Subgroups — #72256347

Order 2048.

At least 12136 conjugacy classes of subgroups; only the 1560 normal subgroups are shown.

The subgroup lattice has 995 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72256341	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256261	C₂	1	1	yes	maximal, characteristic, complemented
3	#72256042	C₂	1	1	yes	maximal, characteristic, complemented
4	#72255903	C₂	1	1	yes	maximal, characteristic, complemented
5	#72255856	C₂	1	1	yes	maximal, characteristic, complemented
6	#72255812	C₂	1	1	yes	maximal, characteristic, complemented
7	#72255742	C₂	1	1	yes	maximal, characteristic, complemented
8	#72255712	C₂	1	1	yes	maximal, characteristic, complemented
9	#72255644	C₂	1	1	yes	maximal, characteristic, complemented
10	#72255623	C₂	1	1	yes	maximal, characteristic, complemented
11	#72255598	C₂	1	1	yes	maximal, characteristic, complemented
12	#72252206	C₂	1	1	yes	maximal, characteristic, complemented
13	#72252154	C₂	1	1	yes	maximal, characteristic, complemented
14	#72252141	C₂	1	1	yes	maximal, characteristic, complemented
15	#72252122	C₂	1	1	yes	maximal, characteristic, complemented
16	#72252109	C₂	1	1	yes	maximal, characteristic, complemented
17	#72252102	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#418531	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#419456	C₂	1	1	yes	maximal, characteristic, complemented
20	#72251207	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#394602	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#404012	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#10576378	C₂	1	1	yes	maximal, characteristic, complemented
24	#72237672	C₂	1	1	yes	maximal, characteristic, complemented
25	#72237670	C₂	1	1	yes	maximal, characteristic, complemented
26	#72237508	C₂	1	1	yes	maximal, characteristic, complemented
27	#72236779	C₂	1	1	yes	maximal, characteristic, complemented
28	#72236747	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#394249	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#359558	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#394102	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×#60423	C₂²	1	1	yes	characteristic, complemented
40	C₂×#60454	C₂²	1	1	yes	characteristic
41	C₂×#60444	C₂²	1	1	yes	characteristic
42	C₂×#60367	C₂²	1	1	yes	characteristic
43	C₂×#60367	C₂²	1	1	yes	characteristic
44	C₂²×#3003	C₂²	1	1	yes	characteristic
45	C₂²×#3003	C₂²	1	1	yes	characteristic
46	C₂×#60141	C₂²	1	1	yes	characteristic
47	C₂×#60168	C₂²	1	1	yes	characteristic
48	C₂×#60087	C₂²	1	1	yes	characteristic
49	C₂³×#418	C₂²	1	1	yes	characteristic
50	C₂×#34171	C₂²	1	1	yes	characteristic
51	C₂×#23525	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#2048	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#2048	C₂²	1	1	yes	characteristic, complemented
54	C₂×#23472	C₂²	1	1	yes	characteristic, complemented
55	C₂×#23443	C₂²	1	1	yes	characteristic
56	C₂×#23443	C₂²	1	1	yes	characteristic, complemented
57	C₂×#23414	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#2010	C₂²	1	1	yes	characteristic
59	C₂²×#2008	C₂²	1	1	yes	characteristic
60	C₂×#23407	C₂²	1	1	yes	characteristic
61	#6431722	C₂²	1	1	yes	characteristic, complemented
62	C₂×#23400	C₂²	1	1	yes	characteristic
63	C₂×#21012	C₂²	1	1	yes	characteristic, complemented
64	C₂²×#1911	C₂²	1	1	yes	characteristic
65	C₂²×#1911	C₂²	1	1	yes	characteristic
66	C₂×#20998	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#1904	C₂²	1	1	yes	characteristic
68	C₂²×#1904	C₂²	1	1	yes	characteristic, complemented
69	C₂²×#1904	C₂²	1	1	yes	characteristic, complemented
70	C₂×#20995	C₂²	1	1	yes	characteristic, complemented
71	C₂×#20989	C₂²	1	1	yes	characteristic, complemented
72	C₂×#20979	C₂²	1	1	yes	characteristic, complemented
73	C₂×#20953	C₂²	1	1	yes	characteristic
74	C₂×#20953	C₂²	1	1	yes	characteristic
75	C₂×#20867	C₂²	1	1	yes	characteristic, complemented
76	C₂×#20851	C₂²	1	1	yes	characteristic, complemented
77	C₂²×#1795	C₂²	1	1	yes	characteristic
78	C₂×#20616	C₂²	1	1	yes	characteristic
79	C₂×#20616	C₂²	1	1	yes	characteristic
80	C₂×#20598	C₂²	1	1	yes	characteristic
81	C₂²×#1783	C₂²	1	1	yes	characteristic
82	C₂×#11389	C₂²	1	1	yes	characteristic, complemented
83	C₂×#11389	C₂²	1	1	yes	characteristic, complemented
84	#358798	C₂²	1	1	yes	characteristic, complemented
85	#358479	C₂²	1	1	yes	characteristic, complemented
86	C₂×#11265	C₂²	1	1	yes	characteristic, complemented
87	C₂×#11251	C₂²	1	1	yes	characteristic, complemented
88	C₂×#11245	C₂²	1	1	yes	characteristic, complemented
89	C₂×#11187	C₂²	1	1	yes	characteristic, complemented
90	C₂×#11187	C₂²	1	1	yes	characteristic, complemented
91	C₂×#11187	C₂²	1	1	yes	characteristic, complemented
92	C₂×#11181	C₂²	1	1	yes	characteristic, complemented
93	#357917	C₂²	1	1	yes	characteristic, complemented
94	C₂×#11142	C₂²	1	1	yes	characteristic
95	C₂×#11142	C₂²	1	1	yes	characteristic
96	C₂×#11138	C₂²	1	1	yes	characteristic, complemented
97	#357823	C₂²	1	1	yes	characteristic, complemented
98	C₂×#11132	C₂²	1	1	yes	characteristic, complemented
99	C₂×#11131	C₂²	1	1	yes	characteristic, complemented
