Subgroups — #72256533

Order 2048.

At least 11927 conjugacy classes of subgroups; only the 1448 normal subgroups are shown.

The subgroup lattice has 967 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72256532	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256531	C₂	1	1	yes	maximal, characteristic, complemented
3	#72256528	C₂	1	1	yes	maximal, characteristic, complemented
4	#72256522	C₂	1	1	yes	maximal, characteristic, complemented
5	#72256519	C₂	1	1	yes	maximal, characteristic, complemented
6	#72256513	C₂	1	1	yes	maximal, characteristic, complemented
7	#72256488	C₂	1	1	yes	maximal, characteristic, complemented
8	#72256482	C₂	1	1	yes	maximal, characteristic, complemented
9	#72256481	C₂	1	1	yes	maximal, characteristic, complemented
10	#72256474	C₂	1	1	yes	maximal, characteristic, complemented
11	#72256385	C₂	1	1	yes	maximal, characteristic, complemented
12	#72255635	C₂	1	1	yes	maximal, characteristic, complemented
13	#72255621	C₂	1	1	yes	maximal, characteristic, complemented
14	#72252148	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#468843	C₂	1	1	yes	maximal, characteristic, complemented
16	#72250767	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#464072	C₂	1	1	yes	maximal, characteristic, complemented
18	#72250589	C₂	1	1	yes	maximal, characteristic, complemented
19	#72250462	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#404012	C₂	1	1	yes	maximal, characteristic, complemented
21	#72239650	C₂	1	1	yes	maximal, characteristic, complemented
22	#72239625	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#10576378	C₂	1	1	yes	maximal, characteristic, complemented
24	#72237671	C₂	1	1	yes	maximal, characteristic, complemented
25	#72237670	C₂	1	1	yes	maximal, characteristic, complemented
26	#72237516	C₂	1	1	yes	maximal, characteristic, complemented
27	#72237191	C₂	1	1	yes	maximal, characteristic, complemented
28	#72236778	C₂	1	1	yes	maximal, characteristic, complemented
29	#72236737	C₂	1	1	yes	maximal, characteristic, complemented
30	#72235076	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#393975	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#62814	C₂²	1	1	yes	characteristic
33	C₂²×#3484	C₂²	1	1	yes	characteristic
34	C₂×#60619	C₂²	1	1	yes	characteristic
35	C₂×#60518	C₂²	1	1	yes	characteristic
36	C₂×#60511	C₂²	1	1	yes	characteristic
37	C₂×#60490	C₂²	1	1	yes	characteristic
38	C₂×#60426	C₂²	1	1	yes	characteristic
39	C₂×#60454	C₂²	1	1	yes	characteristic
40	C₂×#60444	C₂²	1	1	yes	characteristic
41	C₂×#60367	C₂²	1	1	yes	characteristic
42	C₂²×#3019	C₂²	1	1	yes	characteristic
43	C₂²×#3003	C₂²	1	1	yes	characteristic
44	C₂×#60141	C₂²	1	1	yes	characteristic
45	C₂×#60168	C₂²	1	1	yes	characteristic
46	C₂×#60087	C₂²	1	1	yes	characteristic
47	C₂³×#418	C₂²	1	1	yes	characteristic
48	C₂×#35222	C₂²	1	1	yes	characteristic
49	C₂×#23649	C₂²	1	1	yes	characteristic, complemented
50	C₂×#23521	C₂²	1	1	yes	characteristic
51	C₂×#23472	C₂²	1	1	yes	characteristic, complemented
52	C₂×#23443	C₂²	1	1	yes	characteristic, complemented
53	C₂×#23414	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#2010	C₂²	1	1	yes	characteristic
55	C₂²×#2010	C₂²	1	1	yes	characteristic
56	C₂×#23412	C₂²	1	1	yes	characteristic, complemented
57	C₂×#23400	C₂²	1	1	yes	characteristic, complemented
58	C₂×#23402	C₂²	1	1	yes	characteristic
59	C₂×#23402	C₂²	1	1	yes	characteristic
60	#6431707	C₂²	1	1	yes	characteristic
61	#6371707	C₂²	1	1	yes	characteristic, complemented
62	C₂×#21012	C₂²	1	1	yes	characteristic, complemented
63	C₂²×#1911	C₂²	1	1	yes	characteristic
64	#6371536	C₂²	1	1	yes	characteristic, complemented
65	C₂×#20998	C₂²	1	1	yes	characteristic, complemented
66	C₂×#20979	C₂²	1	1	yes	characteristic, complemented
67	#6371477	C₂²	1	1	yes	characteristic, complemented
68	C₂²×#1795	C₂²	1	1	yes	characteristic
69	C₂×#20616	C₂²	1	1	yes	characteristic
70	#6370719	C₂²	1	1	yes	characteristic
71	C₂×#20598	C₂²	1	1	yes	characteristic
72	C₂×#20598	C₂²	1	1	yes	characteristic
73	C₂²×#1783	C₂²	1	1	yes	characteristic
74	C₂×#11389	C₂²	1	1	yes	characteristic, complemented
75	C₂×#11389	C₂²	1	1	yes	characteristic, complemented
76	#358798	C₂²	1	1	yes	characteristic, complemented
77	C₂×#11356	C₂²	1	1	yes	characteristic, complemented
78	C₂×#11356	C₂²	1	1	yes	characteristic, complemented
79	#358608	C₂²	1	1	yes	characteristic, complemented
80	C₂×#11284	C₂²	1	1	yes	characteristic, complemented
81	C₂×#11277	C₂²	1	1	yes	characteristic, complemented
82	#358031	C₂²	1	1	yes	characteristic, complemented
83	#357936	C₂²	1	1	yes	characteristic, complemented
84	C₂×#11178	C₂²	1	1	yes	characteristic, complemented
85	#357917	C₂²	1	1	yes	characteristic, complemented
86	C₂×#11157	C₂²	1	1	yes	characteristic
87	C₂×#11157	C₂²	1	1	yes	characteristic
88	C₂×#11157	C₂²	1	1	yes	characteristic
89	C₂×#11157	C₂²	1	1	yes	characteristic, complemented
90	C₂×#11157	C₂²	1	1	yes	characteristic, complemented
91	C₂×#11141	C₂²	1	1	yes	characteristic, complemented
92	C₂×#11132	C₂²	1	1	yes	characteristic, complemented
93	#357723	C₂²	1	1	yes	characteristic, complemented
94	C₂×#11058	C₂²	1	1	yes	characteristic, complemented
95	#357687	C₂²	1	1	yes	characteristic, complemented
96	#357651	C₂²	1	1	yes	characteristic, complemented
97	C₂×#11071	C₂²	1	1	yes	characteristic, complemented
98	C₂×#11037	C₂²	1	1	yes	characteristic, complemented
99	C₂×#11037	C₂²	1	1	yes	characteristic, complemented
100	C₂×#11037	C₂²	1	1	yes	characteristic, complemented
101	#357593	C₂²	1	1	yes	characteristic, complemented
102	C₂×#11034	C₂²	1	1	yes	characteristic, complemented
103	#357586	C₂²	1	1	yes	characteristic, complemented
