Subgroups — #72263554

Order 2048.

At least 13877 conjugacy classes of subgroups; only the 1588 normal subgroups are shown.

The subgroup lattice has 873 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263553	C₂	1	4	yes	maximal, complemented
2	#72263552	C₂	1	4	yes	maximal, complemented
3	#72263551	C₂	1	2	yes	maximal, complemented
4	#72263550	C₂	1	2	yes	maximal, complemented
5	#72263548	C₂	1	1	yes	maximal, characteristic, complemented
6	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236670	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#493370	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#128073	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#6437445	C₂	1	1	yes	maximal, characteristic
11	C₂×#187928	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234545	C₂	1	2	yes	maximal, complemented
13	#72234139	C₂	1	2	yes	maximal, complemented
14	#72210503	C₂	1	4	yes	maximal, complemented
15	#72210479	C₂	1	4	yes	maximal, complemented
16	C₂²×#3484	C₂²	1	1	yes	characteristic
17	C₂³×#535	C₂²	1	1	yes	characteristic
18	C₂²×#3019	C₄	1	2	yes	complemented
19	#6437445	C₄	1	4	yes	complemented
20	#6437445	C₄	1	4	yes	complemented
21	#6437445	C₂²	1	2	yes	—
22	#6437445	C₂²	1	2	yes	—
23	#6437445	C₂²	1	2	yes	—
24	#6437445	C₂²	1	2	yes	—
25	C₂×#23912	C₄	1	4	yes	complemented
26	C₂×#23907	C₂²	1	2	yes	—
27	C₂×#23906	C₂²	1	2	yes	—
28	C₂×#20953	C₄	1	2	yes	complemented
29	C₂²×#1783	C₂²	1	1	yes	characteristic
30	C₂²×#1781	C₂²	1	1	yes	characteristic
31	C₂²×#1781	C₂²	1	1	yes	characteristic
32	#581605	C₂²	1	2	yes	complemented
33	#581603	C₂²	1	2	yes	complemented
34	#559859	C₂²	1	1	yes	characteristic, complemented
35	#559850	C₂²	1	1	yes	characteristic, complemented
36	#552678	C₂²	1	2	yes	complemented
37	#552671	C₂²	1	2	yes	complemented
38	#532187	C₂²	1	1	yes	characteristic, complemented
39	#531766	C₂²	1	1	yes	characteristic, complemented
40	#517411	C₂²	1	1	yes	characteristic
41	C₂×#13867	C₂²	1	1	yes	characteristic
42	#493370	C₂²	1	2	yes	complemented
43	#493370	C₂²	1	2	yes	complemented
44	#493370	C₂²	1	2	yes	complemented
45	#493370	C₂²	1	2	yes	complemented
46	C₂×#12694	C₂²	1	2	yes	complemented
47	C₂×#12693	C₂²	1	2	yes	complemented
48	#187944	C₂²	1	4	yes	complemented
49	#187928	C₂²	1	2	yes	—
50	#187928	C₂²	1	2	yes	—
51	#187928	C₂²	1	2	yes	—
52	#187928	C₂²	1	2	yes	—
53	#187928	C₂²	1	4	yes	complemented
54	#187928	C₂²	1	4	yes	complemented
55	C₂×#8534	C₂²	1	4	yes	complemented
56	#139779	C₂²	1	8	yes	complemented
57	#139778	C₂²	1	8	yes	complemented
58	#139777	C₂²	1	8	yes	complemented
59	#139776	C₂²	1	8	yes	complemented
60	#139707	C₂²	1	8	yes	complemented
61	#139707	C₂²	1	8	yes	complemented
62	#139706	C₂²	1	8	yes	complemented
63	#139706	C₂²	1	8	yes	complemented
64	#128073	C₂²	1	4	yes	complemented
65	#128073	C₂²	1	2	yes	complemented
66	#128073	C₂²	1	2	yes	complemented
67	#128073	C₂²	1	4	yes	complemented
68	#128073	C₂²	1	2	yes	complemented
69	#128073	C₂²	1	2	yes	complemented
70	#128033	C₂²	1	4	yes	complemented
71	C₂×#7304	C₂²	1	4	yes	complemented
72	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂⁴×#41	D₄	1	1	yes	characteristic
74	C₂⁵×D₄	C₂³	1	1	yes	characteristic
75	C₂×#3484	C₂×C₄	1	2	yes	complemented
76	C₂×#3484	C₂×C₄	1	2	yes	complemented
77	C₂×#3484	C₂×C₄	1	2	yes	complemented
78	C₂×#3484	C₂³	1	2	yes	—
79	C₂×#3484	C₂³	1	2	yes	—
80	C₂×#3484	C₂³	1	2	yes	—
81	C₂²×#535	C₂×C₄	1	2	yes	—
82	C₂²×#535	C₂×C₄	1	2	yes	—
83	C₂²×#535	C₂×C₄	1	2	yes	—
84	C₂²×#535	C₂×C₄	1	2	yes	—
85	C₂²×#535	D₄	1	2	yes	—
86	C₂²×#535	D₄	1	2	yes	—
87	C₂²×#535	D₄	1	2	yes	—
88	C₂²×#535	D₄	1	2	yes	—
89	C₂²×#535	D₄	1	1	yes	characteristic
90	C₂²×#535	D₄	1	1	yes	characteristic
91	C₂²×#535	D₄	1	1	yes	characteristic
92	C₂²×#535	D₄	1	1	yes	characteristic
93	C₂²×#535	C₂³	1	1	yes	characteristic
94	C₂²×#535	C₂³	1	1	yes	characteristic
95	C₂²×#535	C₂³	1	1	yes	characteristic
96	C₂²×#535	C₂³	1	1	yes	characteristic
97	C₂³×#127	D₄	1	1	yes	characteristic
98	C₂³×#127	C₂³	1	1	yes	characteristic
99	C₂³×#124	D₄	1	1	yes	characteristic
100	C₂³×#124	C₂³	1	1	yes	characteristic
101	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂³×#117	D₄	1	1	yes	characteristic
103	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×#3019	C₂×C₄	1	4	yes	complemented
105	C₂×#3019	C₂×C₄	1	4	yes	complemented
106	C₂×#3019	C₂×C₄	1	4	yes	complemented
107	C₂×#3019	C₂×C₄	1	4	yes	complemented
108	C₂²×#455	C₂×C₄	1	4	yes	complemented
109	C₂²×#453	C₂×C₄	1	4	yes	complemented
110	C₂³×#100	C₂×C₄	1	2	yes	complemented
111	C₂²×#379	D₄	1	1	yes	characteristic
112	C₂²×#379	D₄	1	1	yes	characteristic
113	C₂²×#379	D₄	1	1	yes	characteristic
114	#23912	C₂×C₄	1	8	yes	complemented
115	#23912	C₂×C₄	1	8	yes	complemented
116	#23912	C₂×C₄	1	8	yes	complemented
117	#23912	C₂×C₄	1	8	yes	complemented
118	#23907	C₂×C₄	1	8	yes	complemented
119	#23907	C₂³	1	4	yes	—
120	#23907	C₂³	1	4	yes	—
121	#23906	C₂×C₄	1	8	yes	complemented
122	#23906	C₂³	1	4	yes	—
123	#23906	C₂³	1	4	yes	—