100	C₂×#11119	C₂²	1	1	yes	characteristic, complemented
101	#357758	C₂²	1	1	yes	characteristic, complemented
102	#357758	C₂²	1	1	yes	characteristic, complemented
103	C₂×#11110	C₂²	1	1	yes	characteristic, complemented
104	C₂×#11073	C₂²	1	1	yes	characteristic
105	C₂×#11071	C₂²	1	1	yes	characteristic, complemented
106	C₂×#11037	C₂²	1	1	yes	characteristic, complemented
107	C₂×#11034	C₂²	1	1	yes	characteristic
108	C₂×#11034	C₂²	1	1	yes	characteristic
109	C₂×#11034	C₂²	1	1	yes	characteristic
110	C₂×#11033	C₂²	1	1	yes	characteristic, complemented
111	C₂×#11030	C₂²	1	1	yes	characteristic
112	C₂×#11030	C₂²	1	1	yes	characteristic
113	#357581	C₂²	1	1	yes	characteristic
114	#357575	C₂²	1	1	yes	characteristic, complemented
115	C₂×#11014	C₂²	1	1	yes	characteristic, complemented
116	#357561	C₂²	1	1	yes	characteristic, complemented
117	C₂×#11004	C₂²	1	1	yes	characteristic
118	C₂×#11003	C₂²	1	1	yes	characteristic, complemented
119	C₂×#11000	C₂²	1	1	yes	characteristic, complemented
120	C₂×#11000	C₂²	1	1	yes	characteristic, complemented
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
125	C₂×#10994	C₂²	1	1	yes	characteristic
126	C₂×#10994	C₂²	1	1	yes	characteristic, complemented
127	C₂×#10994	C₂²	1	1	yes	characteristic, complemented
128	C₂×#10994	C₂²	1	1	yes	characteristic, complemented
129	#357541	C₂²	1	1	yes	characteristic, complemented
130	C₂×#10993	C₂²	1	1	yes	characteristic
131	C₂×#10993	C₂²	1	1	yes	characteristic, complemented
132	#357493	C₂²	1	1	yes	characteristic, complemented
133	#357486	C₂²	1	1	yes	characteristic, complemented
134	C₂×#10987	C₂²	1	1	yes	characteristic
135	#357470	C₂²	1	1	yes	characteristic, complemented
136	#354118	C₂²	1	1	yes	characteristic, complemented
137	#353922	C₂²	1	1	yes	characteristic, complemented
138	C₂×#10787	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, complemented
142	C₂×#10785	C₂²	1	1	yes	characteristic, complemented
143	C₂×#10785	C₂²	1	1	yes	characteristic, complemented
144	C₂×#10785	C₂²	1	1	yes	characteristic, complemented
145	C₂×#10783	C₂²	1	1	yes	characteristic, complemented
146	C₂×#10783	C₂²	1	1	yes	characteristic, complemented
147	#353462	C₂²	1	1	yes	characteristic, complemented
148	C₂×#10743	C₂²	1	1	yes	characteristic, complemented
149	C₂×#10740	C₂²	1	1	yes	characteristic
150	C₂×#10740	C₂²	1	1	yes	characteristic
151	C₂×#10738	C₂²	1	1	yes	characteristic, complemented
152	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
153	#353407	C₂²	1	1	yes	characteristic, complemented
154	#353397	C₂²	1	1	yes	characteristic, complemented
155	C₂×#10792	C₂²	1	1	yes	characteristic, complemented
156	C₂×#10776	C₂²	1	1	yes	characteristic, complemented
157	#353352	C₂²	1	1	yes	characteristic, complemented
158	C₂×#10716	C₂²	1	1	yes	characteristic, complemented
159	#123999	C₂²	1	1	yes	characteristic, complemented
160	#123992	C₂²	1	1	yes	characteristic, complemented
161	#123991	C₂²	1	1	yes	characteristic, complemented
162	#123976	C₂²	1	1	yes	characteristic, complemented
163	#123941	C₂²	1	1	yes	characteristic, complemented
164	#123919	C₂²	1	1	yes	characteristic, complemented
165	#123917	C₂²	1	1	yes	characteristic, complemented
166	#123896	C₂²	1	1	yes	characteristic, complemented
167	#123644	C₂²	1	1	yes	characteristic
168	#123637	C₂²	1	1	yes	characteristic, complemented
169	#123627	C₂²	1	1	yes	characteristic, complemented
170	#123623	C₂²	1	1	yes	characteristic, complemented
171	#123622	C₂²	1	1	yes	characteristic, complemented
172	#123619	C₂²	1	1	yes	characteristic
173	#123618	C₂²	1	1	yes	characteristic, complemented
174	#123609	C₂²	1	1	yes	characteristic, complemented
175	#123607	C₂²	1	1	yes	characteristic, complemented
176	#123602	C₂²	1	1	yes	characteristic, complemented
177	#123600	C₂²	1	1	yes	characteristic
178	#123600	C₂²	1	1	yes	characteristic
179	#123600	C₂²	1	1	yes	characteristic
180	#123600	C₂²	1	1	yes	characteristic
181	#123569	C₂²	1	1	yes	characteristic, complemented
182	#123549	C₂²	1	1	yes	characteristic, complemented
183	#123535	C₂²	1	1	yes	characteristic, complemented
184	#123532	C₂²	1	1	yes	characteristic, complemented
185	#123458	C₂²	1	1	yes	characteristic, complemented
186	#123458	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	C₂³×AGL(1,ℤ/8)	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	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
195	C₂²×#568	C₂³	1	1	yes	characteristic
196	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
197	C₂×#3484	D₄	1	4	yes	complemented
198	C₂×#3484	D₄	1	4	yes	complemented
199	C₂×#3458	C₂³	1	1	yes	characteristic
200	C₂×#3449	C₂³	1	1	yes	characteristic
201	C₂×#3449	C₂³	1	1	yes	characteristic
202	C₂×#3449	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	C₂²×#518	C₂³	1	1	yes	characteristic
213	C₂²×#518	C₂³	1	1	yes	characteristic
214	C₂³×#117	C₂³	1	1	yes	characteristic
215	C₂×#3140	D₄	1	4	yes	complemented
216	C₂×#3138	D₄	1	4	yes	complemented
217	#60518	D₄	1	8	yes	complemented
218	#60454	D₄	1	8	yes	complemented
219	C₂×#3043	D₄	1	4	yes	complemented
220	C₂×#3041	D₄	1	4	yes	complemented
221	C₂×#3003	D₄	1	8	yes	complemented
