Subgroups — #46825135

Order 34432.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771346	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771343	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771343	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771343	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771306	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771305	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771304	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771304	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771300	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771288	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771287	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771276	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771273	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771256	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771253	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771212	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771210	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771207	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771206	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771205	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771205	C₂	1	1	yes	maximal, characteristic, complemented
22	#31771203	C₂	1	1	yes	maximal, characteristic, complemented
23	#31771202	C₂	1	1	yes	maximal, characteristic, complemented
24	#31771197	C₂	1	1	yes	maximal, characteristic, complemented
25	#31771196	C₂	1	1	yes	maximal, characteristic, complemented
26	#31771184	C₂	1	1	yes	maximal, characteristic, complemented
27	#31771182	C₂	1	1	yes	maximal, characteristic, complemented
28	#31771114	C₂	1	1	yes	maximal, characteristic, complemented
29	#31771114	C₂	1	1	yes	maximal, characteristic, complemented
30	#31771113	C₂	1	1	yes	maximal, characteristic, complemented
31	#553×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864402	C₂²	1	1	yes	characteristic
33	C₂×#16864402	C₂²	1	1	yes	characteristic
34	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
35	C₂×#16864401	C₂²	1	1	yes	characteristic
36	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
38	#22575452	C₂²	1	1	yes	characteristic, complemented
39	#22575450	C₂²	1	1	yes	characteristic
40	#22575449	C₂²	1	1	yes	characteristic
41	#22575449	C₂²	1	1	yes	characteristic
42	#22575449	C₂²	1	1	yes	characteristic
43	#22575449	C₂²	1	1	yes	characteristic, complemented
44	#22575448	C₂²	1	1	yes	characteristic
45	#22575448	C₂²	1	1	yes	characteristic
46	#22575448	C₂²	1	1	yes	characteristic
47	#22575448	C₂²	1	1	yes	characteristic, complemented
48	#22575447	C₂²	1	1	yes	characteristic
49	#22575447	C₂²	1	1	yes	characteristic, complemented
50	#22575446	C₂²	1	1	yes	characteristic
51	#22575446	C₂²	1	1	yes	characteristic
52	#22575446	C₂²	1	1	yes	characteristic
53	#22575446	C₂²	1	1	yes	characteristic, complemented
54	#22575445	C₂²	1	1	yes	characteristic, complemented
55	#22575445	C₂²	1	1	yes	characteristic, complemented
56	#22575444	C₂²	1	1	yes	characteristic, complemented
57	#22575443	C₂²	1	1	yes	characteristic, complemented
58	#22575443	C₂²	1	1	yes	characteristic, complemented
59	#22575443	C₂²	1	1	yes	characteristic, complemented
60	#22575443	C₂²	1	1	yes	characteristic, complemented
61	#22575443	C₂²	1	1	yes	characteristic, complemented
62	#22575443	C₂²	1	1	yes	characteristic, complemented
63	#22575438	C₂²	1	1	yes	characteristic
64	#22575438	C₂²	1	1	yes	characteristic
65	#22575438	C₂²	1	1	yes	characteristic
66	#22575438	C₂²	1	1	yes	characteristic
67	#22575438	C₂²	1	1	yes	characteristic
68	#22575438	C₂²	1	1	yes	characteristic
69	#22575438	C₂²	1	1	yes	characteristic
70	#22575438	C₂²	1	1	yes	characteristic
71	#22575438	C₂²	1	1	yes	characteristic, complemented
72	#22575438	C₂²	1	1	yes	characteristic, complemented
73	#22575437	C₂²	1	1	yes	characteristic
74	#22575437	C₂²	1	1	yes	characteristic
75	#22575437	C₂²	1	1	yes	characteristic
76	#22575436	C₂²	1	1	yes	characteristic
