Subgroups — #46825104

Order 34432.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771352	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771351	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771350	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771311	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771309	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771265	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771263	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771257	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771253	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771252	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771248	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771247	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771247	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771244	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771244	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771230	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771230	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771223	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771219	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771203	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771198	C₂	1	1	yes	maximal, characteristic, complemented
22	#31771191	C₂	1	1	yes	maximal, characteristic, complemented
23	#31771189	C₂	1	1	yes	maximal, characteristic, complemented
24	#31771185	C₂	1	1	yes	maximal, characteristic, complemented
25	#31771184	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	#31771113	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂²⋊Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
30	#121×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
31	#562×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
33	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
34	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
35	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
36	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
37	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
38	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
39	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
41	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
42	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
44	#22575452	C₂²	1	1	yes	characteristic, complemented
45	#22575451	C₂²	1	1	yes	characteristic, complemented
46	#22575448	C₂²	1	1	yes	characteristic, complemented
47	#22575447	C₂²	1	1	yes	characteristic, complemented
48	#22575446	C₂²	1	1	yes	characteristic, complemented
49	#22575446	C₂²	1	1	yes	characteristic, complemented
50	#22575444	C₂²	1	1	yes	characteristic, complemented
51	#22575443	C₂²	1	1	yes	characteristic, complemented
52	#22575443	C₂²	1	1	yes	characteristic, complemented
53	#22575442	C₂²	1	1	yes	characteristic, complemented
54	#22575440	C₂²	1	1	yes	characteristic, complemented
55	#22575439	C₂²	1	1	yes	characteristic, complemented
56	#22575439	C₂²	1	1	yes	characteristic, complemented
57	#22575439	C₂²	1	1	yes	characteristic, complemented
58	#22575439	C₂²	1	1	yes	characteristic, complemented
59	#22575439	C₂²	1	1	yes	characteristic, complemented
60	#22575439	C₂²	1	1	yes	characteristic, complemented
61	#22575438	C₂²	1	1	yes	characteristic, complemented
62	#22575438	C₂²	1	1	yes	characteristic, complemented
63	#22575438	C₂²	1	1	yes	characteristic, complemented
64	#22575438	C₂²	1	1	yes	characteristic, complemented
65	#22575438	C₂²	1	1	yes	characteristic, complemented
66	#22575437	C₂²	1	1	yes	characteristic, complemented
67	#22575436	C₂²	1	1	yes	characteristic, complemented
68	#22575435	C₂²	1	1	yes	characteristic, complemented
69	#22575435	C₂²	1	1	yes	characteristic, complemented
70	#22575435	C₂²	1	1	yes	characteristic, complemented
71	#22575435	C₂²	1	1	yes	characteristic, complemented
72	#22575435	C₂²	1	1	yes	characteristic, complemented
73	#22575434	C₂²	1	1	yes	characteristic, complemented
74	#22575434	C₂²	1	1	yes	characteristic, complemented
75	#22575433	C₂²	1	1	yes	characteristic
76	#22575433	C₂²	1	1	yes	characteristic
77	#22575433	C₂²	1	1	yes	characteristic, complemented
78	#22575433	C₂²	1	1	yes	characteristic, complemented
79	#22575433	C₂²	1	1	yes	characteristic, complemented
80	#22575432	C₂²	1	1	yes	characteristic, complemented
81	#22575432	C₂²	1	1	yes	characteristic, complemented