222	C₂²×#430	C₂³	1	1	yes	characteristic
223	C₂²×#430	C₂³	1	1	yes	characteristic
224	C₂×#2911	C₂³	1	1	yes	characteristic
225	C₂×#2911	C₂³	1	1	yes	characteristic
226	C₂×#2911	C₂³	1	1	yes	characteristic
227	C₂×#2905	C₂³	1	1	yes	characteristic
228	C₂×#2905	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	C₂²×#421	C₂³	1	1	yes	characteristic
239	C₂²×#421	C₂³	1	1	yes	characteristic
240	C₂²×#421	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	C₂×#2896	C₂³	1	1	yes	characteristic
251	C₂×#2896	C₂³	1	1	yes	characteristic
252	C₂×#2896	C₂³	1	1	yes	characteristic
253	C₂²×#418	D₄	1	8	yes	complemented
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×#418	C₂³	1	1	yes	characteristic
265	C₂²×#418	C₂³	1	1	yes	characteristic
266	C₂²×#413	C₂³	1	1	yes	characteristic
267	C₂²×#413	C₂³	1	1	yes	characteristic
268	C₂²×#413	C₂³	1	1	yes	characteristic
269	C₂²×#413	C₂³	1	1	yes	characteristic
270	C₂³×#100	C₂³	1	1	yes	characteristic
271	C₂³×#100	C₂³	1	1	yes	characteristic
272	C₂³×#100	C₂³	1	1	yes	characteristic
273	C₂³×#100	C₂³	1	1	yes	characteristic
274	C₂²×#410	C₂³	1	1	yes	characteristic
275	C₂²×#410	C₂³	1	1	yes	characteristic
276	C₂²×#410	C₂³	1	1	yes	characteristic
277	C₂²×#410	C₂³	1	1	yes	characteristic
278	C₂×#2879	C₂³	1	1	yes	characteristic
279	C₂×#2879	C₂³	1	1	yes	characteristic
280	C₂×#2879	C₂³	1	1	yes	characteristic
281	C₂²×#407	C₂³	1	1	yes	characteristic
282	C₂²×#407	C₂³	1	1	yes	characteristic
283	C₂²×#407	C₂³	1	1	yes	characteristic
284	C₂²×#407	C₂³	1	1	yes	characteristic
285	C₂²×#407	C₂³	1	1	yes	characteristic
286	C₂×#2873	C₂³	1	1	yes	characteristic
287	C₂×#2309	C₂³	1	1	yes	characteristic
288	C₂×#2309	C₂³	1	1	yes	characteristic
289	C₂×#2280	C₂³	1	1	yes	characteristic
290	C₂×#2280	C₂³	1	1	yes	characteristic
291	C₂×#2280	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	C₂×#1742	C₂³	1	1	yes	characteristic
309	C₂×#1742	C₂³	1	1	yes	characteristic
310	C₂×#1742	C₂³	1	1	yes	characteristic
311	C₂×#1742	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×#1733	C₂³	1	1	yes	characteristic
324	C₂×#1733	C₂³	1	1	yes	characteristic
325	C₂×#1733	C₂³	1	1	yes	characteristic
326	C₂×#1733	C₂³	1	1	yes	characteristic
327	C₂×#1733	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	C₂²×#338	C₂³	1	1	yes	characteristic
338	C₂²×H(3,ℤ/4)	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	#20335	C₂³	1	1	yes	characteristic
352	#10994	D₄	1	8	yes	complemented
353	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
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	C₂³×#41	C₂⁴	1	1	yes	characteristic
358	C₂⁴×D₄	C₂×D₄	1	4	yes	—
359	C₂⁴×D₄	C₂×D₄	1	4	yes	—
360	C₂⁴×D₄	C₂×D₄	1	2	yes	—
361	C₂⁴×D₄	C₂×D₄	1	2	yes	—
362	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
363	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
364	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×#137	C₂×D₄	1	2	yes	—
366	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
367	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	—
368	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
369	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
370	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
371	C₂³×D₈	C₂×D₄	1	2	yes	—
372	C₂×#568	C₂×D₄	1	4	yes	—
373	C₂³×M₁₆	C₂×D₄	1	4	yes	—
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	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
380	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
381	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
382	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
383	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
384	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
385	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
386	#3449	C₂×D₄	1	4	yes	—
387	C₂×#535	C₂×D₄	1	4	yes	—
388	C₂×#535	C₂×D₄	1	4	yes	—
389	C₂×#535	C₂×D₄	1	4	yes	—
390	C₂×#535	C₂×D₄	1	4	yes	—
391	C₂×#535	C₂×D₄	1	4	yes	—
392	C₂×#533	C₂×D₄	1	4	yes	—
393	C₂²×#127	C₂×D₄	1	2	yes	—
394	C₂²×#124	C₂×D₄	1	2	yes	—
395	C₂×#525	C₂×D₄	1	4	yes	—
396	C₂×#525	C₂×D₄	1	2	yes	—
397	C₂×#525	C₂×D₄	1	2	yes	—
398	C₂×#525	C₂×D₄	1	2	yes	—
399	C₂×#525	C₂×D₄	1	2	yes	—
400	C₂×#525	C₂×D₄	1	4	yes	—
401	C₂×#525	#41	1	4	yes	—
402	#3428	C₂×D₄	1	4	yes	—
403	C₂×#519	C₂×D₄	1	2	yes	—
404	C₂×#518	C₂×D₄	1	2	yes	—
405	C₂×#518	C₂×D₄	1	4	yes	—
406	C₂²×#117	C₂×D₄	1	4	yes	—
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	C₂²×#117	C₂⁴	1	1	yes	characteristic
417	C₂²×#117	C₂⁴	1	1	yes	characteristic
418	C₂²×#117	C₂⁴	1	1	yes	characteristic
419	#2911	C₂×D₄	1	4	yes	—
420	#2911	C₂×D₄	1	4	yes	—
421	#2911	C₂×D₄	1	4	yes	—
422	C₂×#424	C₂×D₄	1	4	yes	—
423	C₂×#421	C₂×D₄	1	4	yes	—
424	#2896	C₂×D₄	1	4	yes	—
425	#2896	C₂×D₄	1	4	yes	—
426	C₂×#419	C₂×D₄	1	2	yes	—
427	C₂×#419	C₂×D₄	1	2	yes	—
428	C₂×#418	C₂×D₄	1	4	yes	—
429	C₂×#418	C₂×D₄	1	4	yes	—
430	C₂×#418	C₂×D₄	1	4	yes	—
431	C₂×#418	C₂×D₄	1	2	yes	—
432	C₂×#418	C₂×D₄	1	2	yes	—
433	C₂×#418	C₂×D₄	1	4	yes	—
434	C₂×#418	C₂×D₄	1	4	yes	—
435	C₂×#418	C₂×D₄	1	4	yes	—
436	C₂×#418	C₂×D₄	1	4	yes	—
437	C₂×#418	C₂×D₄	1	4	yes	—
438	C₂×#418	C₂×D₄	1	4	yes	—
439	C₂×#418	C₂×D₄	1	4	yes	—
440	C₂×#418	C₂×D₄	1	4	yes	—