77	#22575436	C₂²	1	1	yes	characteristic
78	#22575436	C₂²	1	1	yes	characteristic
79	#22575436	C₂²	1	1	yes	characteristic
80	#22575436	C₂²	1	1	yes	characteristic, complemented
81	#22575436	C₂²	1	1	yes	characteristic, complemented
82	#22575435	C₂²	1	1	yes	characteristic
83	#22575435	C₂²	1	1	yes	characteristic
84	#22575435	C₂²	1	1	yes	characteristic, complemented
85	#22575435	C₂²	1	1	yes	characteristic, complemented
86	#22575434	C₂²	1	1	yes	characteristic, complemented
87	#22575433	C₂²	1	1	yes	characteristic, complemented
88	#22575432	C₂²	1	1	yes	characteristic, complemented
89	#22575431	C₂²	1	1	yes	characteristic
90	#22575431	C₂²	1	1	yes	characteristic
91	#22575431	C₂²	1	1	yes	characteristic
92	#22575431	C₂²	1	1	yes	characteristic
93	#22575431	C₂²	1	1	yes	characteristic, complemented
94	#22575431	C₂²	1	1	yes	characteristic, complemented
95	#22575430	C₂²	1	1	yes	characteristic
96	#22575430	C₂²	1	1	yes	characteristic
97	#22575430	C₂²	1	1	yes	characteristic, complemented
98	#22575430	C₂²	1	1	yes	characteristic, complemented
99	#22575428	C₂²	1	1	yes	characteristic
100	#22575428	C₂²	1	1	yes	characteristic
101	#22575428	C₂²	1	1	yes	characteristic
102	#22575427	C₂²	1	1	yes	characteristic
103	#22575427	C₂²	1	1	yes	characteristic
104	#22575427	C₂²	1	1	yes	characteristic
105	#22575427	C₂²	1	1	yes	characteristic, complemented
106	#22575427	C₂²	1	1	yes	characteristic, complemented
107	#22575426	C₂²	1	1	yes	characteristic
108	#22575426	C₂²	1	1	yes	characteristic
109	#22575426	C₂²	1	1	yes	characteristic
110	#22575426	C₂²	1	1	yes	characteristic
111	#22575426	C₂²	1	1	yes	characteristic
112	#22575426	C₂²	1	1	yes	characteristic
113	#22575426	C₂²	1	1	yes	characteristic
114	#22575426	C₂²	1	1	yes	characteristic
115	#22575426	C₂²	1	1	yes	characteristic
116	#22575426	C₂²	1	1	yes	characteristic
117	#22575426	C₂²	1	1	yes	characteristic, complemented
118	#22575426	C₂²	1	1	yes	characteristic, complemented
119	#22575426	C₂²	1	1	yes	characteristic, complemented
120	#22575426	C₂²	1	1	yes	characteristic, complemented
121	#22575425	C₂²	1	1	yes	characteristic
122	#22575425	C₂²	1	1	yes	characteristic
123	#22575425	C₂²	1	1	yes	characteristic
124	#22575425	C₂²	1	1	yes	characteristic
125	#22575425	C₂²	1	1	yes	characteristic
126	#22575425	C₂²	1	1	yes	characteristic
127	#22575425	C₂²	1	1	yes	characteristic
128	#22575425	C₂²	1	1	yes	characteristic
129	#22575425	C₂²	1	1	yes	characteristic, complemented
130	#22575425	C₂²	1	1	yes	characteristic, complemented
131	#22575424	C₂²	1	1	yes	characteristic
132	#22575424	C₂²	1	1	yes	characteristic
133	#22575424	C₂²	1	1	yes	characteristic
134	#22575424	C₂²	1	1	yes	characteristic, complemented
135	#22575423	C₂²	1	1	yes	characteristic
136	#22575423	C₂²	1	1	yes	characteristic
137	#22575423	C₂²	1	1	yes	characteristic
138	#22575421	C₂²	1	1	yes	characteristic
139	#22575421	C₂²	1	1	yes	characteristic
140	#22575421	C₂²	1	1	yes	characteristic
141	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
142	#22575418	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
144	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
145	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
146	#22575415	C₂²	1	1	yes	characteristic
147	#22575415	C₂²	1	1	yes	characteristic
148	#22575415	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
152	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
153	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
154	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
155	#22575413	C₂²	1	1	yes	characteristic
156	#22575413	C₂²	1	1	yes	characteristic
157	#22575413	C₂²	1	1	yes	characteristic, complemented
158	#22575413	C₂²	1	1	yes	characteristic, complemented
159	#22575413	C₂²	1	1	yes	characteristic, complemented
160	#22575413	C₂²	1	1	yes	characteristic, complemented
161	#22575411	C₂²	1	1	yes	characteristic, complemented
162	#22575410	C₂²	1	1	yes	characteristic
163	#22575410	C₂²	1	1	yes	characteristic
164	#22575410	C₂²	1	1	yes	characteristic, complemented
165	#22575409	C₂²	1	1	yes	characteristic
