Subgroups — #72261368

Order 2048.

Only the 2332 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 862 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261350	C₂	1	1	yes	maximal, characteristic, complemented
2	#72261344	C₂	1	1	yes	maximal, characteristic, complemented
3	#72261337	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#511829	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#511830	C₂	1	1	yes	maximal, characteristic, complemented
6	#72261310	C₂	1	1	yes	maximal, characteristic, complemented
7	#72261294	C₂	1	1	yes	maximal, characteristic, complemented
8	#72261282	C₂	1	2	yes	maximal, complemented
9	C₂×#511828	C₂	1	2	yes	maximal, complemented
10	#72261267	C₂	1	2	yes	maximal, complemented
11	#72261251	C₂	1	2	yes	maximal, complemented
12	#72261238	C₂	1	1	yes	maximal, characteristic, complemented
13	#72261217	C₂	1	1	yes	maximal, characteristic, complemented
14	#72261210	C₂	1	1	yes	maximal, characteristic, complemented
15	#72261199	C₂	1	2	yes	maximal, complemented
16	#72261190	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#511826	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10586400	C₂	1	1	yes	maximal, characteristic, complemented
19	#72261075	C₂	1	1	yes	maximal, characteristic, complemented
20	#72260846	C₂	1	2	yes	maximal, complemented
21	#72260453	C₂	1	2	yes	maximal, complemented
22	C₂×#511825	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#511827	C₂	1	2	yes	maximal, complemented
24	C₂×#63066	C₂²	1	1	yes	characteristic
25	C₂×#63048	C₂²	1	1	yes	characteristic
26	C₂×#63044	C₂²	1	2	yes	—
27	C₂×#63063	C₂²	1	1	yes	characteristic
28	C₂×#63045	C₂²	1	1	yes	characteristic
29	C₂×#63041	C₂²	1	2	yes	—
30	C₂×#62759	C₂²	1	1	yes	characteristic
31	C₂×#62729	C₂²	1	2	yes	—
32	C₂²×#3529	C₂²	1	1	yes	characteristic
33	C₂×#62812	C₂²	1	1	yes	characteristic
34	C₂×#62811	C₂²	1	2	yes	—
35	#10574842	C₂²	1	1	yes	characteristic, complemented
36	C₂×#33572	C₂²	1	2	yes	complemented
37	C₂×#33571	C₂²	1	1	yes	characteristic, complemented
38	C₂×#33570	C₂²	1	1	yes	characteristic, complemented
39	C₂×#33556	C₂²	1	2	yes	complemented
40	C₂×#33555	C₂²	1	2	yes	complemented
41	C₂×#33554	C₂²	1	2	yes	complemented
42	C₂×#33553	C₂²	1	2	yes	complemented
43	C₂×#33550	C₂²	1	1	yes	characteristic, complemented
44	C₂×#33550	C₂²	1	2	yes	complemented
45	C₂×#33550	C₂²	1	1	yes	characteristic, complemented
46	#6437625	C₂²	1	1	yes	characteristic, complemented
47	#6437616	C₂²	1	2	yes	complemented
48	C₂×#23873	C₂²	1	1	yes	characteristic, complemented
49	C₂×#23875	C₂²	1	1	yes	characteristic, complemented
50	C₂×#23874	C₂²	1	1	yes	characteristic, complemented
51	C₂×#23872	C₂²	1	1	yes	characteristic, complemented
52	C₂×#23885	C₂²	1	2	yes	complemented
53	C₂×#23884	C₂²	1	2	yes	complemented
54	C₂×#23883	C₂²	1	2	yes	complemented
55	C₂×#23882	C₂²	1	2	yes	complemented
56	#6437451	C₂²	1	2	yes	complemented
57	#6437437	C₂²	1	1	yes	characteristic, complemented
58	C₂×#12780	C₂²	1	2	yes	complemented
59	C₂×#12780	C₂²	1	2	yes	complemented
60	C₂×#12779	C₂²	1	1	yes	characteristic, complemented
61	C₂×#12779	C₂²	1	1	yes	characteristic, complemented
62	C₂×#12778	C₂²	1	1	yes	characteristic, complemented
63	C₂×#12778	C₂²	1	1	yes	characteristic, complemented
64	#493616	C₂²	1	2	yes	complemented
65	#493615	C₂²	1	1	yes	characteristic, complemented
66	#493614	C₂²	1	1	yes	characteristic, complemented
67	C₂×#12766	C₂²	1	1	yes	characteristic, complemented
68	C₂×#12766	C₂²	1	2	yes	complemented
69	C₂×#12766	C₂²	1	1	yes	characteristic, complemented
70	C₂×#12766	C₂²	1	2	yes	complemented
71	C₂×#12766	C₂²	1	1	yes	characteristic, complemented
72	C₂×#12766	C₂²	1	1	yes	characteristic, complemented
73	#493587	C₂²	1	2	yes	complemented
74	#493586	C₂²	1	2	yes	complemented
75	#493585	C₂²	1	2	yes	complemented
76	#493584	C₂²	1	2	yes	complemented
77	#493581	C₂²	1	2	yes	complemented
78	#493581	C₂²	1	1	yes	characteristic, complemented
79	#493581	C₂²	1	1	yes	characteristic, complemented
80	C₂×#12758	C₂²	1	2	yes	complemented
81	C₂×#12758	C₂²	1	2	yes	complemented
82	C₂×#12756	C₂²	1	2	yes	complemented
83	C₂×#12756	C₂²	1	2	yes	complemented
84	C₂×#12757	C₂²	1	2	yes	complemented
85	C₂×#12757	C₂²	1	2	yes	complemented
86	C₂×#12755	C₂²	1	2	yes	complemented
87	C₂×#12755	C₂²	1	2	yes	complemented
88	C₂×#12718	C₂²	1	2	yes	complemented
89	C₂×#12716	C₂²	1	1	yes	characteristic, complemented
90	C₂×#12716	C₂²	1	1	yes	characteristic, complemented
91	C₂×#12717	C₂²	1	2	yes	complemented
92	C₂×#12715	C₂²	1	1	yes	characteristic, complemented
93	C₂×#12715	C₂²	1	1	yes	characteristic, complemented
94	C₂×#12714	C₂²	1	2	yes	complemented
95	C₂×#12714	C₂²	1	2	yes	complemented