82	#22575432	C₂²	1	1	yes	characteristic, complemented
83	#22575431	C₂²	1	1	yes	characteristic
84	#22575431	C₂²	1	1	yes	characteristic
85	#22575431	C₂²	1	1	yes	characteristic
86	#22575431	C₂²	1	1	yes	characteristic
87	#22575431	C₂²	1	1	yes	characteristic
88	#22575431	C₂²	1	1	yes	characteristic, complemented
89	#22575431	C₂²	1	1	yes	characteristic, complemented
90	#22575431	C₂²	1	1	yes	characteristic, complemented
91	#22575431	C₂²	1	1	yes	characteristic, complemented
92	#22575431	C₂²	1	1	yes	characteristic, complemented
93	#22575431	C₂²	1	1	yes	characteristic, complemented
94	#22575431	C₂²	1	1	yes	characteristic, complemented
95	#22575430	C₂²	1	1	yes	characteristic, complemented
96	#22575430	C₂²	1	1	yes	characteristic, complemented
97	#22575430	C₂²	1	1	yes	characteristic, complemented
98	#22575430	C₂²	1	1	yes	characteristic, complemented
99	#22575430	C₂²	1	1	yes	characteristic, complemented
100	#22575430	C₂²	1	1	yes	characteristic, complemented
101	#22575430	C₂²	1	1	yes	characteristic, complemented
102	#22575430	C₂²	1	1	yes	characteristic, complemented
103	#22575429	C₂²	1	1	yes	characteristic
104	#22575429	C₂²	1	1	yes	characteristic
105	#22575429	C₂²	1	1	yes	characteristic, complemented
106	#22575429	C₂²	1	1	yes	characteristic, complemented
107	#22575428	C₂²	1	1	yes	characteristic
108	#22575428	C₂²	1	1	yes	characteristic, complemented
109	#22575428	C₂²	1	1	yes	characteristic, complemented
110	#22575427	C₂²	1	1	yes	characteristic
111	#22575427	C₂²	1	1	yes	characteristic, complemented
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, complemented
116	#22575426	C₂²	1	1	yes	characteristic, complemented
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	#22575426	C₂²	1	1	yes	characteristic, complemented
122	#22575426	C₂²	1	1	yes	characteristic, complemented
123	#22575425	C₂²	1	1	yes	characteristic
124	#22575425	C₂²	1	1	yes	characteristic
125	#22575425	C₂²	1	1	yes	characteristic, complemented
126	#22575425	C₂²	1	1	yes	characteristic, complemented
127	#22575425	C₂²	1	1	yes	characteristic, complemented
128	#22575425	C₂²	1	1	yes	characteristic, complemented
129	#22575425	C₂²	1	1	yes	characteristic, complemented
130	#22575424	C₂²	1	1	yes	characteristic
131	#22575424	C₂²	1	1	yes	characteristic, complemented
132	#22575424	C₂²	1	1	yes	characteristic, complemented
133	#22575424	C₂²	1	1	yes	characteristic, complemented
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, complemented
145	#22575415	C₂²	1	1	yes	characteristic
146	#22575415	C₂²	1	1	yes	characteristic
147	#22575415	C₂²	1	1	yes	characteristic, complemented
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, complemented
151	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
152	#22575413	C₂²	1	1	yes	characteristic
153	#22575413	C₂²	1	1	yes	characteristic
154	#22575413	C₂²	1	1	yes	characteristic, complemented
155	#22575413	C₂²	1	1	yes	characteristic, complemented
156	#22575413	C₂²	1	1	yes	characteristic, complemented
157	#22575409	C₂²	1	1	yes	characteristic, complemented
158	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
160	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
161	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
164	C₂×#16864379	C₂²	1	1	yes	characteristic
165	C₂×#16864379	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
172	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
173	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
174	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
175	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
176	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
177	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
178	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
183	#121×C₂₆₉	C₂²	1	1	yes	characteristic
184	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
185	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
186	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
188	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
189	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
190	#16864403	—	4	2	no	—
191	#16864402	—	4	2	no	—
192	#16864402	—	4	2	no	—
193	#16864402	—	4	2	no	—
194	#16864401	—	4	2	no	—
195	#16864401	—	4	2	no	—
196	#16864401	—	4	2	no	—
197	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
198	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