166	#22575409	C₂²	1	1	yes	characteristic, complemented
167	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
168	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
170	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
171	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
172	#126×C₂₆₉	C₂²	1	1	yes	characteristic
173	#126×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
174	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
175	#123×C₂₆₉	C₂²	1	1	yes	characteristic
176	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
177	#121×C₂₆₉	C₂²	1	1	yes	characteristic
178	#121×C₂₆₉	C₂²	1	1	yes	characteristic
179	#121×C₂₆₉	C₂²	1	1	yes	characteristic
180	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
183	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
185	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
188	#16864402	—	4	2	no	—
189	#16864402	—	4	2	no	—
190	#16864402	—	4	2	no	—
191	#16864401	—	4	2	no	—
192	#16864401	—	4	2	no	—
193	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
194	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
195	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
196	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
197	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
198	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
199	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
200	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
201	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
202	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
203	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
204	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
223	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
224	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
225	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
226	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
227	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₂₆₉	—	4	2	no	—
229	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
249	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
250	#16864381	C₂³	1	1	yes	characteristic
251	#16864381	C₂³	1	1	yes	characteristic
252	#16864381	C₂³	1	1	yes	characteristic
253	#16864381	C₂³	1	1	yes	characteristic
254	#16864381	C₂³	1	1	yes	characteristic
255	#16864381	C₂³	1	1	yes	characteristic
256	#16864381	C₂³	1	1	yes	characteristic
257	#16864381	C₂³	1	1	yes	characteristic
258	#16864381	C₂³	1	1	yes	characteristic
259	#16864381	C₂³	1	1	yes	characteristic
260	#16864381	C₂³	1	1	yes	characteristic
261	#16864381	C₂³	1	1	yes	characteristic
262	#16864381	C₂³	1	1	yes	characteristic
263	#16864381	C₂³	1	1	yes	characteristic
264	#16864381	C₂³	1	1	yes	characteristic
265	#16864381	C₂³	1	1	yes	characteristic
266	#16864381	C₂³	1	1	yes	characteristic
267	#16864381	C₂³	1	1	yes	characteristic
268	#16864381	C₂³	1	1	yes	characteristic
269	#16864381	C₂³	1	1	yes	characteristic
270	#16864381	C₂³	1	1	yes	characteristic
271	#16864381	C₂³	1	1	yes	characteristic
272	#16864381	C₂³	1	1	yes	characteristic
273	#16864381	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
282	#16864379	C₂³	1	1	yes	characteristic
283	#16864379	C₂³	1	1	yes	characteristic
284	#16864379	C₂³	1	1	yes	characteristic
285	#16864379	C₂³	1	1	yes	characteristic
286	#16864379	C₂³	1	1	yes	characteristic
287	#16864379	C₂³	1	1	yes	characteristic
288	#16864379	C₂³	1	1	yes	characteristic
289	#16864379	C₂³	1	1	yes	characteristic
290	#16864379	C₂³	1	1	yes	characteristic
291	#16864379	C₂³	1	1	yes	characteristic
292	#16864379	C₂³	1	1	yes	characteristic
293	#16864379	C₂³	1	1	yes	characteristic
294	#16864379	C₂³	1	1	yes	characteristic
295	#16864379	C₂³	1	1	yes	characteristic
296	#16864379	C₂³	1	1	yes	characteristic
297	#16864379	C₂³	1	1	yes	characteristic
298	#16864379	C₂³	1	1	yes	characteristic
299	#16864379	C₂³	1	1	yes	characteristic
300	#16864379	C₂³	1	1	yes	characteristic
301	#16864379	C₂³	1	1	yes	characteristic
302	#16864379	C₂³	1	1	yes	characteristic