104	C₂×#11030	C₂²	1	1	yes	characteristic, complemented
105	#357581	C₂²	1	1	yes	characteristic, complemented
106	#357575	C₂²	1	1	yes	characteristic, complemented
107	#357567	C₂²	1	1	yes	characteristic, complemented
108	C₂×#11014	C₂²	1	1	yes	characteristic
109	C₂×#11012	C₂²	1	1	yes	characteristic
110	#357561	C₂²	1	1	yes	characteristic, complemented
111	#357561	C₂²	1	1	yes	characteristic, complemented
112	C₂×#11004	C₂²	1	1	yes	characteristic
113	C₂×#11004	C₂²	1	1	yes	characteristic
114	C₂×#11004	C₂²	1	1	yes	characteristic
115	C₂×#11004	C₂²	1	1	yes	characteristic
116	C₂×#11004	C₂²	1	1	yes	characteristic, complemented
117	C₂×#11004	C₂²	1	1	yes	characteristic, complemented
118	C₂×#11003	C₂²	1	1	yes	characteristic, complemented
119	C₂×#11000	C₂²	1	1	yes	characteristic, complemented
120	C₂×#10994	C₂²	1	1	yes	characteristic
121	C₂×#10994	C₂²	1	1	yes	characteristic
122	C₂×#10994	C₂²	1	1	yes	characteristic
123	C₂×#10994	C₂²	1	1	yes	characteristic
124	C₂×#10994	C₂²	1	1	yes	characteristic, complemented
125	C₂×#10994	C₂²	1	1	yes	characteristic, complemented
126	C₂×#10993	C₂²	1	1	yes	characteristic
127	C₂×#10993	C₂²	1	1	yes	characteristic, complemented
128	C₂×#10993	C₂²	1	1	yes	characteristic, complemented
129	#357529	C₂²	1	1	yes	characteristic
130	C₂×#10989	C₂²	1	1	yes	characteristic
131	C₂×#10989	C₂²	1	1	yes	characteristic
132	C₂×#10987	C₂²	1	1	yes	characteristic
133	C₂×#10987	C₂²	1	1	yes	characteristic, complemented
134	C₂×#10984	C₂²	1	1	yes	characteristic
135	#357454	C₂²	1	1	yes	characteristic
136	#353518	C₂²	1	1	yes	characteristic, complemented
137	#353497	C₂²	1	1	yes	characteristic, complemented
138	#353497	C₂²	1	1	yes	characteristic, complemented
139	#353468	C₂²	1	1	yes	characteristic, complemented
140	C₂×#10785	C₂²	1	1	yes	characteristic
141	C₂×#10785	C₂²	1	1	yes	characteristic
142	C₂×#10783	C₂²	1	1	yes	characteristic, complemented
143	C₂×#10783	C₂²	1	1	yes	characteristic, complemented
144	C₂×#10743	C₂²	1	1	yes	characteristic, complemented
145	C₂×#10740	C₂²	1	1	yes	characteristic
146	C₂×#10738	C₂²	1	1	yes	characteristic, complemented
147	#353407	C₂²	1	1	yes	characteristic, complemented
148	#353388	C₂²	1	1	yes	characteristic, complemented
149	C₂×#10792	C₂²	1	1	yes	characteristic, complemented
150	C₂×#10778	C₂²	1	1	yes	characteristic, complemented
151	C₂×#10778	C₂²	1	1	yes	characteristic, complemented
152	#353354	C₂²	1	1	yes	characteristic, complemented
153	#353352	C₂²	1	1	yes	characteristic, complemented
154	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
155	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
156	C₂×#10716	C₂²	1	1	yes	characteristic, complemented
157	#123999	C₂²	1	1	yes	characteristic, complemented
158	#123992	C₂²	1	1	yes	characteristic, complemented
159	#123941	C₂²	1	1	yes	characteristic, complemented
160	#123940	C₂²	1	1	yes	characteristic, complemented
161	#123927	C₂²	1	1	yes	characteristic, complemented
162	#123926	C₂²	1	1	yes	characteristic, complemented
163	#123628	C₂²	1	1	yes	characteristic
164	#123622	C₂²	1	1	yes	characteristic, complemented
165	#123619	C₂²	1	1	yes	characteristic
166	#123619	C₂²	1	1	yes	characteristic
167	#123619	C₂²	1	1	yes	characteristic, complemented
168	#123619	C₂²	1	1	yes	characteristic, complemented
169	#123619	C₂²	1	1	yes	characteristic, complemented
170	#123616	C₂²	1	1	yes	characteristic, complemented
171	#123616	C₂²	1	1	yes	characteristic, complemented
172	#123616	C₂²	1	1	yes	characteristic, complemented
173	#123605	C₂²	1	1	yes	characteristic
174	#123605	C₂²	1	1	yes	characteristic
175	#123605	C₂²	1	1	yes	characteristic, complemented
176	#123605	C₂²	1	1	yes	characteristic, complemented
177	#123605	C₂²	1	1	yes	characteristic, complemented
178	#123604	C₂²	1	1	yes	characteristic, complemented
179	#123604	C₂²	1	1	yes	characteristic, complemented
180	#123604	C₂²	1	1	yes	characteristic, complemented
181	#123600	C₂²	1	1	yes	characteristic
182	#123556	C₂²	1	1	yes	characteristic, complemented
183	#123555	C₂²	1	1	yes	characteristic, complemented
184	#123554	C₂²	1	1	yes	characteristic, complemented
185	#123532	C₂²	1	1	yes	characteristic, complemented
186	#123531	C₂²	1	1	yes	characteristic, complemented
187	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
188	C₂⁵×D₄	C₂³	1	1	yes	characteristic
189	C₂²×#575	C₂³	1	1	yes	characteristic
190	C₂²×#575	C₂³	1	1	yes	characteristic
191	C₂²×#575	C₂³	1	1	yes	characteristic
192	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
193	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
194	C₂²×#568	C₂³	1	1	yes	characteristic
195	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
196	#62814	D₄	1	8	yes	complemented
197	C₂×#3484	D₄	1	8	yes	complemented
198	C₂×#3458	C₂³	1	1	yes	characteristic
199	C₂×#3449	C₂³	1	1	yes	characteristic
200	C₂×#3449	C₂³	1	1	yes	characteristic
201	C₂²×#535	C₂³	1	1	yes	characteristic
202	C₂²×#535	C₂³	1	1	yes	characteristic
203	C₂²×#535	C₂³	1	1	yes	characteristic
204	C₂²×#535	C₂³	1	1	yes	characteristic
205	C₂²×#525	C₂³	1	1	yes	characteristic
206	C₂²×#525	C₂³	1	1	yes	characteristic
207	C₂²×#525	C₂³	1	1	yes	characteristic
208	C₂²×#525	C₂³	1	1	yes	characteristic
209	C₂×#3428	C₂³	1	1	yes	characteristic
210	C₂×#3428	C₂³	1	1	yes	characteristic
211	C₂²×#518	C₂³	1	1	yes	characteristic
212	C₂³×#117	C₂³	1	1	yes	characteristic
213	C₂×#3140	D₄	1	4	yes	complemented
214	C₂×#3138	D₄	1	4	yes	complemented
215	#60490	D₄	1	8	yes	complemented
216	#60426	D₄	1	8	yes	complemented
217	C₂×#2949	D₄	1	4	yes	complemented
218	C₂×#2948	D₄	1	4	yes	complemented
219	C₂×#2930	D₄	1	4	yes	complemented
220	C₂×#2929	D₄	1	4	yes	complemented
221	C₂×#2911	C₂³	1	1	yes	characteristic