124	#20953	C₂×C₄	1	4	yes	complemented
125	#20953	C₂×C₄	1	4	yes	complemented
126	#20953	C₂×C₄	1	4	yes	complemented
127	#20953	C₂×C₄	1	4	yes	complemented
128	C₂×#1887	C₂×C₄	1	4	yes	complemented
129	C₂×#1885	C₂×C₄	1	4	yes	complemented
130	C₂×#1783	C₂×C₄	1	2	yes	complemented
131	C₂×#1783	C₂×C₄	1	2	yes	complemented
132	C₂×#1783	C₂×C₄	1	2	yes	complemented
133	C₂×#1783	C₂³	1	2	yes	—
134	C₂×#1783	C₂³	1	2	yes	—
135	C₂×#1783	C₂³	1	2	yes	—
136	C₂×#1781	C₂³	1	2	yes	—
137	C₂×#1781	C₂³	1	2	yes	—
138	C₂×#1781	C₂³	1	2	yes	—
139	C₂×#1781	C₂³	1	2	yes	—
140	C₂×#1781	C₂³	1	2	yes	—
141	C₂×#1781	C₂³	1	2	yes	—
142	#14662	C₂³	1	2	yes	complemented
143	#14661	C₂³	1	2	yes	complemented
144	#14492	C₂³	1	2	yes	complemented
145	#14492	C₂³	1	2	yes	complemented
146	#14419	C₂³	1	2	yes	complemented
147	#14419	C₂³	1	2	yes	complemented
148	#14335	D₄	1	2	yes	—
149	#14335	C₂³	1	2	yes	—
150	#14169	C₂³	1	2	yes	complemented
151	#14154	C₂³	1	2	yes	complemented
152	#13867	D₄	1	2	yes	—
153	#13867	D₄	1	1	yes	characteristic
154	#13867	D₄	1	1	yes	characteristic
155	#13867	D₄	1	1	yes	characteristic
156	#13867	D₄	1	2	yes	—
157	#13867	D₄	1	1	yes	characteristic
158	#13867	C₂³	1	1	yes	characteristic
159	#13867	C₂³	1	1	yes	characteristic
160	#13867	C₂³	1	1	yes	characteristic
161	#13867	C₂³	1	1	yes	characteristic
162	#13867	C₂³	1	2	yes	—
163	#13867	C₂³	1	2	yes	—
164	C₂×#1438	D₄	1	2	yes	—
165	C₂×#1438	C₂³	1	2	yes	—
166	#12694	C₂³	1	4	yes	complemented
167	#12694	C₂³	1	4	yes	complemented
168	#12693	C₂³	1	4	yes	complemented
169	#12693	C₂³	1	4	yes	complemented
170	#8534	C₂³	1	8	yes	—
171	#8534	C₂³	1	8	yes	—
172	#8534	C₂³	1	8	yes	—
173	#8534	C₂³	1	8	yes	—
174	#7304	C₂³	1	8	yes	complemented
175	#7304	C₂³	1	8	yes	complemented
176	#7304	C₂³	1	8	yes	complemented
177	#7304	C₂³	1	8	yes	complemented
178	C₂⁷	C₂×D₄	1	1	yes	characteristic
179	C₂⁷	C₂×D₄	1	1	yes	characteristic
180	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
181	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
182	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
183	C₂³×#41	C₂²⋊C₄	1	2	yes	—
184	C₂³×#41	C₂²⋊C₄	1	2	yes	—
185	C₂³×#41	C₂²⋊C₄	1	2	yes	—
186	C₂³×#41	C₂²⋊C₄	1	2	yes	—
187	C₂³×#41	C₂×D₄	1	1	yes	characteristic
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic
189	C₂³×#41	C₂×D₄	1	1	yes	characteristic
190	C₂³×#41	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
193	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
202	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
203	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
205	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
206	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
207	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
208	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
209	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
210	C₂⁴×D₄	#41	1	1	yes	characteristic
211	C₂⁴×D₄	#41	1	1	yes	characteristic
212	C₂⁴×D₄	#41	1	1	yes	characteristic
213	C₂⁴×D₄	#41	1	1	yes	characteristic
214	C₂⁴×D₄	#41	1	1	yes	characteristic
215	C₂⁴×D₄	#41	1	1	yes	characteristic
216	C₂⁴×D₄	#41	1	1	yes	characteristic
217	C₂⁴×D₄	#41	1	1	yes	characteristic
218	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
219	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
220	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
221	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
222	#3484	C₂²×C₄	1	4	yes	—
223	#3484	C₂²×C₄	1	4	yes	—
224	#3484	C₂²×C₄	1	4	yes	—
225	#3484	C₂⁴	1	4	yes	—
226	C₂×#535	C₂²⋊C₄	1	2	yes	—
227	C₂×#535	C₂²⋊C₄	1	2	yes	—
228	C₂×#535	C₂²⋊C₄	1	2	yes	—
229	C₂×#535	C₂²⋊C₄	1	2	yes	—
230	C₂×#535	C₂²⋊C₄	1	2	yes	—
231	C₂×#535	C₂²⋊C₄	1	2	yes	—
232	C₂×#535	C₂²⋊C₄	1	2	yes	—
233	C₂×#535	C₂²⋊C₄	1	2	yes	—
234	C₂×#535	C₂²⋊C₄	1	2	yes	—
235	C₂×#535	C₂²⋊C₄	1	2	yes	—
236	C₂×#535	C₂²⋊C₄	1	2	yes	—
237	C₂×#535	C₂²⋊C₄	1	2	yes	—
238	C₂×#535	C₂²⋊C₄	1	2	yes	—
239	C₂×#535	C₂²⋊C₄	1	2	yes	—
240	C₂×#535	C₂²⋊C₄	1	2	yes	—
241	C₂×#535	C₂²⋊C₄	1	2	yes	—
242	C₂×#535	C₂²×C₄	1	2	yes	—
243	C₂×#535	C₂²×C₄	1	2	yes	—
244	C₂×#535	C₂²×C₄	1	2	yes	—
245	C₂×#535	C₂²×C₄	1	2	yes	—
246	C₂×#535	C₂²×C₄	1	2	yes	—
247	C₂×#535	C₂²×C₄	1	2	yes	—
248	C₂×#535	C₂²×C₄	1	2	yes	—
249	C₂×#535	C₂²×C₄	1	2	yes	—
250	C₂×#535	C₂×D₄	1	2	yes	—
251	C₂×#535	C₂×D₄	1	2	yes	—
252	C₂×#535	C₂×D₄	1	2	yes	—
253	C₂×#535	C₂×D₄	1	2	yes	—
254	C₂×#535	C₂×D₄	1	2	yes	—
255	C₂×#535	C₂×D₄	1	2	yes	—
256	C₂×#535	C₂×D₄	1	2	yes	—
257	C₂×#535	C₂×D₄	1	2	yes	—
258	C₂²×#127	C₂²⋊C₄	1	2	yes	—
259	C₂²×#127	C₂²⋊C₄	1	2	yes	—
260	C₂²×#127	C₂²⋊C₄	1	2	yes	—
261	C₂²×#127	C₂²⋊C₄	1	2	yes	—
262	C₂²×#127	C₂²×C₄	1	2	yes	—
263	C₂²×#127	C₂²×C₄	1	2	yes	—
264	C₂²×#127	C₂×D₄	1	1	yes	characteristic
265	C₂²×#127	C₂×D₄	1	1	yes	characteristic
266	C₂²×#127	C₂×D₄	1	2	yes	—
267	C₂²×#127	C₂×D₄	1	1	yes	characteristic
268	C₂²×#127	C₂×D₄	1	1	yes	characteristic
269	C₂²×#127	C₂×D₄	1	1	yes	characteristic
270	C₂²×#127	C₂×D₄	1	1	yes	characteristic
271	C₂²×#127	C₂×D₄	1	2	yes	—
272	C₂²×#127	C₂⁴	1	1	yes	characteristic