199	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
200	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
201	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
202	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
203	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
204	Q₈×D₂₆₉	—	4	2	no	—
205	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
206	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
207	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
208	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
209	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
210	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
211	C₂×D₁₀₇₆	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	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
226	D₄×D₂₆₉	—	4	2	no	—
227	D₄×D₂₆₉	—	4	2	no	—
228	D₄×D₂₆₉	—	4	2	no	—
229	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
230	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
231	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
232	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
233	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₂₆₉	—	4	2	no	—
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	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
252	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
253	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
254	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
255	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
256	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
257	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
258	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
259	C₄⋊Dic₂₆₉	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	#16864381	C₂³	1	1	yes	characteristic
275	#16864381	C₂³	1	1	yes	characteristic
276	#16864381	C₂³	1	1	yes	characteristic
277	#16864381	C₂³	1	1	yes	characteristic
278	#16864381	C₂³	1	1	yes	characteristic
279	#16864381	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₂₆₉	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	#16864379	C₂³	1	1	yes	characteristic
307	#16864379	C₂³	1	1	yes	characteristic
308	#16864379	C₂³	1	1	yes	characteristic
309	#16864379	C₂³	1	1	yes	characteristic
310	#16864379	C₂³	1	1	yes	characteristic
311	#16864379	C₂³	1	1	yes	characteristic
312	#16864379	C₂³	1	1	yes	characteristic
313	#16864379	C₂³	1	1	yes	characteristic
314	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
315	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
316	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
317	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
318	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
319	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
320	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
322	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
323	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
324	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
325	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
326	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
327	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
328	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
329	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
330	C₂²×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	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
338	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
339	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
340	C₄⋊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	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
349	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
350	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
351	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
352	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
353	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
354	C₂²×D₂₆₉	—	2	2	no	—
355	C₂²×D₂₆₉	—	2	2	no	—
356	C₂²×D₂₆₉	—	2	2	no	—
357	C₂²×D₂₆₉	—	2	2	no	—
358	C₂²×D₂₆₉	—	4	1	no	—
359	C₂²×D₂₆₉	—	4	1	no	—
360	C₂²×D₂₆₉	—	4	1	no	—
361	C₂²×D₂₆₉	—	4	1	no	—
362	C₂²×D₂₆₉	—	4	1	no	—
363	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
364	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
365	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
366	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
367	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