441	C₂×#418	C₂×D₄	1	4	yes	—
442	C₂×#416	C₂×D₄	1	4	yes	—
443	C₂²×#102	#41	1	4	yes	complemented
444	#2879	C₂×D₄	1	4	yes	—
445	C₂×#407	C₂×D₄	1	4	yes	—
446	C₂×#407	C₂×D₄	1	4	yes	—
447	C₂×C₄×M₁₆	C₂×D₄	1	4	yes	—
448	#2309	#41	1	4	yes	complemented
449	#2280	C₂×D₄	1	4	yes	—
450	#1733	C₂×D₄	1	4	yes	—
451	C₂×H(3,ℤ/4)	C₂×D₄	1	4	yes	—
452	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
453	C₂²×#41	C₂²×D₄	1	2	yes	—
454	C₂²×#41	C₂²×D₄	1	2	yes	—
455	C₂²×#41	C₂²×D₄	1	2	yes	—
456	C₂²×#41	C₂²×D₄	1	2	yes	—
457	C₂²×#41	C₂²×D₄	1	2	yes	—
458	C₂²×#41	C₂²×D₄	1	2	yes	—
459	C₂²×#41	C₂²×D₄	1	2	yes	—
460	C₂²×#41	C₂²×D₄	1	2	yes	—
461	C₂²×#41	C₂×#41	1	2	yes	—
462	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
463	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
464	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
465	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
466	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
467	C₂³×D₄	#120	1	8	yes	—
468	C₂³×D₄	#120	1	8	yes	—
469	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
470	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
471	C₂³×D₄	C₂²×D₄	1	2	yes	—
472	C₂³×D₄	C₂²×D₄	1	2	yes	—
473	C₂³×D₄	C₂²×D₄	1	2	yes	—
474	C₂³×D₄	C₂²×D₄	1	2	yes	—
475	C₂³×D₄	C₂²×D₄	1	2	yes	—
476	C₂³×D₄	C₂²×D₄	1	2	yes	—
477	C₂³×D₄	C₂²×D₄	1	2	yes	—
478	C₂³×D₄	C₂²×D₄	1	2	yes	—
479	C₂³×D₄	C₂²×D₄	1	2	yes	—
480	C₂³×D₄	C₂²×D₄	1	2	yes	—
481	C₂³×D₄	C₂×#41	1	2	yes	—
482	C₂³×D₄	C₂×#41	1	2	yes	—
483	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
484	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
485	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
486	C₂³×D₄	2₋¹⁺⁴	1	2	yes	—
487	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
490	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
491	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
492	C₂⁴×C₄	C₂×#41	1	2	yes	—
493	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
494	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
495	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
496	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
497	C₂²×SD₁₆	#120	1	8	yes	—
498	C₂²×D₈	#120	1	8	yes	—
499	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
500	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
501	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
502	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
503	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
504	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
505	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
506	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
507	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
508	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
509	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
510	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
511	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
512	C₂²×M₁₆	H(5,𝔽₂)	1	2	yes	—
513	C₂²×M₁₆	H(5,𝔽₂)	1	2	yes	—
514	C₂³×C₈	C₂²×D₄	1	2	yes	—
515	C₂³×C₈	C₂×#41	1	2	yes	—
516	#535	#120	1	16	yes	—
517	C₂×#127	#120	1	8	yes	—
518	C₂×#124	#120	1	8	yes	—
519	#525	#121	1	8	yes	—
520	#525	#121	1	8	yes	—
521	C₂×#117	C₂²×D₄	1	2	yes	—
522	C₂×#117	C₂²×D₄	1	2	yes	—
523	C₂×#117	C₂²×D₄	1	2	yes	—
524	C₂×#117	C₂²×D₄	1	2	yes	—
525	C₂×#117	C₂²×D₄	1	2	yes	—
526	C₂×#117	C₂²×D₄	1	2	yes	—
527	C₂×#117	C₂²×D₄	1	2	yes	—
528	C₂×#117	C₂²×D₄	1	2	yes	—
529	C₂×#117	C₂²×D₄	1	2	yes	—
530	C₂×#117	C₂²×D₄	1	2	yes	—
531	C₂×#117	C₂²×D₄	1	2	yes	—
532	C₂×#117	C₂²×D₄	1	2	yes	—
533	C₂×#117	C₂²×D₄	1	2	yes	—
534	C₂×#117	C₂²×D₄	1	2	yes	—
535	C₂×#117	C₂²×D₄	1	2	yes	—
536	C₂×#117	C₂²×D₄	1	2	yes	—
537	C₂×#117	C₂²×D₄	1	2	yes	—
538	C₂×#117	C₂×#41	1	2	yes	—
539	C₂×#117	C₂×#41	1	2	yes	—
540	C₂×#117	C₂×#41	1	2	yes	—
541	C₂×#117	H(5,𝔽₂)	1	2	yes	—
542	C₂×#117	H(5,𝔽₂)	1	2	yes	—
543	C₂×#117	H(5,𝔽₂)	1	2	yes	—
544	C₂×#117	H(5,𝔽₂)	1	2	yes	—
545	C₂²×C₄⋊C₄	C₂×#41	1	2	yes	—
546	C₂²×C₄²	C₂²×D₄	1	2	yes	—
547	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
548	#418	#120	1	16	yes	—
549	#418	#120	1	16	yes	—
550	#418	#120	1	16	yes	—
551	C₂⁵	#534	1	1	yes	characteristic
552	C₂⁵	#534	1	1	yes	characteristic
553	C₂⁵	D₄²	1	2	yes	—
554	C₂⁵	#546	1	2	yes	—
555	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₂×#41	C₂×#120	1	4	yes	—
557	C₂×#41	C₂×#121	1	4	yes	—
558	C₂×#41	D₄²	1	4	yes	—
559	C₂×#41	#546	1	4	yes	—
560	C₂²×Q₈	C₂×#120	1	2	yes	—
561	C₂²×Q₈	C₂×#120	1	2	yes	—
562	C₂²×Q₈	#534	1	2	yes	—
563	C₂²×Q₈	D₄²	1	2	yes	—
564	C₂²×Q₈	#546	1	2	yes	—
565	C₂²×D₄	C₂×#120	1	2	yes	—
566	C₂²×D₄	C₂×#120	1	2	yes	—
567	C₂²×D₄	C₂×#120	1	4	yes	—
568	C₂²×D₄	C₂×#120	1	4	yes	—
569	C₂²×D₄	C₂×#120	1	4	yes	—
570	C₂²×D₄	C₂×#120	1	4	yes	—
571	C₂²×D₄	C₂×#120	1	4	yes	—
572	C₂²×D₄	C₂×#120	1	4	yes	—
573	C₂²×D₄	C₂×#120	1	4	yes	—
574	C₂²×D₄	C₂×#120	1	4	yes	—
575	C₂²×D₄	#532	1	4	yes	—
576	C₂²×D₄	#534	1	2	yes	—
577	C₂²×D₄	#537	1	4	yes	—
578	C₂²×D₄	D₄²	1	2	yes	—
579	C₂²×D₄	#546	1	2	yes	—
580	C₂²×D₄	#546	1	4	yes	—
581	C₂²×D₄	#546	1	4	yes	—
582	C₂²×D₄	#547	1	4	yes	—
583	C₂²×D₄	#547	1	4	yes	—
584	C₂³×C₄	C₂×#120	1	2	yes	—
585	C₂³×C₄	C₂×#120	1	2	yes	—
586	C₂³×C₄	C₂×#121	1	2	yes	—