222	C₂×#2911	C₂³	1	1	yes	characteristic
223	C₂×#2911	C₂³	1	1	yes	characteristic
224	C₂×#2905	C₂³	1	1	yes	characteristic
225	C₂×#2905	C₂³	1	1	yes	characteristic
226	C₂²×#421	C₂³	1	1	yes	characteristic
227	C₂²×#421	C₂³	1	1	yes	characteristic
228	C₂²×#421	C₂³	1	1	yes	characteristic
229	C₂²×#421	C₂³	1	1	yes	characteristic
230	C₂²×#421	C₂³	1	1	yes	characteristic
231	C₂²×#421	C₂³	1	1	yes	characteristic
232	C₂²×#421	C₂³	1	1	yes	characteristic
233	C₂²×#421	C₂³	1	1	yes	characteristic
234	C₂²×#421	C₂³	1	1	yes	characteristic
235	C₂²×#421	C₂³	1	1	yes	characteristic
236	C₂²×#421	C₂³	1	1	yes	characteristic
237	C₂²×#421	C₂³	1	1	yes	characteristic
238	C₂×#2896	C₂³	1	1	yes	characteristic
239	C₂×#2896	C₂³	1	1	yes	characteristic
240	C₂×#2896	C₂³	1	1	yes	characteristic
241	C₂×#2896	C₂³	1	1	yes	characteristic
242	C₂×#2896	C₂³	1	1	yes	characteristic
243	C₂×#2896	C₂³	1	1	yes	characteristic
244	C₂×#2896	C₂³	1	1	yes	characteristic
245	C₂×#2896	C₂³	1	1	yes	characteristic
246	C₂×#2896	C₂³	1	1	yes	characteristic
247	C₂×#2896	C₂³	1	1	yes	characteristic
248	C₂×#2896	C₂³	1	1	yes	characteristic
249	C₂×#2896	C₂³	1	1	yes	characteristic
250	C₂²×#418	C₂³	1	1	yes	characteristic
251	C₂²×#418	C₂³	1	1	yes	characteristic
252	C₂²×#418	C₂³	1	1	yes	characteristic
253	C₂²×#418	C₂³	1	1	yes	characteristic
254	C₂²×#418	C₂³	1	1	yes	characteristic
255	C₂²×#418	C₂³	1	1	yes	characteristic
256	C₂²×#418	C₂³	1	1	yes	characteristic
257	C₂²×#418	C₂³	1	1	yes	characteristic
258	C₂²×#418	C₂³	1	1	yes	characteristic
259	C₂²×#418	C₂³	1	1	yes	characteristic
260	C₂²×#418	C₂³	1	1	yes	characteristic
261	C₂²×#418	C₂³	1	1	yes	characteristic
262	C₂²×#418	C₂³	1	1	yes	characteristic
263	C₂²×#418	C₂³	1	1	yes	characteristic
264	C₂²×#413	C₂³	1	1	yes	characteristic
265	C₂²×#413	C₂³	1	1	yes	characteristic
266	C₂²×#413	C₂³	1	1	yes	characteristic
267	C₂³×#100	C₂³	1	1	yes	characteristic
268	C₂³×#100	C₂³	1	1	yes	characteristic
269	C₂³×#100	C₂³	1	1	yes	characteristic
270	C₂³×#100	C₂³	1	1	yes	characteristic
271	C₂²×#410	C₂³	1	1	yes	characteristic
272	C₂²×#410	C₂³	1	1	yes	characteristic
273	C₂²×#410	C₂³	1	1	yes	characteristic
274	C₂×#2879	C₂³	1	1	yes	characteristic
275	C₂×#2879	C₂³	1	1	yes	characteristic
276	C₂×#2879	C₂³	1	1	yes	characteristic
277	C₂×#2879	C₂³	1	1	yes	characteristic
278	C₂²×#407	C₂³	1	1	yes	characteristic
279	C₂²×#407	C₂³	1	1	yes	characteristic
280	C₂²×#407	C₂³	1	1	yes	characteristic
281	C₂²×#407	C₂³	1	1	yes	characteristic
282	C₂²×#407	C₂³	1	1	yes	characteristic
283	C₂×#2873	C₂³	1	1	yes	characteristic
284	#34044	C₂³	1	1	yes	characteristic
285	C₂×#2309	C₂³	1	1	yes	characteristic
286	C₂×#2309	C₂³	1	1	yes	characteristic
287	C₂×#2280	C₂³	1	1	yes	characteristic
288	C₂×#2280	C₂³	1	1	yes	characteristic
289	C₂×#2280	C₂³	1	1	yes	characteristic
290	C₂²×#344	C₂³	1	1	yes	characteristic
291	C₂²×#344	C₂³	1	1	yes	characteristic
292	C₂²×#344	C₂³	1	1	yes	characteristic
293	C₂²×#344	C₂³	1	1	yes	characteristic
294	C₂²×#344	C₂³	1	1	yes	characteristic
295	C₂²×#344	C₂³	1	1	yes	characteristic
296	C₂²×#344	C₂³	1	1	yes	characteristic
297	C₂²×#344	C₂³	1	1	yes	characteristic
298	C₂²×#344	C₂³	1	1	yes	characteristic
299	C₂²×#344	C₂³	1	1	yes	characteristic
300	C₂²×#344	C₂³	1	1	yes	characteristic
301	C₂²×#344	C₂³	1	1	yes	characteristic
302	C₂²×#344	C₂³	1	1	yes	characteristic
303	C₂²×#344	C₂³	1	1	yes	characteristic
304	C₂²×#344	C₂³	1	1	yes	characteristic
305	C₂²×#344	C₂³	1	1	yes	characteristic
306	C₂²×#344	C₂³	1	1	yes	characteristic
307	C₂²×#344	C₂³	1	1	yes	characteristic
308	C₂²×#344	C₂³	1	1	yes	characteristic
309	C₂²×#344	C₂³	1	1	yes	characteristic
310	C₂×#1742	C₂³	1	1	yes	characteristic
311	C₂×#1740	C₂³	1	1	yes	characteristic
312	C₂×#1740	C₂³	1	1	yes	characteristic
313	C₂×#1740	C₂³	1	1	yes	characteristic
314	C₂×#1740	C₂³	1	1	yes	characteristic
315	C₂×#1740	C₂³	1	1	yes	characteristic
316	C₂×#1740	C₂³	1	1	yes	characteristic
317	C₂×#1740	C₂³	1	1	yes	characteristic
318	C₂×#1738	C₂³	1	1	yes	characteristic
319	C₂×#1738	C₂³	1	1	yes	characteristic
320	C₂×#1738	C₂³	1	1	yes	characteristic
321	C₂×#1738	C₂³	1	1	yes	characteristic
322	C₂×#1738	C₂³	1	1	yes	characteristic
323	C₂×#1738	C₂³	1	1	yes	characteristic
324	C₂×#1738	C₂³	1	1	yes	characteristic
325	#20347	C₂³	1	1	yes	characteristic
326	#20347	C₂³	1	1	yes	characteristic
327	#20347	C₂³	1	1	yes	characteristic
328	C₂×#1733	C₂³	1	1	yes	characteristic
329	C₂×#1733	C₂³	1	1	yes	characteristic
330	C₂×#1733	C₂³	1	1	yes	characteristic
331	C₂×#1733	C₂³	1	1	yes	characteristic
332	C₂×#1733	C₂³	1	1	yes	characteristic
333	C₂×#1733	C₂³	1	1	yes	characteristic
334	C₂×#1733	C₂³	1	1	yes	characteristic
335	C₂×#1733	C₂³	1	1	yes	characteristic
336	C₂×#1733	C₂³	1	1	yes	characteristic
337	C₂×#1733	C₂³	1	1	yes	characteristic
338	C₂²×#338	C₂³	1	1	yes	characteristic
339	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
340	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
341	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
342	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
343	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
344	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
345	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
346	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
347	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
348	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
349	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
350	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
351	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
352	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
353	C₂³×#41	C₂⁴	1	1	yes	characteristic
354	C₂³×#41	C₂⁴	1	1	yes	characteristic