273	C₂²×#127	C₂⁴	1	1	yes	characteristic
274	C₂²×#124	C₂²⋊C₄	1	2	yes	—
275	C₂²×#124	C₂²⋊C₄	1	2	yes	—
276	C₂²×#124	C₂²⋊C₄	1	2	yes	—
277	C₂²×#124	C₂²⋊C₄	1	2	yes	—
278	C₂²×#124	C₂²×C₄	1	2	yes	—
279	C₂²×#124	C₂²×C₄	1	2	yes	—
280	C₂²×#124	C₂×D₄	1	1	yes	characteristic
281	C₂²×#124	C₂×D₄	1	1	yes	characteristic
282	C₂²×#124	C₂×D₄	1	2	yes	—
283	C₂²×#124	C₂×D₄	1	1	yes	characteristic
284	C₂²×#124	C₂×D₄	1	1	yes	characteristic
285	C₂²×#124	C₂×D₄	1	1	yes	characteristic
286	C₂²×#124	C₂×D₄	1	1	yes	characteristic
287	C₂²×#124	C₂×D₄	1	2	yes	—
288	C₂²×#124	C₂⁴	1	1	yes	characteristic
289	C₂²×#124	C₂⁴	1	1	yes	characteristic
290	C₂×#518	C₂²×C₄	1	2	yes	—
291	C₂×#518	C₂²×C₄	1	2	yes	—
292	C₂×#518	C₂²×C₄	1	2	yes	—
293	C₂²×#117	C₂²⋊C₄	1	2	yes	—
294	C₂²×#117	C₂²⋊C₄	1	2	yes	—
295	C₂²×#117	C₂²⋊C₄	1	2	yes	—
296	C₂²×#117	C₂²⋊C₄	1	2	yes	—
297	C₂²×#117	C₂×D₄	1	1	yes	characteristic
298	C₂²×#117	C₂×D₄	1	1	yes	characteristic
299	C₂²×#117	C₂×D₄	1	1	yes	characteristic
300	C₂²×#117	C₂×D₄	1	1	yes	characteristic
301	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
302	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
303	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
307	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
308	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
309	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
310	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
311	C₂×#455	C₂²×C₄	1	8	yes	complemented
312	C₂×#455	C₂²×C₄	1	8	yes	complemented
313	C₂×#453	C₂²×C₄	1	8	yes	complemented
314	C₂×#453	C₂²×C₄	1	8	yes	complemented
315	C₂²×#100	C₂²×C₄	1	4	yes	—
316	C₂²×#100	C₂²×C₄	1	4	yes	—
317	C₂²×#100	C₂²×C₄	1	4	yes	—
318	C₂×#379	C₂×D₄	1	2	yes	—
319	C₂×#379	C₂×D₄	1	2	yes	—
320	C₂×#379	C₂×D₄	1	1	yes	characteristic
321	C₂×#379	C₂×D₄	1	1	yes	characteristic
322	C₂×#379	C₂×D₄	1	1	yes	characteristic
323	C₂×#379	C₂×D₄	1	1	yes	characteristic
324	C₂×#379	C₂×D₄	1	2	yes	—
325	C₂×#379	C₂×D₄	1	2	yes	—
326	#1887	C₂²×C₄	1	8	yes	complemented
327	#1887	C₂²×C₄	1	8	yes	complemented
328	#1885	C₂²×C₄	1	8	yes	complemented
329	#1885	C₂²×C₄	1	8	yes	complemented
330	#1783	C₂²×C₄	1	4	yes	—
331	#1783	C₂²×C₄	1	4	yes	—
332	#1783	C₂²×C₄	1	4	yes	—
333	#1783	C₂⁴	1	4	yes	—
334	#1781	C₂⁴	1	4	yes	—
335	#1781	C₂⁴	1	4	yes	—
336	#1438	C₂×D₄	1	2	yes	—
337	#1438	C₂×D₄	1	2	yes	—
338	#1438	C₂×D₄	1	2	yes	—
339	#1438	C₂×D₄	1	2	yes	—
340	#1438	C₂×D₄	1	2	yes	—
341	#1438	C₂×D₄	1	2	yes	—
342	#1438	C₂×D₄	1	2	yes	—
343	#1438	C₂×D₄	1	2	yes	—
344	#1438	C₂×D₄	1	2	yes	—
345	#1438	C₂×D₄	1	2	yes	—
346	#1438	C₂×D₄	1	2	yes	—
347	#1438	C₂×D₄	1	2	yes	—
348	#1438	C₂⁴	1	2	yes	—
349	#1438	C₂⁴	1	2	yes	—
350	#1438	C₂⁴	1	2	yes	—
351	#1438	C₂⁴	1	2	yes	—
352	C₂⁶	C₄×D₄	1	1	yes	characteristic
353	C₂⁶	C₄×D₄	1	1	yes	characteristic
354	C₂⁶	C₄×D₄	1	1	yes	characteristic
355	C₂⁶	C₄×D₄	1	1	yes	characteristic
356	C₂⁶	C₄×D₄	1	1	yes	characteristic
357	C₂⁶	C₄×D₄	1	1	yes	characteristic
358	C₂⁶	C₄×D₄	1	1	yes	characteristic
359	C₂⁶	C₄×D₄	1	1	yes	characteristic
360	C₂⁶	#120	1	1	yes	characteristic
361	C₂⁶	#120	1	1	yes	characteristic
362	C₂⁶	#120	1	1	yes	characteristic
363	C₂⁶	#120	1	1	yes	characteristic
364	C₂⁶	#120	1	1	yes	characteristic
365	C₂⁶	#120	1	1	yes	characteristic
366	C₂⁶	#120	1	1	yes	characteristic
367	C₂⁶	#121	1	1	yes	characteristic
368	C₂⁶	#121	1	1	yes	characteristic
369	C₂⁶	#121	1	1	yes	characteristic
370	C₂⁶	#121	1	1	yes	characteristic
371	C₂⁶	#121	1	1	yes	characteristic
372	C₂⁶	#121	1	1	yes	characteristic
373	C₂⁶	#121	1	1	yes	characteristic
374	C₂⁶	#121	1	1	yes	characteristic
375	C₂⁶	C₂²×D₄	1	1	yes	characteristic
376	C₂⁶	C₂²×D₄	1	1	yes	characteristic
377	C₂⁶	C₂²×D₄	1	1	yes	characteristic
378	C₂⁶	C₂²×D₄	1	1	yes	characteristic
379	C₂⁶	C₂²×D₄	1	1	yes	characteristic
380	C₂⁶	C₂²×D₄	1	1	yes	characteristic
381	C₂×H(5,𝔽₂)	C₂³×C₄	1	4	yes	—
382	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
383	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
384	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
385	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
386	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
387	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
388	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
389	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
390	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
391	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
392	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
393	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
394	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
402	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
403	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
406	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
408	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
409	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
410	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
