
816	#97	—	61	1	no	—
817	#97	—	61	1	no	—
818	#97	—	61	1	no	—
819	#97	—	61	2	no	—
820	#97	—	61	2	no	—
821	#97	—	61	2	no	—
822	#97	—	61	2	no	—
823	#97	—	61	2	no	—
824	#97	—	61	2	no	—
825	#97	—	61	2	no	—
826	#97	—	61	2	no	—
827	#97	—	61	2	no	—
828	#97	—	61	2	no	—
829	C₄×C₈	—	61	1	no	—
830	C₄×C₈	—	61	1	no	—
831	C₄×C₈	—	61	1	no	—
832	C₄×C₈	—	61	1	no	—
833	C₄×C₈	—	61	2	no	—
834	C₄×C₈	—	61	2	no	—
835	C₄×C₈	—	61	2	no	—
836	C₄×C₈	—	61	2	no	—
837	C₄×C₈	—	61	2	no	—
838	C₄×C₈	—	61	2	no	—
839	C₄×C₈	—	61	2	no	—
840	C₄×C₈	—	61	2	no	—
841	C₄×C₈	—	61	2	no	—
842	C₄×C₈	—	61	2	no	—
843	C₂⁴	—	61	1	no	—
844	C₂×Q₈	—	61	2	no	—
845	C₂×Q₈	—	61	2	no	—
846	C₂×Q₈	—	61	2	no	—
847	C₂×Q₈	—	61	2	no	—
848	C₂×Q₈	—	61	2	no	—
849	C₂×Q₈	—	61	2	no	—
850	C₂×Q₈	C₂²×#6923	1	2	yes	—
851	C₂×Q₈	C₂²×#6923	1	2	yes	—
852	C₂²×C₄	—	61	1	no	—
853	C₂²×C₄	—	61	1	no	—
854	C₂²×C₄	—	61	2	no	—
855	C₂²×C₄	—	61	1	no	—
856	C₂²×C₄	—	61	1	no	—
857	C₂²×C₄	—	61	1	no	—
858	C₂²×C₄	—	61	1	no	—
859	C₂²×C₄	—	61	1	no	—
860	C₂²×C₄	—	61	2	no	—
861	C₂²×C₄	—	61	1	no	—
862	C₂²×C₄	—	61	1	no	—
863	C₂²×C₄	—	61	2	no	—
864	C₂²×C₄	—	122	2	no	—
865	C₂²×C₄	—	122	2	no	—
866	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
867	C₂²×C₄	C₂²×#6923	1	2	yes	—
868	M₁₆	—	122	2	no	—
869	M₁₆	—	122	2	no	—
870	M₁₆	—	122	2	no	—
871	M₁₆	—	122	2	no	—
872	C₂×C₈	—	61	1	no	—
873	C₂×C₈	—	61	1	no	—
874	C₂×C₈	—	61	2	no	—
875	C₂×C₈	—	61	2	no	—
876	C₂×C₈	—	61	2	no	—
877	C₂×C₈	—	61	2	no	—
878	C₂×C₈	—	61	1	no	—
879	C₂×C₈	—	61	1	no	—
880	C₂×C₈	—	61	1	no	—
881	C₂×C₈	—	61	1	no	—
882	C₂×C₈	—	61	1	no	—
883	C₂×C₈	—	61	1	no	—
884	C₂×C₈	—	122	2	no	—
885	C₂×C₈	—	122	2	no	—
886	C₂×C₈	—	122	2	no	—
887	C₂×C₈	—	122	2	no	—
888	C₄⋊C₄	—	61	1	no	—
889	C₄⋊C₄	—	61	1	no	—
890	C₄⋊C₄	—	61	2	no	—
891	C₄⋊C₄	—	61	1	no	—
892	C₄⋊C₄	—	61	1	no	—
893	C₄⋊C₄	—	61	2	no	—
894	C₄⋊C₄	—	61	2	no	—
895	C₄⋊C₄	—	61	1	no	—
896	C₄⋊C₄	—	61	1	no	—
897	C₄⋊C₄	—	61	1	no	—
898	C₄⋊C₄	—	61	1	no	—
899	C₄⋊C₄	—	61	1	no	—
900	C₄⋊C₄	—	61	1	no	—
901	C₄⋊C₄	—	61	2	no	—
902	C₄⋊C₄	—	61	2	no	—
903	C₄⋊C₄	—	61	2	no	—
904	C₄⋊C₄	—	61	2	no	—
905	C₄⋊C₄	—	61	2	no	—
906	C₄⋊C₄	—	61	2	no	—
907	C₄⋊C₄	—	61	2	no	—
908	C₄⋊C₄	—	61	2	no	—
909	C₄⋊C₄	—	61	2	no	—
910	C₄⋊C₄	—	61	2	no	—
911	C₄⋊C₄	—	61	2	no	—
912	C₄⋊C₄	—	61	2	no	—
913	C₄⋊C₄	—	61	2	no	—
914	C₄⋊C₄	—	61	2	no	—
915	C₄⋊C₄	—	61	2	no	—
916	C₄⋊C₄	—	61	2	no	—
917	C₄⋊C₄	—	61	2	no	—
918	C₄⋊C₄	—	61	2	no	—
919	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
920	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
922	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
923	C₄⋊C₄	C₂²×#6923	1	2	yes	—
924	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
925	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
926	C₄⋊C₄	C₂²×#6923	1	2	yes	—