355	C₂³×#41	C₂⁴	1	1	yes	characteristic
356	C₂³×#41	C₂⁴	1	1	yes	characteristic
357	C₂⁴×D₄	C₂×D₄	1	4	yes	—
358	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
359	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
360	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
361	C₂×#575	C₂×D₄	1	4	yes	—
362	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
363	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
364	C₂³×D₈	C₂×D₄	1	2	yes	—
365	C₂²×#131	C₂×D₄	1	4	yes	—
366	C₂³×M₁₆	C₂×D₄	1	2	yes	—
367	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
368	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
369	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
370	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
371	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
372	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
373	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
374	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
375	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
376	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
377	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
378	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₈	C₂×D₄	1	2	yes	—
380	#3458	C₂×D₄	1	4	yes	—
381	#3458	C₂×D₄	1	4	yes	—
382	#3449	C₂×D₄	1	4	yes	—
383	C₂×#535	C₂×D₄	1	4	yes	—
384	C₂×#535	C₂×D₄	1	4	yes	—
385	C₂×#535	C₂×D₄	1	4	yes	—
386	C₂×#533	C₂×D₄	1	4	yes	—
387	C₂²×#127	C₂×D₄	1	2	yes	—
388	C₂²×#124	C₂×D₄	1	2	yes	—
389	C₂×#525	C₂×D₄	1	2	yes	—
390	C₂×#525	C₂×D₄	1	2	yes	—
391	C₂×#525	C₂×D₄	1	4	yes	—
392	C₂×#525	C₂×D₄	1	4	yes	—
393	C₂×#525	C₂×D₄	1	4	yes	—
394	C₂×#525	C₂×D₄	1	4	yes	—
395	#3428	C₂×D₄	1	4	yes	—
396	#3428	C₂×D₄	1	4	yes	—
397	#3428	C₂×D₄	1	4	yes	—
398	C₂×#519	C₂×D₄	1	2	yes	—
399	C₂×#518	C₂×D₄	1	4	yes	—
400	C₂×#518	C₂×D₄	1	4	yes	—
401	C₂×#518	C₂×D₄	1	4	yes	—
402	C₂×#518	C₂×D₄	1	2	yes	—
403	C₂²×#117	C₂×D₄	1	4	yes	—
404	C₂²×#117	C₂⁴	1	1	yes	characteristic
405	C₂²×#117	C₂⁴	1	1	yes	characteristic
406	C₂²×#117	C₂⁴	1	1	yes	characteristic
407	C₂²×#117	C₂⁴	1	1	yes	characteristic
408	C₂²×#117	C₂⁴	1	1	yes	characteristic
409	C₂²×#117	C₂⁴	1	1	yes	characteristic
410	C₂²×#117	C₂⁴	1	1	yes	characteristic
411	C₂²×#117	C₂⁴	1	1	yes	characteristic
412	C₂²×#117	C₂⁴	1	1	yes	characteristic
413	C₂²×#117	C₂⁴	1	1	yes	characteristic
414	C₂²×#117	C₂⁴	1	1	yes	characteristic
415	C₂²×#117	C₂⁴	1	1	yes	characteristic
416	#2911	C₂×D₄	1	4	yes	—
417	#2911	C₂×D₄	1	4	yes	—
418	C₂×#427	C₂×D₄	1	4	yes	—
419	#2905	C₂×D₄	1	4	yes	—
420	#2905	C₂×D₄	1	4	yes	—
421	C₂×#424	C₂×D₄	1	4	yes	—
422	#2896	C₂×D₄	1	4	yes	—
423	C₂×#419	C₂×D₄	1	2	yes	—
424	C₂×#419	C₂×D₄	1	2	yes	—
425	C₂×#419	C₂×D₄	1	2	yes	—
426	C₂×#418	C₂×D₄	1	2	yes	—
427	C₂×#418	C₂×D₄	1	4	yes	—
428	C₂×#418	C₂×D₄	1	2	yes	—
429	C₂×#418	C₂×D₄	1	4	yes	—
430	C₂×#418	C₂×D₄	1	2	yes	—
431	C₂×#418	C₂×D₄	1	4	yes	—
432	C₂×#418	C₂×D₄	1	4	yes	—
433	C₂×#418	C₂×D₄	1	4	yes	—
434	C₂×#418	C₂×D₄	1	4	yes	—
435	C₂²×#100	#41	1	4	yes	complemented
436	C₂×#408	C₂×D₄	1	4	yes	—
437	C₂×#407	C₂×D₄	1	2	yes	—
438	C₂×#407	C₂×D₄	1	2	yes	—
439	C₂×#405	C₂×D₄	1	4	yes	—
440	C₂×#405	C₂×D₄	1	4	yes	—
441	C₂×C₄×M₁₆	C₂×D₄	1	4	yes	—
442	#2309	#41	1	4	yes	complemented
443	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×#41	C₂²×D₄	1	2	yes	—
445	C₂²×#41	C₂²×D₄	1	2	yes	—
446	C₂²×#41	C₂²×D₄	1	2	yes	—
447	C₂²×#41	C₂²×D₄	1	2	yes	—
448	C₂²×#41	C₂²×D₄	1	2	yes	—
449	C₂²×#41	C₂²×D₄	1	2	yes	—
450	C₂²×#41	C₂²×D₄	1	2	yes	—
451	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
452	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
453	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
454	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
455	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
456	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
457	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
458	C₂³×D₄	C₂²×D₄	1	2	yes	—
459	C₂³×D₄	C₂²×D₄	1	2	yes	—
460	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
461	C₂³×D₄	C₂²×D₄	1	2	yes	—
462	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
463	C₂³×D₄	C₂²×D₄	1	2	yes	—
464	C₂³×D₄	C₂²×D₄	1	2	yes	—
465	C₂³×D₄	C₂²×D₄	1	2	yes	—
466	C₂³×D₄	C₂×#41	1	2	yes	—
467	C₂³×D₄	C₂×#41	1	2	yes	—
468	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
469	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
470	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
471	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
472	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
473	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
474	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
475	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
476	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
477	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
478	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
479	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
480	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
481	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
482	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
483	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
484	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
485	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
486	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
487	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
488	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
489	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
490	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
491	C₂²×M₁₆	C₂×#41	1	2	yes	—
492	C₂²×M₁₆	C₂×#41	1	2	yes	—
493	C₂³×C₈	C₂²×D₄	1	2	yes	—