96	C₂×#12712	C₂²	1	2	yes	complemented
97	C₂×#12712	C₂²	1	2	yes	complemented
98	C₂×#12713	C₂²	1	2	yes	complemented
99	C₂×#12713	C₂²	1	2	yes	complemented
100	C₂×#12711	C₂²	1	2	yes	complemented
101	C₂×#12711	C₂²	1	2	yes	complemented
102	#493387	C₂²	1	2	yes	complemented
103	#493378	C₂²	1	1	yes	characteristic, complemented
104	#493374	C₂²	1	2	yes	complemented
105	#493365	C₂²	1	1	yes	characteristic, complemented
106	#493361	C₂²	1	2	yes	complemented
107	#493352	C₂²	1	2	yes	complemented
108	#493352	C₂²	1	2	yes	complemented
109	#392134	C₂²	1	2	yes	complemented
110	#392134	C₂²	1	1	yes	characteristic, complemented
111	#359672	C₂²	1	1	yes	characteristic, complemented
112	#359671	C₂²	1	1	yes	characteristic, complemented
113	#359670	C₂²	1	1	yes	characteristic, complemented
114	#359669	C₂²	1	1	yes	characteristic, complemented
115	#359648	C₂²	1	2	yes	complemented
116	#359647	C₂²	1	2	yes	complemented
117	#359646	C₂²	1	2	yes	complemented
118	#359645	C₂²	1	2	yes	complemented
119	#359515	C₂²	1	2	yes	complemented
120	#359507	C₂²	1	2	yes	complemented
121	#359470	C₂²	1	1	yes	characteristic, complemented
122	#359446	C₂²	1	1	yes	characteristic, complemented
123	C₂²×#585	D₄	1	1	yes	characteristic, complemented
124	C₂²×#585	C₂³	1	1	yes	characteristic
125	C₂⁴×#41	D₄	1	2	yes	complemented
126	C₂×#3586	C₂³	1	1	yes	characteristic
127	C₂×#3585	C₂³	1	1	yes	characteristic
128	#63066	D₄	1	8	yes	complemented
129	#63063	D₄	1	8	yes	complemented
130	#63048	D₄	1	8	yes	complemented
131	#63045	D₄	1	8	yes	complemented
132	#63044	D₄	1	16	yes	complemented
133	#63041	D₄	1	16	yes	complemented
134	#62811	C₂³	1	1	yes	characteristic
135	C₂×#3500	D₄	1	1	yes	characteristic, complemented
136	C₂×#3500	D₄	1	1	yes	characteristic, complemented
137	C₂×#3500	C₂³	1	1	yes	characteristic
138	C₂×#3500	C₂³	1	1	yes	characteristic
139	C₂×#3499	D₄	1	1	yes	characteristic, complemented
140	C₂×#3499	C₂³	1	1	yes	characteristic
141	C₂×#3498	D₄	1	1	yes	characteristic, complemented
142	C₂×#3498	C₂³	1	1	yes	characteristic
143	C₂×#3487	D₄	1	2	yes	complemented
144	C₂×#3487	C₂³	1	2	yes	—
145	C₂×#3486	D₄	1	2	yes	complemented
146	C₂×#3486	C₂³	1	2	yes	—
147	C₂×#3485	D₄	1	2	yes	complemented
148	C₂×#3485	C₂³	1	2	yes	—
149	C₂×#3484	D₄	1	2	yes	complemented
150	C₂×#3484	C₂³	1	2	yes	—
151	C₂×#3550	C₂³	1	1	yes	characteristic
152	C₂×#3549	C₂³	1	1	yes	characteristic
153	C₂×#3545	D₄	1	2	yes	complemented
154	C₂×#3544	D₄	1	2	yes	complemented
155	C₂×#3551	C₂³	1	2	yes	—
156	C₂×#3540	C₂³	1	2	yes	—
157	C₂×#3540	C₂³	1	2	yes	—
158	C₂×#3533	D₄	1	4	yes	complemented
159	C₂×#3538	C₂³	1	2	yes	—
160	C₂×#3537	C₂³	1	2	yes	—
161	C₂×#3532	D₄	1	4	yes	complemented
162	C₂×#3483	D₄	1	2	yes	complemented
163	C₂×#3481	D₄	1	4	yes	complemented
164	C₂×#3529	D₄	1	2	yes	complemented
165	C₂×#3529	D₄	1	1	yes	characteristic, complemented
166	C₂×#3529	D₄	1	1	yes	characteristic, complemented
167	C₂×#3529	D₄	1	4	yes	complemented
168	C₂×#3529	D₄	1	2	yes	complemented
169	C₂×#3529	C₂³	1	1	yes	characteristic
170	C₂×#3529	C₂³	1	2	yes	—
171	C₂×#3529	C₂³	1	1	yes	characteristic
172	C₂²×#563	D₄	1	1	yes	characteristic, complemented
173	C₂²×H(3,𝔽₄)	D₄	1	1	yes	characteristic, complemented
174	C₂²×#560	D₄	1	2	yes	complemented
175	C₂×#3449	D₄	1	2	yes	complemented
176	C₂×#3449	D₄	1	1	yes	characteristic, complemented
177	C₂×#3449	C₂³	1	1	yes	characteristic
178	C₂×#3449	C₂³	1	2	yes	—
179	C₂²×#532	D₄	1	1	yes	characteristic, complemented
180	C₂²×#532	C₂³	1	1	yes	characteristic
181	C₂²×#525	D₄	1	2	yes	complemented
182	C₂²×#525	C₂³	1	2	yes	—
183	C₂×#3428	D₄	1	2	yes	complemented
184	C₂²×C₄×#41	D₄	1	1	yes	characteristic, complemented
185	C₂×#3028	C₂³	1	1	yes	characteristic
186	C₂×#3027	C₂³	1	1	yes	characteristic
187	C₂×#3025	C₂³	1	2	yes	—
188	C₂×#3025	C₂³	1	2	yes	—
189	C₂×#3022	C₂³	1	2	yes	—
190	C₂×#3021	C₂³	1	2	yes	—
191	C₂×#3018	C₂³	1	1	yes	characteristic
192	C₂×#3018	C₂³	1	1	yes	characteristic
193	#60088	C₂³	1	1	yes	characteristic
194	#60087	C₂³	1	1	yes	characteristic
195	#60064	C₂³	1	1	yes	characteristic
196	C₂×#2135	C₂³	1	2	yes	—
197	C₂×#2135	C₂³	1	2	yes	—
198	C₂×#2134	C₂³	1	2	yes	—
199	C₂×#2134	C₂³	1	2	yes	—
200	C₂×#2132	C₂³	1	1	yes	characteristic
201	C₂×#2132	C₂³	1	1	yes	characteristic
202	C₂×#2132	C₂³	1	2	yes	—
203	C₂×#2129	C₂³	1	2	yes	—
204	C₂×#2129	C₂³	1	2	yes	—
205	C₂×#2128	C₂³	1	2	yes	—
206	C₂×#2128	C₂³	1	2	yes	—
207	C₂×#2126	C₂³	1	1	yes	characteristic
208	C₂×#2126	C₂³	1	1	yes	characteristic
209	C₂×#2126	C₂³	1	2	yes	—
210	C₂×#2123	C₂³	1	2	yes	—
211	C₂×#2123	C₂³	1	2	yes	—
212	C₂×#2122	C₂³	1	2	yes	—
213	C₂×#2122	C₂³	1	2	yes	—
214	C₂×#2120	C₂³	1	2	yes	—
215	C₂×#2120	C₂³	1	2	yes	—
216	C₂×#2120	C₂³	1	2	yes	—