368	Dic₅₃₈	—	2	2	no	—
369	Dic₅₃₈	—	2	2	no	—
370	Dic₅₃₈	—	4	1	no	—
371	Dic₅₃₈	—	4	1	no	—
372	Dic₅₃₈	—	4	1	no	—
373	Dic₅₃₈	—	4	1	no	—
374	Dic₅₃₈	—	4	1	no	—
375	D₁₀₇₆	—	2	2	no	—
376	D₁₀₇₆	—	2	2	no	—
377	D₁₀₇₆	—	2	2	no	—
378	D₁₀₇₆	—	2	2	no	—
379	D₁₀₇₆	—	4	1	no	—
380	D₁₀₇₆	—	4	1	no	—
381	D₁₀₇₆	—	4	1	no	—
382	C₂²⋊D₂₆₉	—	2	2	no	—
383	C₂²⋊D₂₆₉	—	2	2	no	—
384	C₂²⋊D₂₆₉	—	2	2	no	—
385	C₂²⋊D₂₆₉	—	2	2	no	—
386	C₂²⋊D₂₆₉	—	2	2	no	—
387	C₂²⋊D₂₆₉	—	2	2	no	—
388	C₂²⋊D₂₆₉	—	4	1	no	—
389	C₂²⋊D₂₆₉	—	4	1	no	—
390	C₂²⋊D₂₆₉	—	4	1	no	—
391	C₂²⋊D₂₆₉	—	4	1	no	—
392	C₂²⋊D₂₆₉	—	4	1	no	—
393	C₂²⋊D₂₆₉	—	4	1	no	—
394	C₂²⋊D₂₆₉	—	4	1	no	—
395	C₂²⋊D₂₆₉	—	4	1	no	—
396	C₂×Dic₂₆₉	—	2	2	no	—
397	C₂×Dic₂₆₉	—	2	2	no	—
398	C₂×Dic₂₆₉	—	4	1	no	—
399	C₂×Dic₂₆₉	—	4	1	no	—
400	C₂×Dic₂₆₉	—	4	1	no	—
401	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
412	C₄×D₂₆₉	—	2	2	no	—
413	C₄×D₂₆₉	—	2	2	no	—
414	C₄×D₂₆₉	—	2	2	no	—
415	C₄×D₂₆₉	—	2	2	no	—
416	C₄×D₂₆₉	—	2	2	no	—
417	C₄×D₂₆₉	—	4	1	no	—
418	C₄×D₂₆₉	—	4	1	no	—
419	C₄×D₂₆₉	—	4	1	no	—
420	C₄×D₂₆₉	—	4	1	no	—
421	C₄×D₂₆₉	—	4	1	no	—
422	C₄×D₂₆₉	—	4	1	no	—
423	C₄×D₂₆₉	—	4	1	no	—
424	C₄×D₂₆₉	—	4	1	no	—
425	C₄×D₂₆₉	—	4	1	no	—
426	C₄×D₂₆₉	—	4	1	no	—
427	C₄×D₂₆₉	—	4	1	no	—
428	C₄×D₂₆₉	—	4	1	no	—
429	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
430	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
431	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
432	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
433	Q₈×C₂₆₉	—	4	1	no	—
434	Q₈×C₂₆₉	—	4	1	no	—
435	D₄×C₂₆₉	—	4	1	no	—
436	D₄×C₂₆₉	—	4	1	no	—
437	D₄×C₂₆₉	—	4	1	no	—
438	D₄×C₂₆₉	—	4	1	no	—
439	D₄×C₂₆₉	—	4	1	no	—
440	D₄×C₂₆₉	—	4	1	no	—
441	C₂×C₄×C₂₆₉	—	4	1	no	—
442	C₂×C₄×C₂₆₉	—	4	1	no	—
443	C₂×C₄×C₂₆₉	—	4	1	no	—
444	C₂×C₄×C₂₆₉	—	4	1	no	—
445	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
446	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
447	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
448	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
449	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
450	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
451	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
452	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
453	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
454	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
455	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
456	C₂²×C₂₆₉	—	2	1	no	—
457	C₂²×C₂₆₉	—	2	1	no	—
458	C₂²×C₂₆₉	—	2	1	no	—
459	C₂²×C₂₆₉	—	2	1	no	—
460	C₂²×C₂₆₉	—	2	1	no	—
461	C₂²×C₂₆₉	—	2	1	no	—
462	C₂²×C₂₆₉	—	2	1	no	—
463	C₂²×C₂₆₉	—	2	1	no	—
464	C₂²×C₂₆₉	—	2	1	no	—
465	C₂²×C₂₆₉	—	2	1	no	—
466	C₂²×C₂₆₉	—	2	1	no	—
467	C₂²×C₂₆₉	—	2	1	no	—
468	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
469	C₂×D₂₆₉	—	2	1	no	—
470	C₂×D₂₆₉	—	2	1	no	—
471	C₂×D₂₆₉	—	2	1	no	—
472	C₂×D₂₆₉	—	2	1	no	—
473	C₂×D₂₆₉	—	2	1	no	—
474	C₂×D₂₆₉	—	2	1	no	—
475	C₂×D₂₆₉	—	2	1	no	—
476	C₂×D₂₆₉	—	2	1	no	—
477	C₂×D₂₆₉	—	2	1	no	—
478	C₂×D₂₆₉	—	2	1	no	—
479	C₂×D₂₆₉	—	2	1	no	—
480	C₂×D₂₆₉	—	2	1	no	—
481	C₂×D₂₆₉	—	2	1	no	—
482	C₂×D₂₆₉	—	4	4	no	—
483	C₂×D₂₆₉	—	8	2	no	—
484	C₂×D₂₆₉	—	8	2	no	—
485	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	—
486	C₂×D₂₆₉	2₋¹⁺⁴	1	2	yes	—
487	C₄×C₂₆₉	—	2	1	no	—
488	C₄×C₂₆₉	—	2	1	no	—
489	C₄×C₂₆₉	—	2	1	no	—
490	C₄×C₂₆₉	—	2	1	no	—
491	C₄×C₂₆₉	—	2	1	no	—
492	C₄×C₂₆₉	—	2	1	no	—
493	C₄×C₂₆₉	—	2	1	no	—
494	C₄×C₂₆₉	—	2	1	no	—
495	C₄×C₂₆₉	—	2	1	no	—
496	C₄×C₂₆₉	—	2	1	no	—
497	C₄×C₂₆₉	—	2	1	no	—
498	Dic₂₆₉	—	2	1	no	—
499	Dic₂₆₉	—	2	1	no	—
500	Dic₂₆₉	—	2	1	no	—
501	Dic₂₆₉	—	2	1	no	—
502	Dic₂₆₉	—	2	1	no	—
503	Dic₂₆₉	—	2	1	no	—
504	Dic₂₆₉	—	2	1	no	—
505	Dic₂₆₉	—	2	1	no	—
506	Dic₂₆₉	—	2	1	no	—
507	Dic₂₆₉	—	2	1	no	—
508	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₂₆₉	—	4	1	no	—
510	C₂×C₂₆₉	—	4	1	no	—
511	C₂×C₂₆₉	—	4	1	no	—
512	C₂×C₂₆₉	—	4	1	no	—
513	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	D₂₆₉	—	2	2	no	—
517	D₂₆₉	—	2	2	no	—
518	D₂₆₉	—	4	1	no	—
519	D₂₆₉	—	4	1	no	—
520	D₂₆₉	—	4	1	no	—
521	C₂₆₉	#3536	1	1	yes	characteristic, complemented, Sylow
522	#3536	—	269	1	no	maximal, Sylow
523	#562	—	269	1	no	—
524	#562	—	269	1	no	—
525	#562	—	269	1	no	—
526	#562	D₂₆₉	1	1	yes	characteristic, complemented
527	#554	—	269	1	no	—
528	#554	—	269	1	no	—
529	#548	—	269	1	no	—
530	#548	—	269	1	no	—
531	#547	—	269	1	no	—
532	#547	—	269	1	no	—
533	#546	—	269	1	no	—
534	#546	—	269	1	no	—