411	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
412	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
413	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
414	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
415	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
416	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
417	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
418	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
419	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
420	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
421	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
422	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
423	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
424	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
425	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
426	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
427	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
428	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
429	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
430	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
431	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
432	C₂³×D₄	#120	1	1	yes	characteristic
433	C₂³×D₄	#120	1	1	yes	characteristic
434	C₂³×D₄	#120	1	1	yes	characteristic
435	C₂³×D₄	#120	1	1	yes	characteristic
436	C₂³×D₄	#120	1	1	yes	characteristic
437	C₂³×D₄	#120	1	1	yes	characteristic
438	C₂³×D₄	#121	1	1	yes	characteristic
439	C₂³×D₄	#121	1	1	yes	characteristic
440	C₂³×D₄	#121	1	1	yes	characteristic
441	C₂³×D₄	#121	1	1	yes	characteristic
442	C₂³×D₄	#121	1	1	yes	characteristic
443	C₂³×D₄	#121	1	1	yes	characteristic
444	C₂³×D₄	#121	1	1	yes	characteristic
445	C₂³×D₄	#121	1	1	yes	characteristic
446	C₂³×D₄	#121	1	1	yes	characteristic
447	C₂³×D₄	#121	1	1	yes	characteristic
448	C₂³×D₄	#121	1	1	yes	characteristic
449	C₂³×D₄	#121	1	1	yes	characteristic
450	C₂³×D₄	#121	1	1	yes	characteristic
451	C₂³×D₄	#121	1	1	yes	characteristic
452	C₂³×D₄	#121	1	1	yes	characteristic
453	C₂³×D₄	#121	1	1	yes	characteristic
454	C₂³×D₄	#121	1	1	yes	characteristic
455	C₂³×D₄	#121	1	1	yes	characteristic
456	C₂³×D₄	#121	1	1	yes	characteristic
457	C₂³×D₄	#121	1	1	yes	characteristic
458	C₂³×D₄	#121	1	1	yes	characteristic
459	C₂³×D₄	#121	1	1	yes	characteristic
460	C₂³×D₄	#121	1	1	yes	characteristic
461	C₂³×D₄	#121	1	1	yes	characteristic
462	C₂³×D₄	#123	1	1	yes	characteristic
463	C₂³×D₄	#123	1	1	yes	characteristic
464	C₂³×D₄	#123	1	1	yes	characteristic
465	C₂³×D₄	#123	1	1	yes	characteristic
466	C₂³×D₄	#123	1	1	yes	characteristic
467	C₂³×D₄	#123	1	1	yes	characteristic
468	C₂³×D₄	#123	1	1	yes	characteristic
469	C₂³×D₄	#123	1	1	yes	characteristic
470	C₂³×D₄	#123	1	1	yes	characteristic
471	C₂³×D₄	#123	1	1	yes	characteristic
472	C₂³×D₄	#123	1	1	yes	characteristic
473	C₂³×D₄	#123	1	1	yes	characteristic
474	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
475	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
476	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
477	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
478	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
479	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
480	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
481	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
482	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
483	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
484	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
485	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
486	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
487	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
488	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
489	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
490	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
491	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
492	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
493	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
494	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
495	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
496	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
497	C₂³×D₄	C₂×#41	1	1	yes	characteristic
498	C₂³×D₄	C₂×#41	1	1	yes	characteristic
499	C₂³×D₄	C₂×#41	1	1	yes	characteristic
500	C₂³×D₄	C₂×#41	1	1	yes	characteristic
501	C₂³×D₄	C₂×#41	1	1	yes	characteristic
502	C₂³×D₄	C₂×#41	1	1	yes	characteristic
503	C₂³×D₄	C₂×#41	1	1	yes	characteristic
504	C₂³×D₄	C₂×#41	1	1	yes	characteristic
505	C₂³×D₄	C₂×#41	1	1	yes	characteristic
506	C₂³×D₄	C₂×#41	1	1	yes	characteristic
507	C₂³×D₄	C₂×#41	1	1	yes	characteristic
508	C₂³×D₄	C₂×#41	1	1	yes	characteristic
509	C₂³×D₄	C₂⁵	1	1	yes	characteristic
510	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
511	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂⁴×C₄	#120	1	1	yes	characteristic
515	C₂⁴×C₄	#120	1	1	yes	characteristic