217	C₂×#2120	C₂³	1	2	yes	—
218	C₂×#2120	C₂³	1	2	yes	—
219	C₂×#2120	C₂³	1	2	yes	—
220	C₂×#2120	C₂³	1	2	yes	—
221	C₂×#2120	C₂³	1	2	yes	—
222	C₂×#1915	C₂³	1	1	yes	characteristic
223	C₂×#1915	C₂³	1	1	yes	characteristic
224	C₂×#1914	C₂³	1	1	yes	characteristic
225	C₂×#1914	C₂³	1	1	yes	characteristic
226	C₂×#1910	C₂³	1	2	yes	—
227	C₂×#1910	C₂³	1	2	yes	—
228	C₂×#1909	C₂³	1	2	yes	—
229	C₂×#1909	C₂³	1	2	yes	—
230	C₂×#1891	C₂³	1	2	yes	—
231	C₂×#1891	C₂³	1	2	yes	—
232	C₂×#1891	C₂³	1	2	yes	—
233	C₂×#1891	C₂³	1	2	yes	—
234	#20962	C₂³	1	1	yes	characteristic
235	#20961	C₂³	1	1	yes	characteristic
236	#20959	C₂³	1	2	yes	—
237	#20959	C₂³	1	2	yes	—
238	#20956	C₂³	1	2	yes	—
239	#20955	C₂³	1	2	yes	—
240	#20952	C₂³	1	1	yes	characteristic
241	#20952	C₂³	1	1	yes	characteristic
242	C₂×#1884	C₂³	1	1	yes	characteristic
243	C₂×#1884	C₂³	1	1	yes	characteristic
244	C₂×#1884	C₂³	1	1	yes	characteristic
245	C₂×#1884	C₂³	1	1	yes	characteristic
246	C₂×#1796	C₂³	1	1	yes	characteristic
247	C₂×#1796	C₂³	1	1	yes	characteristic
248	C₂×#1796	C₂³	1	2	yes	—
249	C₂×#1796	C₂³	1	2	yes	—
250	C₂×#1795	C₂³	1	1	yes	characteristic
251	C₂×#1795	C₂³	1	1	yes	characteristic
252	C₂×#1795	C₂³	1	2	yes	—
253	C₂×#1795	C₂³	1	2	yes	—
254	#20591	C₂³	1	1	yes	characteristic
255	#20591	C₂³	1	2	yes	—
256	#20584	C₂³	1	1	yes	characteristic
257	#20584	C₂³	1	2	yes	—
258	C₂×#585	C₂⁴	1	1	yes	characteristic
259	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
260	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
261	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
262	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
263	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
264	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
265	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
266	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
267	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
268	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
269	C₂³×#41	C₂×D₄	1	1	yes	characteristic
270	C₂³×#41	C₂×D₄	1	1	yes	characteristic
271	C₂³×#41	C₂×D₄	1	1	yes	characteristic
272	C₂³×#41	C₂×D₄	1	2	yes	—
273	C₂³×#41	C₂×D₄	1	2	yes	—
274	C₂³×#41	C₂×D₄	1	2	yes	—
275	C₂³×#41	C₂×D₄	1	1	yes	characteristic
276	C₂³×#41	C₂×D₄	1	2	yes	—
277	C₂³×#41	C₂×D₄	1	2	yes	—
278	C₂³×#41	C₂⁴	1	1	yes	characteristic
279	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
280	C₂⁴×D₄	C₂×D₄	1	2	yes	—
281	C₂⁵×C₄	C₂×D₄	1	2	yes	—
282	C₂×#568	C₂⁴	1	1	yes	characteristic
283	C₂×#568	C₂⁴	1	1	yes	characteristic
284	#3551	C₂×D₄	1	8	yes	—
285	#3551	C₂×D₄	1	8	yes	—
286	#3550	C₂×D₄	1	4	yes	—
287	#3550	C₂×D₄	1	4	yes	—
288	#3549	C₂×D₄	1	4	yes	—
289	#3549	C₂×D₄	1	4	yes	—
290	#3540	C₂×D₄	1	8	yes	—
291	#3540	C₂×D₄	1	8	yes	—
292	#3540	C₂×D₄	1	8	yes	—
293	#3540	C₂×D₄	1	8	yes	—
294	#3538	C₂×D₄	1	8	yes	—
295	#3538	C₂×D₄	1	8	yes	—
296	#3537	C₂×D₄	1	8	yes	—
297	#3537	C₂×D₄	1	8	yes	—
298	#3529	C₂×D₄	1	8	yes	—
299	#3529	C₂×D₄	1	8	yes	—
300	#3529	C₂×D₄	1	4	yes	—
301	#3529	C₂×D₄	1	4	yes	—
302	#3529	C₂×D₄	1	4	yes	—
303	#3529	C₂×D₄	1	4	yes	—
304	C₂×#563	C₂×D₄	1	1	yes	characteristic
305	C₂×#563	C₂×D₄	1	2	yes	—
306	C₂×#563	C₂×D₄	1	1	yes	characteristic
307	C₂×#563	C₂×D₄	1	4	yes	—
308	C₂×#563	C₂×D₄	1	4	yes	—
309	C₂×#563	C₂×D₄	1	2	yes	—
310	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
311	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	—
312	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
313	C₂×H(3,𝔽₄)	C₂×D₄	1	4	yes	—
314	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	—
315	C₂×#560	C₂×D₄	1	2	yes	—
316	C₂×#560	C₂×D₄	1	2	yes	—
317	C₂×#560	C₂×D₄	1	2	yes	—
318	C₂×#560	C₂×D₄	1	2	yes	—
319	C₂×#560	C₂×D₄	1	4	yes	—
320	C₂×#560	C₂×D₄	1	4	yes	—
321	#3500	C₂×D₄	1	4	yes	—
322	#3500	C₂×D₄	1	4	yes	—
323	#3500	C₂×D₄	1	4	yes	—
324	#3500	C₂×D₄	1	4	yes	—
325	#3499	C₂×D₄	1	8	yes	—
326	#3498	C₂×D₄	1	8	yes	—
327	#3487	C₂×D₄	1	8	yes	—
328	#3487	C₂×D₄	1	8	yes	—
329	#3486	C₂×D₄	1	8	yes	—
330	#3486	C₂×D₄	1	8	yes	—
331	#3485	C₂×D₄	1	8	yes	—
332	#3485	C₂×D₄	1	8	yes	—
333	#3484	C₂×D₄	1	8	yes	—
334	#3484	C₂×D₄	1	8	yes	—
335	C₂×#559	C₂×D₄	1	4	yes	—
336	C₂×Q₈²	C₂×D₄	1	2	yes	—
337	C₂×#555	C₂×D₄	1	4	yes	—
338	C₂×#555	C₂×D₄	1	2	yes	—
339	C₂×#551	C₂×D₄	1	4	yes	—
340	C₂×#551	C₂×D₄	1	4	yes	—
341	C₂×D₄²	C₂×D₄	1	4	yes	—
342	C₂×#536	C₂×D₄	1	4	yes	—
343	C₂×#536	C₂×D₄	1	1	yes	characteristic
344	C₂×#536	C₂×D₄	1	2	yes	—
345	C₂×#536	C₂×D₄	1	2	yes	—
346	C₂×#536	C₂×D₄	1	2	yes	—
347	C₂×#536	C₂×D₄	1	1	yes	characteristic
348	C₂×#536	C₂×D₄	1	1	yes	characteristic
349	C₂×#536	C₂⁴	1	1	yes	characteristic
350	C₂×#536	C₂⁴	1	2	yes	—
351	C₂×#535	C₂×D₄	1	4	yes	—
352	C₂×#535	C₂×D₄	1	1	yes	characteristic
353	C₂×#535	C₂×D₄	1	2	yes	—