303	#16864379	C₂³	1	1	yes	characteristic
304	#16864379	C₂³	1	1	yes	characteristic
305	#16864379	C₂³	1	1	yes	characteristic
306	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
307	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
308	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
309	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
310	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
311	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
312	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
313	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
345	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
346	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
347	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
348	C₂²×D₂₆₉	—	4	1	no	—
349	C₂²×D₂₆₉	—	4	1	no	—
350	C₂²×D₂₆₉	—	4	1	no	—
351	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
352	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
353	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
354	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
355	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
356	Dic₅₃₈	—	2	2	no	—
357	Dic₅₃₈	—	2	2	no	—
358	Dic₅₃₈	—	4	1	no	—
359	D₁₀₇₆	—	4	1	no	—
360	D₁₀₇₆	—	4	1	no	—
361	D₁₀₇₆	—	4	1	no	—
362	D₁₀₇₆	—	4	1	no	—
363	D₁₀₇₆	—	4	1	no	—
364	D₁₀₇₆	—	4	1	no	—
365	D₁₀₇₆	—	4	1	no	—
366	D₁₀₇₆	—	4	1	no	—
367	D₁₀₇₆	—	4	1	no	—
368	C₂²⋊D₂₆₉	—	2	2	no	—
369	C₂²⋊D₂₆₉	—	2	2	no	—
370	C₂²⋊D₂₆₉	—	4	1	no	—
371	C₂²⋊D₂₆₉	—	4	1	no	—
372	C₂²⋊D₂₆₉	—	4	1	no	—
373	C₂²⋊D₂₆₉	—	4	1	no	—
374	C₂²⋊D₂₆₉	—	4	1	no	—
375	C₂²⋊D₂₆₉	—	4	1	no	—
376	C₂²⋊D₂₆₉	—	4	1	no	—
377	C₂²⋊D₂₆₉	—	4	1	no	—
378	C₂²⋊D₂₆₉	—	4	1	no	—
379	C₂²⋊D₂₆₉	—	4	1	no	—
380	C₂²⋊D₂₆₉	—	4	1	no	—
381	C₂²⋊D₂₆₉	—	4	1	no	—
382	C₂²⋊D₂₆₉	—	4	1	no	—
383	C₂²⋊D₂₆₉	—	4	1	no	—
384	C₂²⋊D₂₆₉	—	4	1	no	—
385	C₂²⋊D₂₆₉	—	4	1	no	—
386	C₂×Dic₂₆₉	—	2	2	no	—
387	C₂×Dic₂₆₉	—	2	2	no	—
388	C₂×Dic₂₆₉	—	4	1	no	—
389	C₂×Dic₂₆₉	—	4	1	no	—
390	C₂×Dic₂₆₉	—	4	1	no	—
391	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
402	C₄×D₂₆₉	—	2	2	no	—
403	C₄×D₂₆₉	—	2	2	no	—
404	C₄×D₂₆₉	—	2	2	no	—
405	C₄×D₂₆₉	—	4	1	no	—
406	C₄×D₂₆₉	—	4	1	no	—
407	C₄×D₂₆₉	—	4	1	no	—
408	C₄×D₂₆₉	—	4	1	no	—
409	C₄×D₂₆₉	—	4	1	no	—
410	C₄×D₂₆₉	—	4	1	no	—
411	C₄×D₂₆₉	—	4	1	no	—
412	C₄×D₂₆₉	—	4	1	no	—
413	C₄×D₂₆₉	—	4	1	no	—
414	C₄×D₂₆₉	—	4	1	no	—
415	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
416	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
417	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
418	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
419	D₄×C₂₆₉	—	4	1	no	—
420	D₄×C₂₆₉	—	4	1	no	—
421	D₄×C₂₆₉	—	4	1	no	—
422	D₄×C₂₆₉	—	4	1	no	—
423	D₄×C₂₆₉	—	4	1	no	—
424	D₄×C₂₆₉	—	4	1	no	—
425	C₂×C₄×C₂₆₉	—	4	1	no	—
426	C₂×C₄×C₂₆₉	—	4	1	no	—
427	C₂×C₄×C₂₆₉	—	4	1	no	—
428	C₂×C₄×C₂₆₉	—	4	1	no	—
429	C₂×C₄×C₂₆₉	—	4	1	no	—
430	C₂×C₄×C₂₆₉	—	4	1	no	—
431	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
432	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
434	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
435	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
436	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
437	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
438	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
439	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
440	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
441	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
442	C₂²×C₂₆₉	—	2	1	no	—
443	C₂²×C₂₆₉	—	2	1	no	—
444	C₂²×C₂₆₉	—	2	1	no	—
445	C₂²×C₂₆₉	—	2	1	no	—
446	C₂²×C₂₆₉	—	2	1	no	—
447	C₂²×C₂₆₉	—	2	1	no	—
448	C₂²×C₂₆₉	—	2	1	no	—
449	C₂²×C₂₆₉	—	2	1	no	—
450	C₂²×C₂₆₉	—	2	1	no	—
451	C₂²×C₂₆₉	—	2	1	no	—
452	C₂²×C₂₆₉	—	2	1	no	—
453	C₂²×C₂₆₉	—	2	1	no	—
454	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
455	C₂×D₂₆₉	—	2	1	no	—
456	C₂×D₂₆₉	—	2	1	no	—
457	C₂×D₂₆₉	—	2	1	no	—
458	C₂×D₂₆₉	—	2	1	no	—
459	C₂×D₂₆₉	—	2	1	no	—
460	C₂×D₂₆₉	—	2	1	no	—
461	C₂×D₂₆₉	—	2	1	no	—
462	C₂×D₂₆₉	—	2	1	no	—
463	C₂×D₂₆₉	—	2	1	no	—
464	C₂×D₂₆₉	—	2	1	no	—
465	C₂×D₂₆₉	—	2	1	no	—