516	C₂⁴×C₄	#120	1	1	yes	characteristic
517	C₂⁴×C₄	#123	1	1	yes	characteristic
518	C₂⁴×C₄	#123	1	1	yes	characteristic
519	C₂⁴×C₄	#123	1	1	yes	characteristic
520	C₂⁴×C₄	#123	1	1	yes	characteristic
521	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
524	#535	#99	1	16	yes	complemented
525	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
526	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
527	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
528	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
529	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
530	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
531	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
532	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
533	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
534	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
535	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
536	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
537	C₂×#127	C₂³×C₄	1	2	yes	—
538	C₂×#127	C₂³×C₄	1	2	yes	—
539	C₂×#127	C₂²×D₄	1	2	yes	—
540	C₂×#127	C₂²×D₄	1	2	yes	—
541	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
542	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
543	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
544	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
545	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
546	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
547	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
548	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
549	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
550	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
551	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
552	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
553	C₂×#124	C₂³×C₄	1	2	yes	—
554	C₂×#124	C₂³×C₄	1	2	yes	—
555	C₂×#124	C₂²×D₄	1	2	yes	—
556	C₂×#124	C₂²×D₄	1	2	yes	—
557	#518	C₂³×C₄	1	4	yes	—
558	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
559	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
560	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
561	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
562	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
563	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
564	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
565	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
566	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
567	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
568	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
569	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
570	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
571	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
572	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
573	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
574	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
575	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
576	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
577	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
578	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
579	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
580	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
581	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
582	C₂×#100	C₂³×C₄	1	8	yes	—
583	C₂⁵	#386	1	1	yes	characteristic
584	C₂⁵	#386	1	1	yes	characteristic
585	C₂⁵	#386	1	1	yes	characteristic
586	C₂⁵	#386	1	1	yes	characteristic
587	C₂⁵	#386	1	1	yes	characteristic
588	C₂⁵	#386	1	1	yes	characteristic
589	C₂⁵	#386	1	1	yes	characteristic
590	C₂⁵	#386	1	1	yes	characteristic
591	C₂⁵	#386	1	1	yes	characteristic
592	C₂⁵	#386	1	1	yes	characteristic
593	C₂⁵	#386	1	1	yes	characteristic
594	C₂⁵	#386	1	1	yes	characteristic
595	C₂⁵	#386	1	1	yes	characteristic
596	C₂⁵	#386	1	1	yes	characteristic
597	C₂⁵	#386	1	1	yes	characteristic
598	C₂⁵	#386	1	1	yes	characteristic
599	C₂⁵	#386	1	1	yes	characteristic
600	C₂⁵	#386	1	1	yes	characteristic
601	C₂⁵	#386	1	1	yes	characteristic
602	C₂⁵	#386	1	1	yes	characteristic
603	C₂⁵	#386	1	1	yes	characteristic
604	C₂⁵	#386	1	1	yes	characteristic
605	C₂⁵	#386	1	1	yes	characteristic
606	C₂⁵	#386	1	1	yes	characteristic
607	C₂⁵	#386	1	1	yes	characteristic
608	C₂⁵	#386	1	1	yes	characteristic
609	C₂⁵	#386	1	1	yes	characteristic
610	C₂⁵	#386	1	1	yes	characteristic
611	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
612	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
613	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
614	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
615	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
616	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
617	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
618	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