354	C₂×#535	C₂×D₄	1	2	yes	—
355	C₂×#535	C₂×D₄	1	2	yes	—
356	C₂×#535	C₂×D₄	1	1	yes	characteristic
357	C₂×#535	C₂×D₄	1	1	yes	characteristic
358	C₂×#535	C₂⁴	1	1	yes	characteristic
359	C₂×#535	C₂⁴	1	2	yes	—
360	C₂×#534	C₂×D₄	1	4	yes	—
361	C₂×#532	C₂×D₄	1	1	yes	characteristic
362	C₂×#532	C₂×D₄	1	1	yes	characteristic
363	C₂×#532	C₂×D₄	1	1	yes	characteristic
364	C₂×#532	C₂×D₄	1	1	yes	characteristic
365	C₂×#532	C₂×D₄	1	4	yes	—
366	C₂×#532	C₂×D₄	1	1	yes	characteristic
367	C₂×#532	C₂×D₄	1	1	yes	characteristic
368	C₂×#532	C₂×D₄	1	4	yes	—
369	C₂×#532	C₂⁴	1	1	yes	characteristic
370	C₂×#532	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
373	C₂²×#127	C₂×D₄	1	1	yes	characteristic
374	C₂²×#127	C₂×D₄	1	1	yes	characteristic
375	C₂²×#124	C₂×D₄	1	1	yes	characteristic
376	C₂²×#124	C₂×D₄	1	1	yes	characteristic
377	C₂²×#124	C₂×D₄	1	1	yes	characteristic
378	C₂²×#124	C₂×D₄	1	1	yes	characteristic
379	C₂×#525	C₂×D₄	1	2	yes	—
380	C₂×#525	C₂×D₄	1	2	yes	—
381	C₂×#525	C₂×D₄	1	2	yes	—
382	C₂×#525	C₂×D₄	1	2	yes	—
383	C₂×#525	C₂×D₄	1	4	yes	—
384	C₂×#525	C₂×D₄	1	2	yes	—
385	C₂×#525	C₂×D₄	1	2	yes	—
386	C₂×#525	C₂×D₄	1	2	yes	—
387	C₂×#525	C₂×D₄	1	2	yes	—
388	C₂×#525	C₂×D₄	1	2	yes	—
389	C₂×#525	C₂×D₄	1	2	yes	—
390	C₂×#525	C₂⁴	1	2	yes	—
391	C₂×#525	C₂⁴	1	2	yes	—
392	C₂²×#123	C₂×D₄	1	2	yes	—
393	C₂²×#123	C₂×D₄	1	2	yes	—
394	C₂²×#120	C₂×D₄	1	2	yes	—
395	C₂²×#120	C₂×D₄	1	2	yes	—
396	#3428	C₂⁴	1	1	yes	characteristic
397	C₂×#519	C₂×D₄	1	2	yes	—
398	C₂×#519	C₂×D₄	1	2	yes	—
399	C₂×#518	C₂×D₄	1	2	yes	—
400	C₂×#518	C₂×D₄	1	2	yes	—
401	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
402	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
403	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
404	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
405	C₂²×#117	C₂×D₄	1	1	yes	characteristic
406	C₂²×#117	C₂×D₄	1	2	yes	—
407	C₂²×#117	C₂×D₄	1	2	yes	—
408	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
409	C₂×#413	C₂⁴	1	1	yes	characteristic
410	C₂×#413	C₂⁴	1	1	yes	characteristic
411	C₂×#413	C₂⁴	1	2	yes	—
412	C₂×#413	C₂⁴	1	2	yes	—
413	C₂×#410	C₂⁴	1	2	yes	—
414	C₂×#410	C₂⁴	1	2	yes	—
415	C₂×#410	C₂⁴	1	1	yes	characteristic
416	C₂×#410	C₂⁴	1	1	yes	characteristic
417	C₂⁶	#120	1	2	yes	—
418	C₂×2₋¹⁺⁴	#120	1	4	yes	complemented
419	C₂×2₋¹⁺⁴	#120	1	4	yes	complemented
420	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	—
421	C₂×2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
422	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	—
423	C₂×H(5,𝔽₂)	#120	1	4	yes	complemented
424	C₂×H(5,𝔽₂)	#120	1	4	yes	complemented
425	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
426	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
427	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
428	C₂²×#41	#120	1	2	yes	—
429	C₂²×#41	#120	1	2	yes	—
430	C₂²×#41	#120	1	2	yes	—
431	C₂²×#41	#120	1	1	yes	characteristic
432	C₂²×#41	#120	1	1	yes	characteristic
433	C₂²×#41	#120	1	4	yes	—
434	C₂²×#41	#120	1	4	yes	—
435	C₂²×#41	#120	1	1	yes	characteristic
436	C₂²×#41	#120	1	2	yes	—
437	C₂²×#41	#120	1	1	yes	characteristic
438	C₂²×#41	#120	1	8	yes	complemented
439	C₂²×#41	#120	1	8	yes	complemented
440	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
441	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
442	C₂²×#41	C₂²×D₄	1	2	yes	—
443	C₂²×#41	C₂²×D₄	1	2	yes	—
444	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
445	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
446	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
447	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
448	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
449	C₂²×#41	C₂²×D₄	1	2	yes	—
450	C₂²×#41	C₂²×D₄	1	2	yes	—
451	C₂²×#41	C₂⁵	1	1	yes	characteristic
452	C₂³×Q₈	#120	1	2	yes	—
453	C₂³×Q₈	#120	1	1	yes	characteristic
454	C₂³×Q₈	#120	1	1	yes	characteristic
455	C₂³×Q₈	#120	1	8	yes	complemented
456	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
457	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
458	C₂³×Q₈	C₂²×D₄	1	2	yes	—
459	C₂³×Q₈	C₂²×D₄	1	2	yes	—
460	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
461	C₂³×D₄	#120	1	2	yes	—
462	C₂³×D₄	#120	1	1	yes	characteristic
463	C₂³×D₄	#120	1	1	yes	characteristic
464	C₂³×D₄	#120	1	2	yes	—
465	C₂³×D₄	#120	1	8	yes	complemented
466	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
467	C₂³×D₄	C₂²×D₄	1	2	yes	—
468	C₂³×D₄	C₂²×D₄	1	2	yes	—
469	C₂³×D₄	C₂²×D₄	1	2	yes	—
470	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
471	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
472	C₂⁴×C₄	#120	1	2	yes	—
473	C₂⁴×C₄	#120	1	2	yes	—
474	C₂⁴×C₄	#120	1	2	yes	—
475	C₂⁴×C₄	#120	1	2	yes	—