927	C₄⋊C₄	C₂²×#6923	1	2	yes	—
928	C₄⋊C₄	C₂²×#6923	1	2	yes	—
929	C₄⋊C₄	C₂²×#6923	1	2	yes	—
930	C₄⋊C₄	C₂²×#6923	1	2	yes	—
931	C₄⋊C₄	C₂²×#6923	1	2	yes	—
932	C₂²⋊C₄	—	61	1	no	—
933	C₂²⋊C₄	—	61	1	no	—
934	C₂²⋊C₄	—	61	2	no	—
935	C₂²⋊C₄	—	61	2	no	—
936	C₂²⋊C₄	—	61	2	no	—
937	C₂²⋊C₄	—	61	2	no	—
938	C₂²⋊C₄	—	61	2	no	—
939	C₂²⋊C₄	—	61	2	no	—
940	C₂²⋊C₄	—	61	1	no	—
941	C₂²⋊C₄	—	61	1	no	—
942	C₂²⋊C₄	—	61	2	no	—
943	C₂²⋊C₄	—	61	1	no	—
944	C₂²⋊C₄	—	61	1	no	—
945	C₂²⋊C₄	C₂²×#6923	1	1	yes	characteristic
946	C₂²⋊C₄	C₂²×#6923	1	1	yes	characteristic
947	C₂²⋊C₄	C₂²×#6923	1	2	yes	—
948	C₄²	—	61	2	no	—
949	C₄²	—	61	2	no	—
950	C₄²	—	61	1	no	—
951	C₄²	—	61	1	no	—
952	C₄²	—	61	2	no	—
953	C₄²	—	61	1	no	—
954	C₄²	—	61	1	no	—
955	C₄²	—	61	2	no	—
956	C₄²	—	61	2	no	—
957	C₄²	—	61	2	no	—
958	C₄²	—	61	2	no	—
959	C₄²	—	61	1	no	—
960	C₄²	—	61	1	no	—
961	C₄²	C₂²×#6923	1	2	yes	—
962	C₄²	C₂²×#6923	1	1	yes	characteristic
963	C₄²	C₂²×#6923	1	1	yes	characteristic
964	C₂³	—	61	1	no	—
965	C₂³	—	61	1	no	—
966	C₂³	—	122	2	no	—
967	C₂³	—	244	1	no	—
968	C₂³	—	244	1	no	—
969	C₂³	C₂³×#6923	1	1	yes	characteristic
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	244	2	no	—
973	Q₈	—	244	2	no	—
974	Q₈	—	244	2	no	—
975	Q₈	—	244	2	no	—
976	Q₈	—	244	2	no	—
977	Q₈	—	244	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	4	2	no	—
980	C₂×C₄	—	61	1	no	—
981	C₂×C₄	—	61	2	no	—
982	C₂×C₄	—	61	2	no	—
983	C₂×C₄	—	61	1	no	—
984	C₂×C₄	—	61	1	no	—
985	C₂×C₄	—	61	1	no	—
986	C₂×C₄	—	61	2	no	—
987	C₂×C₄	—	61	2	no	—
988	C₂×C₄	—	61	2	no	—
989	C₂×C₄	—	61	1	no	—
990	C₂×C₄	—	61	1	no	—
991	C₂×C₄	—	61	2	no	—
992	C₂×C₄	—	122	1	no	—
993	C₂×C₄	—	122	1	no	—
994	C₂×C₄	—	122	2	no	—
995	C₂×C₄	—	122	1	no	—
996	C₂×C₄	—	122	1	no	—
997	C₂×C₄	—	122	2	no	—
998	C₂×C₄	—	244	1	no	—
999	C₂×C₄	—	244	1	no	—
1000	C₂×C₄	—	244	2	no	—
1001	C₂×C₄	—	244	1	no	—
1002	C₂×C₄	—	244	1	no	—
1003	C₂×C₄	—	244	2	no	—
1004	C₂×C₄	—	244	2	no	—
1005	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
1006	C₂×C₄	C₂³×#6923	1	2	yes	—
1007	C₂×C₄	C₂³×#6923	1	2	yes	—
1008	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
1009	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
1010	C₂×C₄	C₂³×#6923	1	2	yes	—
1011	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
1012	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
1013	C₂×C₄	C₂³×#6923	1	2	yes	—
1014	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
1015	C₈	—	122	1	no	—
1016	C₈	—	122	1	no	—
1017	C₈	—	122	1	no	—
1018	C₈	—	122	1	no	—
1019	C₈	—	122	1	no	—
1020	C₈	—	122	1	no	—
1021	C₈	—	122	1	no	—
1022	C₈	—	122	1	no	—
1023	C₈	—	122	2	no	—
1024	C₈	—	122	2	no	—
1025	C₈	—	122	2	no	—
1026	C₈	—	122	2	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	61	2	no	—