535	#546	—	269	1	no	—
536	#546	—	269	1	no	—
537	#546	—	269	1	no	—
538	#546	—	269	1	no	—
539	#543	—	269	1	no	—
540	#543	—	269	1	no	—
541	#542	—	269	1	no	—
542	#542	—	269	1	no	—
543	#539	—	269	1	no	—
544	#539	—	269	1	no	—
545	#538	—	269	1	no	—
546	#538	—	269	1	no	—
547	#537	—	269	1	no	—
548	#537	—	269	1	no	—
549	#537	—	269	1	no	—
550	#537	—	269	1	no	—
551	#525	—	269	1	no	—
552	C₂×C₂²⋊Q₈	—	269	1	no	—
553	C₂×#121	—	269	1	no	—
554	C₂×#41	—	269	1	no	—
555	C₂×#41	—	269	1	no	—
556	C₂×#41	—	269	1	no	—
557	C₂×#41	—	269	1	no	—
558	C₂×#41	—	269	1	no	—
559	C₂×#41	—	269	1	no	—
560	C₂×#41	—	269	1	no	—
561	C₂²×Q₈	—	269	1	no	—
562	C₂²×D₄	—	269	1	no	—
563	C₂²×D₄	—	269	1	no	—
564	C₂²×D₄	—	269	1	no	—
565	C₂³×C₄	—	269	1	no	—
566	C₄⋊Q₈	—	269	1	no	—
567	C₄⋊Q₈	—	269	1	no	—
568	#126	—	269	1	no	—
569	#126	—	269	1	no	—
570	#126	—	269	1	no	—
571	#126	—	269	1	no	—
572	#125	—	269	1	no	—
573	#125	—	269	1	no	—
574	#125	—	269	1	no	—
575	#125	C₂×D₂₆₉	1	1	yes	characteristic, complemented
576	#124	—	269	1	no	—
577	#124	—	269	1	no	—
578	#124	—	269	1	no	—
579	#124	—	269	1	no	—
580	#124	—	269	1	no	—
581	#124	—	269	1	no	—
582	#124	—	269	1	no	—
583	#124	—	269	1	no	—
584	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
585	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	—	269	1	no	—
597	#123	—	269	1	no	—
598	#123	—	269	1	no	—
599	#123	—	269	1	no	—
600	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
601	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
602	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
603	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	C₂²⋊Q₈	—	269	1	no	—
611	C₂²⋊Q₈	—	269	1	no	—
612	C₂²⋊Q₈	—	269	1	no	—
613	C₂²⋊Q₈	—	269	1	no	—
614	C₂²⋊Q₈	—	269	1	no	—
615	C₂²⋊Q₈	—	269	1	no	—
616	C₂²⋊Q₈	—	269	1	no	—
617	C₂²⋊Q₈	—	269	1	no	—
618	C₂²⋊Q₈	—	269	1	no	—
619	C₂²⋊Q₈	—	269	1	no	—
620	C₂²⋊Q₈	—	269	1	no	—
621	C₂²⋊Q₈	—	269	1	no	—
622	C₂²⋊Q₈	—	269	1	no	—
623	C₂²⋊Q₈	—	269	1	no	—
624	C₂²⋊Q₈	—	269	1	no	—
625	C₂²⋊Q₈	—	269	1	no	—
626	C₂²⋊Q₈	—	269	1	no	—
627	C₂²⋊Q₈	—	269	1	no	—
628	C₂²⋊Q₈	—	269	1	no	—
629	C₂²⋊Q₈	—	269	1	no	—
630	C₂²⋊Q₈	—	269	1	no	—
631	C₂²⋊Q₈	—	269	1	no	—
632	C₂²⋊Q₈	—	269	1	no	—
633	C₂²⋊Q₈	—	269	1	no	—
634	C₂²⋊Q₈	—	269	1	no	—
635	C₂²⋊Q₈	—	269	1	no	—
636	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
637	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
638	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
639	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	—	269	1	no	—
647	#121	—	269	1	no	—
648	#121	—	269	1	no	—
649	#121	—	269	1	no	—
650	#121	—	269	1	no	—
651	#121	—	269	1	no	—
652	#121	—	269	1	no	—
653	#121	—	269	1	no	—
654	#121	—	269	1	no	—
655	#121	—	269	1	no	—
656	#121	—	269	1	no	—
657	#121	—	269	1	no	—
658	#121	—	269	1	no	—
659	#121	—	269	1	no	—
660	#121	—	269	1	no	—
661	#121	—	269	1	no	—
662	#121	—	269	1	no	—
663	#121	—	269	1	no	—
664	#121	—	269	1	no	—
665	#121	—	269	1	no	—
666	#121	—	269	1	no	—
667	#121	—	269	1	no	—
668	#121	C₂×D₂₆₉	1	1	yes	characteristic
669	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
670	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
671	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
672	#120	—	269	1	no	—
673	#120	—	269	1	no	—
674	#120	—	269	1	no	—
675	#120	—	269	1	no	—
676	#120	—	269	1	no	—
677	#120	—	269	1	no	—
678	C₄×Q₈	—	269	1	no	—
679	C₄×Q₈	—	269	1	no	—
680	C₄×D₄	—	269	1	no	—
681	C₄×D₄	—	269	1	no	—
682	C₄×D₄	—	269	1	no	—
683	C₄×D₄	—	269	1	no	—
684	C₄×D₄	—	269	1	no	—
685	C₄×D₄	—	269	1	no	—
686	C₄×D₄	—	269	1	no	—
687	C₄×D₄	—	269	1	no	—
688	C₄×D₄	—	269	1	no	—
689	C₄×D₄	—	269	1	no	—
690	C₄×D₄	—	269	1	no	—
691	C₄×D₄	—	269	1	no	—
692	C₄×D₄	—	269	1	no	—
693	C₄×D₄	—	269	1	no	—
694	#117	—	269	1	no	—
695	C₂×C₄⋊C₄	—	269	1	no	—
696	C₂×C₄⋊C₄	—	269	1	no	—
697	C₂×C₄⋊C₄	—	269	1	no	—
698	C₂×C₄⋊C₄	—	269	1	no	—
699	C₂×C₄⋊C₄	—	269	1	no	—
700	C₂×C₄⋊C₄	—	269	1	no	—
701	C₂×C₂²⋊C₄	—	269	1	no	—
702	C₂×C₂²⋊C₄	—	269	1	no	—
703	C₂×C₂²⋊C₄	—	269	1	no	—
704	C₂×C₂²⋊C₄	—	269	1	no	—
705	C₂×C₂²⋊C₄	—	269	1	no	—
706	C₂×C₂²⋊C₄	—	269	1	no	—
707	C₂×C₂²⋊C₄	—	269	1	no	—
708	C₂×C₂²⋊C₄	—	269	1	no	—
709	C₂⁴	—	269	1	no	—
710	C₂⁴	—	269	1	no	—
711	C₂⁴	—	269	1	no	—
712	#41	—	1076	2	no	—
713	#41	—	1076	2	no	—
714	#41	—	1076	2	no	—
715	#41	—	1076	2	no	—
716	#41	—	1076	2	no	—
717	#41	—	1076	2	no	—
718	#41	—	1076	2	no	—
719	C₂×Q₈	—	269	1	no	—
720	C₂×Q₈	—	269	1	no	—
721	C₂×Q₈	—	269	1	no	—
722	C₂×Q₈	—	269	1	no	—
723	C₂×Q₈	—	269	1	no	—
724	C₂×Q₈	—	269	1	no	—