619	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
620	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
621	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
622	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
623	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
624	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
625	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
626	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
627	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
628	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
629	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
630	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
631	C₂⁵	C₂×#120	1	1	yes	characteristic
632	C₂⁵	C₂×#120	1	1	yes	characteristic
633	C₂⁵	C₂×#120	1	1	yes	characteristic
634	C₂⁵	C₂×#120	1	1	yes	characteristic
635	C₂⁵	C₂×#120	1	1	yes	characteristic
636	C₂⁵	C₂×#120	1	1	yes	characteristic
637	C₂⁵	C₂×#120	1	1	yes	characteristic
638	C₂⁵	C₂×#120	1	1	yes	characteristic
639	C₂⁵	C₂×#120	1	1	yes	characteristic
640	C₂⁵	C₂×#121	1	1	yes	characteristic
641	C₂⁵	C₂×#121	1	1	yes	characteristic
642	C₂⁵	C₂×#121	1	1	yes	characteristic
643	C₂⁵	C₂×#121	1	1	yes	characteristic
644	C₂⁵	C₂×#121	1	1	yes	characteristic
645	C₂⁵	C₂×#121	1	1	yes	characteristic
646	C₂⁵	C₂×#121	1	1	yes	characteristic
647	C₂⁵	C₂×#121	1	1	yes	characteristic
648	C₂⁵	C₂×#121	1	1	yes	characteristic
649	C₂⁵	C₂×#121	1	1	yes	characteristic
650	C₂⁵	C₂×#121	1	1	yes	characteristic
651	C₂⁵	C₂×#121	1	1	yes	characteristic
652	C₂⁵	C₂³×D₄	1	1	yes	characteristic
653	C₂⁵	C₂³×D₄	1	1	yes	characteristic
654	C₂×#41	C₂×#99	1	8	yes	complemented
655	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
656	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
657	C₂²×D₄	#386	1	1	yes	characteristic
658	C₂²×D₄	#386	1	1	yes	characteristic
659	C₂²×D₄	#386	1	1	yes	characteristic
660	C₂²×D₄	#386	1	1	yes	characteristic
661	C₂²×D₄	#386	1	1	yes	characteristic
662	C₂²×D₄	#386	1	1	yes	characteristic
663	C₂²×D₄	#386	1	1	yes	characteristic
664	C₂²×D₄	#386	1	1	yes	characteristic
665	C₂²×D₄	#386	1	1	yes	characteristic
666	C₂²×D₄	#386	1	1	yes	characteristic
667	C₂²×D₄	#386	1	1	yes	characteristic
668	C₂²×D₄	#386	1	1	yes	characteristic
669	C₂²×D₄	#386	1	1	yes	characteristic
670	C₂²×D₄	#386	1	1	yes	characteristic
671	C₂²×D₄	#386	1	1	yes	characteristic
672	C₂²×D₄	#386	1	1	yes	characteristic
673	C₂²×D₄	#386	1	1	yes	characteristic
674	C₂²×D₄	#386	1	1	yes	characteristic
675	C₂²×D₄	#386	1	1	yes	characteristic
676	C₂²×D₄	#386	1	1	yes	characteristic
677	C₂²×D₄	#386	1	1	yes	characteristic
678	C₂²×D₄	#386	1	1	yes	characteristic
679	C₂²×D₄	#386	1	1	yes	characteristic
680	C₂²×D₄	#386	1	1	yes	characteristic
681	C₂²×D₄	C₂×#99	1	8	yes	—
682	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
683	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
684	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
685	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
686	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
687	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
688	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
689	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
690	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
691	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
692	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
693	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
694	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
695	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
696	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
697	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
698	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
699	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
700	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
701	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
702	C₂²×D₄	C₂×#121	1	1	yes	characteristic
703	C₂²×D₄	C₂×#121	1	1	yes	characteristic
704	C₂²×D₄	C₂×#121	1	1	yes	characteristic
705	C₂²×D₄	C₂×#121	1	1	yes	characteristic
706	C₂²×D₄	C₂×#121	1	1	yes	characteristic
707	C₂²×D₄	C₂×#121	1	1	yes	characteristic
708	C₂²×D₄	C₂×#121	1	1	yes	characteristic
709	C₂²×D₄	C₂×#121	1	1	yes	characteristic
710	C₂²×D₄	C₂×#121	1	1	yes	characteristic
711	C₂²×D₄	C₂×#121	1	1	yes	characteristic
712	C₂²×D₄	C₂×#121	1	1	yes	characteristic
713	C₂²×D₄	C₂×#121	1	1	yes	characteristic
714	C₂²×D₄	C₂×#123	1	1	yes	characteristic
715	C₂²×D₄	C₂×#123	1	1	yes	characteristic
716	C₂²×D₄	C₂×#123	1	1	yes	characteristic
717	C₂²×D₄	C₂×#123	1	1	yes	characteristic
718	C₂²×D₄	C₂×#123	1	1	yes	characteristic
719	C₂²×D₄	C₂×#123	1	1	yes	characteristic
720	C₂²×D₄	C₂⁴×C₄	1	1	yes	characteristic
721	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
722	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
723	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
724	C₂³×C₄	#386	1	1	yes	characteristic