476	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
477	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
478	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
479	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
480	#563	#120	1	8	yes	—
481	#563	#120	1	4	yes	—
482	#563	#120	1	4	yes	—
483	#563	#120	1	16	yes	complemented
484	#563	#120	1	8	yes	complemented
485	#563	#120	1	16	yes	complemented
486	H(3,𝔽₄)	#120	1	8	yes	—
487	H(3,𝔽₄)	#120	1	4	yes	—
488	H(3,𝔽₄)	#120	1	4	yes	—
489	H(3,𝔽₄)	#120	1	16	yes	complemented
490	H(3,𝔽₄)	#120	1	8	yes	complemented
491	#560	#120	1	8	yes	—
492	#560	#120	1	8	yes	—
493	#560	#120	1	8	yes	—
494	#560	#120	1	8	yes	—
495	#560	#120	1	16	yes	complemented
496	#560	#120	1	16	yes	complemented
497	#559	#120	1	16	yes	complemented
498	Q₈²	#120	1	8	yes	complemented
499	#555	#120	1	8	yes	complemented
500	#555	#120	1	16	yes	complemented
501	#551	#120	1	16	yes	complemented
502	#551	#120	1	16	yes	complemented
503	D₄²	#120	1	16	yes	complemented
504	#536	#120	1	8	yes	complemented
505	#536	#120	1	8	yes	complemented
506	#536	#120	1	4	yes	complemented
507	#536	#120	1	4	yes	complemented
508	#536	C₂²×D₄	1	4	yes	—
509	#536	C₂²×D₄	1	2	yes	—
510	#536	C₂²×D₄	1	2	yes	—
511	#536	C₂²×D₄	1	4	yes	—
512	#536	C₂²×D₄	1	4	yes	—
513	#536	C₂²×D₄	1	4	yes	—
514	#536	C₂²×D₄	1	4	yes	—
515	#535	#120	1	8	yes	complemented
516	#535	#120	1	8	yes	complemented
517	#535	#120	1	4	yes	complemented
518	#535	#120	1	4	yes	complemented
519	#535	C₂²×D₄	1	4	yes	—
520	#535	C₂²×D₄	1	2	yes	—
521	#535	C₂²×D₄	1	2	yes	—
522	#535	C₂²×D₄	1	4	yes	—
523	#535	C₂²×D₄	1	4	yes	—
524	#535	C₂²×D₄	1	4	yes	—
525	#535	C₂²×D₄	1	4	yes	—
526	#532	C₂²×D₄	1	4	yes	—
527	#532	C₂²×D₄	1	4	yes	—
528	#532	C₂²×D₄	1	2	yes	—
529	#532	C₂²×D₄	1	2	yes	—
530	#532	C₂²×D₄	1	2	yes	—
531	#532	C₂²×D₄	1	2	yes	—
532	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
533	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
534	C₂×C₄⋊Q₈	#120	1	4	yes	—
535	C₂×C₄⋊Q₈	#120	1	4	yes	complemented
536	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄⋊Q₈	C₂²×D₄	1	4	yes	—
539	C₂×#127	#120	1	1	yes	characteristic
540	C₂×#127	#120	1	1	yes	characteristic
541	C₂×#127	#120	1	4	yes	—
542	C₂×#127	#120	1	4	yes	complemented
543	C₂×#127	C₂²×D₄	1	1	yes	characteristic
544	C₂×#127	C₂²×D₄	1	1	yes	characteristic
545	C₂×#127	C₂²×D₄	1	4	yes	—
546	C₂×#124	#120	1	1	yes	characteristic
547	C₂×#124	#120	1	1	yes	characteristic
548	C₂×#124	#120	1	1	yes	characteristic
549	C₂×#124	#120	1	1	yes	characteristic
550	C₂×#124	#120	1	4	yes	—
551	C₂×#124	#120	1	4	yes	—
552	C₂×#124	#120	1	4	yes	complemented
553	C₂×#124	#120	1	4	yes	complemented
554	C₂×#124	C₂²×D₄	1	1	yes	characteristic
555	C₂×#124	C₂²×D₄	1	1	yes	characteristic
556	C₂×#124	C₂²×D₄	1	4	yes	—
557	C₂×#124	C₂²×D₄	1	1	yes	characteristic
558	C₂×#124	C₂²×D₄	1	1	yes	characteristic
559	C₂×#124	C₂²×D₄	1	4	yes	—
560	#525	#120	1	8	yes	complemented
561	#525	#120	1	8	yes	complemented
562	#525	#120	1	8	yes	complemented
563	#525	#120	1	8	yes	complemented
564	#525	C₂²×D₄	1	4	yes	—
565	#525	C₂²×D₄	1	4	yes	—
566	#525	C₂²×D₄	1	4	yes	—
567	#525	C₂²×D₄	1	4	yes	—
568	#525	C₂²×D₄	1	4	yes	—
569	#525	C₂²×D₄	1	4	yes	—
570	#525	C₂²×D₄	1	4	yes	—
571	#525	C₂²×D₄	1	4	yes	—
572	C₂×#123	#120	1	2	yes	—
573	C₂×#123	#120	1	2	yes	—
574	C₂×#123	#120	1	2	yes	—
575	C₂×#123	#120	1	2	yes	—
576	C₂×#123	#120	1	4	yes	—
577	C₂×#123	C₂²×D₄	1	2	yes	—
578	C₂×#123	C₂²×D₄	1	2	yes	—
579	C₂×#123	C₂²×D₄	1	2	yes	—
580	C₂×#123	C₂²×D₄	1	2	yes	—
581	C₂×#123	C₂²×D₄	1	4	yes	—
582	C₂×#120	#120	1	2	yes	—
583	C₂×#120	#120	1	2	yes	—
584	C₂×#120	#120	1	2	yes	—
585	C₂×#120	#120	1	2	yes	—
586	C₂×#120	#120	1	4	yes	—
587	C₂×#120	C₂²×D₄	1	2	yes	—
588	C₂×#120	C₂²×D₄	1	2	yes	—
589	C₂×#120	C₂²×D₄	1	2	yes	—
590	C₂×#120	C₂²×D₄	1	2	yes	—
591	C₂×#120	C₂²×D₄	1	4	yes	—
592	#519	#120	1	8	yes	complemented
593	#519	#120	1	8	yes	complemented
594	#518	#120	1	8	yes	complemented
595	#518	#120	1	8	yes	complemented
596	C₄×#41	#120	1	4	yes	complemented
597	C₄×#41	#120	1	4	yes	complemented
598	C₄×#41	#120	1	4	yes	complemented
599	C₄×#41	#120	1	4	yes	complemented
600	C₂×#117	#120	1	4	yes	—
601	C₂×#117	#120	1	2	yes	—
602	C₂×#117	#120	1	2	yes	—
603	C₂×#117	#120	1	2	yes	—
604	C₂×#117	C₂²×D₄	1	2	yes	—
605	C₂×#117	C₂²×D₄	1	2	yes	—
606	C₂×#117	C₂²×D₄	1	1	yes	characteristic
607	C₂×#117	C₂²×D₄	1	1	yes	characteristic
608	C₂×#117	C₂²×D₄	1	2	yes	—
609	C₂×#117	C₂²×D₄	1	2	yes	—
610	C₂²×C₂²⋊C₄	#120	1	2	yes	—
611	C₂²×C₂²⋊C₄	#120	1	2	yes	—
612	C₂²×C₂²⋊C₄	#120	1	2	yes	—
613	C₂²×C₄²	#120	1	1	yes	characteristic
614	C₂²×C₄²	#120	1	1	yes	characteristic
615	C₂²×C₄²	#120	1	1	yes	characteristic