725	C₂×Q₈	—	269	1	no	—
726	C₂×Q₈	—	1076	2	no	—
727	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
728	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
729	C₂×D₄	—	269	1	no	—
730	C₂×D₄	—	269	1	no	—
731	C₂×D₄	—	269	1	no	—
732	C₂×D₄	—	269	1	no	—
733	C₂×D₄	—	269	1	no	—
734	C₂×D₄	—	269	1	no	—
735	C₂×D₄	—	269	1	no	—
736	C₂×D₄	—	269	1	no	—
737	C₂×D₄	—	269	1	no	—
738	C₂×D₄	—	269	1	no	—
739	C₂×D₄	—	269	1	no	—
740	C₂×D₄	—	269	1	no	—
741	C₂×D₄	—	269	1	no	—
742	C₂×D₄	—	269	1	no	—
743	C₂×D₄	—	269	1	no	—
744	C₂×D₄	—	269	1	no	—
745	C₂×D₄	—	269	1	no	—
746	C₂×D₄	—	269	1	no	—
747	C₂×D₄	—	269	1	no	—
748	C₂×D₄	—	269	1	no	—
749	C₂×D₄	—	269	1	no	—
750	C₂×D₄	—	1076	2	no	—
751	C₂×D₄	—	1076	2	no	—
752	C₂×D₄	—	1076	2	no	—
753	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
754	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
755	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
756	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
757	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
758	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
759	C₂²×C₄	—	269	1	no	—
760	C₂²×C₄	—	269	1	no	—
761	C₂²×C₄	—	269	1	no	—
762	C₂²×C₄	—	269	1	no	—
763	C₂²×C₄	—	269	1	no	—
764	C₂²×C₄	—	269	1	no	—
765	C₂²×C₄	—	269	1	no	—
766	C₂²×C₄	—	269	1	no	—
767	C₂²×C₄	—	269	1	no	—
768	C₂²×C₄	—	269	1	no	—
769	C₂²×C₄	—	269	1	no	—
770	C₂²×C₄	—	269	1	no	—
771	C₂²×C₄	—	269	1	no	—
772	C₂²×C₄	—	269	1	no	—
773	C₂²×C₄	—	269	1	no	—
774	C₂²×C₄	—	269	1	no	—
775	C₂²×C₄	—	269	1	no	—
776	C₂²×C₄	—	269	1	no	—
777	C₂²×C₄	—	269	1	no	—
778	C₂²×C₄	—	269	1	no	—
779	C₂²×C₄	—	269	1	no	—
780	C₂²×C₄	—	269	1	no	—
781	C₂²×C₄	—	1076	2	no	—
782	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
783	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
784	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
785	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
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	—	269	1	no	—
793	C₄⋊C₄	—	269	1	no	—
794	C₄⋊C₄	—	269	1	no	—
795	C₄⋊C₄	—	269	1	no	—
796	C₄⋊C₄	—	269	1	no	—
797	C₄⋊C₄	—	269	1	no	—
798	C₄⋊C₄	—	269	1	no	—
799	C₄⋊C₄	—	269	1	no	—
800	C₄⋊C₄	—	269	1	no	—
801	C₄⋊C₄	—	269	1	no	—
802	C₄⋊C₄	—	269	1	no	—
803	C₄⋊C₄	—	269	1	no	—
804	C₄⋊C₄	—	269	1	no	—
805	C₄⋊C₄	—	269	1	no	—
806	C₄⋊C₄	—	269	1	no	—
807	C₄⋊C₄	—	269	1	no	—
808	C₄⋊C₄	—	269	1	no	—
809	C₄⋊C₄	—	269	1	no	—
810	C₄⋊C₄	—	269	1	no	—
811	C₄⋊C₄	—	269	1	no	—
812	C₄⋊C₄	—	269	1	no	—
813	C₄⋊C₄	—	269	1	no	—
814	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
815	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
816	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
817	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
818	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
819	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
820	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
822	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
823	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
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	—	269	1	no	—
835	C₂²⋊C₄	—	269	1	no	—
836	C₂²⋊C₄	—	269	1	no	—
837	C₂²⋊C₄	—	269	1	no	—
838	C₂²⋊C₄	—	269	1	no	—
839	C₂²⋊C₄	—	269	1	no	—
840	C₂²⋊C₄	—	269	1	no	—
841	C₂²⋊C₄	—	269	1	no	—
842	C₂²⋊C₄	—	269	1	no	—
843	C₂²⋊C₄	—	269	1	no	—
844	C₂²⋊C₄	—	269	1	no	—
845	C₂²⋊C₄	—	269	1	no	—
846	C₂²⋊C₄	—	269	1	no	—
847	C₂²⋊C₄	—	269	1	no	—
848	C₂²⋊C₄	—	269	1	no	—
849	C₂²⋊C₄	—	269	1	no	—
850	C₂²⋊C₄	—	269	1	no	—
851	C₂²⋊C₄	—	269	1	no	—
852	C₂²⋊C₄	—	269	1	no	—
853	C₂²⋊C₄	—	269	1	no	—
854	C₂²⋊C₄	—	269	1	no	—
855	C₂²⋊C₄	—	269	1	no	—
856	C₂²⋊C₄	—	269	1	no	—
857	C₂²⋊C₄	—	269	1	no	—
858	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
859	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
860	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
869	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
870	C₄²	—	269	1	no	—
871	C₄²	—	269	1	no	—
872	C₄²	—	269	1	no	—
873	C₄²	—	269	1	no	—
874	C₄²	—	269	1	no	—
875	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
876	C₂³	—	269	1	no	—
877	C₂³	—	269	1	no	—
878	C₂³	—	269	1	no	—
879	C₂³	—	269	1	no	—
880	C₂³	—	269	1	no	—
881	C₂³	—	538	2	no	—
882	C₂³	—	538	2	no	—
883	C₂³	—	538	2	no	—
884	C₂³	—	538	2	no	—
885	C₂³	—	1076	1	no	—
886	C₂³	—	1076	1	no	—
887	C₂³	—	1076	1	no	—
888	C₂³	—	1076	1	no	—
889	C₂³	—	1076	1	no	—
890	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
891	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