587	C₂³×C₄	C₂×#121	1	2	yes	—
588	C₂³×C₄	#534	1	1	yes	characteristic
589	C₂³×C₄	#534	1	1	yes	characteristic
590	C₂³×C₄	D₄²	1	2	yes	—
591	C₂³×C₄	D₄²	1	2	yes	—
592	C₂³×C₄	D₄²	1	2	yes	—
593	C₂³×C₄	#546	1	2	yes	—
594	C₂³×C₄	#546	1	2	yes	—
595	C₂³×C₄	#546	1	2	yes	—
596	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
597	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
598	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
599	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
600	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
601	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
602	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
603	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
604	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
605	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
606	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
607	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂³×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
620	C₂³×C₄	#585	1	1	yes	characteristic
621	C₂³×C₄	#585	1	1	yes	characteristic
622	C₂³×C₄	#585	1	1	yes	characteristic
623	C₂³×C₄	#585	1	1	yes	characteristic
624	C₂³×C₄	#585	1	1	yes	characteristic
625	C₂³×C₄	#585	1	1	yes	characteristic
626	C₂×M₁₆	C₂×#120	1	4	yes	—
627	C₂×M₁₆	C₂×#120	1	4	yes	—
628	C₂×M₁₆	C₂×#120	1	4	yes	—
629	C₂²×C₈	C₂×#120	1	4	yes	—
630	#117	C₂×#120	1	4	yes	—
631	#117	C₂×#120	1	4	yes	—
632	#117	C₂×#120	1	4	yes	—
633	#117	C₂×#120	1	4	yes	—
634	#117	C₂×#121	1	4	yes	—
635	#117	#534	1	4	yes	—
636	#117	D₄²	1	4	yes	—
637	#117	#546	1	4	yes	—
638	C₂×C₄²	C₂×#120	1	4	yes	—
639	C₂×C₄²	D₄²	1	4	yes	—
640	C₂×C₄²	#546	1	4	yes	—
641	C₂×C₄²	#546	1	4	yes	—
642	C₂⁴	#2410	1	2	yes	—
643	C₂⁴	#2410	1	2	yes	—
644	C₂⁴	C₂×#534	1	1	yes	characteristic
645	C₂⁴	C₂×D₄²	1	1	yes	characteristic
646	C₂⁴	C₂×#546	1	1	yes	characteristic
647	C₂⁴	#3484	1	1	yes	characteristic
648	C₂⁴	#3484	1	1	yes	characteristic
649	C₂⁴	#3484	1	1	yes	characteristic
650	C₂⁴	#3484	1	1	yes	characteristic
651	C₂⁴	#3490	1	1	yes	characteristic
652	C₂⁴	#3513	1	1	yes	characteristic
653	C₂⁴	#3532	1	1	yes	characteristic
654	C₂⁴	#3534	1	1	yes	characteristic
655	C₂⁴	#3534	1	1	yes	characteristic
656	C₂⁴	#3535	1	1	yes	characteristic
657	C₂⁴	#3558	1	1	yes	characteristic
658	C₂⁴	#3558	1	1	yes	characteristic
659	C₂×Q₈	#2410	1	4	yes	—
660	C₂×D₄	#2410	1	4	yes	—
661	C₂×D₄	#2430	1	8	yes	—
662	C₂×D₄	#2846	1	8	yes	—
663	C₂²×C₄	#2410	1	2	yes	—
664	C₂²×C₄	#2410	1	2	yes	—
665	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
666	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
667	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
668	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
669	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
670	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
671	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
672	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
673	C₂²×C₄	C₂×#532	1	1	yes	characteristic
674	C₂²×C₄	C₂×#534	1	1	yes	characteristic
675	C₂²×C₄	C₂×#534	1	1	yes	characteristic
676	C₂²×C₄	C₂×#537	1	1	yes	characteristic
677	C₂²×C₄	#3449	1	1	yes	characteristic
678	C₂²×C₄	#3449	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
684	C₂²×C₄	C₂×#546	1	1	yes	characteristic
685	C₂²×C₄	C₂×#546	1	1	yes	characteristic
686	C₂²×C₄	C₂×#546	1	1	yes	characteristic
687	C₂²×C₄	C₂×#546	1	1	yes	characteristic
688	C₂²×C₄	C₂×#546	1	1	yes	characteristic
689	C₂²×C₄	C₂×#546	1	1	yes	characteristic
690	C₂²×C₄	C₂×#546	1	1	yes	characteristic
691	C₂²×C₄	C₂×#546	1	1	yes	characteristic
692	C₂²×C₄	C₂×#547	1	1	yes	characteristic
693	C₂²×C₄	C₂×#547	1	1	yes	characteristic
694	C₂²×C₄	D₄×#41	1	1	yes	characteristic
695	C₂²×C₄	D₄×#41	1	1	yes	characteristic
696	C₂²×C₄	D₄×#41	1	1	yes	characteristic
697	C₂²×C₄	D₄×#41	1	1	yes	characteristic
698	C₂²×C₄	D₄×#41	1	1	yes	characteristic
699	C₂²×C₄	D₄×#41	1	1	yes	characteristic
700	C₂²×C₄	D₄×#41	1	1	yes	characteristic
701	C₂²×C₄	D₄×#41	1	1	yes	characteristic
702	C₂²×C₄	D₄×#41	1	1	yes	characteristic
703	C₂²×C₄	#3475	1	1	yes	characteristic
704	C₂²×C₄	#3481	1	1	yes	characteristic
705	C₂²×C₄	#3484	1	1	yes	characteristic
706	C₂²×C₄	#3484	1	1	yes	characteristic
707	C₂²×C₄	#3484	1	1	yes	characteristic
708	C₂²×C₄	#3484	1	1	yes	characteristic
709	C₂²×C₄	#3484	1	1	yes	characteristic
710	C₂²×C₄	#3484	1	1	yes	characteristic
711	C₂²×C₄	#3484	1	1	yes	characteristic
712	C₂²×C₄	#3484	1	1	yes	characteristic
713	C₂²×C₄	#3484	1	1	yes	characteristic
714	C₂²×C₄	#3484	1	1	yes	characteristic
715	C₂²×C₄	#3484	1	1	yes	characteristic
716	C₂²×C₄	#3484	1	1	yes	characteristic
717	C₂²×C₄	#3484	1	1	yes	characteristic
718	C₂²×C₄	#3484	1	1	yes	characteristic
719	C₂²×C₄	#3484	1	1	yes	characteristic
720	C₂²×C₄	#3484	1	1	yes	characteristic
721	C₂²×C₄	#3484	1	1	yes	characteristic
722	C₂²×C₄	#3484	1	1	yes	characteristic
723	C₂²×C₄	#3484	1	1	yes	characteristic
724	C₂²×C₄	#3484	1	1	yes	characteristic
725	C₂²×C₄	#3485	1	1	yes	characteristic
726	C₂²×C₄	#3485	1	1	yes	characteristic
727	C₂²×C₄	#3485	1	1	yes	characteristic
728	C₂²×C₄	#3485	1	1	yes	characteristic