466	C₂×D₂₆₉	—	2	1	no	—
467	C₂×D₂₆₉	—	2	1	no	—
468	C₂×D₂₆₉	—	2	1	no	—
469	C₂×D₂₆₉	—	2	1	no	—
470	C₂×D₂₆₉	—	4	4	no	—
471	C₄×C₂₆₉	—	2	1	no	—
472	C₄×C₂₆₉	—	2	1	no	—
473	C₄×C₂₆₉	—	2	1	no	—
474	C₄×C₂₆₉	—	2	1	no	—
475	C₄×C₂₆₉	—	2	1	no	—
476	C₄×C₂₆₉	—	2	1	no	—
477	C₄×C₂₆₉	—	2	1	no	—
478	C₄×C₂₆₉	—	2	1	no	—
479	C₄×C₂₆₉	—	2	1	no	—
480	C₄×C₂₆₉	—	2	1	no	—
481	C₄×C₂₆₉	—	2	1	no	—
482	Dic₂₆₉	—	2	1	no	—
483	Dic₂₆₉	—	2	1	no	—
484	Dic₂₆₉	—	2	1	no	—
485	Dic₂₆₉	—	2	1	no	—
486	Dic₂₆₉	—	2	1	no	—
487	Dic₂₆₉	—	2	1	no	—
488	Dic₂₆₉	—	2	1	no	—
489	Dic₂₆₉	—	2	1	no	—
490	Dic₂₆₉	—	2	1	no	—
491	Dic₂₆₉	—	2	1	no	—
492	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
493	C₂×C₂₆₉	—	4	1	no	—
494	C₂×C₂₆₉	—	4	1	no	—
495	C₂×C₂₆₉	—	4	1	no	—
496	C₂×C₂₆₉	—	4	1	no	—
497	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂×C₂₆₉	#585	1	1	yes	characteristic
499	C₂×C₂₆₉	#585	1	1	yes	characteristic
500	D₂₆₉	—	4	1	no	—
501	D₂₆₉	—	4	1	no	—
502	D₂₆₉	—	4	1	no	—
503	D₂₆₉	—	4	1	no	—
504	D₂₆₉	—	4	1	no	—
505	C₂₆₉	#3539	1	1	yes	characteristic, complemented, Sylow
506	#3539	—	269	1	no	maximal, Sylow
507	#560	—	269	1	no	—
508	#560	—	269	1	no	—
509	#560	—	269	1	no	—
510	#560	—	269	1	no	—
511	#553	—	269	1	no	—
512	#553	—	269	1	no	—
513	#553	—	269	1	no	—
514	#553	—	269	1	no	—
515	#553	—	269	1	no	—
516	#553	D₂₆₉	1	1	yes	characteristic, complemented
517	#552	—	269	1	no	—
518	#552	—	269	1	no	—
519	#550	—	269	1	no	—
520	#550	—	269	1	no	—
521	#547	—	269	1	no	—
522	#547	—	269	1	no	—
523	#541	—	269	1	no	—
524	#540	—	269	1	no	—
525	#540	—	269	1	no	—
526	#540	—	269	1	no	—
527	#540	—	269	1	no	—
528	#540	—	269	1	no	—
529	#539	—	269	1	no	—
530	#539	—	269	1	no	—
531	#539	—	269	1	no	—
532	#539	—	269	1	no	—
533	#537	—	269	1	no	—
534	#537	—	269	1	no	—
535	#525	—	269	1	no	—
536	#525	—	269	1	no	—
537	#525	—	269	1	no	—
538	C₂×#41	—	269	1	no	—
539	C₂×#41	—	269	1	no	—
540	C₂×#41	—	269	1	no	—
541	C₂×#41	—	269	1	no	—
542	C₂×#41	—	269	1	no	—
543	C₂³×C₄	—	269	1	no	—
544	C₄⋊Q₈	—	269	1	no	—
545	#127	—	269	1	no	—
546	#127	—	269	1	no	—
547	#127	—	269	1	no	—
548	#127	—	269	1	no	—
549	#127	—	269	1	no	—
550	#126	—	269	1	no	—
551	#126	—	269	1	no	—
552	#126	—	269	1	no	—
553	#126	—	269	1	no	—
554	#126	—	269	1	no	—
555	#126	—	269	1	no	—
556	#126	—	269	1	no	—
557	#126	—	269	1	no	—
558	#126	—	269	1	no	—
559	#126	—	269	1	no	—
560	#126	C₂×D₂₆₉	1	1	yes	characteristic
561	#126	C₂×D₂₆₉	1	1	yes	characteristic, complemented
562	#125	—	269	1	no	—
563	#125	—	269	1	no	—
564	#125	—	269	1	no	—
565	#125	—	269	1	no	—
566	#125	—	269	1	no	—
567	#125	—	269	1	no	—
568	#125	—	269	1	no	—
569	#125	—	269	1	no	—
570	#125	—	269	1	no	—
571	#125	C₂×D₂₆₉	1	1	yes	characteristic, complemented
572	#123	—	269	1	no	—
573	#123	—	269	1	no	—
574	#123	—	269	1	no	—
575	#123	—	269	1	no	—
576	#123	—	269	1	no	—
577	#123	—	269	1	no	—
578	#123	—	269	1	no	—
579	#123	—	269	1	no	—
580	#123	—	269	1	no	—
581	#123	—	269	1	no	—
582	#123	—	269	1	no	—
583	#123	—	269	1	no	—
584	#123	—	269	1	no	—
585	#123	—	269	1	no	—
586	#123	—	269	1	no	—
587	#123	—	269	1	no	—
588	#123	—	269	1	no	—
589	#123	—	269	1	no	—
590	#123	—	269	1	no	—
591	#123	—	269	1	no	—
592	#123	—	269	1	no	—
593	#123	—	269	1	no	—
594	#123	—	269	1	no	—
595	#123	—	269	1	no	—
596	#123	C₂×D₂₆₉	1	1	yes	characteristic
597	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
598	C₂²⋊Q₈	—	269	1	no	—
599	C₂²⋊Q₈	—	269	1	no	—
600	C₂²⋊Q₈	—	269	1	no	—
601	C₂²⋊Q₈	—	269	1	no	—
602	C₂²⋊Q₈	—	269	1	no	—
603	C₂²⋊Q₈	—	269	1	no	—
604	C₂²⋊Q₈	—	269	1	no	—
605	C₂²⋊Q₈	—	269	1	no	—
606	C₂²⋊Q₈	—	269	1	no	—
607	C₂²⋊Q₈	—	269	1	no	—
608	C₂²⋊Q₈	—	269	1	no	—
609	C₂²⋊Q₈	—	269	1	no	—
610	#121	—	269	1	no	—
611	#121	—	269	1	no	—
612	#121	—	269	1	no	—
613	#121	—	269	1	no	—
614	#121	—	269	1	no	—
615	#121	—	269	1	no	—
616	#121	—	269	1	no	—
617	#121	—	269	1	no	—
618	#121	—	269	1	no	—
619	#121	—	269	1	no	—
620	#121	—	269	1	no	—
621	#121	—	269	1	no	—
622	#121	—	269	1	no	—
623	#121	—	269	1	no	—
624	#121	—	269	1	no	—
625	#121	—	269	1	no	—
626	#121	—	269	1	no	—
627	#121	—	269	1	no	—
628	#121	—	269	1	no	—
629	#121	—	269	1	no	—