494	C₂³×C₈	C₂²×D₄	1	2	yes	—
495	C₂³×C₈	C₂²×D₄	1	2	yes	—
496	#533	#120	1	16	yes	complemented
497	C₂×#127	#120	1	8	yes	—
498	C₂×#124	#120	1	8	yes	—
499	#525	#120	1	8	yes	—
500	#525	#120	1	8	yes	—
501	#519	#120	1	8	yes	complemented
502	#518	#120	1	16	yes	—
503	#518	#120	1	8	yes	complemented
504	C₂×#117	C₂²×D₄	1	2	yes	—
505	C₂×#117	C₂²×D₄	1	2	yes	—
506	C₂×#117	C₂²×D₄	1	2	yes	—
507	C₂×#117	C₂²×D₄	1	2	yes	—
508	C₂×#117	C₂²×D₄	1	2	yes	—
509	C₂×#117	C₂²×D₄	1	2	yes	—
510	C₂×#117	C₂²×D₄	1	2	yes	—
511	C₂×#117	C₂²×D₄	1	2	yes	—
512	C₂×#117	C₂²×D₄	1	2	yes	—
513	C₂×#117	C₂²×D₄	1	2	yes	—
514	C₂×#117	C₂²×D₄	1	2	yes	—
515	C₂×#117	C₂²×D₄	1	2	yes	—
516	C₂×#117	C₂²×D₄	1	2	yes	—
517	C₂×#117	C₂²×D₄	1	2	yes	—
518	C₂×#117	C₂²×D₄	1	2	yes	—
519	C₂×#117	C₂²×D₄	1	2	yes	—
520	C₂×#117	C₂²×D₄	1	2	yes	—
521	C₂×#117	C₂²×D₄	1	2	yes	—
522	C₂×#117	C₂×#41	1	2	yes	—
523	C₂×#117	C₂×#41	1	2	yes	—
524	C₂×#117	H(5,𝔽₂)	1	2	yes	—
525	C₂×#117	H(5,𝔽₂)	1	2	yes	—
526	C₂²×C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
527	C₂²×C₄²	C₂²×D₄	1	2	yes	—
528	#424	#120	1	16	yes	complemented
529	C₂×#97	#120	1	8	yes	complemented
530	C₂×C₄×C₈	#120	1	8	yes	complemented
531	C₂⁵	#534	1	2	yes	—
532	C₂⁵	#534	1	2	yes	—
533	C₂⁵	#535	1	1	yes	characteristic
534	C₂⁵	#535	1	1	yes	characteristic
535	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂×#41	C₂×#120	1	4	yes	—
537	C₂×#41	#534	1	4	yes	—
538	C₂×#41	#534	1	4	yes	—
539	C₂×#41	#535	1	4	yes	—
540	C₂²×Q₈	C₂×#120	1	2	yes	—
541	C₂²×Q₈	C₂×#120	1	2	yes	—
542	C₂²×Q₈	#534	1	2	yes	—
543	C₂²×Q₈	#534	1	2	yes	—
544	C₂²×Q₈	#535	1	2	yes	—
545	C₂²×D₄	C₂×#120	1	2	yes	—
546	C₂²×D₄	C₂×#120	1	4	yes	—
547	C₂²×D₄	C₂×#120	1	2	yes	—
548	C₂²×D₄	C₂×#120	1	4	yes	—
549	C₂²×D₄	#532	1	4	yes	—
550	C₂²×D₄	#534	1	2	yes	—
551	C₂²×D₄	#534	1	2	yes	—
552	C₂²×D₄	#535	1	2	yes	—
553	C₂²×D₄	#535	1	4	yes	—
554	C₂²×D₄	#546	1	4	yes	—
555	C₂²×D₄	#546	1	4	yes	—
556	C₂²×D₄	#550	1	4	yes	—
557	C₂²×D₄	#550	1	4	yes	—
558	C₂³×C₄	C₂×#120	1	2	yes	—
559	C₂³×C₄	C₂×#120	1	2	yes	—
560	C₂³×C₄	#534	1	2	yes	—
561	C₂³×C₄	#534	1	2	yes	—
562	C₂³×C₄	#534	1	2	yes	—
563	C₂³×C₄	#534	1	2	yes	—
564	C₂³×C₄	#534	1	2	yes	—
565	C₂³×C₄	#534	1	2	yes	—
566	C₂³×C₄	#535	1	1	yes	characteristic
567	C₂³×C₄	#535	1	1	yes	characteristic
568	C₂³×C₄	#535	1	2	yes	—
569	C₂³×C₄	#535	1	2	yes	—
570	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
571	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
572	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
573	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
574	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
575	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
576	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
577	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
578	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
579	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂³×C₄	#585	1	1	yes	characteristic
593	C₂³×C₄	#585	1	1	yes	characteristic
594	C₂³×C₄	#585	1	1	yes	characteristic
595	C₂³×C₄	#585	1	1	yes	characteristic
596	C₂³×C₄	#585	1	1	yes	characteristic
597	C₂³×C₄	#585	1	1	yes	characteristic
598	C₂³×C₄	#585	1	1	yes	characteristic
599	C₂³×C₄	#585	1	1	yes	characteristic
600	C₂×M₁₆	C₂×#120	1	4	yes	—
601	C₂²×C₈	C₂×#120	1	4	yes	—
602	C₂²×C₈	C₂×#120	1	4	yes	—
603	C₂²×C₈	C₂×#120	1	4	yes	—
604	#117	C₂×#120	1	4	yes	—
605	#117	C₂×#120	1	4	yes	—
606	#117	C₂×#120	1	4	yes	—
607	#117	C₂×#120	1	4	yes	—
608	#117	C₂×#120	1	4	yes	—
609	#117	C₂×#120	1	4	yes	—
610	#117	C₂×#120	1	4	yes	—
611	#117	C₂×#120	1	4	yes	—
612	C₂×C₄²	C₂×#120	1	4	yes	—
613	C₂×C₄²	C₂×#120	1	4	yes	—
614	C₂×C₄²	C₂×#120	1	4	yes	—
615	C₂⁴	#2613	1	2	yes	—
616	C₂⁴	#2613	1	2	yes	—
617	C₂⁴	C₂×#534	1	1	yes	characteristic
618	C₂⁴	C₂×#534	1	1	yes	characteristic
619	C₂⁴	C₂×#535	1	1	yes	characteristic
620	C₂⁴	#3484	1	1	yes	characteristic
621	C₂⁴	#3484	1	1	yes	characteristic
622	C₂⁴	#3484	1	1	yes	characteristic
623	C₂⁴	#3484	1	1	yes	characteristic
624	C₂⁴	#3490	1	1	yes	characteristic
625	C₂⁴	#3494	1	1	yes	characteristic
626	C₂⁴	#3532	1	1	yes	characteristic
627	C₂⁴	#3534	1	1	yes	characteristic
628	C₂⁴	#3534	1	1	yes	characteristic
629	C₂⁴	#3534	1	1	yes	characteristic
630	C₂⁴	#3545	1	1	yes	characteristic
631	C₂⁴	#3560	1	1	yes	characteristic
632	C₂×Q₈	#2613	1	4	yes	—
633	C₂×D₄	#2431	1	8	yes	—
634	C₂×D₄	#2613	1	4	yes	—
635	C₂²×C₄	#2613	1	2	yes	—
636	C₂²×C₄	#2613	1	2	yes	—
637	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
638	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
639	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
640	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
641	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
642	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
643	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
644	C₂²×C₄	C₂×#532	1	1	yes	characteristic
645	C₂²×C₄	C₂×#534	1	1	yes	characteristic
646	C₂²×C₄	C₂×#534	1	1	yes	characteristic
647	C₂²×C₄	C₂×#534	1	1	yes	characteristic
648	C₂²×C₄	C₂×#534	1	1	yes	characteristic
649	C₂²×C₄	C₂×#534	1	1	yes	characteristic
650	C₂²×C₄	C₂×#534	1	1	yes	characteristic
651	C₂²×C₄	C₂×#535	1	1	yes	characteristic
652	C₂²×C₄	C₂×#535	1	1	yes	characteristic
653	C₂²×C₄	C₂×#535	1	1	yes	characteristic
654	C₂²×C₄	C₂×#535	1	1	yes	characteristic
655	C₂²×C₄	#3449	1	1	yes	characteristic
656	C₂²×C₄	#3449	1	1	yes	characteristic
657	C₂²×C₄	C₂×#546	1	1	yes	characteristic
658	C₂²×C₄	C₂×#546	1	1	yes	characteristic
659	C₂²×C₄	C₂×#550	1	1	yes	characteristic
660	C₂²×C₄	C₂×#550	1	1	yes	characteristic
661	C₂²×C₄	D₄×#41	1	1	yes	characteristic
662	C₂²×C₄	D₄×#41	1	1	yes	characteristic
663	C₂²×C₄	D₄×#41	1	1	yes	characteristic