729	C₂²×C₄	#3485	1	1	yes	characteristic
730	C₂²×C₄	#3488	1	1	yes	characteristic
731	C₂²×C₄	#3488	1	1	yes	characteristic
732	C₂²×C₄	#3488	1	1	yes	characteristic
733	C₂²×C₄	#3488	1	1	yes	characteristic
734	C₂²×C₄	#3488	1	1	yes	characteristic
735	C₂²×C₄	#3488	1	1	yes	characteristic
736	C₂²×C₄	#3488	1	1	yes	characteristic
737	C₂²×C₄	#3488	1	1	yes	characteristic
738	C₂²×C₄	#3488	1	1	yes	characteristic
739	C₂²×C₄	#3488	1	1	yes	characteristic
740	C₂²×C₄	#3489	1	1	yes	characteristic
741	C₂²×C₄	#3489	1	1	yes	characteristic
742	C₂²×C₄	#3489	1	1	yes	characteristic
743	C₂²×C₄	#3489	1	1	yes	characteristic
744	C₂²×C₄	#3489	1	1	yes	characteristic
745	C₂²×C₄	#3490	1	1	yes	characteristic
746	C₂²×C₄	#3490	1	1	yes	characteristic
747	C₂²×C₄	#3494	1	1	yes	characteristic
748	C₂²×C₄	#3496	1	1	yes	characteristic
749	C₂²×C₄	#3496	1	1	yes	characteristic
750	C₂²×C₄	#3496	1	1	yes	characteristic
751	C₂²×C₄	#3496	1	1	yes	characteristic
752	C₂²×C₄	#3496	1	1	yes	characteristic
753	C₂²×C₄	#3496	1	1	yes	characteristic
754	C₂²×C₄	#3496	1	1	yes	characteristic
755	C₂²×C₄	#3496	1	1	yes	characteristic
756	C₂²×C₄	#3496	1	1	yes	characteristic
757	C₂²×C₄	#3496	1	1	yes	characteristic
758	C₂²×C₄	#3498	1	1	yes	characteristic
759	C₂²×C₄	#3498	1	1	yes	characteristic
760	C₂²×C₄	#3498	1	1	yes	characteristic
761	C₂²×C₄	#3498	1	1	yes	characteristic
762	C₂²×C₄	#3508	1	1	yes	characteristic
763	C₂²×C₄	#3508	1	1	yes	characteristic
764	C₂²×C₄	#3513	1	1	yes	characteristic
765	C₂²×C₄	#3513	1	1	yes	characteristic
766	C₂²×C₄	#3513	1	1	yes	characteristic
767	C₂²×C₄	#3514	1	1	yes	characteristic
768	C₂²×C₄	#3514	1	1	yes	characteristic
769	C₂²×C₄	#3519	1	1	yes	characteristic
770	C₂²×C₄	#3519	1	1	yes	characteristic
771	C₂²×C₄	#3519	1	1	yes	characteristic
772	C₂²×C₄	#3519	1	1	yes	characteristic
773	C₂²×C₄	#3519	1	1	yes	characteristic
774	C₂²×C₄	#3520	1	1	yes	characteristic
775	C₂²×C₄	#3532	1	1	yes	characteristic
776	C₂²×C₄	#3532	1	1	yes	characteristic
777	C₂²×C₄	#3533	1	1	yes	characteristic
778	C₂²×C₄	#3534	1	1	yes	characteristic
779	C₂²×C₄	#3534	1	1	yes	characteristic
780	C₂²×C₄	#3534	1	1	yes	characteristic
781	C₂²×C₄	#3534	1	1	yes	characteristic
782	C₂²×C₄	#3534	1	1	yes	characteristic
783	C₂²×C₄	#3536	1	1	yes	characteristic
784	C₂²×C₄	#3536	1	1	yes	characteristic
785	C₂²×C₄	#3536	1	1	yes	characteristic
786	C₂²×C₄	#3536	1	1	yes	characteristic
787	C₂²×C₄	#3536	1	1	yes	characteristic
788	C₂²×C₄	#3540	1	1	yes	characteristic
789	C₂²×C₄	#3542	1	1	yes	characteristic
790	C₂²×C₄	#3542	1	1	yes	characteristic
791	C₂²×C₄	#3542	1	1	yes	characteristic
792	C₂²×C₄	#3542	1	1	yes	characteristic
793	C₂²×C₄	#3543	1	1	yes	characteristic
794	C₂²×C₄	#3543	1	1	yes	characteristic
795	C₂²×C₄	#3545	1	1	yes	characteristic
796	C₂²×C₄	#3546	1	1	yes	characteristic
797	C₂²×C₄	#3546	1	1	yes	characteristic
798	C₂²×C₄	#3551	1	1	yes	characteristic
799	C₂²×C₄	#3558	1	1	yes	characteristic
800	C₂²×C₄	#3558	1	1	yes	characteristic
801	C₂²×C₄	#3560	1	1	yes	characteristic
802	C₂²×C₄	#3560	1	1	yes	characteristic
803	C₂²×C₄	#3562	1	1	yes	characteristic
804	C₂²×C₄	#3562	1	1	yes	characteristic
805	C₄²	#2410	1	8	yes	—
806	C₂³	C₂×#2410	1	1	yes	characteristic
807	C₂³	#34980	1	1	yes	characteristic
808	C₂³	#34980	1	1	yes	characteristic
809	C₂³	D₄×#120	1	1	yes	characteristic
810	C₂³	D₄×#120	1	1	yes	characteristic
811	C₂³	#36152	1	1	yes	characteristic
812	C₂³	#36152	1	1	yes	characteristic
813	C₂³	#36318	1	1	yes	characteristic
814	C₂³	#37860	1	1	yes	characteristic
815	C₂³	#38028	1	1	yes	characteristic
816	C₂³	#38076	1	1	yes	characteristic
817	C₂³	#38077	1	1	yes	characteristic
818	C₂³	#38900	1	1	yes	characteristic
819	C₂³	#40585	1	1	yes	characteristic
820	C₂³	#40585	1	1	yes	characteristic
821	C₂³	#43010	1	1	yes	characteristic
822	C₂³	#43013	1	1	yes	characteristic
823	C₂³	#43023	1	1	yes	characteristic
824	C₂³	#43023	1	1	yes	characteristic
825	C₂³	#43105	1	1	yes	characteristic
826	C₂³	#43118	1	1	yes	characteristic
827	C₂³	#43118	1	1	yes	characteristic
828	C₂³	#43926	1	1	yes	characteristic
829	C₂³	#44228	1	1	yes	characteristic
830	C₂³	#44231	1	1	yes	characteristic
831	C₂³	#47830	1	1	yes	characteristic
832	C₂³	#47843	1	1	yes	characteristic
833	C₂³	#47938	1	1	yes	characteristic
834	C₂³	#47952	1	1	yes	characteristic
835	C₂³	#51068	1	1	yes	characteristic
836	C₂³	#51415	1	1	yes	characteristic
837	C₂³	#51577	1	1	yes	characteristic
838	C₂³	#51889	1	1	yes	characteristic
839	C₂³	#58991	1	1	yes	characteristic
840	C₂³	#58995	1	1	yes	characteristic
841	C₂×C₄	C₂×#2410	1	1	yes	characteristic
842	C₂×C₄	C₂×#2410	1	1	yes	characteristic
843	C₂×C₄	C₂×#2430	1	1	yes	characteristic
844	C₂×C₄	#34738	1	1	yes	characteristic
845	C₂×C₄	#34738	1	1	yes	characteristic
846	C₂×C₄	#34980	1	1	yes	characteristic
847	C₂×C₄	#35088	1	1	yes	characteristic
848	C₂×C₄	#35251	1	1	yes	characteristic
849	C₂×C₄	#35251	1	1	yes	characteristic
850	C₂×C₄	#35346	1	1	yes	characteristic
851	C₂×C₄	#35346	1	1	yes	characteristic
852	C₂×C₄	#35347	1	1	yes	characteristic
853	C₂×C₄	#35347	1	1	yes	characteristic
854	C₂×C₄	#35512	1	1	yes	characteristic
855	C₂×C₄	#35527	1	1	yes	characteristic