630	#121	—	269	1	no	—
631	#121	—	269	1	no	—
632	#121	—	269	1	no	—
633	#121	—	269	1	no	—
634	#121	—	269	1	no	—
635	#121	—	269	1	no	—
636	#121	—	269	1	no	—
637	#121	—	269	1	no	—
638	#121	—	269	1	no	—
639	#121	—	269	1	no	—
640	#121	—	269	1	no	—
641	#121	—	269	1	no	—
642	#121	—	269	1	no	—
643	#121	—	269	1	no	—
644	#121	—	269	1	no	—
645	#121	—	269	1	no	—
646	#121	C₂×D₂₆₉	1	1	yes	characteristic
647	#121	C₂×D₂₆₉	1	1	yes	characteristic
648	#121	C₂×D₂₆₉	1	1	yes	characteristic
649	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
650	#120	—	269	1	no	—
651	#120	—	269	1	no	—
652	#120	—	269	1	no	—
653	#120	—	269	1	no	—
654	#120	—	269	1	no	—
655	#120	—	269	1	no	—
656	C₄×Q₈	—	269	1	no	—
657	C₄×Q₈	—	269	1	no	—
658	C₄×D₄	—	269	1	no	—
659	C₄×D₄	—	269	1	no	—
660	C₄×D₄	—	269	1	no	—
661	C₄×D₄	—	269	1	no	—
662	C₄×D₄	—	269	1	no	—
663	C₄×D₄	—	269	1	no	—
664	C₄×D₄	—	269	1	no	—
665	C₄×D₄	—	269	1	no	—
666	C₄×D₄	—	269	1	no	—
667	C₄×D₄	—	269	1	no	—
668	C₄×D₄	—	269	1	no	—
669	C₄×D₄	—	269	1	no	—
670	C₄×D₄	—	269	1	no	—
671	C₄×D₄	—	269	1	no	—
672	C₄×D₄	—	269	1	no	—
673	C₄×D₄	—	269	1	no	—
674	C₄×D₄	—	269	1	no	—
675	C₄×D₄	—	269	1	no	—
676	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
677	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
678	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
679	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
680	#117	—	269	1	no	—
681	#117	—	269	1	no	—
682	#117	—	269	1	no	—
683	#117	—	269	1	no	—
684	#117	—	269	1	no	—
685	#117	—	269	1	no	—
686	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
687	C₂×C₄⋊C₄	—	269	1	no	—
688	C₂×C₄⋊C₄	—	269	1	no	—
689	C₂×C₄⋊C₄	—	269	1	no	—
690	C₂×C₄⋊C₄	—	269	1	no	—
691	C₂×C₄⋊C₄	—	269	1	no	—
692	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
693	C₂⁴	—	269	1	no	—
694	#41	—	1076	2	no	—
695	#41	—	1076	2	no	—
696	#41	—	1076	2	no	—
697	#41	—	1076	2	no	—
698	#41	—	1076	2	no	—
699	C₂×Q₈	—	269	1	no	—
700	C₂×Q₈	—	269	1	no	—
701	C₂×Q₈	—	269	1	no	—
702	C₂×D₄	—	269	1	no	—
703	C₂×D₄	—	269	1	no	—
704	C₂×D₄	—	269	1	no	—
705	C₂×D₄	—	269	1	no	—
706	C₂×D₄	—	269	1	no	—
707	C₂×D₄	—	269	1	no	—
708	C₂×D₄	—	269	1	no	—
709	C₂×D₄	—	269	1	no	—
710	C₂×D₄	—	269	1	no	—
711	C₂×D₄	—	269	1	no	—
712	C₂×D₄	—	269	1	no	—
713	C₂×D₄	—	269	1	no	—
714	C₂×D₄	—	269	1	no	—
715	C₂×D₄	—	269	1	no	—
716	C₂×D₄	—	269	1	no	—
717	C₂×D₄	—	269	1	no	—
718	C₂×D₄	—	269	1	no	—
719	C₂×D₄	—	269	1	no	—
720	C₂×D₄	—	269	1	no	—
721	C₂×D₄	—	269	1	no	—
722	C₂×D₄	—	269	1	no	—
723	C₂×D₄	—	269	1	no	—
724	C₂×D₄	—	269	1	no	—
725	C₂×D₄	—	269	1	no	—
726	C₂×D₄	—	269	1	no	—
727	C₂×D₄	—	269	1	no	—
728	C₂×D₄	—	269	1	no	—
729	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
730	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
731	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
735	C₂²×C₄	—	269	1	no	—
736	C₂²×C₄	—	269	1	no	—
737	C₂²×C₄	—	269	1	no	—
738	C₂²×C₄	—	269	1	no	—
739	C₂²×C₄	—	269	1	no	—
740	C₂²×C₄	—	269	1	no	—
741	C₂²×C₄	—	269	1	no	—
742	C₂²×C₄	—	269	1	no	—
743	C₂²×C₄	—	269	1	no	—
744	C₂²×C₄	—	269	1	no	—
745	C₂²×C₄	—	269	1	no	—
746	C₂²×C₄	—	269	1	no	—
747	C₂²×C₄	—	269	1	no	—
748	C₂²×C₄	—	269	1	no	—
749	C₂²×C₄	—	269	1	no	—
750	C₂²×C₄	—	269	1	no	—
751	C₂²×C₄	—	269	1	no	—
752	C₂²×C₄	—	269	1	no	—
753	C₂²×C₄	—	1076	2	no	—
754	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
758	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
759	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
760	C₄⋊C₄	—	269	1	no	—
761	C₄⋊C₄	—	269	1	no	—
762	C₄⋊C₄	—	269	1	no	—
763	C₄⋊C₄	—	269	1	no	—
764	C₄⋊C₄	—	269	1	no	—
765	C₄⋊C₄	—	269	1	no	—
766	C₄⋊C₄	—	269	1	no	—
767	C₄⋊C₄	—	269	1	no	—
768	C₄⋊C₄	—	269	1	no	—
769	C₄⋊C₄	—	269	1	no	—
770	C₄⋊C₄	—	269	1	no	—
771	C₄⋊C₄	—	269	1	no	—
772	C₄⋊C₄	—	269	1	no	—
773	C₄⋊C₄	—	269	1	no	—
774	C₄⋊C₄	—	269	1	no	—
775	C₄⋊C₄	—	269	1	no	—
776	C₄⋊C₄	—	269	1	no	—
777	C₄⋊C₄	—	269	1	no	—
778	C₄⋊C₄	—	269	1	no	—
779	C₄⋊C₄	—	269	1	no	—
780	C₄⋊C₄	—	269	1	no	—
781	C₄⋊C₄	—	269	1	no	—
782	C₄⋊C₄	—	269	1	no	—
783	C₄⋊C₄	—	269	1	no	—
784	C₄⋊C₄	—	269	1	no	—
785	C₄⋊C₄	—	269	1	no	—
786	C₄⋊C₄	—	269	1	no	—