892	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
893	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
894	Q₈	—	4	1	no	—
895	Q₈	—	4	1	no	—
896	Q₈	—	538	2	no	—
897	Q₈	—	538	2	no	—
898	Q₈	—	1076	1	no	—
899	Q₈	—	1076	1	no	—
900	Q₈	—	1076	1	no	—
901	Q₈	—	1076	1	no	—
902	Q₈	—	1076	1	no	—
903	D₄	—	4	1	no	—
904	D₄	—	4	1	no	—
905	D₄	—	4	1	no	—
906	D₄	—	4	1	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	538	2	no	—
910	D₄	—	538	2	no	—
911	D₄	—	538	2	no	—
912	D₄	—	538	2	no	—
913	D₄	—	538	2	no	—
914	D₄	—	538	2	no	—
915	D₄	—	538	2	no	—
916	D₄	—	538	2	no	—
917	D₄	—	538	2	no	—
918	D₄	—	538	2	no	—
919	D₄	—	1076	1	no	—
920	D₄	—	1076	1	no	—
921	D₄	—	1076	1	no	—
922	D₄	—	1076	1	no	—
923	D₄	—	1076	1	no	—
924	D₄	—	1076	1	no	—
925	D₄	—	1076	1	no	—
926	D₄	—	1076	1	no	—
927	D₄	—	1076	1	no	—
928	D₄	—	1076	1	no	—
929	D₄	—	1076	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	269	1	no	—
935	C₂×C₄	—	269	1	no	—
936	C₂×C₄	—	269	1	no	—
937	C₂×C₄	—	269	1	no	—
938	C₂×C₄	—	269	1	no	—
939	C₂×C₄	—	269	1	no	—
940	C₂×C₄	—	269	1	no	—
941	C₂×C₄	—	269	1	no	—
942	C₂×C₄	—	269	1	no	—
943	C₂×C₄	—	269	1	no	—
944	C₂×C₄	—	269	1	no	—
945	C₂×C₄	—	538	2	no	—
946	C₂×C₄	—	538	2	no	—
947	C₂×C₄	—	538	2	no	—
948	C₂×C₄	—	538	2	no	—
949	C₂×C₄	—	538	2	no	—
950	C₂×C₄	—	538	2	no	—
951	C₂×C₄	—	538	2	no	—
952	C₂×C₄	—	1076	1	no	—
953	C₂×C₄	—	1076	1	no	—
954	C₂×C₄	—	1076	1	no	—
955	C₂×C₄	—	1076	1	no	—
956	C₂×C₄	—	1076	1	no	—
957	C₂×C₄	—	1076	1	no	—
958	C₂×C₄	—	1076	1	no	—
959	C₂×C₄	—	1076	1	no	—
960	C₂×C₄	—	1076	1	no	—
961	C₂×C₄	—	1076	1	no	—
962	C₂×C₄	—	1076	1	no	—
963	C₂×C₄	—	1076	1	no	—
964	C₂×C₄	—	1076	1	no	—
965	C₂×C₄	—	1076	1	no	—
966	C₂×C₄	—	1076	1	no	—
967	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
968	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
969	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
970	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
971	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
972	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
973	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
974	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
975	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
976	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
977	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	269	2	no	—
991	C₂²	—	269	2	no	—
992	C₂²	—	538	1	no	—
993	C₂²	—	538	1	no	—
994	C₂²	—	538	1	no	—
995	C₂²	—	538	1	no	—
996	C₂²	—	538	1	no	—
997	C₂²	—	538	1	no	—
998	C₂²	—	538	1	no	—
999	C₂²	—	538	1	no	—
1000	C₂²	—	538	1	no	—
1001	C₂²	—	538	1	no	—
1002	C₂²	—	538	1	no	—
1003	C₂²	—	538	1	no	—
1004	C₂²	—	538	1	no	—
1005	C₂²	—	1076	4	no	—
1006	C₂²	—	2152	2	no	—
1007	C₂²	—	2152	2	no	—
1008	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	269	2	no	—
1021	C₄	—	538	1	no	—
1022	C₄	—	538	1	no	—
1023	C₄	—	538	1	no	—
1024	C₄	—	538	1	no	—
1025	C₄	—	538	1	no	—
1026	C₄	—	538	1	no	—
1027	C₄	—	538	1	no	—
1028	C₄	—	538	1	no	—
1029	C₄	—	538	1	no	—
1030	C₄	—	538	1	no	—
1031	C₂	—	4	1	no	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	538	2	no	—
1036	C₂	—	538	2	no	—
1037	C₂	—	1076	1	no	—
1038	C₂	—	1076	1	no	—
1039	C₂	—	1076	1	no	—
1040	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
1041	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
1042	C₂	2₋¹⁺⁴×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#562×C₂₆₉	C₂
hypercenter	#562	D₂₆₉
hypocenter	C₂₆₉	#3536
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #31771352	C₂	semidirect
2. #31771351	C₂	semidirect
3. #31771350	C₂	semidirect
4. #31771311	C₂	semidirect
5. #31771309	C₂	semidirect
6. #31771265	C₂	semidirect
7. #31771263	C₂	semidirect
8. #31771257	C₂	semidirect
9. #31771253	C₂	semidirect
10. #31771252	C₂	semidirect
11. #31771248	C₂	semidirect
12. #31771247	C₂	semidirect
13. #31771247	C₂	semidirect
14. #31771244	C₂	semidirect
15. #31771244	C₂	semidirect
16. #31771230	C₂	semidirect
17. #31771230	C₂	semidirect
18. #31771223	C₂	semidirect
19. #31771219	C₂	semidirect
20. #31771203	C₂	semidirect
21. #31771198	C₂	semidirect
22. #31771191	C₂	semidirect
23. #31771189	C₂	semidirect
24. #31771185	C₂	semidirect
25. #31771184	C₂	semidirect
26. #31771184	C₂	semidirect
27. #31771182	C₂	semidirect
28. #31771113	C₂	semidirect
29. C₂²⋊Q₈×D₂₆₉	C₂	semidirect
30. #121×D₂₆₉	C₂	semidirect
31. #562×C₂₆₉	C₂	semidirect
32. C₂×#16864403	C₂²	semidirect
33. C₂×#16864402	C₂²	semidirect
34. C₂×#16864402	C₂²	semidirect