856	C₂×C₄	#35680	1	1	yes	characteristic
857	C₂×C₄	#35680	1	1	yes	characteristic
858	C₂×C₄	#35680	1	1	yes	characteristic
859	C₂×C₄	#35680	1	1	yes	characteristic
860	C₂×C₄	#35680	1	1	yes	characteristic
861	C₂×C₄	#35680	1	1	yes	characteristic
862	C₂×C₄	#35680	1	1	yes	characteristic
863	C₂×C₄	#35680	1	1	yes	characteristic
864	C₂×C₄	#35694	1	1	yes	characteristic
865	C₂×C₄	#35694	1	1	yes	characteristic
866	C₂×C₄	#35761	1	1	yes	characteristic
867	C₂×C₄	#35761	1	1	yes	characteristic
868	C₂×C₄	D₄×#120	1	1	yes	characteristic
869	C₂×C₄	D₄×#120	1	1	yes	characteristic
870	C₂×C₄	#36123	1	1	yes	characteristic
871	C₂×C₄	#36152	1	1	yes	characteristic
872	C₂×C₄	#36152	1	1	yes	characteristic
873	C₂×C₄	#36153	1	1	yes	characteristic
874	C₂×C₄	#36212	1	1	yes	characteristic
875	C₂×C₄	#36212	1	1	yes	characteristic
876	C₂×C₄	#36212	1	1	yes	characteristic
877	C₂×C₄	#36212	1	1	yes	characteristic
878	C₂×C₄	#36213	1	1	yes	characteristic
879	C₂×C₄	#36213	1	1	yes	characteristic
880	C₂×C₄	#36213	1	1	yes	characteristic
881	C₂×C₄	#36213	1	1	yes	characteristic
882	C₂×C₄	#36214	1	1	yes	characteristic
883	C₂×C₄	C₂×#2846	1	1	yes	characteristic
884	C₂×C₄	#37652	1	1	yes	characteristic
885	C₂×C₄	#37673	1	1	yes	characteristic
886	C₂×C₄	#37832	1	1	yes	characteristic
887	C₂×C₄	#38036	1	1	yes	characteristic
888	C₂×C₄	#38916	1	1	yes	characteristic
889	C₂×C₄	#39332	1	1	yes	characteristic
890	C₂×C₄	#39464	1	1	yes	characteristic
891	C₂×C₄	#40496	1	1	yes	characteristic
892	C₂×C₄	#40498	1	1	yes	characteristic
893	C₂×C₄	#40508	1	1	yes	characteristic
894	C₂×C₄	#40510	1	1	yes	characteristic
895	C₂×C₄	#40521	1	1	yes	characteristic
896	C₂×C₄	#40524	1	1	yes	characteristic
897	C₂×C₄	#40586	1	1	yes	characteristic
898	C₂×C₄	#40586	1	1	yes	characteristic
899	C₂×C₄	#42432	1	1	yes	characteristic
900	C₂×C₄	#42435	1	1	yes	characteristic
901	C₂×C₄	#43079	1	1	yes	characteristic
902	C₂×C₄	#43079	1	1	yes	characteristic
903	C₂×C₄	#43095	1	1	yes	characteristic
904	C₂×C₄	#43095	1	1	yes	characteristic
905	C₂×C₄	#43096	1	1	yes	characteristic
906	C₂×C₄	#43096	1	1	yes	characteristic
907	C₂×C₄	#43098	1	1	yes	characteristic
908	C₂×C₄	#43101	1	1	yes	characteristic
909	C₂×C₄	#43107	1	1	yes	characteristic
910	C₂×C₄	#43113	1	1	yes	characteristic
911	C₂×C₄	#43118	1	1	yes	characteristic
912	C₂×C₄	#43886	1	1	yes	characteristic
913	C₂×C₄	#43896	1	1	yes	characteristic
914	C₂×C₄	#43901	1	1	yes	characteristic
915	C₂×C₄	#43907	1	1	yes	characteristic
916	C₂×C₄	#43907	1	1	yes	characteristic
917	C₂×C₄	#43910	1	1	yes	characteristic
918	C₂×C₄	#43923	1	1	yes	characteristic
919	C₂×C₄	#44001	1	1	yes	characteristic
920	C₂×C₄	#44022	1	1	yes	characteristic
921	C₂×C₄	#44228	1	1	yes	characteristic
922	C₂×C₄	#44433	1	1	yes	characteristic
923	C₂×C₄	#44877	1	1	yes	characteristic
924	C₂×C₄	#44927	1	1	yes	characteristic
925	C₂×C₄	#45002	1	1	yes	characteristic
926	C₂×C₄	#45057	1	1	yes	characteristic
927	C₂×C₄	#45079	1	1	yes	characteristic
928	C₂×C₄	#45103	1	1	yes	characteristic
929	C₂×C₄	#45353	1	1	yes	characteristic
930	C₂×C₄	#45422	1	1	yes	characteristic
931	C₂×C₄	#47826	1	1	yes	characteristic
932	C₂×C₄	#47828	1	1	yes	characteristic
933	C₂×C₄	#47934	1	1	yes	characteristic
934	C₂×C₄	#47951	1	1	yes	characteristic
935	C₂×C₄	#48774	1	1	yes	characteristic
936	C₂×C₄	#49544	1	1	yes	characteristic
937	C₂×C₄	#49546	1	1	yes	characteristic
938	C₂×C₄	#49559	1	1	yes	characteristic
939	C₂×C₄	#50864	1	1	yes	characteristic
940	C₂×C₄	#50893	1	1	yes	characteristic
941	C₂×C₄	#51522	1	1	yes	characteristic
942	C₂×C₄	#51776	1	1	yes	characteristic
943	C₂×C₄	#58992	1	1	yes	characteristic
944	C₂×C₄	#59004	1	1	yes	characteristic
945	C₂×C₄	#59009	1	1	yes	characteristic
946	C₂×C₄	#59029	1	1	yes	characteristic
947	C₂×C₄	#59044	1	1	yes	characteristic
948	C₂×C₄	#59090	1	1	yes	characteristic
949	C₂×C₄	#59091	1	1	yes	characteristic
950	C₂×C₄	#59095	1	1	yes	characteristic
951	C₂×C₄	#59099	1	1	yes	characteristic
952	C₂×C₄	#59123	1	1	yes	characteristic
953	C₂×C₄	#59129	1	1	yes	characteristic
954	C₂×C₄	#59129	1	1	yes	characteristic
955	C₂×C₄	#59407	1	1	yes	characteristic
956	C₂×C₄	#59412	1	1	yes	characteristic
957	C₂×C₄	#59414	1	1	yes	characteristic
958	C₂×C₄	#59568	1	1	yes	characteristic
959	C₂×C₄	#59800	1	1	yes	characteristic
960	C₂×C₄	#59814	1	1	yes	characteristic
961	C₂²	#612433	1	1	yes	characteristic
962	C₂²	#649102	1	1	yes	characteristic
963	C₂²	#686261	1	1	yes	characteristic
964	C₂²	#782010	1	1	yes	characteristic
965	C₂²	#782975	1	1	yes	characteristic
966	C₂²	#1259671	1	1	yes	characteristic
967	C₂²	#1260440	1	1	yes	characteristic
968	C₂²	#1262353	1	1	yes	characteristic
969	C₂²	#1262738	1	1	yes	characteristic
970	C₂²	#1263122	1	1	yes	characteristic
971	C₂²	#1263505	1	1	yes	characteristic
972	C₂²	#1418355	1	1	yes	characteristic
973	C₂²	#1418362	1	1	yes	characteristic
974	C₂²	#1418388	1	1	yes	characteristic
975	C₂²	#1418391	1	1	yes	characteristic
976	C₄	#613197	1	1	yes	characteristic
977	C₄	#695458	1	1	yes	characteristic
978	C₄	#772799	1	1	yes	characteristic
979	C₄	#772807	1	1	yes	characteristic
980	C₄	#773158	1	1	yes	characteristic
981	C₄	#773166	1	1	yes	characteristic