787	C₄⋊C₄	—	269	1	no	—
788	C₄⋊C₄	—	269	1	no	—
789	C₄⋊C₄	—	269	1	no	—
790	C₄⋊C₄	—	269	1	no	—
791	C₄⋊C₄	—	269	1	no	—
792	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
796	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
802	C₂²⋊C₄	—	269	1	no	—
803	C₂²⋊C₄	—	269	1	no	—
804	C₂²⋊C₄	—	269	1	no	—
805	C₂²⋊C₄	—	269	1	no	—
806	C₂²⋊C₄	—	269	1	no	—
807	C₂²⋊C₄	—	269	1	no	—
808	C₂²⋊C₄	—	269	1	no	—
809	C₂²⋊C₄	—	269	1	no	—
810	C₂²⋊C₄	—	269	1	no	—
811	C₂²⋊C₄	—	269	1	no	—
812	C₂²⋊C₄	—	269	1	no	—
813	C₂²⋊C₄	—	269	1	no	—
814	C₂²⋊C₄	—	269	1	no	—
815	C₂²⋊C₄	—	269	1	no	—
816	C₂²⋊C₄	—	269	1	no	—
817	C₂²⋊C₄	—	269	1	no	—
818	C₂²⋊C₄	—	269	1	no	—
819	C₂²⋊C₄	—	269	1	no	—
820	C₂²⋊C₄	—	269	1	no	—
821	C₂²⋊C₄	—	269	1	no	—
822	C₂²⋊C₄	—	269	1	no	—
823	C₂²⋊C₄	—	269	1	no	—
824	C₂²⋊C₄	—	269	1	no	—
825	C₂²⋊C₄	—	269	1	no	—
826	C₂²⋊C₄	—	269	1	no	—
827	C₂²⋊C₄	—	269	1	no	—
828	C₂²⋊C₄	—	269	1	no	—
829	C₂²⋊C₄	—	269	1	no	—
830	C₂²⋊C₄	—	269	1	no	—
831	C₂²⋊C₄	—	269	1	no	—
832	C₂²⋊C₄	—	269	1	no	—
833	C₂²⋊C₄	—	269	1	no	—
834	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
844	C₄²	—	269	1	no	—
845	C₄²	—	269	1	no	—
846	C₄²	—	269	1	no	—
847	C₄²	—	269	1	no	—
848	C₄²	—	269	1	no	—
849	C₄²	—	269	1	no	—
850	C₄²	—	269	1	no	—
851	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
852	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
853	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
854	C₂³	—	269	1	no	—
855	C₂³	—	269	1	no	—
856	C₂³	—	269	1	no	—
857	C₂³	—	269	1	no	—
858	C₂³	—	269	1	no	—
859	C₂³	—	1076	1	no	—
860	C₂³	—	1076	1	no	—
861	C₂³	—	1076	1	no	—
862	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
863	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
864	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
865	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
866	Q₈	—	538	2	no	—
867	Q₈	—	538	2	no	—
868	Q₈	—	1076	1	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	1	no	—
872	D₄	—	4	1	no	—
873	D₄	—	4	1	no	—
874	D₄	—	4	1	no	—
875	D₄	—	538	2	no	—
876	D₄	—	538	2	no	—
877	D₄	—	1076	1	no	—
878	D₄	—	1076	1	no	—
879	D₄	—	1076	1	no	—
880	D₄	—	1076	1	no	—
881	D₄	—	1076	1	no	—
882	D₄	—	1076	1	no	—
883	D₄	—	1076	1	no	—
884	D₄	—	1076	1	no	—
885	D₄	—	1076	1	no	—
886	D₄	—	1076	1	no	—
887	D₄	—	1076	1	no	—
888	D₄	—	1076	1	no	—
889	D₄	—	1076	1	no	—
890	D₄	—	1076	1	no	—
891	D₄	—	1076	1	no	—
892	D₄	—	1076	1	no	—
893	D₄	—	1076	1	no	—
894	D₄	—	1076	1	no	—
895	D₄	—	1076	1	no	—
896	D₄	—	1076	1	no	—
897	D₄	—	1076	1	no	—
898	D₄	—	1076	1	no	—
899	D₄	—	1076	1	no	—
900	D₄	—	1076	1	no	—
901	D₄	—	1076	1	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	269	1	no	—
909	C₂×C₄	—	269	1	no	—
910	C₂×C₄	—	269	1	no	—
911	C₂×C₄	—	269	1	no	—
912	C₂×C₄	—	269	1	no	—
913	C₂×C₄	—	269	1	no	—
914	C₂×C₄	—	269	1	no	—
915	C₂×C₄	—	269	1	no	—
916	C₂×C₄	—	269	1	no	—
917	C₂×C₄	—	269	1	no	—
918	C₂×C₄	—	269	1	no	—
919	C₂×C₄	—	538	2	no	—
920	C₂×C₄	—	538	2	no	—
921	C₂×C₄	—	538	2	no	—
922	C₂×C₄	—	538	2	no	—
923	C₂×C₄	—	538	2	no	—
924	C₂×C₄	—	1076	1	no	—
925	C₂×C₄	—	1076	1	no	—
926	C₂×C₄	—	1076	1	no	—
927	C₂×C₄	—	1076	1	no	—
928	C₂×C₄	—	1076	1	no	—
929	C₂×C₄	—	1076	1	no	—
930	C₂×C₄	—	1076	1	no	—
931	C₂×C₄	—	1076	1	no	—
932	C₂×C₄	—	1076	1	no	—
933	C₂×C₄	—	1076	1	no	—
934	C₂×C₄	—	1076	1	no	—
935	C₂×C₄	—	1076	1	no	—
936	C₂×C₄	—	1076	1	no	—
937	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
938	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
948	C₂²	—	2	1	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	538	1	no	—
961	C₂²	—	538	1	no	—
962	C₂²	—	538	1	no	—
963	C₂²	—	538	1	no	—
964	C₂²	—	538	1	no	—
965	C₂²	—	538	1	no	—
966	C₂²	—	538	1	no	—
967	C₂²	—	538	1	no	—
968	C₂²	—	538	1	no	—
969	C₂²	—	538	1	no	—
970	C₂²	—	538	1	no	—
971	C₂²	—	538	1	no	—
972	C₂²	—	538	1	no	—
973	C₂²	—	538	1	no	—
974	C₂²	—	538	1	no	—
975	C₂²	—	1076	4	no	—
976	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	269	2	no	—
989	C₄	—	538	1	no	—
990	C₄	—	538	1	no	—
991	C₄	—	538	1	no	—
992	C₄	—	538	1	no	—
993	C₄	—	538	1	no	—
994	C₄	—	538	1	no	—
995	C₄	—	538	1	no	—
996	C₄	—	538	1	no	—