664	C₂²×C₄	D₄×#41	1	1	yes	characteristic
665	C₂²×C₄	D₄×#41	1	1	yes	characteristic
666	C₂²×C₄	D₄×#41	1	1	yes	characteristic
667	C₂²×C₄	D₄×#41	1	1	yes	characteristic
668	C₂²×C₄	D₄×#41	1	1	yes	characteristic
669	C₂²×C₄	#3484	1	1	yes	characteristic
670	C₂²×C₄	#3484	1	1	yes	characteristic
671	C₂²×C₄	#3484	1	1	yes	characteristic
672	C₂²×C₄	#3484	1	1	yes	characteristic
673	C₂²×C₄	#3484	1	1	yes	characteristic
674	C₂²×C₄	#3484	1	1	yes	characteristic
675	C₂²×C₄	#3484	1	1	yes	characteristic
676	C₂²×C₄	#3484	1	1	yes	characteristic
677	C₂²×C₄	#3484	1	1	yes	characteristic
678	C₂²×C₄	#3484	1	1	yes	characteristic
679	C₂²×C₄	#3484	1	1	yes	characteristic
680	C₂²×C₄	#3484	1	1	yes	characteristic
681	C₂²×C₄	#3484	1	1	yes	characteristic
682	C₂²×C₄	#3484	1	1	yes	characteristic
683	C₂²×C₄	#3484	1	1	yes	characteristic
684	C₂²×C₄	#3485	1	1	yes	characteristic
685	C₂²×C₄	#3485	1	1	yes	characteristic
686	C₂²×C₄	#3485	1	1	yes	characteristic
687	C₂²×C₄	#3485	1	1	yes	characteristic
688	C₂²×C₄	#3485	1	1	yes	characteristic
689	C₂²×C₄	#3487	1	1	yes	characteristic
690	C₂²×C₄	#3487	1	1	yes	characteristic
691	C₂²×C₄	#3488	1	1	yes	characteristic
692	C₂²×C₄	#3488	1	1	yes	characteristic
693	C₂²×C₄	#3488	1	1	yes	characteristic
694	C₂²×C₄	#3488	1	1	yes	characteristic
695	C₂²×C₄	#3488	1	1	yes	characteristic
696	C₂²×C₄	#3488	1	1	yes	characteristic
697	C₂²×C₄	#3488	1	1	yes	characteristic
698	C₂²×C₄	#3488	1	1	yes	characteristic
699	C₂²×C₄	#3488	1	1	yes	characteristic
700	C₂²×C₄	#3488	1	1	yes	characteristic
701	C₂²×C₄	#3488	1	1	yes	characteristic
702	C₂²×C₄	#3488	1	1	yes	characteristic
703	C₂²×C₄	#3488	1	1	yes	characteristic
704	C₂²×C₄	#3488	1	1	yes	characteristic
705	C₂²×C₄	#3488	1	1	yes	characteristic
706	C₂²×C₄	#3488	1	1	yes	characteristic
707	C₂²×C₄	#3488	1	1	yes	characteristic
708	C₂²×C₄	#3488	1	1	yes	characteristic
709	C₂²×C₄	#3490	1	1	yes	characteristic
710	C₂²×C₄	#3490	1	1	yes	characteristic
711	C₂²×C₄	#3490	1	1	yes	characteristic
712	C₂²×C₄	#3494	1	1	yes	characteristic
713	C₂²×C₄	#3494	1	1	yes	characteristic
714	C₂²×C₄	#3494	1	1	yes	characteristic
715	C₂²×C₄	#3496	1	1	yes	characteristic
716	C₂²×C₄	#3496	1	1	yes	characteristic
717	C₂²×C₄	#3496	1	1	yes	characteristic
718	C₂²×C₄	#3496	1	1	yes	characteristic
719	C₂²×C₄	#3496	1	1	yes	characteristic
720	C₂²×C₄	#3496	1	1	yes	characteristic
721	C₂²×C₄	#3498	1	1	yes	characteristic
722	C₂²×C₄	#3498	1	1	yes	characteristic
723	C₂²×C₄	#3498	1	1	yes	characteristic
724	C₂²×C₄	#3500	1	1	yes	characteristic
725	C₂²×C₄	#3500	1	1	yes	characteristic
726	C₂²×C₄	#3500	1	1	yes	characteristic
727	C₂²×C₄	#3513	1	1	yes	characteristic
728	C₂²×C₄	#3513	1	1	yes	characteristic
729	C₂²×C₄	#3513	1	1	yes	characteristic
730	C₂²×C₄	#3513	1	1	yes	characteristic
731	C₂²×C₄	#3519	1	1	yes	characteristic
732	C₂²×C₄	#3519	1	1	yes	characteristic
733	C₂²×C₄	#3519	1	1	yes	characteristic
734	C₂²×C₄	#3519	1	1	yes	characteristic
735	C₂²×C₄	#3532	1	1	yes	characteristic
736	C₂²×C₄	#3532	1	1	yes	characteristic
737	C₂²×C₄	#3532	1	1	yes	characteristic
738	C₂²×C₄	#3532	1	1	yes	characteristic
739	C₂²×C₄	#3532	1	1	yes	characteristic
740	C₂²×C₄	#3532	1	1	yes	characteristic
741	C₂²×C₄	#3532	1	1	yes	characteristic
742	C₂²×C₄	#3533	1	1	yes	characteristic
743	C₂²×C₄	#3533	1	1	yes	characteristic
744	C₂²×C₄	#3533	1	1	yes	characteristic
745	C₂²×C₄	#3533	1	1	yes	characteristic
746	C₂²×C₄	#3534	1	1	yes	characteristic
747	C₂²×C₄	#3534	1	1	yes	characteristic
748	C₂²×C₄	#3534	1	1	yes	characteristic
749	C₂²×C₄	#3534	1	1	yes	characteristic
750	C₂²×C₄	#3534	1	1	yes	characteristic
751	C₂²×C₄	#3534	1	1	yes	characteristic
752	C₂²×C₄	#3534	1	1	yes	characteristic
753	C₂²×C₄	#3534	1	1	yes	characteristic
754	C₂²×C₄	#3534	1	1	yes	characteristic
755	C₂²×C₄	#3534	1	1	yes	characteristic
756	C₂²×C₄	#3534	1	1	yes	characteristic
757	C₂²×C₄	#3534	1	1	yes	characteristic
758	C₂²×C₄	#3534	1	1	yes	characteristic
759	C₂²×C₄	#3542	1	1	yes	characteristic
760	C₂²×C₄	#3542	1	1	yes	characteristic
761	C₂²×C₄	#3542	1	1	yes	characteristic
762	C₂²×C₄	#3542	1	1	yes	characteristic
763	C₂²×C₄	#3545	1	1	yes	characteristic
764	C₂²×C₄	#3545	1	1	yes	characteristic
765	C₂²×C₄	#3545	1	1	yes	characteristic
766	C₂²×C₄	#3558	1	1	yes	characteristic
767	C₂²×C₄	#3558	1	1	yes	characteristic
768	C₂²×C₄	#3558	1	1	yes	characteristic
769	C₂²×C₄	#3558	1	1	yes	characteristic
770	C₂²×C₄	#3560	1	1	yes	characteristic
771	C₂²×C₄	#3560	1	1	yes	characteristic
772	C₂²×C₄	#3560	1	1	yes	characteristic
773	C₂²×C₄	#3560	1	1	yes	characteristic
774	C₂²×C₄	#3560	1	1	yes	characteristic
775	C₂²×C₄	#3560	1	1	yes	characteristic
776	C₂²×C₄	#3560	1	1	yes	characteristic
777	C₄²	#2846	1	8	yes	—
778	C₂³	C₂×#2613	1	1	yes	characteristic
779	C₂³	#34980	1	1	yes	characteristic
780	C₂³	#34980	1	1	yes	characteristic
781	C₂³	#34980	1	1	yes	characteristic
782	C₂³	#34980	1	1	yes	characteristic
783	C₂³	#35222	1	1	yes	characteristic
784	C₂³	#35222	1	1	yes	characteristic
785	C₂³	#35922	1	1	yes	characteristic
786	C₂³	#37832	1	1	yes	characteristic
787	C₂³	#37834	1	1	yes	characteristic
788	C₂³	#38420	1	1	yes	characteristic
789	C₂³	#38423	1	1	yes	characteristic
790	C₂³	#38424	1	1	yes	characteristic
791	C₂³	#38428	1	1	yes	characteristic
792	C₂³	#40508	1	1	yes	characteristic
793	C₂³	#40510	1	1	yes	characteristic
794	C₂³	#40588	1	1	yes	characteristic
795	C₂³	#40588	1	1	yes	characteristic
796	C₂³	#40606	1	1	yes	characteristic
797	C₂³	#41410	1	1	yes	characteristic
798	C₂³	#41981	1	1	yes	characteristic
799	C₂³	#41981	1	1	yes	characteristic
800	C₂³	#41989	1	1	yes	characteristic
801	C₂³	#43013	1	1	yes	characteristic
802	C₂³	#43099	1	1	yes	characteristic
803	C₂³	#43099	1	1	yes	characteristic