982	C₄	#781994	1	1	yes	characteristic
983	C₄	#782991	1	1	yes	characteristic
984	C₄	#1259288	1	1	yes	characteristic
985	C₄	#1260055	1	1	yes	characteristic
986	C₄	#1419343	1	1	yes	characteristic
987	C₄	#1419348	1	1	yes	characteristic
988	C₄	#1419372	1	1	yes	characteristic
989	C₄	#1419377	1	1	yes	characteristic
990	C₄	#4417865	1	1	yes	characteristic
991	C₄	#4928938	1	1	yes	characteristic
992	C₂	#72216203	1	2	yes	—
993	C₂	#72250300	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#1262353
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. #72256341	C₂	semidirect
2. #72256261	C₂	semidirect
3. #72256042	C₂	semidirect
4. #72255903	C₂	semidirect
5. #72255856	C₂	semidirect
6. #72255812	C₂	semidirect
7. #72255742	C₂	semidirect
8. #72255712	C₂	semidirect
9. #72255644	C₂	semidirect
10. #72255623	C₂	semidirect
11. #72255598	C₂	semidirect
12. #72252206	C₂	semidirect
13. #72252154	C₂	semidirect
14. #72252141	C₂	semidirect
15. #72252122	C₂	semidirect
16. #72252109	C₂	semidirect
17. #72252102	C₂	semidirect
18. C₂×#418531	C₂	semidirect
19. C₂×#419456	C₂	semidirect
20. #72251207	C₂	semidirect
21. C₂×#394602	C₂	semidirect
22. C₂×#404012	C₂	semidirect
23. C₂×#10576378	C₂	semidirect
24. #72237672	C₂	semidirect
25. #72237670	C₂	semidirect
26. #72237508	C₂	semidirect
27. #72236779	C₂	semidirect
28. #72236747	C₂	semidirect
29. C₂×#394249	C₂	semidirect
30. C₂×#359558	C₂	semidirect
31. C₂×#394102	C₂	semidirect
39. C₂×#60423	C₂²	semidirect
51. C₂×#23525	C₂²	semidirect
52. C₂²×#2048	C₂²	semidirect
53. C₂²×#2048	C₂²	semidirect
54. C₂×#23472	C₂²	semidirect
56. C₂×#23443	C₂²	semidirect
57. C₂×#23414	C₂²	semidirect
61. #6431722	C₂²	semidirect
63. C₂×#21012	C₂²	semidirect
66. C₂×#20998	C₂²	semidirect
68. C₂²×#1904	C₂²	semidirect
69. C₂²×#1904	C₂²	semidirect
70. C₂×#20995	C₂²	semidirect
71. C₂×#20989	C₂²	semidirect
72. C₂×#20979	C₂²	semidirect
75. C₂×#20867	C₂²	semidirect
76. C₂×#20851	C₂²	semidirect
82. C₂×#11389	C₂²	semidirect
83. C₂×#11389	C₂²	semidirect
84. #358798	C₂²	semidirect
85. #358479	C₂²	semidirect
86. C₂×#11265	C₂²	semidirect
87. C₂×#11251	C₂²	semidirect
88. C₂×#11245	C₂²	semidirect
89. C₂×#11187	C₂²	semidirect
90. C₂×#11187	C₂²	semidirect
91. C₂×#11187	C₂²	semidirect
92. C₂×#11181	C₂²	semidirect
93. #357917	C₂²	semidirect
96. C₂×#11138	C₂²	semidirect
97. #357823	C₂²	semidirect
98. C₂×#11132	C₂²	semidirect
99. C₂×#11131	C₂²	semidirect
100. C₂×#11119	C₂²	semidirect
101. #357758	C₂²	semidirect
102. #357758	C₂²	semidirect
103. C₂×#11110	C₂²	semidirect
105. C₂×#11071	C₂²	semidirect
106. C₂×#11037	C₂²	semidirect
110. C₂×#11033	C₂²	semidirect
114. #357575	C₂²	semidirect
115. C₂×#11014	C₂²	semidirect
116. #357561	C₂²	semidirect
118. C₂×#11003	C₂²	semidirect
119. C₂×#11000	C₂²	semidirect
120. C₂×#11000	C₂²	semidirect
126. C₂×#10994	C₂²	semidirect
127. C₂×#10994	C₂²	semidirect
128. C₂×#10994	C₂²	semidirect
129. #357541	C₂²	semidirect
131. C₂×#10993	C₂²	semidirect
132. #357493	C₂²	semidirect
133. #357486	C₂²	semidirect
135. #357470	C₂²	semidirect
136. #354118	C₂²	semidirect
137. #353922	C₂²	semidirect
138. C₂×#10787	C₂²	semidirect
139. #353468	C₂²	semidirect
141. C₂×#10785	C₂²	semidirect
142. C₂×#10785	C₂²	semidirect
143. C₂×#10785	C₂²	semidirect
144. C₂×#10785	C₂²	semidirect
145. C₂×#10783	C₂²	semidirect
146. C₂×#10783	C₂²	semidirect
147. #353462	C₂²	semidirect
148. C₂×#10743	C₂²	semidirect
151. C₂×#10738	C₂²	semidirect
152. C₂×#10737	C₂²	semidirect
153. #353407	C₂²	semidirect
154. #353397	C₂²	semidirect
155. C₂×#10792	C₂²	semidirect
156. C₂×#10776	C₂²	semidirect
157. #353352	C₂²	semidirect
158. C₂×#10716	C₂²	semidirect
159. #123999	C₂²	semidirect
160. #123992	C₂²	semidirect
161. #123991	C₂²	semidirect
162. #123976	C₂²	semidirect
163. #123941	C₂²	semidirect
164. #123919	C₂²	semidirect
165. #123917	C₂²	semidirect
166. #123896	C₂²	semidirect
168. #123637	C₂²	semidirect
169. #123627	C₂²	semidirect
170. #123623	C₂²	semidirect
171. #123622	C₂²	semidirect
173. #123618	C₂²	semidirect
174. #123609	C₂²	semidirect
175. #123607	C₂²	semidirect
176. #123602	C₂²	semidirect
181. #123569	C₂²	semidirect
182. #123549	C₂²	semidirect
183. #123535	C₂²	semidirect
184. #123532	C₂²	semidirect
185. #123458	C₂²	semidirect
186. #123458	C₂²	semidirect
197. C₂×#3484	D₄	semidirect
198. C₂×#3484	D₄	semidirect
215. C₂×#3140	D₄	semidirect
216. C₂×#3138	D₄	semidirect
217. #60518	D₄	semidirect
218. #60454	D₄	semidirect
219. C₂×#3043	D₄	semidirect
220. C₂×#3041	D₄	semidirect
221. C₂×#3003	D₄	semidirect
253. C₂²×#418	D₄	semidirect
352. #10994	D₄	semidirect
443. C₂²×#102	#41	semidirect
448. #2309	#41	semidirect

Maximal subgroups

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

subgroup	index
#72256341	2
#72256261	2
#72256042	2
#72255903	2
#72255856	2
#72255812	2
#72255742	2
#72255712	2
#72255644	2
#72255623	2
#72255598	2
#72252206	2
#72252154	2
#72252141	2
#72252122	2
#72252109	2
#72252102	2
C₂×#418531	2
C₂×#419456	2
#72251207	2
C₂×#394602	2
C₂×#404012	2
C₂×#10576378	2
#72237672	2
#72237670	2
#72237508	2
#72236779	2
#72236747	2
C₂×#394249	2
C₂×#359558	2
C₂×#394102	2