997	C₄	—	538	1	no	—
998	C₄	—	538	1	no	—
999	C₂	—	4	1	no	—
1000	C₂	—	4	1	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	1076	1	no	—
1004	C₂	—	1076	1	no	—
1005	C₂	—	1076	1	no	—
1006	C₂	—	1076	1	no	—
1007	C₂	—	1076	1	no	—
1008	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
1009	C₂	#31771441	1	1	yes	characteristic
1010	C₂	#31771441	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#553×C₂₆₉	C₂
hypercenter	#553	D₂₆₉
hypocenter	C₂₆₉	#3539
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #31771346	C₂	semidirect
2. #31771343	C₂	semidirect
3. #31771343	C₂	semidirect
4. #31771343	C₂	semidirect
5. #31771306	C₂	semidirect
6. #31771305	C₂	semidirect
7. #31771304	C₂	semidirect
8. #31771304	C₂	semidirect
9. #31771300	C₂	semidirect
10. #31771288	C₂	semidirect
11. #31771287	C₂	semidirect
12. #31771276	C₂	semidirect
13. #31771273	C₂	semidirect
14. #31771256	C₂	semidirect
15. #31771253	C₂	semidirect
16. #31771212	C₂	semidirect
17. #31771210	C₂	semidirect
18. #31771207	C₂	semidirect
19. #31771206	C₂	semidirect
20. #31771205	C₂	semidirect
21. #31771205	C₂	semidirect
22. #31771203	C₂	semidirect
23. #31771202	C₂	semidirect
24. #31771197	C₂	semidirect
25. #31771196	C₂	semidirect
26. #31771184	C₂	semidirect
27. #31771182	C₂	semidirect
28. #31771114	C₂	semidirect
29. #31771114	C₂	semidirect
30. #31771113	C₂	semidirect
31. #553×C₂₆₉	C₂	semidirect
34. C₂×#16864402	C₂²	semidirect
36. C₂×#16864401	C₂²	semidirect
38. #22575452	C₂²	semidirect
43. #22575449	C₂²	semidirect
47. #22575448	C₂²	semidirect
49. #22575447	C₂²	semidirect
53. #22575446	C₂²	semidirect
54. #22575445	C₂²	semidirect
55. #22575445	C₂²	semidirect
56. #22575444	C₂²	semidirect
57. #22575443	C₂²	semidirect
58. #22575443	C₂²	semidirect
59. #22575443	C₂²	semidirect
60. #22575443	C₂²	semidirect
61. #22575443	C₂²	semidirect
62. #22575443	C₂²	semidirect
71. #22575438	C₂²	semidirect
72. #22575438	C₂²	semidirect
80. #22575436	C₂²	semidirect
81. #22575436	C₂²	semidirect
84. #22575435	C₂²	semidirect
85. #22575435	C₂²	semidirect
86. #22575434	C₂²	semidirect
87. #22575433	C₂²	semidirect
88. #22575432	C₂²	semidirect
93. #22575431	C₂²	semidirect
94. #22575431	C₂²	semidirect
97. #22575430	C₂²	semidirect
98. #22575430	C₂²	semidirect
105. #22575427	C₂²	semidirect
106. #22575427	C₂²	semidirect
117. #22575426	C₂²	semidirect
118. #22575426	C₂²	semidirect
119. #22575426	C₂²	semidirect
120. #22575426	C₂²	semidirect
129. #22575425	C₂²	semidirect
130. #22575425	C₂²	semidirect
134. #22575424	C₂²	semidirect
141. C₄×Dic₅₃₈	C₂²	semidirect
142. #22575418	C₂²	semidirect
145. C₄×D₁₀₇₆	C₂²	semidirect
148. #22575415	C₂²	semidirect
153. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
154. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
157. #22575413	C₂²	semidirect
158. #22575413	C₂²	semidirect
159. #22575413	C₂²	semidirect
160. #22575413	C₂²	semidirect
161. #22575411	C₂²	semidirect
164. #22575410	C₂²	semidirect
166. #22575409	C₂²	semidirect
167. C₂×#16864381	C₂²	semidirect
168. C₂×#16864381	C₂²	semidirect
169. C₄⋊C₄×D₂₆₉	C₂²	semidirect
170. C₄⋊C₄×D₂₆₉	C₂²	semidirect
171. C₄⋊C₄×D₂₆₉	C₂²	semidirect
173. #126×C₂₆₉	C₂²	semidirect
174. #125×C₂₆₉	C₂²	semidirect
176. #123×C₂₆₉	C₂²	semidirect
180. #121×C₂₆₉	C₂²	semidirect
183. C₄×D₄×C₂₆₉	C₂²	semidirect
184. C₄×D₄×C₂₆₉	C₂²	semidirect
185. #117×C₂₆₉	C₂²	semidirect
186. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
505. C₂₆₉	#3539	semidirect
516. #553	D₂₆₉	semidirect
561. #126	C₂×D₂₆₉	semidirect
571. #125	C₂×D₂₆₉	semidirect
597. #123	C₂×D₂₆₉	semidirect
649. #121	C₂×D₂₆₉	semidirect
678. C₄×D₄	C₂×D₂₆₉	semidirect
679. C₄×D₄	C₂×D₂₆₉	semidirect
686. #117	C₂×D₂₆₉	semidirect
692. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31771346	2
#31771343	2
#31771306	2
#31771305	2
#31771304	2
#31771300	2
#31771288	2
#31771287	2
#31771276	2
#31771273	2
#31771256	2
#31771253	2
#31771212	2
#31771210	2
#31771207	2
#31771206	2
#31771205	2
#31771203	2
#31771202	2
#31771197	2
#31771196	2
#31771184	2
#31771182	2
#31771114	2
#31771113	2
#553×C₂₆₉	2
#3539	269