35. C₂×#16864402	C₂²	semidirect
36. C₂×#16864401	C₂²	semidirect
37. C₂×#16864401	C₂²	semidirect
38. C₂×#16864401	C₂²	semidirect
39. C₂×Q₈×D₂₆₉	C₂²	semidirect
44. #22575452	C₂²	semidirect
45. #22575451	C₂²	semidirect
46. #22575448	C₂²	semidirect
47. #22575447	C₂²	semidirect
48. #22575446	C₂²	semidirect
49. #22575446	C₂²	semidirect
50. #22575444	C₂²	semidirect
51. #22575443	C₂²	semidirect
52. #22575443	C₂²	semidirect
53. #22575442	C₂²	semidirect
54. #22575440	C₂²	semidirect
55. #22575439	C₂²	semidirect
56. #22575439	C₂²	semidirect
57. #22575439	C₂²	semidirect
58. #22575439	C₂²	semidirect
59. #22575439	C₂²	semidirect
60. #22575439	C₂²	semidirect
61. #22575438	C₂²	semidirect
62. #22575438	C₂²	semidirect
63. #22575438	C₂²	semidirect
64. #22575438	C₂²	semidirect
65. #22575438	C₂²	semidirect
66. #22575437	C₂²	semidirect
67. #22575436	C₂²	semidirect
68. #22575435	C₂²	semidirect
69. #22575435	C₂²	semidirect
70. #22575435	C₂²	semidirect
71. #22575435	C₂²	semidirect
72. #22575435	C₂²	semidirect
73. #22575434	C₂²	semidirect
74. #22575434	C₂²	semidirect
77. #22575433	C₂²	semidirect
78. #22575433	C₂²	semidirect
79. #22575433	C₂²	semidirect
80. #22575432	C₂²	semidirect
81. #22575432	C₂²	semidirect
82. #22575432	C₂²	semidirect
88. #22575431	C₂²	semidirect
89. #22575431	C₂²	semidirect
90. #22575431	C₂²	semidirect
91. #22575431	C₂²	semidirect
92. #22575431	C₂²	semidirect
93. #22575431	C₂²	semidirect
94. #22575431	C₂²	semidirect
95. #22575430	C₂²	semidirect
96. #22575430	C₂²	semidirect
97. #22575430	C₂²	semidirect
98. #22575430	C₂²	semidirect
99. #22575430	C₂²	semidirect
100. #22575430	C₂²	semidirect
101. #22575430	C₂²	semidirect
102. #22575430	C₂²	semidirect
105. #22575429	C₂²	semidirect
106. #22575429	C₂²	semidirect
108. #22575428	C₂²	semidirect
109. #22575428	C₂²	semidirect
111. #22575427	C₂²	semidirect
115. #22575426	C₂²	semidirect
116. #22575426	C₂²	semidirect
117. #22575426	C₂²	semidirect
118. #22575426	C₂²	semidirect
119. #22575426	C₂²	semidirect
120. #22575426	C₂²	semidirect
121. #22575426	C₂²	semidirect
122. #22575426	C₂²	semidirect
125. #22575425	C₂²	semidirect
126. #22575425	C₂²	semidirect
127. #22575425	C₂²	semidirect
128. #22575425	C₂²	semidirect
129. #22575425	C₂²	semidirect
131. #22575424	C₂²	semidirect
132. #22575424	C₂²	semidirect
133. #22575424	C₂²	semidirect
134. #22575424	C₂²	semidirect
141. C₄×Dic₅₃₈	C₂²	semidirect
142. #22575418	C₂²	semidirect
144. C₄×D₁₀₇₆	C₂²	semidirect
147. #22575415	C₂²	semidirect
148. #22575415	C₂²	semidirect
150. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
151. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
154. #22575413	C₂²	semidirect
155. #22575413	C₂²	semidirect
156. #22575413	C₂²	semidirect
157. #22575409	C₂²	semidirect
158. C₂×#16864381	C₂²	semidirect
160. C₄⋊C₄×D₂₆₉	C₂²	semidirect
161. C₄⋊C₄×D₂₆₉	C₂²	semidirect
162. C₄⋊C₄×D₂₆₉	C₂²	semidirect
163. C₄⋊C₄×D₂₆₉	C₂²	semidirect
172. #125×C₂₆₉	C₂²	semidirect
173. #124×C₂₆₉	C₂²	semidirect
174. #124×C₂₆₉	C₂²	semidirect
175. #123×C₂₆₉	C₂²	semidirect
176. #123×C₂₆₉	C₂²	semidirect
177. #123×C₂₆₉	C₂²	semidirect
178. #123×C₂₆₉	C₂²	semidirect
179. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
180. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
181. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
182. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
184. #121×C₂₆₉	C₂²	semidirect
185. #121×C₂₆₉	C₂²	semidirect
186. #121×C₂₆₉	C₂²	semidirect
521. C₂₆₉	#3536	semidirect
526. #562	D₂₆₉	semidirect
575. #125	C₂×D₂₆₉	semidirect
584. #124	C₂×D₂₆₉	semidirect
585. #124	C₂×D₂₆₉	semidirect
600. #123	C₂×D₂₆₉	semidirect
601. #123	C₂×D₂₆₉	semidirect
602. #123	C₂×D₂₆₉	semidirect
603. #123	C₂×D₂₆₉	semidirect
636. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
637. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
638. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
639. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
669. #121	C₂×D₂₆₉	semidirect
670. #121	C₂×D₂₆₉	semidirect
671. #121	C₂×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31771352	2
#31771351	2
#31771350	2
#31771311	2
#31771309	2
#31771265	2
#31771263	2
#31771257	2
#31771253	2
#31771252	2
#31771248	2
#31771247	2
#31771244	2
#31771230	2
#31771223	2
#31771219	2
#31771203	2
#31771198	2
#31771191	2
#31771189	2
#31771185	2
#31771184	2
#31771182	2
#31771113	2
C₂²⋊Q₈×D₂₆₉	2
#121×D₂₆₉	2
#562×C₂₆₉	2
#3536	269