616	C₂²×C₄²	#120	1	1	yes	characteristic
617	C₂²×C₄²	#120	1	4	yes	—
618	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
619	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
620	C₂⁵	C₂×#120	1	2	yes	—
621	C₂⁵	C₂×#120	1	1	yes	characteristic
622	C₂⁵	C₂×#120	1	2	yes	—
623	C₂⁵	C₂×#120	1	2	yes	—
624	C₂⁵	C₂×#120	1	2	yes	—
625	C₂×#41	B(4,𝔽₂)	1	4	yes	—
626	C₂×#41	C₂×#120	1	2	yes	—
627	C₂×#41	C₂×#120	1	2	yes	—
628	C₂×#41	C₂×#120	1	2	yes	—
629	C₂×#41	C₂×#120	1	2	yes	—
630	C₂×#41	C₂×#120	1	4	yes	—
631	C₂×#41	C₂×#120	1	4	yes	—
632	C₂×#41	C₂×#120	1	4	yes	—
633	C₂×#41	C₂×#120	1	4	yes	—
634	C₂×#41	C₂×#120	1	2	yes	—
635	C₂×#41	C₂×#120	1	2	yes	—
636	C₂×#41	C₂×#120	1	2	yes	—
637	C₂×#41	C₂×#120	1	2	yes	—
638	C₂×#41	C₂³×D₄	1	1	yes	characteristic
639	C₂×#41	C₂³×D₄	1	2	yes	—
640	C₂×#41	C₂³×D₄	1	1	yes	characteristic
641	C₂×#41	C₂³×D₄	1	1	yes	characteristic
642	C₂×#41	C₂³×D₄	1	2	yes	—
643	C₂×#41	C₂³×D₄	1	1	yes	characteristic
644	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
645	C₂²×Q₈	C₂×#120	1	2	yes	—
646	C₂²×Q₈	C₂×#120	1	2	yes	—
647	C₂²×Q₈	C₂×#120	1	2	yes	—
648	C₂²×Q₈	C₂×#120	1	4	yes	—
649	C₂²×Q₈	C₂×#120	1	4	yes	—
650	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
651	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
652	C₂²×Q₈	C₂×#120	1	4	yes	—
653	C₂²×Q₈	C₂×#120	1	2	yes	—
654	C₂²×Q₈	C₂×#120	1	2	yes	—
655	C₂²×Q₈	C₂×#120	1	4	yes	—
656	C₂²×Q₈	C₂×#120	1	4	yes	—
657	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
658	C₂²×Q₈	C₂×#120	1	2	yes	—
659	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
660	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
661	C₂²×D₄	C₂×#120	1	2	yes	—
662	C₂²×D₄	C₂×#120	1	2	yes	—
663	C₂²×D₄	C₂×#120	1	2	yes	—
664	C₂²×D₄	C₂×#120	1	4	yes	—
665	C₂²×D₄	C₂×#120	1	4	yes	—
666	C₂²×D₄	C₂×#120	1	1	yes	characteristic
667	C₂²×D₄	C₂×#120	1	1	yes	characteristic
668	C₂²×D₄	C₂×#120	1	4	yes	—
669	C₂²×D₄	C₂×#120	1	2	yes	—
670	C₂²×D₄	C₂×#120	1	2	yes	—
671	C₂²×D₄	C₂×#120	1	4	yes	—
672	C₂²×D₄	C₂×#120	1	4	yes	—
673	C₂²×D₄	C₂×#120	1	1	yes	characteristic
674	C₂²×D₄	C₂×#120	1	2	yes	—
675	C₂²×D₄	C₂×#120	1	1	yes	characteristic
676	C₂²×D₄	C₂×#120	1	1	yes	characteristic
677	C₂²×D₄	C₂×#120	1	2	yes	—
678	C₂²×D₄	C₂×#120	1	2	yes	—
679	C₂²×D₄	C₂×#120	1	2	yes	—
680	C₂²×D₄	C₂³×D₄	1	2	yes	—
681	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
682	C₂³×C₄	C₂×#120	1	2	yes	—
683	C₂³×C₄	C₂×#120	1	1	yes	characteristic
684	C₂³×C₄	C₂×#120	1	2	yes	—
685	C₂³×C₄	C₂×#120	1	2	yes	—
686	C₂³×C₄	C₂×#120	1	2	yes	—
687	C₂³×C₄	C₂×#120	1	2	yes	—
688	C₂³×C₄	C₂×#120	1	4	yes	—
689	C₂³×C₄	C₂×#120	1	4	yes	—
690	C₂³×C₄	C₂×#120	1	4	yes	—
691	C₂³×C₄	C₂×#120	1	4	yes	—
692	C₂³×C₄	C₂×#120	1	1	yes	characteristic
693	C₂³×C₄	C₂×#120	1	2	yes	—
694	C₂³×C₄	C₂×#120	1	1	yes	characteristic
695	C₂³×C₄	C₂×#120	1	2	yes	—
696	C₂³×C₄	C₂×#120	1	1	yes	characteristic
697	C₂³×C₄	C₂×#120	1	1	yes	characteristic
698	C₂³×C₄	C₂³×D₄	1	2	yes	—
699	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
700	C₄⋊Q₈	C₂×#120	1	2	yes	—
701	C₄⋊Q₈	C₂×#120	1	2	yes	—
702	C₄⋊Q₈	C₂×#120	1	4	yes	—
703	C₄⋊Q₈	C₂×#120	1	8	yes	—
704	C₄⋊Q₈	C₂×#120	1	8	yes	—
705	#127	C₂×#120	1	4	yes	—
706	#127	C₂×#120	1	2	yes	—
707	#127	C₂×#120	1	2	yes	—
708	#127	C₂×#120	1	8	yes	—
709	#127	C₂×#120	1	8	yes	—
710	#124	C₂×#120	1	4	yes	—
711	#124	C₂×#120	1	2	yes	—
712	#124	C₂×#120	1	2	yes	—
713	#124	C₂×#120	1	8	yes	—
714	#124	C₂×#120	1	8	yes	—
715	#124	C₂×#120	1	4	yes	—
716	#124	C₂×#120	1	2	yes	—
717	#124	C₂×#120	1	2	yes	—
718	#124	C₂×#120	1	8	yes	—
719	#124	C₂×#120	1	8	yes	—
720	#123	C₂×#120	1	4	yes	—
721	#123	C₂×#120	1	4	yes	—
722	#123	C₂×#120	1	4	yes	—
723	#123	C₂×#120	1	4	yes	—
724	#123	C₂×#120	1	4	yes	—
725	#123	C₂×#120	1	4	yes	—
726	#123	C₂×#120	1	4	yes	—
727	#123	C₂×#120	1	4	yes	—
728	#123	C₂×#120	1	8	yes	—
729	#123	C₂×#120	1	8	yes	—
730	#120	C₂×#120	1	4	yes	—
731	#120	C₂×#120	1	4	yes	—
732	#120	C₂×#120	1	4	yes	—
733	#120	C₂×#120	1	4	yes	—
734	#120	C₂×#120	1	4	yes	—
735	#120	C₂×#120	1	4	yes	—
736	#120	C₂×#120	1	4	yes	—
737	#120	C₂×#120	1	4	yes	—
738	#120	C₂×#120	1	8	yes	—
739	#120	C₂×#120	1	8	yes	—
740	#117	C₂×#120	1	4	yes	—
741	#117	C₂×#120	1	4	yes	—
742	#117	C₂×#120	1	4	yes	—
743	#117	C₂×#120	1	4	yes	—
744	#117	C₂×#120	1	2	yes	—
745	#117	C₂×#120	1	2	yes	—
746	#117	C₂×#120	1	2	yes	—
747	#117	C₂×#120	1	2	yes	—
748	#117	C₂×#120	1	4	yes	—
749	#117	C₂×#120	1	4	yes	—
750	#117	C₂×#120	1	4	yes	—
751	#117	C₂×#120	1	4	yes	—
752	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
758	C₂×C₄²	C₂×#120	1	4	yes	—
759	C₂×C₄²	C₂×#120	1	4	yes	—
760	C₂×C₄²	C₂×#120	1	2	yes	—
761	C₂×C₄²	C₂×#120	1	2	yes	—
762	C₂×C₄²	C₂×#120	1	2	yes	—
763	C₂×C₄²	C₂×#120	1	2	yes	—
764	C₂×C₄²	C₂×#120	1	1	yes	characteristic