804	C₂³	#43901	1	1	yes	characteristic
805	C₂³	#44228	1	1	yes	characteristic
806	C₂³	#44779	1	1	yes	characteristic
807	C₂³	#47830	1	1	yes	characteristic
808	C₂³	#47944	1	1	yes	characteristic
809	C₂³	#47948	1	1	yes	characteristic
810	C₂³	#49550	1	1	yes	characteristic
811	C₂³	#50864	1	1	yes	characteristic
812	C₂³	#50864	1	1	yes	characteristic
813	C₂×C₄	C₂×#2613	1	1	yes	characteristic
814	C₂×C₄	C₂×#2431	1	1	yes	characteristic
815	C₂×C₄	#34738	1	1	yes	characteristic
816	C₂×C₄	#34738	1	1	yes	characteristic
817	C₂×C₄	#34980	1	1	yes	characteristic
818	C₂×C₄	#34980	1	1	yes	characteristic
819	C₂×C₄	#34980	1	1	yes	characteristic
820	C₂×C₄	#34980	1	1	yes	characteristic
821	C₂×C₄	#35149	1	1	yes	characteristic
822	C₂×C₄	#35222	1	1	yes	characteristic
823	C₂×C₄	#35222	1	1	yes	characteristic
824	C₂×C₄	#35250	1	1	yes	characteristic
825	C₂×C₄	#35250	1	1	yes	characteristic
826	C₂×C₄	#35512	1	1	yes	characteristic
827	C₂×C₄	#35512	1	1	yes	characteristic
828	C₂×C₄	#35512	1	1	yes	characteristic
829	C₂×C₄	#35513	1	1	yes	characteristic
830	C₂×C₄	#35513	1	1	yes	characteristic
831	C₂×C₄	#35513	1	1	yes	characteristic
832	C₂×C₄	#35680	1	1	yes	characteristic
833	C₂×C₄	#35680	1	1	yes	characteristic
834	C₂×C₄	#35680	1	1	yes	characteristic
835	C₂×C₄	#35750	1	1	yes	characteristic
836	C₂×C₄	#35750	1	1	yes	characteristic
837	C₂×C₄	#35750	1	1	yes	characteristic
838	C₂×C₄	#35906	1	1	yes	characteristic
839	C₂×C₄	#35906	1	1	yes	characteristic
840	C₂×C₄	#35922	1	1	yes	characteristic
841	C₂×C₄	#36082	1	1	yes	characteristic
842	C₂×C₄	#36091	1	1	yes	characteristic
843	C₂×C₄	#36212	1	1	yes	characteristic
844	C₂×C₄	#36212	1	1	yes	characteristic
845	C₂×C₄	#36212	1	1	yes	characteristic
846	C₂×C₄	#36212	1	1	yes	characteristic
847	C₂×C₄	#36429	1	1	yes	characteristic
848	C₂×C₄	#36429	1	1	yes	characteristic
849	C₂×C₄	#36429	1	1	yes	characteristic
850	C₂×C₄	#36429	1	1	yes	characteristic
851	C₂×C₄	C₂×#2846	1	1	yes	characteristic
852	C₂×C₄	#37832	1	1	yes	characteristic
853	C₂×C₄	#37834	1	1	yes	characteristic
854	C₂×C₄	#38076	1	1	yes	characteristic
855	C₂×C₄	#38076	1	1	yes	characteristic
856	C₂×C₄	#38076	1	1	yes	characteristic
857	C₂×C₄	#38076	1	1	yes	characteristic
858	C₂×C₄	#38358	1	1	yes	characteristic
859	C₂×C₄	#38358	1	1	yes	characteristic
860	C₂×C₄	#38362	1	1	yes	characteristic
861	C₂×C₄	#38362	1	1	yes	characteristic
862	C₂×C₄	#38364	1	1	yes	characteristic
863	C₂×C₄	#38364	1	1	yes	characteristic
864	C₂×C₄	#38368	1	1	yes	characteristic
865	C₂×C₄	#38368	1	1	yes	characteristic
866	C₂×C₄	#38420	1	1	yes	characteristic
867	C₂×C₄	#38423	1	1	yes	characteristic
868	C₂×C₄	#38424	1	1	yes	characteristic
869	C₂×C₄	#38428	1	1	yes	characteristic
870	C₂×C₄	#40508	1	1	yes	characteristic
871	C₂×C₄	#40510	1	1	yes	characteristic
872	C₂×C₄	#40512	1	1	yes	characteristic
873	C₂×C₄	#40512	1	1	yes	characteristic
874	C₂×C₄	#40512	1	1	yes	characteristic
875	C₂×C₄	#40512	1	1	yes	characteristic
876	C₂×C₄	#40585	1	1	yes	characteristic
877	C₂×C₄	#40585	1	1	yes	characteristic
878	C₂×C₄	#40588	1	1	yes	characteristic
879	C₂×C₄	#40588	1	1	yes	characteristic
880	C₂×C₄	#40588	1	1	yes	characteristic
881	C₂×C₄	#40588	1	1	yes	characteristic
882	C₂×C₄	#40602	1	1	yes	characteristic
883	C₂×C₄	#40602	1	1	yes	characteristic
884	C₂×C₄	#40606	1	1	yes	characteristic
885	C₂×C₄	#41404	1	1	yes	characteristic
886	C₂×C₄	#41404	1	1	yes	characteristic
887	C₂×C₄	#41410	1	1	yes	characteristic
888	C₂×C₄	#41932	1	1	yes	characteristic
889	C₂×C₄	#41932	1	1	yes	characteristic
890	C₂×C₄	#41936	1	1	yes	characteristic
891	C₂×C₄	#41936	1	1	yes	characteristic
892	C₂×C₄	#41981	1	1	yes	characteristic
893	C₂×C₄	#41981	1	1	yes	characteristic
894	C₂×C₄	#41986	1	1	yes	characteristic
895	C₂×C₄	#41986	1	1	yes	characteristic
896	C₂×C₄	#41989	1	1	yes	characteristic
897	C₂×C₄	#43006	1	1	yes	characteristic
898	C₂×C₄	#43006	1	1	yes	characteristic
899	C₂×C₄	#43013	1	1	yes	characteristic
900	C₂×C₄	#43099	1	1	yes	characteristic
901	C₂×C₄	#43099	1	1	yes	characteristic
902	C₂×C₄	#43114	1	1	yes	characteristic
903	C₂×C₄	#43114	1	1	yes	characteristic
904	C₂×C₄	#43118	1	1	yes	characteristic
905	C₂×C₄	#43118	1	1	yes	characteristic
906	C₂×C₄	#43894	1	1	yes	characteristic
907	C₂×C₄	#43894	1	1	yes	characteristic
908	C₂×C₄	#43901	1	1	yes	characteristic
909	C₂×C₄	#44228	1	1	yes	characteristic
910	C₂×C₄	#44231	1	1	yes	characteristic
911	C₂×C₄	#44231	1	1	yes	characteristic
912	C₂×C₄	#44433	1	1	yes	characteristic
913	C₂×C₄	#44433	1	1	yes	characteristic
914	C₂×C₄	#44779	1	1	yes	characteristic
915	C₂×C₄	#47830	1	1	yes	characteristic
916	C₂×C₄	#47840	1	1	yes	characteristic
917	C₂×C₄	#47840	1	1	yes	characteristic
918	C₂×C₄	#47934	1	1	yes	characteristic
919	C₂×C₄	#47934	1	1	yes	characteristic
920	C₂×C₄	#47934	1	1	yes	characteristic
921	C₂×C₄	#47934	1	1	yes	characteristic
922	C₂×C₄	#47944	1	1	yes	characteristic
923	C₂×C₄	#47948	1	1	yes	characteristic
924	C₂×C₄	#49550	1	1	yes	characteristic
925	C₂×C₄	#49556	1	1	yes	characteristic
926	C₂×C₄	#49556	1	1	yes	characteristic
927	C₂×C₄	#50864	1	1	yes	characteristic
928	C₂×C₄	#50864	1	1	yes	characteristic
929	C₂×C₄	#51068	1	1	yes	characteristic
930	C₂×C₄	#51068	1	1	yes	characteristic
931	C₂×C₄	#51072	1	1	yes	characteristic
932	C₂×C₄	#51072	1	1	yes	characteristic
933	C₂²	#725988	1	1	yes	characteristic
934	C₂²	#758246	1	1	yes	characteristic
935	C₂²	#758255	1	1	yes	characteristic
936	C₂²	#1262353	1	1	yes	characteristic
937	C₂²	#1262354	1	1	yes	characteristic
938	C₂²	#1265713	1	1	yes	characteristic
939	C₂²	#1265714	1	1	yes	characteristic
940	C₂²	#1265729	1	1	yes	characteristic
941	C₂²	#1265730	1	1	yes	characteristic
942	C₂²	#1394857	1	1	yes	characteristic