725	C₂³×C₄	#386	1	1	yes	characteristic
726	C₂³×C₄	#386	1	1	yes	characteristic
727	C₂³×C₄	#386	1	1	yes	characteristic
728	C₂³×C₄	#386	1	1	yes	characteristic
729	C₂³×C₄	#386	1	1	yes	characteristic
730	C₂³×C₄	#386	1	1	yes	characteristic
731	C₂³×C₄	#386	1	1	yes	characteristic
732	C₂³×C₄	#386	1	1	yes	characteristic
733	C₂³×C₄	#386	1	1	yes	characteristic
734	C₂³×C₄	#386	1	1	yes	characteristic
735	C₂³×C₄	#386	1	1	yes	characteristic
736	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
737	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
738	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
739	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
740	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
741	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
742	C₂³×C₄	C₂×#120	1	1	yes	characteristic
743	C₂³×C₄	C₂×#120	1	1	yes	characteristic
744	C₂³×C₄	C₂×#120	1	1	yes	characteristic
745	C₂³×C₄	C₂×#123	1	1	yes	characteristic
746	C₂³×C₄	C₂×#123	1	1	yes	characteristic
747	C₂³×C₄	C₂×#123	1	1	yes	characteristic
748	C₂³×C₄	C₂×#123	1	1	yes	characteristic
749	C₂³×C₄	C₂×#123	1	1	yes	characteristic
750	C₂³×C₄	C₂×#123	1	1	yes	characteristic
751	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
752	#127	C₂×#99	1	8	yes	complemented
753	#127	C₂×#99	1	8	yes	complemented
754	#124	C₂×#99	1	8	yes	complemented
755	#124	C₂×#99	1	8	yes	complemented
756	#117	C₂×#99	1	8	yes	complemented
757	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
758	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
759	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
760	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
761	C₂⁴	#1889	1	1	yes	characteristic
762	C₂⁴	#1889	1	1	yes	characteristic
763	C₂⁴	#1889	1	1	yes	characteristic
764	C₂⁴	#1889	1	1	yes	characteristic
765	C₂⁴	#1889	1	1	yes	characteristic
766	C₂⁴	#1889	1	1	yes	characteristic
767	C₂⁴	#1889	1	1	yes	characteristic
768	C₂⁴	#1889	1	1	yes	characteristic
769	C₂⁴	#1889	1	1	yes	characteristic
770	C₂⁴	#1889	1	1	yes	characteristic
771	C₂⁴	#1889	1	1	yes	characteristic
772	C₂⁴	#1889	1	1	yes	characteristic
773	C₂⁴	#1889	1	1	yes	characteristic
774	C₂⁴	#1889	1	1	yes	characteristic
775	C₂⁴	#1889	1	1	yes	characteristic
776	C₂⁴	#1889	1	1	yes	characteristic
777	C₂⁴	#1898	1	4	yes	—
778	C₂⁴	#1898	1	4	yes	—
779	C₂⁴	C₂×#386	1	1	yes	characteristic
780	C₂⁴	C₂×#386	1	1	yes	characteristic
781	C₂⁴	C₂×#386	1	1	yes	characteristic
782	C₂⁴	C₂×#386	1	1	yes	characteristic
783	C₂⁴	C₂×#386	1	1	yes	characteristic
784	C₂⁴	C₂×#386	1	1	yes	characteristic
785	C₂⁴	C₂×#386	1	1	yes	characteristic
786	C₂⁴	C₂×#386	1	1	yes	characteristic
787	C₂⁴	C₂×#386	1	1	yes	characteristic
788	C₂⁴	C₂×#386	1	1	yes	characteristic
789	C₂⁴	C₂×#386	1	1	yes	characteristic
790	C₂⁴	C₂×#386	1	1	yes	characteristic
791	C₂⁴	C₂×#386	1	1	yes	characteristic
792	C₂⁴	C₂×#386	1	1	yes	characteristic
793	C₂⁴	C₂×#386	1	1	yes	characteristic
794	C₂⁴	C₂×#386	1	1	yes	characteristic
795	C₂⁴	C₂×#386	1	1	yes	characteristic
796	C₂⁴	C₂×#386	1	1	yes	characteristic
797	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
798	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
799	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
800	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
801	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
802	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
803	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
804	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
805	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
806	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
807	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
808	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
809	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
810	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
811	C₂⁴	C₂²×#120	1	1	yes	characteristic
812	C₂⁴	C₂²×#121	1	1	yes	characteristic
813	C₂⁴	C₂²×#121	1	1	yes	characteristic
814	C₂×Q₈	C₂²×#99	1	4	yes	complemented
815	C₂×D₄	#1898	1	4	yes	—
816	C₂×D₄	#1898	1	4	yes	—
817	C₂×D₄	C₂²×#99	1	4	yes	—
818	C₂×D₄	C₂²×#99	1	4	yes	—
819	C₂×D₄	C₂²×#99	1	4	yes	complemented
820	C₂²×C₄	#1913	1	4	yes	—
821	C₂²×C₄	C₂×#386	1	1	yes	characteristic
822	C₂²×C₄	C₂×#386	1	1	yes	characteristic
823	C₂²×C₄	C₂×#386	1	1	yes	characteristic
824	C₂²×C₄	C₂×#386	1	1	yes	characteristic
825	C₂²×C₄	C₂×#386	1	1	yes	characteristic
826	C₂²×C₄	C₂×#386	1	1	yes	characteristic
827	C₂²×C₄	C₂²×#99	1	4	yes	—
828	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
829	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
830	C₄²	C₂²×#99	1	4	yes	complemented
831	C₄²	C₂²×#99	1	4	yes	complemented
832	C₂³	C₂×#1889	1	1	yes	characteristic
833	C₂³	C₂×#1889	1	1	yes	characteristic
834	C₂³	C₂×#1889	1	1	yes	characteristic
835	C₂³	C₂×#1889	1	1	yes	characteristic
836	C₂³	C₂×#1889	1	1	yes	characteristic
837	C₂³	C₂×#1889	1	1	yes	characteristic
838	C₂³	C₂×#1889	1	1	yes	characteristic