765	C₂×C₄²	C₂×#120	1	1	yes	characteristic
766	C₂×C₄²	C₂×#120	1	1	yes	characteristic
767	C₂×C₄²	C₂×#120	1	1	yes	characteristic
768	C₂⁴	#2846	1	4	yes	—
769	C₂⁴	#2846	1	4	yes	—
770	C₂⁴	#2846	1	4	yes	—
771	C₂⁴	#2846	1	2	yes	—
772	C₂⁴	#2846	1	1	yes	characteristic
773	C₂⁴	#2846	1	1	yes	characteristic
774	C₂⁴	C₂²×#120	1	1	yes	characteristic
775	C₂⁴	C₂²×#120	1	2	yes	—
776	C₂×Q₈	#2846	1	8	yes	—
777	C₂×Q₈	#2846	1	2	yes	—
778	C₂×Q₈	#2846	1	2	yes	—
779	C₂×Q₈	#2846	1	4	yes	—
780	C₂×Q₈	#2846	1	2	yes	—
781	C₂×Q₈	#2846	1	2	yes	—
782	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
783	C₂×Q₈	#3026	1	2	yes	—
784	C₂×Q₈	C₂²×#120	1	1	yes	characteristic
785	C₂×Q₈	C₂²×#120	1	2	yes	—
786	C₂×Q₈	C₂²×#120	1	1	yes	characteristic
787	C₂×D₄	#2846	1	8	yes	—
788	C₂×D₄	#2846	1	2	yes	—
789	C₂×D₄	#2846	1	2	yes	—
790	C₂×D₄	#2846	1	4	yes	—
791	C₂×D₄	#2846	1	2	yes	—
792	C₂×D₄	#2846	1	2	yes	—
793	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
794	C₂×D₄	#3026	1	2	yes	—
795	C₂×D₄	C₂²×#120	1	2	yes	—
796	C₂×D₄	C₂²×#120	1	2	yes	—
797	C₂×D₄	C₂²×#120	1	1	yes	characteristic
798	C₂×D₄	C₂²×#120	1	2	yes	—
799	C₂×D₄	C₂²×#120	1	1	yes	characteristic
800	C₂×D₄	C₂²×#120	1	2	yes	—
801	C₂×D₄	C₂²×#120	1	2	yes	—
802	C₂²×C₄	#2846	1	1	yes	characteristic
803	C₂²×C₄	#2846	1	4	yes	—
804	C₂²×C₄	#2846	1	4	yes	—
805	C₂²×C₄	#2846	1	4	yes	—
806	C₂²×C₄	#2846	1	2	yes	—
807	C₂²×C₄	#2846	1	1	yes	characteristic
808	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
809	C₂²×C₄	#3026	1	2	yes	—
810	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
811	C₂²×C₄	C₂²×#120	1	2	yes	—
812	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
813	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
814	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
815	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
816	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
817	C₂²×C₄	C₂²×#120	1	2	yes	—
818	C₂²×C₄	C₂²×#120	1	2	yes	—
819	C₂²×C₄	C₂²×#120	1	2	yes	—
820	C₂²×C₄	C₂²×#120	1	2	yes	—
821	C₂²⋊C₄	#2846	1	4	yes	—
822	C₂²⋊C₄	#2846	1	4	yes	—
823	C₂²⋊C₄	#2846	1	4	yes	—
824	C₂²⋊C₄	#2846	1	4	yes	—
825	C₂²⋊C₄	#2846	1	4	yes	—
826	C₂²⋊C₄	#2846	1	4	yes	—
827	C₄²	#2846	1	2	yes	—
828	C₄²	#2846	1	2	yes	—
829	C₄²	#2846	1	2	yes	—
830	C₄²	#2846	1	2	yes	—
831	C₄²	#2846	1	8	yes	—
832	C₄²	#2846	1	8	yes	—
833	C₂³	#32898	1	2	yes	—
834	C₂³	C₂×#2846	1	1	yes	characteristic
835	C₂³	C₂×#2846	1	1	yes	characteristic
836	C₂³	C₂×#2846	1	2	yes	—
837	C₂³	C₂×#2846	1	2	yes	—
838	C₂³	C₂×#2846	1	1	yes	characteristic
839	Q₈	#32898	1	4	yes	—
840	D₄	#32898	1	4	yes	—
841	C₂×C₄	#32898	1	2	yes	—
842	C₂×C₄	C₂×#2846	1	1	yes	characteristic
843	C₂×C₄	C₂×#2846	1	1	yes	characteristic
844	C₂×C₄	C₂×#2846	1	2	yes	—
845	C₂×C₄	C₂×#2846	1	1	yes	characteristic
846	C₂×C₄	C₂×#2846	1	1	yes	characteristic
847	C₂×C₄	C₂×#2846	1	2	yes	—
848	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
849	C₂×C₄	C₂×#3026	1	1	yes	characteristic
850	C₂×C₄	C₂×#3026	1	1	yes	characteristic
851	C₂×C₄	C₂×#3026	1	1	yes	characteristic
852	C₂²	#6342371	1	1	yes	characteristic
853	C₂²	C₂×#32898	1	1	yes	characteristic
854	C₂²	#6628892	1	1	yes	characteristic
855	C₄	C₂×#32898	1	1	yes	characteristic
856	C₄	C₂×#32898	1	1	yes	characteristic
857	C₄	#6628892	1	1	yes	characteristic
858	C₄	#6628892	1	1	yes	characteristic
859	C₂	#72219118	1	1	yes	characteristic
860	C₂	#72260417	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261350	C₂	semidirect
2. #72261344	C₂	semidirect
3. #72261337	C₂	semidirect
4. C₂×#511829	C₂	semidirect
5. C₂×#511830	C₂	semidirect
6. #72261310	C₂	semidirect
7. #72261294	C₂	semidirect
8. #72261282	C₂	semidirect
9. C₂×#511828	C₂	semidirect
10. #72261267	C₂	semidirect
11. #72261251	C₂	semidirect
12. #72261238	C₂	semidirect
13. #72261217	C₂	semidirect
14. #72261210	C₂	semidirect
15. #72261199	C₂	semidirect
16. #72261190	C₂	semidirect
17. C₂×#511826	C₂	semidirect
18. C₂×#10586400	C₂	semidirect
19. #72261075	C₂	semidirect
20. #72260846	C₂	semidirect
21. #72260453	C₂	semidirect
22. C₂×#511825	C₂	semidirect
23. C₂×#511827	C₂	semidirect
35. #10574842	C₂²	semidirect
36. C₂×#33572	C₂²	semidirect
37. C₂×#33571	C₂²	semidirect
38. C₂×#33570	C₂²	semidirect
39. C₂×#33556	C₂²	semidirect
40. C₂×#33555	C₂²	semidirect
41. C₂×#33554	C₂²	semidirect
42. C₂×#33553	C₂²	semidirect
43. C₂×#33550	C₂²	semidirect
44. C₂×#33550	C₂²	semidirect
45. C₂×#33550	C₂²	semidirect
46. #6437625	C₂²	semidirect
47. #6437616	C₂²	semidirect
48. C₂×#23873	C₂²	semidirect
49. C₂×#23875	C₂²	semidirect
50. C₂×#23874	C₂²	semidirect
51. C₂×#23872	C₂²	semidirect
52. C₂×#23885	C₂²	semidirect
53. C₂×#23884	C₂²	semidirect
54. C₂×#23883	C₂²	semidirect