1031	C₂²	—	122	1	no	—
1032	C₂²	—	122	1	no	—
1033	C₂²	—	122	1	no	—
1034	C₂²	—	122	1	no	—
1035	C₂²	—	122	1	no	—
1036	C₂²	—	488	2	no	—
1037	C₂²	C₂⁴×#6923	1	1	yes	characteristic
1038	C₄	—	2	1	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	61	1	no	—
1048	C₄	—	61	1	no	—
1049	C₄	—	122	1	no	—
1050	C₄	—	122	1	no	—
1051	C₄	—	122	1	no	—
1052	C₄	—	122	2	no	—
1053	C₄	—	122	1	no	—
1054	C₄	—	122	1	no	—
1055	C₄	—	122	2	no	—
1056	C₄	—	122	2	no	—
1057	C₄	—	122	2	no	—
1058	C₄	#16840830	1	2	yes	—
1059	C₂	—	4	1	no	—
1060	C₂	—	122	2	no	—
1061	C₂	—	244	1	no	—
1062	C₂	C₂×#16840830	1	1	yes	characteristic
1063	C₂	#21462814	1	1	yes	characteristic
1064	C₂	#21462815	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×#6923
commutator, socle	C₂²×C₆₁	C₂⁴×C₄
Fitting	C₆₁×#544	C₄
prime radical	C₂³×D₆₁	C₂²×C₄
cosocle	C₂×Dic₆₁	C₂⁵
hypercenter	#544	#6923
hypocenter	C₆₁	#60252
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. #21462732	C₂	semidirect
2. #21462731	C₂	semidirect
3. #21462729	C₂	semidirect
4. #21462728	C₂	semidirect
5. #21462727	C₂	semidirect
6. #21462725	C₂	semidirect
7. #21462724	C₂	semidirect
8. #21462723	C₂	semidirect
9. #21462617	C₂	semidirect
10. #21462617	C₂	semidirect
11. #21462615	C₂	semidirect
12. #21462613	C₂	semidirect
13. #21462612	C₂	semidirect
14. #21462611	C₂	semidirect
15. #21462609	C₂	semidirect
16. #21462608	C₂	semidirect
24. #16840814	C₂²	semidirect
25. #16840814	C₂²	semidirect
26. #16840814	C₂²	semidirect
27. #16840814	C₂²	semidirect
28. #16840814	C₂²	semidirect
29. #16840814	C₂²	semidirect
30. #16840814	C₂²	semidirect
31. #16840814	C₂²	semidirect
32. #16840814	C₂²	semidirect
33. #16840814	C₂²	semidirect
34. #16840814	C₂²	semidirect
35. #16840814	C₂²	semidirect
36. #16840813	C₂²	semidirect
37. #16840813	C₂²	semidirect
38. #16840813	C₂²	semidirect
39. #16840813	C₂²	semidirect
40. #16840813	C₂²	semidirect
41. #16840813	C₂²	semidirect
42. #16840812	C₂²	semidirect
43. #16840812	C₂²	semidirect
44. #16840812	C₂²	semidirect
45. #16840812	C₂²	semidirect
46. #16840812	C₂²	semidirect
47. #16840812	C₂²	semidirect
48. #16840811	C₂²	semidirect
49. #16840811	C₂²	semidirect
50. #16840811	C₂²	semidirect
51. #16840811	C₂²	semidirect
52. #16840811	C₂²	semidirect
53. #16840811	C₂²	semidirect
54. Q₈×#92420	C₂²	semidirect
55. Q₈×#92420	C₂²	semidirect
667. C₆₁	#60252	semidirect

Maximal subgroups

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

subgroup	index
#21462732	2
#21462731	2
#21462729	2
#21462728	2
#21462727	2
#21462725	2
#21462724	2
#21462723	2
#21462617	2
#21462615	2
#21462613	2
#21462612	2
#21462611	2
#21462609	2
#21462608	2
#21462512	2
#21462510	2
#21462509	2
#21462500	2
D₆₁⋊#433	2
#21459223	2
#60252	61