839	C₂³	C₂×#1889	1	1	yes	characteristic
840	C₂³	C₂×#1889	1	1	yes	characteristic
841	C₂³	C₂×#1889	1	1	yes	characteristic
842	C₂³	C₂×#1889	1	1	yes	characteristic
843	C₂³	C₂×#1889	1	1	yes	characteristic
844	C₂³	C₂×#1898	1	2	yes	—
845	C₂³	C₂×#1898	1	2	yes	—
846	C₂³	C₂×#1898	1	2	yes	—
847	C₂³	C₂×#1898	1	2	yes	—
848	C₂³	C₂×#1898	1	2	yes	—
849	C₂³	C₂×#1913	1	2	yes	—
850	C₂³	#33551	1	2	yes	—
851	C₂³	#33552	1	2	yes	—
852	C₂³	C₂²×#386	1	1	yes	characteristic
853	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
854	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
855	C₂×C₄	C₂×#1898	1	2	yes	—
856	C₂×C₄	C₂×#1913	1	2	yes	—
857	C₂×C₄	C₂×#1913	1	2	yes	—
858	C₂×C₄	C₂³×#99	1	2	yes	—
859	C₂²	#201664	1	2	yes	—
860	C₂²	#201664	1	2	yes	—
861	C₂²	#494600	1	2	yes	—
862	C₂²	#494600	1	2	yes	—
863	C₂²	C₂²×#1889	1	1	yes	characteristic
864	C₂²	C₂²×#1898	1	1	yes	characteristic
865	C₂²	C₂²×#1913	1	1	yes	characteristic
866	C₂²	C₂×#33551	1	1	yes	characteristic
867	C₂²	C₂×#33552	1	1	yes	characteristic
868	C₂²	#7622875	1	2	yes	—
869	C₂	C₂×#494600	1	1	yes	characteristic
870	C₂	C₂×#201664	1	1	yes	characteristic
871	C₂	#72256610	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1889
commutator	C₂²×D₄	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	C₂×#6437445	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72263553	C₂	semidirect
2. #72263552	C₂	semidirect
3. #72263551	C₂	semidirect
4. #72263550	C₂	semidirect
5. #72263548	C₂	semidirect
6. #72237398	C₂	semidirect
7. #72236670	C₂	semidirect
8. C₂×#493370	C₂	semidirect
9. C₂×#128073	C₂	semidirect
11. C₂×#187928	C₂	semidirect
12. #72234545	C₂	semidirect
13. #72234139	C₂	semidirect
14. #72210503	C₂	semidirect
15. #72210479	C₂	semidirect
18. C₂²×#3019	C₄	semidirect
19. #6437445	C₄	semidirect
20. #6437445	C₄	semidirect
25. C₂×#23912	C₄	semidirect
28. C₂×#20953	C₄	semidirect
32. #581605	C₂²	semidirect
33. #581603	C₂²	semidirect
34. #559859	C₂²	semidirect
35. #559850	C₂²	semidirect
36. #552678	C₂²	semidirect
37. #552671	C₂²	semidirect
38. #532187	C₂²	semidirect
39. #531766	C₂²	semidirect
42. #493370	C₂²	semidirect
43. #493370	C₂²	semidirect
44. #493370	C₂²	semidirect
45. #493370	C₂²	semidirect
46. C₂×#12694	C₂²	semidirect
47. C₂×#12693	C₂²	semidirect
48. #187944	C₂²	semidirect
53. #187928	C₂²	semidirect
54. #187928	C₂²	semidirect
55. C₂×#8534	C₂²	semidirect
56. #139779	C₂²	semidirect
57. #139778	C₂²	semidirect
58. #139777	C₂²	semidirect
59. #139776	C₂²	semidirect
60. #139707	C₂²	semidirect
61. #139707	C₂²	semidirect
62. #139706	C₂²	semidirect
63. #139706	C₂²	semidirect
64. #128073	C₂²	semidirect
65. #128073	C₂²	semidirect
66. #128073	C₂²	semidirect
67. #128073	C₂²	semidirect
68. #128073	C₂²	semidirect
69. #128073	C₂²	semidirect
70. #128033	C₂²	semidirect
71. C₂×#7304	C₂²	semidirect
72. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
75. C₂×#3484	C₂×C₄	semidirect
76. C₂×#3484	C₂×C₄	semidirect
77. C₂×#3484	C₂×C₄	semidirect
101. C₂²×#518	C₂×C₄	semidirect
104. C₂×#3019	C₂×C₄	semidirect
105. C₂×#3019	C₂×C₄	semidirect
106. C₂×#3019	C₂×C₄	semidirect
107. C₂×#3019	C₂×C₄	semidirect
108. C₂²×#455	C₂×C₄	semidirect
109. C₂²×#453	C₂×C₄	semidirect
110. C₂³×#100	C₂×C₄	semidirect
114. #23912	C₂×C₄	semidirect
115. #23912	C₂×C₄	semidirect
116. #23912	C₂×C₄	semidirect
117. #23912	C₂×C₄	semidirect
118. #23907	C₂×C₄	semidirect
121. #23906	C₂×C₄	semidirect
124. #20953	C₂×C₄	semidirect
125. #20953	C₂×C₄	semidirect
126. #20953	C₂×C₄	semidirect
127. #20953	C₂×C₄	semidirect
128. C₂×#1887	C₂×C₄	semidirect
129. C₂×#1885	C₂×C₄	semidirect
130. C₂×#1783	C₂×C₄	semidirect
131. C₂×#1783	C₂×C₄	semidirect
132. C₂×#1783	C₂×C₄	semidirect
142. #14662	C₂³	semidirect
143. #14661	C₂³	semidirect
144. #14492	C₂³	semidirect
145. #14492	C₂³	semidirect
146. #14419	C₂³	semidirect
147. #14419	C₂³	semidirect
150. #14169	C₂³	semidirect
151. #14154	C₂³	semidirect
166. #12694	C₂³	semidirect
167. #12694	C₂³	semidirect
168. #12693	C₂³	semidirect
169. #12693	C₂³	semidirect
174. #7304	C₂³	semidirect
175. #7304	C₂³	semidirect
176. #7304	C₂³	semidirect
177. #7304	C₂³	semidirect
311. C₂×#455	C₂²×C₄	semidirect
312. C₂×#455	C₂²×C₄	semidirect
313. C₂×#453	C₂²×C₄	semidirect
314. C₂×#453	C₂²×C₄	semidirect
326. #1887	C₂²×C₄	semidirect
327. #1887	C₂²×C₄	semidirect
328. #1885	C₂²×C₄	semidirect
329. #1885	C₂²×C₄	semidirect
524. #535	#99	semidirect
654. C₂×#41	C₂×#99	semidirect
752. #127	C₂×#99	semidirect
753. #127	C₂×#99	semidirect
754. #124	C₂×#99	semidirect
755. #124	C₂×#99	semidirect
756. #117	C₂×#99	semidirect
814. C₂×Q₈	C₂²×#99	semidirect
819. C₂×D₄	C₂²×#99	semidirect
830. C₄²	C₂²×#99	semidirect
831. C₄²	C₂²×#99	semidirect

Maximal subgroups

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

subgroup	index
#72263553	2
#72263552	2
#72263551	2
#72263550	2
#72263548	2
#72237398	2
#72236670	2
C₂×#493370	2
C₂×#128073	2
C₂×#6437445	2
C₂×#187928	2
#72234545	2
#72234139	2
#72210503	2
#72210479	2