55. C₂×#23882	C₂²	semidirect
56. #6437451	C₂²	semidirect
57. #6437437	C₂²	semidirect
58. C₂×#12780	C₂²	semidirect
59. C₂×#12780	C₂²	semidirect
60. C₂×#12779	C₂²	semidirect
61. C₂×#12779	C₂²	semidirect
62. C₂×#12778	C₂²	semidirect
63. C₂×#12778	C₂²	semidirect
64. #493616	C₂²	semidirect
65. #493615	C₂²	semidirect
66. #493614	C₂²	semidirect
67. C₂×#12766	C₂²	semidirect
68. C₂×#12766	C₂²	semidirect
69. C₂×#12766	C₂²	semidirect
70. C₂×#12766	C₂²	semidirect
71. C₂×#12766	C₂²	semidirect
72. C₂×#12766	C₂²	semidirect
73. #493587	C₂²	semidirect
74. #493586	C₂²	semidirect
75. #493585	C₂²	semidirect
76. #493584	C₂²	semidirect
77. #493581	C₂²	semidirect
78. #493581	C₂²	semidirect
79. #493581	C₂²	semidirect
80. C₂×#12758	C₂²	semidirect
81. C₂×#12758	C₂²	semidirect
82. C₂×#12756	C₂²	semidirect
83. C₂×#12756	C₂²	semidirect
84. C₂×#12757	C₂²	semidirect
85. C₂×#12757	C₂²	semidirect
86. C₂×#12755	C₂²	semidirect
87. C₂×#12755	C₂²	semidirect
88. C₂×#12718	C₂²	semidirect
89. C₂×#12716	C₂²	semidirect
90. C₂×#12716	C₂²	semidirect
91. C₂×#12717	C₂²	semidirect
92. C₂×#12715	C₂²	semidirect
93. C₂×#12715	C₂²	semidirect
94. C₂×#12714	C₂²	semidirect
95. C₂×#12714	C₂²	semidirect
96. C₂×#12712	C₂²	semidirect
97. C₂×#12712	C₂²	semidirect
98. C₂×#12713	C₂²	semidirect
99. C₂×#12713	C₂²	semidirect
100. C₂×#12711	C₂²	semidirect
101. C₂×#12711	C₂²	semidirect
102. #493387	C₂²	semidirect
103. #493378	C₂²	semidirect
104. #493374	C₂²	semidirect
105. #493365	C₂²	semidirect
106. #493361	C₂²	semidirect
107. #493352	C₂²	semidirect
108. #493352	C₂²	semidirect
109. #392134	C₂²	semidirect
110. #392134	C₂²	semidirect
111. #359672	C₂²	semidirect
112. #359671	C₂²	semidirect
113. #359670	C₂²	semidirect
114. #359669	C₂²	semidirect
115. #359648	C₂²	semidirect
116. #359647	C₂²	semidirect
117. #359646	C₂²	semidirect
118. #359645	C₂²	semidirect
119. #359515	C₂²	semidirect
120. #359507	C₂²	semidirect
121. #359470	C₂²	semidirect
122. #359446	C₂²	semidirect
123. C₂²×#585	D₄	semidirect
125. C₂⁴×#41	D₄	semidirect
128. #63066	D₄	semidirect
129. #63063	D₄	semidirect
130. #63048	D₄	semidirect
131. #63045	D₄	semidirect
132. #63044	D₄	semidirect
133. #63041	D₄	semidirect
135. C₂×#3500	D₄	semidirect
136. C₂×#3500	D₄	semidirect
139. C₂×#3499	D₄	semidirect
141. C₂×#3498	D₄	semidirect
143. C₂×#3487	D₄	semidirect
145. C₂×#3486	D₄	semidirect
147. C₂×#3485	D₄	semidirect
149. C₂×#3484	D₄	semidirect
153. C₂×#3545	D₄	semidirect
154. C₂×#3544	D₄	semidirect
158. C₂×#3533	D₄	semidirect
161. C₂×#3532	D₄	semidirect
162. C₂×#3483	D₄	semidirect
163. C₂×#3481	D₄	semidirect
164. C₂×#3529	D₄	semidirect
165. C₂×#3529	D₄	semidirect
166. C₂×#3529	D₄	semidirect
167. C₂×#3529	D₄	semidirect
168. C₂×#3529	D₄	semidirect
172. C₂²×#563	D₄	semidirect
173. C₂²×H(3,𝔽₄)	D₄	semidirect
174. C₂²×#560	D₄	semidirect
175. C₂×#3449	D₄	semidirect
176. C₂×#3449	D₄	semidirect
179. C₂²×#532	D₄	semidirect
181. C₂²×#525	D₄	semidirect
183. C₂×#3428	D₄	semidirect
184. C₂²×C₄×#41	D₄	semidirect
418. C₂×2₋¹⁺⁴	#120	semidirect
419. C₂×2₋¹⁺⁴	#120	semidirect
423. C₂×H(5,𝔽₂)	#120	semidirect
424. C₂×H(5,𝔽₂)	#120	semidirect
438. C₂²×#41	#120	semidirect
439. C₂²×#41	#120	semidirect
455. C₂³×Q₈	#120	semidirect
465. C₂³×D₄	#120	semidirect
483. #563	#120	semidirect
484. #563	#120	semidirect
485. #563	#120	semidirect
489. H(3,𝔽₄)	#120	semidirect
490. H(3,𝔽₄)	#120	semidirect
495. #560	#120	semidirect
496. #560	#120	semidirect
497. #559	#120	semidirect
498. Q₈²	#120	semidirect
499. #555	#120	semidirect
500. #555	#120	semidirect
501. #551	#120	semidirect
502. #551	#120	semidirect
503. D₄²	#120	semidirect
504. #536	#120	semidirect
505. #536	#120	semidirect
506. #536	#120	semidirect
507. #536	#120	semidirect
515. #535	#120	semidirect
516. #535	#120	semidirect
517. #535	#120	semidirect
518. #535	#120	semidirect
535. C₂×C₄⋊Q₈	#120	semidirect
542. C₂×#127	#120	semidirect
552. C₂×#124	#120	semidirect
553. C₂×#124	#120	semidirect
560. #525	#120	semidirect
561. #525	#120	semidirect
562. #525	#120	semidirect
563. #525	#120	semidirect
592. #519	#120	semidirect
593. #519	#120	semidirect
594. #518	#120	semidirect
595. #518	#120	semidirect
596. C₄×#41	#120	semidirect
597. C₄×#41	#120	semidirect
598. C₄×#41	#120	semidirect
599. C₄×#41	#120	semidirect

Maximal subgroups

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

subgroup	index
#72261350	2
#72261344	2
#72261337	2
C₂×#511829	2
C₂×#511830	2
#72261310	2
#72261294	2
#72261282	2
C₂×#511828	2
#72261267	2
#72261251	2
#72261238	2
#72261217	2
#72261210	2
#72261199	2
#72261190	2
C₂×#511826	2
C₂×#10586400	2
#72261075	2
#72260846	2
#72260453	2
C₂×#511825	2
C₂×#511827	2