943	C₂²	#1394858	1	1	yes	characteristic
944	C₂²	#4307937	1	1	yes	characteristic
945	C₂²	#4419437	1	1	yes	characteristic
946	C₂²	#4420593	1	1	yes	characteristic
947	C₂²	#4421184	1	1	yes	characteristic
948	C₄	#613444	1	1	yes	characteristic
949	C₄	#737656	1	1	yes	characteristic
950	C₄	#758036	1	1	yes	characteristic
951	C₄	#758045	1	1	yes	characteristic
952	C₄	#1262353	1	1	yes	characteristic
953	C₄	#1262354	1	1	yes	characteristic
954	C₄	#1265713	1	1	yes	characteristic
955	C₄	#1265714	1	1	yes	characteristic
956	C₄	#1265729	1	1	yes	characteristic
957	C₄	#1265730	1	1	yes	characteristic
958	C₄	#1394857	1	1	yes	characteristic
959	C₄	#1394858	1	1	yes	characteristic
960	C₄	#4420353	1	1	yes	characteristic
961	C₄	#4420361	1	1	yes	characteristic
962	C₄	#4420595	1	1	yes	characteristic
963	C₄	#4929082	1	1	yes	characteristic
964	C₂	#72216037	1	2	yes	—
965	C₂	#72250293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#4421184
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72256532	C₂	semidirect
2. #72256531	C₂	semidirect
3. #72256528	C₂	semidirect
4. #72256522	C₂	semidirect
5. #72256519	C₂	semidirect
6. #72256513	C₂	semidirect
7. #72256488	C₂	semidirect
8. #72256482	C₂	semidirect
9. #72256481	C₂	semidirect
10. #72256474	C₂	semidirect
11. #72256385	C₂	semidirect
12. #72255635	C₂	semidirect
13. #72255621	C₂	semidirect
14. #72252148	C₂	semidirect
15. C₂×#468843	C₂	semidirect
16. #72250767	C₂	semidirect
17. C₂×#464072	C₂	semidirect
18. #72250589	C₂	semidirect
19. #72250462	C₂	semidirect
20. C₂×#404012	C₂	semidirect
21. #72239650	C₂	semidirect
22. #72239625	C₂	semidirect
23. C₂×#10576378	C₂	semidirect
24. #72237671	C₂	semidirect
25. #72237670	C₂	semidirect
26. #72237516	C₂	semidirect
27. #72237191	C₂	semidirect
28. #72236778	C₂	semidirect
29. #72236737	C₂	semidirect
30. #72235076	C₂	semidirect
31. C₂×#393975	C₂	semidirect
49. C₂×#23649	C₂²	semidirect
51. C₂×#23472	C₂²	semidirect
52. C₂×#23443	C₂²	semidirect
53. C₂×#23414	C₂²	semidirect
56. C₂×#23412	C₂²	semidirect
57. C₂×#23400	C₂²	semidirect
61. #6371707	C₂²	semidirect
62. C₂×#21012	C₂²	semidirect
64. #6371536	C₂²	semidirect
65. C₂×#20998	C₂²	semidirect
66. C₂×#20979	C₂²	semidirect
67. #6371477	C₂²	semidirect
74. C₂×#11389	C₂²	semidirect
75. C₂×#11389	C₂²	semidirect
76. #358798	C₂²	semidirect
77. C₂×#11356	C₂²	semidirect
78. C₂×#11356	C₂²	semidirect
79. #358608	C₂²	semidirect
80. C₂×#11284	C₂²	semidirect
81. C₂×#11277	C₂²	semidirect
82. #358031	C₂²	semidirect
83. #357936	C₂²	semidirect
84. C₂×#11178	C₂²	semidirect
85. #357917	C₂²	semidirect
89. C₂×#11157	C₂²	semidirect
90. C₂×#11157	C₂²	semidirect
91. C₂×#11141	C₂²	semidirect
92. C₂×#11132	C₂²	semidirect
93. #357723	C₂²	semidirect
94. C₂×#11058	C₂²	semidirect
95. #357687	C₂²	semidirect
96. #357651	C₂²	semidirect
97. C₂×#11071	C₂²	semidirect
98. C₂×#11037	C₂²	semidirect
99. C₂×#11037	C₂²	semidirect
100. C₂×#11037	C₂²	semidirect
101. #357593	C₂²	semidirect
102. C₂×#11034	C₂²	semidirect
103. #357586	C₂²	semidirect
104. C₂×#11030	C₂²	semidirect
105. #357581	C₂²	semidirect
106. #357575	C₂²	semidirect
107. #357567	C₂²	semidirect
110. #357561	C₂²	semidirect
111. #357561	C₂²	semidirect
116. C₂×#11004	C₂²	semidirect
117. C₂×#11004	C₂²	semidirect
118. C₂×#11003	C₂²	semidirect
119. C₂×#11000	C₂²	semidirect
124. C₂×#10994	C₂²	semidirect
125. C₂×#10994	C₂²	semidirect
127. C₂×#10993	C₂²	semidirect
128. C₂×#10993	C₂²	semidirect
133. C₂×#10987	C₂²	semidirect
136. #353518	C₂²	semidirect
137. #353497	C₂²	semidirect
138. #353497	C₂²	semidirect
139. #353468	C₂²	semidirect
142. C₂×#10783	C₂²	semidirect
143. C₂×#10783	C₂²	semidirect
144. C₂×#10743	C₂²	semidirect
146. C₂×#10738	C₂²	semidirect
147. #353407	C₂²	semidirect
148. #353388	C₂²	semidirect
149. C₂×#10792	C₂²	semidirect
150. C₂×#10778	C₂²	semidirect
151. C₂×#10778	C₂²	semidirect
152. #353354	C₂²	semidirect
153. #353352	C₂²	semidirect
154. C₂×#10729	C₂²	semidirect
155. C₂×#10729	C₂²	semidirect
156. C₂×#10716	C₂²	semidirect
157. #123999	C₂²	semidirect
158. #123992	C₂²	semidirect
159. #123941	C₂²	semidirect
160. #123940	C₂²	semidirect
161. #123927	C₂²	semidirect
162. #123926	C₂²	semidirect
164. #123622	C₂²	semidirect
167. #123619	C₂²	semidirect
168. #123619	C₂²	semidirect
169. #123619	C₂²	semidirect
170. #123616	C₂²	semidirect
171. #123616	C₂²	semidirect
172. #123616	C₂²	semidirect
175. #123605	C₂²	semidirect
176. #123605	C₂²	semidirect
177. #123605	C₂²	semidirect
178. #123604	C₂²	semidirect
179. #123604	C₂²	semidirect
180. #123604	C₂²	semidirect
182. #123556	C₂²	semidirect
183. #123555	C₂²	semidirect
184. #123554	C₂²	semidirect
185. #123532	C₂²	semidirect
186. #123531	C₂²	semidirect
196. #62814	D₄	semidirect
197. C₂×#3484	D₄	semidirect
213. C₂×#3140	D₄	semidirect
214. C₂×#3138	D₄	semidirect
215. #60490	D₄	semidirect
216. #60426	D₄	semidirect
217. C₂×#2949	D₄	semidirect
218. C₂×#2948	D₄	semidirect
219. C₂×#2930	D₄	semidirect
220. C₂×#2929	D₄	semidirect
435. C₂²×#100	#41	semidirect
442. #2309	#41	semidirect
496. #533	#120	semidirect
501. #519	#120	semidirect
503. #518	#120	semidirect
528. #424	#120	semidirect
529. C₂×#97	#120	semidirect
530. C₂×C₄×C₈	#120	semidirect

Maximal subgroups

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

subgroup	index
#72256532	2
#72256531	2
#72256528	2
#72256522	2
#72256519	2
#72256513	2
#72256488	2
#72256482	2
#72256481	2
#72256474	2
#72256385	2
#72255635	2
#72255621	2
#72252148	2
C₂×#468843	2
#72250767	2
C₂×#464072	2
#72250589	2
#72250462	2
C₂×#404012	2
#72239650	2
#72239625	2
C₂×#10576378	2
#72237671	2
#72237670	2
#72237516	2
#72237191	2
#72236778	2
#72236737	2
#72235076	2
C₂×#393975	2